%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP134-1.003 : 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 12:38:43 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.57s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of clauses : 156 ( 40 unt; 72 nHn; 156 RR)
% Number of literals : 385 ( 0 equ; 156 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 94 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| 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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
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(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(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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(qg4,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg4) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
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(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(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
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(c_0_14,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| 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_15,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_14 ).
cnf(c_0_16,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_17,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_18,plain,
( ~ group_element(X1)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_20,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_17 ).
cnf(c_0_21,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_22,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_23,plain,
~ equalish(e_2,e_3),
c_0_19 ).
cnf(c_0_24,plain,
( ~ product(e_3,X1,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_22 ).
cnf(c_0_26,plain,
( ~ product(e_3,e_2,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_28,plain,
( ~ product(X1,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[qg4]) ).
cnf(c_0_30,plain,
( ~ group_element(X1)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_31,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_32,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_33,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_34,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X2) ),
c_0_29 ).
cnf(c_0_36,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_37,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_38,plain,
( ~ group_element(X1)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_15,c_0_32]) ).
cnf(c_0_39,plain,
~ equalish(e_1,e_3),
c_0_33 ).
cnf(c_0_40,plain,
( ~ product(X1,e_3,e_2)
| ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( ~ product(e_2,e_2,X1)
| product(X1,e_1,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_43,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_44,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_27]) ).
cnf(c_0_45,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_3,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35]) ).
cnf(c_0_46,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_47,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_48,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_41,c_0_36]) ).
cnf(c_0_49,plain,
( ~ product(e_2,X1,e_3)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_42]) ).
cnf(c_0_50,plain,
~ equalish(e_2,e_1),
c_0_43 ).
cnf(c_0_51,plain,
( ~ product(e_2,X1,e_1)
| equalish(X1,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_44]) ).
cnf(c_0_52,plain,
( ~ product(e_2,e_3,e_3)
| product(e_3,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_35]) ).
cnf(c_0_53,plain,
~ equalish(e_1,e_2),
c_0_47 ).
cnf(c_0_54,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_55,negated_conjecture,
( ~ product(e_1,X1,e_2)
| equalish(X1,e_1)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_48]) ).
cnf(c_0_56,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_49]) ).
cnf(c_0_57,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,plain,
( ~ product(X1,e_2,e_3)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_52]) ).
cnf(c_0_59,plain,
( ~ product(e_1,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_61,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_55]) ).
cnf(c_0_62,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_58]) ).
cnf(c_0_64,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]) ).
cnf(c_0_65,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_58]) ).
cnf(c_0_66,plain,
( ~ product(e_2,X1,e_2)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_62]) ).
cnf(c_0_67,plain,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_68,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
cnf(c_0_69,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_42]),c_0_68]) ).
cnf(c_0_70,plain,
( ~ product(X1,e_2,e_1)
| equalish(X1,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_71,negated_conjecture,
( ~ product(e_3,e_2,X1)
| ~ product(e_2,e_2,e_1)
| product(X1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_69]) ).
cnf(c_0_72,plain,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_70]) ).
cnf(c_0_73,plain,
( ~ product(e_2,X1,e_2)
| ~ product(e_2,e_2,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_23,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_74]),c_0_75]) ).
cnf(c_0_77,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(sr,[status(thm)],[c_0_36,c_0_76]) ).
cnf(c_0_78,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_79,negated_conjecture,
( ~ product(e_2,e_2,X1)
| product(X1,e_3,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_77]) ).
cnf(c_0_80,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_81,plain,
( ~ product(X1,e_1,e_1)
| equalish(X1,e_3)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_79,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( ~ product(e_3,e_1,X1)
| product(X1,e_1,e_1)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_80]) ).
cnf(c_0_84,plain,
( ~ product(e_1,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_81]) ).
cnf(c_0_85,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( ~ product(e_1,e_3,X1)
| product(X1,e_1,e_3)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_78]) ).
cnf(c_0_87,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_78]),c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( ~ product(e_3,X1,e_2)
| equalish(X1,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_82]) ).
cnf(c_0_89,negated_conjecture,
( ~ product(e_1,e_3,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_85]) ).
cnf(c_0_90,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_39,c_0_88]) ).
cnf(c_0_92,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_93,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_3,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_94,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_95,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_92 ).
cnf(c_0_96,negated_conjecture,
( ~ product(e_1,e_3,X1)
| product(X1,e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_93]) ).
cnf(c_0_97,plain,
~ equalish(e_3,e_2),
c_0_94 ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_3,e_3,X1)
| equalish(X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_95,c_0_82]) ).
cnf(c_0_99,negated_conjecture,
( product(e_2,e_2,e_2)
| product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_80]),c_0_89]) ).
