TSTP Solution File: GRP125-2.005 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : GRP125-2.005 : TPTP v8.2.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 20:45:46 EDT 2024
% Result : Unsatisfiable 1.26s 0.62s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 30
% Syntax : Number of clauses : 337 ( 115 unt; 153 nHn; 335 RR)
% Number of literals : 850 ( 0 equ; 247 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 : 150 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_5)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
cnf(no_redundancy,axiom,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_redundancy) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
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_5,axiom,
group_element(e_5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_5) ).
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_3_then_e_4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_then_e_4) ).
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(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
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(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_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(e_2_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_then_e_3) ).
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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
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,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
cnf(qg3,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
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,
~ equalish(e_1,e_5),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_5]) ).
cnf(c_0_31,plain,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_32,plain,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_5)
| ~ group_element(X1)
| ~ group_element(X2) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_33,plain,
~ equalish(e_1,e_5),
c_0_30 ).
cnf(c_0_34,plain,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
c_0_31 ).
cnf(c_0_35,plain,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_36,plain,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| product(X1,X2,e_5)
| ~ group_element(X1)
| ~ group_element(X2) ),
c_0_32 ).
cnf(c_0_37,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_38,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_40,plain,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
inference(fof_simplification,[status(thm)],[no_redundancy]) ).
cnf(c_0_41,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_42,plain,
~ equalish(e_3,e_5),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_5]) ).
cnf(c_0_43,plain,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
c_0_35 ).
cnf(c_0_44,plain,
( product(X1,e_1,e_5)
| product(X1,e_1,e_4)
| product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,axiom,
group_element(e_5),
element_5 ).
cnf(c_0_46,plain,
~ product(e_5,e_1,e_1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
c_0_40 ).
cnf(c_0_48,axiom,
greater(e_5,e_4),
e_5_greater_e_4 ).
cnf(c_0_49,plain,
~ equalish(e_3,e_1),
c_0_41 ).
cnf(c_0_50,plain,
~ equalish(e_3,e_5),
c_0_42 ).
cnf(c_0_51,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_52,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)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_53,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_4) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,axiom,
next(e_3,e_4),
e_3_then_e_4 ).
cnf(c_0_55,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_34]) ).
cnf(c_0_56,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_57,plain,
~ equalish(e_2,e_5),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_5]) ).
cnf(c_0_58,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_59,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_51,c_0_52]),c_0_39])]) ).
cnf(c_0_60,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_61,plain,
~ product(e_3,e_1,e_5),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_62,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_55,c_0_39]) ).
cnf(c_0_63,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_64,axiom,
greater(e_5,e_3),
e_5_greater_e_3 ).
cnf(c_0_65,axiom,
greater(e_4,e_3),
e_4_greater_e_3 ).
cnf(c_0_66,plain,
~ equalish(e_2,e_1),
c_0_56 ).
cnf(c_0_67,plain,
~ equalish(e_1,e_4),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_4]) ).
cnf(c_0_68,plain,
~ equalish(e_2,e_5),
c_0_57 ).
cnf(c_0_69,plain,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| ~ product(e_3,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_70,plain,
( 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)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_60]),c_0_61]),c_0_62]) ).
cnf(c_0_71,plain,
~ equalish(e_3,e_2),
c_0_63 ).
cnf(c_0_72,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_47,c_0_64]) ).
cnf(c_0_73,axiom,
next(e_2,e_3),
e_2_then_e_3 ).
cnf(c_0_74,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_47,c_0_65]) ).
cnf(c_0_75,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_34]) ).
cnf(c_0_76,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_77,plain,
~ equalish(e_1,e_4),
c_0_67 ).
cnf(c_0_78,plain,
~ equalish(e_4,e_5),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_5]) ).
cnf(c_0_79,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_34]) ).
cnf(c_0_80,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_81,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_34]) ).
cnf(c_0_82,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_83,plain,
~ product(e_2,e_1,e_5),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_84,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_74,c_0_73]) ).
cnf(c_0_85,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_75,c_0_39]) ).
cnf(c_0_86,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_87,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_88,plain,
( product(X1,e_4,e_5)
| product(X1,e_4,e_4)
| product(X1,e_4,e_3)
| product(X1,e_4,e_2)
| product(X1,e_4,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_76]) ).
