%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP125-2.005 : 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 : n026.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 01:31:11 PM UTC 2026
% Result : Unsatisfiable 4.10s 1.22s
% Output : CNFRefutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 39
% Syntax : Number of formulae : 271 ( 79 unt; 0 def)
% Number of atoms : 745 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 849 ( 375 ~; 474 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 184 ( 0 sgn 184 !; 0 ?; 162 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f2,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
fof(f3,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).
fof(f10,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_2) ).
fof(f12,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).
fof(f13,axiom,
greater(e_5,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_3) ).
fof(f14,axiom,
greater(e_5,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_4) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
fof(f16,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f17,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f18,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f19,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f20,axiom,
group_element(e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_5) ).
fof(f21,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f22,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f23,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f24,axiom,
~ equalish(e_1,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_5) ).
fof(f25,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f26,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f27,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f28,axiom,
~ equalish(e_2,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_5) ).
fof(f29,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f30,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f31,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f32,axiom,
~ equalish(e_3,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_5) ).
fof(f33,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f34,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f35,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f36,axiom,
~ equalish(e_4,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_5) ).
fof(f37,axiom,
~ equalish(e_5,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_is_not_e_1) ).
fof(f38,axiom,
~ equalish(e_5,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_is_not_e_2) ).
fof(f39,axiom,
~ equalish(e_5,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_is_not_e_3) ).
fof(f40,axiom,
~ equalish(e_5,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_is_not_e_4) ).
fof(f41,axiom,
! [X0,X1] :
( product(X0,X1,e_5)
| 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(f42,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(f43,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(f44,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(f45,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f46,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
tcf(c_95,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_96,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_5)
| 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,[],[f41]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_102,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f35]) ).
tcf(c_103,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[],[f34]) ).
tcf(c_104,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[],[f33]) ).
tcf(c_105,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f31]) ).
tcf(c_106,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[],[f30]) ).
tcf(c_107,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_108,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[],[f27]) ).
tcf(c_109,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f26]) ).
tcf(c_110,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_111,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f23]) ).
tcf(c_112,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f22]) ).
tcf(c_113,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f21]) ).
tcf(c_114,plain,
~ equalish(e_5,e_1),
inference(cnf_transformation,[],[f37]) ).
tcf(c_115,plain,
~ equalish(e_1,e_5),
inference(cnf_transformation,[],[f24]) ).
tcf(c_120,plain,
~ equalish(e_5,e_2),
inference(cnf_transformation,[],[f38]) ).
tcf(c_121,plain,
~ equalish(e_2,e_5),
inference(cnf_transformation,[],[f28]) ).
tcf(c_123,plain,
greater(e_4,e_2),
inference(cnf_transformation,[],[f10]) ).
tcf(c_125,plain,
~ equalish(e_5,e_3),
inference(cnf_transformation,[],[f39]) ).
tcf(c_126,plain,
~ equalish(e_3,e_5),
inference(cnf_transformation,[],[f32]) ).
tcf(c_127,plain,
greater(e_5,e_3),
inference(cnf_transformation,[],[f13]) ).
tcf(c_128,plain,
greater(e_4,e_3),
inference(cnf_transformation,[],[f12]) ).
tcf(c_129,plain,
~ equalish(e_5,e_4),
inference(cnf_transformation,[],[f40]) ).
tcf(c_130,plain,
~ equalish(e_4,e_5),
inference(cnf_transformation,[],[f36]) ).
tcf(c_131,plain,
greater(e_5,e_4),
inference(cnf_transformation,[],[f14]) ).
tcf(c_132,plain,
group_element(e_5),
inference(cnf_transformation,[],[f20]) ).
tcf(c_133,plain,
group_element(e_4),
inference(cnf_transformation,[],[f19]) ).
tcf(c_134,plain,
group_element(e_3),
inference(cnf_transformation,[],[f18]) ).
