%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 01:25:16 PM UTC 2026
% Result : Unsatisfiable 6.96s 1.49s
% Output : Proof 6.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 18
% Syntax : Number of formulae : 137 ( 38 unt; 0 def)
% Number of atoms : 518 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 523 ( 142 ~; 381 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 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 : 158 ( 0 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f3_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
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(p31,plain,
( product(e_4,e_2,X0)
| product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(f5,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f5_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p71,plain,
( product(e_4,e_2,e_4)
| product(e_3,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p31,c5]) ).
cnf(f20,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f20_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f22,axiom,
product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f22_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p54,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c20,c22]) ).
cnf(p181,plain,
( equalish(e_4,e_2)
| product(e_3,e_2,e_4)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p71,p54]) ).
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(p35,plain,
( product(e_2,e_4,X0)
| product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(f4,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f4_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p96,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[p35,c4]) ).
cnf(f23,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f23_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p45,plain,
( equalish(X2,X0)
| ~ product(X3,X0,X1)
| ~ product(X3,X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c22,c23]) ).
cnf(p330,plain,
( equalish(e_3,e_2)
| ~ product(X0,e_2,e_4)
| ~ product(X0,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[p96,p45]) ).
cnf(p404,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_2,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[p330,c22]) ).
cnf(p1044,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p181,p404]) ).
cnf(f21,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f21_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p55,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c21,c22]) ).
cnf(p1465,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1044,p55]) ).
cnf(p1476,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1465]) ).
cnf(f19,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f19_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p1480,plain,
( equalish(e_4,X0)
| ~ product(e_2,e_2,X0)
| equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1476,c19]) ).
cnf(p1817,plain,
( equalish(e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1480,c22]) ).
cnf(p1828,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1817]) ).
cnf(p1832,plain,
( equalish(e_3,X0)
| ~ product(e_2,e_2,X0)
| equalish(e_3,e_2)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1828,c19]) ).
cnf(p1877,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1832,c22]) ).
cnf(p1878,plain,
( equalish(e_3,e_2)
| product(e_2,e_1,e_3)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1877]) ).
cnf(f24,negated_conjecture,
( equalish(Y1,Y2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
fof(f24_nnf,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p43,plain,
( equalish(X2,X1)
| ~ product(X3,X0,X1)
| ~ product(X3,X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c22,c24]) ).
cnf(p1034,plain,
( equalish(e_4,e_2)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_4,e_4)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p181,p43]) ).
cnf(p1051,plain,
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_4,e_4)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1034]) ).
cnf(p1052,plain,
( ~ product(e_4,e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1051,c22]) ).
cnf(p32,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)],[c4,c0]) ).
cnf(p75,plain,
( product(e_4,e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[p32,c3]) ).
cnf(p1056,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1052,p75]) ).
cnf(p53,plain,
( equalish(X0,X1)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[c19,c22]) ).
cnf(p1062,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1056,p53]) ).
cnf(p1076,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_2)
| equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1062,c20]) ).
cnf(p1143,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1076,c22]) ).
cnf(p1146,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_2,e_4)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1143]) ).
cnf(p1150,plain,
( equalish(e_4,X0)
| ~ product(e_2,e_2,X0)
| equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1146,c19]) ).
cnf(p1186,plain,
( equalish(e_4,e_2)
| equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1150,c22]) ).
cnf(p1187,plain,
( equalish(e_3,e_2)
| product(e_1,e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1186]) ).
cnf(p28,plain,
( equalish(X1,X2)
| ~ product(X2,X0,X1)
| ~ product(X2,X2,X2)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[c24]) ).
cnf(p1190,plain,
( equalish(e_3,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(e_2,e_2,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1187,p28]) ).
cnf(p1208,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_2,e_2,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1190]) ).
cnf(p1209,plain,
( ~ product(e_2,e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1208,c22]) ).
cnf(p1893,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[p1878,p1209]) ).
cnf(p1901,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1893]) ).
cnf(p1904,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1901]) ).
cnf(p1906,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_1,e_2,e_4) ),
inference(factoring,[status(thm)],[p1904]) ).
cnf(p1914,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1906,c21]) ).
cnf(f18,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(f18_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)],[f18]) ).
fof(f18_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)],[f18_nnf]) ).
cnf(c18,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)],[f18_sk]) ).
cnf(p49,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)],[c18,c4]) ).
cnf(p150,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p49,c3]) ).
cnf(p1931,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1914,p150]) ).
cnf(p2134,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1931,p54]) ).
cnf(p2140,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p2134]) ).
cnf(p2146,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p2140,c21]) ).
cnf(p2203,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p2146,c22]) ).
cnf(p2204,plain,
( product(e_3,e_2,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p2203]) ).
cnf(p2211,plain,
( equalish(e_1,e_3)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_1,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p2204,p45]) ).
cnf(p2242,plain,
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_1,e_1)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p2211]) ).
cnf(p2243,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p2242,c22]) ).
cnf(p1913,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1906,c20]) ).
cnf(f2,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f2_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p47,plain,
( product(e_1,X0,e_4)
| product(e_1,X0,e_3)
| product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c18,c2]) ).
cnf(p131,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p47,c4]) ).
cnf(p1930,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1913,p131]) ).
cnf(p2094,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1930,p55]) ).
cnf(p2244,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p2243,p2094]) ).
cnf(p3244,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_3,e_2)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p2244]) ).
cnf(p3246,plain,
( equalish(e_3,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p3244]) ).
cnf(p3251,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p3246,p54]) ).
cnf(p3257,plain,
( equalish(e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p3251]) ).
cnf(f16,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f16_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p3271,plain,
( equalish(e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_1,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3257,c16]) ).
cnf(f13,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f13_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p3272,plain,
( equalish(e_3,e_1)
| equalish(e_2,e_3)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p3271,c13]) ).
cnf(f12,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f12_nnf,plain,
~ equalish(e_3,e_1),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ equalish(e_3,e_1),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p3273,plain,
( equalish(e_2,e_3)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p3272,c12]) ).
cnf(f10,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p3274,plain,
equalish(e_1,e_3),
inference(resolution,[status(thm)],[p3273,c10]) ).
cnf(f7,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p3282,plain,
$false,
inference(resolution,[status(thm)],[p3274,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:39:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.96/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.96/1.49 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------