cnf(c_0_89,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_43]) ).
cnf(c_0_90,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_34]) ).
cnf(c_0_91,plain,
~ equalish(e_4,e_5),
c_0_78 ).
cnf(c_0_92,plain,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_93,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_82]),c_0_83]),c_0_84]),c_0_85]) ).
cnf(c_0_94,plain,
~ equalish(e_3,e_4),
c_0_86 ).
cnf(c_0_95,plain,
~ equalish(e_2,e_4),
c_0_87 ).
cnf(c_0_96,plain,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_97,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_98,plain,
( product(e_1,e_4,e_1)
| 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(spm,[status(thm)],[c_0_88,c_0_37]) ).
cnf(c_0_99,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_89,c_0_39]) ).
cnf(c_0_100,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_90,c_0_39]) ).
cnf(c_0_101,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_34]) ).
cnf(c_0_102,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_34]) ).
cnf(c_0_104,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_34]) ).
cnf(c_0_105,plain,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
c_0_96 ).
cnf(c_0_106,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
c_0_97 ).
cnf(c_0_107,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) ),
inference(sr,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_108,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)],[inference(spm,[status(thm)],[c_0_44,c_0_76]),c_0_100]) ).
cnf(c_0_109,plain,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_104]) ).
cnf(c_0_110,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_91,c_0_105]) ).
cnf(c_0_111,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(X1,e_5,e_4)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,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_108,c_0_109]) ).
cnf(c_0_113,plain,
~ product(e_5,e_5,e_4),
inference(spm,[status(thm)],[c_0_110,c_0_39]) ).
cnf(c_0_114,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_115,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(X1,e_5,e_1)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_114]),c_0_39])]) ).
cnf(c_0_117,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,e_5,e_1)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_118,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_115,c_0_117]) ).
cnf(c_0_119,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_118]),c_0_39])]) ).
cnf(c_0_120,plain,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_80]),c_0_103]) ).
cnf(c_0_121,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_104,c_0_119]) ).
cnf(c_0_122,plain,
( product(X1,e_3,e_5)
| product(X1,e_3,e_4)
| product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_60]) ).
cnf(c_0_123,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_124,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_120,c_0_119]) ).
cnf(c_0_125,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_121,c_0_93]) ).
cnf(c_0_126,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)
| product(e_5,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_122,c_0_45]) ).
cnf(c_0_127,plain,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_123,c_0_39]) ).
cnf(c_0_128,axiom,
greater(e_3,e_2),
e_3_greater_e_2 ).
cnf(c_0_129,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_124]),c_0_125]) ).
cnf(c_0_130,plain,
( 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(sr,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_131,plain,
( ~ product(X1,e_1,e_3)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_47,c_0_128]) ).
cnf(c_0_132,axiom,
next(e_1,e_2),
e_1_then_e_2 ).
cnf(c_0_133,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_129]),c_0_125]) ).
cnf(c_0_134,negated_conjecture,
( product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_4)
| product(X1,e_1,e_3)
| ~ product(e_3,e_5,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_130]) ).
cnf(c_0_135,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_136,negated_conjecture,
( product(e_2,e_5,e_1)
| product(X1,e_1,e_5)
| ~ product(e_5,e_3,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_133]),c_0_135]) ).
cnf(c_0_138,negated_conjecture,
( product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| product(e_4,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_139,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_4,e_1,e_5)
| product(e_5,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_138]),c_0_39])]) ).
cnf(c_0_140,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_139]),c_0_83]) ).
cnf(c_0_141,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_140]),c_0_113]) ).
cnf(c_0_142,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_141]),c_0_39])]) ).
cnf(c_0_143,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_2)
| product(X1,e_3,e_4)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_142]) ).
cnf(c_0_144,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_43]) ).
cnf(c_0_145,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_146,negated_conjecture,
( product(e_2,e_5,e_1)
| product(X1,e_5,e_1)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_140]) ).
cnf(c_0_147,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_143,c_0_140]) ).
cnf(c_0_148,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)
| product(e_5,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_88,c_0_45]) ).
cnf(c_0_149,plain,
~ product(e_5,e_4,e_5),
inference(spm,[status(thm)],[c_0_144,c_0_39]) ).
