%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP127-2.005 : 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 : n005.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 04:24:01 PM UTC 2026
% Result : Satisfiable 1.67s 1.82s
% Output : Saturation 1.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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_5_greater_e_2,axiom,
greater(e_5,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_2) ).
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(qg3,negated_conjecture,
( product(X4,X1,X2)
| ~ product(X1,X2,X3)
| ~ product(X3,X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
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(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_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_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(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(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(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_2_greater_e_1,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_1) ).
cnf(e_3_greater_e_1,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_1) ).
cnf(e_4_greater_e_1,axiom,
greater(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_1) ).
cnf(e_5_greater_e_1,axiom,
greater(e_5,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_1) ).
cnf(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_is_not_e_4) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_is_not_e_3) ).
cnf(e_5_is_not_e_2,axiom,
~ equalish(e_5,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_is_not_e_2) ).
cnf(e_5_is_not_e_1,axiom,
~ equalish(e_5,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_is_not_e_1) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_4_then_e_5,axiom,
next(e_4,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_then_e_5) ).
cnf(c_0_46,axiom,
~ equalish(e_1,e_5),
e_1_is_not_e_5,
[final] ).
cnf(c_0_47,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation,
[final] ).
cnf(c_0_48,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,
[final] ).
cnf(c_0_49,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(c_0_50,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]),
[final] ).
cnf(c_0_51,axiom,
product(X1,X1,X1),
product_idempotence,
[final] ).
cnf(c_0_52,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation,
[final] ).
cnf(c_0_53,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_48,c_0_49]),
[final] ).
cnf(c_0_54,axiom,
group_element(e_5),
element_5,
[final] ).
cnf(c_0_55,plain,
~ product(e_5,e_1,e_1),
inference(spm,[status(thm)],[c_0_50,c_0_51]),
[final] ).
cnf(c_0_56,axiom,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
no_redundancy,
[final] ).
cnf(c_0_57,axiom,
greater(e_5,e_4),
e_5_greater_e_4,
[final] ).
cnf(c_0_58,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1,
[final] ).
cnf(c_0_59,axiom,
~ equalish(e_3,e_5),
e_3_is_not_e_5,
[final] ).
cnf(c_0_60,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_52]),
[final] ).
cnf(c_0_61,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_53,c_0_54]),c_0_55]) ).
cnf(c_0_62,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_4) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]),
[final] ).
cnf(c_0_63,axiom,
next(e_3,e_4),
e_3_then_e_4,
[final] ).
cnf(c_0_64,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_47]),
[final] ).
cnf(c_0_65,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_47]),
[final] ).
cnf(c_0_66,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_60,c_0_61]),c_0_51])]) ).
cnf(c_0_67,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(c_0_68,plain,
~ product(e_3,e_1,e_5),
inference(spm,[status(thm)],[c_0_62,c_0_63]),
[final] ).
cnf(c_0_69,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_64,c_0_51]),
[final] ).
cnf(c_0_70,axiom,
greater(e_5,e_3),
e_5_greater_e_3,
[final] ).
cnf(c_0_71,axiom,
greater(e_4,e_3),
e_4_greater_e_3,
[final] ).
cnf(c_0_72,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1,
[final] ).
cnf(c_0_73,axiom,
greater(e_5,e_2),
e_5_greater_e_2,
[final] ).
cnf(c_0_74,axiom,
~ equalish(e_2,e_5),
e_2_is_not_e_5,
[final] ).
cnf(c_0_75,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_65,c_0_66]) ).
cnf(c_0_76,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_53,c_0_67]),c_0_68]),c_0_69]) ).
cnf(c_0_77,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2,
[final] ).
cnf(c_0_78,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_56,c_0_70]),
[final] ).
cnf(c_0_79,axiom,
next(e_2,e_3),
e_2_then_e_3,
[final] ).
cnf(c_0_80,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_56,c_0_71]),
[final] ).
cnf(c_0_81,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_47]),
[final] ).
cnf(c_0_82,negated_conjecture,
( product(X4,X1,X2)
| ~ product(X1,X2,X3)
| ~ product(X3,X1,X4) ),
qg3,
[final] ).
cnf(c_0_83,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_48,c_0_54]),
[final] ).
cnf(c_0_84,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_73]),
[final] ).
cnf(c_0_85,axiom,
next(e_1,e_2),
e_1_then_e_2,
[final] ).
cnf(c_0_86,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_47]),
[final] ).
cnf(c_0_87,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_75,c_0_76]) ).
cnf(c_0_88,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_47]),
[final] ).
cnf(c_0_89,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(c_0_90,plain,
~ product(e_2,e_1,e_5),
inference(spm,[status(thm)],[c_0_78,c_0_79]),
[final] ).
cnf(c_0_91,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_80,c_0_79]),
[final] ).
cnf(c_0_92,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_81,c_0_51]),
[final] ).
cnf(c_0_93,negated_conjecture,
( product(X1,X1,X2)
| ~ product(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_51]),
[final] ).
cnf(c_0_94,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_83,c_0_49]) ).
cnf(c_0_95,plain,
~ product(e_1,e_1,e_5),
inference(spm,[status(thm)],[c_0_84,c_0_85]),
[final] ).
cnf(c_0_96,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_86,c_0_87]),c_0_88]) ).
cnf(c_0_97,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_53,c_0_89]),c_0_90]),c_0_91]),c_0_92]) ).
cnf(c_0_98,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_52]),
[final] ).
cnf(c_0_99,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(c_0_100,axiom,
greater(e_4,e_2),
e_4_greater_e_2,
[final] ).
cnf(c_0_101,negated_conjecture,
( 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)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
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_96,c_0_97]) ).
cnf(c_0_103,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_48,c_0_89]),
[final] ).
cnf(c_0_104,plain,
~ product(e_1,e_2,e_1),
inference(spm,[status(thm)],[c_0_98,c_0_51]),
[final] ).
cnf(c_0_105,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_48,c_0_99]),
[final] ).
cnf(c_0_106,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_100]),
[final] ).
cnf(c_0_107,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_52]),
[final] ).
cnf(c_0_108,negated_conjecture,
( 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_50,c_0_101]),c_0_51])]) ).
cnf(c_0_109,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,X1)
| ~ product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_102]) ).
cnf(c_0_110,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4)
| product(e_1,e_2,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_49]),c_0_104]) ).
cnf(c_0_111,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,X1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_97]) ).
cnf(c_0_112,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_105,c_0_49]) ).
cnf(c_0_113,plain,
~ product(e_1,e_1,e_4),
inference(spm,[status(thm)],[c_0_106,c_0_85]),
[final] ).
cnf(c_0_114,axiom,
~ equalish(e_4,e_5),
e_4_is_not_e_5,
[final] ).
cnf(c_0_115,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_116,negated_conjecture,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111]) ).
cnf(c_0_117,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4,
[final] ).
cnf(c_0_118,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4,
[final] ).
cnf(c_0_119,negated_conjecture,
( 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)],[inference(spm,[status(thm)],[c_0_93,c_0_112]),c_0_113]) ).
cnf(c_0_120,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_52]),
[final] ).
cnf(c_0_121,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_122,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_52]),
[final] ).
cnf(c_0_123,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_47]),
[final] ).
cnf(c_0_124,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_119]),c_0_91]) ).
cnf(c_0_125,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_1,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),
[final] ).
cnf(c_0_126,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_51])]) ).
cnf(c_0_127,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_47]),
[final] ).
cnf(c_0_128,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_118,c_0_52]),
[final] ).
cnf(c_0_129,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4,
[final] ).
cnf(c_0_130,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_131,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_105,c_0_89]) ).
cnf(c_0_132,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_127,c_0_51]),
[final] ).
cnf(c_0_133,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_128,c_0_97]),
[final] ).
cnf(c_0_134,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_83,c_0_89]) ).
cnf(c_0_135,plain,
~ product(e_2,e_5,e_5),
inference(spm,[status(thm)],[c_0_86,c_0_51]),
[final] ).
cnf(c_0_136,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_60,c_0_97]),
[final] ).
cnf(c_0_137,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_105,c_0_54]) ).
cnf(c_0_138,plain,
~ product(e_5,e_4,e_5),
inference(spm,[status(thm)],[c_0_120,c_0_51]),
[final] ).
cnf(c_0_139,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_123,c_0_51]),
[final] ).
cnf(c_0_140,plain,
( ~ product(e_5,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_114,c_0_47]),
[final] ).
cnf(c_0_141,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_129,c_0_47]),
[final] ).
cnf(c_0_142,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_1,e_4,e_2)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_130]),c_0_68]) ).
cnf(c_0_143,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_144,plain,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_133]),c_0_51])]),
[final] ).
cnf(c_0_145,plain,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_3)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_146,plain,
~ product(e_2,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_136]),c_0_51])]),
[final] ).
cnf(c_0_147,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_137,c_0_138]) ).
cnf(c_0_148,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_53,c_0_99]),c_0_139]) ).
