%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP134-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:25:23 PM UTC 2026
% Result : Unsatisfiable 38.38s 20.74s
% Output : Proof 38.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 11
% Syntax : Number of formulae : 185 ( 23 unt; 0 def)
% Number of atoms : 755 ( 0 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 667 ( 97 ~; 570 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 106 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,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(f9_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)],[f9]) ).
fof(f9_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)],[f9_nnf]) ).
cnf(c9,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)],[f9_sk]) ).
cnf(f0,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f0_nnf,plain,
group_element(e_1),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(p18,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)],[c9,c0]) ).
cnf(f1,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f1_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(p25,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)],[p18,c1]) ).
cnf(f12,axiom,
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f12_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p78,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)],[p25,c12]) ).
cnf(p19,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)],[c9,c1]) ).
cnf(p38,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)],[p19,c0]) ).
cnf(f13,negated_conjecture,
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
fof(f13_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p73,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)],[p25,c13]) ).
cnf(p137,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)],[p38,p73]) ).
cnf(p14,plain,
( product(X1,X1,X0)
| ~ product(X0,X0,X1) ),
inference(factoring,[status(thm)],[c13]) ).
cnf(p178,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)],[p137,p14]) ).
cnf(p373,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)],[p78,p178]) ).
cnf(p1058,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)],[p373]) ).
cnf(p1257,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)],[p1058]) ).
cnf(f11,axiom,
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f11_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p1276,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)],[p1257,c11]) ).
cnf(p1285,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)],[p1276]) ).
cnf(p17,plain,
( product(X0,X0,e_3)
| product(X0,X0,e_2)
| product(X0,X0,e_1)
| ~ group_element(X0) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(p23,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)],[p17,c1]) ).
cnf(p372,plain,
( product(e_2,e_2,e_2)
| product(e_2,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)],[p78,p23]) ).
cnf(p1293,plain,
( product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,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)],[p1285,p372]) ).
cnf(p5881,plain,
( product(e_2,e_2,e_1)
| equalish(e_1,e_2)
| product(e_1,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)],[p1293]) ).
cnf(p9913,plain,
( product(e_2,e_2,e_1)
| equalish(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)],[p5881]) ).
cnf(p9915,plain,
( 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)],[p9913]) ).
cnf(p9920,plain,
( product(e_1,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)],[p9915,p14]) ).
cnf(f2,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f2_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p20,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)],[c9,c2]) ).
cnf(p48,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)],[p20,c1]) ).
cnf(p226,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)],[p48,c12]) ).
cnf(p699,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)],[p226,p23]) ).
cnf(p54,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)],[p23,p14]) ).
cnf(p62,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)],[p54,c11]) ).
cnf(p3254,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)],[p699,p62]) ).
cnf(p4204,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)],[p3254]) ).
cnf(p4211,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)],[p4204]) ).
cnf(p4212,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)],[p4211]) ).
cnf(p4213,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)],[p4212,c13]) ).
cnf(p39,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)],[p19,c2]) ).
cnf(p142,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)],[p39,c11]) ).
cnf(p483,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)],[p142,p23]) ).
cnf(p63,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)],[p54,c12]) ).
cnf(p2037,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)],[p483,p63]) ).
cnf(p3317,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)],[p2037]) ).
cnf(p3320,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)],[p3317]) ).
cnf(p3326,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)],[p3320]) ).
cnf(p4232,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)],[p4213,p3326]) ).
cnf(p8445,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)],[p4232]) ).
cnf(p8448,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)],[p8445]) ).
cnf(p8455,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)],[p8448]) ).
cnf(p139,plain,
( product(e_3,X0,e_3)
| ~ product(e_3,e_2,X0)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p39,c13]) ).
cnf(p227,plain,
( product(e_3,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p48,p139]) ).
cnf(p245,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p227,c11]) ).
cnf(p434,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p245,p48]) ).
cnf(p1525,plain,
( product(e_3,e_2,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p434]) ).
cnf(p1527,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p1525]) ).
cnf(p1528,plain,
( product(e_2,X0,e_2)
| ~ product(e_2,e_3,X0)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p1527,c13]) ).
cnf(p1569,plain,
( ~ product(e_2,e_3,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p1528]) ).
cnf(p1571,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p1569,p39]) ).
cnf(p1580,plain,
( product(e_2,e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p1571]) ).
cnf(p1582,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p1580]) ).
cnf(p24,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p17,c2]) ).
cnf(p71,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p24,c12]) ).
cnf(p336,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p71,p39]) ).
cnf(p941,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[p336,p14]) ).
cnf(p980,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_1)
| product(e_2,e_2,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p941,c11]) ).
cnf(p1098,plain,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_2,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p980]) ).
cnf(p1594,plain,
( product(e_2,e_2,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)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p1582,p1098]) ).
cnf(p2898,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p1594]) ).
cnf(p2903,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p2898]) ).
cnf(p2905,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p2903]) ).
cnf(p221,plain,
( product(e_3,X0,e_2)
| ~ product(e_2,e_3,X0)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p48,c13]) ).
cnf(p228,plain,
( ~ product(e_2,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p221]) ).
cnf(p2912,plain,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p2905,p228]) ).
cnf(p2906,plain,
( product(e_2,X0,e_3)
| ~ product(e_3,e_2,X0)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p2905,c13]) ).
cnf(p2963,plain,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p2906]) ).
cnf(p3015,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p2912,p2963]) ).
cnf(p4038,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p3015]) ).
cnf(p4042,plain,
( equalish(e_3,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p4038]) ).
