## TSTP Solution File: GRP125-1.003 by Drodi---3.3.3

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Drodi---3.3.3
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 16 21:06:25 EDT 2022

% Result   : Unsatisfiable 0.13s 0.38s
% Output   : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   68 (  18 unt;   0 def)
%            Number of atoms       :  147 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  146 (  67   ~;  72   |;   0   &)
%                                         (   7 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (  10 usr;   8 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   63 (  63   !;   0   ?)

%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
! [X,Y,W,Z] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
! [X,W,Y,Z] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f13,axiom,
! [W,Y,X,Z] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f18,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f20,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f22,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f23,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f25,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product(X0,X1,e_1)
| product(X0,X1,e_2)
| product(X0,X1,e_3) ),
inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f26,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f11]) ).

fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product(X,W,Y)
| ~ product(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f12]) ).

fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product(W,Y,X)
| ~ product(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f13]) ).

fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f33,plain,
! [X,Z1,Z2] :
( ! [Y] :
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2) )
| product(Z1,Z2,X) ),
inference(miniscoping,[status(esa)],[f15]) ).

fof(f34,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X1,X0,X3)
| product(X2,X3,X0) ),
inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f37,plain,
! [X0] :
( ~ group_element(X0)
| product(e_3,X0,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f25,f18]) ).

fof(f39,plain,
! [X0] :
( ~ group_element(X0)
| product(e_1,X0,e_1)
| product(e_1,X0,e_2)
| product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f25,f16]) ).

fof(f40,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f27,f32]) ).

fof(f41,plain,
! [X0,X1] :
( ~ product(X0,X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f29,f32]) ).

fof(f42,plain,
! [X0,X1] :
( ~ product(X0,X1,X1)
| equalish(X1,X0) ),
inference(resolution,[status(thm)],[f31,f32]) ).

fof(f68,plain,
( spl0_6
<=> product(e_3,e_1,e_1) ),
introduced(split_symbol_definition) ).

fof(f69,plain,
( product(e_3,e_1,e_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f68]) ).

fof(f71,plain,
( spl0_7
<=> product(e_3,e_1,e_2) ),
introduced(split_symbol_definition) ).

fof(f72,plain,
( product(e_3,e_1,e_2)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f71]) ).

fof(f74,plain,
( spl0_8
<=> product(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).

fof(f75,plain,
( product(e_3,e_1,e_3)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f74]) ).

fof(f77,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolution,[status(thm)],[f37,f16]) ).

fof(f78,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f77,f68,f71,f74]) ).

fof(f79,plain,
( equalish(e_3,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f75,f41]) ).

fof(f80,plain,
( \$false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f23]) ).

fof(f81,plain,
~ spl0_8,

fof(f85,plain,
! [X0] :
( ~ product(e_1,e_3,X0)
| product(e_2,X0,e_3)
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f72,f34]) ).

fof(f103,plain,
( spl0_14
<=> product(e_2,e_2,e_3) ),
introduced(split_symbol_definition) ).

fof(f104,plain,
( product(e_2,e_2,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f103]) ).

fof(f119,plain,
( equalish(e_1,e_3)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f69,f42]) ).

fof(f120,plain,
( \$false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f20]) ).

fof(f121,plain,
~ spl0_6,

fof(f142,plain,
( equalish(e_2,e_3)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f104,f40]) ).

fof(f143,plain,
( \$false
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f22]) ).

fof(f144,plain,
~ spl0_14,

fof(f151,plain,
( spl0_18
<=> product(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).

fof(f152,plain,
( product(e_1,e_3,e_1)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f151]) ).

fof(f154,plain,
( spl0_19
<=> product(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).

fof(f155,plain,
( product(e_1,e_3,e_2)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f154]) ).

fof(f157,plain,
( spl0_20
<=> product(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).

fof(f158,plain,
( product(e_1,e_3,e_3)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f157]) ).

fof(f160,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolution,[status(thm)],[f39,f18]) ).

fof(f161,plain,
( spl0_18
| spl0_19
| spl0_20 ),
inference(split_clause,[status(thm)],[f160,f151,f154,f157]) ).

fof(f208,plain,
( equalish(e_3,e_1)
| ~ spl0_20 ),
inference(resolution,[status(thm)],[f158,f42]) ).

fof(f209,plain,
( \$false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f23]) ).

fof(f210,plain,
~ spl0_20,

fof(f215,plain,
( equalish(e_1,e_3)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f152,f41]) ).

fof(f216,plain,
( \$false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f20]) ).

fof(f217,plain,
~ spl0_18,

fof(f223,plain,
( product(e_2,e_2,e_3)
| ~ spl0_7
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f85,f155]) ).

fof(f224,plain,
( spl0_14
| ~ spl0_7
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f223,f103,f71,f154]) ).

fof(f225,plain,
\$false,
inference(sat_refutation,[status(thm)],[f78,f81,f121,f144,f161,f210,f217,f224]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 31 14:54:26 EDT 2022
% 0.13/0.35  % CPUTime  :
% 0.13/0.36  % Drodi V3.3.3
% 0.13/0.38  % Refutation found
% 0.13/0.38  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.026412 seconds
% 0.13/0.38  % CPU time: 0.045554 seconds
% 0.13/0.38  % Memory used: 17.157 MB
%------------------------------------------------------------------------------
```