cnf(c_0_149,plain,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_102]),c_0_141]),c_0_127]),
[final] ).
cnf(c_0_150,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_111,c_0_142]) ).
cnf(c_0_151,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_2,X1)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_116]) ).
cnf(c_0_152,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_153,plain,
~ product(e_4,e_2,e_4),
inference(spm,[status(thm)],[c_0_122,c_0_51]),
[final] ).
cnf(c_0_154,plain,
( product(e_2,e_5,e_1)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4) ),
inference(sr,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_155,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_4)
| product(e_1,e_4,X1)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_147]) ).
cnf(c_0_156,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_148,c_0_149]) ).
cnf(c_0_157,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_128,c_0_51]),
[final] ).
cnf(c_0_158,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,X1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_150]) ).
cnf(c_0_159,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_160,negated_conjecture,
( product(e_3,e_1,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_142]),c_0_128]),
[final] ).
cnf(c_0_161,plain,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_120,c_0_154]) ).
cnf(c_0_162,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_157]) ).
cnf(c_0_163,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_149]),c_0_160]) ).
cnf(c_0_164,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| ~ product(e_2,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_108]) ).
cnf(c_0_165,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_161,c_0_152]) ).
cnf(c_0_166,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_5,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_140,c_0_162]),c_0_51])]) ).
cnf(c_0_167,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_1,X1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_163]) ).
cnf(c_0_168,negated_conjecture,
( product(e_2,e_5,e_2)
| product(e_2,e_4,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_164,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_4,e_2)
| product(e_3,e_4,X1)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_166]) ).
cnf(c_0_170,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_5,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_90]) ).
cnf(c_0_171,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_128,c_0_102]),
[final] ).
cnf(c_0_172,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_5,e_4,e_2)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_169,c_0_156]) ).
cnf(c_0_173,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_5,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_170]),c_0_68]) ).
cnf(c_0_174,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_3,e_4,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_175,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_5,e_2)
| product(e_2,e_4,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_173]),c_0_51])]) ).
cnf(c_0_176,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_4,e_1)
| product(e_4,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_174]),c_0_51])]) ).
cnf(c_0_177,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| ~ product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_81,c_0_119]) ).
cnf(c_0_178,negated_conjecture,
( 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_107,c_0_175]),c_0_51])]) ).
cnf(c_0_179,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_176]),c_0_97]) ).
cnf(c_0_180,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_177,c_0_178]) ).
cnf(c_0_181,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_48,c_0_67]),
[final] ).
cnf(c_0_182,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_129,c_0_52]),
[final] ).
cnf(c_0_183,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_4,e_1)
| product(e_2,e_1,X1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_179]) ).
cnf(c_0_184,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_180]),c_0_51])]) ).
cnf(c_0_185,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_1,e_5)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_158,c_0_121]) ).
cnf(c_0_186,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_181,c_0_99]) ).
cnf(c_0_187,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_182,c_0_51]),
[final] ).
cnf(c_0_188,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_3,e_4,e_1)
| product(e_2,e_4,X1)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_172]) ).
cnf(c_0_189,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_1,e_4,e_2)
| product(e_3,e_4,e_1)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_91]) ).
cnf(c_0_190,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_4,e_1,e_5)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_185]),c_0_68]) ).
cnf(c_0_191,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_186,c_0_187]) ).
cnf(c_0_192,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_52]),
[final] ).
cnf(c_0_193,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_188,c_0_156]) ).
cnf(c_0_194,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_4,e_1)
| ~ product(e_5,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_189]),c_0_86]) ).
cnf(c_0_195,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_190]),c_0_149]) ).
cnf(c_0_196,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_5)
| product(e_1,e_3,X1)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_191]) ).
cnf(c_0_197,plain,
~ product(e_1,e_3,e_1),
inference(spm,[status(thm)],[c_0_192,c_0_51]),
[final] ).
cnf(c_0_198,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_193]),c_0_51])]) ).
cnf(c_0_199,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_3,e_4,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_194,c_0_172]) ).
cnf(c_0_200,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_192,c_0_195]),
[final] ).
cnf(c_0_201,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_3,e_5)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_150]),c_0_197]) ).
cnf(c_0_202,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_140,c_0_87]),c_0_141]) ).
cnf(c_0_203,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_127,c_0_198]) ).
cnf(c_0_204,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_4,e_1)
| product(e_4,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_199]),c_0_51])]) ).
cnf(c_0_205,negated_conjecture,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_200,c_0_201]) ).
cnf(c_0_206,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_202,c_0_198]) ).
cnf(c_0_207,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_203,c_0_97]) ).
cnf(c_0_208,negated_conjecture,
( product(e_3,e_4,e_1)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_204]),c_0_97]) ).
cnf(c_0_209,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_205]),c_0_51])]) ).
cnf(c_0_210,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_4,e_1)
| product(e_2,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_206]),c_0_207]) ).
cnf(c_0_211,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_88,c_0_208]),
[final] ).
cnf(c_0_212,negated_conjecture,
( product(e_3,e_1,e_2)
| ~ product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_209]),c_0_192]),
[final] ).
cnf(c_0_213,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_3,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_210]),c_0_207]) ).
cnf(c_0_214,negated_conjecture,
~ product(e_2,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_211]),c_0_51])]),
[final] ).
cnf(c_0_215,negated_conjecture,
( product(e_2,e_1,X1)
| ~ product(e_2,e_3,e_2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_212]),
[final] ).
cnf(c_0_216,negated_conjecture,
product(e_3,e_4,e_1),
inference(sr,[status(thm)],[c_0_213,c_0_214]),
[final] ).
cnf(c_0_217,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_181,c_0_89]) ).
cnf(c_0_218,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_88,c_0_51]),
[final] ).
cnf(c_0_219,negated_conjecture,
( product(e_2,e_4,e_2)
| ~ product(e_2,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_182,c_0_178]),
[final] ).
cnf(c_0_220,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2,
[final] ).
cnf(c_0_221,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_184]),c_0_91]),c_0_182]) ).
cnf(c_0_222,negated_conjecture,
( product(e_1,e_4,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_216]),
[final] ).
cnf(c_0_223,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_217,c_0_218]) ).
cnf(c_0_224,negated_conjecture,
~ product(e_2,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_219]),c_0_51])]),
[final] ).
cnf(c_0_225,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_117,c_0_220]),
[final] ).
cnf(c_0_226,negated_conjecture,
( product(e_3,e_1,e_4)
| ~ product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_221]),c_0_192]) ).
cnf(c_0_227,negated_conjecture,
~ product(e_4,e_1,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_222]),c_0_113]),
[final] ).
cnf(c_0_228,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_223,c_0_224]) ).
cnf(c_0_229,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_212]),
[final] ).
cnf(c_0_230,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[c_0_156,c_0_227]) ).
cnf(c_0_231,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_5)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_127,c_0_191]) ).
cnf(c_0_232,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_228,c_0_229]) ).
cnf(c_0_233,plain,
( product(e_4,e_1,e_4)
| ~ product(e_4,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_192,c_0_230]),
[final] ).
cnf(c_0_234,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_83,c_0_67]) ).
cnf(c_0_235,plain,
~ product(e_3,e_5,e_5),
inference(spm,[status(thm)],[c_0_65,c_0_51]),
[final] ).
cnf(c_0_236,plain,
( product(e_2,e_3,e_4)
| product(e_4,e_3,e_5)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_231,c_0_232]) ).
cnf(c_0_237,plain,
~ product(e_4,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_233]),c_0_51])]),
[final] ).
cnf(c_0_238,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_234,c_0_235]) ).
cnf(c_0_239,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_5)
| product(e_1,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_223]) ).
cnf(c_0_240,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_3,e_3)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_241,plain,
( 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_4,e_1) ),
inference(spm,[status(thm)],[c_0_120,c_0_238]) ).
cnf(c_0_242,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_5)
| product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_163]),c_0_197]) ).
cnf(c_0_243,plain,
( product(e_2,e_3,e_4)
| product(e_4,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_240]),c_0_51])]) ).
cnf(c_0_244,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_241,c_0_213]) ).
cnf(c_0_245,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_5)
| product(e_2,e_4,e_5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_242]),c_0_51])]) ).
cnf(c_0_246,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,X1)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_243]) ).
cnf(c_0_247,negated_conjecture,
( product(e_3,e_5,e_2)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_4) ),
inference(sr,[status(thm)],[c_0_244,c_0_214]) ).
cnf(c_0_248,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_245,c_0_224]) ).
cnf(c_0_249,plain,
( ~ product(X1,e_5,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_52]),
[final] ).
cnf(c_0_250,negated_conjecture,
( product(e_3,e_5,e_3)
| product(e_3,e_5,e_2)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_247]),c_0_224]) ).
cnf(c_0_251,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_248,c_0_229]) ).
cnf(c_0_252,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_3,e_5,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_51])]) ).
cnf(c_0_253,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_5,e_4,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_251]) ).
cnf(c_0_254,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_1,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_232]) ).
