%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP125-2.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:41:56 PM UTC 2026
% Result : Unsatisfiable 2.35s 0.84s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 81
% Number of leaves : 30
% Syntax : Number of clauses : 343 ( 99 unt; 175 nHn; 341 RR)
% Number of literals : 905 ( 0 equ; 241 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 152 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_5) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(no_redundancy,axiom,
( ~ greater(X2,X3)
| ~ next(X1,X3)
| ~ product(X1,e_1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_5,axiom,
group_element(e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_5) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(e_5_greater_e_4,axiom,
greater(e_5,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_4) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_5) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_3) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_greater_e_3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_5) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_4) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_4_is_not_e_5) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(qg3,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_greater_e_2) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_5_greater_e_2) ).
cnf(c_0_30,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| 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_31,plain,
~ equalish(e_1,e_5),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_5]) ).
cnf(c_0_32,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_33,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_30 ).
cnf(c_0_34,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_35,plain,
~ equalish(e_1,e_5),
c_0_31 ).
cnf(c_0_36,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_32 ).
cnf(c_0_37,plain,
( ~ greater(X2,X3)
| ~ next(X1,X3)
| ~ product(X1,e_1,X2) ),
inference(fof_simplification,[status(thm)],[no_redundancy]) ).
cnf(c_0_38,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_39,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_1,e_2)
| product(X1,e_1,e_3)
| product(X1,e_1,e_4)
| product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,axiom,
group_element(e_5),
element_5 ).
cnf(c_0_41,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_43,plain,
( ~ greater(X2,X3)
| ~ next(X1,X3)
| ~ product(X1,e_1,X2) ),
c_0_37 ).
cnf(c_0_44,axiom,
greater(e_5,e_4),
e_5_greater_e_4 ).
cnf(c_0_45,plain,
~ equalish(e_1,e_3),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_3]) ).
cnf(c_0_46,plain,
~ equalish(e_3,e_5),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_5]) ).
cnf(c_0_47,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_38 ).
cnf(c_0_48,plain,
( product(e_5,e_1,e_5)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,plain,
~ product(e_5,e_1,e_1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_51,plain,
( ~ next(X1,e_4)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,axiom,
next(e_3,e_4),
e_3_then_e_4 ).
cnf(c_0_53,plain,
~ equalish(e_1,e_3),
c_0_45 ).
cnf(c_0_54,axiom,
greater(e_5,e_3),
e_5_greater_e_3 ).
cnf(c_0_55,plain,
~ equalish(e_3,e_5),
c_0_46 ).
cnf(c_0_56,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_57,plain,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_5) ),
inference(sr,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_58,plain,
( product(e_3,e_1,e_5)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_39,c_0_50]) ).
cnf(c_0_59,plain,
~ product(e_3,e_1,e_5),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_36]) ).
cnf(c_0_61,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_62,plain,
( ~ next(X1,e_3)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_63,axiom,
next(e_2,e_3),
e_2_then_e_3 ).
cnf(c_0_64,axiom,
greater(e_4,e_3),
e_4_greater_e_3 ).
cnf(c_0_65,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_66,plain,
~ equalish(e_2,e_5),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_5]) ).
cnf(c_0_67,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_36]) ).
cnf(c_0_68,plain,
( product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_42])]) ).
cnf(c_0_69,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_60,c_0_42]) ).
cnf(c_0_71,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_72,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_39,c_0_61]) ).
cnf(c_0_73,plain,
~ product(e_2,e_1,e_5),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_74,plain,
( ~ next(X1,e_3)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_43,c_0_64]) ).
cnf(c_0_75,plain,
~ equalish(e_2,e_1),
c_0_65 ).
cnf(c_0_76,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_77,plain,
~ equalish(e_2,e_5),
c_0_66 ).
cnf(c_0_78,plain,
( ~ product(e_3,e_1,e_4)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_79,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
~ equalish(e_2,e_3),
c_0_71 ).
cnf(c_0_81,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_82,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_74,c_0_63]) ).
cnf(c_0_83,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_36]) ).
cnf(c_0_84,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_85,plain,
~ equalish(e_1,e_4),
c_0_76 ).
