## TSTP Solution File: GRP125-1.003 by Metis---2.4

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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  : 600s
% DateTime : Sat Jul 16 10:36:37 EDT 2022

% Result   : Unsatisfiable 0.19s 0.37s
% Output   : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of clauses     :   47 (  12 unt;  19 nHn;  43 RR)
%            Number of literals    :  115 (   0 equ;  39 neg)
%            Maximal clause size   :    5 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   40 (   0 sgn)

%------------------------------------------------------------------------------
cnf(element_1,axiom,
group_element(e_1) ).

cnf(element_3,axiom,
group_element(e_3) ).

cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3) ).

cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1) ).

cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2) ).

cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3) ) ).

cnf(product_total_function2,axiom,
( ~ product(X,Y,W)
| ~ product(X,Y,Z)
| equalish(W,Z) ) ).

cnf(product_right_cancellation,axiom,
( ~ product(X,W,Y)
| ~ product(X,Z,Y)
| equalish(W,Z) ) ).

cnf(product_left_cancellation,axiom,
( ~ product(W,Y,X)
| ~ product(Z,Y,X)
| equalish(W,Z) ) ).

cnf(product_idempotence,axiom,
product(X,X,X) ).

cnf(qg3,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Y,X,Z2)
| product(Z1,Z2,X) ) ).

cnf(refute_0_0,plain,
product(X_18,X_18,X_18),
inference(subst,[],[product_idempotence:[bind(X,\$fot(X_18))]]) ).

cnf(refute_0_1,plain,
( ~ product(X_18,X_16,X_18)
| ~ product(X_18,X_18,X_18)
| equalish(X_16,X_18) ),
inference(subst,[],[product_right_cancellation:[bind(W,\$fot(X_16)),bind(X,\$fot(X_18)),bind(Y,\$fot(X_18)),bind(Z,\$fot(X_18))]]) ).

cnf(refute_0_2,plain,
( ~ product(X_18,X_16,X_18)
| equalish(X_16,X_18) ),
inference(resolve,[\$cnf( product(X_18,X_18,X_18) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_2:[bind(X_16,\$fot(e_3)),bind(X_18,\$fot(e_1))]]) ).

cnf(refute_0_4,plain,
product(X_11,X_11,X_11),
inference(subst,[],[product_idempotence:[bind(X,\$fot(X_11))]]) ).

cnf(refute_0_5,plain,
( ~ product(X_11,X_11,X_11)
| ~ product(X_11,X_11,X_8)
| equalish(X_8,X_11) ),
inference(subst,[],[product_total_function2:[bind(W,\$fot(X_8)),bind(X,\$fot(X_11)),bind(Y,\$fot(X_11)),bind(Z,\$fot(X_11))]]) ).

cnf(refute_0_6,plain,
( ~ product(X_11,X_11,X_8)
| equalish(X_8,X_11) ),
inference(resolve,[\$cnf( product(X_11,X_11,X_11) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
( ~ product(e_2,e_2,e_3)
| equalish(e_3,e_2) ),
inference(subst,[],[refute_0_6:[bind(X_11,\$fot(e_2)),bind(X_8,\$fot(e_3))]]) ).

cnf(refute_0_8,plain,
product(X_25,X_25,X_25),
inference(subst,[],[product_idempotence:[bind(X,\$fot(X_25))]]) ).

cnf(refute_0_9,plain,
( ~ product(X_25,X_25,X_25)
| ~ product(X_27,X_25,X_25)
| equalish(X_25,X_27) ),
inference(subst,[],[product_left_cancellation:[bind(W,\$fot(X_25)),bind(X,\$fot(X_25)),bind(Y,\$fot(X_25)),bind(Z,\$fot(X_27))]]) ).

cnf(refute_0_10,plain,
( ~ product(X_27,X_25,X_25)
| equalish(X_25,X_27) ),
inference(resolve,[\$cnf( product(X_25,X_25,X_25) )],[refute_0_8,refute_0_9]) ).

cnf(refute_0_11,plain,
( ~ product(e_3,e_1,e_1)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_10:[bind(X_25,\$fot(e_1)),bind(X_27,\$fot(e_3))]]) ).

cnf(refute_0_12,plain,
( ~ product(e_1,e_3,Z2)
| ~ product(e_3,e_1,e_2)
| product(e_2,Z2,e_3) ),
inference(subst,[],[qg3:[bind(X,\$fot(e_3)),bind(Y,\$fot(e_1)),bind(Z1,\$fot(e_2))]]) ).

cnf(refute_0_13,plain,
( ~ product(e_3,e_1,e_3)
| equalish(e_1,e_3) ),
inference(subst,[],[refute_0_2:[bind(X_16,\$fot(e_1)),bind(X_18,\$fot(e_3))]]) ).