cnf(c_0_255,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_5,X1)
| ~ product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_252]) ).
cnf(c_0_256,negated_conjecture,
( product(e_5,e_4,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_253,c_0_243]) ).
cnf(c_0_257,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_4,e_1,X1)
| ~ product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_66]) ).
cnf(c_0_258,negated_conjecture,
( product(e_1,e_3,e_5)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_254,c_0_252]) ).
cnf(c_0_259,negated_conjecture,
( product(e_2,e_5,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
cnf(c_0_260,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_258]),c_0_227]) ).
cnf(c_0_261,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_3,X1)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_209]) ).
cnf(c_0_262,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_4,e_5,X1)
| ~ product(e_5,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_259]) ).
cnf(c_0_263,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_260]),c_0_256]) ).
cnf(c_0_264,plain,
( product(e_4,e_1,e_4)
| ~ product(e_4,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_98,c_0_230]),
[final] ).
cnf(c_0_265,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_261,c_0_150]) ).
cnf(c_0_266,negated_conjecture,
( product(e_4,e_5,e_1)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_262,c_0_263]) ).
cnf(c_0_267,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_99]),c_0_153]) ).
cnf(c_0_268,plain,
~ product(e_4,e_2,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_264]),c_0_51])]),
[final] ).
cnf(c_0_269,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_52]),
[final] ).
cnf(c_0_270,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_177,c_0_251]) ).
cnf(c_0_271,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_1,X1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_265]) ).
cnf(c_0_272,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_107,c_0_266]),
[final] ).
cnf(c_0_273,plain,
( product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_267,c_0_268]) ).
cnf(c_0_274,plain,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_269,c_0_243]),
[final] ).
cnf(c_0_275,plain,
( product(e_5,e_4,e_2)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_4)
| ~ product(e_3,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_147]) ).
cnf(c_0_276,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_86,c_0_147]) ).
cnf(c_0_277,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_1,X1)
| ~ product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_263]) ).
cnf(c_0_278,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_2,e_3,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_270]),c_0_51])]) ).
cnf(c_0_279,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_1,e_4,e_2)
| product(e_2,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_271,c_0_184]),c_0_91]) ).
cnf(c_0_280,plain,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_249,c_0_154]) ).
cnf(c_0_281,negated_conjecture,
( product(e_4,e_2,e_3)
| product(e_2,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_274]) ).
cnf(c_0_282,negated_conjecture,
( product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_213]),c_0_276]) ).
cnf(c_0_283,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_277,c_0_258]) ).
cnf(c_0_284,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_1,e_4,e_2)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_278]) ).
cnf(c_0_285,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_2,e_4,e_2)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_111,c_0_279]) ).
cnf(c_0_286,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_280,c_0_232]) ).
cnf(c_0_287,negated_conjecture,
( product(e_2,e_4,e_2)
| ~ product(e_2,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_122,c_0_178]),
[final] ).
cnf(c_0_288,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_114,c_0_220]),
[final] ).
cnf(c_0_289,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_3,e_2,X1)
| ~ product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_281]) ).
cnf(c_0_290,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_5,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_282]),c_0_51])]) ).
cnf(c_0_291,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_3,e_1,X1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_283]) ).
cnf(c_0_292,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_284,c_0_256]) ).
cnf(c_0_293,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_5,e_3,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_258]) ).
cnf(c_0_294,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_3,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_285]),c_0_265]) ).
cnf(c_0_295,plain,
( product(e_2,e_5,e_2)
| ~ product(e_2,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_286]),c_0_269]),
[final] ).
cnf(c_0_296,negated_conjecture,
~ product(e_2,e_2,e_5),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_287]),c_0_288]),
[final] ).
cnf(c_0_297,negated_conjecture,
( product(e_3,e_2,e_5)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_289,c_0_259]) ).
cnf(c_0_298,negated_conjecture,
( product(e_5,e_4,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_290]),
[final] ).
cnf(c_0_299,negated_conjecture,
( product(e_3,e_1,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_291,c_0_292]) ).
cnf(c_0_300,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_1,e_5,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_266]) ).
cnf(c_0_301,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_293,c_0_216]) ).
cnf(c_0_302,negated_conjecture,
( product(e_2,e_3,e_1)
| product(e_2,e_4,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_294]),c_0_51])]) ).
cnf(c_0_303,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_295]),c_0_296]),
[final] ).
cnf(c_0_304,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_5,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_297]) ).
cnf(c_0_305,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_86,c_0_298]),
[final] ).
cnf(c_0_306,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_1,e_4,e_2)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_184]) ).
cnf(c_0_307,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_4,e_1,X1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_299]) ).
cnf(c_0_308,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_300,c_0_301]) ).
cnf(c_0_309,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_118,c_0_220]),
[final] ).
cnf(c_0_310,negated_conjecture,
product(e_2,e_3,e_1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_302]),c_0_303]),
[final] ).
cnf(c_0_311,negated_conjecture,
( product(e_5,e_2,e_1)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_304,c_0_283]) ).
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_105,c_0_67]) ).
cnf(c_0_313,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_141,c_0_51]),
[final] ).
cnf(c_0_314,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_184]),c_0_305]) ).
cnf(c_0_315,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_1,e_4,e_2)
| product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_306,c_0_290]) ).
cnf(c_0_316,axiom,
greater(e_3,e_2),
e_3_greater_e_2,
[final] ).
cnf(c_0_317,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_269,c_0_51]),
[final] ).
cnf(c_0_318,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_307,c_0_308]) ).
cnf(c_0_319,negated_conjecture,
~ product(e_2,e_3,e_4),
inference(spm,[status(thm)],[c_0_309,c_0_310]),
[final] ).
cnf(c_0_320,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_1,e_2,X1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_311]) ).
cnf(c_0_321,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_322,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_314]),c_0_298]),
[final] ).
cnf(c_0_323,negated_conjecture,
~ product(e_3,e_4,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_315]),c_0_88]),c_0_65]),
[final] ).
cnf(c_0_324,plain,
( ~ product(X1,e_1,e_3)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_56,c_0_316]),
[final] ).
cnf(c_0_325,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_67]),c_0_317]) ).
cnf(c_0_326,negated_conjecture,
product(e_4,e_1,e_5),
inference(sr,[status(thm)],[c_0_318,c_0_319]),
[final] ).
cnf(c_0_327,negated_conjecture,
product(e_4,e_5,e_1),
inference(sr,[status(thm)],[c_0_266,c_0_319]),
[final] ).
cnf(c_0_328,negated_conjecture,
( product(e_1,e_2,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_320,c_0_251]) ).
cnf(c_0_329,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_191,c_0_237]) ).
cnf(c_0_330,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_181,c_0_54]) ).
cnf(c_0_331,plain,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_249,c_0_51]),
[final] ).
cnf(c_0_332,plain,
( product(e_3,e_4,e_1)
| product(e_3,e_4,e_5) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_321,c_0_322]),c_0_323]) ).
cnf(c_0_333,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_181,c_0_49]) ).
cnf(c_0_334,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_324,c_0_85]),
[final] ).
cnf(c_0_335,negated_conjecture,
( product(e_3,e_2,e_5)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_1,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_325]) ).
cnf(c_0_336,negated_conjecture,
product(e_5,e_3,e_4),
inference(sr,[status(thm)],[c_0_301,c_0_319]),
[final] ).
cnf(c_0_337,negated_conjecture,
product(e_1,e_3,e_5),
inference(sr,[status(thm)],[c_0_258,c_0_319]),
[final] ).
cnf(c_0_338,negated_conjecture,
product(e_2,e_4,e_5),
inference(sr,[status(thm)],[c_0_251,c_0_319]),
[final] ).
cnf(c_0_339,negated_conjecture,
( product(e_5,e_1,X1)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_326]),
[final] ).
cnf(c_0_340,negated_conjecture,
( product(e_1,e_5,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_327]),
[final] ).
cnf(c_0_341,negated_conjecture,
product(e_1,e_2,e_4),
inference(sr,[status(thm)],[c_0_328,c_0_319]),
[final] ).
cnf(c_0_342,negated_conjecture,
product(e_5,e_2,e_1),
inference(sr,[status(thm)],[c_0_311,c_0_319]),
[final] ).
cnf(c_0_343,negated_conjecture,
product(e_3,e_2,e_5),
inference(sr,[status(thm)],[c_0_297,c_0_319]),
[final] ).
cnf(c_0_344,negated_conjecture,
product(e_4,e_2,e_3),
inference(sr,[status(thm)],[c_0_281,c_0_319]),
[final] ).
cnf(c_0_345,plain,
( product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_127,c_0_329]) ).
cnf(c_0_346,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_77,c_0_220]),
[final] ).
cnf(c_0_347,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_1,e_4,e_2)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_284,c_0_290]) ).
cnf(c_0_348,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_330,c_0_331]) ).
cnf(c_0_349,plain,
( product(e_3,e_4,e_5)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_88,c_0_332]),
[final] ).