cnf(c_0_150,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_43]) ).
cnf(c_0_151,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_93]) ).
cnf(c_0_152,plain,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| ~ product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_145,c_0_59]) ).
cnf(c_0_153,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_154,plain,
( 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(sr,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_155,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_4)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_88,c_0_82]) ).
cnf(c_0_156,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_104,c_0_39]) ).
cnf(c_0_157,plain,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_39])]) ).
cnf(c_0_158,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_159,negated_conjecture,
( product(e_2,e_5,e_1)
| product(X1,e_4,e_3)
| ~ product(e_3,e_5,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_153]) ).
cnf(c_0_160,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_1) ),
inference(spm,[status(thm)],[c_0_79,c_0_154]) ).
cnf(c_0_161,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_155,c_0_156]),c_0_157]) ).
cnf(c_0_162,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_2,e_5,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_158]) ).
cnf(c_0_163,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_159,c_0_133]) ).
cnf(c_0_164,plain,
( product(e_2,e_4,e_2)
| product(e_2,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) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_165,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_162,c_0_93]) ).
cnf(c_0_166,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_38,c_0_163]) ).
cnf(c_0_167,plain,
( product(e_5,e_4,e_2)
| product(e_5,e_4,e_3)
| product(e_2,e_4,e_5)
| product(e_2,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_164]),c_0_39])]) ).
cnf(c_0_168,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_89,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_5)
| product(e_5,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_170,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_171,plain,
( product(X1,e_5,e_5)
| product(X1,e_5,e_4)
| product(X1,e_5,e_3)
| product(X1,e_5,e_2)
| product(X1,e_5,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
cnf(c_0_172,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_170]),c_0_39])]) ).
cnf(c_0_173,plain,
( product(e_1,e_5,e_1)
| 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(spm,[status(thm)],[c_0_171,c_0_37]) ).
cnf(c_0_174,plain,
~ product(e_1,e_5,e_1),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_175,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_43]) ).
cnf(c_0_176,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_172]),c_0_161]) ).
cnf(c_0_177,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) ),
inference(sr,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_178,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_122,c_0_82]) ).
cnf(c_0_179,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_81,c_0_39]) ).
cnf(c_0_180,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_95,c_0_43]) ).
cnf(c_0_181,negated_conjecture,
( product(e_2,e_4,e_2)
| ~ product(e_2,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_175,c_0_176]) ).
cnf(c_0_182,plain,
( product(e_1,e_5,e_2)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_177]),c_0_39])]) ).
cnf(c_0_183,plain,
( product(e_2,e_3,e_5)
| 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_178,c_0_179]) ).
cnf(c_0_184,negated_conjecture,
~ product(e_2,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_39])]) ).
cnf(c_0_185,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_68,c_0_43]) ).
cnf(c_0_186,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_79,c_0_153]) ).
cnf(c_0_187,plain,
( product(X1,e_2,e_5)
| product(X1,e_2,e_4)
| product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_82]) ).
cnf(c_0_188,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(X1,e_4,e_5)
| ~ product(e_5,e_1,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_182]) ).
cnf(c_0_189,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_43]) ).
cnf(c_0_190,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_191,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_192,plain,
( product(e_1,e_2,e_1)
| 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(spm,[status(thm)],[c_0_187,c_0_37]) ).
cnf(c_0_193,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_150,c_0_39]) ).
cnf(c_0_194,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(X1,e_2,e_1)
| ~ product(e_1,e_5,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_102]) ).
cnf(c_0_195,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_1,e_5,e_2)
| product(e_1,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_188,c_0_102]) ).
cnf(c_0_196,plain,
( product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_191]) ).
cnf(c_0_197,negated_conjecture,
( product(e_2,e_1,e_2)
| product(X1,e_3,e_1)
| ~ product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_93]) ).
cnf(c_0_198,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) ),
inference(sr,[status(thm)],[c_0_192,c_0_193]) ).
cnf(c_0_199,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_2,e_4,e_5)
| 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_194,c_0_195]) ).
cnf(c_0_200,plain,
~ product(e_2,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_196]),c_0_39])]) ).