tcf(c_135,plain,
group_element(e_2),
inference(cnf_transformation,[],[f17]) ).
tcf(c_136,plain,
group_element(e_1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_138,plain,
next(e_3,e_4),
inference(cnf_transformation,[],[f3]) ).
tcf(c_139,plain,
next(e_2,e_3),
inference(cnf_transformation,[],[f2]) ).
tcf(c_140,plain,
next(e_1,e_2),
inference(cnf_transformation,[],[f1]) ).
tcf(c_141,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_268,plain,
! [X0: $i] :
( ~ greater(X0,e_2)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[c_140,c_101]) ).
tcf(c_276,plain,
! [X0: $i] :
( ~ greater(X0,e_3)
| ~ product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[c_139,c_101]) ).
tcf(c_284,plain,
! [X0: $i] :
( ~ greater(X0,e_4)
| ~ product(e_3,e_1,X0) ),
inference(resolution,[status(thm)],[c_138,c_101]) ).
tcf(c_312,plain,
~ product(e_1,e_1,e_4),
inference(resolution,[status(thm)],[c_123,c_268]) ).
tcf(c_320,plain,
~ product(e_2,e_1,e_4),
inference(resolution,[status(thm)],[c_128,c_276]) ).
tcf(c_324,plain,
~ product(e_2,e_1,e_5),
inference(resolution,[status(thm)],[c_127,c_276]) ).
tcf(c_328,plain,
~ product(e_3,e_1,e_5),
inference(resolution,[status(thm)],[c_131,c_284]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_113,c_98]) ).
tcf(c_347,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_346]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_113,c_97]) ).
tcf(c_355,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_112,c_98]) ).
tcf(c_370,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_369]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_112,c_97]) ).
tcf(c_378,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_377]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_111,c_97]) ).
tcf(c_401,plain,
( ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_400]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] :
( ~ product(e_5,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_115,c_97]) ).
tcf(c_424,plain,
( ~ product(e_5,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_423]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_3)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_1074,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_98]) ).
tcf(c_1077,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_98]) ).
tcf(c_1078,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_97]) ).
tcf(c_1080,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_98]) ).
tcf(c_1083,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_98]) ).
tcf(c_1084,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_97]) ).
tcf(c_1085,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_2)
| ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_1086,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_98]) ).
tcf(c_1087,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_97]) ).
tcf(c_1089,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_98]) ).
tcf(c_1090,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_97]) ).
tcf(c_1092,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_98]) ).
tcf(c_1093,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_97]) ).
tcf(c_1095,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_98]) ).
tcf(c_1098,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_98]) ).
tcf(c_1099,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_97]) ).
tcf(c_1101,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_98]) ).
tcf(c_1102,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_97]) ).
tcf(c_1104,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_98]) ).
tcf(c_1107,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_98]) ).
tcf(c_1110,plain,
! [X0: $i,X1: $i] :
( equalish(e_5,e_1)
| ~ product(X0,e_5,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_1115,plain,
! [X0: $i,X1: $i] :
( equalish(e_5,e_2)
| ~ product(X0,X1,e_5)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_1117,plain,
! [X0: $i,X1: $i] :
( equalish(e_5,e_2)
| ~ product(e_5,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1119,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_5)
| ~ product(X0,e_5,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_1120,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_5)
| ~ product(e_5,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1122,plain,
! [X0: $i,X1: $i] :
( equalish(e_5,e_3)
| ~ product(X0,e_5,X1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_1123,plain,
! [X0: $i,X1: $i] :
( equalish(e_5,e_3)
| ~ product(e_5,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i] :
( equalish(e_3,e_5)
| ~ product(e_5,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i] :
( equalish(e_5,e_4)
| ~ product(X0,e_5,X1)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_5)
| ~ product(e_5,X0,X1)
| ~ product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_1134,plain,
! [X0: $i] :
( product(e_3,X0,e_5)
| 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_100]) ).