cnf(c_0_350,plain,
( product(e_3,e_4,e_5)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_182,c_0_332]),
[final] ).
cnf(c_0_351,plain,
( product(e_3,e_4,e_5)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_122,c_0_332]),
[final] ).
cnf(c_0_352,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4)
| ~ product(e_1,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_182,c_0_119]) ).
cnf(c_0_353,negated_conjecture,
( product(e_1,e_3,e_5)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_333]),c_0_334]) ).
cnf(c_0_354,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_5) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_335,c_0_97]),c_0_104]) ).
cnf(c_0_355,negated_conjecture,
( product(e_4,e_3,X1)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_336]),
[final] ).
cnf(c_0_356,negated_conjecture,
( product(e_5,e_3,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_337]),
[final] ).
cnf(c_0_357,negated_conjecture,
( product(e_5,e_4,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_338]),
[final] ).
cnf(c_0_358,negated_conjecture,
( product(e_1,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_310]),
[final] ).
cnf(c_0_359,negated_conjecture,
( product(e_5,e_1,e_5)
| ~ product(e_5,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_339,c_0_340]),
[final] ).
cnf(c_0_360,negated_conjecture,
( product(e_4,e_2,X1)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_341]),
[final] ).
cnf(c_0_361,negated_conjecture,
( product(e_1,e_2,X1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_342]),
[final] ).
cnf(c_0_362,negated_conjecture,
( product(e_5,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_343]),
[final] ).
cnf(c_0_363,negated_conjecture,
( product(e_3,e_2,X1)
| ~ product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_344]),
[final] ).
cnf(c_0_364,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_345,c_0_310])]) ).
cnf(c_0_365,negated_conjecture,
~ product(e_1,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_258]),c_0_81]),
[final] ).
cnf(c_0_366,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_5,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_346,c_0_256]),
[final] ).
cnf(c_0_367,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_5,e_4,e_2)
| product(e_3,e_1,e_4)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_111,c_0_347]) ).
cnf(c_0_368,plain,
( product(e_2,e_3,e_4)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_269,c_0_232]),
[final] ).
cnf(c_0_369,negated_conjecture,
( ~ product(e_5,e_4,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_222]),
[final] ).
cnf(c_0_370,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_59,c_0_220]),
[final] ).
cnf(c_0_371,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_220]),
[final] ).
cnf(c_0_372,plain,
( product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_86,c_0_348]) ).
cnf(c_0_373,negated_conjecture,
( product(e_5,e_4,X1)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_349]),
[final] ).
cnf(c_0_374,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_72,c_0_220]),
[final] ).
cnf(c_0_375,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_58,c_0_220]),
[final] ).
cnf(c_0_376,negated_conjecture,
( product(e_5,e_4,X1)
| ~ product(e_3,e_3,e_1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_350]),
[final] ).
cnf(c_0_377,negated_conjecture,
( product(e_5,e_4,X1)
| ~ product(e_3,e_2,e_1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_351]),
[final] ).
cnf(c_0_378,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_352,c_0_353]) ).
cnf(c_0_379,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_1,X1)
| ~ product(e_1,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_156]) ).
cnf(c_0_380,plain,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| ~ product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_128,c_0_87]) ).
cnf(c_0_381,negated_conjecture,
( product(e_2,e_4,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_122,c_0_213]),
[final] ).
cnf(c_0_382,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_5,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_354]) ).
cnf(c_0_383,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_83,c_0_99]) ).
cnf(c_0_384,plain,
~ product(e_4,e_5,e_5),
inference(spm,[status(thm)],[c_0_140,c_0_51]),
[final] ).
cnf(c_0_385,plain,
~ product(e_5,e_2,e_5),
inference(spm,[status(thm)],[c_0_107,c_0_51]),
[final] ).
cnf(c_0_386,negated_conjecture,
( ~ product(e_1,e_4,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_120,c_0_340]),
[final] ).
cnf(c_0_387,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_249,c_0_340]),
[final] ).
cnf(c_0_388,negated_conjecture,
( ~ product(e_1,e_2,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_107,c_0_340]),
[final] ).
cnf(c_0_389,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_269,c_0_355]),
[final] ).
cnf(c_0_390,negated_conjecture,
( ~ product(e_5,e_2,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_269,c_0_356]),
[final] ).
cnf(c_0_391,negated_conjecture,
( ~ product(e_5,e_3,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_182,c_0_357]),
[final] ).
cnf(c_0_392,negated_conjecture,
( ~ product(e_5,e_2,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_122,c_0_357]),
[final] ).
cnf(c_0_393,negated_conjecture,
( ~ product(e_1,e_2,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_269,c_0_358]),
[final] ).
cnf(c_0_394,negated_conjecture,
( ~ product(e_1,e_2,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_222]),
[final] ).
cnf(c_0_395,negated_conjecture,
( ~ product(e_1,e_3,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_222]),
[final] ).
cnf(c_0_396,negated_conjecture,
( product(e_5,e_1,X1)
| ~ product(e_5,e_4,e_4)
| ~ product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_359]),
[final] ).
cnf(c_0_397,negated_conjecture,
( product(X1,e_2,X2)
| ~ product(e_2,X2,e_4)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_360]),
[final] ).
cnf(c_0_398,negated_conjecture,
product(e_2,e_5,e_4),
inference(sr,[status(thm)],[c_0_259,c_0_319]),
[final] ).
cnf(c_0_399,negated_conjecture,
( product(X1,e_2,X2)
| ~ product(e_2,X2,e_1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_361]),
[final] ).
cnf(c_0_400,negated_conjecture,
( product(X1,e_2,X2)
| ~ product(e_2,X2,e_5)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_362]),
[final] ).
cnf(c_0_401,negated_conjecture,
( product(X1,e_2,X2)
| ~ product(e_2,X2,e_3)
| ~ product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_363]),
[final] ).
cnf(c_0_402,negated_conjecture,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[c_0_283,c_0_319]),
[final] ).
cnf(c_0_403,negated_conjecture,
( product(X1,e_5,X2)
| ~ product(e_5,X2,e_1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_340]),
[final] ).
cnf(c_0_404,negated_conjecture,
( product(X1,e_3,X2)
| ~ product(e_3,X2,e_4)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_355]),
[final] ).
cnf(c_0_405,negated_conjecture,
product(e_3,e_1,e_4),
inference(sr,[status(thm)],[c_0_299,c_0_319]),
[final] ).
cnf(c_0_406,negated_conjecture,
( product(X1,e_3,X2)
| ~ product(e_3,X2,e_5)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_356]),
[final] ).
cnf(c_0_407,negated_conjecture,
( product(X1,e_4,X2)
| ~ product(e_4,X2,e_5)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_357]),
[final] ).
cnf(c_0_408,negated_conjecture,
( product(X1,e_3,X2)
| ~ product(e_3,X2,e_1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_358]),
[final] ).
cnf(c_0_409,negated_conjecture,
product(e_1,e_5,e_3),
inference(sr,[status(thm)],[c_0_308,c_0_319]),
[final] ).
cnf(c_0_410,negated_conjecture,
( product(X1,e_4,X2)
| ~ product(e_4,X2,e_1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_222]),
[final] ).
cnf(c_0_411,negated_conjecture,
product(e_5,e_1,e_2),
inference(sr,[status(thm)],[c_0_263,c_0_319]),
[final] ).
cnf(c_0_412,negated_conjecture,
product(e_3,e_5,e_2),
inference(sr,[status(thm)],[c_0_252,c_0_319]),
[final] ).
cnf(c_0_413,negated_conjecture,
product(e_1,e_4,e_2),
inference(sr,[status(thm)],[c_0_292,c_0_319]),
[final] ).
cnf(c_0_414,negated_conjecture,
product(e_5,e_4,e_3),
inference(sr,[status(thm)],[c_0_256,c_0_319]),
[final] ).
cnf(c_0_415,plain,
product(e_4,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_364]),c_0_51])]),
[final] ).
cnf(c_0_416,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_129,c_0_220]),
[final] ).
cnf(c_0_417,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_5) ),
inference(sr,[status(thm)],[c_0_353,c_0_365]) ).
cnf(c_0_418,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_4)
| product(e_2,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_366,c_0_367]) ).
cnf(c_0_419,negated_conjecture,
( product(e_4,e_3,X1)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_368]),
[final] ).
cnf(c_0_420,negated_conjecture,
( product(e_5,e_4,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_369,c_0_290]),
[final] ).
cnf(c_0_421,negated_conjecture,
( ~ product(e_1,e_4,e_3)
| ~ product(e_4,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_370,c_0_222]),
[final] ).
cnf(c_0_422,negated_conjecture,
( ~ product(e_1,e_4,e_2)
| ~ product(e_4,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_371,c_0_222]) ).
cnf(c_0_423,negated_conjecture,
( ~ product(e_1,e_4,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_346,c_0_222]) ).
cnf(c_0_424,negated_conjecture,
( product(e_2,e_1,X1)
| ~ product(e_2,e_4,e_2)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_160]),
[final] ).
