%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 01:31:13 PM UTC 2026
% Result : Unsatisfiable 2.63s 1.24s
% Output : CNFRefutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 128 ( 37 unt; 0 def)
% Number of atoms : 342 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 418 ( 204 ~; 214 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 119 ( 0 sgn 119 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f29,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f32,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f33,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f35,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f36,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f37,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f42,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f43,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
tcf(c_92,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X0)
| ~ product(X1,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_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_715,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_111,c_95]) ).
tcf(c_716,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_715]) ).
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_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_1017,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_2)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_2)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_96]) ).
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_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_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_1032,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_4)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1033,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_4)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_96]) ).
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_1037,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_1)
| ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
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_1042,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_4)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1043,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_3)
| ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1047,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_2)
| ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_95]) ).
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,X2,X0)
| ~ product(X1,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_1095,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_1099,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_4,X1)
| ~ product(X1,X0,e_4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
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_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_1175,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_1176,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,X0)
| ~ product(X1,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
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_1183,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_2,X1)
| ~ product(X1,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1185,plain,
! [X0: $i] :
( product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1186,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_1302,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_1308,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_1315,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1018]) ).
tcf(c_1325,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_1365,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_1381,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_1183]) ).
tcf(c_1382,plain,
! [X0: $i,X1: $i] :
( product(e_2,X1,X0)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_1177]) ).
tcf(c_1402,plain,
! [X0: $i] :
( equalish(e_4,e_3)
| ~ product(e_4,X0,e_2)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_1403,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1402]) ).
tcf(c_1415,plain,
! [X0: $i,X1: $i] :
( product(e_2,X1,e_4)
| ~ product(X0,e_4,e_2)
| ~ product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_1177]) ).
tcf(c_1426,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_4,e_2)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1043]) ).
tcf(c_1499,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,X0)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_1092]) ).
tcf(c_1503,plain,
( equalish(e_1,e_2)
| ~ product(e_3,e_2,e_4)
| ~ product(e_3,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1047]) ).
tcf(c_1580,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_1589,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_1647,plain,
! [X0: $i,X1: $i] :
( product(X1,e_4,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_1099]) ).
tcf(c_1658,plain,
! [X0: $i] :
( equalish(e_1,e_4)
| ~ product(e_2,X0,e_4)
| ~ product(e_2,X0,e_1) ),
inference(instantiation,[status(thm)],[c_1042]) ).
tcf(c_1659,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(e_2,X0,e_4)
| ~ product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_1033]) ).
tcf(c_1985,plain,
! [X0: $i] :
( product(e_2,e_2,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1381]) ).
tcf(c_1986,plain,
( product(e_2,e_2,e_4)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1985]) ).
tcf(c_2041,plain,
! [X0: $i] :
( product(e_3,e_4,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1647]) ).
tcf(c_2042,plain,
( product(e_3,e_4,e_2)
| ~ product(e_2,e_1,e_4)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2041]) ).
tcf(c_2415,plain,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1415]) ).
tcf(c_2417,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_1,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_1031]) ).
tcf(c_2753,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1382]) ).
tcf(c_2754,plain,
! [X0: $i] :
( product(e_3,e_2,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1381]) ).
tcf(c_2756,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(X0,e_4,e_3)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1032]) ).
tcf(c_2759,plain,
! [X0: $i] :
( equalish(e_4,e_2)
| ~ product(X0,e_4,e_3)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1017]) ).
tcf(c_2762,plain,
( equalish(e_4,e_2)
| ~ product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2759]) ).
tcf(c_2765,plain,
( equalish(e_2,e_4)
| ~ product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2756]) ).
tcf(c_2767,plain,
( product(e_3,e_2,e_4)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2754]) ).
tcf(c_2768,plain,
( product(e_2,e_3,e_1)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2753]) ).
tcf(c_2844,plain,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_2,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1499]) ).
tcf(c_3246,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_1589]) ).
tcf(c_3260,plain,
( equalish(e_1,e_4)
| ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_3286,plain,
( equalish(e_2,e_4)
| ~ product(e_2,e_2,e_4)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1659]) ).
tcf(c_3310,plain,
! [X0: $i] :
( product(e_4,e_4,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1647]) ).
tcf(c_3315,plain,
( product(e_4,e_4,e_2)
| ~ product(e_2,e_1,e_4)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_3310]) ).
tcf(c_3385,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3315,c_3286,c_3260,c_3246,c_2844,c_2768,c_2767,c_2765,c_2762,c_2415,c_2417,c_2042,c_1986,c_1580,c_1503,c_1426,c_1403,c_1365,c_1325,c_1315,c_1308,c_1302,c_1186,c_1180,c_1176,c_1175,c_1138,c_1134,c_1133,c_1102,c_1095,c_1091,c_764,c_756,c_732,c_716,c_708,c_135,c_100,c_101,c_102,c_104,c_105,c_106,c_107,c_108,c_109,c_110,c_111,c_121,c_122,c_123,c_124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 13:42:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running EPR theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 2.63/1.24 % SZS status Started for theBenchmark.p
% 2.63/1.24 % SZS status Unsatisfiable for theBenchmark.p
% 2.63/1.24
% 2.63/1.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.63/1.24
% 2.63/1.24 % ------ iProver source info
% 2.63/1.24
% 2.63/1.24 % git: date: 2026-07-19 20:42:38 +0200
% 2.63/1.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.63/1.24 % git: non_committed_changes: false
% 2.63/1.24
% 2.63/1.24 % ------ Parsing...% successful
% 2.63/1.24
% 2.63/1.24
% 2.63/1.24 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.63/1.24 %
% 2.63/1.24
% 2.63/1.24 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.63/1.24
% 2.63/1.24 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.63/1.24 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.63/1.24 % ------ Proving...
% 2.63/1.24 % ------ Problem Properties
% 2.63/1.24
% 2.63/1.24 %
% 2.63/1.24 % clauses 43
% 2.63/1.24 % conjectures 1
% 2.63/1.24 % EPR 43
% 2.63/1.24 % Horn 41
% 2.63/1.24 % unary 32
% 2.63/1.24 % binary 0
% 2.63/1.24 % lits 78
% 2.63/1.24 % lits eq 0
% 2.63/1.24 % fd_pure 0
% 2.63/1.24 % fd_pseudo 0
% 2.63/1.24 % fd_cond 0
% 2.63/1.24 % fd_pseudo_cond 0
% 2.63/1.24 % AC symbols 0
% 2.63/1.24
% 2.63/1.24 % ------ Schedule EPR non Horn non eq is on
% 2.63/1.24
% 2.63/1.24 % ------ no equalities: superposition off
% 2.63/1.24
% 2.63/1.24 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.63/1.24
% 2.63/1.24
% 2.63/1.24 % ------
% 2.63/1.24 % Current options:
% 2.63/1.24 % ------
% 2.63/1.24
% 2.63/1.24
% 2.63/1.24 %
% 2.63/1.24
% 2.63/1.24 % ------ Proving...
% 2.63/1.24 %
% 2.63/1.24
% 2.63/1.24 % SZS status Unsatisfiable for theBenchmark.p
% 2.63/1.24
% 2.63/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.63/1.25
% 2.63/1.25
%------------------------------------------------------------------------------