%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP124-4.004 : 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 : n006.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 01:31:10 PM UTC 2026
% Result : Unsatisfiable 2.67s 1.21s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 115 ( 34 unt; 0 def)
% Number of atoms : 358 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 438 ( 195 ~; 243 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 135 ( 0 sgn 135 !; 0 ?; 104 :)
% 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,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f6,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
fof(f7,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f8,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f9,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
fof(f10,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f12,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
fof(f13,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
fof(f15,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
fof(f18,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
fof(f19,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(f20,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(f21,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(f22,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(f23,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f24,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_1) ).
fof(f25,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_75,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_76,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f23]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_80,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,[],[f19]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( product(X1,e_4,X0)
| product(X1,e_3,X0)
| product(X1,e_2,X0)
| product(X1,e_1,X0)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( product(e_4,X1,X0)
| product(e_3,X1,X0)
| product(e_2,X1,X0)
| product(e_1,X1,X0)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_85,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f10]) ).
tcf(c_86,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[],[f9]) ).
tcf(c_87,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f7]) ).
tcf(c_89,plain,
group_element(e_1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_90,plain,
group_element(e_4),
inference(cnf_transformation,[],[f6]) ).
tcf(c_91,plain,
group_element(e_3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_92,plain,
group_element(e_2),
inference(cnf_transformation,[],[f4]) ).
tcf(c_95,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[],[f12]) ).
tcf(c_96,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f11]) ).
tcf(c_97,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[],[f18]) ).
tcf(c_98,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[],[f15]) ).
tcf(c_99,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_88,c_79]) ).
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_88,c_78]) ).
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_268,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_87,c_78]) ).
tcf(c_269,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_268]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_87,c_77]) ).
tcf(c_291,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_86,c_79]) ).
tcf(c_312,plain,
( ~ product(e_1,e_1,e_4)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_2,e_1)
| ~ product(X3,X2,e_1)
| ~ product(X3,X0,e_2)
| ~ product(X2,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_1,e_4)
| ~ product(X3,X2,e_4)
| ~ product(X3,X0,e_1)
| ~ product(X2,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_1,e_2)
| ~ product(X3,X2,e_2)
| ~ product(X3,X0,e_1)
| ~ product(X2,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_2,e_4)
| ~ product(e_4,X2,X3)
| ~ product(e_2,X1,X3)
| ~ product(X0,e_4,X2)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_650,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_77]) ).
tcf(c_651,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_77]) ).
tcf(c_654,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_77]) ).
tcf(c_662,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_78]) ).
tcf(c_664,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_78]) ).
tcf(c_666,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_78]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_2)
| ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_675,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_79]) ).
tcf(c_686,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_650]) ).
tcf(c_687,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_694,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_651]) ).
tcf(c_695,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_697,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_80]) ).
tcf(c_700,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_81]) ).
tcf(c_701,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_700]) ).
tcf(c_703,plain,
product(e_4,e_4,e_4),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_716,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_82]) ).
tcf(c_717,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_716]) ).
tcf(c_741,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_81]) ).
tcf(c_742,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_741]) ).
tcf(c_920,plain,
! [X0: $i] :
( product(e_4,e_2,X0)
| product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_921,plain,
( product(e_4,e_2,e_1)
| product(e_3,e_2,e_1)
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_920]) ).
tcf(c_925,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_80]) ).
tcf(c_926,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_925]) ).
tcf(c_1125,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_664]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_2,X1,e_4)
| ~ product(X0,e_4,e_4)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_642]) ).
tcf(c_1205,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_76,c_77]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i] :
( equalish(X1,X0)
| ~ product(X0,X1,X1) ),
inference(superposition,[status(thm)],[c_76,c_77]) ).
tcf(c_1233,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(superposition,[status(thm)],[c_76,c_78]) ).
tcf(c_1242,plain,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ product(X0,X1,X0) ),
inference(superposition,[status(thm)],[c_76,c_78]) ).
tcf(c_1320,plain,
! [X0: $i] :
( equalish(e_4,X0)
| 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(superposition,[status(thm)],[c_80,c_1205]) ).
tcf(c_1321,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1320,c_90]) ).
tcf(c_1402,plain,
! [X0: $i] :
( equalish(e_4,X0)
| 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(superposition,[status(thm)],[c_80,c_1214]) ).
tcf(c_1403,plain,
! [X0: $i] :
( equalish(e_4,X0)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1402,c_90]) ).
tcf(c_2058,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_2,e_1)
| ~ product(e_3,e_2,X1)
| ~ product(X2,e_3,e_2)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_631]) ).
tcf(c_2059,plain,
( equalish(e_2,e_1)
| ~ product(e_3,e_2,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2058]) ).
tcf(c_2062,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_1,e_2)
| ~ product(e_3,e_2,X1)
| ~ product(X2,e_3,e_2)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_637]) ).