cnf(c_0_425,plain,
( ~ product(X1,X2,e_5)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_46,c_0_220]),
[final] ).
cnf(c_0_426,plain,
( product(e_2,e_3,e_4)
| product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_372,c_0_232]) ).
cnf(c_0_427,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_5,e_4,e_2)
| product(e_2,e_4,X1)
| ~ product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_315]) ).
cnf(c_0_428,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_373]),c_0_374]) ).
cnf(c_0_429,negated_conjecture,
( ~ product(e_5,e_4,e_3)
| ~ product(e_3,e_3,e_1)
| ~ product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_375,c_0_376]) ).
cnf(c_0_430,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| ~ product(e_3,e_3,e_1)
| ~ product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_374,c_0_376]) ).
cnf(c_0_431,negated_conjecture,
( ~ product(e_5,e_4,e_3)
| ~ product(e_3,e_2,e_1)
| ~ product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_375,c_0_377]) ).
cnf(c_0_432,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_374,c_0_377]) ).
cnf(c_0_433,plain,
~ product(e_5,e_5,e_4),
inference(spm,[status(thm)],[c_0_288,c_0_51]),
[final] ).
cnf(c_0_434,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| ~ product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_50,c_0_221]),
[final] ).
cnf(c_0_435,negated_conjecture,
( product(e_5,e_4,e_2)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_290]),
[final] ).
cnf(c_0_436,negated_conjecture,
( product(e_5,e_4,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_290]),
[final] ).
cnf(c_0_437,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_378]),c_0_51])]) ).
cnf(c_0_438,negated_conjecture,
( product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_5,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_379,c_0_108]) ).
cnf(c_0_439,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_380,c_0_290]) ).
cnf(c_0_440,negated_conjecture,
( product(e_3,e_2,e_5)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_381,c_0_325]) ).
cnf(c_0_441,negated_conjecture,
( product(e_5,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_382,c_0_97]) ).
cnf(c_0_442,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_383,c_0_384]) ).
cnf(c_0_443,plain,
( product(e_5,e_2,e_1)
| product(e_5,e_2,e_2)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_54]),c_0_385]) ).
cnf(c_0_444,axiom,
greater(e_2,e_1),
e_2_greater_e_1,
[final] ).
cnf(c_0_445,axiom,
greater(e_3,e_1),
e_3_greater_e_1,
[final] ).
cnf(c_0_446,axiom,
greater(e_4,e_1),
e_4_greater_e_1,
[final] ).
cnf(c_0_447,axiom,
greater(e_5,e_1),
e_5_greater_e_1,
[final] ).
cnf(c_0_448,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_358]),c_0_334]),
[final] ).
cnf(c_0_449,plain,
( product(e_4,e_1,e_4)
| ~ product(e_4,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_128,c_0_230]),
[final] ).
cnf(c_0_450,plain,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_98,c_0_97]),
[final] ).
cnf(c_0_451,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_386,c_0_222]),
[final] ).
cnf(c_0_452,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_387,c_0_358]),
[final] ).
cnf(c_0_453,negated_conjecture,
( ~ product(e_5,X1,e_4)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_388,c_0_361]),
[final] ).
cnf(c_0_454,negated_conjecture,
( ~ product(e_3,X1,e_5)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_389,c_0_360]),
[final] ).
cnf(c_0_455,negated_conjecture,
( ~ product(e_3,X1,e_1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_390,c_0_362]),
[final] ).
cnf(c_0_456,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_391,c_0_356]),
[final] ).
cnf(c_0_457,negated_conjecture,
( ~ product(e_4,X1,e_2)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_392,c_0_362]),
[final] ).
cnf(c_0_458,negated_conjecture,
( ~ product(e_3,X1,e_2)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_393,c_0_361]),
[final] ).
cnf(c_0_459,negated_conjecture,
( ~ product(e_3,e_2,X1)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_141,c_0_360]),
[final] ).
cnf(c_0_460,negated_conjecture,
( ~ product(e_2,e_2,X1)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_127,c_0_360]),
[final] ).
cnf(c_0_461,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_394,c_0_361]),
[final] ).
cnf(c_0_462,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_123,c_0_361]),
[final] ).
cnf(c_0_463,negated_conjecture,
( ~ product(e_5,e_2,X1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_50,c_0_361]),
[final] ).
cnf(c_0_464,negated_conjecture,
( ~ product(e_2,e_2,X1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_81,c_0_361]),
[final] ).
cnf(c_0_465,negated_conjecture,
( ~ product(e_3,e_2,X1)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_64,c_0_361]),
[final] ).
cnf(c_0_466,negated_conjecture,
( ~ product(e_4,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_140,c_0_362]),
[final] ).
cnf(c_0_467,negated_conjecture,
( ~ product(e_3,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_362]),
[final] ).
cnf(c_0_468,negated_conjecture,
( ~ product(e_2,e_2,X1)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_86,c_0_362]),
[final] ).
cnf(c_0_469,negated_conjecture,
( ~ product(e_2,e_2,X1)
| ~ product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_88,c_0_363]),
[final] ).
cnf(c_0_470,negated_conjecture,
( ~ product(e_4,e_5,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_123,c_0_340]),
[final] ).
cnf(c_0_471,negated_conjecture,
( ~ product(e_5,e_5,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_50,c_0_340]),
[final] ).
cnf(c_0_472,negated_conjecture,
( ~ product(e_2,e_5,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_340]),
[final] ).
cnf(c_0_473,negated_conjecture,
( ~ product(e_3,e_5,X1)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_64,c_0_340]),
[final] ).
cnf(c_0_474,negated_conjecture,
( ~ product(e_3,e_3,X1)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_141,c_0_355]),
[final] ).
cnf(c_0_475,negated_conjecture,
( ~ product(e_2,e_3,X1)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_127,c_0_355]),
[final] ).
cnf(c_0_476,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_140,c_0_356]),
[final] ).
cnf(c_0_477,negated_conjecture,
( ~ product(e_3,e_3,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_356]),
[final] ).
cnf(c_0_478,negated_conjecture,
( ~ product(e_2,e_3,X1)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_86,c_0_356]),
[final] ).
cnf(c_0_479,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_140,c_0_357]),
[final] ).
cnf(c_0_480,negated_conjecture,
( ~ product(e_3,e_4,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_357]),
[final] ).
cnf(c_0_481,negated_conjecture,
( ~ product(e_2,e_4,X1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_86,c_0_357]),
[final] ).
cnf(c_0_482,negated_conjecture,
( ~ product(e_4,X1,e_3)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_395,c_0_358]),
[final] ).
cnf(c_0_483,negated_conjecture,
( ~ product(e_4,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_123,c_0_358]),
[final] ).
cnf(c_0_484,negated_conjecture,
( ~ product(e_5,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_50,c_0_358]),
[final] ).
cnf(c_0_485,negated_conjecture,
( ~ product(e_2,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_81,c_0_358]),
[final] ).
cnf(c_0_486,negated_conjecture,
( ~ product(e_3,e_3,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_64,c_0_358]),
[final] ).
cnf(c_0_487,negated_conjecture,
( product(e_5,e_1,e_3)
| ~ product(e_5,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_396,c_0_337]),
[final] ).
cnf(c_0_488,negated_conjecture,
( product(X1,e_2,e_5)
| ~ product(e_2,X1,e_1) ),
inference(spm,[status(thm)],[c_0_397,c_0_398]),
[final] ).
cnf(c_0_489,negated_conjecture,
( product(X1,e_2,e_3)
| ~ product(e_2,X1,e_5) ),
inference(spm,[status(thm)],[c_0_399,c_0_310]),
[final] ).
cnf(c_0_490,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(e_2,X1,e_3) ),
inference(spm,[status(thm)],[c_0_400,c_0_338]),
[final] ).
cnf(c_0_491,negated_conjecture,
( product(X1,e_2,e_1)
| ~ product(e_2,X1,e_4) ),
inference(spm,[status(thm)],[c_0_401,c_0_402]),
[final] ).
cnf(c_0_492,negated_conjecture,
( product(X1,e_5,e_2)
| ~ product(e_5,X1,e_4) ),
inference(spm,[status(thm)],[c_0_403,c_0_342]),
[final] ).
cnf(c_0_493,negated_conjecture,
( product(X1,e_3,e_1)
| ~ product(e_3,X1,e_5) ),
inference(spm,[status(thm)],[c_0_404,c_0_405]),
[final] ).
cnf(c_0_494,negated_conjecture,
( product(X1,e_3,e_2)
| ~ product(e_3,X1,e_1) ),
inference(spm,[status(thm)],[c_0_406,c_0_343]),
[final] ).
cnf(c_0_495,negated_conjecture,
( product(X1,e_4,e_1)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_407,c_0_326]),
[final] ).
cnf(c_0_496,negated_conjecture,
( product(X1,e_3,e_4)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_408,c_0_216]),
[final] ).
