%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP125-2.005 : TPTP v9.2.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : Tue May 5 04:23:58 PM UTC 2026
% Result : Unsatisfiable 1.52s 1.77s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 30
% Syntax : Number of clauses : 329 ( 109 unt; 154 nHn; 327 RR)
% Number of literals : 826 ( 0 equ; 229 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 : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(element_5,axiom,
group_element(e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_5) ).
cnf(no_redundancy,axiom,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
cnf(e_5_greater_e_4,axiom,
greater(e_5,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_4) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_5) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_then_e_4) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_3) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_3) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_5) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_2) ).
cnf(c_0_30,axiom,
~ equalish(e_1,e_5),
e_1_is_not_e_5 ).
cnf(c_0_31,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).
cnf(c_0_32,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) ),
product_total_function1 ).
cnf(c_0_33,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_34,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_36,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).
cnf(c_0_37,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_32,c_0_33]) ).
cnf(c_0_38,axiom,
group_element(e_5),
element_5 ).
cnf(c_0_39,plain,
~ product(e_5,e_1,e_1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,axiom,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
no_redundancy ).
cnf(c_0_41,axiom,
greater(e_5,e_4),
e_5_greater_e_4 ).
cnf(c_0_42,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).
cnf(c_0_43,axiom,
~ equalish(e_3,e_5),
e_3_is_not_e_5 ).
cnf(c_0_44,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_45,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_37,c_0_38]),c_0_39]) ).
cnf(c_0_46,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_4) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,axiom,
next(e_3,e_4),
e_3_then_e_4 ).
cnf(c_0_48,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_31]) ).
cnf(c_0_49,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_50,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_44,c_0_45]),c_0_35])]) ).
cnf(c_0_51,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_52,plain,
~ product(e_3,e_1,e_5),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_48,c_0_35]) ).
cnf(c_0_54,axiom,
greater(e_5,e_3),
e_5_greater_e_3 ).
cnf(c_0_55,axiom,
greater(e_4,e_3),
e_4_greater_e_3 ).
cnf(c_0_56,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).
cnf(c_0_57,axiom,
~ equalish(e_2,e_5),
e_2_is_not_e_5 ).
cnf(c_0_58,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_49,c_0_50]) ).
cnf(c_0_59,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_37,c_0_51]),c_0_52]),c_0_53]) ).
cnf(c_0_60,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2 ).
cnf(c_0_61,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
cnf(c_0_62,axiom,
next(e_2,e_3),
e_2_then_e_3 ).
cnf(c_0_63,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_40,c_0_55]) ).
cnf(c_0_64,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_31]) ).
cnf(c_0_65,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_66,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4 ).
cnf(c_0_67,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_31]) ).
cnf(c_0_68,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_58,c_0_59]) ).
cnf(c_0_69,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_31]) ).
cnf(c_0_70,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_71,plain,
~ product(e_2,e_1,e_5),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_72,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_63,c_0_62]) ).
cnf(c_0_73,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_64,c_0_35]) ).
cnf(c_0_74,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_32,c_0_65]) ).
cnf(c_0_75,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_36]) ).
cnf(c_0_76,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_31]) ).
cnf(c_0_77,axiom,
~ equalish(e_4,e_5),
e_4_is_not_e_5 ).
cnf(c_0_78,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_67,c_0_68]),c_0_69]) ).
cnf(c_0_79,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_37,c_0_70]),c_0_71]),c_0_72]),c_0_73]) ).
cnf(c_0_80,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4 ).
cnf(c_0_81,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4 ).
cnf(c_0_82,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_74,c_0_33]) ).
cnf(c_0_83,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_75,c_0_35]) ).
cnf(c_0_84,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_76,c_0_35]) ).
cnf(c_0_85,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_31]) ).
cnf(c_0_86,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_78,c_0_79]) ).
cnf(c_0_87,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_31]) ).
cnf(c_0_88,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_31]) ).
