%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:31:13 PM UTC 2026
% Result : Unsatisfiable 1.13s 11.33s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 138 ( 27 unt; 0 def)
% Number of atoms : 489 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 582 ( 231 ~; 351 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 164 ( 0 sgn 164 !; 0 ?; 133 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f2,axiom,
! [X0,X1] :
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
fof(f3,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product(X1,X0,X3)
| ~ product(X2,X3,X1)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_1) ).
fof(f4,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product(X1,X0,X3)
| ~ product(X3,X2,X0)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4_2) ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f8,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f9,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f10,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f11,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f13,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f17,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f20,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f21,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(f22,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(f23,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(f24,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(f25,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f26,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X1,X0,X3)
| ~ product(X3,X2,X0)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_78,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X1,X0,X3)
| ~ product(X2,X3,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_79,plain,
group_element(e_1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_80,plain,
group_element(e_2),
inference(cnf_transformation,[],[f6]) ).
tcf(c_81,plain,
group_element(e_3),
inference(cnf_transformation,[],[f7]) ).
tcf(c_82,plain,
group_element(e_4),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f9]) ).
tcf(c_84,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f10]) ).
tcf(c_85,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f11]) ).
tcf(c_87,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f13]) ).
tcf(c_91,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f17]) ).
tcf(c_94,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f20]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( 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) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_99,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f25]) ).
tcf(c_100,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_101,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_83,c_96]) ).
tcf(c_210,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_209]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_83,c_97]) ).
tcf(c_218,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_217]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_83,c_98]) ).
tcf(c_226,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_225]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_84,c_96]) ).
tcf(c_234,plain,
( ~ product(e_1,e_1,e_3)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_84,c_97]) ).
tcf(c_242,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_241]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_84,c_98]) ).
tcf(c_250,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_249]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_85,c_96]) ).
tcf(c_258,plain,
( ~ product(e_1,e_1,e_4)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_408,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_97]) ).
tcf(c_409,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_98]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_3)
| ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_411,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_97]) ).
tcf(c_412,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_98]) ).
tcf(c_414,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_97]) ).
tcf(c_415,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_98]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_3)
| ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_421,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_98]) ).
tcf(c_431,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_96]) ).
tcf(c_432,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_97]) ).
tcf(c_440,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_96]) ).
tcf(c_447,plain,
! [X0: $i] :
( product(X0,e_4,e_2)
| product(X0,e_3,e_2)
| product(X0,e_2,e_2)
| product(X0,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_448,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_2,e_2)
| product(e_1,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_456,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_2,X0)
| ~ product(e_2,X2,X1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X0,X2)
| ~ product(X1,X2,e_2)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_478,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_479,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_478]) ).
tcf(c_486,plain,
! [X0: $i] :
( product(X0,e_4,e_3)
| product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_487,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_486]) ).
tcf(c_494,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_410]) ).
tcf(c_495,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_3,X0)
| ~ product(e_3,X2,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_505,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_506,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_505]) ).
tcf(c_510,plain,
! [X0: $i] :
( product(e_3,e_4,X0)
| product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| product(e_3,e_1,X0)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_511,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_510]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X0)
| ~ product(X1,X0,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_513,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X0,X2)
| ~ product(X1,X2,e_3)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_522,plain,
! [X0: $i] :
( product(e_4,X0,e_4)
| product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(e_4)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_523,plain,
( product(e_4,e_1,e_4)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_4)
| product(e_1,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_522]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X2,e_4)
| ~ product(e_4,X0,X2)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_534,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_556,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_602,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X1)
| product(e_2,X2,X1)
| product(e_1,X2,X1)
| product(X2,e_4,X0)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,e_4) ),
inference(superposition,[status(thm)],[c_75,c_77]) ).
tcf(c_638,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X1)
| product(e_2,X2,X1)
| product(e_1,X2,X1)
| product(X2,e_4,X0)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,e_4) ),
inference(superposition,[status(thm)],[c_75,c_77]) ).
tcf(c_1061,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_408]) ).
tcf(c_1063,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_409]) ).
tcf(c_1081,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_419]) ).
tcf(c_1086,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_411]) ).
tcf(c_1089,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_421]) ).
tcf(c_1090,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_412]) ).
tcf(c_1114,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| product(X1,e_4,e_4)
| product(e_3,X1,X0)
| product(e_2,X1,X0)
| product(e_1,X1,X0)
| ~ group_element(e_4)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_75,c_602]) ).
