%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-6.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 26.86s 5.52s
% Output : Proof 26.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 14
% Syntax : Number of formulae : 124 ( 31 unt; 0 def)
% Number of atoms : 470 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 429 ( 83 ~; 346 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 119 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f16,axiom,
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f16_nnf,plain,
! [X,Y] :
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] :
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( product1(X0,X1,e_4)
| product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(f3,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f3_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p32,plain,
( product1(e_4,X0,e_4)
| product1(e_4,X0,e_3)
| product1(e_4,X0,e_2)
| product1(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c16,c3]) ).
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(p77,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p32,c1]) ).
cnf(f18,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f18_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(f20,axiom,
product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f20_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p36,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c18,c20]) ).
cnf(p275,plain,
( equalish(e_4,e_2)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p77,p36]) ).
cnf(f26,negated_conjecture,
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2a) ).
fof(f26_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p1248,plain,
( product2(X0,e_2,e_4)
| ~ product1(e_3,e_4,X0)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p275,c26]) ).
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(p31,plain,
( product1(e_3,X0,e_4)
| product1(e_3,X0,e_3)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c16,c2]) ).
cnf(p67,plain,
( product1(e_3,e_4,e_4)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p31,c3]) ).
cnf(f19,axiom,
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f19_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p37,plain,
( equalish(X1,X0)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[c19,c20]) ).
cnf(p208,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p67,p37]) ).
cnf(p961,plain,
( product2(X0,e_4,e_3)
| ~ product1(e_3,e_3,X0)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p208,c26]) ).
cnf(p972,plain,
( product2(e_3,e_4,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p961,c20]) ).
cnf(f23,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f23_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p974,plain,
( equalish(e_4,X0)
| ~ product2(e_3,X0,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p972,c23]) ).
cnf(f25,axiom,
product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f25_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p977,plain,
( equalish(e_4,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p974,c25]) ).
cnf(p988,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p977]) ).
cnf(p1258,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| product2(e_2,e_2,e_4)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1248,p988]) ).
cnf(f22,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f22_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p1264,plain,
( equalish(e_4,X0)
| ~ product2(e_2,e_2,X0)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1258,c22]) ).
cnf(p1279,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1264,c25]) ).
cnf(p1282,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(factoring,[status(thm)],[p1279]) ).
cnf(p1286,plain,
( equalish(e_4,X0)
| ~ product1(X0,e_2,e_2)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1282,c19]) ).
cnf(p1302,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[p1286,c20]) ).
cnf(p1303,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2)
| product1(e_4,e_2,e_1) ),
inference(factoring,[status(thm)],[p1302]) ).
cnf(p1307,plain,
( equalish(e_4,X0)
| ~ product1(X0,e_2,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1303,c19]) ).
cnf(p1322,plain,
( ~ product1(e_3,e_2,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1307]) ).
cnf(p66,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p31,c1]) ).
cnf(p30,plain,
( product1(e_2,X0,e_4)
| product1(e_2,X0,e_3)
| product1(e_2,X0,e_2)
| product1(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(p55,plain,
( product1(e_2,e_4,e_4)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p30,c3]) ).
cnf(p87,plain,
( equalish(e_4,e_2)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p55,p37]) ).
cnf(p88,plain,
( product2(X0,e_4,e_2)
| ~ product1(e_3,e_2,X0)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[p87,c26]) ).
cnf(p190,plain,
( product2(e_4,e_4,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p66,p88]) ).
cnf(p43,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c22,c25]) ).
cnf(p193,plain,
( equalish(e_4,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p190,p43]) ).
cnf(p196,plain,
( equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p193]) ).
cnf(p200,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p196,p36]) ).
cnf(p213,plain,
( equalish(e_3,X0)
| ~ product1(X0,e_2,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p200,c19]) ).
cnf(p229,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[p213,c20]) ).
cnf(p230,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| product1(e_3,e_2,e_1) ),
inference(factoring,[status(thm)],[p229]) ).
cnf(p1325,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1322,p230]) ).
cnf(p1333,plain,
( equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1325]) ).
cnf(p1336,plain,
( equalish(e_4,X0)
| ~ product1(e_3,X0,e_1)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1333,c18]) ).
cnf(p1354,plain,
( ~ product1(e_3,e_2,e_1)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1336]) ).
cnf(p1358,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p1354,p230]) ).
cnf(p7443,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| product1(e_2,e_4,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p1358]) ).
cnf(p7451,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7443]) ).
cnf(p7453,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7451]) ).
cnf(p7455,plain,
( equalish(e_3,e_2)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7453]) ).
cnf(p7458,plain,
( equalish(e_4,X0)
| ~ product1(e_2,X0,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7455,c18]) ).
cnf(p7573,plain,
( equalish(e_4,e_2)
| equalish(e_3,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7458,c20]) ).
cnf(p7574,plain,
( equalish(e_3,e_2)
| product1(e_2,e_4,e_1)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7573]) ).
cnf(p989,plain,
( product2(X0,e_4,e_3)
| ~ product1(e_2,e_3,X0)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p988,c26]) ).
cnf(p54,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[p30,c2]) ).
cnf(p1000,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| product2(e_4,e_4,e_3)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p989,p54]) ).
cnf(p1074,plain,
( equalish(e_4,e_3)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[p1000,p43]) ).
cnf(p1077,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3)
| product1(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1074]) ).
cnf(p1081,plain,
( equalish(e_3,X0)
| ~ product1(X0,e_4,e_1)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[p1077,c19]) ).
cnf(p7580,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7574,p1081]) ).
cnf(p7735,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7580]) ).
cnf(p7737,plain,
( product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7735]) ).
cnf(p7742,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7737,p37]) ).
cnf(p7748,plain,
( product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7742]) ).
cnf(p7752,plain,
( equalish(e_3,X0)
| ~ product1(e_2,X0,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7748,c18]) ).
cnf(p7813,plain,
( equalish(e_3,e_2)
| product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7752,c20]) ).
cnf(p7820,plain,
( product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7813]) ).
cnf(p7577,plain,
( equalish(e_4,X0)
| ~ product1(e_2,X0,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7574,c18]) ).
cnf(p7618,plain,
( ~ product1(e_2,e_3,e_1)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7577]) ).
cnf(p7844,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7820,p7618]) ).
cnf(p7862,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7844]) ).
cnf(p7865,plain,
( equalish(e_3,e_2)
| equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7862]) ).
cnf(p7869,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7865]) ).
cnf(f15,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f15_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p7870,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7869,c15]) ).
cnf(f14,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f14_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p7871,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p7870,c14]) ).
cnf(f11,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f11_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p7872,plain,
$false,
inference(resolution,[status(thm)],[p7871,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-6.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 13:43:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.86/5.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.86/5.52 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------