%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP129-3.004 : 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 : n012.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 01:31:28 PM UTC 2026
% Result : Unsatisfiable 3.29s 1.03s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 334 ( 33 unt; 0 def)
% Number of atoms : 1186 ( 0 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1466 ( 614 ~; 852 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 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 : 257 ( 0 sgn 257 !; 0 ?; 239 :)
% 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(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
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,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X0,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X1,X3,X2)
| ~ product(X3,X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_92,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_93,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_94,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_95,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_98,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f37]) ).
tcf(c_99,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[],[f36]) ).
tcf(c_100,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_101,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f34]) ).
tcf(c_102,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[],[f33]) ).
tcf(c_103,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f32]) ).
tcf(c_104,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[],[f31]) ).
tcf(c_105,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f30]) ).
tcf(c_106,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_107,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f28]) ).
tcf(c_108,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f27]) ).
tcf(c_109,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f26]) ).
tcf(c_119,plain,
group_element(e_4),
inference(cnf_transformation,[],[f25]) ).
tcf(c_120,plain,
group_element(e_3),
inference(cnf_transformation,[],[f24]) ).
tcf(c_121,plain,
group_element(e_2),
inference(cnf_transformation,[],[f23]) ).
tcf(c_122,plain,
group_element(e_1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_137,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_703,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_109,c_92]) ).
tcf(c_704,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_703]) ).
tcf(c_735,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_108,c_93]) ).
tcf(c_736,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_735]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_107,c_92]) ).
tcf(c_752,plain,
( ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_751]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_107,c_93]) ).
tcf(c_760,plain,
( ~ product(e_1,e_4,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_759]) ).
tcf(c_778,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[c_105,c_92]) ).
tcf(c_779,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_778]) ).
tcf(c_1009,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_92]) ).
tcf(c_1010,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_93]) ).
tcf(c_1012,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_92]) ).
tcf(c_1013,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_93]) ).
tcf(c_1014,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_94]) ).
tcf(c_1016,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_93]) ).
tcf(c_1018,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_4)
| ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1019,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_93]) ).
tcf(c_1020,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_4)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1021,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_92]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_2)
| ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1024,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_92]) ).
tcf(c_1025,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_93]) ).
tcf(c_1027,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_92]) ).
tcf(c_1028,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_93]) ).
tcf(c_1029,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_94]) ).
tcf(c_1030,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_92]) ).
tcf(c_1031,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_93]) ).
tcf(c_1034,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_93]) ).
tcf(c_1036,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_4)
| ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_4)
| ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1039,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_92]) ).
tcf(c_1040,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_93]) ).
tcf(c_1042,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_92]) ).
tcf(c_1043,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_93]) ).
tcf(c_1044,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_2)
| ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_4,X2,X1)
| ~ product(X2,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1092,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_95]) ).
tcf(c_1093,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_1092]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,e_4,X2)
| ~ product(e_4,X0,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1096,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_95]) ).
tcf(c_1097,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_1096]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X1)
| ~ product(X2,X0,e_3)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1118,plain,
! [X0: $i] :
( equalish(e_3,e_2)
| ~ product(e_3,X0,e_1)
| ~ product(e_2,X0,e_1) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_1119,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_95]) ).
tcf(c_1120,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_1119]) ).
tcf(c_1121,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,e_3,X2)
| ~ product(e_3,X0,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1123,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_95]) ).
tcf(c_1124,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_1123]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,X1)
| ~ product(X2,X0,e_2)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1146,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_95]) ).
tcf(c_1147,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_1146]) ).
tcf(c_1148,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,e_2,X2)
| ~ product(e_2,X0,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1150,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_95]) ).
tcf(c_1151,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_1150]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_4)
| ~ product(X1,X2,e_4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1185,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_3)
| ~ product(X1,X2,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1189,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_2)
| ~ product(X1,X2,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1234,plain,
! [X0: $i,X1: $i] :
( product(X1,e_4,e_2)
| ~ product(e_4,X0,X1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_1239,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,e_2)
| ~ product(e_2,X0,X1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_1148]) ).
