%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:25:19 PM UTC 2026
% Result : Unsatisfiable 210.43s 166.19s
% Output : Proof 210.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 14
% Syntax : Number of formulae : 146 ( 20 unt; 0 def)
% Number of atoms : 506 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 468 ( 108 ~; 360 |; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 157 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f1_nnf,plain,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f7,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f7_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p36,plain,
( product(e_4,e_4,X0)
| product(e_4,e_3,X0)
| product(e_4,e_2,X0)
| product(e_4,e_1,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(f6,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f6_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p136,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p36,c6]) ).
cnf(f24,axiom,
product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f24_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(f25,negated_conjecture,
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
fof(f25_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p39,plain,
( product(X0,X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c24,c25]) ).
cnf(p1030,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p136,p39]) ).
cnf(f22,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f22_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p1062,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p1030,c22]) ).
cnf(p2821,plain,
( equalish(e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p1062,c24]) ).
cnf(f23,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f23_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p49,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c23,c24]) ).
cnf(p2842,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p2821,p49]) ).
cnf(p2854,plain,
( equalish(e_3,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p2842]) ).
cnf(f0,axiom,
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f0_nnf,plain,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( product(e_4,e_3,X0)
| product(e_3,e_3,X0)
| product(e_2,e_3,X0)
| product(e_1,e_3,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c6,c0]) ).
cnf(p70,plain,
( product(e_4,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p30,c7]) ).
cnf(f2,negated_conjecture,
( ~ product(Y,X,Z2)
| ~ product(Z1,Z2,Y)
| product(X,Y,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_1) ).
fof(f2_nnf,plain,
! [X,Y,Z1,Z2] :
( ~ product(Y,X,Z2)
| ~ product(Z1,Z2,Y)
| product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z1,Z2] :
( ~ product(Y,X,Z2)
| ~ product(Z1,Z2,Y)
| product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ product(X1,X0,X3)
| ~ product(X2,X3,X1)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p37,plain,
( ~ product(X1,X0,X1)
| product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c24,c2]) ).
cnf(p462,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p70,p37]) ).
cnf(p474,plain,
( equalish(e_3,X0)
| ~ product(X0,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p462,c23]) ).
cnf(p722,plain,
( equalish(e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p474,c24]) ).
cnf(f21,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f21_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p46,plain,
( equalish(X0,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c21,c24]) ).
cnf(p731,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p722,p46]) ).
cnf(p737,plain,
( equalish(e_3,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(factoring,[status(thm)],[p731]) ).
cnf(p738,plain,
( ~ product(e_4,X0,e_3)
| product(X0,e_4,e_2)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p737,c2]) ).
cnf(p2862,plain,
( product(e_2,e_4,e_2)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p2854,p738]) ).
cnf(p2947,plain,
( product(e_2,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(factoring,[status(thm)],[p2862]) ).
cnf(p2955,plain,
( product(e_1,e_4,e_2)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_2,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p2947,p738]) ).
cnf(p43801,plain,
( product(e_1,e_4,e_2)
| equalish(e_3,e_4)
| product(e_2,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p2955]) ).
cnf(p43802,plain,
( product(e_1,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p43801]) ).
cnf(f3,negated_conjecture,
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,Y)
| product(Y,X,Z2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_2) ).
fof(f3_nnf,plain,
! [Y,X,Z2,Z1] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,Y)
| product(Y,X,Z2) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Y,X,Z2,Z1] :
( ~ product(X,Y,Z1)
| ~ product(Z1,Z2,Y)
| product(Y,X,Z2) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ product(X1,X0,X3)
| ~ product(X3,X2,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p43804,plain,
( ~ product(X0,e_2,e_2)
| product(e_2,X0,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p43802,c3]) ).
cnf(p44387,plain,
( product(e_2,e_2,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p43804,c24]) ).
cnf(p26,plain,
( product(X1,X1,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c25]) ).
cnf(p44391,plain,
( product(e_4,e_4,e_2)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p44387,p26]) ).
cnf(p44407,plain,
( product(e_4,e_2,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p44391,p39]) ).
cnf(p44424,plain,
( product(e_2,e_4,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p44407,p37]) ).
cnf(p742,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_4)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p737,c22]) ).
cnf(p760,plain,
( ~ product(e_2,e_4,e_4)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(factoring,[status(thm)],[p742]) ).
cnf(p44450,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p44424,p760]) ).
cnf(p44595,plain,
( equalish(e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p44450]) ).
cnf(p44620,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p44595]) ).
cnf(p739,plain,
( ~ product(X0,e_4,e_2)
| product(e_4,X0,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p737,c3]) ).
cnf(p44629,plain,
( product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p44620,p739]) ).
cnf(p44866,plain,
( product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p44629]) ).
cnf(p44867,plain,
( product(e_4,e_1,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p44866]) ).
cnf(f20,axiom,
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f20_nnf,plain,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p43,plain,
( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c20,c6]) ).