cnf(c_0_201,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_5,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_197,c_0_198]) ).
cnf(c_0_202,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_165]),c_0_81]) ).
cnf(c_0_203,negated_conjecture,
( product(e_3,e_2,e_1)
| product(e_2,e_4,e_5)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_199]),c_0_200]) ).
cnf(c_0_204,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_185,c_0_133]) ).
cnf(c_0_205,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)
| product(e_5,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_187,c_0_45]) ).
cnf(c_0_206,plain,
~ product(e_5,e_2,e_5),
inference(spm,[status(thm)],[c_0_185,c_0_39]) ).
cnf(c_0_207,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_51,c_0_93]) ).
cnf(c_0_208,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_180,c_0_163]) ).
cnf(c_0_209,negated_conjecture,
( product(e_5,e_3,e_1)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_4,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_197,c_0_201]) ).
cnf(c_0_210,axiom,
greater(e_5,e_2),
e_5_greater_e_2 ).
cnf(c_0_211,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_203]),c_0_204]) ).
cnf(c_0_212,plain,
( 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(sr,[status(thm)],[c_0_205,c_0_206]) ).
cnf(c_0_213,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_66,c_0_105]) ).
cnf(c_0_214,plain,
( product(e_2,e_5,e_1)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_3)
| product(e_2,e_5,e_4)
| product(e_2,e_5,e_5) ),
inference(spm,[status(thm)],[c_0_171,c_0_82]) ).
cnf(c_0_215,plain,
~ product(e_2,e_5,e_5),
inference(spm,[status(thm)],[c_0_79,c_0_39]) ).
cnf(c_0_216,plain,
~ product(e_2,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_207]),c_0_39])]) ).
cnf(c_0_217,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_3,e_1)
| product(e_1,e_2,e_2)
| product(e_5,e_3,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_218,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_47,c_0_210]) ).
cnf(c_0_219,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_4,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_211]),c_0_39])]) ).
cnf(c_0_220,negated_conjecture,
( product(e_5,e_2,e_2)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_4)
| product(X1,e_1,e_2)
| ~ product(e_2,e_5,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_212]) ).
cnf(c_0_221,plain,
~ product(e_1,e_1,e_2),
inference(spm,[status(thm)],[c_0_213,c_0_39]) ).
cnf(c_0_222,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)],[inference(sr,[status(thm)],[c_0_214,c_0_215]),c_0_216]) ).
cnf(c_0_223,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_5,e_3,e_1)
| product(e_4,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_75,c_0_217]),c_0_39])]) ).
cnf(c_0_224,plain,
~ product(e_1,e_1,e_5),
inference(spm,[status(thm)],[c_0_218,c_0_132]) ).
cnf(c_0_225,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_4,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_194,c_0_182]) ).
cnf(c_0_226,negated_conjecture,
( product(e_2,e_4,e_5)
| product(X1,e_1,e_5)
| ~ product(e_5,e_2,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_219]) ).
cnf(c_0_227,negated_conjecture,
( product(e_2,e_4,e_5)
| 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_220,c_0_219]),c_0_221]) ).
cnf(c_0_228,negated_conjecture,
( product(e_2,e_5,e_2)
| product(e_2,e_5,e_4)
| product(X1,e_1,e_5)
| ~ product(e_5,e_2,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_222]) ).
cnf(c_0_229,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_3,e_1)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_223]),c_0_224]) ).
cnf(c_0_230,negated_conjecture,
( product(e_4,e_2,e_1)
| product(e_1,e_5,e_2)
| 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_194,c_0_225]) ).
cnf(c_0_231,negated_conjecture,
( product(e_5,e_2,e_2)
| product(e_5,e_2,e_3)
| product(e_4,e_1,e_5)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_232,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_5,e_4)
| product(e_2,e_5,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_212]),c_0_224]) ).
cnf(c_0_233,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_1,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_189,c_0_229]) ).
cnf(c_0_234,negated_conjecture,
( product(e_3,e_2,e_1)
| product(e_4,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_230]),c_0_200]) ).
cnf(c_0_235,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_5,e_2,e_2)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_231]),c_0_61]) ).
