%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 01:31:24 PM UTC 2026
% Result : Unsatisfiable 0.66s 1.09s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 130 ( 39 unt; 0 def)
% Number of atoms : 355 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 430 ( 205 ~; 225 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 116 ( 0 sgn 116 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f29,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f32,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f33,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f35,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f36,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f37,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f38,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f39,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f40,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f41,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f42,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f43,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
tcf(c_92,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_93,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f42]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_100,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f37]) ).
tcf(c_101,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_103,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f34]) ).
tcf(c_104,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[],[f33]) ).
tcf(c_105,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f32]) ).
tcf(c_106,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[],[f31]) ).
tcf(c_107,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f30]) ).
tcf(c_108,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_109,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f27]) ).
tcf(c_111,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f26]) ).
tcf(c_121,plain,
group_element(e_4),
inference(cnf_transformation,[],[f25]) ).
tcf(c_122,plain,
group_element(e_3),
inference(cnf_transformation,[],[f24]) ).
tcf(c_123,plain,
group_element(e_2),
inference(cnf_transformation,[],[f23]) ).
tcf(c_124,plain,
group_element(e_1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_135,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_707,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_111,c_94]) ).
tcf(c_708,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_707]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_110,c_94]) ).
tcf(c_732,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_731]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_110,c_95]) ).
tcf(c_740,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_739]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_109,c_94]) ).
tcf(c_756,plain,
( ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_755]) ).
tcf(c_763,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_109,c_95]) ).
tcf(c_764,plain,
( ~ product(e_1,e_4,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_763]) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_3)
| ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1014,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_3)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1016,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_2)
| ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_1)
| ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1020,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_1)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1021,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_1)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_4)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1025,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_2)
| ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1028,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_1)
| ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1029,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_1)
| ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1031,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_4)
| ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_3)
| ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1035,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_3)
| ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1038,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_1)
| ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_3)
| ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1046,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1090,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_4,e_4)
| ~ product(e_3,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_1091,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1092,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_4,X0,X1)
| ~ product(X2,X0,e_4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1094,plain,
! [X0: $i] :
( product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1101,plain,
! [X0: $i] :
( product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1102,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1101]) ).
tcf(c_1133,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1025]) ).
tcf(c_1134,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1137,plain,
! [X0: $i] :
( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1138,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1137]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,e_3,X2)
| ~ product(e_3,X2,X0)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1143,plain,
! [X0: $i] :
( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1144,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1143]) ).
tcf(c_1176,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1179,plain,
! [X0: $i] :
( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1180,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1179]) ).
tcf(c_1222,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,e_4)
| ~ product(X1,e_4,X0)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,e_3)
| ~ product(X1,e_3,X0)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1305,plain,
( equalish(e_4,e_1)
| ~ product(e_4,e_4,e_4)
| ~ product(e_1,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_1311,plain,
( equalish(e_4,e_1)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1020]) ).
tcf(c_1313,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1014]) ).
tcf(c_1317,plain,
( equalish(e_4,e_1)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_1324,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_1328,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_1370,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1038]) ).
tcf(c_1397,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_1400,plain,
( equalish(e_3,e_1)
| ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_1432,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_1101]) ).
tcf(c_1435,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_4,e_2)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_1440,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(X0,e_4,e_2)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1023]) ).
tcf(c_1447,plain,
( equalish(e_3,e_4)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1440]) ).
tcf(c_1514,plain,
! [X0: $i] :
( equalish(e_2,e_3)
| ~ product(e_3,X0,e_4)
| ~ product(e_2,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1034]) ).
tcf(c_1519,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_1,e_4)
| ~ product(e_2,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1514]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i] :
( product(e_4,X0,X1)
| ~ product(e_3,X0,e_4)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1092]) ).
tcf(c_1590,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_1143]) ).
tcf(c_1599,plain,
! [X0: $i] :
( equalish(e_2,e_3)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1035]) ).
tcf(c_1680,plain,
! [X0: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(e_1,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1046]) ).
tcf(c_1759,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,e_3)
| product(X0,X2,e_2)
| product(X0,X2,e_1)
| product(X1,X0,X2)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(e_4,X0,X1) ),
inference(superposition,[status(thm)],[c_97,c_92]) ).
tcf(c_2123,plain,
! [X0: $i] :
( equalish(e_4,e_2)
| ~ product(e_4,X0,e_3)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1016]) ).
tcf(c_2126,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_1,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_2123]) ).
tcf(c_2160,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| ~ product(X0,e_4,e_3)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_1222]) ).