tcf(c_1259,plain,
! [X0: $i] :
( equalish(e_4,e_1)
| ~ product(X0,e_4,e_2)
| ~ product(X0,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1016]) ).
tcf(c_1261,plain,
( equalish(e_4,e_1)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1259]) ).
tcf(c_1278,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_1)
| ~ product(e_4,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_1286,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_1092]) ).
tcf(c_1287,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_1)
| ~ product(e_4,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_1289,plain,
! [X0: $i] :
( product(e_2,X0,e_1)
| ~ product(e_4,e_2,e_1)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1143]) ).
tcf(c_1290,plain,
( equalish(e_1,e_2)
| ~ product(e_4,e_2,e_1)
| ~ product(e_4,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_1043]) ).
tcf(c_1292,plain,
( product(e_2,e_1,e_1)
| ~ product(e_4,e_2,e_1)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1289]) ).
tcf(c_1293,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_1092]) ).
tcf(c_1294,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_1)
| ~ product(e_4,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_1297,plain,
( equalish(e_2,e_3)
| ~ product(e_4,e_3,e_1)
| ~ product(e_4,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_1031]) ).
tcf(c_1302,plain,
! [X0: $i] :
( product(e_1,X0,e_2)
| ~ product(e_4,e_1,e_2)
| ~ product(X0,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_1306,plain,
( product(e_1,e_1,e_2)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1302]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i] :
( product(e_1,X0,X1)
| ~ product(e_4,e_1,X1)
| ~ product(X0,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1308,plain,
( product(e_1,e_1,e_1)
| ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1307]) ).
tcf(c_1309,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_1096]) ).
tcf(c_1311,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_1)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_1312,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1042]) ).
tcf(c_1315,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_1)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1036]) ).
tcf(c_1317,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_1096]) ).
tcf(c_1318,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_1)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1018]) ).
tcf(c_1319,plain,
! [X0: $i] :
( product(e_1,e_3,X0)
| ~ product(e_3,e_4,e_1)
| ~ product(e_4,e_1,X0) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_1322,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_4,e_1)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1030]) ).
tcf(c_1323,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_4,e_1)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1024]) ).
tcf(c_1325,plain,
( product(e_1,e_3,e_1)
| ~ product(e_4,e_1,e_1)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1319]) ).
tcf(c_1330,plain,
( equalish(e_1,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(e_3,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_1332,plain,
! [X0: $i] :
( product(e_4,e_3,e_2)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_1337,plain,
( product(e_4,e_3,e_2)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1332]) ).
tcf(c_1340,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_1119]) ).
tcf(c_1348,plain,
! [X0: $i,X1: $i] :
( product(e_4,e_3,X1)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_1352,plain,
! [X0: $i] :
( equalish(e_3,e_1)
| ~ product(e_3,X0,e_4)
| ~ product(e_1,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1024]) ).
tcf(c_1355,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1352]) ).
tcf(c_1361,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_1119]) ).
tcf(c_1363,plain,
( equalish(e_4,e_3)
| ~ product(e_3,e_4,e_4)
| ~ product(e_3,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_1369,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(e_3,X0,e_4)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_1029]) ).
tcf(c_1381,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| ~ product(e_3,X1,e_4)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_1181]) ).
tcf(c_1626,plain,
! [X0: $i] :
( product(e_4,X0,e_2)
| ~ product(e_3,e_4,e_2)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_1628,plain,
! [X0: $i] :
( product(e_3,e_4,e_4)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_1629,plain,
( product(e_3,e_4,e_4)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1628]) ).
tcf(c_1631,plain,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_4,e_2)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1626]) ).
tcf(c_1633,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_1123]) ).
tcf(c_1643,plain,
! [X0: $i] :
( equalish(e_4,e_3)
| ~ product(X0,e_4,e_4)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_1666,plain,
! [X0: $i,X1: $i] :
( product(e_4,X0,X1)
| ~ product(e_3,e_4,X1)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1089]) ).
tcf(c_1667,plain,
( product(e_4,e_1,e_1)
| ~ product(e_3,e_4,e_1)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1666]) ).
tcf(c_1686,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_95,c_91]) ).
tcf(c_1751,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_95,c_91]) ).
