%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP134-2.003 : 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 01:25:24 PM UTC 2026
% Result : Unsatisfiable 29.43s 10.66s
% Output : Proof 29.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 14
% Syntax : Number of formulae : 137 ( 29 unt; 0 def)
% Number of atoms : 479 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 438 ( 96 ~; 342 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 108 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( 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(f15_nnf,plain,
! [X,Y] :
( 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)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( 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)],[f15_nnf]) ).
cnf(c15,plain,
( 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)],[f15_sk]) ).
cnf(f6,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f6_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(p23,plain,
( 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)],[c15,c6]) ).
cnf(f7,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f7_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(p43,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p23,c7]) ).
cnf(f18,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f18_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p135,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p43,c18]) ).
cnf(p24,plain,
( 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)],[c15,c7]) ).
cnf(p53,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p24,c6]) ).
cnf(f19,negated_conjecture,
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
fof(f19_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p130,plain,
( product(e_3,X0,e_2)
| ~ product(e_2,e_1,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p43,c19]) ).
cnf(p192,plain,
( product(e_3,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p53,p130]) ).
cnf(p20,plain,
( product(X1,X1,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(p195,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[p192,p20]) ).
cnf(p415,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p135,p195]) ).
cnf(p1051,plain,
( product(e_1,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p415]) ).
cnf(p1589,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p1051]) ).
cnf(f17,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f17_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1593,plain,
( equalish(e_1,X0)
| ~ product(e_2,X0,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p1589,c17]) ).
cnf(p1609,plain,
( ~ product(e_2,e_2,e_2)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p1593]) ).
cnf(p22,plain,
( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c15]) ).
cnf(p29,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p22,c7]) ).
cnf(p73,plain,
( equalish(e_2,X0)
| ~ product(X0,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p29,c18]) ).
cnf(p336,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p73,p43]) ).
cnf(p1617,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p1609,p336]) ).
cnf(p5754,plain,
( product(e_1,e_2,e_2)
| equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p1617]) ).
cnf(p7207,plain,
( equalish(e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p5754]) ).
cnf(p7209,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p7207,p20]) ).
cnf(p28,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c6]) ).
cnf(f5,axiom,
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
fof(f5_nnf,plain,
! [X,Y,X1] :
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,X1] :
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p33,plain,
( ~ greater(e_3,X0)
| ~ next(e_1,X0)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p28,c5]) ).
cnf(f0,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f0_nnf,plain,
next(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p92,plain,
( ~ greater(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p33,c0]) ).
cnf(f4,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
fof(f4_nnf,plain,
greater(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
greater(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p373,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p92,c4]) ).
cnf(p882,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p373,c18]) ).
cnf(p3490,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p882,p1589]) ).
cnf(p3691,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p3490]) ).
cnf(p3695,plain,
( equalish(e_1,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p3691,c17]) ).
cnf(p3977,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p3695]) ).
cnf(p878,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p373,p20]) ).
cnf(p3979,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p3977,p878]) ).
cnf(p3980,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p3979]) ).
cnf(p881,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p373,c17]) ).
cnf(p3986,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p3980,p881]) ).
cnf(p3991,plain,
( equalish(e_1,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p3986]) ).
cnf(p3994,plain,
( product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p3991]) ).
cnf(p3998,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p3994,c18]) ).
cnf(p4002,plain,
( ~ product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p3998]) ).
cnf(p4006,plain,
( product(e_1,e_1,e_1)
| equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p4002,p878]) ).
cnf(p4007,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p4006]) ).
cnf(p4012,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p4007,c18]) ).
cnf(p4027,plain,
( ~ product(e_2,e_1,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4012]) ).
cnf(p7231,plain,
( equalish(e_1,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p7209,p4027]) ).
cnf(p7246,plain,
( product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p7231]) ).
cnf(p7250,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p7246,c18]) ).
cnf(p7271,plain,
( ~ product(e_2,e_2,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p7250]) ).
cnf(f8,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f8_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p25,plain,
( 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)],[c15,c8]) ).
cnf(p60,plain,
( 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)],[p25,c7]) ).
cnf(p251,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p60,c18]) ).
cnf(p685,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p251,p29]) ).
cnf(p68,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p29,p20]) ).
cnf(p76,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p68,c17]) ).
cnf(p2712,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p685,p76]) ).
cnf(p4891,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p2712]) ).
cnf(p4896,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p4891]) ).
cnf(p4897,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p4896]) ).
cnf(p4898,plain,
( product(e_1,X0,e_2)
| ~ product(e_2,e_3,X0)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4897,c19]) ).
cnf(p54,plain,
( 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)],[p24,c8]) ).
cnf(p212,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p54,c17]) ).
cnf(p505,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p212,p29]) ).
cnf(p77,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[p68,c18]) ).
cnf(p1605,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p505,p77]) ).
cnf(p4485,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p1605]) ).
cnf(p4488,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p4485]) ).
cnf(p4491,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p4488]) ).
cnf(p4913,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4898,p4491]) ).
cnf(p5874,plain,
( product(e_2,e_2,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4913]) ).
cnf(p5877,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5874]) ).
cnf(p5878,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p5877]) ).
cnf(p7307,plain,
( product(e_1,e_1,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p7271,p5878]) ).
cnf(p7410,plain,
( product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p7307]) ).
cnf(p7412,plain,
( product(e_1,e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p7410,p20]) ).
cnf(p7429,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p7412]) ).
cnf(p4011,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p4007,c17]) ).
cnf(p4026,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4011]) ).
cnf(p7441,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p7429,p4026]) ).
cnf(p7444,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p7441]) ).
cnf(f16,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f16_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p4010,plain,
( equalish(e_1,X0)
| ~ product(e_1,e_1,X0)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p4007,c16]) ).
cnf(p4017,plain,
( ~ product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p4010]) ).
cnf(p7463,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p7444,p4017]) ).
cnf(p7478,plain,
( equalish(e_3,e_2)
| equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p7463]) ).
cnf(f14,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f14_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p7479,plain,
( equalish(e_2,e_1)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p7478,c14]) ).
cnf(f11,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f11_nnf,plain,
~ equalish(e_2,e_1),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ equalish(e_2,e_1),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p7480,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p7479,c11]) ).
cnf(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f9_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p7481,plain,
$false,
inference(resolution,[status(thm)],[p7480,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP134-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 13:49:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 29.43/10.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.43/10.66 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------