cnf(c_0_236,negated_conjecture,
( product(e_5,e_2,e_3)
| product(e_5,e_2,e_2)
| product(e_4,e_1,e_5)
| product(e_2,e_5,e_4)
| product(e_2,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_228,c_0_232]) ).
cnf(c_0_237,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_202]),c_0_204]) ).
cnf(c_0_238,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_4,e_1,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_235]),c_0_39])]) ).
cnf(c_0_239,plain,
( 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_4,e_5) ),
inference(spm,[status(thm)],[c_0_75,c_0_107]) ).
cnf(c_0_240,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_5,e_2,e_2)
| product(e_2,e_5,e_4)
| product(e_2,e_5,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_228,c_0_236]),c_0_61]) ).
cnf(c_0_241,negated_conjecture,
product(e_2,e_5,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_237]),c_0_39])]) ).
cnf(c_0_242,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_77,c_0_105]) ).
cnf(c_0_243,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_4,e_4,e_5)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_188,c_0_59]) ).
cnf(c_0_244,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_238]),c_0_113]),c_0_239]) ).
cnf(c_0_245,negated_conjecture,
( product(e_2,e_5,e_2)
| product(e_2,e_5,e_4)
| product(e_4,e_1,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_240]),c_0_39])]) ).
cnf(c_0_246,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(spm,[status(thm)],[c_0_213,c_0_241]) ).
cnf(c_0_247,negated_conjecture,
~ product(e_2,e_5,e_4),
inference(spm,[status(thm)],[c_0_242,c_0_241]) ).
cnf(c_0_248,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_4,e_4,e_5)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_144,c_0_243]) ).
cnf(c_0_249,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_244]),c_0_39])]) ).
cnf(c_0_250,negated_conjecture,
~ product(e_4,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_238]),c_0_104]) ).
cnf(c_0_251,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_33,c_0_105]) ).
cnf(c_0_252,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_3,e_5,e_1)
| product(X1,e_2,e_4)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_117]) ).
cnf(c_0_253,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_105]) ).
cnf(c_0_254,negated_conjecture,
product(e_4,e_1,e_5),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_245,c_0_246]),c_0_247]) ).
cnf(c_0_255,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(X1,e_4,e_1)
| ~ product(e_1,e_5,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_59]) ).
cnf(c_0_256,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_1,e_5,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_249]),c_0_250]) ).
cnf(c_0_257,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_219]),c_0_251]) ).
cnf(c_0_258,negated_conjecture,
( product(e_5,e_2,e_4)
| product(e_3,e_5,e_1)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_252,c_0_112]) ).
cnf(c_0_259,negated_conjecture,
~ product(e_4,e_1,e_3),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_260,negated_conjecture,
~ product(e_4,e_1,e_4),
inference(spm,[status(thm)],[c_0_110,c_0_254]) ).
cnf(c_0_261,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_257]) ).
cnf(c_0_262,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_229]),c_0_123]) ).
cnf(c_0_263,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_187,c_0_60]) ).
cnf(c_0_264,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_189,c_0_39]) ).
cnf(c_0_265,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_5,e_2,e_4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_258,c_0_259]),c_0_260]) ).
cnf(c_0_266,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(X1,e_2,e_4)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_261]) ).
cnf(c_0_267,plain,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| ~ product(e_5,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_150,c_0_59]) ).
cnf(c_0_268,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_262]),c_0_39])]) ).
cnf(c_0_269,plain,
( product(e_3,e_2,e_5)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_263,c_0_264]) ).
cnf(c_0_270,negated_conjecture,
( product(e_3,e_5,e_1)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_58,c_0_265]) ).
cnf(c_0_271,negated_conjecture,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_254]),c_0_267]) ).
cnf(c_0_272,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_190,c_0_268]) ).
cnf(c_0_273,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_5)
| product(X1,e_1,e_2)
| ~ product(e_2,e_3,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_269]) ).
cnf(c_0_274,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_270]),c_0_241])]) ).
cnf(c_0_275,negated_conjecture,
( product(e_5,e_1,e_2)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_89,c_0_271]) ).
cnf(c_0_276,negated_conjecture,
( product(e_2,e_3,e_2)
| product(X1,e_4,e_3)
| ~ product(e_3,e_2,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_272]) ).