tcf(c_1137,plain,
! [X0: $i] :
( product(e_4,X0,e_5)
| 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_100]) ).
tcf(c_1138,plain,
( product(e_4,e_1,e_5)
| 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_1137]) ).
tcf(c_1140,plain,
! [X0: $i] :
( product(e_5,X0,e_5)
| product(e_5,X0,e_4)
| product(e_5,X0,e_3)
| product(e_5,X0,e_2)
| product(e_5,X0,e_1)
| ~ group_element(e_5)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_1141,plain,
( product(e_5,e_1,e_5)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1)
| ~ group_element(e_5)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1140]) ).
tcf(c_1145,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_1074]) ).
tcf(c_1146,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_4,X2,X1)
| ~ product(X1,X0,e_4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1186,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_1086]) ).
tcf(c_1187,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_3,X0)
| ~ product(X1,X0,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1190,plain,
! [X0: $i] :
( product(X0,e_3,e_5)
| 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_100]) ).
tcf(c_1200,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X1)
| ~ product(X1,X0,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1233,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_1098]) ).
tcf(c_1234,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,X1)
| ~ product(X1,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1243,plain,
! [X0: $i] :
( product(e_2,X0,e_5)
| 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_100]) ).
tcf(c_1244,plain,
( product(e_2,e_1,e_5)
| 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_1243]) ).
tcf(c_1275,plain,
( equalish(e_5,e_1)
| ~ product(e_5,e_5,e_5)
| ~ product(e_5,e_1,e_5) ),
inference(instantiation,[status(thm)],[c_1110]) ).
tcf(c_1276,plain,
product(e_5,e_5,e_5),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_1283,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_5,X2,X1)
| ~ product(X1,X0,e_5)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_1419,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1073]) ).
tcf(c_1423,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_1080]) ).
tcf(c_1424,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1077]) ).
tcf(c_1430,plain,
( equalish(e_4,e_2)
| ~ product(e_4,e_4,e_4)
| ~ product(e_2,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_1078]) ).
tcf(c_1435,plain,
( equalish(e_3,e_2)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1085]) ).
tcf(c_1438,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_1089]) ).
tcf(c_1442,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_1090]) ).
tcf(c_1443,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_1087]) ).
tcf(c_1507,plain,
( product(e_3,e_2,e_5)
| 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_1134]) ).
tcf(c_1521,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_1092]) ).
tcf(c_1523,plain,
( equalish(e_4,e_1)
| ~ product(e_3,e_4,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1080]) ).
tcf(c_1526,plain,
( product(e_3,e_5,e_5)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1)
| ~ group_element(e_5)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_1134]) ).
tcf(c_1528,plain,
( equalish(e_5,e_4)
| ~ product(e_3,e_5,e_2)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1128]) ).
tcf(c_1612,plain,
( product(e_4,e_2,e_5)
| 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_1137]) ).
tcf(c_1615,plain,
( product(e_4,e_3,e_5)
| 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_1137]) ).
tcf(c_1621,plain,
! [X0: $i] :
( equalish(e_1,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_1102]) ).
tcf(c_1622,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_1093]) ).
tcf(c_1698,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_5,X0)
| 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)
| ~ product(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_100,c_95]) ).
tcf(c_1700,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(superposition,[status(thm)],[c_100,c_324]) ).
tcf(c_1701,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(superposition,[status(thm)],[c_100,c_328]) ).
tcf(c_1712,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) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1701,c_134,c_136]) ).
tcf(c_1717,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1700,c_320,c_135,c_136]) ).
tcf(c_1879,plain,
( product(e_5,e_3,e_5)
| product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2)
| product(e_5,e_3,e_1)
| ~ group_element(e_5)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_1140]) ).
tcf(c_1882,plain,
( equalish(e_3,e_1)
| ~ product(e_5,e_3,e_2)
| ~ product(e_5,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1089]) ).