cnf(c_0_86,plain,
~ equalish(e_4,e_5),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_5]) ).
cnf(c_0_87,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_36]) ).
cnf(c_0_88,plain,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_89,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_36]) ).
cnf(c_0_90,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(sr,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_83,c_0_42]) ).
cnf(c_0_92,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_93,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_94,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)
| product(X1,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_33,c_0_84]) ).
cnf(c_0_95,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_47]) ).
cnf(c_0_96,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_36]) ).
cnf(c_0_97,plain,
~ equalish(e_4,e_5),
c_0_86 ).
cnf(c_0_98,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
cnf(c_0_99,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_100,plain,
~ equalish(e_3,e_4),
c_0_92 ).
cnf(c_0_101,plain,
~ equalish(e_2,e_4),
c_0_93 ).
cnf(c_0_102,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_103,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_104,plain,
( product(e_1,e_4,e_5)
| 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_94,c_0_34]) ).
cnf(c_0_105,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_95,c_0_42]) ).
cnf(c_0_106,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_39,c_0_84]) ).
cnf(c_0_107,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_96,c_0_42]) ).
cnf(c_0_108,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_36]) ).
cnf(c_0_109,plain,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_110,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_36]) ).
cnf(c_0_111,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_36]) ).
cnf(c_0_112,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_102 ).
cnf(c_0_113,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
c_0_103 ).
cnf(c_0_114,plain,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_115,plain,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_116,plain,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_111]) ).
cnf(c_0_117,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_97,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_5,e_4)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_119,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,plain,
~ product(e_5,e_5,e_4),
inference(spm,[status(thm)],[c_0_117,c_0_42]) ).
cnf(c_0_121,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]) ).
cnf(c_0_122,negated_conjecture,
( ~ product(e_1,e_4,X1)
| product(X1,e_5,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_113,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_121]),c_0_42])]) ).
cnf(c_0_124,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_3,e_5,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_122,c_0_123]) ).
cnf(c_0_125,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_122,c_0_124]) ).
cnf(c_0_126,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| product(e_4,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_125]),c_0_42])]) ).
cnf(c_0_127,plain,
( ~ product(e_4,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_88]),c_0_110]) ).
cnf(c_0_128,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_111,c_0_126]) ).
cnf(c_0_129,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)
| product(X1,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_130,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_47]) ).
cnf(c_0_131,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_127,c_0_126]) ).
cnf(c_0_132,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_128,c_0_99]) ).
cnf(c_0_133,plain,
( product(e_5,e_3,e_5)
| product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2)
| product(e_5,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_129,c_0_40]) ).
cnf(c_0_134,plain,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_130,c_0_42]) ).
cnf(c_0_135,axiom,
greater(e_3,e_2),
e_3_greater_e_2 ).
cnf(c_0_136,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_131]),c_0_132]) ).
cnf(c_0_137,plain,
( product(e_5,e_3,e_1)
| product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_138,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_43,c_0_135]) ).
cnf(c_0_139,axiom,
next(e_1,e_2),
e_1_then_e_2 ).
cnf(c_0_140,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_136]),c_0_132]) ).
cnf(c_0_141,negated_conjecture,
( ~ product(e_3,e_5,X1)
| product(X1,e_1,e_3)
| product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_137]) ).
cnf(c_0_142,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_143,negated_conjecture,
( ~ product(e_5,e_3,X1)
| product(X1,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_140]) ).
cnf(c_0_144,negated_conjecture,
( product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_4)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_140]),c_0_142]) ).
cnf(c_0_145,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_4,e_1,e_5)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_146,negated_conjecture,
( product(e_5,e_3,e_2)
| product(e_4,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_145]),c_0_42])]) ).
cnf(c_0_147,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_146]),c_0_73]) ).
cnf(c_0_148,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_147]),c_0_120]) ).
cnf(c_0_149,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_148]),c_0_42])]) ).
cnf(c_0_150,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_149]) ).
cnf(c_0_151,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_47]) ).
cnf(c_0_152,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_47]) ).
cnf(c_0_153,negated_conjecture,
( ~ product(e_1,e_4,X1)
| product(X1,e_5,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_147]) ).
cnf(c_0_154,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_2)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_150,c_0_147]) ).
