%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP126-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:31:12 PM UTC 2026
% Result : Unsatisfiable 2.56s 1.25s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 22
% Syntax : Number of formulae : 155 ( 39 unt; 0 def)
% Number of atoms : 420 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 521 ( 256 ~; 265 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 136 ( 0 sgn 136 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f8,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f11,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f12,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f14,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f15,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f16,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f17,axiom,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f18,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(f19,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(f20,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(f21,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f22,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg4) ).
tcf(c_71,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,[],[f22]) ).
tcf(c_72,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_76,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,[],[f17]) ).
tcf(c_77,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[],[f14]) ).
tcf(c_78,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f8]) ).
tcf(c_80,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f7]) ).
tcf(c_81,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_83,plain,
group_element(e_4),
inference(cnf_transformation,[],[f4]) ).
tcf(c_84,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
group_element(e_2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_86,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_87,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[],[f15]) ).
tcf(c_88,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[],[f12]) ).
tcf(c_89,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[],[f10]) ).
tcf(c_90,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_91,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f13]) ).
tcf(c_93,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_82,c_75]) ).
tcf(c_166,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_165]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_82,c_74]) ).
tcf(c_174,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_81,c_75]) ).
tcf(c_190,plain,
( ~ product(e_1,e_1,e_3)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_189]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_81,c_74]) ).
tcf(c_198,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_197]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_80,c_74]) ).
tcf(c_222,plain,
( ~ product(e_1,e_4,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_221]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_80,c_73]) ).
tcf(c_230,plain,
( ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_229]) ).
tcf(c_364,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_74]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_1)
| ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_367,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_74]) ).
tcf(c_368,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_73]) ).
tcf(c_371,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_73]) ).
tcf(c_374,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_73]) ).
tcf(c_376,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_74]) ).
tcf(c_377,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_73]) ).
tcf(c_382,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_74]) ).
tcf(c_383,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_73]) ).
tcf(c_385,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_74]) ).
tcf(c_386,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_73]) ).
tcf(c_388,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_74]) ).
tcf(c_389,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_73]) ).
tcf(c_391,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_74]) ).
tcf(c_392,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_73]) ).
tcf(c_394,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_74]) ).
tcf(c_395,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_73]) ).
tcf(c_398,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_73]) ).
tcf(c_400,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_404,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_76]) ).
tcf(c_405,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_404]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_4,X1)
| ~ product(X1,X0,e_4)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_410,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_76]) ).
tcf(c_411,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_410]) ).
tcf(c_416,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X2,e_3)
| ~ product(e_3,X0,X2)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_420,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_76]) ).
tcf(c_421,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_420]) ).
tcf(c_430,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_71]) ).
tcf(c_432,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X2,e_2)
| ~ product(e_2,X0,X2)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_436,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_76]) ).
tcf(c_437,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_436]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_2,X1)
| ~ product(X1,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,X0)
| ~ product(X1,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_606,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_394]) ).
tcf(c_608,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_382]) ).
tcf(c_610,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_364]) ).
tcf(c_612,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_4,e_4)
| ~ product(e_3,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_395]) ).
tcf(c_614,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_383]) ).
tcf(c_616,plain,
( equalish(e_4,e_1)
| ~ product(e_4,e_4,e_4)
| ~ product(e_1,e_4,e_4) ),
inference(instantiation,[status(thm)],[c_365]) ).
tcf(c_629,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_385]) ).
tcf(c_631,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_367]) ).
tcf(c_633,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_386]) ).
tcf(c_635,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_368]) ).
tcf(c_722,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_371]) ).
tcf(c_744,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_404]) ).
tcf(c_747,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_404]) ).
tcf(c_750,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_377]) ).
tcf(c_751,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_368]) ).
tcf(c_769,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,X0)
| ~ product(X0,e_4,e_2)
| ~ product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_440]) ).
tcf(c_904,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_410]) ).
tcf(c_907,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_410]) ).
tcf(c_910,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_376]) ).
tcf(c_915,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_389]) ).
tcf(c_917,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_374]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i] :
( product(e_2,X1,X0)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_446]) ).
tcf(c_1036,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_420]) ).
tcf(c_1039,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_391]) ).
tcf(c_1187,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,e_3)
| ~ product(e_3,X0,e_2)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_417]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,e_2)
| ~ product(e_2,X0,e_2)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_1554,plain,
! [X0: $i] :
( equalish(e_3,e_2)
| ~ product(X0,e_3,e_4)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_385]) ).
tcf(c_1559,plain,
( equalish(e_3,e_2)
| ~ product(e_1,e_3,e_4)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1554]) ).
tcf(c_1567,plain,
! [X0: $i,X1: $i] :
( product(X1,e_4,X0)
| ~ product(X0,e_3,e_4)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_408]) ).
tcf(c_1832,plain,
! [X0: $i] :
( product(X0,e_1,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,e_2,X0) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_1833,plain,
( product(e_1,e_1,e_2)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1832]) ).
tcf(c_1847,plain,
( equalish(e_2,e_4)
| ~ product(e_3,e_4,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_1852,plain,
! [X0: $i] :
( product(X0,e_1,e_3)
| ~ product(e_3,e_4,e_1)
| ~ product(e_4,e_3,X0) ),
inference(instantiation,[status(thm)],[c_417]) ).
tcf(c_1853,plain,
( product(e_1,e_1,e_3)
| ~ product(e_4,e_3,e_1)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1852]) ).
tcf(c_1860,plain,
( product(e_1,e_2,e_2)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1221]) ).
tcf(c_1865,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_2,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_398]) ).
tcf(c_1878,plain,
( product(e_1,e_2,e_3)
| ~ product(e_4,e_3,e_1)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1187]) ).
