%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP124-9.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 36.54s 6.47s
% Output : Proof 36.54s
% 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(f18,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(f18_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)],[f18]) ).
fof(f18_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)],[f18_nnf]) ).
cnf(c18,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)],[f18_sk]) ).
cnf(f5,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f5_nnf,plain,
group_element(e_4),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(p43,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)],[c18,c5]) ).
cnf(f3,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3_nnf,plain,
group_element(e_2),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p122,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)],[p43,c3]) ).
cnf(f20,axiom,
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f20_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f22,axiom,
product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f22_nnf,plain,
! [X] : product1(X,X,X),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [X] : product1(X,X,X),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p48,plain,
( equalish(X0,X1)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[c20,c22]) ).
cnf(p320,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)],[p122,p48]) ).
cnf(f28,negated_conjecture,
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg2a) ).
fof(f28_nnf,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p1264,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)],[p320,c28]) ).
cnf(f4,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4_nnf,plain,
group_element(e_3),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(p42,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)],[c18,c4]) ).
cnf(p112,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)],[p42,c5]) ).
cnf(f21,axiom,
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f21_nnf,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p50,plain,
( equalish(X1,X0)
| ~ product1(X0,X1,X1) ),
inference(resolution,[status(thm)],[c21,c22]) ).
cnf(p253,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)],[p112,p50]) ).
cnf(p1004,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)],[p253,c28]) ).
cnf(p1015,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)],[p1004,c22]) ).
cnf(f25,axiom,
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_right_cancellation) ).
fof(f25_nnf,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p1017,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)],[p1015,c25]) ).
cnf(f27,axiom,
product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f27_nnf,plain,
! [X] : product2(X,X,X),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [X] : product2(X,X,X),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c27,plain,
product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p1020,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)],[p1017,c27]) ).
cnf(p1031,plain,
( equalish(e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(factoring,[status(thm)],[p1020]) ).
cnf(p1274,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)],[p1264,p1031]) ).
cnf(f24,axiom,
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f24_nnf,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p1280,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)],[p1274,c24]) ).
cnf(p1295,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)],[p1280,c27]) ).
cnf(p1298,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)],[p1295]) ).
cnf(p1302,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)],[p1298,c21]) ).
cnf(p1317,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)],[p1302,c22]) ).
cnf(p1318,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)],[p1317]) ).
cnf(p1322,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)],[p1318,c21]) ).
cnf(p1337,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)],[p1322]) ).
cnf(p111,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)],[p42,c3]) ).
cnf(p41,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)],[c18,c3]) ).
cnf(p100,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)],[p41,c5]) ).
cnf(p132,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)],[p100,p50]) ).
cnf(p133,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)],[p132,c28]) ).
cnf(p235,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)],[p111,p133]) ).
cnf(p51,plain,
( equalish(X0,X1)
| ~ product2(X0,X0,X1) ),
inference(resolution,[status(thm)],[c24,c27]) ).
cnf(p238,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)],[p235,p51]) ).
cnf(p241,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)],[p238]) ).
cnf(p245,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)],[p241,p48]) ).
cnf(p258,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)],[p245,c21]) ).
cnf(p274,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)],[p258,c22]) ).
cnf(p275,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)],[p274]) ).
cnf(p1340,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)],[p1337,p275]) ).
cnf(p1348,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)],[p1340]) ).
cnf(p1351,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)],[p1348,c20]) ).
cnf(p1369,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)],[p1351]) ).
cnf(p1373,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)],[p1369,p275]) ).
cnf(p7513,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)],[p1373]) ).
cnf(p7517,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)],[p7513]) ).
cnf(p7519,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)],[p7517]) ).
cnf(p7521,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)],[p7519]) ).
cnf(p7533,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)],[p7521,c20]) ).
cnf(p7629,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)],[p7533,c22]) ).
cnf(p7630,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)],[p7629]) ).
cnf(p1032,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)],[p1031,c28]) ).
cnf(p99,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)],[p41,c4]) ).
cnf(p1043,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)],[p1032,p99]) ).
cnf(p1126,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)],[p1043,p51]) ).
cnf(p1129,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)],[p1126]) ).
cnf(p1133,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)],[p1129,c21]) ).
cnf(p7636,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)],[p7630,p1133]) ).
cnf(p7800,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)],[p7636]) ).
cnf(p7802,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)],[p7800]) ).
cnf(p7814,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)],[p7802,p50]) ).
cnf(p7820,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)],[p7814]) ).
cnf(p7823,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)],[p7820,c20]) ).
cnf(p7882,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)],[p7823,c22]) ).
cnf(p7883,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)],[p7882]) ).
cnf(p7633,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)],[p7630,c20]) ).
cnf(p7666,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)],[p7633]) ).
cnf(p7907,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)],[p7883,p7666]) ).
cnf(p7943,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)],[p7907]) ).
cnf(p7946,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)],[p7943]) ).
cnf(p7948,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_3)
| equalish(e_4,e_2) ),
inference(factoring,[status(thm)],[p7946]) ).
cnf(f17,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f17_nnf,plain,
~ equalish(e_4,e_3),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
~ equalish(e_4,e_3),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p7949,plain,
( equalish(e_3,e_2)
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[p7948,c17]) ).
cnf(f16,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f16_nnf,plain,
~ equalish(e_4,e_2),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
~ equalish(e_4,e_2),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p7950,plain,
equalish(e_3,e_2),
inference(resolution,[status(thm)],[p7949,c16]) ).
cnf(f13,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f13_nnf,plain,
~ equalish(e_3,e_2),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ equalish(e_3,e_2),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p7951,plain,
$false,
inference(resolution,[status(thm)],[p7950,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP124-9.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n011.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 13:39:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 36.54/6.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.54/6.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------