tcf(c_1799,plain,
! [X0: $i] :
( product(e_4,e_2,e_2)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_1805,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(e_4,X0,e_4)
| ~ product(e_2,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_1809,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_1146]) ).
tcf(c_1812,plain,
! [X0: $i] :
( product(e_2,X0,e_4)
| ~ product(e_2,e_2,e_4)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1143]) ).
tcf(c_1819,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(e_2,X0,e_4)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1020]) ).
tcf(c_1823,plain,
! [X0: $i,X1: $i] :
( product(e_4,e_2,X1)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_1089]) ).
tcf(c_1824,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| ~ product(e_2,X1,e_4)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_1181]) ).
tcf(c_1899,plain,
! [X0: $i] :
( product(e_4,X0,e_2)
| ~ product(e_2,e_4,e_2)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_1901,plain,
! [X0: $i] :
( product(e_2,e_4,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_1902,plain,
( product(e_2,e_4,e_4)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1901]) ).
tcf(c_1912,plain,
! [X0: $i,X1: $i] :
( product(e_2,X0,e_4)
| ~ product(X1,e_2,e_4)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_1143]) ).
tcf(c_1932,plain,
! [X0: $i,X1: $i] :
( product(e_4,X0,X1)
| ~ product(e_2,e_4,X1)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1089]) ).
tcf(c_1933,plain,
( product(e_4,e_1,e_1)
| ~ product(e_2,e_4,e_1)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1932]) ).
tcf(c_2015,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_2)
| ~ product(X1,e_3,e_2)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_2016,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,e_3)
| ~ product(e_2,X0,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1148]) ).
tcf(c_2017,plain,
! [X0: $i,X1: $i] :
( product(X1,e_4,e_3)
| ~ product(e_4,X0,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_2018,plain,
( product(e_1,e_4,e_3)
| ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_2017]) ).
tcf(c_2059,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_3)
| ~ product(X1,e_3,e_3)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2062,plain,
( product(e_4,e_3,e_3)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2063,plain,
! [X0: $i] :
( product(e_4,X0,e_3)
| ~ product(e_2,e_4,e_3)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2067,plain,
! [X0: $i] :
( product(e_1,X0,e_3)
| ~ product(e_4,e_1,e_3)
| ~ product(X0,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2068,plain,
( product(e_1,e_1,e_3)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_2067]) ).
tcf(c_2069,plain,
! [X0: $i] :
( product(e_4,e_3,e_3)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2070,plain,
! [X0: $i] :
( product(e_4,e_2,e_3)
| ~ product(e_2,X0,e_4)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2105,plain,
! [X0: $i] :
( product(e_2,e_4,e_3)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2276,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(e_4)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_95,c_1686]) ).
tcf(c_2277,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2276,c_119]) ).
tcf(c_2302,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(e_4)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_95,c_1751]) ).
tcf(c_2303,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2302,c_119]) ).
tcf(c_2315,plain,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_4,e_2)
| ~ product(e_1,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_2325,plain,
( equalish(e_4,e_2)
| ~ product(e_1,e_4,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1014]) ).
tcf(c_2327,plain,
! [X0: $i] :
( product(e_4,e_1,X0)
| ~ product(e_1,e_4,e_4)
| ~ product(e_4,e_4,X0) ),
inference(instantiation,[status(thm)],[c_1089]) ).
tcf(c_2328,plain,
( product(e_4,e_1,e_1)
| ~ product(e_4,e_4,e_1)
| ~ product(e_1,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_2327]) ).
tcf(c_2360,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_4,X2,e_4)
| product(e_4,X0,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| product(X2,X1,e_3)
| product(X2,X1,e_2)
| product(X2,X1,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,e_4) ),
inference(superposition,[status(thm)],[c_2277,c_91]) ).
tcf(c_2364,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_4)
| product(e_3,X1,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_2277,c_1686]) ).
tcf(c_2368,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| ~ group_element(e_4) ),
inference(equality_factoring,[status(thm)],[c_2277]) ).
tcf(c_2370,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2368,c_119]) ).
tcf(c_2538,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_4)
| product(e_3,X1,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2364,c_120]) ).