cnf(c_0_100,negated_conjecture,
( ~ product(e_3,e_3,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
product(e_2,e_2,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_99]),c_0_100]) ).
cnf(c_0_102,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_101]) ).
cnf(c_0_103,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_53,c_0_102]) ).
cnf(c_0_104,plain,
( ~ product(e_2,e_1,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_37]) ).
cnf(c_0_105,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_44,c_0_103]) ).
cnf(c_0_106,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_97,c_0_102]) ).
cnf(c_0_107,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]) ).
cnf(c_0_108,plain,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_3,e_3)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_52]) ).
cnf(c_0_109,plain,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_107]) ).
cnf(c_0_110,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_53,c_0_108]) ).
cnf(c_0_111,plain,
~ product(e_3,e_1,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_109]),c_0_110]) ).
cnf(c_0_112,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_113,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_90,c_0_111]) ).
cnf(c_0_114,plain,
~ equalish(e_3,e_1),
c_0_112 ).
cnf(c_0_115,negated_conjecture,
( ~ product(X1,e_3,e_2)
| equalish(X1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( ~ product(e_3,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_117,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_101]) ).
cnf(c_0_118,negated_conjecture,
( ~ product(e_3,e_3,X1)
| product(X1,e_1,e_3)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_119,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_31,c_0_106]) ).
cnf(c_0_120,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_3,e_3,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_20,c_0_116]) ).
cnf(c_0_121,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_53,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
( product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_118,c_0_21]) ).
cnf(c_0_123,plain,
( ~ product(X1,e_3,e_1)
| equalish(X1,e_2)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_119]) ).
cnf(c_0_124,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_114,c_0_120]) ).
cnf(c_0_125,plain,
( ~ product(e_1,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_39,c_0_70]) ).
cnf(c_0_126,plain,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_60,c_0_121]) ).
cnf(c_0_127,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_97,c_0_117]) ).
cnf(c_0_128,negated_conjecture,
( ~ product(X1,e_1,e_3)
| equalish(X1,e_1)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_25,c_0_122]) ).
cnf(c_0_129,plain,
( ~ product(e_3,e_3,e_1)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_97,c_0_123]) ).
cnf(c_0_130,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_21,c_0_124]) ).
cnf(c_0_131,plain,
( product(e_3,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_127]) ).
cnf(c_0_132,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_128]) ).
cnf(c_0_133,plain,
( product(e_2,e_3,e_3)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_134,negated_conjecture,
( ~ product(e_2,e_3,X1)
| product(X1,e_1,e_3)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_135,plain,
( ~ product(e_1,X1,e_3)
| equalish(X1,e_2)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
( ~ product(e_3,X1,e_3)
| ~ product(e_2,e_1,e_3)
| equalish(X1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_20,c_0_132]) ).
cnf(c_0_137,plain,
( ~ product(e_3,X1,e_3)
| equalish(X1,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_20,c_0_133]) ).
cnf(c_0_138,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_1,e_1,e_3)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_31]),c_0_52]) ).
cnf(c_0_139,plain,
( ~ product(e_1,e_1,e_3)
| product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_53,c_0_135]) ).
cnf(c_0_140,plain,
( ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_81]) ).
cnf(c_0_141,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_1,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_23,c_0_136]) ).
cnf(c_0_142,plain,
( ~ product(e_3,e_2,e_3)
| product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_23,c_0_137]) ).
cnf(c_0_143,negated_conjecture,
product(e_3,e_2,e_3),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_138,c_0_106]),c_0_127]),c_0_139]) ).
cnf(c_0_144,plain,
( ~ product(e_2,e_1,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_111,c_0_140]) ).
cnf(c_0_145,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_124,c_0_141]) ).
cnf(c_0_146,plain,
product(e_2,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_143])]) ).
cnf(c_0_147,plain,
( ~ product(X1,e_1,e_2)
| ~ product(e_2,e_1,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_25,c_0_144]) ).
cnf(c_0_148,negated_conjecture,
~ product(e_2,e_1,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_143])]) ).
cnf(c_0_149,plain,
~ product(e_1,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_146])]) ).
cnf(c_0_150,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_39,c_0_147]) ).
cnf(c_0_151,plain,
product(e_2,e_1,e_1),
inference(sr,[status(thm)],[c_0_105,c_0_148]) ).
cnf(c_0_152,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_153,plain,
product(e_1,e_2,e_1),
inference(sr,[status(thm)],[c_0_126,c_0_149]) ).
cnf(c_0_154,plain,
~ product(e_1,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151])]) ).
cnf(c_0_155,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_103]),c_0_148]),c_0_154]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP134-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:03:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 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
% 0.28/0.57 % Version: 3.5.1
% 0.28/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.57 % Starting sh5l with 300s (1) cores
% 0.28/0.57 % new_bool_1 with pid 64210 completed with status 0
% 0.28/0.57 % Result found by new_bool_1
% 0.28/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.57 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.28/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.57 % SubtermCWHack with pid 64215 completed with status 0
% 0.28/0.57 % Result found by SubtermCWHack
% 0.28/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.57 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.28/0.57 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.57 % Starting SubtermCWHack with 31s (1) cores
% 0.28/0.57 % Preprocessing time : 0.002 s
% 0.28/0.57
% 0.28/0.57 % Proof found!