tcf(c_2028,plain,
! [X0: $i] :
( product(X0,e_1,e_2)
| ~ product(e_2,e_3,e_1)
| ~ product(e_3,e_2,X0) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_2029,plain,
( product(e_1,e_1,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_2028]) ).
tcf(c_2059,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(e_4,X0,e_2)
| ~ product(X0,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_927]) ).
tcf(c_2063,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(X0,e_4,e_3)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_388]) ).
tcf(c_2064,plain,
! [X0: $i] :
( equalish(e_4,e_2)
| ~ product(X0,e_4,e_3)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_382]) ).
tcf(c_2069,plain,
( equalish(e_4,e_2)
| ~ product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2064]) ).
tcf(c_2070,plain,
( equalish(e_2,e_4)
| ~ product(e_1,e_4,e_3)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_2063]) ).
tcf(c_2144,plain,
! [X0: $i] :
( product(e_3,e_2,X0)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_769]) ).
tcf(c_2159,plain,
( product(e_3,e_2,e_1)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_2144]) ).
tcf(c_2162,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,X0)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_430]) ).
tcf(c_2241,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_1039]) ).
tcf(c_2927,plain,
! [X0: $i] :
( product(X0,e_4,e_2)
| ~ product(e_2,e_3,e_4)
| ~ product(e_3,e_2,X0) ),
inference(instantiation,[status(thm)],[c_1567]) ).
tcf(c_2930,plain,
( product(e_1,e_4,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_2927]) ).
tcf(c_2944,plain,
( product(e_2,e_3,e_3)
| ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_2059]) ).
tcf(c_3336,plain,
( product(e_3,e_2,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1187]) ).
tcf(c_3337,plain,
( equalish(e_2,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_4,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_391]) ).
tcf(c_3338,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_385]) ).
tcf(c_3354,plain,
! [X0: $i] :
( product(e_3,X0,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_4,X0) ),
inference(instantiation,[status(thm)],[c_2162]) ).
tcf(c_3357,plain,
( product(e_3,e_1,e_3)
| ~ product(e_4,e_3,e_3)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_3354]) ).
tcf(c_3468,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_915]) ).
tcf(c_3522,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_917]) ).
tcf(c_3623,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_4,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_392]) ).
tcf(c_3635,plain,
! [X0: $i] :
( product(X0,e_3,e_3)
| ~ product(e_3,e_4,e_3)
| ~ product(e_4,e_3,X0) ),
inference(instantiation,[status(thm)],[c_417]) ).
tcf(c_3636,plain,
( product(e_1,e_3,e_3)
| ~ product(e_4,e_3,e_1)
| ~ product(e_3,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_3635]) ).
tcf(c_3637,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3636,c_3623,c_3522,c_3468,c_3357,c_3336,c_3337,c_3338,c_2944,c_2930,c_2241,c_2159,c_2070,c_2069,c_2029,c_1878,c_1865,c_1860,c_1853,c_1847,c_1833,c_1559,c_1036,c_910,c_907,c_904,c_750,c_751,c_747,c_744,c_722,c_633,c_635,c_629,c_631,c_612,c_614,c_616,c_606,c_608,c_610,c_437,c_432,c_421,c_416,c_411,c_405,c_400,c_230,c_222,c_198,c_190,c_174,c_166,c_93,c_77,c_78,c_79,c_80,c_81,c_87,c_88,c_89,c_90,c_91,c_92,c_83,c_84,c_85,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Wed Sep 23 13:41:18 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.43 Running EPR theorem proving
% 0.12/0.43 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.56/1.25 % SZS status Started for theBenchmark.p
% 2.56/1.25 % SZS status Unsatisfiable for theBenchmark.p
% 2.56/1.25
% 2.56/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.56/1.25
% 2.56/1.25 % ------ iProver source info
% 2.56/1.25
% 2.56/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 2.56/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.56/1.25 % git: non_committed_changes: false
% 2.56/1.25
% 2.56/1.25 % ------ Parsing...% successful
% 2.56/1.25
% 2.56/1.25
% 2.56/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.56/1.25 %
% 2.56/1.25
% 2.56/1.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.56/1.25
% 2.56/1.25 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.56/1.25 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.56/1.25 % ------ Proving...
% 2.56/1.25 % ------ Problem Properties
% 2.56/1.25
% 2.56/1.25 %
% 2.56/1.25 % clauses 22
% 2.56/1.25 % conjectures 1
% 2.56/1.25 % EPR 22
% 2.56/1.25 % Horn 21
% 2.56/1.25 % unary 17
% 2.56/1.25 % binary 0
% 2.56/1.25 % lits 35
% 2.56/1.25 % lits eq 0
% 2.56/1.25 % fd_pure 0
% 2.56/1.25 % fd_pseudo 0
% 2.56/1.25 % fd_cond 0
% 2.56/1.25 % fd_pseudo_cond 0
% 2.56/1.25 % AC symbols 0
% 2.56/1.25
% 2.56/1.25 % ------ Schedule EPR non Horn non eq is on
% 2.56/1.25
% 2.56/1.25 % ------ no equalities: superposition off
% 2.56/1.25
% 2.56/1.25 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.56/1.25
% 2.56/1.25
% 2.56/1.25 % ------
% 2.56/1.25 % Current options:
% 2.56/1.25 % ------
% 2.56/1.25
% 2.56/1.25
% 2.56/1.25 %
% 2.56/1.25
% 2.56/1.25 % ------ Proving...
% 2.56/1.25 %
% 2.56/1.25
% 2.56/1.25 % SZS status Unsatisfiable for theBenchmark.p
% 2.56/1.25
% 2.56/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.56/1.25
% 2.56/1.25
%------------------------------------------------------------------------------