## TSTP Solution File: GRP125-1.003 by SnakeForV-SAT---1.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n007.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 : Wed Aug 31 16:20:22 EDT 2022

% Result   : Unsatisfiable 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  17 unt;   0 def)
%            Number of atoms       :   87 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   78 (  32   ~;  46   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 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   :   47 (  47   !;   0   ?)

%------------------------------------------------------------------------------
fof(f129,plain,
\$false,
inference(subsumption_resolution,[],[f126,f29]) ).

fof(f29,plain,
~ equalish(e_3,e_1),
inference(literal_reordering,[],[f8]) ).

fof(f8,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

fof(f126,plain,
equalish(e_3,e_1),
inference(resolution,[],[f115,f35]) ).

fof(f35,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| equalish(X1,X0) ),
inference(resolution,[],[f18,f28]) ).

fof(f28,plain,
! [X0] : product(X0,X0,X0),
inference(literal_reordering,[],[f14]) ).

fof(f14,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).

fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ),
inference(literal_reordering,[],[f11]) ).

fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X3)
| ~ product(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).

fof(f115,plain,
product(e_1,e_1,e_3),
inference(resolution,[],[f107,f102]) ).

fof(f102,plain,
product(e_2,e_3,e_1),
inference(subsumption_resolution,[],[f101,f17]) ).

fof(f17,plain,
~ equalish(e_3,e_2),
inference(literal_reordering,[],[f9]) ).

fof(f9,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).

fof(f101,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[],[f90,f36]) ).

fof(f36,plain,
! [X0,X1] :
( ~ product(X1,X0,X1)
| equalish(X0,X1) ),
inference(resolution,[],[f26,f28]) ).

fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X1)
| equalish(X2,X3)
| ~ product(X0,X2,X1) ),
inference(literal_reordering,[],[f12]) ).

fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X3,X1)
| equalish(X2,X3)
| ~ product(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).

fof(f90,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(subsumption_resolution,[],[f89,f17]) ).

fof(f89,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolution,[],[f49,f33]) ).

fof(f33,plain,
! [X0,X1] :
( ~ product(X1,X0,X0)
| equalish(X0,X1) ),
inference(resolution,[],[f16,f28]) ).

fof(f16,plain,
! [X2,X3,X0,X1] :
( ~ product(X2,X1,X0)
| equalish(X2,X3)
| ~ product(X3,X1,X0) ),
inference(literal_reordering,[],[f13]) ).

fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ product(X2,X1,X0)
| equalish(X2,X3)
| ~ product(X3,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).

fof(f49,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_1)
| product(e_2,e_3,e_2) ),
inference(resolution,[],[f39,f21]) ).

fof(f21,plain,
group_element(e_3),
inference(literal_reordering,[],[f3]) ).

fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).

fof(f39,plain,
! [X2] :
( ~ group_element(X2)
| product(e_2,X2,e_2)
| product(e_2,X2,e_3)
| product(e_2,X2,e_1) ),
inference(resolution,[],[f27,f24]) ).

fof(f24,plain,
group_element(e_2),
inference(literal_reordering,[],[f2]) ).

fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).

fof(f27,plain,
! [X0,X1] :
( ~ group_element(X0)
| product(X0,X1,e_2)
| product(X0,X1,e_3)
| ~ group_element(X1)
| product(X0,X1,e_1) ),
inference(literal_reordering,[],[f10]) ).

fof(f10,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| ~ group_element(X1)
| ~ group_element(X0)
| product(X0,X1,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).

fof(f107,plain,
! [X3] :
( ~ product(e_2,e_3,X3)
| product(e_1,X3,e_3) ),
inference(resolution,[],[f96,f23]) ).

fof(f23,plain,
! [X0,X1,X4,X5] :
( ~ product(X0,X1,X4)
| product(X4,X5,X0)
| ~ product(X1,X0,X5) ),
inference(literal_reordering,[],[f15]) ).

fof(f15,axiom,
! [X0,X1,X4,X5] :
( ~ product(X1,X0,X5)
| product(X4,X5,X0)
| ~ product(X0,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).

fof(f96,plain,
product(e_3,e_2,e_1),
inference(subsumption_resolution,[],[f95,f19]) ).

fof(f19,plain,
~ equalish(e_2,e_3),
inference(literal_reordering,[],[f7]) ).

fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

fof(f95,plain,
( product(e_3,e_2,e_1)
| equalish(e_2,e_3) ),
inference(resolution,[],[f72,f33]) ).

fof(f72,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(subsumption_resolution,[],[f71,f19]) ).

fof(f71,plain,
( product(e_3,e_2,e_1)
| equalish(e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(resolution,[],[f47,f36]) ).

fof(f47,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(resolution,[],[f38,f24]) ).

fof(f38,plain,
! [X1] :
( ~ group_element(X1)
| product(e_3,X1,e_3)
| product(e_3,X1,e_2)
| product(e_3,X1,e_1) ),
inference(resolution,[],[f27,f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n007.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   : Mon Aug 29 21:59:30 EDT 2022
% 0.13/0.35  % CPUTime    :
% 0.19/0.50  % (29541)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (29538)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (29549)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.51  % (29539)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (29549)First to succeed.
% 0.19/0.51  % (29558)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.51  % (29548)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51  Detected maximum model sizes of [3]
% 0.19/0.51  % (29550)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.51  TRYING [1]
% 0.19/0.51  TRYING [2]
% 0.19/0.51  TRYING [3]
% 0.19/0.51  % (29552)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.52  % (29556)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.52  % (29559)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.52  % (29557)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.52  % (29560)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.52  % (29549)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (29549)------------------------------
% 0.19/0.52  % (29549)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (29549)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (29549)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52  % (29549)Memory used [KB]: 5756
% 0.19/0.52  % (29549)Time elapsed: 0.007 s
% 0.19/0.52  % (29549)Instructions burned: 10 (million)
% 0.19/0.52  % (29549)------------------------------
% 0.19/0.52  % (29549)------------------------------
% 0.19/0.52  % (29532)Success in time 0.165 s
%------------------------------------------------------------------------------
```