%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 190.34s 37.95s
% Output : Proof 190.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 12
% Syntax : Number of formulae : 115 ( 31 unt; 0 def)
% Number of atoms : 496 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 469 ( 88 ~; 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 : 91 ( 0 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f37,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/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f37_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)],[f37]) ).
fof(f37_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)],[f37_nnf]) ).
cnf(c37,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)],[f37_sk]) ).
cnf(f23,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f23_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p77,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)],[c37,c23]) ).
cnf(f24,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f24_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p145,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)],[p77,c24]) ).
cnf(f40,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f40_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(f41,axiom,
product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f41_nnf,plain,
! [X] : product(X,X,X),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [X] : product(X,X,X),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c41,plain,
product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(p79,plain,
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[c40,c41]) ).
cnf(p386,plain,
( equalish(e_4,e_3)
| 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)],[p145,p79]) ).
cnf(f39,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f39_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p73,plain,
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[c39,c41]) ).
cnf(p1019,plain,
( equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p386,p73]) ).
cnf(p78,plain,
( product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c37,c24]) ).
cnf(f22,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f22_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(p149,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p78,c22]) ).
cnf(p434,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p149,p73]) ).
cnf(f42,negated_conjecture,
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2_1) ).
fof(f42_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)],[f42]) ).
fof(f42_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)],[f42_nnf]) ).
cnf(c42,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)],[f42_sk]) ).
cnf(p47,plain,
( equalish(X0,X2)
| ~ product(X2,X0,X1)
| ~ product(X2,X2,X2)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[c42]) ).
cnf(p1164,plain,
( equalish(e_4,e_3)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_3,e_3)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p434,p47]) ).
cnf(p1191,plain,
( equalish(e_4,e_3)
| ~ product(e_3,e_4,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1164,c41]) ).
cnf(p5223,plain,
( equalish(e_4,e_3)
| equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1019,p1191]) ).
cnf(p5301,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5223]) ).
cnf(p5307,plain,
( equalish(e_4,X0)
| ~ product(X0,e_2,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5301,c40]) ).
cnf(p5383,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5307,c41]) ).
cnf(p5385,plain,
( equalish(e_4,e_2)
| product(e_4,e_2,e_1)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5383]) ).
cnf(p5394,plain,
( equalish(e_4,X0)
| ~ product(X0,e_2,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5385,c40]) ).
cnf(p5404,plain,
( ~ product(e_3,e_2,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5394]) ).
cnf(p144,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)],[p77,c22]) ).
cnf(p76,plain,
( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c37,c22]) ).
cnf(p140,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p76,c24]) ).
cnf(p277,plain,
( equalish(e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p140,p79]) ).
cnf(p65,plain,
( equalish(X2,X0)
| ~ product(X3,X0,X1)
| ~ product(X3,X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c41,c42]) ).
cnf(p302,plain,
( equalish(e_3,e_2)
| ~ product(X0,e_2,e_4)
| ~ product(X0,e_3,e_3)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p277,p65]) ).
cnf(p309,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_2,e_4)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p302,c41]) ).
cnf(p372,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| 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)],[p144,p309]) ).
cnf(p656,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p372,p73]) ).
cnf(p669,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p656]) ).
cnf(p675,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p669,c40]) ).
cnf(p680,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p675,c41]) ).
cnf(p681,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p680]) ).
cnf(p5410,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5404,p681]) ).
cnf(p5579,plain,
( equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p5410]) ).
cnf(p5587,plain,
( equalish(e_4,X0)
| ~ product(e_3,X0,e_1)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p5579,c39]) ).
cnf(p5638,plain,
( ~ product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p5587]) ).
cnf(p5641,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p5638,p681]) ).
cnf(p13577,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product(e_2,e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p5641]) ).
cnf(p13581,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13577]) ).
cnf(p13583,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13581]) ).
cnf(p13585,plain,
( equalish(e_3,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13583]) ).
cnf(p13590,plain,
( equalish(e_4,X0)
| ~ product(e_2,X0,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13585,c39]) ).
cnf(p13605,plain,
( equalish(e_4,e_2)
| equalish(e_3,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13590,c41]) ).
cnf(p13607,plain,
( equalish(e_3,e_2)
| product(e_2,e_4,e_1)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13605]) ).
cnf(p5213,plain,
( equalish(e_3,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_2,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1019,p47]) ).
cnf(p5252,plain,
( equalish(e_3,e_2)
| ~ product(e_2,e_3,e_4)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5213,c41]) ).
cnf(p139,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p76,c23]) ).
cnf(p5253,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p5252,p139]) ).
cnf(p5456,plain,
( equalish(e_3,X0)
| ~ product(X0,e_4,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p5253,c40]) ).
cnf(p6065,plain,
( ~ product(e_2,e_4,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p5456]) ).
cnf(p13644,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13607,p6065]) ).
cnf(p13974,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13644]) ).
cnf(p13977,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13974]) ).
cnf(p13979,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13977]) ).
cnf(p13986,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13979,p79]) ).
cnf(p14024,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13986]) ).
cnf(p14029,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p14024,c39]) ).
cnf(p14102,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p14029,c41]) ).
cnf(p14103,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p14102]) ).
cnf(p13616,plain,
( equalish(e_4,X0)
| ~ product(e_2,X0,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p13607,c39]) ).
cnf(p13666,plain,
( ~ product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p13616]) ).
cnf(p14146,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p14103,p13666]) ).
cnf(p14173,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p14146]) ).
cnf(p14177,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p14173]) ).
cnf(p14180,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p14177]) ).
cnf(p14183,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4)
| equalish(e_4,e_3) ),
inference(factoring,[status(thm)],[p14180]) ).
cnf(f36,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f36_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p14184,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p14183,c36]) ).
cnf(f35,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f35_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p14185,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[p14184,c35]) ).
cnf(f33,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f33_nnf,plain,
~ equalish(e_3,e_4),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
~ equalish(e_3,e_4),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p14186,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p14185,c33]) ).
cnf(f32,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f32_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p14191,plain,
$false,
inference(resolution,[status(thm)],[p14186,c32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/10.38 % Computer : n010.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Wed Sep 23 13:38:41 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 190.34/37.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 190.34/37.95 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------