cnf(c_0_89,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2 ).
cnf(c_0_90,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
qg3 ).
cnf(c_0_91,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_82,c_0_83]) ).
cnf(c_0_92,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_37,c_0_65]),c_0_84]) ).
cnf(c_0_93,plain,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]),c_0_88]) ).
cnf(c_0_94,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_77,c_0_89]) ).
cnf(c_0_95,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_90,c_0_91]) ).
cnf(c_0_96,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_92,c_0_93]) ).
cnf(c_0_97,plain,
~ product(e_5,e_5,e_4),
inference(spm,[status(thm)],[c_0_94,c_0_35]) ).
cnf(c_0_98,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_95,c_0_96]),c_0_97]) ).
cnf(c_0_99,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_90,c_0_96]) ).
cnf(c_0_100,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_76,c_0_98]),c_0_35])]) ).
cnf(c_0_101,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_99,c_0_100]) ).
cnf(c_0_102,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_99,c_0_101]) ).
cnf(c_0_103,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_75,c_0_102]),c_0_35])]) ).
cnf(c_0_104,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_85,c_0_68]),c_0_87]) ).
cnf(c_0_105,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_88,c_0_103]) ).
cnf(c_0_106,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_32,c_0_51]) ).
cnf(c_0_107,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_36]) ).
cnf(c_0_108,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_104,c_0_103]) ).
cnf(c_0_109,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_105,c_0_79]) ).
cnf(c_0_110,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_106,c_0_38]) ).
cnf(c_0_111,plain,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_107,c_0_35]) ).
cnf(c_0_112,axiom,
greater(e_3,e_2),
e_3_greater_e_2 ).
cnf(c_0_113,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_67,c_0_108]),c_0_109]) ).
cnf(c_0_114,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_110,c_0_111]) ).
cnf(c_0_115,plain,
( ~ product(X1,e_1,e_3)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_112]) ).
cnf(c_0_116,axiom,
next(e_1,e_2),
e_1_then_e_2 ).
cnf(c_0_117,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_69,c_0_113]),c_0_109]) ).
cnf(c_0_118,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_90,c_0_114]) ).
cnf(c_0_119,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,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_90,c_0_117]) ).
cnf(c_0_121,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_118,c_0_117]),c_0_119]) ).
cnf(c_0_122,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_120,c_0_121]) ).
cnf(c_0_123,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_49,c_0_122]),c_0_35])]) ).
cnf(c_0_124,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_120,c_0_123]),c_0_71]) ).
cnf(c_0_125,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_95,c_0_124]),c_0_97]) ).
cnf(c_0_126,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_76,c_0_125]),c_0_35])]) ).
cnf(c_0_127,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_90,c_0_126]) ).
cnf(c_0_128,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_36]) ).
cnf(c_0_129,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_130,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_90,c_0_124]) ).
cnf(c_0_131,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_127,c_0_124]) ).
cnf(c_0_132,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_74,c_0_38]) ).
cnf(c_0_133,plain,
~ product(e_5,e_4,e_5),
inference(spm,[status(thm)],[c_0_128,c_0_35]) ).
cnf(c_0_134,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_36]) ).
cnf(c_0_135,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_79]) ).
cnf(c_0_136,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_129,c_0_50]) ).
cnf(c_0_137,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_138,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_132,c_0_133]) ).
cnf(c_0_139,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_74,c_0_70]) ).
cnf(c_0_140,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_88,c_0_35]) ).
cnf(c_0_141,plain,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_35])]) ).
cnf(c_0_142,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_136,c_0_137]) ).
cnf(c_0_143,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_90,c_0_137]) ).
cnf(c_0_144,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_67,c_0_138]) ).
cnf(c_0_145,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_139,c_0_140]),c_0_141]) ).
cnf(c_0_146,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_67,c_0_142]) ).
cnf(c_0_147,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_143,c_0_117]) ).
cnf(c_0_148,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_144,c_0_145]) ).