tcf(c_2063,plain,
( equalish(e_1,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2062]) ).
tcf(c_2190,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_1,e_4)
| ~ product(e_3,e_4,X1)
| ~ product(X2,e_3,e_4)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_633]) ).
tcf(c_2191,plain,
( equalish(e_1,e_4)
| ~ product(e_3,e_4,e_1)
| ~ product(e_1,e_3,e_4)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_2190]) ).
tcf(c_2214,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(superposition,[status(thm)],[c_1321,c_1233]) ).
tcf(c_2216,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2214,c_97,c_98,c_91]) ).
tcf(c_2287,plain,
( equalish(e_4,e_3)
| equalish(e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_3) ),
inference(superposition,[status(thm)],[c_1403,c_1242]) ).
tcf(c_2289,plain,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2287,c_97,c_98,c_91]) ).
tcf(c_2367,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_674]) ).
tcf(c_2383,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_675]) ).
tcf(c_2386,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_666]) ).
tcf(c_2410,plain,
! [X0: $i] :
( equalish(e_3,X0)
| product(e_3,e_4,e_1)
| ~ product(X0,e_4,e_2) ),
inference(superposition,[status(thm)],[c_2216,c_77]) ).
tcf(c_2438,plain,
( equalish(e_3,e_1)
| product(e_3,e_4,e_1)
| ~ product(e_1,e_4,e_2) ),
inference(instantiation,[status(thm)],[c_2410]) ).
tcf(c_2441,plain,
product(e_3,e_4,e_1),
inference(global_subsumption_just,[status(thm)],[c_2289,c_92,c_91,c_89,c_88,c_87,c_84,c_99,c_210,c_291,c_686,c_687,c_695,c_701,c_742,c_2063,c_2383,c_2438]) ).
tcf(c_2673,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_697]) ).
tcf(c_2675,plain,
( equalish(e_1,e_2)
| ~ product(e_3,e_2,e_4)
| ~ product(e_3,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_662]) ).
tcf(c_3261,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_654]) ).
tcf(c_4416,plain,
! [X0: $i] :
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_2,X0)
| ~ product(e_2,X0,e_4) ),
inference(instantiation,[status(thm)],[c_1128]) ).
tcf(c_4417,plain,
( equalish(e_2,e_4)
| ~ product(e_4,e_4,e_4)
| ~ product(e_4,e_2,e_1)
| ~ product(e_2,e_1,e_4) ),
inference(instantiation,[status(thm)],[c_4416]) ).
tcf(c_4418,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4417,c_3261,c_2675,c_2673,c_2441,c_2386,c_2367,c_2191,c_2059,c_1125,c_926,c_921,c_717,c_703,c_695,c_694,c_687,c_312,c_269,c_218,c_99,c_85,c_86,c_87,c_88,c_95,c_96,c_89,c_90,c_91,c_92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:38:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running EPR theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.67/1.21 % SZS status Started for theBenchmark.p
% 2.67/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 2.67/1.21
% 2.67/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.67/1.21
% 2.67/1.21 % ------ iProver source info
% 2.67/1.21
% 2.67/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.67/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.67/1.21 % git: non_committed_changes: false
% 2.67/1.21
% 2.67/1.21 % ------ Parsing...% successful
% 2.67/1.21
% 2.67/1.21
% 2.67/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.67/1.21 %
% 2.67/1.21
% 2.67/1.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.67/1.21
% 2.67/1.21 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.67/1.21 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.67/1.21 % ------ Proving...
% 2.67/1.21 % ------ Problem Properties
% 2.67/1.21
% 2.67/1.21 %
% 2.67/1.21 % clauses 25
% 2.67/1.21 % conjectures 2
% 2.67/1.21 % EPR 25
% 2.67/1.21 % Horn 22
% 2.67/1.21 % unary 17
% 2.67/1.21 % binary 0
% 2.67/1.21 % lits 54
% 2.67/1.21 % lits eq 0
% 2.67/1.21 % fd_pure 0
% 2.67/1.21 % fd_pseudo 0
% 2.67/1.21 % fd_cond 0
% 2.67/1.21 % fd_pseudo_cond 0
% 2.67/1.21 % AC symbols 0
% 2.67/1.21
% 2.67/1.21 % ------ Schedule EPR non Horn non eq is on
% 2.67/1.21
% 2.67/1.21 % ------ no equalities: superposition off
% 2.67/1.21
% 2.67/1.21 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.67/1.21
% 2.67/1.21
% 2.67/1.21 % ------
% 2.67/1.21 % Current options:
% 2.67/1.21 % ------
% 2.67/1.21
% 2.67/1.21
% 2.67/1.21 %
% 2.67/1.21
% 2.67/1.21 % ------ Proving...
% 2.67/1.21 %
% 2.67/1.21
% 2.67/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 2.67/1.21
% 2.67/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.67/1.21
% 2.67/1.21
%------------------------------------------------------------------------------