%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:31:13 PM UTC 2026
% Result : Unsatisfiable 2.39s 6.24s
% Output : CNFRefutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 21
% Syntax : Number of formulae : 122 ( 37 unt; 0 def)
% Number of atoms : 341 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 409 ( 190 ~; 219 |; 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 : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 113 ( 0 sgn 113 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f12,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f13,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f14,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f15,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f16,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f17,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f18,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f19,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f20,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f21,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f23,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f24,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
fof(f25,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
fof(f26,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f27,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(f28,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(f29,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(f30,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(f31,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f32,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_81,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X2,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_82,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_87,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f26]) ).
tcf(c_88,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[],[f25]) ).
tcf(c_89,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[],[f24]) ).
tcf(c_90,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f23]) ).
tcf(c_92,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f21]) ).
tcf(c_93,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f19]) ).
tcf(c_95,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f18]) ).
tcf(c_96,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f17]) ).
tcf(c_97,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f16]) ).
tcf(c_98,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f15]) ).
tcf(c_99,plain,
group_element(e_4),
inference(cnf_transformation,[],[f14]) ).
tcf(c_100,plain,
group_element(e_3),
inference(cnf_transformation,[],[f13]) ).
tcf(c_101,plain,
group_element(e_2),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,plain,
group_element(e_1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_103,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_98,c_85]) ).
tcf(c_176,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_98,c_84]) ).
tcf(c_184,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_97,c_84]) ).
tcf(c_208,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_207]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_97,c_83]) ).
tcf(c_216,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_96,c_84]) ).
tcf(c_232,plain,
( ~ product(e_1,e_4,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_96,c_83]) ).
tcf(c_240,plain,
( ~ product(e_4,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_239]) ).
tcf(c_374,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_84]) ).
tcf(c_377,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_84]) ).
tcf(c_378,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_83]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] :
( equalish(e_4,e_1)
| ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_380,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_84]) ).
tcf(c_381,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_83]) ).
tcf(c_384,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_83]) ).
tcf(c_389,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_84]) ).
tcf(c_390,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_83]) ).
tcf(c_392,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_84]) ).
tcf(c_393,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_83]) ).
tcf(c_395,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_84]) ).
tcf(c_399,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_83]) ).
tcf(c_408,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_83]) ).
tcf(c_410,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_413,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_86]) ).
tcf(c_414,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_413]) ).
tcf(c_419,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_86]) ).
tcf(c_420,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_419]) ).
tcf(c_459,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_3,X1)
| ~ product(X1,X0,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_462,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_86]) ).
tcf(c_463,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_462]) ).
tcf(c_501,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_504,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_86]) ).
tcf(c_505,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_504]) ).
tcf(c_508,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_81]) ).
tcf(c_563,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_81]) ).
tcf(c_615,plain,
( equalish(e_4,e_1)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_379]) ).
tcf(c_621,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_380]) ).
tcf(c_622,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_377]) ).
tcf(c_627,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_381]) ).
tcf(c_628,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_378]) ).
tcf(c_642,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_389]) ).
tcf(c_646,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_390]) ).
tcf(c_683,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_4,X1)
| 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_86,c_81]) ).
tcf(c_733,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_399]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i] :
( product(e_2,X1,e_4)
| ~ product(X0,e_4,e_2)
| ~ product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_508]) ).
tcf(c_755,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_413]) ).
tcf(c_764,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_392]) ).
tcf(c_768,plain,
! [X0: $i] :
( equalish(e_4,e_3)
| ~ product(X0,e_4,e_2)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_374]) ).
tcf(c_769,plain,
( equalish(e_4,e_3)
| ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_768]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i] :
( product(e_4,e_4,X0)
| product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_86,c_683]) ).
tcf(c_915,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_419]) ).
tcf(c_925,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_393]) ).
tcf(c_926,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(e_4,X0,e_2)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_384]) ).
tcf(c_933,plain,
( equalish(e_3,e_4)
| ~ product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_926]) ).
tcf(c_1222,plain,
! [X0: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,X0,e_3)
| ~ product(e_1,X0,e_3) ),
inference(instantiation,[status(thm)],[c_408]) ).
tcf(c_1483,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_377]) ).
tcf(c_1486,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_1483]) ).
tcf(c_1596,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_4)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_4,X1) ),
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1953,plain,
! [X0: $i] :
( equalish(e_2,e_3)
| ~ product(X0,e_3,e_4)
| ~ product(X0,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_395]) ).
