%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:42:35 PM UTC 2026
% Result : Unsatisfiable 0.69s 0.54s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 22
% Syntax : Number of clauses : 160 ( 57 unt; 79 nHn; 160 RR)
% Number of literals : 412 ( 0 equ; 129 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 : 118 ( 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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(qg3_1,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X3,X1,X4)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3_1) ).
cnf(column_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_4,X2)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',column_surjectivity) ).
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_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(row_surjectivity,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',row_surjectivity) ).
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_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
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_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_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(qg3,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
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(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
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_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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_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_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_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(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) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_23,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_22 ).
cnf(c_0_24,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_25,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X3,X1,X4)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[qg3_1]) ).
cnf(c_0_26,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_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X3,X1,X4)
| product(X1,X2,X3) ),
c_0_25 ).
cnf(c_0_28,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ product(X1,e_2,e_1)
| product(e_2,X1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( ~ product(X1,e_2,e_4)
| product(e_2,X1,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_33,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_4,X2)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
inference(fof_simplification,[status(thm)],[column_surjectivity]) ).
cnf(c_0_34,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_35,negated_conjecture,
( ~ product(X1,e_2,e_3)
| product(e_2,X1,e_2)
| product(e_2,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_36,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,e_4,X2)
| product(X1,e_3,X2)
| product(X1,e_2,X2)
| product(X1,e_1,X2) ),
c_0_33 ).
cnf(c_0_37,plain,
~ equalish(e_1,e_2),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_2]) ).
cnf(c_0_38,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_34 ).
cnf(c_0_39,negated_conjecture,
product(e_2,e_2,e_2),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_40,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
inference(fof_simplification,[status(thm)],[row_surjectivity]) ).
cnf(c_0_41,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_42,plain,
( ~ group_element(X1)
| product(X1,e_1,e_2)
| product(X1,e_2,e_2)
| product(X1,e_3,e_2)
| product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_36,c_0_24]) ).
cnf(c_0_43,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_44,plain,
~ equalish(e_1,e_2),
c_0_37 ).
cnf(c_0_45,negated_conjecture,
( ~ product(X1,e_2,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(e_4,X1,X2)
| product(e_3,X1,X2)
| product(e_2,X1,X2)
| product(e_1,X1,X2) ),
c_0_40 ).
cnf(c_0_47,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_41 ).
cnf(c_0_48,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) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( ~ group_element(X1)
| product(e_1,X1,e_2)
| product(e_2,X1,e_2)
| product(e_3,X1,e_2)
| product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_24]) ).
cnf(c_0_51,negated_conjecture,
( ~ product(e_2,X1,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_52,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_53,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( product(e_4,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_55,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_44,c_0_51]) ).
cnf(c_0_56,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_52 ).
cnf(c_0_57,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(e_1,X1,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_53]) ).
cnf(c_0_58,plain,
( product(e_1,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
( ~ product(e_1,e_1,X1)
| product(e_1,e_4,e_2)
| product(e_1,e_3,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_4,e_2)
| product(e_1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_57,c_0_53]) ).
cnf(c_0_61,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_62,plain,
( ~ product(e_1,X1,e_2)
| product(e_4,e_1,e_2)
| product(e_3,e_1,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_47,c_0_58]) ).
cnf(c_0_63,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_44]) ).
cnf(c_0_64,plain,
~ equalish(e_4,e_1),
c_0_61 ).
cnf(c_0_65,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_66,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_67,plain,
~ equalish(e_3,e_1),
c_0_65 ).
cnf(c_0_68,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(e_4,X1,e_1)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_63]) ).
cnf(c_0_69,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_66]),c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_71,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_4,e_4,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
( ~ product(X1,e_4,e_2)
| product(e_1,X1,e_4)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_69]) ).
cnf(c_0_73,plain,
~ equalish(e_4,e_2),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_2]) ).
cnf(c_0_74,negated_conjecture,
( ~ product(X2,X3,X4)
| ~ product(X1,X2,X3)
| product(X3,X1,X4) ),
c_0_70 ).