tcf(c_2619,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_4,X2,e_4)
| product(e_4,X0,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| product(X2,X1,e_3)
| product(X2,X1,e_2)
| product(X2,X1,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,e_4) ),
inference(superposition,[status(thm)],[c_2303,c_91]) ).
tcf(c_2838,plain,
( product(e_1,e_4,e_3)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2856,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_3)
| ~ product(e_3,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1018]) ).
tcf(c_2858,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_4,e_3)
| ~ product(e_3,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1009]) ).
tcf(c_2859,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1039]) ).
tcf(c_2861,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_4,e_3)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1024]) ).
tcf(c_2862,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_4,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_2876,plain,
! [X0: $i] :
( product(e_3,e_3,X0)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,X0) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_2880,plain,
( equalish(e_3,e_1)
| ~ product(e_3,e_2,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1024]) ).
tcf(c_2882,plain,
( product(e_3,e_3,e_1)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_2876]) ).
tcf(c_2890,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_2893,plain,
( equalish(e_2,e_4)
| ~ product(e_2,e_4,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_2932,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_2936,plain,
( equalish(e_2,e_1)
| ~ product(e_4,e_2,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1034]) ).
tcf(c_2964,plain,
( product(e_2,e_4,e_4)
| ~ product(e_4,e_2,e_2)
| ~ product(e_2,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1812]) ).
tcf(c_2975,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_3)
| ~ product(e_4,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_2976,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_3)
| ~ product(e_4,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_2977,plain,
! [X0: $i] :
( product(e_2,X0,e_3)
| ~ product(e_4,e_2,e_3)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1143]) ).
tcf(c_2978,plain,
( equalish(e_1,e_2)
| ~ product(e_4,e_2,e_3)
| ~ product(e_4,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_1043]) ).
tcf(c_2980,plain,
( product(e_2,e_1,e_3)
| ~ product(e_4,e_2,e_3)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_2977]) ).
tcf(c_2984,plain,
! [X0: $i] :
( equalish(e_1,e_4)
| ~ product(e_3,e_4,X0)
| ~ product(e_3,e_1,X0) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_2987,plain,
( equalish(e_1,e_4)
| ~ product(e_3,e_4,e_1)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2984]) ).
tcf(c_2988,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_3)
| ~ product(e_3,X0,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_2989,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_2)
| ~ product(e_3,X0,X1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_3000,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(e_3,e_4,X0)
| ~ product(e_3,e_2,X0) ),
inference(instantiation,[status(thm)],[c_1028]) ).
tcf(c_3012,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_1)
| ~ product(X1,e_3,e_1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_3030,plain,
( product(e_1,e_3,e_4)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_3035,plain,
! [X0: $i,X1: $i] :
( product(X0,e_3,X1)
| ~ product(e_3,e_3,X0)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_3075,plain,
( product(e_4,e_2,e_3)
| ~ product(e_4,e_4,e_3)
| ~ product(e_2,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_2070]) ).
tcf(c_3076,plain,
( product(e_4,e_4,e_3)
| ~ product(e_4,e_2,e_4)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2063]) ).
tcf(c_3078,plain,
! [X0: $i] :
( product(e_3,e_4,e_3)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_3079,plain,
( product(e_3,e_4,e_3)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_3078]) ).
tcf(c_3080,plain,
( product(e_2,e_4,e_3)
| ~ product(e_4,e_2,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2105]) ).
tcf(c_3087,plain,
! [X0: $i] :
( equalish(e_4,e_3)
| ~ product(e_4,X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1009]) ).
tcf(c_3088,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_1,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_3087]) ).
tcf(c_3095,plain,
! [X0: $i,X1: $i] :
( product(e_3,e_4,X1)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_3097,plain,
( product(e_3,e_4,e_1)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_3095]) ).
tcf(c_3405,plain,
( product(e_4,e_4,e_2)
| ~ product(e_4,e_3,e_4)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1234]) ).
tcf(c_3493,plain,
( product(e_2,e_2,e_2)
| ~ product(e_4,e_2,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1239]) ).