tcf(c_1958,plain,
( equalish(e_2,e_3)
| ~ product(e_1,e_3,e_4)
| ~ product(e_1,e_2,e_4) ),
inference(instantiation,[status(thm)],[c_1953]) ).
tcf(c_1989,plain,
! [X0: $i] :
( product(e_2,e_3,e_4)
| ~ product(e_4,X0,e_3)
| ~ product(X0,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_747]) ).
tcf(c_1990,plain,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_1,e_3)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_1989]) ).
tcf(c_2022,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_563]) ).
tcf(c_2023,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_2022]) ).
tcf(c_2077,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_82,c_83]) ).
tcf(c_2354,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_764]) ).
tcf(c_2371,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(e_4,e_4,X0)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_794,c_2077]) ).
tcf(c_2407,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(e_4,e_4,X0)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2371,c_100]) ).
tcf(c_2418,plain,
( equalish(e_3,e_1)
| product(e_4,e_4,e_1)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_2407]) ).
tcf(c_2608,plain,
( product(e_1,e_3,e_4)
| ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1596]) ).
tcf(c_2644,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_4,e_3)
| ~ product(e_1,e_4,e_3) ),
inference(instantiation,[status(thm)],[c_1222]) ).
tcf(c_3027,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_925]) ).
tcf(c_3048,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_3,e_4)
| ~ product(e_1,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_399]) ).
tcf(c_3465,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3048,c_3027,c_2644,c_2608,c_2418,c_2354,c_2023,c_1990,c_1958,c_1486,c_933,c_915,c_769,c_755,c_733,c_646,c_642,c_627,c_628,c_621,c_622,c_615,c_505,c_501,c_463,c_459,c_420,c_414,c_410,c_240,c_232,c_216,c_208,c_184,c_176,c_103,c_87,c_88,c_89,c_90,c_92,c_93,c_94,c_95,c_98,c_99,c_100,c_101,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n015.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 13:44:45 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running EPR theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.46 % Proving...
% 2.39/6.24 % SZS status Started for theBenchmark.p
% 2.39/6.24 % SZS status Unsatisfiable for theBenchmark.p
% 2.39/6.24
% 2.39/6.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.39/6.24
% 2.39/6.24 % ------ iProver source info
% 2.39/6.24
% 2.39/6.24 % git: date: 2026-07-19 20:42:38 +0200
% 2.39/6.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.39/6.24 % git: non_committed_changes: false
% 2.39/6.24
% 2.39/6.24 % ------ Parsing...% successful
% 2.39/6.24
% 2.39/6.24
% 2.39/6.24 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.39/6.24 %
% 2.39/6.24
% 2.39/6.24 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.39/6.24
% 2.39/6.24 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.39/6.24 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.39/6.24 % ------ Proving...
% 2.39/6.24 % ------ Problem Properties
% 2.39/6.24
% 2.39/6.24 %
% 2.39/6.24 % clauses 22
% 2.39/6.24 % conjectures 1
% 2.39/6.24 % EPR 22
% 2.39/6.24 % Horn 21
% 2.39/6.24 % unary 17
% 2.39/6.24 % binary 0
% 2.39/6.24 % lits 35
% 2.39/6.24 % lits eq 0
% 2.39/6.24 % fd_pure 0
% 2.39/6.24 % fd_pseudo 0
% 2.39/6.24 % fd_cond 0
% 2.39/6.24 % fd_pseudo_cond 0
% 2.39/6.24 % AC symbols 0
% 2.39/6.24
% 2.39/6.24 % ------ Schedule EPR non Horn non eq is on
% 2.39/6.24
% 2.39/6.24 % ------ no equalities: superposition off
% 2.39/6.24
% 2.39/6.24 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.39/6.24
% 2.39/6.24
% 2.39/6.24 % ------
% 2.39/6.24 % Current options:
% 2.39/6.24 % ------
% 2.39/6.24
% 2.39/6.24
% 2.39/6.24 %
% 2.39/6.24
% 2.39/6.24 % ------ Proving...
% 2.39/6.24 %
% 2.39/6.24
% 2.39/6.24 % SZS status Unsatisfiable for theBenchmark.p
% 2.39/6.24
% 2.39/6.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.39/6.25
% 2.39/6.25
%------------------------------------------------------------------------------