tcf(c_1892,plain,
! [X0: $i] :
( equalish(e_4,e_5)
| ~ product(e_5,X0,e_2)
| ~ product(e_4,X0,e_2) ),
inference(instantiation,[status(thm)],[c_1132]) ).
tcf(c_1907,plain,
( equalish(e_4,e_5)
| ~ product(e_5,e_1,e_2)
| ~ product(e_4,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1892]) ).
tcf(c_1923,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_1099]) ).
tcf(c_1925,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_2) ),
inference(global_subsumption_just,[status(thm)],[c_1712,c_107,c_141,c_378,c_1187,c_1438,c_1712]) ).
tcf(c_1934,plain,
! [X0: $i] :
( product(e_3,e_1,e_2)
| product(X0,e_4,e_1)
| ~ product(e_1,e_3,X0) ),
inference(superposition,[status(thm)],[c_1925,c_95]) ).
tcf(c_1981,plain,
( equalish(e_5,e_2)
| ~ product(e_5,e_5,e_5)
| ~ product(e_5,e_5,e_2) ),
inference(instantiation,[status(thm)],[c_1115]) ).
tcf(c_1987,plain,
( equalish(e_5,e_3)
| ~ product(e_5,e_5,e_5)
| ~ product(e_5,e_3,e_5) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_1995,plain,
( equalish(e_5,e_3)
| ~ product(e_5,e_5,e_5)
| ~ product(e_3,e_5,e_5) ),
inference(instantiation,[status(thm)],[c_1123]) ).
tcf(c_2001,plain,
product(e_2,e_1,e_3),
inference(global_subsumption_just,[status(thm)],[c_1717,c_136,c_135,c_110,c_141,c_320,c_324,c_355,c_1233,c_1234,c_1244]) ).
tcf(c_2006,plain,
! [X0: $i] :
( product(X0,e_3,e_1)
| ~ product(e_1,e_2,X0) ),
inference(superposition,[status(thm)],[c_2001,c_95]) ).
tcf(c_2054,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(X0,e_4,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1092]) ).
tcf(c_2071,plain,
! [X0: $i,X1: $i] :
( product(e_2,X1,X0)
| ~ product(X0,e_3,e_2)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_1241]) ).
tcf(c_2079,plain,
( product(e_2,e_3,e_5)
| 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_1190]) ).
tcf(c_2083,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_1095]) ).
tcf(c_2133,plain,
( product(e_5,e_3,e_1)
| 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(superposition,[status(thm)],[c_100,c_2006]) ).
tcf(c_2134,plain,
( product(e_5,e_3,e_1)
| 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) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2133,c_135,c_136]) ).
tcf(c_2219,plain,
( product(e_5,e_4,e_1)
| product(e_3,e_1,e_2)
| 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(superposition,[status(thm)],[c_100,c_1934]) ).
tcf(c_2220,plain,
( product(e_5,e_4,e_1)
| product(e_3,e_1,e_2)
| 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) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2219,c_134,c_136]) ).
tcf(c_2241,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,e_2)
| ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_1200]) ).
tcf(c_2242,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,X0)
| ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_1188]) ).
tcf(c_2284,plain,
( product(e_4,e_5,e_3)
| product(e_3,e_1,e_2)
| 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(superposition,[status(thm)],[c_1925,c_1698]) ).
tcf(c_2285,plain,
( product(e_3,e_5,e_2)
| 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(superposition,[status(thm)],[c_2001,c_1698]) ).
tcf(c_2292,plain,
( product(e_3,e_5,e_2)
| 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) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2285,c_135,c_136]) ).
tcf(c_2298,plain,
( product(e_4,e_5,e_3)
| product(e_3,e_1,e_2)
| 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) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2284,c_134,c_136]) ).
tcf(c_2762,plain,
! [X0: $i] :
( equalish(e_1,e_4)
| ~ product(X0,e_4,e_3)
| ~ product(X0,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_1101]) ).