cnf(c_0_149,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_146,c_0_79]) ).
cnf(c_0_150,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_34,c_0_147]) ).
cnf(c_0_151,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_85,c_0_148]),c_0_35])]) ).
cnf(c_0_152,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_75,c_0_149]) ).
cnf(c_0_153,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_150,c_0_151]) ).
cnf(c_0_154,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_152,c_0_153]) ).
cnf(c_0_155,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_32,c_0_38]) ).
cnf(c_0_156,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_134,c_0_154]),c_0_35])]) ).
cnf(c_0_157,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_155,c_0_33]) ).
cnf(c_0_158,plain,
~ product(e_1,e_5,e_1),
inference(spm,[status(thm)],[c_0_44,c_0_35]) ).
cnf(c_0_159,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_36]) ).
cnf(c_0_160,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_128,c_0_156]),c_0_145]) ).
cnf(c_0_161,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_157,c_0_158]) ).
cnf(c_0_162,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_106,c_0_70]) ).
cnf(c_0_163,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_69,c_0_35]) ).
cnf(c_0_164,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_36]) ).
cnf(c_0_165,negated_conjecture,
( product(e_2,e_4,e_2)
| ~ product(e_2,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_166,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_34,c_0_161]),c_0_35])]) ).
cnf(c_0_167,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_162,c_0_163]) ).
cnf(c_0_168,negated_conjecture,
~ product(e_2,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_35])]) ).
cnf(c_0_169,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_170,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_67,c_0_137]) ).
cnf(c_0_171,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_32,c_0_70]) ).
cnf(c_0_172,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_90,c_0_166]) ).
cnf(c_0_173,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_36]) ).
cnf(c_0_174,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_167,c_0_168]) ).
cnf(c_0_175,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_176,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_171,c_0_33]) ).
cnf(c_0_177,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_134,c_0_35]) ).
cnf(c_0_178,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_90,c_0_86]) ).
cnf(c_0_179,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_172,c_0_86]) ).
cnf(c_0_180,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_173,c_0_174]),c_0_175]) ).
cnf(c_0_181,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_90,c_0_79]) ).
cnf(c_0_182,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_176,c_0_177]) ).
cnf(c_0_183,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_178,c_0_179]) ).
cnf(c_0_184,plain,
~ product(e_2,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_180]),c_0_35])]) ).
cnf(c_0_185,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_181,c_0_182]) ).
cnf(c_0_186,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_49,c_0_149]),c_0_69]) ).
cnf(c_0_187,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_178,c_0_183]),c_0_184]) ).
cnf(c_0_188,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_169,c_0_117]) ).
cnf(c_0_189,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_171,c_0_38]) ).
cnf(c_0_190,plain,
~ product(e_5,e_2,e_5),
inference(spm,[status(thm)],[c_0_169,c_0_35]) ).
cnf(c_0_191,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_79]) ).
cnf(c_0_192,negated_conjecture,
( product(e_2,e_5,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_164,c_0_147]) ).
cnf(c_0_193,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_181,c_0_185]) ).
cnf(c_0_194,axiom,
greater(e_5,e_2),
e_5_greater_e_2 ).
cnf(c_0_195,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_186,c_0_187]),c_0_188]) ).
cnf(c_0_196,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_189,c_0_190]) ).
cnf(c_0_197,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_89]) ).
cnf(c_0_198,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_155,c_0_70]) ).
cnf(c_0_199,plain,
~ product(e_2,e_5,e_5),
inference(spm,[status(thm)],[c_0_67,c_0_35]) ).
cnf(c_0_200,plain,
~ product(e_2,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_191]),c_0_35])]) ).
cnf(c_0_201,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_192,c_0_193]) ).
cnf(c_0_202,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_40,c_0_194]) ).
cnf(c_0_203,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_134,c_0_195]),c_0_35])]) ).
cnf(c_0_204,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_90,c_0_196]) ).
