%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP128-2.004 : 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 : n004.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 04:24:05 PM UTC 2026
% Result : Satisfiable 1.30s 1.74s
% Output : Saturation 1.30s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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_4_greater_e_2,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).
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(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ 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(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(e_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(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(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(product_total_function2,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(qg3,negated_conjecture,
( product(X1,X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
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_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
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_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
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_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
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_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_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_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(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_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
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_3_then_e_4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_then_e_4) ).
cnf(c_0_31,axiom,
( ~ product(X1,e_1,X2)
| ~ next(X1,X3)
| ~ greater(X2,X3) ),
no_redundancy,
[final] ).
cnf(c_0_32,axiom,
greater(e_4,e_2),
e_4_greater_e_2,
[final] ).
cnf(c_0_33,axiom,
greater(e_3,e_2),
e_3_greater_e_2,
[final] ).
cnf(c_0_34,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| product(X1,X2,e_4)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1,
[final] ).
cnf(c_0_35,axiom,
group_element(e_1),
element_1,
[final] ).
cnf(c_0_36,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]),
[final] ).
cnf(c_0_37,axiom,
next(e_1,e_2),
e_1_then_e_2,
[final] ).
cnf(c_0_38,plain,
( ~ product(X1,e_1,e_3)
| ~ next(X1,e_2) ),
inference(spm,[status(thm)],[c_0_31,c_0_33]),
[final] ).
cnf(c_0_39,axiom,
~ equalish(e_4,e_1),
e_4_is_not_e_1,
[final] ).
cnf(c_0_40,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation,
[final] ).
cnf(c_0_41,plain,
( 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_34,c_0_35]),
[final] ).
cnf(c_0_42,plain,
~ product(e_1,e_1,e_4),
inference(spm,[status(thm)],[c_0_36,c_0_37]),
[final] ).
cnf(c_0_43,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_38,c_0_37]),
[final] ).
cnf(c_0_44,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]),
[final] ).
cnf(c_0_45,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_35]),c_0_42]),c_0_43]),
[final] ).
cnf(c_0_46,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1,
[final] ).
cnf(c_0_47,axiom,
( equalish(X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X2,X4) ),
product_total_function2,
[final] ).
cnf(c_0_48,negated_conjecture,
( product(X1,X3,X4)
| ~ product(X1,X2,X3)
| ~ product(X3,X2,X4) ),
qg3,
[final] ).
cnf(c_0_49,plain,
( product(e_1,e_1,e_2)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]),
[final] ).
cnf(c_0_50,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]),
[final] ).
cnf(c_0_51,axiom,
group_element(e_4),
element_4,
[final] ).
cnf(c_0_52,axiom,
greater(e_4,e_3),
e_4_greater_e_3,
[final] ).
cnf(c_0_53,negated_conjecture,
( ~ product(e_4,e_1,e_1)
| ~ product(X1,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),
[final] ).
cnf(c_0_54,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_41,c_0_51]) ).
cnf(c_0_55,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_40]),
[final] ).
cnf(c_0_56,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_52]),
[final] ).
cnf(c_0_57,axiom,
next(e_2,e_3),
e_2_then_e_3,
[final] ).
cnf(c_0_58,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation,
[final] ).
cnf(c_0_60,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_45]),
[final] ).
cnf(c_0_61,axiom,
group_element(e_2),
element_2,
[final] ).
cnf(c_0_62,plain,
~ product(e_2,e_1,e_4),
inference(spm,[status(thm)],[c_0_56,c_0_57]),
[final] ).
cnf(c_0_63,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1,
[final] ).
cnf(c_0_64,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_58,c_0_54]) ).
cnf(c_0_65,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_59]),
[final] ).
cnf(c_0_66,negated_conjecture,
( ~ product(e_2,e_1,e_1)
| ~ product(X1,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_60]),c_0_50]),
[final] ).
cnf(c_0_67,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_61]),c_0_62]) ).
cnf(c_0_68,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_40]),
[final] ).
cnf(c_0_69,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| ~ product(X1,e_1,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_64]),c_0_65]) ).
cnf(c_0_70,negated_conjecture,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,axiom,
~ equalish(e_4,e_2),
e_4_is_not_e_2,
[final] ).
cnf(c_0_72,plain,
( product(e_1,e_1,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_45]),
[final] ).
cnf(c_0_73,axiom,
group_element(e_3),
element_3,
[final] ).
cnf(c_0_74,axiom,
~ equalish(e_4,e_3),
e_4_is_not_e_3,
[final] ).
cnf(c_0_75,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_59]),
[final] ).
cnf(c_0_76,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_69,c_0_64]) ).