cnf(p4046,plain,
( product(e_3,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p4042]) ).
cnf(p22,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)],[p17,c0]) ).
cnf(p28,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,p14]) ).
cnf(p36,plain,
( equalish(e_3,X0)
| ~ product(e_3,X0,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p28,c11]) ).
cnf(p4051,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p4046,p36]) ).
cnf(p4099,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p4051]) ).
cnf(p37,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p28,c12]) ).
cnf(p4114,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p4099,p37]) ).
cnf(p8137,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p4114]) ).
cnf(p8140,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8137]) ).
cnf(p8141,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8140]) ).
cnf(f10,axiom,
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f10_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p8146,plain,
( equalish(e_3,X0)
| ~ product(e_2,e_2,X0)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8141,c10]) ).
cnf(p8166,plain,
( ~ product(e_2,e_2,e_2)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8146]) ).
cnf(p8486,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8455,p8166]) ).
cnf(p8568,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8486]) ).
cnf(p8569,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8568]) ).
cnf(p8577,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8569,p14]) ).
cnf(p8583,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8577]) ).
cnf(p8585,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8583,p14]) ).
cnf(p4050,plain,
( equalish(e_3,X0)
| ~ product(X0,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p4046,c12]) ).
cnf(p4082,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(factoring,[status(thm)],[p4050]) ).
cnf(p8610,plain,
( product(e_2,e_2,e_3)
| equalish(e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8585,p4082]) ).
cnf(p8658,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8610]) ).
cnf(p8661,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_1)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8658,c11]) ).
cnf(p8723,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8661]) ).
cnf(p8725,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8723,p8585]) ).
cnf(p8788,plain,
( equalish(e_3,e_2)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8725]) ).
cnf(p8792,plain,
( product(e_2,e_2,e_3)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8788]) ).
cnf(p8794,plain,
( product(e_3,e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8792,p14]) ).
cnf(p8804,plain,
( equalish(e_3,X0)
| ~ product(X0,e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8794,c12]) ).
cnf(p8850,plain,
( ~ product(e_2,e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8804]) ).
cnf(p1586,plain,
( equalish(e_3,X0)
| ~ product(X0,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)],[p1582,c12]) ).
cnf(p1612,plain,
( ~ 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(factoring,[status(thm)],[p1586]) ).
cnf(p8606,plain,
( equalish(e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8585,p1612]) ).
cnf(p8642,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8606]) ).
cnf(p8860,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8850,p8642]) ).
cnf(p8918,plain,
( product(e_2,e_3,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8860]) ).
cnf(p8919,plain,
( product(e_2,e_3,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8918]) ).
cnf(p8922,plain,
( equalish(e_3,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8919,c11]) ).
cnf(p8933,plain,
( ~ product(e_2,e_2,e_1)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8922]) ).
cnf(p8935,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8933,p8585]) ).
cnf(p8941,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8935]) ).
cnf(p8942,plain,
( product(e_1,e_1,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8941]) ).
cnf(p8946,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8942,c12]) ).
cnf(p9943,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p9920,p8946]) ).
cnf(p9949,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p9943]) ).
cnf(p9953,plain,
( equalish(e_1,X0)
| ~ product(X0,e_2,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p9949,c12]) ).
cnf(p9974,plain,
( ~ product(e_2,e_2,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p9953]) ).
cnf(p3327,plain,
( product(e_1,X0,e_3)
| ~ product(e_3,e_2,X0)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p3326,c13]) ).
cnf(p4221,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,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)],[p4212,p3327]) ).
cnf(p8303,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_2)
| equalish(e_3,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)],[p4221]) ).
cnf(p8306,plain,
( product(e_1,e_1,e_3)
| equalish(e_3,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)],[p8303]) ).
cnf(p8307,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2) ),
inference(factoring,[status(thm)],[p8306]) ).
cnf(p10004,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p9974,p8307]) ).
cnf(p10058,plain,
( product(e_1,e_1,e_3)
| product(e_2,e_2,e_1)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p10004]) ).
cnf(p10063,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p10058,p14]) ).
cnf(p10079,plain,
( product(e_1,e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p10063]) ).
cnf(p8945,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8942,c11]) ).
cnf(p10090,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p10079,p8945]) ).
cnf(p10092,plain,
( equalish(e_3,e_2)
| product(e_1,e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p10090]) ).
cnf(p10097,plain,
( product(e_1,e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p10092]) ).
cnf(p8944,plain,
( equalish(e_1,X0)
| ~ product(e_1,e_1,X0)
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[p8942,c10]) ).
cnf(p10108,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p10097,p8944]) ).
cnf(p10131,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_2)
| product(e_1,e_1,e_2)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p10108]) ).
cnf(p10151,plain,
( equalish(e_1,e_2)
| equalish(e_3,e_2)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p10131,p8944]) ).
cnf(p10176,plain,
( equalish(e_3,e_2)
| equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p10151]) ).
cnf(p10178,plain,
( equalish(e_1,e_3)
| equalish(e_3,e_2)
| equalish(e_1,e_2) ),
inference(factoring,[status(thm)],[p10176]) ).
cnf(f8,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f8_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p10181,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[p10178,c8]) ).
cnf(f4,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f4_nnf,plain,
~ equalish(e_1,e_3),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
~ equalish(e_1,e_3),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p10182,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p10181,c4]) ).
cnf(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f3_nnf,plain,
~ equalish(e_1,e_2),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ equalish(e_1,e_2),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p10183,plain,
$false,
inference(resolution,[status(thm)],[p10182,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP134-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:50:34 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 38.38/20.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.38/20.74 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------