%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP127-1.004 : 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 : n007.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 2.60s 1.25s
% Output : CNFRefutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 21
% Syntax : Number of formulae : 133 ( 39 unt; 0 def)
% Number of atoms : 363 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 442 ( 212 ~; 230 |; 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 : 110 ( 0 sgn 110 !; 0 ?; 95 :)
% 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(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(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
tcf(c_71,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X0,X1)
| ~ product(X2,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_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_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_181,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_82,c_73]) ).
tcf(c_182,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_181]) ).
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_205,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_81,c_73]) ).
tcf(c_206,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_205]) ).
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_370,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_74]) ).
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_373,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_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_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_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_397,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_74]) ).
tcf(c_400,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X1,e_4)
| ~ product(X1,e_4,X0)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_71]) ).
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(X1,e_4,X2)
| ~ product(e_4,X2,X0)
| ~ product(X0,e_4,X1) ),
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(X2,X1,e_3)
| ~ product(X1,e_3,X0)
| ~ product(X0,X1,X2) ),
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_426,plain,
! [X0: $i] :
( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_427,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_426]) ).
tcf(c_432,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_72]) ).
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_442,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_76]) ).
tcf(c_443,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_442]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X0,X1)
| ~ product(X2,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_614,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_616,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_618,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_620,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_622,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_637,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_639,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_641,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_726,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_370]) ).
tcf(c_728,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_750,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_753,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_756,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_760,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_388]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_4)
| ~ product(X0,e_4,e_2)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_401]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i] :
( product(e_2,e_4,X0)
| ~ product(X1,e_4,e_2)
| ~ product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_446]) ).
tcf(c_931,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_941,plain,
! [X0: $i] :
( equalish(e_4,e_3)
| ~ product(e_4,X0,e_2)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_395]) ).
tcf(c_942,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_950,plain,
( equalish(e_4,e_3)
| ~ product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_941]) ).
tcf(c_1059,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_1061,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_371]) ).
tcf(c_1525,plain,
! [X0: $i] :
( equalish(e_3,e_4)
| ~ product(X0,e_4,e_3)
| ~ product(X0,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_397]) ).
tcf(c_1528,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_1529,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_373]) ).
tcf(c_1533,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_1528]) ).
tcf(c_1574,plain,
! [X0: $i,X1: $i] :
( product(X0,e_4,X1)
| ~ product(e_4,X1,e_3)
| ~ product(e_3,e_4,X0) ),
inference(instantiation,[status(thm)],[c_408]) ).
tcf(c_1575,plain,
( product(e_1,e_4,e_1)
| ~ product(e_4,e_1,e_3)
| ~ product(e_3,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_1574]) ).
tcf(c_1742,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_391]) ).
tcf(c_1749,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_1742]) ).
tcf(c_1756,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_3)
| ~ product(X0,e_3,e_4)
| ~ product(e_4,X0,X1) ),
inference(instantiation,[status(thm)],[c_417]) ).
tcf(c_1779,plain,
! [X0: $i] :
( equalish(e_2,e_3)
| ~ product(e_3,X0,e_4)
| ~ product(e_2,X0,e_4) ),
inference(instantiation,[status(thm)],[c_392]) ).
tcf(c_1786,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_1,e_4)
| ~ product(e_2,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_1779]) ).
tcf(c_1938,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_4,e_1)
| ~ product(e_2,e_4,e_1) ),
inference(instantiation,[status(thm)],[c_392]) ).
tcf(c_2312,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_760]) ).
tcf(c_2523,plain,
( product(e_1,e_3,e_4)
| ~ product(e_3,e_4,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_2537,plain,
( product(e_1,e_2,e_3)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(instantiation,[status(thm)],[c_1756]) ).
tcf(c_3075,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_942]) ).
tcf(c_3117,plain,
( equalish(e_3,e_4)
| ~ product(e_3,e_4,e_3)
| ~ product(e_3,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_1525]) ).
tcf(c_3203,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_1529]) ).
tcf(c_4008,plain,
( product(e_2,e_4,e_2)
| ~ product(e_4,e_2,e_3)
| ~ product(e_3,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_776]) ).
tcf(c_4015,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4008,c_3203,c_3117,c_3075,c_2537,c_2523,c_2312,c_1938,c_1786,c_1749,c_1575,c_1533,c_1061,c_1059,c_950,c_931,c_756,c_753,c_750,c_728,c_726,c_639,c_641,c_637,c_618,c_620,c_622,c_614,c_616,c_443,c_437,c_432,c_427,c_421,c_416,c_411,c_405,c_400,c_230,c_222,c_206,c_198,c_182,c_174,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 : GRP127-1.004 : 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 : n007.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 13:39:52 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
% 0.12/0.46 % Proving...
% 2.60/1.25 % SZS status Started for theBenchmark.p
% 2.60/1.25 % SZS status Unsatisfiable for theBenchmark.p
% 2.60/1.25
% 2.60/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.60/1.25
% 2.60/1.25 % ------ iProver source info
% 2.60/1.25
% 2.60/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 2.60/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.60/1.25 % git: non_committed_changes: false
% 2.60/1.25
% 2.60/1.25 % ------ Parsing...% successful
% 2.60/1.25
% 2.60/1.25
% 2.60/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.60/1.25 %
% 2.60/1.25
% 2.60/1.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.60/1.25
% 2.60/1.25 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.60/1.25 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.60/1.25 % ------ Proving...
% 2.60/1.25 % ------ Problem Properties
% 2.60/1.25
% 2.60/1.25 %
% 2.60/1.25 % clauses 22
% 2.60/1.25 % conjectures 1
% 2.60/1.25 % EPR 22
% 2.60/1.25 % Horn 21
% 2.60/1.25 % unary 17
% 2.60/1.25 % binary 0
% 2.60/1.25 % lits 35
% 2.60/1.25 % lits eq 0
% 2.60/1.25 % fd_pure 0
% 2.60/1.25 % fd_pseudo 0
% 2.60/1.25 % fd_cond 0
% 2.60/1.25 % fd_pseudo_cond 0
% 2.60/1.25 % AC symbols 0
% 2.60/1.25
% 2.60/1.25 % ------ Schedule EPR non Horn non eq is on
% 2.60/1.25
% 2.60/1.25 % ------ no equalities: superposition off
% 2.60/1.25
% 2.60/1.25 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.60/1.25
% 2.60/1.25
% 2.60/1.25 % ------
% 2.60/1.25 % Current options:
% 2.60/1.25 % ------
% 2.60/1.25
% 2.60/1.25
% 2.60/1.25 %
% 2.60/1.25
% 2.60/1.25 % ------ Proving...
% 2.60/1.25 %
% 2.60/1.25
% 2.60/1.25 % SZS status Unsatisfiable for theBenchmark.p
% 2.60/1.25
% 2.60/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.60/1.25
% 2.60/1.25
%------------------------------------------------------------------------------