cnf(c_0_277,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_2,e_5)
| product(e_3,e_2,e_2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_272]),c_0_109]),c_0_274]) ).
cnf(c_0_278,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_275]) ).
cnf(c_0_279,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_5,e_4,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_276,c_0_277]) ).
cnf(c_0_280,negated_conjecture,
( product(e_3,e_2,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_279]),c_0_145]) ).
cnf(c_0_281,plain,
( product(e_4,e_5,e_1)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_4)
| product(e_4,e_5,e_5) ),
inference(spm,[status(thm)],[c_0_171,c_0_76]) ).
cnf(c_0_282,plain,
~ product(e_4,e_5,e_5),
inference(spm,[status(thm)],[c_0_101,c_0_39]) ).
cnf(c_0_283,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_280]),c_0_39])]) ).
cnf(c_0_284,negated_conjecture,
( product(e_5,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_79,c_0_271]) ).
cnf(c_0_285,negated_conjecture,
( product(e_2,e_4,e_5)
| product(X1,e_5,e_1)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_238]) ).
cnf(c_0_286,plain,
( product(e_4,e_5,e_4)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_2)
| product(e_4,e_5,e_1) ),
inference(sr,[status(thm)],[c_0_281,c_0_282]) ).
cnf(c_0_287,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_4)
| product(e_4,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_122,c_0_76]) ).
cnf(c_0_288,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_175,c_0_39]) ).
cnf(c_0_289,plain,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[c_0_93,c_0_283]) ).
cnf(c_0_290,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_58,c_0_284]) ).
cnf(c_0_291,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,e_5,e_1)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_285,c_0_249]) ).
cnf(c_0_292,plain,
( product(e_4,e_5,e_2)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_4)
| ~ product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_103,c_0_286]) ).
cnf(c_0_293,plain,
( product(e_4,e_5,e_2)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_4)
| ~ product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_104,c_0_286]) ).
cnf(c_0_294,plain,
( product(e_4,e_3,e_5)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_287,c_0_288]) ).
cnf(c_0_295,negated_conjecture,
~ product(e_4,e_3,e_5),
inference(spm,[status(thm)],[c_0_145,c_0_254]) ).
cnf(c_0_296,negated_conjecture,
( product(X1,e_2,e_1)
| ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_5,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_284]) ).
cnf(c_0_297,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(X1,e_3,e_5)
| ~ product(e_5,e_1,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_225]) ).
cnf(c_0_298,negated_conjecture,
product(e_5,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_284,c_0_289])]) ).
cnf(c_0_299,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_290,c_0_289])]) ).
cnf(c_0_300,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_3,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_291]),c_0_176]) ).
cnf(c_0_301,negated_conjecture,
( product(e_4,e_5,e_4)
| product(e_4,e_5,e_3)
| product(e_4,e_5,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_133]),c_0_293]) ).
cnf(c_0_302,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[c_0_294,c_0_295]) ).
cnf(c_0_303,negated_conjecture,
( product(X1,e_2,e_1)
| ~ product(e_1,e_5,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_296,c_0_289])]) ).
cnf(c_0_304,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_298]),c_0_299]),c_0_283]),c_0_184]) ).
cnf(c_0_305,negated_conjecture,
( product(X1,e_5,e_1)
| ~ product(e_1,e_4,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_254]) ).
cnf(c_0_306,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)
| product(e_3,e_5,e_5) ),
inference(spm,[status(thm)],[c_0_171,c_0_60]) ).
cnf(c_0_307,plain,
~ product(e_3,e_5,e_5),
inference(spm,[status(thm)],[c_0_58,c_0_39]) ).
cnf(c_0_308,negated_conjecture,
product(e_2,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_300]),c_0_219]) ).
cnf(c_0_309,negated_conjecture,
( product(e_4,e_5,e_2)
| product(e_4,e_5,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_301]),c_0_39])]) ).
cnf(c_0_310,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_189,c_0_302]) ).
cnf(c_0_311,negated_conjecture,
product(e_4,e_2,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_304]),c_0_200]) ).
cnf(c_0_312,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_4)
| product(e_3,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_88,c_0_60]) ).
cnf(c_0_313,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_103,c_0_39]) ).
cnf(c_0_314,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_305,c_0_249]) ).