tcf(c_3495,plain,
! [X0: $i] :
( product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2538,c_120,c_119,c_98,c_1096,c_1123,c_1643]) ).
tcf(c_3517,plain,
! [X0: $i,X1: $i] :
( product(e_4,X0,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1)
| ~ product(X0,X1,e_4) ),
inference(superposition,[status(thm)],[c_3495,c_91]) ).
tcf(c_3644,plain,
( equalish(e_3,e_4)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_3663,plain,
( product(e_3,e_2,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2016]) ).
tcf(c_3664,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_3665,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_3666,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1042]) ).
tcf(c_3670,plain,
( equalish(e_4,e_3)
| ~ product(e_2,e_4,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_3694,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_4,X2,e_4)
| product(e_4,X1,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X2,X0,e_3)
| product(X2,X0,e_2)
| product(X2,X0,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_95,c_2619]) ).
tcf(c_3732,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_2)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1036]) ).
tcf(c_3735,plain,
( product(e_4,e_4,e_2)
| ~ product(e_4,e_1,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1234]) ).
tcf(c_3737,plain,
( equalish(e_1,e_2)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1044]) ).
tcf(c_3743,plain,
( equalish(e_4,e_3)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1010]) ).
tcf(c_3913,plain,
( product(e_3,e_4,e_1)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_3940,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_95,c_3517]) ).
tcf(c_4015,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| 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) ),
inference(equality_factoring,[status(thm)],[c_3940]) ).
tcf(c_4017,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4015,c_119]) ).
tcf(c_4376,plain,
( product(e_1,e_1,e_3)
| ~ product(e_3,e_1,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1185]) ).
tcf(c_4377,plain,
( product(e_1,e_1,e_2)
| ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1189]) ).
tcf(c_4426,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1118]) ).
tcf(c_4436,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_1024]) ).
tcf(c_4474,plain,
( equalish(e_2,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1369]) ).
tcf(c_4596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(e_4,X3,e_4)
| product(e_4,X2,e_3)
| product(e_4,X0,e_2)
| product(X1,e_4,e_1)
| product(X3,X1,e_3)
| product(X3,X1,e_2)
| product(X3,X1,e_1)
| product(X2,X1,e_3)
| product(X2,X1,e_2)
| product(X2,X1,e_1)
| ~ group_element(X3)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,e_4) ),
inference(superposition,[status(thm)],[c_3694,c_91]) ).
tcf(c_5393,plain,
( equalish(e_3,e_4)
| ~ product(e_2,e_4,e_4)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1819]) ).
tcf(c_5443,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_1039]) ).
tcf(c_5470,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_3)
| ~ product(e_4,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_5495,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_1019]) ).
tcf(c_5548,plain,
! [X0: $i] :
( equalish(e_1,e_4)
| ~ product(e_4,X0,e_3)
| ~ product(e_1,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1036]) ).
tcf(c_5551,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_5548]) ).
tcf(c_5577,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_1042]) ).
tcf(c_5630,plain,
( product(e_1,e_2,e_2)
| ~ product(e_4,e_1,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1239]) ).
tcf(c_5639,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_1009]) ).
tcf(c_5704,plain,
! [X0: $i] :
( product(e_2,e_4,X0)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_2,X0) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_5705,plain,
( product(e_2,e_4,e_1)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_5704]) ).
tcf(c_5723,plain,
! [X0: $i] :
( product(e_4,e_4,X0)
| ~ product(e_4,e_2,e_4)
| ~ product(e_2,e_4,X0) ),
inference(instantiation,[status(thm)],[c_1094]) ).
tcf(c_5727,plain,
( product(e_4,e_4,e_1)
| ~ product(e_4,e_2,e_4)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_5723]) ).
tcf(c_5750,plain,
! [X0: $i] :
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_4,X0,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(superposition,[status(thm)],[c_2370,c_2360]) ).
tcf(c_5754,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| ~ product(e_4,X0,e_4) ),
inference(superposition,[status(thm)],[c_2370,c_93]) ).
tcf(c_5755,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| ~ product(X0,e_4,e_4) ),
inference(superposition,[status(thm)],[c_2370,c_92]) ).