tcf(c_1115,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| product(X1,e_4,e_4)
| product(e_3,X1,X0)
| product(e_2,X1,X0)
| product(e_1,X1,X0)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1114,c_82]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| product(X1,e_4,e_4)
| product(e_3,X1,X0)
| product(e_2,X1,X0)
| product(e_1,X1,X0)
| ~ group_element(e_4)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_75,c_638]) ).
tcf(c_1140,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| product(X1,e_4,e_4)
| product(e_3,X1,X0)
| product(e_2,X1,X0)
| product(e_1,X1,X0)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1139,c_82]) ).
tcf(c_1360,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_431]) ).
tcf(c_1366,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_432]) ).
tcf(c_1368,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_414]) ).
tcf(c_1374,plain,
( equalish(e_1,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_1,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_415]) ).
tcf(c_1428,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_4,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(equality_factoring,[status(thm)],[c_1115]) ).
tcf(c_1435,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_3,e_4)
| product(e_2,e_4,e_4)
| product(e_2,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_1,e_3,e_4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1428,c_82,c_81]) ).
tcf(c_1672,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| product(X2,e_4,e_4)
| product(X1,e_4,e_3)
| product(e_3,X2,X0)
| product(e_2,X2,X0)
| product(e_1,X2,X0)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(X0,e_3,X1) ),
inference(superposition,[status(thm)],[c_1140,c_100]) ).
tcf(c_2089,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_415]) ).
tcf(c_2093,plain,
! [X0: $i,X1: $i] :
( product(e_2,X0,e_3)
| ~ product(X1,e_3,e_2)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_474]) ).
tcf(c_2494,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,e_2)
| ~ product(X0,e_2,e_3)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_512]) ).
tcf(c_2773,plain,
! [X0: $i,X1: $i] :
( product(e_4,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_3,X1,e_3)
| product(e_3,X0,e_3)
| product(e_2,X1,e_3)
| product(e_2,X0,e_3)
| product(e_1,X1,e_3)
| product(e_1,X0,e_3)
| product(X1,e_4,e_4)
| product(X0,e_4,e_4)
| ~ group_element(e_3)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_1140,c_1672]) ).
tcf(c_2788,plain,
! [X0: $i,X1: $i] :
( product(e_4,e_4,e_3)
| product(e_2,e_3,e_4)
| product(e_1,e_3,e_4)
| product(e_3,X1,e_3)
| product(e_3,X0,e_3)
| product(e_2,X1,e_3)
| product(e_2,X0,e_3)
| product(e_1,X1,e_3)
| product(e_1,X0,e_3)
| product(X1,e_4,e_4)
| product(X0,e_4,e_4)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2773,c_81]) ).
tcf(c_2819,plain,
( product(e_4,e_4,e_3)
| product(e_3,e_1,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_1,e_3)
| product(e_1,e_4,e_4)
| product(e_1,e_3,e_4)
| product(e_1,e_1,e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_2788]) ).
tcf(c_3049,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,X0)
| ~ product(e_2,X1,e_3)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_462]) ).
tcf(c_3050,plain,
( product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_3049]) ).
tcf(c_3552,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,e_4)
| ~ product(e_4,e_3,X1)
| ~ product(e_3,e_4,X0) ),
inference(instantiation,[status(thm)],[c_527]) ).
tcf(c_3553,plain,
( product(e_1,e_1,e_4)
| ~ product(e_4,e_3,e_1)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_3552]) ).
tcf(c_3711,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,X0)
| ~ product(e_3,X1,e_4)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_501]) ).
tcf(c_3712,plain,
( product(e_1,e_3,e_1)
| ~ product(e_3,e_1,e_4)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_3711]) ).
tcf(c_3796,plain,
! [X0: $i] :
( equalish(e_4,e_3)
| ~ product(e_2,X0,e_4)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_440]) ).
tcf(c_3807,plain,
( equalish(e_4,e_3)
| ~ product(e_2,e_1,e_4)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_3796]) ).
tcf(c_3822,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,X0)
| ~ product(e_2,X1,e_4)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_462]) ).
tcf(c_3823,plain,
( product(e_1,e_2,e_1)
| ~ product(e_2,e_1,e_4)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_3822]) ).
tcf(c_3856,plain,
( product(e_1,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(global_subsumption_just,[status(thm)],[c_1435,c_81,c_79,c_101,c_91,c_85,c_84,c_218,c_234,c_242,c_495,c_506,c_534,c_1086,c_1090,c_1360,c_1374,c_2819,c_3050]) ).