cnf(refute_0_14,plain,
( ~ group_element(X_41)
| ~ group_element(e_3)
| product(e_3,X_41,e_1)
| product(e_3,X_41,e_2)
| product(e_3,X_41,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,\$fot(e_3)),bind(Y,\$fot(X_41))]]) ).

cnf(refute_0_15,plain,
( ~ group_element(X_41)
| product(e_3,X_41,e_1)
| product(e_3,X_41,e_2)
| product(e_3,X_41,e_3) ),
inference(resolve,[\$cnf( group_element(e_3) )],[element_3,refute_0_14]) ).

cnf(refute_0_16,plain,
( ~ group_element(e_1)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(subst,[],[refute_0_15:[bind(X_41,\$fot(e_1))]]) ).

cnf(refute_0_17,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(resolve,[\$cnf( group_element(e_1) )],[element_1,refute_0_16]) ).

cnf(refute_0_18,plain,
( equalish(e_1,e_3)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[\$cnf( product(e_3,e_1,e_3) )],[refute_0_17,refute_0_13]) ).

cnf(refute_0_19,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(resolve,[\$cnf( equalish(e_1,e_3) )],[refute_0_18,e_1_is_not_e_3]) ).

cnf(refute_0_20,plain,
( ~ product(e_1,e_3,Z2)
| product(e_2,Z2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[\$cnf( product(e_3,e_1,e_2) )],[refute_0_19,refute_0_12]) ).

cnf(refute_0_21,plain,
( ~ product(e_1,e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(subst,[],[refute_0_20:[bind(Z2,\$fot(e_2))]]) ).

cnf(refute_0_22,plain,
( ~ product(e_1,e_3,e_3)
| equalish(e_3,e_1) ),
inference(subst,[],[refute_0_10:[bind(X_25,\$fot(e_3)),bind(X_27,\$fot(e_1))]]) ).

cnf(refute_0_23,plain,
( ~ group_element(X_41)
| ~ group_element(e_1)
| product(e_1,X_41,e_1)
| product(e_1,X_41,e_2)
| product(e_1,X_41,e_3) ),
inference(subst,[],[product_total_function1:[bind(X,\$fot(e_1)),bind(Y,\$fot(X_41))]]) ).

cnf(refute_0_24,plain,
( ~ group_element(X_41)
| product(e_1,X_41,e_1)
| product(e_1,X_41,e_2)
| product(e_1,X_41,e_3) ),
inference(resolve,[\$cnf( group_element(e_1) )],[element_1,refute_0_23]) ).

cnf(refute_0_25,plain,
( ~ group_element(e_3)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(subst,[],[refute_0_24:[bind(X_41,\$fot(e_3))]]) ).

cnf(refute_0_26,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(resolve,[\$cnf( group_element(e_3) )],[element_3,refute_0_25]) ).

cnf(refute_0_27,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[\$cnf( product(e_1,e_3,e_3) )],[refute_0_26,refute_0_22]) ).

cnf(refute_0_28,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2) ),
inference(resolve,[\$cnf( equalish(e_3,e_1) )],[refute_0_27,e_3_is_not_e_1]) ).

cnf(refute_0_29,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_2,e_3)
| product(e_3,e_1,e_1) ),
inference(resolve,[\$cnf( product(e_1,e_3,e_2) )],[refute_0_28,refute_0_21]) ).

cnf(refute_0_30,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_2,e_3) ),
inference(resolve,[\$cnf( product(e_3,e_1,e_1) )],[refute_0_29,refute_0_11]) ).

cnf(refute_0_31,plain,
( product(e_1,e_3,e_1)
| product(e_2,e_2,e_3) ),
inference(resolve,[\$cnf( equalish(e_1,e_3) )],[refute_0_30,e_1_is_not_e_3]) ).

cnf(refute_0_32,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolve,[\$cnf( product(e_2,e_2,e_3) )],[refute_0_31,refute_0_7]) ).

cnf(refute_0_33,plain,
product(e_1,e_3,e_1),
inference(resolve,[\$cnf( equalish(e_3,e_2) )],[refute_0_32,e_3_is_not_e_2]) ).

cnf(refute_0_34,plain,
equalish(e_3,e_1),
inference(resolve,[\$cnf( product(e_1,e_3,e_1) )],[refute_0_33,refute_0_3]) ).

cnf(refute_0_35,plain,
\$false,
inference(resolve,[\$cnf( equalish(e_3,e_1) )],[refute_0_34,e_3_is_not_e_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 13 23:10:42 EDT 2022
% 0.13/0.34  % CPUTime  :
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------
```