cnf(c_0_155,plain,
( product(e_5,e_4,e_5)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_94,c_0_40]) ).
cnf(c_0_156,plain,
~ product(e_5,e_4,e_5),
inference(spm,[status(thm)],[c_0_151,c_0_42]) ).
cnf(c_0_157,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_47]) ).
cnf(c_0_158,plain,
( ~ product(e_2,e_4,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_95,c_0_99]) ).
cnf(c_0_159,plain,
( ~ product(e_5,e_3,e_4)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_152,c_0_68]) ).
cnf(c_0_160,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_153,c_0_154]) ).
cnf(c_0_161,plain,
( product(e_5,e_4,e_1)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_4) ),
inference(sr,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_162,plain,
( product(e_2,e_4,e_5)
| 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_94,c_0_61]) ).
cnf(c_0_163,plain,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_42])]) ).
cnf(c_0_164,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_111,c_0_42]) ).
cnf(c_0_165,negated_conjecture,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_166,negated_conjecture,
( ~ product(e_3,e_5,X1)
| product(X1,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_160]) ).
cnf(c_0_167,plain,
( ~ product(e_2,e_4,e_1)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_87,c_0_161]) ).
cnf(c_0_168,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_162,c_0_163]),c_0_164]) ).
cnf(c_0_169,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_5,e_1)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_87,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_166,c_0_140]) ).
cnf(c_0_171,plain,
( product(e_5,e_4,e_2)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_4)
| product(e_2,e_4,e_5)
| product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_167,c_0_168]) ).
cnf(c_0_172,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_169,c_0_99]) ).
cnf(c_0_173,negated_conjecture,
( ~ product(e_5,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_41,c_0_170]) ).
cnf(c_0_174,plain,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_5)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_171]),c_0_42])]) ).
cnf(c_0_175,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_95,c_0_172]) ).
cnf(c_0_176,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_5,e_4,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_177,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_178,plain,
( ~ group_element(X1)
| product(X1,e_5,e_1)
| product(X1,e_5,e_2)
| product(X1,e_5,e_3)
| product(X1,e_5,e_4)
| product(X1,e_5,e_5) ),
inference(spm,[status(thm)],[c_0_33,c_0_40]) ).
cnf(c_0_179,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_177]),c_0_42])]) ).
cnf(c_0_180,plain,
( product(e_1,e_5,e_5)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_178,c_0_34]) ).
cnf(c_0_181,plain,
~ product(e_1,e_5,e_1),
inference(spm,[status(thm)],[c_0_56,c_0_42]) ).
cnf(c_0_182,plain,
( ~ product(e_2,e_3,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_152,c_0_99]) ).
cnf(c_0_183,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_47]) ).
cnf(c_0_184,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_179]),c_0_168]) ).
cnf(c_0_185,plain,
( product(e_1,e_5,e_2)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_5) ),
inference(sr,[status(thm)],[c_0_180,c_0_181]) ).
cnf(c_0_186,plain,
( product(e_2,e_3,e_5)
| 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_129,c_0_61]) ).
cnf(c_0_187,plain,
~ product(e_2,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_182]),c_0_42])]) ).
cnf(c_0_188,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_47]) ).
cnf(c_0_189,negated_conjecture,
( ~ product(e_2,e_3,e_5)
| product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_190,plain,
( product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_185]),c_0_42])]) ).
cnf(c_0_191,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_5) ),
inference(sr,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_192,negated_conjecture,
~ product(e_2,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_42])]) ).
cnf(c_0_193,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_47]) ).
cnf(c_0_194,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_87,c_0_160]) ).
cnf(c_0_195,negated_conjecture,
( ~ product(e_5,e_1,X1)
| product(X1,e_4,e_5)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_113,c_0_190]) ).
cnf(c_0_196,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_47]) ).
cnf(c_0_197,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_191,c_0_192]) ).
cnf(c_0_198,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_199,negated_conjecture,
( ~ product(e_1,e_5,X1)
| product(X1,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_109]) ).
cnf(c_0_200,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_195,c_0_109]) ).
cnf(c_0_201,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_196,c_0_197]),c_0_198]) ).