cnf(c_0_77,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_70,c_0_67]) ).
cnf(c_0_78,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_40]),
[final] ).
cnf(c_0_79,negated_conjecture,
( ~ product(e_3,e_1,e_1)
| ~ product(X1,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_72]),c_0_50]),
[final] ).
cnf(c_0_80,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_41,c_0_73]) ).
cnf(c_0_81,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_40]),
[final] ).
cnf(c_0_82,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( product(e_2,e_1,e_2)
| product(X1,e_2,e_3)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_77]) ).
cnf(c_0_84,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_78,c_0_76]) ).
cnf(c_0_85,axiom,
~ equalish(e_3,e_2),
e_3_is_not_e_2,
[final] ).
cnf(c_0_86,negated_conjecture,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| ~ product(X1,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_4,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_88,negated_conjecture,
( product(e_4,e_2,e_3)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_77]) ).
cnf(c_0_89,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_3,X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_40]),
[final] ).
cnf(c_0_90,negated_conjecture,
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_86,c_0_80]) ).
cnf(c_0_91,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),
[final] ).
cnf(c_0_92,negated_conjecture,
( product(e_4,e_1,e_2)
| product(X1,e_4,e_3)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_76]) ).
cnf(c_0_93,negated_conjecture,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_94,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_76]) ).
cnf(c_0_95,negated_conjecture,
( product(X1,e_4,e_2)
| ~ product(e_2,e_1,e_3)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_84]) ).
cnf(c_0_96,negated_conjecture,
( product(e_3,e_4,e_3)
| product(e_4,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_97,negated_conjecture,
( product(e_2,e_1,e_2)
| product(X1,e_4,e_2)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_95,c_0_77]) ).
cnf(c_0_98,negated_conjecture,
( product(e_3,e_4,e_3)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_78,c_0_96]),
[final] ).
cnf(c_0_99,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_59]),
[final] ).
cnf(c_0_100,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_4,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_97,c_0_93]) ).
cnf(c_0_101,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(X1,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_98]),c_0_99]),
[final] ).
cnf(c_0_102,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_85,c_0_47]),
[final] ).
cnf(c_0_103,negated_conjecture,
~ product(e_3,e_4,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_100]),c_0_101]),c_0_102]),
[final] ).
cnf(c_0_104,plain,
( 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_34,c_0_51]),
[final] ).
cnf(c_0_105,negated_conjecture,
( product(e_3,e_1,e_3)
| product(X1,e_3,e_4)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_93]) ).
cnf(c_0_106,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_59]),
[final] ).
cnf(c_0_107,negated_conjecture,
product(e_4,e_1,e_2),
inference(sr,[status(thm)],[c_0_96,c_0_103]),
[final] ).
cnf(c_0_108,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) ),
inference(spm,[status(thm)],[c_0_104,c_0_35]) ).
cnf(c_0_109,plain,
( 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_34,c_0_73]),
[final] ).
cnf(c_0_110,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_3,e_4)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_105,c_0_77]) ).
cnf(c_0_111,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(spm,[status(thm)],[c_0_103,c_0_98]),
[final] ).
cnf(c_0_112,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_106,c_0_76]) ).
cnf(c_0_113,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_59]),
[final] ).
cnf(c_0_114,negated_conjecture,
( product(X1,e_4,e_2)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_107]),
[final] ).
cnf(c_0_115,negated_conjecture,
( product(e_4,e_1,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_76]) ).
cnf(c_0_116,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| ~ product(X1,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_108]),c_0_65]) ).
cnf(c_0_117,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) ),
inference(spm,[status(thm)],[c_0_109,c_0_51]) ).
cnf(c_0_118,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,negated_conjecture,
product(e_2,e_1,e_3),
inference(sr,[status(thm)],[c_0_77,c_0_111]),
[final] ).
cnf(c_0_120,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_112]),c_0_113]),
[final] ).
cnf(c_0_121,negated_conjecture,
( product(e_4,e_1,e_2)
| product(e_4,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_76]),c_0_94]) ).
cnf(c_0_122,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_71,c_0_47]),
[final] ).
cnf(c_0_123,negated_conjecture,
( product(e_3,e_1,e_3)
| product(e_3,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_114,c_0_93]) ).
cnf(c_0_124,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_104,c_0_51]) ).
cnf(c_0_125,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_39,c_0_47]),
[final] ).
cnf(c_0_126,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_59]),
[final] ).
cnf(c_0_127,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_78,c_0_115]) ).
cnf(c_0_128,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_116,c_0_108]) ).
cnf(c_0_129,negated_conjecture,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(X1,e_4,e_1)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_117]) ).
