%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:25:21 PM UTC 2026
% Result : Unsatisfiable 18.75s 15.40s
% Output : Proof 18.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 11
% Syntax : Number of formulae : 150 ( 23 unt; 0 def)
% Number of atoms : 568 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 506 ( 88 ~; 418 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 96 ( 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(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(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(p48,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p20,c0]) ).
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(p26,plain,
( 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)],[p18,c2]) ).
cnf(f13,negated_conjecture,
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
fof(f13_nnf,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p14,plain,
( product(X1,X1,X0)
| ~ product(X0,X1,X1) ),
inference(factoring,[status(thm)],[c13]) ).
cnf(p80,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p26,p14]) ).
cnf(p87,plain,
( product(X0,e_3,e_3)
| ~ product(e_3,e_1,X0)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p80,c13]) ).
cnf(p178,plain,
( product(e_3,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p48,p87]) ).
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(p88,plain,
( equalish(e_1,X0)
| ~ product(e_3,e_3,X0)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p80,c10]) ).
cnf(p312,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p178,p88]) ).
cnf(p865,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p312]) ).
cnf(p968,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p865]) ).
cnf(p973,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[p968,p87]) ).
cnf(p3923,plain,
( product(e_2,e_3,e_3)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p973]) ).
cnf(p4310,plain,
( product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1) ),
inference(factoring,[status(thm)],[p3923]) ).
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(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(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(p30,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c11]) ).
cnf(p102,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p30,p26]) ).
cnf(p27,plain,
( product(X0,e_1,e_1)
| ~ product(e_1,e_3,X0)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p22,c13]) ).
cnf(p390,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p102,p27]) ).
cnf(p1088,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p390]) ).
cnf(p1189,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1088]) ).
cnf(p1191,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1189,p14]) ).
cnf(p1195,plain,
( product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1191]) ).
cnf(p33,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p27]) ).
cnf(p1210,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1195,p33]) ).
cnf(p1220,plain,
( product(e_1,e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1210]) ).
cnf(p1222,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1220]) ).
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(p1228,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1222,c12]) ).
cnf(p1238,plain,
( ~ product(e_3,e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1228]) ).
cnf(p1244,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1238,p968]) ).
cnf(p1344,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_3,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1244]) ).
cnf(p1348,plain,
( equalish(e_1,X0)
| ~ product(e_3,X0,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1344,c11]) ).
cnf(p1419,plain,
( ~ product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1348]) ).
cnf(p1421,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1419,p80]) ).
cnf(p1703,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1421]) ).
cnf(p1706,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1703]) ).
cnf(p1227,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1222,c11]) ).
cnf(p1230,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1227]) ).
cnf(p1716,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1706,p1230]) ).
cnf(p1735,plain,
( equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1716]) ).
cnf(p1737,plain,
( product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1735]) ).
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(p69,plain,
( product(X0,e_2,e_1)
| ~ product(e_1,e_3,X0)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p25,c13]) ).
cnf(p76,plain,
( ~ product(e_1,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p69]) ).
cnf(p1747,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1737,p76]) ).
cnf(p1225,plain,
( product(X0,e_1,e_1)
| ~ product(e_1,e_2,X0)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1222,c13]) ).
cnf(p1774,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1747,p1225]) ).
cnf(p2200,plain,
( product(e_2,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1774]) ).
cnf(p2202,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2200]) ).
cnf(p2207,plain,
( equalish(e_1,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2202,c11]) ).
cnf(p2211,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2207]) ).
cnf(p1742,plain,
( product(X0,e_3,e_1)
| ~ product(e_1,e_1,X0)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1737,c13]) ).
cnf(p1765,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p1742,p1222]) ).
cnf(p1800,plain,
( equalish(e_1,e_3)
| product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1765]) ).
cnf(p1802,plain,
( product(e_2,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1800]) ).
cnf(p2213,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2211,p1802]) ).
cnf(p2214,plain,
( equalish(e_1,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2213]) ).
cnf(p2216,plain,
( product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2214]) ).
cnf(p1245,plain,
( ~ product(e_1,e_2,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p1225]) ).
