%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Thu Sep 24 12:37:58 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.62s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of clauses : 142 ( 50 unt; 34 nHn; 140 RR)
% Number of literals : 320 ( 0 equ; 170 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% 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 : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(qg2_2,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg2_2) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(c_0_20,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_21,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_22,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_20 ).
cnf(c_0_23,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_24,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_25,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_21 ).
cnf(c_0_26,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_27,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3)
| product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_29,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_30,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_31,plain,
( ~ group_element(X1)
| product(X1,e_4,e_1)
| product(X1,e_4,e_2)
| product(X1,e_4,e_3)
| product(X1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_32,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_33,plain,
( ~ product(X2,X1,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,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) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
~ equalish(e_3,e_1),
c_0_29 ).
cnf(c_0_36,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_30 ).
cnf(c_0_37,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) ),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_38,plain,
~ equalish(e_4,e_1),
c_0_32 ).
cnf(c_0_39,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_40,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_41,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_42,plain,
( ~ product(X1,X2,X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_26]) ).
cnf(c_0_43,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_37]),c_0_38]) ).
cnf(c_0_44,plain,
~ equalish(e_1,e_4),
c_0_39 ).
cnf(c_0_45,plain,
~ equalish(e_2,e_3),
c_0_40 ).
cnf(c_0_46,plain,
( ~ product(e_1,X1,e_4)
| equalish(X1,e_3)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_41]) ).
cnf(c_0_47,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_48,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
inference(fof_simplification,[status(thm)],[qg2_2]) ).
cnf(c_0_49,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_50,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_51,plain,
( ~ product(e_1,e_2,e_4)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
~ equalish(e_1,e_3),
c_0_47 ).
cnf(c_0_53,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_54,negated_conjecture,
( ~ product(X6,X4,X5)
| ~ product(X6,X1,X2)
| ~ product(X4,X5,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X5) ),
c_0_48 ).
cnf(c_0_55,plain,
~ equalish(e_2,e_4),
c_0_49 ).
cnf(c_0_56,plain,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_50]) ).
cnf(c_0_57,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_58,plain,
( ~ product(e_1,e_2,e_4)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_51]),c_0_52]) ).
cnf(c_0_59,plain,
( ~ group_element(X1)
| product(X1,e_2,e_1)
| product(X1,e_2,e_2)
| product(X1,e_2,e_3)
| product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_22,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( ~ product(X3,X1,X4)
| ~ product(X2,X2,X4)
| ~ product(X2,X3,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_26]) ).
cnf(c_0_61,plain,
( ~ product(e_1,e_2,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_62,plain,
~ equalish(e_2,e_1),
c_0_57 ).
cnf(c_0_63,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_1,e_2,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_58]) ).
cnf(c_0_64,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) ),
inference(spm,[status(thm)],[c_0_59,c_0_28]) ).
cnf(c_0_65,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_1,e_1,X1)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_50]),c_0_35]) ).
cnf(c_0_66,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_1,e_1,X1)
| ~ product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).
cnf(c_0_67,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_38,c_0_63]) ).
cnf(c_0_68,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_64]),c_0_62]) ).
cnf(c_0_69,plain,
( ~ product(X1,e_4,e_3)
| equalish(X1,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_50]) ).
cnf(c_0_70,negated_conjecture,
( ~ product(e_4,e_3,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_26]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_72,plain,
( ~ product(e_4,e_3,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_74,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_75,plain,
( ~ product(e_3,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_1,e_1,X1)
| ~ product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_70]),c_0_62]) ).
cnf(c_0_77,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_2,e_1)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
~ equalish(e_1,e_2),
c_0_73 ).
cnf(c_0_79,plain,
~ equalish(e_3,e_4),
c_0_74 ).
cnf(c_0_80,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_3,e_4,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_25,c_0_75]) ).
cnf(c_0_81,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_76,c_0_26]) ).
cnf(c_0_82,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) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_83,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_77]),c_0_78]) ).
cnf(c_0_84,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_86,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_87,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_62,c_0_69]) ).
cnf(c_0_88,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_84,c_0_58]) ).
cnf(c_0_89,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
( ~ product(e_4,e_2,e_1)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_85]),c_0_79]) ).
cnf(c_0_91,plain,
~ equalish(e_4,e_3),
c_0_86 ).