tcf(c_2847,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,e_3)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_1153]) ).
tcf(c_2853,plain,
! [X0: $i] :
( product(e_2,e_4,X0)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2071]) ).
tcf(c_2860,plain,
( product(e_2,e_4,e_1)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2853]) ).
tcf(c_2896,plain,
! [X0: $i] :
( equalish(e_3,e_5)
| ~ product(e_5,X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1126]) ).
tcf(c_2899,plain,
! [X0: $i] :
( equalish(e_5,e_2)
| ~ product(e_5,X0,e_3)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1117]) ).
tcf(c_2902,plain,
( equalish(e_5,e_2)
| ~ product(e_5,e_1,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_2899]) ).
tcf(c_3285,plain,
( equalish(e_2,e_5)
| ~ product(e_3,e_5,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_1119]) ).
tcf(c_3301,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_2)
| ~ product(X0,e_2,e_3)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_1188]) ).
tcf(c_3305,plain,
! [X0: $i] :
( product(e_3,e_3,e_2)
| ~ product(e_2,X0,e_3)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2241]) ).
tcf(c_3308,plain,
( product(e_3,e_3,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_3305]) ).
tcf(c_3428,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_1095]) ).
tcf(c_3533,plain,
( product(e_5,e_3,e_1)
| product(e_1,e_2,e_4) ),
inference(global_subsumption_just,[status(thm)],[c_2134,c_136,c_135,c_110,c_106,c_141,c_320,c_324,c_347,c_355,c_1187,c_1233,c_1234,c_1244,c_1435,c_1923,c_2134,c_3308]) ).
tcf(c_3541,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(e_1,e_2,e_4)
| ~ product(e_5,X0,e_1) ),
inference(superposition,[status(thm)],[c_3533,c_98]) ).
tcf(c_3643,plain,
( equalish(e_4,e_5)
| ~ product(e_5,e_3,e_1)
| ~ product(e_4,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1132]) ).
tcf(c_3732,plain,
( product(e_3,e_5,e_2)
| product(e_1,e_2,e_4) ),
inference(global_subsumption_just,[status(thm)],[c_2292,c_136,c_135,c_110,c_106,c_141,c_320,c_324,c_347,c_355,c_1187,c_1233,c_1234,c_1244,c_1435,c_1923,c_2292,c_3308]) ).
tcf(c_3740,plain,
! [X0: $i] :
( equalish(e_5,X0)
| product(e_1,e_2,e_4)
| ~ product(e_3,X0,e_2) ),
inference(superposition,[status(thm)],[c_3732,c_98]) ).
tcf(c_3741,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(e_1,e_2,e_4)
| ~ product(X0,e_5,e_2) ),
inference(superposition,[status(thm)],[c_3732,c_97]) ).
tcf(c_3764,plain,
( equalish(e_3,e_1)
| product(e_1,e_2,e_4)
| ~ product(e_1,e_5,e_2) ),
inference(instantiation,[status(thm)],[c_3741]) ).
tcf(c_3765,plain,
( equalish(e_5,e_1)
| product(e_1,e_2,e_4)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_3740]) ).
tcf(c_3973,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1621]) ).
tcf(c_3982,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_2,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_1622]) ).
tcf(c_4137,plain,
( equalish(e_3,e_4)
| ~ product(e_2,e_4,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_1083]) ).
tcf(c_4570,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_2083]) ).
tcf(c_4720,plain,
( product(e_4,e_3,e_1)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_2242]) ).
tcf(c_4721,plain,
( product(e_3,e_4,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_2241]) ).
tcf(c_4771,plain,
! [X0: $i] :
( equalish(e_1,e_2)
| ~ product(X0,e_2,e_4)
| ~ product(X0,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1107]) ).
tcf(c_4977,plain,
! [X0: $i] :
( product(e_4,e_4,e_3)
| ~ product(e_3,X0,e_4)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_2847]) ).