cnf(c_0_202,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_4,e_5)
| product(e_1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_199,c_0_200]) ).
cnf(c_0_203,plain,
~ product(e_2,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_201]),c_0_42])]) ).
cnf(c_0_204,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)
| product(X1,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_33,c_0_61]) ).
cnf(c_0_205,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_172]),c_0_89]) ).
cnf(c_0_206,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_5)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_202]),c_0_203]) ).
cnf(c_0_207,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_193,c_0_140]) ).
cnf(c_0_208,plain,
( product(e_5,e_2,e_5)
| product(e_5,e_2,e_4)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2)
| product(e_5,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_204,c_0_40]) ).
cnf(c_0_209,plain,
~ product(e_5,e_2,e_5),
inference(spm,[status(thm)],[c_0_193,c_0_42]) ).
cnf(c_0_210,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_4,e_5)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_205,c_0_206]),c_0_207]) ).
cnf(c_0_211,plain,
( product(e_5,e_2,e_1)
| product(e_5,e_2,e_2)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_4) ),
inference(sr,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_212,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_112]) ).
cnf(c_0_213,plain,
( ~ product(e_2,e_5,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_99]) ).
cnf(c_0_214,plain,
( product(e_1,e_2,e_5)
| 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_204,c_0_34]) ).
cnf(c_0_215,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_157,c_0_42]) ).
cnf(c_0_216,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_210]),c_0_42])]) ).
cnf(c_0_217,negated_conjecture,
( ~ product(e_2,e_5,X1)
| product(X1,e_1,e_2)
| product(e_5,e_2,e_4)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_211]) ).
cnf(c_0_218,plain,
~ product(e_1,e_1,e_2),
inference(spm,[status(thm)],[c_0_212,c_0_42]) ).
cnf(c_0_219,plain,
( product(e_2,e_5,e_5)
| product(e_2,e_5,e_4)
| product(e_2,e_5,e_3)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_178,c_0_61]) ).
cnf(c_0_220,plain,
~ product(e_2,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_213]),c_0_42])]) ).
cnf(c_0_221,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_5) ),
inference(sr,[status(thm)],[c_0_214,c_0_215]) ).
cnf(c_0_222,negated_conjecture,
( ~ product(e_5,e_2,X1)
| product(X1,e_1,e_5)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_113,c_0_216]) ).
cnf(c_0_223,negated_conjecture,
( product(e_5,e_2,e_2)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_4)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_216]),c_0_218]) ).
cnf(c_0_224,plain,
( product(e_2,e_5,e_1)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4)
| product(e_2,e_5,e_5) ),
inference(sr,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_225,plain,
~ product(e_2,e_5,e_5),
inference(spm,[status(thm)],[c_0_87,c_0_42]) ).
cnf(c_0_226,axiom,
greater(e_5,e_2),
e_5_greater_e_2 ).
cnf(c_0_227,negated_conjecture,
( ~ product(e_2,e_1,X1)
| product(X1,e_5,e_2)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_221]) ).
cnf(c_0_228,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_4,e_1,e_5)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_229,plain,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[c_0_224,c_0_225]) ).
cnf(c_0_230,plain,
( ~ next(X1,e_2)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_43,c_0_226]) ).
cnf(c_0_231,negated_conjecture,
( ~ product(e_1,e_2,X1)
| product(X1,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_99]) ).
cnf(c_0_232,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_3,e_5,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_227,c_0_99]) ).
cnf(c_0_233,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_5,e_2,e_2)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_228]),c_0_59]) ).
cnf(c_0_234,negated_conjecture,
( ~ product(e_5,e_2,X1)
| product(X1,e_1,e_5)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_113,c_0_229]) ).
cnf(c_0_235,plain,
~ product(e_1,e_1,e_5),
inference(spm,[status(thm)],[c_0_230,c_0_139]) ).
cnf(c_0_236,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_3,e_1)
| product(e_3,e_5,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_237,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_2,e_4,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_233]),c_0_42])]) ).
cnf(c_0_238,plain,
( ~ product(e_2,e_4,e_5)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_83,c_0_114]) ).
cnf(c_0_239,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_2)
| product(e_5,e_2,e_4)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_211]),c_0_235]) ).