% 0.28/0.57 % SZS status Unsatisfiable
% 0.28/0.57 % SZS output start CNFRefutation
% See solution above
% 0.28/0.57 % Parsed axioms : 14
% 0.28/0.57 % Removed by relevancy pruning/SinE : 0
% 0.28/0.57 % Initial clauses : 14
% 0.28/0.57 % Removed in clause preprocessing : 0
% 0.28/0.57 % Initial clauses in saturation : 14
% 0.28/0.57 % Processed clauses : 893
% 0.28/0.57 % ...of these trivial : 3
% 0.28/0.57 % ...subsumed : 263
% 0.28/0.57 % ...remaining for further processing : 627
% 0.28/0.57 % Other redundant clauses eliminated : 0
% 0.28/0.57 % Clauses deleted for lack of memory : 0
% 0.28/0.57 % Backward-subsumed : 357
% 0.28/0.57 % Backward-rewritten : 137
% 0.28/0.57 % Generated clauses : 2467
% 0.28/0.57 % ...of the previous two non-redundant : 2363
% 0.28/0.57 % ...aggressively subsumed : 0
% 0.28/0.57 % Contextual simplify-reflections : 22
% 0.28/0.57 % Paramodulations : 2432
% 0.28/0.57 % Factorizations : 0
% 0.28/0.57 % NegExts : 0
% 0.28/0.57 % Equation resolutions : 0
% 0.28/0.57 % Disequality decompositions : 0
% 0.28/0.57 % Total rewrite steps : 142
% 0.28/0.57 % ...of those cached : 136
% 0.28/0.57 % Propositional unsat checks : 0
% 0.28/0.57 % Propositional check models : 0
% 0.28/0.57 % Propositional check unsatisfiable : 0
% 0.28/0.57 % Propositional clauses : 0
% 0.28/0.57 % Propositional clauses after purity: 0
% 0.28/0.57 % Propositional unsat core size : 0
% 0.28/0.57 % Propositional preprocessing time : 0.000
% 0.28/0.57 % Propositional encoding time : 0.000
% 0.28/0.57 % Propositional solver time : 0.000
% 0.28/0.57 % Success case prop preproc time : 0.000
% 0.28/0.57 % Success case prop encoding time : 0.000
% 0.28/0.57 % Success case prop solver time : 0.000
% 0.28/0.57 % Current number of processed clauses : 98
% 0.28/0.57 % Positive orientable unit clauses : 9
% 0.28/0.57 % Positive unorientable unit clauses: 0
% 0.28/0.57 % Negative unit clauses : 22
% 0.28/0.57 % Non-unit-clauses : 67
% 0.28/0.57 % Current number of unprocessed clauses: 1354
% 0.28/0.57 % ...number of literals in the above : 5482
% 0.28/0.57 % Current number of archived formulas : 0
% 0.28/0.57 % Current number of archived clauses : 529
% 0.28/0.57 % Clause-clause subsumption calls (NU) : 8260
% 0.28/0.57 % Rec. Clause-clause subsumption calls : 6502
% 0.28/0.57 % Non-unit clause-clause subsumptions : 433
% 0.28/0.57 % Unit Clause-clause subsumption calls : 1067
% 0.28/0.57 % Rewrite failures with RHS unbound : 0
% 0.28/0.57 % BW rewrite match attempts : 24
% 0.28/0.57 % BW rewrite match successes : 6
% 0.28/0.57 % Condensation attempts : 0
% 0.28/0.57 % Condensation successes : 0
% 0.28/0.57 % Termbank termtop insertions : 29132
% 0.28/0.57 % Search garbage collected termcells : 36
% 0.28/0.57
% 0.28/0.57 % -------------------------------------------------
% 0.28/0.57 % User time : 0.063 s
% 0.28/0.57 % System time : 0.003 s
% 0.28/0.57 % Total time : 0.066 s
% 0.28/0.57 % Maximum resident set size: 3636 pages
% 0.28/0.57
% 0.28/0.57 % -------------------------------------------------
% 0.28/0.57 % User time : 0.069 s
% 0.28/0.57 % System time : 0.006 s
% 0.28/0.57 % Total time : 0.075 s
% 0.28/0.57 % Maximum resident set size: 4864 pages
% 0.28/0.57 % E exiting
%------------------------------------------------------------------------------