cnf(c_0_92,plain,
( ~ product(X1,e_4,e_2)
| ~ product(e_1,e_2,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_61]) ).
cnf(c_0_93,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_25,c_0_87]) ).
cnf(c_0_94,plain,
( ~ product(e_3,e_4,e_3)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_68]),c_0_89]) ).
cnf(c_0_95,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) ),
inference(spm,[status(thm)],[c_0_59,c_0_24]) ).
cnf(c_0_96,negated_conjecture,
~ product(e_4,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_90]),c_0_91]) ).
cnf(c_0_97,plain,
( ~ product(e_3,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_35,c_0_92]) ).
cnf(c_0_98,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_93]) ).
cnf(c_0_99,negated_conjecture,
( ~ product(e_3,e_4,X1)
| ~ product(e_1,e_1,X1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_41]),c_0_38]) ).
cnf(c_0_100,plain,
( ~ product(X1,e_2,e_3)
| ~ product(e_3,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_94]) ).
cnf(c_0_101,plain,
( product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference(sr,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(e_4,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_70]) ).
cnf(c_0_103,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_4,e_2)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_97,c_0_72]) ).
cnf(c_0_104,plain,
( ~ product(e_1,e_2,e_4)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_98,c_0_58]) ).
cnf(c_0_105,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_55,c_0_93]) ).
cnf(c_0_106,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_99,c_0_26]) ).
cnf(c_0_107,plain,
( ~ product(e_4,e_2,e_3)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_100]) ).
cnf(c_0_108,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_101]),c_0_55]) ).
cnf(c_0_109,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_110,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_35,c_0_102]) ).
cnf(c_0_111,plain,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_103]),c_0_78]) ).
cnf(c_0_112,plain,
( ~ product(e_2,e_4,e_3)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_68]),c_0_105]) ).
cnf(c_0_113,plain,
( ~ product(e_1,X1,e_2)
| ~ product(e_1,e_2,e_3)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_114,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_106]),c_0_52]) ).
cnf(c_0_115,plain,
( ~ product(e_3,e_4,e_3)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_116,plain,
~ equalish(e_4,e_2),
c_0_109 ).
cnf(c_0_117,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_82]),c_0_111]) ).
cnf(c_0_118,plain,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_4,e_3)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_112]) ).
cnf(c_0_119,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
( ~ product(e_2,e_4,X1)
| ~ product(e_1,e_1,X1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_68]),c_0_38]) ).
cnf(c_0_121,negated_conjecture,
( ~ product(e_1,X1,e_2)
| ~ product(e_3,e_4,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_114]) ).
cnf(c_0_122,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) ),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_123,plain,
~ product(e_3,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_115]),c_0_116]) ).
cnf(c_0_124,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_117]),c_0_79]) ).
cnf(c_0_125,plain,
( ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_118]) ).
cnf(c_0_126,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_119,c_0_114]) ).
cnf(c_0_127,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_120,c_0_26]) ).
cnf(c_0_128,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_45,c_0_121]) ).
cnf(c_0_129,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_130,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_124]),c_0_91]) ).
cnf(c_0_131,plain,
( ~ product(e_2,e_4,e_3)
| product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_125,c_0_108]) ).
cnf(c_0_132,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_3,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_133,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,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) ),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
cnf(c_0_135,plain,
~ product(e_2,e_4,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_131]),c_0_116]) ).
cnf(c_0_136,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_138,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_136]),c_0_79]) ).
cnf(c_0_139,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_140,plain,
product(e_2,e_4,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_139]),c_0_55]) ).
cnf(c_0_141,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_140]),c_0_116]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n018.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 20:00:43 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.53 Running first-order theorem proving
% 0.23/0.53 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.62 % Version: 3.5.1
% 0.23/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.62 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.62 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.62 % Starting sh5l with 300s (1) cores
% 0.23/0.62 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 57712 completed with status 0
% 0.23/0.62 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.62 % No SInE strategy applied
% 0.23/0.62 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.23/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.23/0.62 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.62 % Starting new_bool_1 with 136s (1) cores
% 0.23/0.62 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 57719 completed with status 0
% 0.23/0.62 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.23/0.62 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.62 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.62 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.62 % No SInE strategy applied
% 0.23/0.62 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.23/0.62 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.62 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.62 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.23/0.62 % Preprocessing time : 0.002 s
% 0.23/0.62 % Presaturation interreduction done
% 0.23/0.62
% 0.23/0.62 % Proof found!