cnf(c_0_315,plain,
( 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(sr,[status(thm)],[c_0_306,c_0_307]) ).
cnf(c_0_316,negated_conjecture,
( product(X1,e_5,e_4)
| ~ product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_308]) ).
cnf(c_0_317,negated_conjecture,
( product(e_4,e_5,e_2)
| ~ product(e_3,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_103,c_0_309]) ).
cnf(c_0_318,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_310,c_0_311])]) ).
cnf(c_0_319,plain,
( product(e_3,e_4,e_5)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_312,c_0_313]) ).
cnf(c_0_320,negated_conjecture,
( product(e_3,e_5,e_1)
| ~ product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_55,c_0_314]) ).
cnf(c_0_321,plain,
( product(e_3,e_5,e_2)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_4)
| ~ product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_81,c_0_315]) ).
cnf(c_0_322,negated_conjecture,
product(e_1,e_5,e_4),
inference(spm,[status(thm)],[c_0_316,c_0_311]) ).
cnf(c_0_323,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_123,c_0_317]) ).
cnf(c_0_324,plain,
product(e_4,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_318]),c_0_39])]) ).
cnf(c_0_325,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_5)
| product(X1,e_1,e_4)
| ~ product(e_4,e_3,X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_319]) ).
cnf(c_0_326,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_320]),c_0_241])]) ).
cnf(c_0_327,plain,
( product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_321,c_0_241])]) ).
cnf(c_0_328,negated_conjecture,
~ product(e_3,e_5,e_4),
inference(spm,[status(thm)],[c_0_55,c_0_322]) ).
cnf(c_0_329,negated_conjecture,
~ product(e_3,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_323,c_0_324])]) ).
cnf(c_0_330,negated_conjecture,
( product(e_3,e_4,e_5)
| product(e_3,e_4,e_3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_324]),c_0_326]),c_0_84]) ).
cnf(c_0_331,plain,
product(e_3,e_5,e_2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_327,c_0_328]),c_0_329]) ).
cnf(c_0_332,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_3,e_2,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_58,c_0_279]) ).
cnf(c_0_333,negated_conjecture,
product(e_3,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_330]),c_0_308])]) ).
cnf(c_0_334,plain,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_104,c_0_324]) ).
cnf(c_0_335,plain,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_185,c_0_331]) ).
cnf(c_0_336,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_332,c_0_333])]),c_0_334]),c_0_335]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP125-2.005 : TPTP v8.2.0. Released v1.2.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 04:40:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 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
% 1.26/0.62 # Version: 3.1.0
% 1.26/0.62 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.26/0.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.26/0.62 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.26/0.62 # Starting new_bool_3 with 300s (1) cores
% 1.26/0.62 # Starting new_bool_1 with 300s (1) cores
% 1.26/0.62 # Starting sh5l with 300s (1) cores
% 1.26/0.62 # new_bool_3 with pid 669 completed with status 0
% 1.26/0.62 # Result found by new_bool_3
% 1.26/0.62 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.26/0.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.26/0.62 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.26/0.62 # Starting new_bool_3 with 300s (1) cores
% 1.26/0.62 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.26/0.62 # Search class: FGHNF-FFSM00-SFFFFFNN
% 1.26/0.62 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.26/0.62 # Starting G----_406_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 181s (1) cores
% 1.26/0.62 # G----_406_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 673 completed with status 0
% 1.26/0.62 # Result found by G----_406_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 1.26/0.62 # Preprocessing class: FSMSSMSSSSSNFFN.
% 1.26/0.62 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.26/0.62 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.26/0.62 # Starting new_bool_3 with 300s (1) cores
% 1.26/0.62 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.26/0.62 # Search class: FGHNF-FFSM00-SFFFFFNN
% 1.26/0.62 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.26/0.62 # Starting G----_406_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 181s (1) cores
% 1.26/0.62 # Preprocessing time : 0.001 s
% 1.26/0.62 # Presaturation interreduction done
% 1.26/0.62
% 1.26/0.62 # Proof found!