cnf(c_0_75,negated_conjecture,
( ~ product(X1,e_1,e_2)
| product(e_3,X1,e_1)
| product(e_3,e_1,e_2)
| product(e_4,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_27,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_1,e_4)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_63]) ).
cnf(c_0_77,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_78,plain,
~ equalish(e_4,e_2),
c_0_73 ).
cnf(c_0_79,negated_conjecture,
( ~ product(X1,e_4,e_1)
| product(e_1,X1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_69]) ).
cnf(c_0_80,negated_conjecture,
( product(e_4,e_4,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_69]) ).
cnf(c_0_81,negated_conjecture,
( ~ product(X1,e_1,e_4)
| product(e_1,X1,e_1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_76]) ).
cnf(c_0_82,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_83,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_42,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_78,c_0_45]) ).
cnf(c_0_85,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( ~ product(e_1,e_1,X1)
| product(e_1,e_3,e_2)
| product(e_3,e_1,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_56,c_0_76]) ).
cnf(c_0_87,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2)
| product(e_1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_81,c_0_76]) ).
cnf(c_0_88,plain,
~ equalish(e_1,e_4),
c_0_82 ).
cnf(c_0_89,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_90,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_3,e_2)
| product(e_4,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( ~ product(e_1,X1,e_2)
| product(e_3,e_4,e_1)
| product(e_3,e_1,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_47,c_0_85]) ).
cnf(c_0_92,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_93,plain,
~ equalish(e_3,e_4),
c_0_89 ).
cnf(c_0_94,plain,
( ~ product(X1,e_1,e_2)
| product(e_4,e_4,e_2)
| product(e_4,e_3,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_38,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_96,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_4,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( ~ product(X1,e_4,e_2)
| product(e_4,X1,e_4)
| product(e_3,e_4,e_1)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_27,c_0_96]) ).
cnf(c_0_98,negated_conjecture,
( ~ product(e_4,e_4,X1)
| product(e_3,e_4,e_1)
| product(e_4,e_3,e_2)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_96]) ).
cnf(c_0_99,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_3,e_4,e_1)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_97,c_0_96]) ).
cnf(c_0_100,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_4,e_3,e_1)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_95]) ).
cnf(c_0_101,plain,
( product(e_4,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_50,c_0_77]) ).
cnf(c_0_102,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_78,c_0_51]) ).
cnf(c_0_103,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_78]) ).
cnf(c_0_104,negated_conjecture,
( ~ product(X1,e_3,e_2)
| product(e_3,e_4,e_1)
| product(e_4,e_3,e_1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_38,c_0_100]) ).
cnf(c_0_105,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_106,plain,
( product(e_1,e_4,e_2)
| product(e_3,e_4,e_2)
| product(e_4,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,negated_conjecture,
( ~ product(e_4,e_3,X1)
| product(e_3,e_4,e_1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_103]) ).
cnf(c_0_108,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_103]),c_0_64]) ).
cnf(c_0_109,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_23,c_0_105]) ).
cnf(c_0_110,plain,
( ~ product(e_1,X1,e_2)
| product(e_4,e_4,e_2)
| product(e_3,e_4,e_2)
| equalish(X1,e_4) ),
inference(spm,[status(thm)],[c_0_47,c_0_106]) ).
cnf(c_0_111,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_112,negated_conjecture,
product(e_3,e_4,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_44]) ).
cnf(c_0_113,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_109,c_0_105]) ).
cnf(c_0_114,negated_conjecture,
( ~ product(e_4,X1,e_2)
| product(e_3,e_1,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_47,c_0_69]) ).
cnf(c_0_115,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_4,e_4,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_92]),c_0_93]) ).
cnf(c_0_116,plain,
~ equalish(e_2,e_1),
c_0_111 ).
cnf(c_0_117,negated_conjecture,
( ~ product(e_3,e_4,X1)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_56,c_0_112]) ).
cnf(c_0_118,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_119,negated_conjecture,
( ~ product(X1,e_3,e_1)
| product(e_3,X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_27,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_64]) ).
cnf(c_0_121,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,plain,
~ equalish(e_3,e_2),
c_0_118 ).