cnf(c_0_497,negated_conjecture,
( product(e_5,e_5,e_1)
| ~ product(e_5,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_93,c_0_359]),
[final] ).
cnf(c_0_498,negated_conjecture,
( product(e_4,e_1,X1)
| ~ product(e_1,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_405]),
[final] ).
cnf(c_0_499,negated_conjecture,
( product(e_3,e_5,X1)
| ~ product(e_5,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_409]),
[final] ).
cnf(c_0_500,negated_conjecture,
( product(e_3,e_1,X1)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_402]),
[final] ).
cnf(c_0_501,negated_conjecture,
( product(X1,e_4,e_5)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_410,c_0_327]),
[final] ).
cnf(c_0_502,negated_conjecture,
( product(e_2,e_1,X1)
| ~ product(e_1,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_411]),
[final] ).
cnf(c_0_503,negated_conjecture,
( product(e_4,e_5,X1)
| ~ product(e_5,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_398]),
[final] ).
cnf(c_0_504,negated_conjecture,
( product(e_2,e_5,X1)
| ~ product(e_5,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_412]),
[final] ).
cnf(c_0_505,negated_conjecture,
( product(e_2,e_4,X1)
| ~ product(e_4,X1,e_1) ),
inference(spm,[status(thm)],[c_0_82,c_0_413]),
[final] ).
cnf(c_0_506,negated_conjecture,
( product(e_3,e_4,X1)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_414]),
[final] ).
cnf(c_0_507,negated_conjecture,
( product(e_2,e_3,X1)
| ~ product(e_3,X1,e_4) ),
inference(spm,[status(thm)],[c_0_82,c_0_415]),
[final] ).
cnf(c_0_508,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_288,c_0_318]),
[final] ).
cnf(c_0_509,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_60,c_0_299]),
[final] ).
cnf(c_0_510,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_98,c_0_299]),
[final] ).
cnf(c_0_511,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_416,c_0_299]),
[final] ).
cnf(c_0_512,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_64,c_0_308]),
[final] ).
cnf(c_0_513,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_120,c_0_308]),
[final] ).
cnf(c_0_514,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_107,c_0_308]),
[final] ).
cnf(c_0_515,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_346,c_0_308]),
[final] ).
cnf(c_0_516,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_4,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_395,c_0_417]),
[final] ).
cnf(c_0_517,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_3,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_64,c_0_417]),
[final] ).
cnf(c_0_518,negated_conjecture,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_269,c_0_417]),
[final] ).
cnf(c_0_519,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_141,c_0_266]),
[final] ).
cnf(c_0_520,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_127,c_0_266]),
[final] ).
cnf(c_0_521,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_120,c_0_266]),
[final] ).
cnf(c_0_522,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_249,c_0_266]),
[final] ).
cnf(c_0_523,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_309,c_0_266]),
[final] ).
cnf(c_0_524,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_374,c_0_266]),
[final] ).
cnf(c_0_525,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_86,c_0_263]),
[final] ).
cnf(c_0_526,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_5,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_98,c_0_263]),
[final] ).
cnf(c_0_527,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_5,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_269,c_0_301]),
[final] ).
cnf(c_0_528,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_5,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_225,c_0_301]),
[final] ).
cnf(c_0_529,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_418]),c_0_88]),
[final] ).
cnf(c_0_530,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_418]),c_0_88]),
[final] ).
cnf(c_0_531,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_3,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_64,c_0_258]),
[final] ).
cnf(c_0_532,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_269,c_0_258]),
[final] ).
cnf(c_0_533,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_370,c_0_258]),
[final] ).
cnf(c_0_534,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_2,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_88,c_0_252]),
[final] ).
cnf(c_0_535,negated_conjecture,
( product(X1,e_4,e_3)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,e_1,e_2)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_410,c_0_419]),
[final] ).
cnf(c_0_536,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_182,c_0_292]),
[final] ).
cnf(c_0_537,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_122,c_0_292]),
[final] ).
cnf(c_0_538,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_369,c_0_256]),
[final] ).
cnf(c_0_539,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_256]),
[final] ).
cnf(c_0_540,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_256]),
[final] ).
cnf(c_0_541,negated_conjecture,
( product(e_2,e_4,X1)
| ~ product(e_4,e_3,e_3)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_420]),
[final] ).
cnf(c_0_542,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_4,e_5,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_421,c_0_278]),c_0_422]),
[final] ).
cnf(c_0_543,negated_conjecture,
( product(e_2,e_4,e_2)
| ~ product(e_4,e_5,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_421,c_0_184]),c_0_422]),
[final] ).
cnf(c_0_544,negated_conjecture,
( ~ product(e_5,e_3,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_420]),
[final] ).
cnf(c_0_545,negated_conjecture,
( ~ product(e_5,e_2,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_420]),
[final] ).
cnf(c_0_546,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_423,c_0_142]),
[final] ).
cnf(c_0_547,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_5,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_222]),c_0_91]),
[final] ).
cnf(c_0_548,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_222]),c_0_91]),
[final] ).
cnf(c_0_549,negated_conjecture,
( ~ product(e_4,e_4,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_123,c_0_222]),
[final] ).
cnf(c_0_550,negated_conjecture,
( ~ product(e_2,e_4,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_222]),
[final] ).
cnf(c_0_551,negated_conjecture,
( ~ product(e_3,e_4,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_64,c_0_222]),
[final] ).
cnf(c_0_552,negated_conjecture,
( ~ product(e_1,e_4,e_4)
| ~ product(e_4,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_288,c_0_222]),
[final] ).
cnf(c_0_553,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_182,c_0_208]),
[final] ).
cnf(c_0_554,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_425,c_0_208]),
[final] ).
cnf(c_0_555,plain,
( product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| ~ product(e_3,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_426]),c_0_88]),
[final] ).
cnf(c_0_556,negated_conjecture,
( product(e_5,e_4,e_2)
| product(e_2,e_4,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_427,c_0_419]),c_0_144]),
[final] ).
cnf(c_0_557,negated_conjecture,
( ~ product(e_1,e_3,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_428]),
[final] ).
cnf(c_0_558,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_428]),
[final] ).
cnf(c_0_559,negated_conjecture,
( product(X1,e_3,X2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,X2,e_4)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_419]),
[final] ).
cnf(c_0_560,negated_conjecture,
( product(X1,e_4,X2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,X2,e_5)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_373]),
[final] ).
cnf(c_0_561,negated_conjecture,
( product(X1,e_4,X2)
| ~ product(e_3,e_3,e_1)
| ~ product(e_4,X2,e_5)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_376]),
[final] ).
cnf(c_0_562,negated_conjecture,
( product(X1,e_4,X2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_4,X2,e_5)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_82,c_0_377]),
[final] ).
cnf(c_0_563,negated_conjecture,
( ~ product(e_2,e_2,e_1)
| ~ product(e_4,e_2,X1)
| ~ product(e_3,X1,e_2) ),
inference(spm,[status(thm)],[c_0_269,c_0_419]),
[final] ).
cnf(c_0_564,negated_conjecture,
( ~ product(e_4,e_3,e_5)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_425,c_0_419]),
[final] ).
cnf(c_0_565,negated_conjecture,
( ~ product(e_4,e_3,e_3)
| ~ product(e_2,e_2,e_1)
| ~ product(e_3,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_375,c_0_419]),
[final] ).
cnf(c_0_566,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_5,e_3,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_373]),
[final] ).
cnf(c_0_567,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_5,e_2,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_373]),
[final] ).
cnf(c_0_568,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| ~ product(e_2,e_4,e_1)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_346,c_0_373]),
[final] ).
cnf(c_0_569,negated_conjecture,
( ~ product(e_3,e_3,e_1)
| ~ product(e_4,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_429,c_0_290]),c_0_430]),
[final] ).
cnf(c_0_570,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_4,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_431,c_0_290]),c_0_432]),
[final] ).
cnf(c_0_571,negated_conjecture,
( ~ product(e_3,e_3,e_1)
| ~ product(e_5,e_3,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_376]),
[final] ).
cnf(c_0_572,negated_conjecture,
( ~ product(e_3,e_3,e_1)
| ~ product(e_5,e_2,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_376]),
[final] ).
cnf(c_0_573,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_5,e_3,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_377]),
[final] ).
cnf(c_0_574,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_5,e_2,X1)
| ~ product(e_4,X1,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_377]),
[final] ).
cnf(c_0_575,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| ~ product(e_3,e_2,e_1)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_346,c_0_377]),
[final] ).
cnf(c_0_576,negated_conjecture,
( ~ product(e_2,e_4,e_1)
| ~ product(e_4,e_5,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_373]),c_0_433]),
[final] ).
cnf(c_0_577,negated_conjecture,
( ~ product(e_3,e_3,e_1)
| ~ product(e_4,e_5,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_376]),c_0_433]),
[final] ).
cnf(c_0_578,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| ~ product(e_4,e_5,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_377]),c_0_433]),
[final] ).