tcf(c_4978,plain,
( product(e_4,e_4,e_3)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_4977]) ).
tcf(c_5484,plain,
! [X0: $i] :
( equalish(e_5,e_3)
| ~ product(e_5,X0,e_4)
| ~ product(e_3,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1123]) ).
tcf(c_5485,plain,
! [X0: $i] :
( equalish(e_2,e_5)
| ~ product(e_5,X0,e_4)
| ~ product(e_2,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1120]) ).
tcf(c_5489,plain,
( equalish(e_5,e_3)
| ~ product(e_5,e_1,e_4)
| ~ product(e_3,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_5484]) ).
tcf(c_5574,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(e_4,X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(instantiation,[status(thm)],[c_1084]) ).
tcf(c_5576,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_1078]) ).
tcf(c_5579,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_5576]) ).
tcf(c_5611,plain,
( equalish(e_5,e_3)
| ~ product(e_3,e_5,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_5641,plain,
! [X0: $i] :
( product(X0,e_3,e_2)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_4,X0) ),
inference(instantiation,[status(thm)],[c_3301]) ).
tcf(c_5746,plain,
( equalish(e_1,e_4)
| ~ product(e_2,e_4,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_2762]) ).
tcf(c_5875,plain,
( product(e_5,e_4,e_1)
| product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(global_subsumption_just,[status(thm)],[c_2220,c_136,c_135,c_114,c_110,c_107,c_104,c_102,c_141,c_320,c_324,c_355,c_370,c_378,c_1146,c_1187,c_1233,c_1234,c_1244,c_1419,c_1438,c_1442,c_1523,c_1712,c_2220,c_3765,c_4721,c_4978]) ).
tcf(c_5877,plain,
( product(e_5,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(global_subsumption_just,[status(thm)],[c_5875,c_136,c_135,c_114,c_110,c_104,c_141,c_320,c_324,c_355,c_1233,c_1234,c_1244,c_1523,c_3765,c_4721,c_5875]) ).
tcf(c_5889,plain,
( equalish(e_3,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_4) ),
inference(superposition,[status(thm)],[c_5877,c_3541]) ).
tcf(c_5890,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_2,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5889,c_105]) ).
tcf(c_5956,plain,
! [X0: $i,X1: $i] :
( product(e_5,X1,X0)
| ~ product(X0,e_3,e_5)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_1283]) ).
tcf(c_5963,plain,
! [X0: $i] :
( equalish(e_1,e_3)
| ~ product(X0,e_3,e_5)
| ~ product(X0,e_1,e_5) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_6043,plain,
( equalish(e_3,e_5)
| ~ product(e_5,e_3,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_2896]) ).
tcf(c_6477,plain,
( equalish(e_2,e_4)
| ~ product(e_2,e_4,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_2054]) ).
tcf(c_6522,plain,
! [X0: $i] :
( product(e_1,e_2,e_4)
| product(X0,e_2,e_3)
| ~ product(e_3,e_1,X0) ),
inference(superposition,[status(thm)],[c_5890,c_95]) ).
tcf(c_6523,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_4,e_1)
| product(e_1,e_2,e_4) ),
inference(superposition,[status(thm)],[c_5890,c_1934]) ).
tcf(c_6823,plain,
( product(e_4,e_2,e_3)
| product(e_3,e_1,e_2)
| product(e_1,e_2,e_4) ),
inference(superposition,[status(thm)],[c_1925,c_6522]) ).
tcf(c_7208,plain,
( product(e_1,e_2,e_4)
| product(e_2,e_4,e_1) ),
inference(global_subsumption_just,[status(thm)],[c_6523,c_136,c_135,c_114,c_110,c_104,c_141,c_320,c_324,c_355,c_1233,c_1234,c_1244,c_1523,c_3765,c_4721,c_6523]) ).
tcf(c_7209,plain,
( product(e_2,e_4,e_1)
| product(e_1,e_2,e_4) ),
inference(renaming,[status(thm)],[c_7208]) ).