cnf(c_0_130,negated_conjecture,
product(e_2,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_118]),c_0_119])]),
[final] ).
cnf(c_0_131,negated_conjecture,
~ product(e_4,e_3,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_112]),c_0_120]),
[final] ).
cnf(c_0_132,negated_conjecture,
~ product(e_4,e_3,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_121]),c_0_122]),
[final] ).
cnf(c_0_133,negated_conjecture,
product(e_3,e_4,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_123]),c_0_119])]),
[final] ).
cnf(c_0_134,negated_conjecture,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| ~ product(X1,e_4,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_124]),c_0_125]) ).
cnf(c_0_135,negated_conjecture,
~ product(e_4,e_4,e_3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_115]),c_0_126]),c_0_127]),
[final] ).
cnf(c_0_136,negated_conjecture,
~ product(e_4,e_4,e_2),
inference(spm,[status(thm)],[c_0_65,c_0_107]),
[final] ).
cnf(c_0_137,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| ~ product(e_4,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_44,c_0_128]) ).
cnf(c_0_138,negated_conjecture,
( product(e_2,e_4,e_1)
| product(e_4,e_3,e_4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_132]) ).
cnf(c_0_139,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_45]),
[final] ).
cnf(c_0_140,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) ),
inference(spm,[status(thm)],[c_0_104,c_0_61]) ).
cnf(c_0_141,negated_conjecture,
( product(X1,e_3,e_2)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_133]),
[final] ).
cnf(c_0_142,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_128]),c_0_135]),c_0_136]),c_0_137]),
[final] ).
cnf(c_0_143,negated_conjecture,
product(e_2,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_138]),c_0_130])]),
[final] ).
cnf(c_0_144,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_77]),
[final] ).
cnf(c_0_145,plain,
( ~ product(X1,X2,e_1)
| ~ product(X1,X2,e_3) ),
inference(spm,[status(thm)],[c_0_63,c_0_47]),
[final] ).
cnf(c_0_146,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_139]),
[final] ).
cnf(c_0_147,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(sr,[status(thm)],[c_0_124,c_0_135]) ).
cnf(c_0_148,plain,
( 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_34,c_0_61]),
[final] ).
cnf(c_0_149,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_88]),
[final] ).
cnf(c_0_150,negated_conjecture,
( product(e_3,e_1,e_3)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_75,c_0_93]),
[final] ).
cnf(c_0_151,negated_conjecture,
product(e_4,e_2,e_3),
inference(sr,[status(thm)],[c_0_88,c_0_111]),
[final] ).
cnf(c_0_152,negated_conjecture,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(X1,e_2,e_1)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_140]) ).
cnf(c_0_153,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_154,negated_conjecture,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_125,c_0_143]),
[final] ).
cnf(c_0_155,negated_conjecture,
~ product(e_2,e_4,e_3),
inference(spm,[status(thm)],[c_0_111,c_0_144]),
[final] ).
cnf(c_0_156,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_89,c_0_133]),
[final] ).
cnf(c_0_157,negated_conjecture,
~ product(e_1,e_2,e_1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_139]),c_0_145]),c_0_146]),
[final] ).
cnf(c_0_158,plain,
( product(e_4,e_4,e_2)
| product(e_4,e_4,e_4)
| ~ product(e_2,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_78,c_0_147]) ).
cnf(c_0_159,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_148,c_0_35]) ).
cnf(c_0_160,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_148,c_0_73]) ).
cnf(c_0_161,negated_conjecture,
~ product(e_3,e_2,e_3),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_98]),c_0_149]),
[final] ).
cnf(c_0_162,negated_conjecture,
( ~ product(e_3,e_4,e_3)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_65,c_0_150]),
[final] ).
cnf(c_0_163,negated_conjecture,
( product(X1,e_4,e_3)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_151]),
[final] ).
cnf(c_0_164,negated_conjecture,
( product(X1,e_2,e_4)
| ~ product(X1,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_130]),
[final] ).
cnf(c_0_165,negated_conjecture,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_155]),c_0_156]),c_0_157]),
[final] ).
cnf(c_0_166,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(sr,[status(thm)],[c_0_117,c_0_131]) ).
cnf(c_0_167,plain,
product(e_4,e_4,e_4),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_143])]),c_0_136]),
[final] ).
cnf(c_0_168,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2) ),
inference(sr,[status(thm)],[c_0_159,c_0_157]) ).
cnf(c_0_169,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_160,c_0_161]) ).
cnf(c_0_170,negated_conjecture,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_126,c_0_133]),
[final] ).