tcf(c_5778,plain,
! [X0: $i] :
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_4,X0,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5750,c_119]) ).
tcf(c_5787,plain,
( equalish(e_4,e_1)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| ~ product(e_1,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_5755]) ).
tcf(c_5788,plain,
( equalish(e_4,e_1)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| ~ product(e_4,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_5754]) ).
tcf(c_5792,plain,
( product(e_4,e_2,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(e_2,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1823]) ).
tcf(c_5807,plain,
! [X0: $i] :
( product(e_4,e_3,X0)
| ~ product(e_3,e_4,e_4)
| ~ product(e_4,e_4,X0) ),
inference(instantiation,[status(thm)],[c_1348]) ).
tcf(c_5809,plain,
( product(e_4,e_3,e_3)
| ~ product(e_4,e_4,e_3)
| ~ product(e_3,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_2069]) ).
tcf(c_5810,plain,
( product(e_4,e_3,e_2)
| ~ product(e_4,e_4,e_2)
| ~ product(e_3,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1332]) ).
tcf(c_5811,plain,
( product(e_4,e_3,e_1)
| ~ product(e_4,e_4,e_1)
| ~ product(e_3,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_5807]) ).
tcf(c_5813,plain,
! [X0: $i] :
( product(e_4,X0,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1381]) ).
tcf(c_5814,plain,
( product(e_4,e_1,e_4)
| ~ product(e_3,e_4,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_5813]) ).
tcf(c_5861,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_2,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_5868,plain,
( equalish(e_4,e_2)
| ~ product(e_2,e_4,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_6025,plain,
( equalish(e_4,e_2)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_6502,plain,
! [X0: $i,X1: $i] :
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| product(X1,X0,e_4)
| ~ group_element(X1)
| ~ product(X0,e_4,X1) ),
inference(superposition,[status(thm)],[c_5778,c_91]) ).
tcf(c_6808,plain,
( product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_4)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1899]) ).
tcf(c_6894,plain,
( equalish(e_3,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_1025]) ).
tcf(c_6939,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1036]) ).
tcf(c_6988,plain,
( equalish(e_1,e_3)
| ~ product(e_2,e_3,e_1)
| ~ product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_1040]) ).
tcf(c_7070,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_2)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1018]) ).
tcf(c_7071,plain,
( product(e_2,e_4,e_3)
| ~ product(e_4,e_4,e_2)
| ~ product(e_4,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2017]) ).
tcf(c_7074,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_7081,plain,
( product(e_4,e_2,e_2)
| ~ product(e_4,e_4,e_2)
| ~ product(e_2,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1799]) ).
tcf(c_7135,plain,
( product(e_2,e_4,e_4)
| ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1912]) ).
tcf(c_7140,plain,
( equalish(e_1,e_3)
| ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1040]) ).
tcf(c_7141,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_1025]) ).
tcf(c_7148,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1009]) ).
tcf(c_7158,plain,
! [X0: $i] :
( product(e_3,X0,e_2)
| ~ product(e_4,e_3,e_2)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2015]) ).
tcf(c_7159,plain,
( product(e_3,e_1,e_2)
| ~ product(e_4,e_3,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_7158]) ).
tcf(c_7160,plain,
! [X0: $i] :
( product(e_2,e_2,X0)
| ~ product(e_2,e_4,e_2)
| ~ product(e_4,e_2,X0) ),
inference(instantiation,[status(thm)],[c_1148]) ).
tcf(c_7162,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_4,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1021]) ).
tcf(c_7163,plain,
( product(e_2,e_2,e_3)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_2016]) ).
tcf(c_7165,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_7166,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_4,e_2)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1042]) ).
tcf(c_7168,plain,
( product(e_2,e_2,e_1)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_7160]) ).
tcf(c_7222,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_2,X0) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_7223,plain,
( product(e_2,e_3,e_1)
| ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_7222]) ).
tcf(c_7227,plain,
( equalish(e_1,e_4)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_2984]) ).
tcf(c_7304,plain,
! [X0: $i] :
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| product(e_4,X0,e_4)
| product(e_3,X0,e_4)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_5778,c_6502]) ).