tcf(c_3857,plain,
( product(e_2,e_3,e_4)
| product(e_1,e_3,e_4) ),
inference(renaming,[status(thm)],[c_3856]) ).
tcf(c_3868,plain,
! [X0: $i] :
( product(e_1,e_3,e_4)
| product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| product(X0,e_4,e_2)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_3857,c_602]) ).
tcf(c_3878,plain,
! [X0: $i] :
( product(e_1,e_3,e_4)
| product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| product(X0,e_4,e_2)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3868,c_81]) ).
tcf(c_3916,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_4)
| product(e_1,e_1,e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_3878]) ).
tcf(c_4461,plain,
! [X0: $i] :
( product(e_3,X0,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(X0,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_513]) ).
tcf(c_4462,plain,
( product(e_3,e_1,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_4461]) ).
tcf(c_5035,plain,
! [X0: $i] :
( product(e_2,e_3,e_3)
| ~ product(e_3,e_2,X0)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_2093]) ).
tcf(c_5036,plain,
( product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_5035]) ).
tcf(c_5159,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_556]) ).
tcf(c_5195,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_2494]) ).
tcf(c_5196,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_5195]) ).
tcf(c_5366,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5196,c_5159,c_5036,c_4462,c_3916,c_3823,c_3807,c_3712,c_3553,c_2089,c_1366,c_1368,c_1089,c_1090,c_1086,c_1081,c_1063,c_1061,c_534,c_523,c_511,c_495,c_494,c_487,c_479,c_456,c_448,c_258,c_250,c_242,c_234,c_226,c_218,c_210,c_83,c_84,c_85,c_87,c_91,c_94,c_101,c_79,c_80,c_81,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP126-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.58 % Computer : n016.cluster.edu
% 0.10/10.58 % Model : x86_64 x86_64
% 0.10/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.58 % Memory : 8046.5625MB
% 0.10/10.58 % OS : Linux 6.8.0-71-generic
% 0.10/10.58 % CPULimit : 300
% 0.10/10.58 % WCLimit : 300
% 0.10/10.58 % DateTime : Wed Sep 23 13:47:06 UTC 2026
% 0.10/10.58 % CPUTime :
% 0.10/10.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.62 Running EPR theorem proving
% 0.14/10.62 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
% 0.14/10.64
% 0.14/10.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.64
% 0.14/10.64 % Detected problem language: tptp
% 0.14/10.65 % Proving...
% 1.13/11.33 % SZS status Started for theBenchmark.p
% 1.13/11.33 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/11.33
% 1.13/11.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.13/11.33
% 1.13/11.33 % ------ iProver source info
% 1.13/11.33
% 1.13/11.33 % git: date: 2026-07-19 20:42:38 +0200
% 1.13/11.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.13/11.33 % git: non_committed_changes: false
% 1.13/11.33
% 1.13/11.33 % ------ Parsing...% successful
% 1.13/11.33
% 1.13/11.33
% 1.13/11.33 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.13/11.33 %
% 1.13/11.33
% 1.13/11.33 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.13/11.33
% 1.13/11.33 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.13/11.33 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.13/11.33 % ------ Proving...
% 1.13/11.33 % ------ Problem Properties
% 1.13/11.33
% 1.13/11.33 %
% 1.13/11.33 % clauses 26
% 1.13/11.33 % conjectures 3
% 1.13/11.33 % EPR 26
% 1.13/11.33 % Horn 23
% 1.13/11.33 % unary 17
% 1.13/11.33 % binary 0
% 1.13/11.33 % lits 53
% 1.13/11.33 % lits eq 0
% 1.13/11.33 % fd_pure 0
% 1.13/11.33 % fd_pseudo 0
% 1.13/11.33 % fd_cond 0
% 1.13/11.33 % fd_pseudo_cond 0
% 1.13/11.33 % AC symbols 0
% 1.13/11.33
% 1.13/11.33 % ------ Schedule EPR non Horn non eq is on
% 1.13/11.33
% 1.13/11.33 % ------ no equalities: superposition off
% 1.13/11.33
% 1.13/11.33 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.13/11.33
% 1.13/11.33
% 1.13/11.33 % ------
% 1.13/11.33 % Current options:
% 1.13/11.33 % ------
% 1.13/11.33
% 1.13/11.33
% 1.13/11.33 %
% 1.13/11.33
% 1.13/11.33 % ------ Proving...
% 1.13/11.33 %
% 1.13/11.33
% 1.13/11.33 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/11.33
% 1.13/11.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.13/11.34
% 1.13/11.34
%------------------------------------------------------------------------------