cnf(p2222,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[p2216,p1245]) ).
cnf(p2228,plain,
( equalish(e_1,e_3)
| equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2222]) ).
cnf(p2230,plain,
( equalish(e_1,e_3)
| product(e_1,e_1,e_1) ),
inference(factoring,[status(thm)],[p2228]) ).
cnf(p2234,plain,
( equalish(e_1,X0)
| ~ product(X0,e_1,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p2230,c12]) ).
cnf(p2238,plain,
( ~ product(e_3,e_1,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p2234]) ).
cnf(p4322,plain,
( equalish(e_1,e_3)
| product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4310,p2238]) ).
cnf(p4325,plain,
( product(e_2,e_3,e_3)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4322]) ).
cnf(p84,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p26,c12]) ).
cnf(p4336,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4325,p84]) ).
cnf(p4393,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4336]) ).
cnf(p4405,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4393]) ).
cnf(p4409,plain,
( equalish(e_1,X0)
| ~ product(X0,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4405,c12]) ).
cnf(p4429,plain,
( ~ product(e_3,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4409]) ).
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(p41,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(p135,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p41,p14]) ).
cnf(p4447,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4429,p135]) ).
cnf(p4430,plain,
( ~ product(e_2,e_3,e_2)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4409]) ).
cnf(p4483,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p4447,p4430]) ).
cnf(p6108,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p4483]) ).
cnf(p6114,plain,
( equalish(e_1,e_2)
| product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p6108]) ).
cnf(p6116,plain,
( product(e_2,e_3,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p6114]) ).
cnf(p72,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p25,c11]) ).
cnf(p286,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p72,p26]) ).
cnf(p783,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p286,p69]) ).
cnf(p2711,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p783]) ).
cnf(p3835,plain,
( product(e_2,e_2,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p2711]) ).
cnf(p3838,plain,
( equalish(e_2,X0)
| ~ product(e_2,X0,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[p3835,c11]) ).
cnf(p3854,plain,
( ~ product(e_2,e_3,e_1)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(factoring,[status(thm)],[p3838]) ).
cnf(p6124,plain,
( product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[p6116,p3854]) ).
cnf(p7340,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1) ),
inference(factoring,[status(thm)],[p6124]) ).
cnf(p2233,plain,
( equalish(e_1,X0)
| ~ product(e_1,X0,e_1)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p2230,c11]) ).
cnf(p2236,plain,
( ~ product(e_1,e_3,e_1)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p2233]) ).
cnf(p7351,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p7340,p2236]) ).
cnf(p7356,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7351]) ).
cnf(p7360,plain,
( equalish(e_2,X0)
| ~ product(e_1,X0,e_2)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p7356,c11]) ).
cnf(p7414,plain,
( ~ product(e_1,e_3,e_2)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7360]) ).
cnf(p7422,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p7414,p4405]) ).
cnf(p7471,plain,
( equalish(e_1,e_2)
| product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7422]) ).
cnf(p7473,plain,
( product(e_1,e_3,e_1)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7471]) ).
cnf(p7479,plain,
( equalish(e_1,e_3)
| equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p7473,p2236]) ).
cnf(p7483,plain,
( equalish(e_2,e_3)
| product(e_1,e_2,e_1)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7479]) ).
cnf(p7490,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3)
| equalish(e_2,e_3)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p7483,p2233]) ).
cnf(p7507,plain,
( equalish(e_1,e_2)
| equalish(e_2,e_3)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7490]) ).
cnf(p7509,plain,
( equalish(e_2,e_3)
| equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(factoring,[status(thm)],[p7507]) ).
cnf(f6,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f6_nnf,plain,
~ equalish(e_2,e_3),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
~ equalish(e_2,e_3),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p7510,plain,
( equalish(e_1,e_2)
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[p7509,c6]) ).
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(p7511,plain,
equalish(e_1,e_2),
inference(resolution,[status(thm)],[p7510,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(p7512,plain,
$false,
inference(resolution,[status(thm)],[p7511,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.37 % Computer : n004.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Wed Sep 23 13:46:17 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.75/15.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.75/15.40 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------