cnf(c_0_240,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_3,e_5,e_2)
| product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_231,c_0_236]) ).
cnf(c_0_241,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_237]),c_0_120]),c_0_238]) ).
cnf(c_0_242,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_2)
| product(e_4,e_1,e_5)
| product(e_5,e_2,e_2)
| product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_234,c_0_239]) ).
cnf(c_0_243,negated_conjecture,
( product(e_4,e_3,e_1)
| product(e_3,e_5,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_240]),c_0_42])]) ).
cnf(c_0_244,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_241]),c_0_42])]) ).
cnf(c_0_245,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_2)
| product(e_5,e_2,e_2)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_242]),c_0_59]) ).
cnf(c_0_246,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_5,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_243]),c_0_89]) ).
cnf(c_0_247,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_3,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_244]) ).
cnf(c_0_248,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_245]),c_0_42])]) ).
cnf(c_0_249,negated_conjecture,
( product(e_3,e_5,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_246,c_0_197]) ).
cnf(c_0_250,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_212,c_0_194]) ).
cnf(c_0_251,plain,
( product(e_3,e_4,e_5)
| 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_94,c_0_50]) ).
cnf(c_0_252,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_110,c_0_42]) ).
cnf(c_0_253,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_5,e_3,e_4)
| product(e_2,e_5,e_4)
| product(e_2,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
cnf(c_0_254,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_249]),c_0_56]),c_0_130]),c_0_250]) ).
cnf(c_0_255,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_151,c_0_140]) ).
cnf(c_0_256,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_251,c_0_252]) ).
cnf(c_0_257,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_5,e_3,e_4)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_258,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_4,e_5)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_259,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_2,e_4)
| product(e_5,e_3,e_4)
| product(e_2,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_113,c_0_257]) ).
cnf(c_0_260,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[c_0_248,c_0_254]) ).
cnf(c_0_261,negated_conjecture,
( ~ product(e_2,e_4,e_5)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_258]) ).
cnf(c_0_262,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_130,c_0_216]) ).
cnf(c_0_263,negated_conjecture,
( ~ product(e_3,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_60,c_0_170]) ).
cnf(c_0_264,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_5,e_3,e_4)
| product(e_5,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_259,c_0_260]) ).
cnf(c_0_265,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_151,c_0_249]) ).
cnf(c_0_266,negated_conjecture,
( ~ product(e_2,e_3,e_1)
| product(e_3,e_4,e_2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_262]),c_0_263]),c_0_130]) ).
cnf(c_0_267,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_5,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_264]),c_0_130]) ).
cnf(c_0_268,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_266]),c_0_197]) ).
cnf(c_0_269,negated_conjecture,
( ~ product(e_2,e_5,X1)
| ~ product(e_2,e_3,e_4)
| product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_267]) ).
cnf(c_0_270,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_268]),c_0_42])]) ).
cnf(c_0_271,negated_conjecture,
( ~ product(e_2,e_5,X1)
| product(X1,e_4,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_269,c_0_270]) ).
cnf(c_0_272,negated_conjecture,
( ~ product(e_5,e_2,X1)
| ~ product(e_2,e_3,e_4)
| product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_113,c_0_194]) ).
cnf(c_0_273,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_1,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_194]),c_0_270]) ).
cnf(c_0_274,negated_conjecture,
( ~ product(e_5,e_2,X1)
| product(X1,e_1,e_5)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_272,c_0_270]) ).
cnf(c_0_275,plain,
( product(e_3,e_2,e_5)
| 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) ),
inference(spm,[status(thm)],[c_0_204,c_0_50]) ).
cnf(c_0_276,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_196,c_0_42]) ).
cnf(c_0_277,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_2,e_4)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_273]) ).
cnf(c_0_278,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_4,e_1,e_5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_274,c_0_267]),c_0_270]) ).
cnf(c_0_279,plain,
( ~ product(e_5,e_2,e_4)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_157,c_0_68]) ).
cnf(c_0_280,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_5) ),
inference(sr,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_281,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_5,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_277,c_0_278]) ).
cnf(c_0_282,negated_conjecture,
( ~ product(e_1,e_4,X1)
| product(X1,e_5,e_1)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_113,c_0_237]) ).