cnf(p168,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p43,c7]) ).
cnf(p38,plain,
( ~ product(X1,X0,X0)
| product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c24,c3]) ).
cnf(p1738,plain,
( product(e_4,e_3,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p168,p38]) ).
cnf(p1752,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1738,c22]) ).
cnf(p3912,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1752,c24]) ).
cnf(p48,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c22,c24]) ).
cnf(p3929,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p3912,p48]) ).
cnf(p3944,plain,
( equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p3929]) ).
cnf(p3958,plain,
( product(e_4,e_3,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p3944,p739]) ).
cnf(p4023,plain,
( product(e_4,e_3,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p3958]) ).
cnf(p4031,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p4023,p49]) ).
cnf(p4039,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p4031]) ).
cnf(p4041,plain,
( ~ product(X0,e_1,e_3)
| product(e_1,X0,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p4039,c3]) ).
cnf(p44905,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p44867,p4041]) ).
cnf(p47762,plain,
( product(e_1,e_4,e_4)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p44905]) ).
cnf(p47763,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p47762]) ).
cnf(p47767,plain,
( product(e_4,e_1,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p47763,p38]) ).
cnf(p35,plain,
( product(e_3,e_4,X0)
| product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| product(e_3,e_1,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c1,c6]) ).
cnf(p118,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p35,c7]) ).
cnf(p922,plain,
( product(e_4,e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p118,p38]) ).
cnf(p936,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p922,c22]) ).
cnf(p1892,plain,
( equalish(e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p936,c24]) ).
cnf(p1906,plain,
( equalish(e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p1892,p46]) ).
cnf(p1913,plain,
( equalish(e_3,e_4)
| product(e_3,e_2,e_4)
| product(e_3,e_1,e_4) ),
inference(factoring,[status(thm)],[p1906]) ).
cnf(p740,plain,
( product(e_4,X0,e_3)
| ~ product(e_3,e_2,X0)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[p737,c25]) ).
cnf(p1924,plain,
( product(e_4,e_4,e_3)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p1913,p740]) ).
cnf(p1975,plain,
( product(e_4,e_4,e_3)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(factoring,[status(thm)],[p1924]) ).
cnf(p1979,plain,
( product(e_3,e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p1975,p26]) ).
cnf(p2012,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[p1979,p46]) ).
cnf(p2018,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(factoring,[status(thm)],[p2012]) ).
cnf(p2024,plain,
( equalish(e_3,X0)
| ~ product(X0,e_1,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p2018,c23]) ).
cnf(p2046,plain,
( ~ product(e_4,e_1,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p2024]) ).
cnf(p47860,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p47767,p2046]) ).
cnf(p48361,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p47860]) ).
cnf(p48370,plain,
( product(e_1,e_3,e_4)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p48361]) ).
cnf(p2855,plain,
( ~ product(e_3,X0,e_2)
| product(X0,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3) ),
inference(resolution,[status(thm)],[p2854,c2]) ).
cnf(p3960,plain,
( product(e_4,e_3,e_4)
| equalish(e_3,e_4)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p3944,p2855]) ).
cnf(p4091,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p3960]) ).
cnf(p4097,plain,
( equalish(e_3,X0)
| ~ product(e_4,X0,e_4)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p4091,c22]) ).
cnf(p4216,plain,
( equalish(e_3,e_4)
| product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p4097,c24]) ).
cnf(p4220,plain,
( product(e_4,e_1,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p4216]) ).
cnf(p4222,plain,
( ~ product(X0,e_3,e_4)
| product(e_3,X0,e_1)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p4220,c3]) ).
cnf(p48386,plain,
( product(e_3,e_1,e_1)
| equalish(e_3,e_4)
| product(e_3,e_4,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p48370,p4222]) ).
cnf(p48711,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_4,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p48386]) ).
cnf(p48372,plain,
( ~ product(X0,e_4,e_1)
| product(e_4,X0,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p48370,c3]) ).
cnf(p48758,plain,
( product(e_4,e_3,e_3)
| equalish(e_3,e_4)
| product(e_3,e_1,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p48711,p48372]) ).
cnf(p49039,plain,
( product(e_4,e_3,e_3)
| product(e_3,e_1,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p48758]) ).
cnf(p49047,plain,
( equalish(e_3,e_4)
| product(e_3,e_1,e_1)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p49039,p49]) ).
cnf(p49073,plain,
( product(e_3,e_1,e_1)
| equalish(e_3,e_4) ),
inference(factoring,[status(thm)],[p49047]) ).
cnf(p49113,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p49073,p49]) ).
cnf(f16,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f16_nnf,plain,
~ equalish(e_3,e_4),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ equalish(e_3,e_4),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p49148,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p49113,c16]) ).
cnf(f9,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f9_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p49149,plain,
$false,
inference(resolution,[status(thm)],[p49148,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Wed Sep 23 13:44:54 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 210.43/166.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 210.43/166.19 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------