cnf(c_0_579,plain,
( ~ product(e_3,e_3,e_5)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_182,c_0_349]),
[final] ).
cnf(c_0_580,plain,
( ~ product(e_3,e_3,e_5)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_182,c_0_351]),
[final] ).
cnf(c_0_581,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_5,e_4,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_182,c_0_315]),
[final] ).
cnf(c_0_582,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_5,e_4,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_122,c_0_315]),
[final] ).
cnf(c_0_583,negated_conjecture,
( ~ product(e_2,e_3,e_2)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_434,c_0_435]),
[final] ).
cnf(c_0_584,negated_conjecture,
( ~ product(e_2,e_3,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_434,c_0_436]),
[final] ).
cnf(c_0_585,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_122,c_0_221]),
[final] ).
cnf(c_0_586,negated_conjecture,
( ~ product(e_1,e_3,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_314]),
[final] ).
cnf(c_0_587,negated_conjecture,
( ~ product(e_1,e_2,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_314]),
[final] ).
cnf(c_0_588,negated_conjecture,
( product(e_2,e_3,e_4)
| ~ product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_371,c_0_248]),c_0_182]),
[final] ).
cnf(c_0_589,negated_conjecture,
( product(e_2,e_4,X1)
| ~ product(e_2,e_3,e_5)
| ~ product(e_4,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_219]),
[final] ).
cnf(c_0_590,negated_conjecture,
( product(e_2,e_2,e_4)
| ~ product(e_2,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_93,c_0_219]),
[final] ).
cnf(c_0_591,negated_conjecture,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| ~ product(e_2,e_2,e_5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_245]),c_0_269]),
[final] ).
cnf(c_0_592,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| ~ product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_128,c_0_212]),
[final] ).
cnf(c_0_593,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_269,c_0_209]),
[final] ).
cnf(c_0_594,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_128,c_0_195]),
[final] ).
cnf(c_0_595,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_98,c_0_195]),
[final] ).
cnf(c_0_596,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_288,c_0_195]),
[final] ).
cnf(c_0_597,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_370,c_0_195]),
[final] ).
cnf(c_0_598,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| ~ product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_437]),c_0_91]),c_0_81]),
[final] ).
cnf(c_0_599,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_1,e_5)
| product(e_1,e_5,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_438]),c_0_90]),
[final] ).
cnf(c_0_600,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_5,e_4,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_439]),c_0_88]),
[final] ).
cnf(c_0_601,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| ~ product(e_5,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_439]),c_0_122]),
[final] ).
cnf(c_0_602,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| ~ product(e_5,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_439]),c_0_182]),
[final] ).
cnf(c_0_603,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| ~ product(e_2,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_88,c_0_440]),
[final] ).
cnf(c_0_604,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_171,c_0_298]),
[final] ).
cnf(c_0_605,negated_conjecture,
( product(e_2,e_4,X1)
| ~ product(e_3,e_4,e_3)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_298]),
[final] ).
cnf(c_0_606,negated_conjecture,
( ~ product(e_5,e_3,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_298]),
[final] ).
cnf(c_0_607,negated_conjecture,
( ~ product(e_5,e_2,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_298]),
[final] ).
cnf(c_0_608,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_435]),
[final] ).
cnf(c_0_609,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_86,c_0_435]),
[final] ).
cnf(c_0_610,negated_conjecture,
( ~ product(e_5,e_2,e_2)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_122,c_0_435]),
[final] ).
cnf(c_0_611,negated_conjecture,
( ~ product(e_3,e_4,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_436]),
[final] ).
cnf(c_0_612,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_86,c_0_436]),
[final] ).
cnf(c_0_613,negated_conjecture,
( ~ product(e_5,e_3,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_436]),
[final] ).
cnf(c_0_614,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_171,c_0_435]),
[final] ).
cnf(c_0_615,negated_conjecture,
( product(e_2,e_4,X1)
| ~ product(e_5,e_3,e_3)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_435]),
[final] ).
cnf(c_0_616,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_171,c_0_436]),
[final] ).
cnf(c_0_617,negated_conjecture,
( product(e_2,e_4,X1)
| ~ product(e_5,e_2,e_3)
| ~ product(e_4,X1,e_5) ),
inference(spm,[status(thm)],[c_0_82,c_0_436]),
[final] ).
cnf(c_0_618,negated_conjecture,
( product(e_2,e_4,e_1)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_182,c_0_213]),
[final] ).
cnf(c_0_619,negated_conjecture,
( product(e_2,e_4,e_1)
| ~ product(e_3,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_425,c_0_213]),
[final] ).
cnf(c_0_620,negated_conjecture,
( product(e_2,e_4,e_1)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_375,c_0_213]),
[final] ).
cnf(c_0_621,negated_conjecture,
( product(e_2,e_4,e_1)
| ~ product(e_3,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_210]),c_0_374]),
[final] ).
cnf(c_0_622,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_64,c_0_121]),
[final] ).
cnf(c_0_623,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_60,c_0_150]),
[final] ).
cnf(c_0_624,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_98,c_0_150]),
[final] ).
cnf(c_0_625,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_416,c_0_150]),c_0_346]),
[final] ).
cnf(c_0_626,negated_conjecture,
( ~ product(e_3,e_2,e_2)
| ~ product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_98,c_0_160]),
[final] ).
cnf(c_0_627,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_142]),c_0_128]),
[final] ).
cnf(c_0_628,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_182,c_0_142]),
[final] ).
cnf(c_0_629,negated_conjecture,
( product(e_1,e_5,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_121]),c_0_269]),
[final] ).
cnf(c_0_630,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| ~ product(e_3,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_172]),c_0_374]),
[final] ).
cnf(c_0_631,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_5,e_1,e_5)
| product(e_1,e_5,e_2)
| ~ product(e_4,e_5,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_438]),c_0_60]),
[final] ).
cnf(c_0_632,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_1,e_5)
| product(e_1,e_5,e_2)
| ~ product(e_3,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_64,c_0_438]),
[final] ).
cnf(c_0_633,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_1,e_5)
| product(e_1,e_5,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_107,c_0_438]),
[final] ).
cnf(c_0_634,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_140,c_0_441]),
[final] ).
cnf(c_0_635,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_441]),c_0_309]),c_0_374]),
[final] ).
cnf(c_0_636,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_86,c_0_441]),
[final] ).
cnf(c_0_637,negated_conjecture,
( product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_2,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_309,c_0_441]),c_0_65]),
[final] ).
cnf(c_0_638,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_374,c_0_441]),c_0_65]),
[final] ).
cnf(c_0_639,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_375,c_0_441]),
[final] ).
cnf(c_0_640,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_5,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_50,c_0_116]),
[final] ).
cnf(c_0_641,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_81,c_0_116]),
[final] ).
cnf(c_0_642,negated_conjecture,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_88,c_0_354]),
[final] ).
cnf(c_0_643,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_98,c_0_102]),
[final] ).
cnf(c_0_644,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| ~ product(e_5,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_192,c_0_102]),
[final] ).
cnf(c_0_645,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_141,c_0_442]),
[final] ).
cnf(c_0_646,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_127,c_0_442]),
[final] ).
cnf(c_0_647,plain,
( 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_4,e_1) ),
inference(spm,[status(thm)],[c_0_120,c_0_442]),
[final] ).
cnf(c_0_648,plain,
( 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_3,e_1) ),
inference(spm,[status(thm)],[c_0_249,c_0_442]),
[final] ).
cnf(c_0_649,plain,
( 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_2,e_1) ),
inference(spm,[status(thm)],[c_0_107,c_0_442]),
[final] ).
cnf(c_0_650,plain,
( product(e_5,e_2,e_4)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_140,c_0_443]),
[final] ).
cnf(c_0_651,plain,
( product(e_5,e_2,e_4)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_443]),
[final] ).
cnf(c_0_652,plain,
( product(e_5,e_2,e_4)
| product(e_5,e_2,e_3)
| product(e_5,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_86,c_0_443]),
[final] ).
cnf(c_0_653,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_60,c_0_76]),
[final] ).
cnf(c_0_654,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_98,c_0_76]),
[final] ).
cnf(c_0_655,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_192,c_0_76]),
[final] ).
cnf(c_0_656,negated_conjecture,
( product(e_2,e_1,X1)
| ~ product(e_2,e_4,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_133]),
[final] ).
cnf(c_0_657,negated_conjecture,
( product(e_2,e_1,X1)
| ~ product(e_2,e_5,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_82,c_0_136]),
[final] ).
cnf(c_0_658,negated_conjecture,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_93,c_0_133]),
[final] ).
cnf(c_0_659,negated_conjecture,
( product(e_2,e_2,e_1)
| ~ product(e_2,e_5,e_3) ),
inference(spm,[status(thm)],[c_0_93,c_0_136]),
[final] ).
cnf(c_0_660,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| ~ product(e_4,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_123,c_0_353]),
[final] ).
cnf(c_0_661,negated_conjecture,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4)
| ~ product(e_2,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_81,c_0_353]),
[final] ).