cnf(c_0_283,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_279,c_0_267]) ).
cnf(c_0_284,negated_conjecture,
( ~ product(e_2,e_3,X1)
| product(X1,e_1,e_2)
| product(e_3,e_2,e_5)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_280]) ).
cnf(c_0_285,negated_conjecture,
( ~ product(e_3,e_2,e_4)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_67,c_0_281]) ).
cnf(c_0_286,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_4,e_4,e_5)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_195,c_0_68]) ).
cnf(c_0_287,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_3,e_5,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_282,c_0_244]) ).
cnf(c_0_288,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_283,c_0_270]) ).
cnf(c_0_289,negated_conjecture,
( ~ product(e_3,e_2,X1)
| product(X1,e_4,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_270]) ).
cnf(c_0_290,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_5)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_270]),c_0_116]),c_0_285]) ).
cnf(c_0_291,negated_conjecture,
( ~ product(e_1,e_4,e_3)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_4,e_4,e_5)
| product(e_1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_151,c_0_286]) ).
cnf(c_0_292,negated_conjecture,
~ product(e_4,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_237]),c_0_111]) ).
cnf(c_0_293,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_35,c_0_112]) ).
cnf(c_0_294,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_4,e_5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_287]),c_0_184]) ).
cnf(c_0_295,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_199,c_0_190]) ).
cnf(c_0_296,negated_conjecture,
( ~ product(e_5,e_4,e_3)
| product(e_2,e_3,e_2)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_95,c_0_288]) ).
cnf(c_0_297,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_5,e_4,e_3)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_289,c_0_290]) ).
cnf(c_0_298,negated_conjecture,
( ~ product(e_1,e_5,X1)
| product(X1,e_4,e_1)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_113,c_0_68]) ).
cnf(c_0_299,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_244]),c_0_292]) ).
cnf(c_0_300,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_216]),c_0_293]) ).
cnf(c_0_301,negated_conjecture,
product(e_2,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_294]),c_0_216]) ).
cnf(c_0_302,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_1,e_5,e_2)
| product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_199,c_0_295]) ).
cnf(c_0_303,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_296,c_0_297]) ).
cnf(c_0_304,negated_conjecture,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_299]),c_0_300]) ).
cnf(c_0_305,negated_conjecture,
( ~ product(e_4,e_2,X1)
| product(X1,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_113,c_0_301]) ).
cnf(c_0_306,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_302]),c_0_203]) ).
cnf(c_0_307,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| product(e_3,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_303]),c_0_152]) ).
cnf(c_0_308,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_2,e_4)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_113,c_0_304]) ).
cnf(c_0_309,negated_conjecture,
( product(e_1,e_5,e_4)
| product(e_3,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_305,c_0_306]) ).
cnf(c_0_310,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_307]),c_0_42])]) ).
cnf(c_0_311,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_4,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_261,c_0_301])]),c_0_263]) ).
cnf(c_0_312,negated_conjecture,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| product(e_2,e_5,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_260]),c_0_279]) ).
cnf(c_0_313,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_1,e_5,e_4) ),
inference(sr,[status(thm)],[c_0_309,c_0_310]) ).
cnf(c_0_314,negated_conjecture,
( ~ product(e_4,e_3,X1)
| product(X1,e_2,e_4)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_311]) ).
cnf(c_0_315,negated_conjecture,
( product(e_3,e_3,e_1)
| product(e_3,e_5,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_243,c_0_310]) ).
cnf(c_0_316,negated_conjecture,
( ~ product(e_3,e_3,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_130,c_0_140]) ).
cnf(c_0_317,negated_conjecture,
( ~ product(e_3,e_5,e_2)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_136]),c_0_212]) ).
cnf(c_0_318,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_5,e_4)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_87,c_0_312]) ).
cnf(c_0_319,negated_conjecture,
( ~ product(e_1,e_2,e_4)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_193,c_0_313]) ).
cnf(c_0_320,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_2,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_314,c_0_315]),c_0_316]),c_0_317]) ).
cnf(c_0_321,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_2,e_5,e_4)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_318,c_0_99]) ).
cnf(c_0_322,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_85,c_0_112]) ).