cnf(c_0_123,negated_conjecture,
( product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_119,c_0_113]) ).
cnf(c_0_124,negated_conjecture,
product(e_3,e_1,e_2),
inference(sr,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_125,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) ),
inference(spm,[status(thm)],[c_0_109,c_0_24]) ).
cnf(c_0_126,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_122,c_0_51]) ).
cnf(c_0_127,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(e_3,X1,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_27,c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( ~ product(e_3,X1,e_2)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_47,c_0_124]) ).
cnf(c_0_129,negated_conjecture,
( ~ product(X1,e_3,e_1)
| product(e_1,X1,e_2)
| product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_74,c_0_95]) ).
cnf(c_0_130,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,negated_conjecture,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_127,c_0_123]) ).
cnf(c_0_132,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_67,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_49]) ).
cnf(c_0_134,negated_conjecture,
( ~ product(X1,e_3,e_1)
| product(e_1,X1,e_2)
| product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_120]) ).
cnf(c_0_135,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_136,negated_conjecture,
product(e_3,e_3,e_3),
inference(sr,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_2,e_1)
| product(X1,e_3,e_1)
| product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_138,negated_conjecture,
( ~ product(e_2,e_2,X1)
| equalish(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_39]) ).
cnf(c_0_139,negated_conjecture,
( ~ product(e_3,e_4,X1)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| equalish(X1,e_1) ),
inference(spm,[status(thm)],[c_0_56,c_0_133]) ).
cnf(c_0_140,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_130]),c_0_49]) ).
cnf(c_0_141,plain,
~ equalish(e_2,e_3),
c_0_135 ).
cnf(c_0_142,negated_conjecture,
( ~ product(X1,e_3,e_3)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_136]) ).
cnf(c_0_143,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_137,c_0_24]) ).
cnf(c_0_144,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(spm,[status(thm)],[c_0_44,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_116]) ).
cnf(c_0_146,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_147,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_148,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_3,e_1)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_149,negated_conjecture,
( ~ product(X1,e_3,e_4)
| product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_74,c_0_112]) ).
cnf(c_0_150,negated_conjecture,
product(e_2,e_3,e_4),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_151,negated_conjecture,
( ~ product(X1,e_4,e_1)
| equalish(X1,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_112]) ).
cnf(c_0_152,plain,
~ equalish(e_1,e_3),
c_0_147 ).
cnf(c_0_153,negated_conjecture,
( ~ product(X1,e_2,e_1)
| product(e_1,X1,e_1)
| product(e_2,e_4,e_1)
| product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_74,c_0_148]) ).
cnf(c_0_154,negated_conjecture,
product(e_4,e_2,e_1),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_155,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(spm,[status(thm)],[c_0_141,c_0_151]) ).
cnf(c_0_156,negated_conjecture,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_152,c_0_151]) ).
cnf(c_0_157,negated_conjecture,
( ~ product(X1,e_3,e_1)
| product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_124]) ).
cnf(c_0_158,negated_conjecture,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_155]),c_0_156]) ).
cnf(c_0_159,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP129-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:03:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.69/0.54 % Version: 3.5.1
% 0.69/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.69/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.69/0.54 % Starting sh5l with 300s (1) cores
% 0.69/0.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1580932 completed with status 0
% 0.69/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.69/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.54 % No SInE strategy applied
% 0.69/0.54 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.69/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.69/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.69/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.69/0.54 % Starting new_bool_1 with 136s (1) cores
% 0.69/0.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1580938 completed with status 0
% 0.69/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.69/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.69/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.69/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.69/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.69/0.54 % No SInE strategy applied
% 0.69/0.54 % Search class: FGUNF-FFSS00-SFFFFFNN
% 0.69/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.69/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.69/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.69/0.54 % Preprocessing time : 0.001 s
% 0.69/0.54 % Presaturation interreduction done
% 0.69/0.54
% 0.69/0.54 % Proof found!