tcf(c_7215,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)
| product(e_1,e_5,e_2)
| product(e_1,e_2,e_4)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(superposition,[status(thm)],[c_7209,c_1698]) ).
tcf(c_7218,plain,
! [X0: $i] :
( product(e_1,e_2,e_4)
| product(X0,e_1,e_4)
| ~ product(e_4,e_2,X0) ),
inference(superposition,[status(thm)],[c_7209,c_95]) ).
tcf(c_7232,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)
| product(e_1,e_5,e_2)
| product(e_1,e_2,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7215,c_133,c_135]) ).
tcf(c_7241,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_1,e_4)
| ~ product(e_4,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_7218]) ).
tcf(c_7556,plain,
( equalish(e_5,e_1)
| ~ product(e_3,e_5,e_4)
| ~ product(e_3,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1110]) ).
tcf(c_7633,plain,
( product(e_4,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(global_subsumption_just,[status(thm)],[c_6823,c_108,c_107,c_103,c_312,c_1146,c_1234,c_1424,c_3764,c_3982,c_7241,c_7232]) ).
tcf(c_7643,plain,
! [X0: $i] :
( product(e_1,e_2,e_4)
| product(X0,e_3,e_2)
| ~ product(e_2,e_4,X0) ),
inference(superposition,[status(thm)],[c_7633,c_95]) ).
tcf(c_7645,plain,
( product(e_3,e_1,e_4)
| product(e_1,e_2,e_4) ),
inference(superposition,[status(thm)],[c_7633,c_7218]) ).
tcf(c_7695,plain,
( equalish(e_2,e_1)
| ~ product(e_4,e_2,e_5)
| ~ product(e_4,e_1,e_5) ),
inference(instantiation,[status(thm)],[c_1098]) ).
tcf(c_7724,plain,
( product(e_5,e_5,e_2)
| ~ product(e_3,e_2,e_5)
| ~ product(e_2,e_3,e_5) ),
inference(instantiation,[status(thm)],[c_5956]) ).
tcf(c_7745,plain,
! [X0: $i] :
( ~ product(e_2,e_4,X0)
| product(X0,e_3,e_2) ),
inference(global_subsumption_just,[status(thm)],[c_7643,c_136,c_135,c_133,c_132,c_130,c_125,c_120,c_114,c_110,c_109,c_108,c_107,c_104,c_103,c_141,c_320,c_324,c_355,c_378,c_401,c_424,c_1138,c_1141,c_1146,c_1187,c_1233,c_1234,c_1244,c_1275,c_1276,c_1424,c_1423,c_1438,c_1523,c_1612,c_1712,c_1907,c_2902,c_3428,c_3765,c_3982,c_4721,c_4720,c_5489,c_5579,c_5641,c_7643,c_7695]) ).
tcf(c_7746,plain,
! [X0: $i] :
( product(X0,e_3,e_2)
| ~ product(e_2,e_4,X0) ),
inference(renaming,[status(thm)],[c_7745]) ).
tcf(c_7747,plain,
( product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_7746]) ).
tcf(c_7752,plain,
( product(e_5,e_3,e_2)
| 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(superposition,[status(thm)],[c_100,c_7746]) ).
tcf(c_7755,plain,
( product(e_5,e_3,e_2)
| 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) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7752,c_133,c_135]) ).
tcf(c_7776,plain,
product(e_1,e_3,e_2),
inference(global_subsumption_just,[status(thm)],[c_2298,c_136,c_135,c_132,c_125,c_120,c_114,c_111,c_110,c_108,c_107,c_104,c_103,c_141,c_320,c_324,c_355,c_378,c_424,c_1141,c_1146,c_1187,c_1233,c_1234,c_1244,c_1275,c_1276,c_1430,c_1438,c_1523,c_1712,c_1882,c_2902,c_3765,c_4721,c_5489,c_5746,c_6477,c_7747,c_7755]) ).