cnf(c_0_205,plain,
~ product(e_1,e_1,e_2),
inference(spm,[status(thm)],[c_0_197,c_0_35]) ).
cnf(c_0_206,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_198,c_0_199]),c_0_200]) ).
cnf(c_0_207,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_64,c_0_201]),c_0_35])]) ).
cnf(c_0_208,plain,
~ product(e_1,e_1,e_5),
inference(spm,[status(thm)],[c_0_202,c_0_116]) ).
cnf(c_0_209,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_178,c_0_166]) ).
cnf(c_0_210,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_90,c_0_203]) ).
cnf(c_0_211,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_204,c_0_203]),c_0_205]) ).
cnf(c_0_212,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_90,c_0_206]) ).
cnf(c_0_213,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_120,c_0_207]),c_0_208]) ).
cnf(c_0_214,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_178,c_0_209]) ).
cnf(c_0_215,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_210,c_0_211]) ).
cnf(c_0_216,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_212,c_0_196]),c_0_208]) ).
cnf(c_0_217,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_173,c_0_213]) ).
cnf(c_0_218,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_178,c_0_214]),c_0_184]) ).
cnf(c_0_219,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_210,c_0_215]),c_0_52]) ).
cnf(c_0_220,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_212,c_0_216]) ).
cnf(c_0_221,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_217,c_0_218]),c_0_186]),c_0_188]) ).
cnf(c_0_222,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_67,c_0_219]),c_0_35])]) ).
cnf(c_0_223,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_64,c_0_91]) ).
cnf(c_0_224,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_212,c_0_220]),c_0_52]) ).
cnf(c_0_225,negated_conjecture,
product(e_2,e_5,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_221]),c_0_35])]) ).
cnf(c_0_226,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_66,c_0_89]) ).
cnf(c_0_227,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_172,c_0_50]) ).
cnf(c_0_228,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_95,c_0_222]),c_0_97]),c_0_223]) ).
cnf(c_0_229,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_67,c_0_224]),c_0_35])]) ).
cnf(c_0_230,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(spm,[status(thm)],[c_0_197,c_0_225]) ).
cnf(c_0_231,negated_conjecture,
~ product(e_2,e_5,e_4),
inference(spm,[status(thm)],[c_0_226,c_0_225]) ).
cnf(c_0_232,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_128,c_0_227]) ).
cnf(c_0_233,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_76,c_0_228]),c_0_35])]) ).
cnf(c_0_234,negated_conjecture,
~ product(e_4,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_222]),c_0_88]) ).
cnf(c_0_235,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_30,c_0_89]) ).
cnf(c_0_236,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_90,c_0_101]) ).
cnf(c_0_237,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_43,c_0_89]) ).
cnf(c_0_238,negated_conjecture,
product(e_4,e_1,e_5),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_229,c_0_230]),c_0_231]) ).
cnf(c_0_239,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_90,c_0_50]) ).
cnf(c_0_240,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_232,c_0_233]),c_0_234]) ).
cnf(c_0_241,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_203]),c_0_235]) ).
cnf(c_0_242,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_236,c_0_96]) ).
cnf(c_0_243,negated_conjecture,
~ product(e_4,e_1,e_3),
inference(spm,[status(thm)],[c_0_237,c_0_238]) ).
cnf(c_0_244,negated_conjecture,
~ product(e_4,e_1,e_4),
inference(spm,[status(thm)],[c_0_94,c_0_238]) ).
cnf(c_0_245,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_239,c_0_240]),c_0_241]) ).
cnf(c_0_246,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_88,c_0_213]),c_0_107]) ).
cnf(c_0_247,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_171,c_0_51]) ).
cnf(c_0_248,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_173,c_0_35]) ).
cnf(c_0_249,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_242,c_0_243]),c_0_244]) ).
cnf(c_0_250,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_90,c_0_245]) ).
cnf(c_0_251,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_134,c_0_50]) ).