% 0.69/0.54 % SZS status Unsatisfiable
% 0.69/0.54 % SZS output start CNFRefutation
% See solution above
% 0.69/0.54 % Parsed axioms : 25
% 0.69/0.54 % Removed by relevancy pruning/SinE : 0
% 0.69/0.54 % Initial clauses : 25
% 0.69/0.54 % Removed in clause preprocessing : 0
% 0.69/0.54 % Initial clauses in saturation : 25
% 0.69/0.54 % Processed clauses : 1182
% 0.69/0.54 % ...of these trivial : 3
% 0.69/0.54 % ...subsumed : 328
% 0.69/0.54 % ...remaining for further processing : 851
% 0.69/0.54 % Other redundant clauses eliminated : 0
% 0.69/0.54 % Clauses deleted for lack of memory : 0
% 0.69/0.54 % Backward-subsumed : 290
% 0.69/0.54 % Backward-rewritten : 135
% 0.69/0.54 % Generated clauses : 4417
% 0.69/0.54 % ...of the previous two non-redundant : 4360
% 0.69/0.54 % ...aggressively subsumed : 0
% 0.69/0.54 % Contextual simplify-reflections : 7
% 0.69/0.54 % Paramodulations : 4300
% 0.69/0.54 % Factorizations : 0
% 0.69/0.54 % NegExts : 0
% 0.69/0.54 % Equation resolutions : 0
% 0.69/0.54 % Disequality decompositions : 0
% 0.69/0.54 % Total rewrite steps : 178
% 0.69/0.54 % ...of those cached : 166
% 0.69/0.54 % Propositional unsat checks : 0
% 0.69/0.54 % Propositional check models : 0
% 0.69/0.54 % Propositional check unsatisfiable : 0
% 0.69/0.54 % Propositional clauses : 0
% 0.69/0.54 % Propositional clauses after purity: 0
% 0.69/0.54 % Propositional unsat core size : 0
% 0.69/0.54 % Propositional preprocessing time : 0.000
% 0.69/0.54 % Propositional encoding time : 0.000
% 0.69/0.54 % Propositional solver time : 0.000
% 0.69/0.54 % Success case prop preproc time : 0.000
% 0.69/0.54 % Success case prop encoding time : 0.000
% 0.69/0.54 % Success case prop solver time : 0.000
% 0.69/0.54 % Current number of processed clauses : 284
% 0.69/0.54 % Positive orientable unit clauses : 16
% 0.69/0.54 % Positive unorientable unit clauses: 0
% 0.69/0.54 % Negative unit clauses : 38
% 0.69/0.54 % Non-unit-clauses : 230
% 0.69/0.54 % Current number of unprocessed clauses: 3063
% 0.69/0.54 % ...number of literals in the above : 15723
% 0.69/0.54 % Current number of archived formulas : 0
% 0.69/0.54 % Current number of archived clauses : 567
% 0.69/0.54 % Clause-clause subsumption calls (NU) : 27038
% 0.69/0.54 % Rec. Clause-clause subsumption calls : 8916
% 0.69/0.54 % Non-unit clause-clause subsumptions : 549
% 0.69/0.54 % Unit Clause-clause subsumption calls : 2136
% 0.69/0.54 % Rewrite failures with RHS unbound : 0
% 0.69/0.54 % BW rewrite match attempts : 44
% 0.69/0.54 % BW rewrite match successes : 12
% 0.69/0.54 % Condensation attempts : 0
% 0.69/0.54 % Condensation successes : 0
% 0.69/0.54 % Termbank termtop insertions : 80570
% 0.69/0.54 % Search garbage collected termcells : 60
% 0.69/0.54
% 0.69/0.54 % -------------------------------------------------
% 0.69/0.54 % User time : 0.071 s
% 0.69/0.54 % System time : 0.004 s
% 0.69/0.54 % Total time : 0.075 s
% 0.69/0.54 % Maximum resident set size: 3644 pages
% 0.69/0.54
% 0.69/0.54 % -------------------------------------------------
% 0.69/0.54 % User time : 0.410 s
% 0.69/0.54 % System time : 0.026 s
% 0.69/0.54 % Total time : 0.436 s
% 0.69/0.54 % Maximum resident set size: 4608 pages
% 0.69/0.54 % E exiting
%------------------------------------------------------------------------------