tcf(c_7865,plain,
product(e_3,e_1,e_4),
inference(global_subsumption_just,[status(thm)],[c_7645,c_136,c_135,c_110,c_104,c_141,c_320,c_324,c_355,c_1233,c_1234,c_1244,c_1523,c_1925,c_4721,c_7645]) ).
tcf(c_7973,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_4771]) ).
tcf(c_8536,plain,
( equalish(e_2,e_5)
| ~ product(e_5,e_3,e_4)
| ~ product(e_2,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_5485]) ).
tcf(c_8660,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_5574]) ).
tcf(c_8725,plain,
( equalish(e_1,e_3)
| ~ product(e_4,e_3,e_5)
| ~ product(e_4,e_1,e_5) ),
inference(instantiation,[status(thm)],[c_5963]) ).
tcf(c_8726,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8725,c_8660,c_8536,c_7973,c_7865,c_7776,c_7724,c_7556,c_6043,c_5611,c_5579,c_5489,c_4721,c_4570,c_4137,c_3973,c_3643,c_3533,c_3285,c_2902,c_2860,c_2079,c_1995,c_1987,c_1981,c_1907,c_1882,c_1879,c_1615,c_1528,c_1526,c_1521,c_1507,c_1443,c_1423,c_1276,c_1275,c_1244,c_1234,c_1233,c_1187,c_1186,c_1146,c_1145,c_1141,c_1138,c_424,c_401,c_355,c_324,c_320,c_141,c_102,c_103,c_104,c_105,c_106,c_107,c_108,c_109,c_110,c_111,c_112,c_113,c_114,c_120,c_121,c_125,c_126,c_129,c_130,c_132,c_133,c_134,c_135,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:42:53 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running EPR theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 4.10/1.22 % SZS status Started for theBenchmark.p
% 4.10/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 4.10/1.22
% 4.10/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.10/1.22
% 4.10/1.22 % ------ iProver source info
% 4.10/1.22
% 4.10/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 4.10/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.10/1.22 % git: non_committed_changes: false
% 4.10/1.22
% 4.10/1.22 % ------ Parsing...% successful
% 4.10/1.22
% 4.10/1.22
% 4.10/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 4.10/1.22 %
% 4.10/1.22
% 4.10/1.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.10/1.22
% 4.10/1.22 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 4.10/1.22 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.10/1.22 % ------ Proving...
% 4.10/1.22 % ------ Problem Properties
% 4.10/1.22
% 4.10/1.22 %
% 4.10/1.22 % clauses 37
% 4.10/1.22 % conjectures 1
% 4.10/1.22 % EPR 37
% 4.10/1.22 % Horn 36
% 4.10/1.22 % unary 32
% 4.10/1.22 % binary 0
% 4.10/1.22 % lits 51
% 4.10/1.22 % lits eq 0
% 4.10/1.22 % fd_pure 0
% 4.10/1.22 % fd_pseudo 0
% 4.10/1.22 % fd_cond 0
% 4.10/1.22 % fd_pseudo_cond 0
% 4.10/1.22 % AC symbols 0
% 4.10/1.22
% 4.10/1.22 % ------ Schedule EPR non Horn non eq is on
% 4.10/1.22
% 4.10/1.22 % ------ no equalities: superposition off
% 4.10/1.22
% 4.10/1.22 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 4.10/1.22
% 4.10/1.22
% 4.10/1.22 % ------
% 4.10/1.22 % Current options:
% 4.10/1.22 % ------
% 4.10/1.22
% 4.10/1.22
% 4.10/1.22 %
% 4.10/1.22
% 4.10/1.22 % ------ Proving...
% 4.10/1.22 %
% 4.10/1.22
% 4.10/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 4.10/1.22
% 4.10/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.10/1.23
% 4.10/1.23
%------------------------------------------------------------------------------