tcf(c_7311,plain,
! [X0: $i] :
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| product(e_4,X0,e_4)
| product(e_3,X0,e_4)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7304,c_120]) ).
tcf(c_7402,plain,
( product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_4,e_1,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| product(e_3,e_1,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_7311]) ).
tcf(c_7713,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2) ),
inference(global_subsumption_just,[status(thm)],[c_4017,c_121,c_120,c_119,c_105,c_104,c_101,c_99,c_1286,c_1293,c_1309,c_1317,c_1322,c_2856,c_2890,c_2975,c_3075,c_3405,c_3493,c_3664,c_4017,c_5809,c_5868,c_6808,c_7168]) ).
tcf(c_7714,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(renaming,[status(thm)],[c_7713]) ).
tcf(c_7729,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(e_4,e_4,e_1)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ product(e_4,X0,e_2) ),
inference(superposition,[status(thm)],[c_7714,c_93]) ).
tcf(c_7822,plain,
( equalish(e_4,e_1)
| product(e_4,e_4,e_1)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_7729]) ).
tcf(c_7976,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_2)
| ~ product(e_4,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_5495]) ).
tcf(c_7987,plain,
( product(e_4,e_2,e_1)
| ~ product(e_4,e_4,e_1)
| ~ product(e_2,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1823]) ).
tcf(c_8033,plain,
( equalish(e_3,e_2)
| ~ product(e_4,e_3,e_3)
| ~ product(e_4,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1022]) ).
tcf(c_8041,plain,
( product(e_2,e_3,e_3)
| ~ product(e_4,e_2,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_2988]) ).
tcf(c_8044,plain,
( product(e_3,e_4,e_3)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_2059]) ).
tcf(c_8424,plain,
( product(e_1,e_4,e_2)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1234]) ).
tcf(c_8867,plain,
( product(e_3,e_3,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2988]) ).
tcf(c_8883,plain,
( product(e_3,e_4,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_3078]) ).
tcf(c_8927,plain,
( equalish(e_3,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_8934,plain,
( equalish(e_1,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_2984]) ).
tcf(c_9015,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_2,X0) ),
inference(instantiation,[status(thm)],[c_1121]) ).
tcf(c_9016,plain,
( product(e_2,e_3,e_1)
| ~ product(e_4,e_2,e_1)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_9015]) ).
tcf(c_9032,plain,
( equalish(e_2,e_4)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_3000]) ).
tcf(c_9100,plain,
( product(e_4,e_3,e_2)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_3035]) ).
tcf(c_9130,plain,
( product(e_1,e_3,e_2)
| ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_2989]) ).
tcf(c_9241,plain,
( product(e_3,e_4,e_2)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2015]) ).
tcf(c_9372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(e_4,X3,e_4)
| product(e_4,X2,e_3)
| product(e_4,X1,e_2)
| product(X0,e_4,e_1)
| product(X3,X0,e_3)
| product(X3,X0,e_2)
| product(X3,X0,e_1)
| product(X2,X0,e_3)
| product(X2,X0,e_2)
| product(X2,X0,e_1)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X3)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_95,c_4596]) ).
tcf(c_9452,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_1,e_4,e_1)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_9372]) ).
tcf(c_9691,plain,
( equalish(e_2,e_3)
| ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1031]) ).
tcf(c_9693,plain,
( product(e_3,e_1,e_4)
| ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1824]) ).
tcf(c_9699,plain,
( product(e_3,e_1,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2015]) ).
tcf(c_9702,plain,
( product(e_3,e_1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_3012]) ).
tcf(c_10416,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_2,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1805]) ).