cnf(c_0_252,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_246]),c_0_35])]) ).
cnf(c_0_253,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_247,c_0_248]) ).
cnf(c_0_254,negated_conjecture,
( product(e_3,e_5,e_1)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_49,c_0_249]) ).
cnf(c_0_255,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_250,c_0_238]),c_0_251]) ).
cnf(c_0_256,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_174,c_0_252]) ).
cnf(c_0_257,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_90,c_0_253]) ).
cnf(c_0_258,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_254]),c_0_225])]) ).
cnf(c_0_259,negated_conjecture,
( product(e_5,e_1,e_2)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_255]) ).
cnf(c_0_260,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_90,c_0_256]) ).
cnf(c_0_261,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_257,c_0_256]),c_0_93]),c_0_258]) ).
cnf(c_0_262,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_67,c_0_259]) ).
cnf(c_0_263,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_260,c_0_261]) ).
cnf(c_0_264,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_262,c_0_263]),c_0_129]) ).
cnf(c_0_265,negated_conjecture,
( product(e_5,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_67,c_0_255]) ).
cnf(c_0_266,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_264]),c_0_35])]) ).
cnf(c_0_267,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_155,c_0_65]) ).
cnf(c_0_268,plain,
~ product(e_4,e_5,e_5),
inference(spm,[status(thm)],[c_0_85,c_0_35]) ).
cnf(c_0_269,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_49,c_0_265]) ).
cnf(c_0_270,plain,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[c_0_79,c_0_266]) ).
cnf(c_0_271,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_267,c_0_268]) ).
cnf(c_0_272,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_155,c_0_51]) ).
cnf(c_0_273,plain,
~ product(e_3,e_5,e_5),
inference(spm,[status(thm)],[c_0_49,c_0_35]) ).
cnf(c_0_274,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_269,c_0_270])]) ).
cnf(c_0_275,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_87,c_0_271]) ).
cnf(c_0_276,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_88,c_0_271]) ).
cnf(c_0_277,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_272,c_0_273]) ).
cnf(c_0_278,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_59,c_0_274]) ).
cnf(c_0_279,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_275,c_0_117]),c_0_276]) ).
cnf(c_0_280,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_69,c_0_277]) ).
cnf(c_0_281,plain,
( product(e_3,e_1,e_3)
| ~ product(e_3,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_44,c_0_278]) ).
cnf(c_0_282,negated_conjecture,
( 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_90,c_0_233]) ).
cnf(c_0_283,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_106,c_0_65]) ).
cnf(c_0_284,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_159,c_0_35]) ).
cnf(c_0_285,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_90,c_0_265]) ).
cnf(c_0_286,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_4,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_76,c_0_209]) ).
cnf(c_0_287,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_128,c_0_279]),c_0_35])]) ).
cnf(c_0_288,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_280,c_0_225])]) ).
cnf(c_0_289,plain,
~ product(e_3,e_5,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_281]),c_0_35])]) ).
cnf(c_0_290,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_282,c_0_238]) ).
cnf(c_0_291,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_283,c_0_284]) ).
cnf(c_0_292,negated_conjecture,
~ product(e_4,e_3,e_5),
inference(spm,[status(thm)],[c_0_129,c_0_238]) ).
cnf(c_0_293,negated_conjecture,
( product(X1,e_2,e_1)
| ~ product(e_1,e_5,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_285,c_0_270])]) ).
cnf(c_0_294,negated_conjecture,
( product(e_4,e_5,e_2)
| product(e_1,e_5,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_287]),c_0_274]),c_0_266]) ).
cnf(c_0_295,plain,
( product(e_3,e_5,e_2)
| product(e_3,e_5,e_3) ),
inference(sr,[status(thm)],[c_0_288,c_0_289]) ).
cnf(c_0_296,negated_conjecture,
( product(e_4,e_5,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_107,c_0_287]) ).