% 0.23/0.62 % SZS status Unsatisfiable
% 0.23/0.62 % SZS output start CNFRefutation
% See solution above
% 0.23/0.63 % Parsed axioms : 23
% 0.23/0.63 % Removed by relevancy pruning/SinE : 0
% 0.23/0.63 % Initial clauses : 23
% 0.23/0.63 % Removed in clause preprocessing : 0
% 0.23/0.63 % Initial clauses in saturation : 23
% 0.23/0.63 % Processed clauses : 508
% 0.23/0.63 % ...of these trivial : 0
% 0.23/0.63 % ...subsumed : 89
% 0.23/0.63 % ...remaining for further processing : 419
% 0.23/0.63 % Other redundant clauses eliminated : 0
% 0.23/0.63 % Clauses deleted for lack of memory : 0
% 0.23/0.63 % Backward-subsumed : 180
% 0.23/0.63 % Backward-rewritten : 5
% 0.23/0.63 % Generated clauses : 1267
% 0.23/0.63 % ...of the previous two non-redundant : 1226
% 0.23/0.63 % ...aggressively subsumed : 0
% 0.23/0.63 % Contextual simplify-reflections : 8
% 0.23/0.63 % Paramodulations : 1259
% 0.23/0.63 % Factorizations : 0
% 0.23/0.63 % NegExts : 0
% 0.23/0.63 % Equation resolutions : 0
% 0.23/0.63 % Disequality decompositions : 0
% 0.23/0.63 % Total rewrite steps : 32
% 0.23/0.63 % ...of those cached : 24
% 0.23/0.63 % Propositional unsat checks : 0
% 0.23/0.63 % Propositional check models : 0
% 0.23/0.63 % Propositional check unsatisfiable : 0
% 0.23/0.63 % Propositional clauses : 0
% 0.23/0.63 % Propositional clauses after purity: 0
% 0.23/0.63 % Propositional unsat core size : 0
% 0.23/0.63 % Propositional preprocessing time : 0.000
% 0.23/0.63 % Propositional encoding time : 0.000
% 0.23/0.63 % Propositional solver time : 0.000
% 0.23/0.63 % Success case prop preproc time : 0.000
% 0.23/0.63 % Success case prop encoding time : 0.000
% 0.23/0.63 % Success case prop solver time : 0.000
% 0.23/0.63 % Current number of processed clauses : 203
% 0.23/0.63 % Positive orientable unit clauses : 7
% 0.23/0.63 % Positive unorientable unit clauses: 0
% 0.23/0.63 % Negative unit clauses : 22
% 0.23/0.63 % Non-unit-clauses : 174
% 0.23/0.63 % Current number of unprocessed clauses: 472
% 0.23/0.63 % ...number of literals in the above : 2294
% 0.23/0.63 % Current number of archived formulas : 0
% 0.23/0.63 % Current number of archived clauses : 216
% 0.23/0.63 % Clause-clause subsumption calls (NU) : 6031
% 0.23/0.63 % Rec. Clause-clause subsumption calls : 3110
% 0.23/0.63 % Non-unit clause-clause subsumptions : 129
% 0.23/0.63 % Unit Clause-clause subsumption calls : 891
% 0.23/0.63 % Rewrite failures with RHS unbound : 0
% 0.23/0.63 % BW rewrite match attempts : 18
% 0.23/0.63 % BW rewrite match successes : 1
% 0.23/0.63 % Condensation attempts : 0
% 0.23/0.63 % Condensation successes : 0
% 0.23/0.63 % Termbank termtop insertions : 15625
% 0.23/0.63 % Search garbage collected termcells : 57
% 0.23/0.63
% 0.23/0.63 % -------------------------------------------------
% 0.23/0.63 % User time : 0.067 s
% 0.23/0.63 % System time : 0.006 s
% 0.23/0.63 % Total time : 0.074 s
% 0.23/0.63 % Maximum resident set size: 3592 pages
% 0.23/0.63
% 0.23/0.63 % -------------------------------------------------
% 0.23/0.63 % User time : 0.283 s
% 0.23/0.63 % System time : 0.024 s
% 0.23/0.63 % Total time : 0.307 s
% 0.23/0.63 % Maximum resident set size: 4608 pages
% 0.23/0.63 % E exiting
%------------------------------------------------------------------------------