tcf(c_10532,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_10857,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10532,c_10416,c_9699,c_9702,c_9691,c_9693,c_9452,c_9241,c_9130,c_9100,c_9032,c_9016,c_8934,c_8927,c_8883,c_8867,c_8424,c_8041,c_8044,c_8033,c_7987,c_7976,c_7822,c_7402,c_7227,c_7223,c_7168,c_7162,c_7163,c_7165,c_7166,c_7159,c_7148,c_7140,c_7141,c_7135,c_7081,c_7074,c_7070,c_7071,c_6988,c_6939,c_6894,c_6808,c_6025,c_5868,c_5861,c_5814,c_5811,c_5809,c_5810,c_5792,c_5788,c_5787,c_5727,c_5705,c_5639,c_5630,c_5577,c_5551,c_5470,c_5443,c_5393,c_4474,c_4436,c_4426,c_4376,c_4377,c_4017,c_3913,c_3743,c_3735,c_3737,c_3732,c_3670,c_3663,c_3665,c_3666,c_3644,c_3493,c_3405,c_3097,c_3088,c_3080,c_3079,c_3076,c_3075,c_3030,c_2987,c_2976,c_2980,c_2978,c_2964,c_2932,c_2936,c_2893,c_2890,c_2882,c_2880,c_2858,c_2859,c_2861,c_2862,c_2838,c_2370,c_2328,c_2325,c_2315,c_2068,c_2062,c_2018,c_1933,c_1902,c_1809,c_1667,c_1633,c_1631,c_1629,c_1363,c_1361,c_1355,c_1340,c_1337,c_1330,c_1318,c_1325,c_1322,c_1323,c_1317,c_1315,c_1311,c_1312,c_1309,c_1308,c_1306,c_1294,c_1297,c_1293,c_1287,c_1292,c_1290,c_1286,c_1278,c_1261,c_1151,c_1147,c_1124,c_1120,c_1097,c_1093,c_779,c_760,c_752,c_736,c_704,c_137,c_98,c_99,c_100,c_101,c_102,c_103,c_104,c_105,c_106,c_107,c_108,c_109,c_119,c_120,c_121,c_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP129-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Wed Sep 23 13:45:06 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running EPR theorem proving
% 0.03/0.32 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
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.32 % Detected problem language: tptp
% 0.03/0.33 % Proving...
% 3.29/1.03 % SZS status Started for theBenchmark.p
% 3.29/1.03 % SZS status Unsatisfiable for theBenchmark.p
% 3.29/1.03
% 3.29/1.03 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.29/1.03
% 3.29/1.03 % ------ iProver source info
% 3.29/1.03
% 3.29/1.03 % git: date: 2026-07-19 20:42:38 +0200
% 3.29/1.03 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.29/1.03 % git: non_committed_changes: false
% 3.29/1.03
% 3.29/1.03 % ------ Parsing...% successful
% 3.29/1.03
% 3.29/1.03
% 3.29/1.03 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 3.29/1.03 %
% 3.29/1.03
% 3.29/1.03 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.29/1.03
% 3.29/1.03 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 3.29/1.03 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.29/1.03 % ------ Proving...
% 3.29/1.03 % ------ Problem Properties
% 3.29/1.03
% 3.29/1.03 %
% 3.29/1.03 % clauses 42
% 3.29/1.03 % conjectures 1
% 3.29/1.03 % EPR 42
% 3.29/1.03 % Horn 40
% 3.29/1.03 % unary 31
% 3.29/1.03 % binary 0
% 3.29/1.03 % lits 77
% 3.29/1.03 % lits eq 0
% 3.29/1.03 % fd_pure 0
% 3.29/1.03 % fd_pseudo 0
% 3.29/1.03 % fd_cond 0
% 3.29/1.03 % fd_pseudo_cond 0
% 3.29/1.03 % AC symbols 0
% 3.29/1.03
% 3.29/1.03 % ------ Schedule EPR non Horn non eq is on
% 3.29/1.03
% 3.29/1.03 % ------ no equalities: superposition off
% 3.29/1.03
% 3.29/1.03 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 3.29/1.03
% 3.29/1.03
% 3.29/1.03 % ------
% 3.29/1.03 % Current options:
% 3.29/1.03 % ------
% 3.29/1.03
% 3.29/1.03
% 3.29/1.03 %
% 3.29/1.03
% 3.29/1.03 % ------ Proving...
% 3.29/1.03 %
% 3.29/1.03
% 3.29/1.03 % SZS status Unsatisfiable for theBenchmark.p
% 3.29/1.03
% 3.29/1.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.29/1.03
% 3.29/1.03
%------------------------------------------------------------------------------