%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-7.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:25:17 PM UTC 2026
% Result : Unsatisfiable 17.63s 2.83s
% Output : Proof 17.63s
% 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(f26,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(f26_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)],[f26]) ).
fof(f26_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)],[f26_nnf]) ).
cnf(c26,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)],[f26_sk]) ).
cnf(f13,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f13_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p42,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)],[c26,c13]) ).
cnf(f11,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f11_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p87,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)],[p42,c11]) ).
cnf(f28,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f28_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(f30,axiom,
product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f30_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p46,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c28,c30]) ).
cnf(p285,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)],[p87,p46]) ).
cnf(f36,negated_conjecture,
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2a) ).
fof(f36_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(p1258,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)],[p285,c36]) ).
cnf(f12,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f12_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p41,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)],[c26,c12]) ).
cnf(p77,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)],[p41,c13]) ).
cnf(f29,axiom,
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f29_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p47,plain,
( equalish(X1,X0)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[c29,c30]) ).
cnf(p218,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)],[p77,p47]) ).
cnf(p971,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)],[p218,c36]) ).
cnf(p982,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)],[p971,c30]) ).
cnf(f33,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f33_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c33,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p984,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)],[p982,c33]) ).
cnf(f35,axiom,
product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f35_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(p987,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)],[p984,c35]) ).
cnf(p998,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p987]) ).
cnf(p1268,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)],[p1258,p998]) ).
cnf(f32,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f32_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p1274,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)],[p1268,c32]) ).
cnf(p1289,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)],[p1274,c35]) ).
cnf(p1292,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)],[p1289]) ).
cnf(p1296,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)],[p1292,c29]) ).
cnf(p1312,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)],[p1296,c30]) ).
cnf(p1313,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)],[p1312]) ).
cnf(p1317,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)],[p1313,c29]) ).
cnf(p1332,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)],[p1317]) ).
cnf(p76,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)],[p41,c11]) ).
cnf(p40,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)],[c26,c11]) ).
cnf(p65,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)],[p40,c13]) ).
cnf(p97,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)],[p65,p47]) ).
cnf(p98,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)],[p97,c36]) ).
cnf(p200,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)],[p76,p98]) ).
cnf(p53,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c32,c35]) ).
cnf(p203,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)],[p200,p53]) ).
cnf(p206,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)],[p203]) ).
cnf(p210,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)],[p206,p46]) ).
cnf(p223,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)],[p210,c29]) ).
cnf(p239,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)],[p223,c30]) ).
cnf(p240,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)],[p239]) ).
cnf(p1335,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)],[p1332,p240]) ).
cnf(p1343,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)],[p1335]) ).
cnf(p1346,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)],[p1343,c28]) ).
cnf(p1364,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)],[p1346]) ).
cnf(p1368,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)],[p1364,p240]) ).
cnf(p7453,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)],[p1368]) ).
cnf(p7461,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)],[p7453]) ).
cnf(p7463,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)],[p7461]) ).
cnf(p7465,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)],[p7463]) ).
cnf(p7468,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)],[p7465,c28]) ).
cnf(p7583,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)],[p7468,c30]) ).
cnf(p7584,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)],[p7583]) ).
cnf(p999,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)],[p998,c36]) ).
cnf(p64,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)],[p40,c12]) ).
cnf(p1010,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)],[p999,p64]) ).
cnf(p1084,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)],[p1010,p53]) ).
cnf(p1087,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)],[p1084]) ).
cnf(p1091,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)],[p1087,c29]) ).
cnf(p7590,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)],[p7584,p1091]) ).
cnf(p7745,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)],[p7590]) ).
cnf(p7747,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)],[p7745]) ).
cnf(p7752,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)],[p7747,p47]) ).
cnf(p7758,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)],[p7752]) ).
cnf(p7762,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)],[p7758,c28]) ).
cnf(p7823,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)],[p7762,c30]) ).
cnf(p7830,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)],[p7823]) ).
cnf(p7587,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)],[p7584,c28]) ).
cnf(p7628,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)],[p7587]) ).
cnf(p7854,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)],[p7830,p7628]) ).
cnf(p7872,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)],[p7854]) ).
cnf(p7875,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)],[p7872]) ).
cnf(p7879,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7875]) ).
cnf(f25,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f25_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p7880,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7879,c25]) ).
cnf(f24,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f24_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p7881,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p7880,c24]) ).
cnf(f21,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f21_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p7882,plain,
$false,
inference(resolution,[status(thm)],[p7881,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-7.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Wed Sep 23 13:44:34 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.63/2.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.63/2.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------