cnf(c_0_297,negated_conjecture,
( product(e_5,e_3,e_4)
| product(X1,e_2,e_4)
| ~ product(e_4,e_1,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_290]) ).
cnf(c_0_298,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_90,c_0_222]) ).
cnf(c_0_299,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_291,c_0_292]) ).
cnf(c_0_300,negated_conjecture,
( product(e_4,e_2,e_1)
| product(e_4,e_5,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_294]),c_0_184]) ).
cnf(c_0_301,plain,
product(e_3,e_5,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_295]),c_0_35])]) ).
cnf(c_0_302,negated_conjecture,
( ~ product(e_3,e_5,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_87,c_0_296]) ).
cnf(c_0_303,negated_conjecture,
( product(e_5,e_2,e_4)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_297,c_0_238]) ).
cnf(c_0_304,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_298,c_0_233]) ).
cnf(c_0_305,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_173,c_0_299]) ).
cnf(c_0_306,negated_conjecture,
product(e_4,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_300]),c_0_301])]) ).
cnf(c_0_307,negated_conjecture,
~ product(e_4,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_302,c_0_301])]) ).
cnf(c_0_308,negated_conjecture,
( product(e_5,e_2,e_4)
| product(X1,e_4,e_3)
| ~ product(e_3,e_5,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_303]) ).
cnf(c_0_309,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_64,c_0_304]),c_0_160]) ).
cnf(c_0_310,plain,
product(e_4,e_3,e_2),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_305,c_0_306])]),c_0_307]) ).
cnf(c_0_311,negated_conjecture,
product(e_5,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_301]),c_0_141]) ).
cnf(c_0_312,negated_conjecture,
product(e_2,e_4,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_309]),c_0_203]) ).
cnf(c_0_313,plain,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_88,c_0_310]) ).
cnf(c_0_314,negated_conjecture,
( product(X1,e_4,e_2)
| ~ product(e_2,e_5,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_311]) ).
cnf(c_0_315,negated_conjecture,
( product(X1,e_5,e_4)
| ~ product(e_4,e_2,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_312]) ).
cnf(c_0_316,plain,
product(e_2,e_3,e_4),
inference(sr,[status(thm)],[c_0_256,c_0_313]) ).
cnf(c_0_317,plain,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_169,c_0_301]) ).
cnf(c_0_318,negated_conjecture,
product(e_1,e_4,e_2),
inference(spm,[status(thm)],[c_0_314,c_0_225]) ).
cnf(c_0_319,negated_conjecture,
product(e_1,e_5,e_4),
inference(spm,[status(thm)],[c_0_315,c_0_306]) ).
cnf(c_0_320,plain,
( 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_2,e_5) ),
inference(spm,[status(thm)],[c_0_48,c_0_182]) ).
cnf(c_0_321,negated_conjecture,
product(e_3,e_2,e_5),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_316]),c_0_317]),c_0_258]),c_0_93]) ).
cnf(c_0_322,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_164,c_0_318]) ).
cnf(c_0_323,negated_conjecture,
~ product(e_1,e_2,e_4),
inference(spm,[status(thm)],[c_0_169,c_0_319]) ).
cnf(c_0_324,negated_conjecture,
( product(X1,e_3,e_1)
| ~ product(e_1,e_2,X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_270]) ).
cnf(c_0_325,plain,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_320,c_0_321])]),c_0_322]),c_0_323]) ).
cnf(c_0_326,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_42,c_0_89]) ).
cnf(c_0_327,negated_conjecture,
product(e_3,e_3,e_1),
inference(spm,[status(thm)],[c_0_324,c_0_325]) ).
cnf(c_0_328,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_327]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP125-2.005 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n029.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 18:23:14 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.52/1.77 % Version : CSE_E---1.7
% 1.52/1.77 % Problem : theBenchmark.p
% 1.52/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.52/1.77 % SZS output start CNFRefutation
% See solution above
% 1.52/1.78 % Total time : 1.371s
%------------------------------------------------------------------------------