cnf(c_0_662,plain,
( ~ product(X1,e_1,e_2)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_56,c_0_444]),
[final] ).
cnf(c_0_663,plain,
( ~ product(X1,e_1,e_3)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_56,c_0_445]),
[final] ).
cnf(c_0_664,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_56,c_0_446]),
[final] ).
cnf(c_0_665,plain,
( ~ product(X1,e_1,e_5)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_56,c_0_447]),
[final] ).
cnf(c_0_666,negated_conjecture,
~ product(e_5,e_4,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_416,c_0_340]),c_0_409])]),
[final] ).
cnf(c_0_667,negated_conjecture,
~ product(e_5,e_1,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_375,c_0_340]),c_0_409])]),
[final] ).
cnf(c_0_668,negated_conjecture,
~ product(e_4,e_1,e_4),
inference(spm,[status(thm)],[c_0_288,c_0_326]),
[final] ).
cnf(c_0_669,negated_conjecture,
~ product(e_3,e_5,e_4),
inference(spm,[status(thm)],[c_0_60,c_0_405]),
[final] ).
cnf(c_0_670,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(spm,[status(thm)],[c_0_98,c_0_405]),
[final] ).
cnf(c_0_671,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_416,c_0_405]),
[final] ).
cnf(c_0_672,negated_conjecture,
~ product(e_3,e_5,e_3),
inference(spm,[status(thm)],[c_0_64,c_0_409]),
[final] ).
cnf(c_0_673,negated_conjecture,
~ product(e_1,e_4,e_3),
inference(spm,[status(thm)],[c_0_120,c_0_409]),
[final] ).
cnf(c_0_674,negated_conjecture,
~ product(e_1,e_2,e_3),
inference(spm,[status(thm)],[c_0_107,c_0_409]),
[final] ).
cnf(c_0_675,negated_conjecture,
~ product(e_1,e_5,e_2),
inference(spm,[status(thm)],[c_0_346,c_0_409]),
[final] ).
cnf(c_0_676,negated_conjecture,
~ product(e_3,e_5,e_1),
inference(spm,[status(thm)],[c_0_141,c_0_327]),
[final] ).
cnf(c_0_677,negated_conjecture,
~ product(e_2,e_5,e_1),
inference(spm,[status(thm)],[c_0_127,c_0_327]),
[final] ).
cnf(c_0_678,negated_conjecture,
~ product(e_4,e_4,e_1),
inference(spm,[status(thm)],[c_0_120,c_0_327]),
[final] ).
cnf(c_0_679,negated_conjecture,
~ product(e_4,e_3,e_1),
inference(spm,[status(thm)],[c_0_249,c_0_327]),
[final] ).
cnf(c_0_680,negated_conjecture,
~ product(e_4,e_2,e_1),
inference(spm,[status(thm)],[c_0_107,c_0_327]),
[final] ).
cnf(c_0_681,negated_conjecture,
~ product(e_4,e_5,e_4),
inference(spm,[status(thm)],[c_0_309,c_0_327]),
[final] ).
cnf(c_0_682,negated_conjecture,
~ product(e_4,e_5,e_2),
inference(spm,[status(thm)],[c_0_374,c_0_327]),
[final] ).
cnf(c_0_683,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_86,c_0_411]),
[final] ).
cnf(c_0_684,negated_conjecture,
~ product(e_5,e_2,e_2),
inference(spm,[status(thm)],[c_0_98,c_0_411]),
[final] ).
cnf(c_0_685,negated_conjecture,
~ product(e_5,e_2,e_4),
inference(spm,[status(thm)],[c_0_269,c_0_336]),
[final] ).
cnf(c_0_686,negated_conjecture,
~ product(e_5,e_3,e_2),
inference(spm,[status(thm)],[c_0_225,c_0_336]),
[final] ).
cnf(c_0_687,negated_conjecture,
~ product(e_3,e_3,e_5),
inference(spm,[status(thm)],[c_0_64,c_0_337]),
[final] ).
cnf(c_0_688,negated_conjecture,
~ product(e_1,e_2,e_5),
inference(spm,[status(thm)],[c_0_269,c_0_337]),
[final] ).
cnf(c_0_689,negated_conjecture,
~ product(e_1,e_3,e_3),
inference(spm,[status(thm)],[c_0_370,c_0_337]),
[final] ).
cnf(c_0_690,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(spm,[status(thm)],[c_0_88,c_0_412]),
[final] ).
cnf(c_0_691,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_107,c_0_412]),
[final] ).
cnf(c_0_692,negated_conjecture,
~ product(e_1,e_3,e_2),
inference(spm,[status(thm)],[c_0_182,c_0_413]),
[final] ).
cnf(c_0_693,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_122,c_0_413]),
[final] ).
cnf(c_0_694,negated_conjecture,
~ product(e_4,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_422,c_0_413])]),
[final] ).
cnf(c_0_695,negated_conjecture,
~ product(e_4,e_3,e_3),
inference(spm,[status(thm)],[c_0_369,c_0_414]),
[final] ).
cnf(c_0_696,negated_conjecture,
~ product(e_5,e_3,e_3),
inference(spm,[status(thm)],[c_0_182,c_0_414]),
[final] ).
cnf(c_0_697,negated_conjecture,
~ product(e_5,e_2,e_3),
inference(spm,[status(thm)],[c_0_122,c_0_414]),
[final] ).
cnf(c_0_698,negated_conjecture,
~ product(e_5,e_4,e_2),
inference(spm,[status(thm)],[c_0_346,c_0_414]),
[final] ).
cnf(c_0_699,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_448,c_0_160]),
[final] ).
cnf(c_0_700,plain,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_269,c_0_415]),
[final] ).
cnf(c_0_701,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(spm,[status(thm)],[c_0_269,c_0_310]),
[final] ).
cnf(c_0_702,negated_conjecture,
~ product(e_3,e_3,e_4),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_301]),c_0_88]),
[final] ).
cnf(c_0_703,plain,
~ product(e_4,e_4,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_449]),c_0_51])]),
[final] ).
cnf(c_0_704,negated_conjecture,
~ product(e_3,e_3,e_1),
inference(spm,[status(thm)],[c_0_182,c_0_216]),
[final] ).
cnf(c_0_705,negated_conjecture,
~ product(e_3,e_2,e_1),
inference(spm,[status(thm)],[c_0_122,c_0_216]),
[final] ).
cnf(c_0_706,negated_conjecture,
~ product(e_3,e_4,e_5),
inference(spm,[status(thm)],[c_0_425,c_0_216]),
[final] ).
cnf(c_0_707,plain,
~ product(e_2,e_2,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_450]),c_0_51])]),
[final] ).
cnf(c_0_708,plain,
~ product(e_5,e_5,e_3),
inference(spm,[status(thm)],[c_0_370,c_0_51]),
[final] ).
cnf(c_0_709,plain,
~ product(e_4,e_4,e_3),
inference(spm,[status(thm)],[c_0_416,c_0_51]),
[final] ).
cnf(c_0_710,plain,
~ product(e_1,e_5,e_1),
inference(spm,[status(thm)],[c_0_60,c_0_51]),
[final] ).
cnf(c_0_711,plain,
~ product(e_1,e_1,e_2),
inference(spm,[status(thm)],[c_0_374,c_0_51]),
[final] ).
cnf(c_0_712,plain,
~ product(e_4,e_4,e_2),
inference(spm,[status(thm)],[c_0_225,c_0_51]),
[final] ).
cnf(c_0_713,plain,
~ product(e_5,e_5,e_2),
inference(spm,[status(thm)],[c_0_371,c_0_51]),
[final] ).
cnf(c_0_714,plain,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_346,c_0_51]),
[final] ).
cnf(c_0_715,axiom,
~ equalish(e_5,e_4),
e_5_is_not_e_4,
[final] ).
cnf(c_0_716,axiom,
~ equalish(e_5,e_3),
e_5_is_not_e_3,
[final] ).
cnf(c_0_717,axiom,
~ equalish(e_5,e_2),
e_5_is_not_e_2,
[final] ).
cnf(c_0_718,axiom,
~ equalish(e_5,e_1),
e_5_is_not_e_1,
[final] ).
cnf(c_0_719,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3,
[final] ).
cnf(c_0_720,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2,
[final] ).
cnf(c_0_721,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1,
[final] ).
cnf(c_0_722,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3,
[final] ).
cnf(c_0_723,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3,
[final] ).
cnf(c_0_724,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2,
[final] ).
cnf(c_0_725,axiom,
next(e_4,e_5),
e_4_then_e_5,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP127-2.005 : TPTP v9.2.1. Released v1.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:23:45 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.67/1.82 % Version : CSE_E---1.7
% 1.67/1.82 % Problem : theBenchmark.p
% 1.67/1.82 % SZS status Satisfiable for theBenchmark.p
% 1.67/1.82 % SZS output start Saturation
% See solution above
% 1.67/1.83 % Total time : 1.374s
%------------------------------------------------------------------------------