cnf(c_0_171,negated_conjecture,
~ product(e_3,e_2,e_4),
inference(spm,[status(thm)],[c_0_162,c_0_163]),
[final] ).
cnf(c_0_172,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_126,c_0_142]),
[final] ).
cnf(c_0_173,negated_conjecture,
product(e_1,e_2,e_4),
inference(spm,[status(thm)],[c_0_164,c_0_165]),
[final] ).
cnf(c_0_174,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_166,c_0_132]) ).
cnf(c_0_175,plain,
~ product(e_4,e_3,e_4),
inference(spm,[status(thm)],[c_0_99,c_0_167]),
[final] ).
cnf(c_0_176,negated_conjecture,
( product(X1,X2,e_3)
| ~ product(X2,e_2,e_4)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_163]),
[final] ).
cnf(c_0_177,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(X1,e_1,e_4)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_168]) ).
cnf(c_0_178,plain,
product(e_3,e_2,e_1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_169,c_0_170]),c_0_171]),
[final] ).
cnf(c_0_179,negated_conjecture,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_113,c_0_165]),
[final] ).
cnf(c_0_180,negated_conjecture,
~ product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_172]),c_0_154]),c_0_155]),c_0_156]),c_0_157]),
[final] ).
cnf(c_0_181,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_78,c_0_94]),
[final] ).
cnf(c_0_182,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_49]),
[final] ).
cnf(c_0_183,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_72]),
[final] ).
cnf(c_0_184,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_109,c_0_73]) ).
cnf(c_0_185,negated_conjecture,
( product(X1,e_1,e_4)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_173]),
[final] ).
cnf(c_0_186,plain,
product(e_4,e_3,e_1),
inference(sr,[status(thm)],[c_0_174,c_0_175]),
[final] ).
cnf(c_0_187,negated_conjecture,
( product(X1,e_1,e_3)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_176,c_0_173]),
[final] ).
cnf(c_0_188,negated_conjecture,
( product(X1,e_1,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_165]),
[final] ).
cnf(c_0_189,negated_conjecture,
product(e_3,e_1,e_4),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_179]),c_0_180]),
[final] ).
cnf(c_0_190,negated_conjecture,
( product(e_4,e_2,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_94]),c_0_181]) ).
cnf(c_0_191,negated_conjecture,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_126,c_0_128]) ).
cnf(c_0_192,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_106,c_0_45]) ).
cnf(c_0_193,plain,
( product(e_1,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_45]),
[final] ).
cnf(c_0_194,plain,
( product(e_4,e_3,e_4)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_174]),
[final] ).
cnf(c_0_195,plain,
( product(e_4,e_3,e_4)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_81,c_0_174]),
[final] ).
cnf(c_0_196,negated_conjecture,
( product(e_1,e_2,e_3)
| ~ product(e_4,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_49]),c_0_182]),
[final] ).
cnf(c_0_197,negated_conjecture,
( product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_60]),c_0_50]),
[final] ).
cnf(c_0_198,negated_conjecture,
( product(e_1,e_2,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_72]),c_0_183]),
[final] ).
cnf(c_0_199,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_77]),
[final] ).
cnf(c_0_200,plain,
( product(e_3,e_3,e_4)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_184]) ).
cnf(c_0_201,negated_conjecture,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_99,c_0_133]),
[final] ).
cnf(c_0_202,negated_conjecture,
( product(X1,e_4,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_114,c_0_185]),
[final] ).
cnf(c_0_203,negated_conjecture,
( product(X1,e_3,e_1)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_178]),
[final] ).
cnf(c_0_204,negated_conjecture,
( product(X1,e_4,e_1)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_48,c_0_186]),
[final] ).
cnf(c_0_205,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_4) ),
inference(spm,[status(thm)],[c_0_74,c_0_47]),
[final] ).
cnf(c_0_206,negated_conjecture,
( product(X1,X2,e_3)
| ~ product(X2,e_4,e_1)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_187]),
[final] ).
cnf(c_0_207,negated_conjecture,
( product(X1,X2,e_2)
| ~ product(X2,e_3,e_1)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_188]),
[final] ).
cnf(c_0_208,negated_conjecture,
( product(X1,e_3,e_2)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_141,c_0_163]),
[final] ).
cnf(c_0_209,negated_conjecture,
( product(X1,e_3,e_4)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_48,c_0_189]),
[final] ).
cnf(c_0_210,negated_conjecture,
( product(X1,e_2,e_3)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_119]),
[final] ).
cnf(c_0_211,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_106,c_0_77]),
[final] ).
cnf(c_0_212,plain,
( product(e_4,e_3,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_78,c_0_174]),
[final] ).