cnf(c_0_323,negated_conjecture,
product(e_2,e_5,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_320]),c_0_207]),c_0_205]) ).
cnf(c_0_324,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_5,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_321,c_0_310]) ).
cnf(c_0_325,negated_conjecture,
~ product(e_2,e_5,e_4),
inference(spm,[status(thm)],[c_0_322,c_0_323]) ).
cnf(c_0_326,negated_conjecture,
product(e_5,e_1,e_2),
inference(sr,[status(thm)],[c_0_324,c_0_325]) ).
cnf(c_0_327,plain,
( product(e_3,e_5,e_5)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_178,c_0_50]) ).
cnf(c_0_328,plain,
~ product(e_3,e_5,e_5),
inference(spm,[status(thm)],[c_0_67,c_0_42]) ).
cnf(c_0_329,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(spm,[status(thm)],[c_0_67,c_0_326]) ).
cnf(c_0_330,plain,
( product(e_3,e_5,e_1)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_4) ),
inference(sr,[status(thm)],[c_0_327,c_0_328]) ).
cnf(c_0_331,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_79,c_0_329]) ).
cnf(c_0_332,plain,
( ~ product(e_2,e_5,e_1)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_330]) ).
cnf(c_0_333,plain,
( ~ product(e_3,e_5,e_4)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_56,c_0_331]) ).
cnf(c_0_334,negated_conjecture,
( ~ product(e_2,e_3,X1)
| product(X1,e_5,e_2)
| product(e_2,e_3,e_2)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_290]) ).
cnf(c_0_335,plain,
( product(e_3,e_5,e_2)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_332,c_0_323])]) ).
cnf(c_0_336,plain,
~ product(e_3,e_5,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_333]),c_0_42])]) ).
cnf(c_0_337,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_3,e_2)
| product(e_4,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_334,c_0_270]) ).
cnf(c_0_338,plain,
( product(e_3,e_5,e_3)
| product(e_3,e_5,e_2) ),
inference(sr,[status(thm)],[c_0_335,c_0_336]) ).
cnf(c_0_339,negated_conjecture,
( ~ product(e_3,e_5,e_2)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_337]),c_0_193]) ).
cnf(c_0_340,plain,
product(e_3,e_5,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_338]),c_0_42])]) ).
cnf(c_0_341,negated_conjecture,
product(e_2,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_339,c_0_340])]) ).
cnf(c_0_342,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_341]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP125-2.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.44 % Computer : n001.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sun Sep 20 20:04:27 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 2.35/0.84 % Version: 3.5.1
% 2.35/0.84 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.35/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.35/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.35/0.84 % Starting new_bool_3 with 300s (1) cores
% 2.35/0.84 % Starting new_bool_1 with 300s (1) cores
% 2.35/0.84 % Starting sh5l with 300s (1) cores
% 2.35/0.84 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1274385 completed with status 0
% 2.35/0.84 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.35/0.84 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.35/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.35/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.35/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.35/0.84 % No SInE strategy applied
% 2.35/0.84 % Search class: FGHNF-FFSM00-SFFFFFNN
% 2.35/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.35/0.84 % Starting SubtermCWHack with 136s (1) cores
% 2.35/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.35/0.84 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 2.35/0.84 % Starting new_bool_3 with 136s (1) cores
% 2.35/0.84 % Starting new_bool_1 with 136s (1) cores
% 2.35/0.84 % G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 1274393 completed with status 0
% 2.35/0.84 % Result found by G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 2.35/0.84 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.35/0.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.35/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.35/0.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.35/0.84 % No SInE strategy applied
% 2.35/0.84 % Search class: FGHNF-FFSM00-SFFFFFNN
% 2.35/0.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.35/0.84 % Starting SubtermCWHack with 136s (1) cores
% 2.35/0.84 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.35/0.84 % Starting G----_404_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 2.35/0.84 % Preprocessing time : 0.002 s
% 2.35/0.84 % Presaturation interreduction done
% 2.35/0.84
% 2.35/0.84 % Proof found!