tcf(c_2379,plain,
! [X0: $i,X1: $i] :
( product(X0,e_3,X1)
| ~ product(e_3,X1,e_2)
| ~ product(e_2,e_3,X0) ),
inference(instantiation,[status(thm)],[c_1141]) ).
tcf(c_2380,plain,
( product(e_1,e_3,e_1)
| ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_2379]) ).
tcf(c_2453,plain,
! [X0: $i] :
( product(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_93,c_1759]) ).
tcf(c_2455,plain,
! [X0: $i] :
( product(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2453,c_121]) ).
tcf(c_2471,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_2455]) ).
tcf(c_2511,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_3,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1031]) ).
tcf(c_2818,plain,
( equalish(e_1,e_3)
| ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1044]) ).
tcf(c_2931,plain,
( equalish(e_2,e_3)
| ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1599]) ).
tcf(c_3459,plain,
( product(e_3,e_3,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_2160]) ).
tcf(c_3460,plain,
! [X0: $i] :
( product(e_2,X0,e_4)
| ~ product(e_3,X0,e_2)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2160]) ).
tcf(c_3461,plain,
( product(e_2,e_1,e_4)
| ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_3460]) ).
tcf(c_3541,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1680]) ).
tcf(c_3555,plain,
( product(e_4,e_3,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_3,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_2160]) ).
tcf(c_3664,plain,
! [X0: $i] :
( product(e_4,X0,e_4)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1536]) ).
tcf(c_3665,plain,
( product(e_4,e_1,e_4)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_3664]) ).
tcf(c_3745,plain,
! [X0: $i] :
( product(X0,e_4,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_4,X0) ),
inference(instantiation,[status(thm)],[c_1242]) ).
tcf(c_3746,plain,
( product(e_1,e_4,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_3745]) ).
tcf(c_3747,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3746,c_3665,c_3555,c_3541,c_3461,c_3459,c_2931,c_2818,c_2511,c_2471,c_2380,c_2126,c_1590,c_1519,c_1447,c_1435,c_1432,c_1400,c_1397,c_1370,c_1328,c_1324,c_1317,c_1311,c_1313,c_1305,c_1180,c_1176,c_1144,c_1138,c_1134,c_1133,c_1102,c_1091,c_1090,c_764,c_756,c_740,c_732,c_708,c_135,c_100,c_101,c_102,c_103,c_104,c_105,c_106,c_107,c_108,c_110,c_111,c_121,c_122,c_123,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n015.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 13:46:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running EPR theorem proving
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 0.66/1.09 % SZS status Started for theBenchmark.p
% 0.66/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 0.66/1.09
% 0.66/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.66/1.09
% 0.66/1.09 % ------ iProver source info
% 0.66/1.09
% 0.66/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.66/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.66/1.09 % git: non_committed_changes: false
% 0.66/1.09
% 0.66/1.09 % ------ Parsing...% successful
% 0.66/1.09
% 0.66/1.09
% 0.66/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.66/1.09 %
% 0.66/1.09
% 0.66/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.66/1.09
% 0.66/1.09 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.66/1.09 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.66/1.09 % ------ Proving...
% 0.66/1.09 % ------ Problem Properties
% 0.66/1.09
% 0.66/1.09 %
% 0.66/1.09 % clauses 43
% 0.66/1.09 % conjectures 1
% 0.66/1.09 % EPR 43
% 0.66/1.09 % Horn 41
% 0.66/1.09 % unary 32
% 0.66/1.09 % binary 0
% 0.66/1.09 % lits 78
% 0.66/1.09 % lits eq 0
% 0.66/1.09 % fd_pure 0
% 0.66/1.09 % fd_pseudo 0
% 0.66/1.09 % fd_cond 0
% 0.66/1.09 % fd_pseudo_cond 0
% 0.66/1.09 % AC symbols 0
% 0.66/1.09
% 0.66/1.09 % ------ Schedule EPR non Horn non eq is on
% 0.66/1.09
% 0.66/1.09 % ------ no equalities: superposition off
% 0.66/1.09
% 0.66/1.09 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 0.66/1.09
% 0.66/1.09
% 0.66/1.09 % ------
% 0.66/1.09 % Current options:
% 0.66/1.09 % ------
% 0.66/1.09
% 0.66/1.09
% 0.66/1.09 %
% 0.66/1.09
% 0.66/1.09 % ------ Proving...
% 0.66/1.09 %
% 0.66/1.09
% 0.66/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 0.66/1.09
% 0.66/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.66/1.09
% 0.66/1.09
%------------------------------------------------------------------------------