% 1.26/0.62 # SZS status Unsatisfiable
% 1.26/0.62 # SZS output start CNFRefutation
% See solution above
% 1.26/0.62 # Parsed axioms : 46
% 1.26/0.62 # Removed by relevancy pruning/SinE : 0
% 1.26/0.62 # Initial clauses : 46
% 1.26/0.62 # Removed in clause preprocessing : 0
% 1.26/0.62 # Initial clauses in saturation : 46
% 1.26/0.62 # Processed clauses : 1487
% 1.26/0.62 # ...of these trivial : 9
% 1.26/0.62 # ...subsumed : 467
% 1.26/0.62 # ...remaining for further processing : 1011
% 1.26/0.62 # Other redundant clauses eliminated : 0
% 1.26/0.62 # Clauses deleted for lack of memory : 0
% 1.26/0.62 # Backward-subsumed : 554
% 1.26/0.62 # Backward-rewritten : 110
% 1.26/0.62 # Generated clauses : 3099
% 1.26/0.62 # ...of the previous two non-redundant : 2765
% 1.26/0.62 # ...aggressively subsumed : 0
% 1.26/0.62 # Contextual simplify-reflections : 56
% 1.26/0.62 # Paramodulations : 3021
% 1.26/0.62 # Factorizations : 0
% 1.26/0.62 # NegExts : 0
% 1.26/0.62 # Equation resolutions : 0
% 1.26/0.62 # Disequality decompositions : 0
% 1.26/0.62 # Total rewrite steps : 196
% 1.26/0.62 # ...of those cached : 177
% 1.26/0.62 # Propositional unsat checks : 0
% 1.26/0.62 # Propositional check models : 0
% 1.26/0.62 # Propositional check unsatisfiable : 0
% 1.26/0.62 # Propositional clauses : 0
% 1.26/0.62 # Propositional clauses after purity: 0
% 1.26/0.62 # Propositional unsat core size : 0
% 1.26/0.62 # Propositional preprocessing time : 0.000
% 1.26/0.62 # Propositional encoding time : 0.000
% 1.26/0.62 # Propositional solver time : 0.000
% 1.26/0.62 # Success case prop preproc time : 0.000
% 1.26/0.62 # Success case prop encoding time : 0.000
% 1.26/0.62 # Success case prop solver time : 0.000
% 1.26/0.62 # Current number of processed clauses : 223
% 1.26/0.62 # Positive orientable unit clauses : 33
% 1.26/0.62 # Positive unorientable unit clauses: 0
% 1.26/0.62 # Negative unit clauses : 96
% 1.26/0.62 # Non-unit-clauses : 94
% 1.26/0.62 # Current number of unprocessed clauses: 207
% 1.26/0.62 # ...number of literals in the above : 816
% 1.26/0.62 # Current number of archived formulas : 0
% 1.26/0.62 # Current number of archived clauses : 788
% 1.26/0.62 # Clause-clause subsumption calls (NU) : 74947
% 1.26/0.62 # Rec. Clause-clause subsumption calls : 40003
% 1.26/0.62 # Non-unit clause-clause subsumptions : 545
% 1.26/0.62 # Unit Clause-clause subsumption calls : 2209
% 1.26/0.62 # Rewrite failures with RHS unbound : 0
% 1.26/0.62 # BW rewrite match attempts : 75
% 1.26/0.62 # BW rewrite match successes : 13
% 1.26/0.62 # Condensation attempts : 0
% 1.26/0.62 # Condensation successes : 0
% 1.26/0.62 # Termbank termtop insertions : 34378
% 1.26/0.62 # Search garbage collected termcells : 72
% 1.26/0.62
% 1.26/0.62 # -------------------------------------------------
% 1.26/0.62 # User time : 0.134 s
% 1.26/0.62 # System time : 0.003 s
% 1.26/0.62 # Total time : 0.138 s
% 1.26/0.62 # Maximum resident set size: 1784 pages
% 1.26/0.62
% 1.26/0.62 # -------------------------------------------------
% 1.26/0.62 # User time : 0.136 s
% 1.26/0.62 # System time : 0.005 s
% 1.26/0.62 # Total time : 0.141 s
% 1.26/0.62 # Maximum resident set size: 1756 pages
% 1.26/0.62 % E---3.1 exiting
% 1.26/0.62 % E exiting
%------------------------------------------------------------------------------