% 2.35/0.84 % SZS status Unsatisfiable
% 2.35/0.84 % SZS output start CNFRefutation
% See solution above
% 2.35/0.85 % Parsed axioms : 46
% 2.35/0.85 % Removed by relevancy pruning/SinE : 0
% 2.35/0.85 % Initial clauses : 46
% 2.35/0.85 % Removed in clause preprocessing : 0
% 2.35/0.85 % Initial clauses in saturation : 46
% 2.35/0.85 % Processed clauses : 1686
% 2.35/0.85 % ...of these trivial : 0
% 2.35/0.85 % ...subsumed : 583
% 2.35/0.85 % ...remaining for further processing : 1103
% 2.35/0.85 % Other redundant clauses eliminated : 0
% 2.35/0.85 % Clauses deleted for lack of memory : 0
% 2.35/0.85 % Backward-subsumed : 536
% 2.35/0.85 % Backward-rewritten : 135
% 2.35/0.85 % Generated clauses : 3437
% 2.35/0.85 % ...of the previous two non-redundant : 3051
% 2.35/0.85 % ...aggressively subsumed : 0
% 2.35/0.85 % Contextual simplify-reflections : 70
% 2.35/0.85 % Paramodulations : 3337
% 2.35/0.85 % Factorizations : 0
% 2.35/0.85 % NegExts : 0
% 2.35/0.85 % Equation resolutions : 0
% 2.35/0.85 % Disequality decompositions : 0
% 2.35/0.85 % Total rewrite steps : 238
% 2.35/0.85 % ...of those cached : 225
% 2.35/0.85 % Propositional unsat checks : 0
% 2.35/0.85 % Propositional check models : 0
% 2.35/0.85 % Propositional check unsatisfiable : 0
% 2.35/0.85 % Propositional clauses : 0
% 2.35/0.85 % Propositional clauses after purity: 0
% 2.35/0.85 % Propositional unsat core size : 0
% 2.35/0.85 % Propositional preprocessing time : 0.000
% 2.35/0.85 % Propositional encoding time : 0.000
% 2.35/0.85 % Propositional solver time : 0.000
% 2.35/0.85 % Success case prop preproc time : 0.000
% 2.35/0.85 % Success case prop encoding time : 0.000
% 2.35/0.85 % Success case prop solver time : 0.000
% 2.35/0.85 % Current number of processed clauses : 286
% 2.35/0.85 % Positive orientable unit clauses : 27
% 2.35/0.85 % Positive unorientable unit clauses: 0
% 2.35/0.85 % Negative unit clauses : 81
% 2.35/0.85 % Non-unit-clauses : 178
% 2.35/0.85 % Current number of unprocessed clauses: 486
% 2.35/0.85 % ...number of literals in the above : 2369
% 2.35/0.85 % Current number of archived formulas : 0
% 2.35/0.85 % Current number of archived clauses : 817
% 2.35/0.85 % Clause-clause subsumption calls (NU) : 86047
% 2.35/0.85 % Rec. Clause-clause subsumption calls : 44765
% 2.35/0.85 % Non-unit clause-clause subsumptions : 692
% 2.35/0.85 % Unit Clause-clause subsumption calls : 1802
% 2.35/0.85 % Rewrite failures with RHS unbound : 0
% 2.35/0.85 % BW rewrite match attempts : 41
% 2.35/0.85 % BW rewrite match successes : 7
% 2.35/0.85 % Condensation attempts : 0
% 2.35/0.85 % Condensation successes : 0
% 2.35/0.85 % Termbank termtop insertions : 39649
% 2.35/0.85 % Search garbage collected termcells : 72
% 2.35/0.85
% 2.35/0.85 % -------------------------------------------------
% 2.35/0.85 % User time : 0.290 s
% 2.35/0.85 % System time : 0.012 s
% 2.35/0.85 % Total time : 0.303 s
% 2.35/0.85 % Maximum resident set size: 3396 pages
% 2.35/0.85
% 2.35/0.85 % -------------------------------------------------
% 2.35/0.85 % User time : 1.377 s
% 2.35/0.85 % System time : 0.049 s
% 2.35/0.85 % Total time : 1.425 s
% 2.35/0.85 % Maximum resident set size: 4608 pages
% 2.35/0.85 % E exiting
%------------------------------------------------------------------------------