cnf(c_0_213,negated_conjecture,
( product(e_4,e_3,e_4)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_78,c_0_121]),
[final] ).
cnf(c_0_214,negated_conjecture,
( product(e_4,e_3,e_4)
| ~ product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_75,c_0_121]),
[final] ).
cnf(c_0_215,negated_conjecture,
( product(e_3,e_1,e_3)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_106,c_0_93]),
[final] ).
cnf(c_0_216,negated_conjecture,
( product(e_3,e_1,e_3)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_65,c_0_93]),
[final] ).
cnf(c_0_217,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_78,c_0_190]),
[final] ).
cnf(c_0_218,plain,
( ~ product(e_4,e_1,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_72]) ).
cnf(c_0_219,negated_conjecture,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_191,c_0_168]) ).
cnf(c_0_220,plain,
( ~ product(e_4,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_60]) ).
cnf(c_0_221,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_192]) ).
cnf(c_0_222,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) ),
inference(spm,[status(thm)],[c_0_109,c_0_35]) ).
cnf(c_0_223,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_193]),
[final] ).
cnf(c_0_224,axiom,
greater(e_2,e_1),
e_2_greater_e_1,
[final] ).
cnf(c_0_225,axiom,
greater(e_3,e_1),
e_3_greater_e_1,
[final] ).
cnf(c_0_226,axiom,
greater(e_4,e_1),
e_4_greater_e_1,
[final] ).
cnf(c_0_227,negated_conjecture,
( product(e_1,e_4,e_2)
| ~ product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_99,c_0_142]),
[final] ).
cnf(c_0_228,plain,
( ~ product(e_2,e_3,e_4)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_78,c_0_194]) ).
cnf(c_0_229,plain,
( ~ product(e_2,e_3,e_4)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_78,c_0_195]) ).
cnf(c_0_230,negated_conjecture,
( ~ product(e_4,e_2,e_3)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_196]) ).
cnf(c_0_231,plain,
( ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_193]) ).
cnf(c_0_232,plain,
( ~ product(e_4,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_192]) ).
cnf(c_0_233,negated_conjecture,
( ~ product(e_4,e_2,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_197]) ).
cnf(c_0_234,negated_conjecture,
( ~ product(e_4,e_2,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_44,c_0_198]) ).
cnf(c_0_235,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_148,c_0_61]) ).
cnf(c_0_236,negated_conjecture,
~ product(e_2,e_2,e_3),
inference(spm,[status(thm)],[c_0_111,c_0_199]),
[final] ).
cnf(c_0_237,negated_conjecture,
~ product(e_2,e_2,e_1),
inference(spm,[status(thm)],[c_0_126,c_0_143]),
[final] ).
cnf(c_0_238,negated_conjecture,
~ product(e_2,e_2,e_4),
inference(spm,[status(thm)],[c_0_113,c_0_130]),
[final] ).
cnf(c_0_239,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_178])]),c_0_201]) ).
cnf(c_0_240,negated_conjecture,
( ~ product(X1,e_2,e_3)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_187]),
[final] ).
cnf(c_0_241,negated_conjecture,
( ~ product(X1,e_3,e_3)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_106,c_0_187]),
[final] ).
cnf(c_0_242,negated_conjecture,
( ~ product(X1,e_1,e_2)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_102,c_0_187]),
[final] ).
cnf(c_0_243,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_99,c_0_202]),
[final] ).
cnf(c_0_244,negated_conjecture,
( ~ product(X1,e_3,e_2)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_50,c_0_203]),
[final] ).
cnf(c_0_245,negated_conjecture,
( ~ product(X1,e_3,e_4)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_125,c_0_203]),
[final] ).
cnf(c_0_246,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_50,c_0_204]),
[final] ).
cnf(c_0_247,negated_conjecture,
( ~ product(X1,e_4,e_3)
| ~ product(X1,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_145,c_0_204]),
[final] ).
cnf(c_0_248,negated_conjecture,
( ~ product(X1,e_3,e_4)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_106,c_0_185]),
[final] ).
cnf(c_0_249,negated_conjecture,
( ~ product(X1,e_4,e_4)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_185]),
[final] ).
cnf(c_0_250,negated_conjecture,
( ~ product(X1,e_1,e_2)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_122,c_0_185]),
[final] ).
cnf(c_0_251,negated_conjecture,
( ~ product(X1,e_1,e_3)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_205,c_0_185]),
[final] ).
cnf(c_0_252,negated_conjecture,
( ~ product(X1,e_2,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_188]),
[final] ).
cnf(c_0_253,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_188]),
[final] ).
cnf(c_0_254,negated_conjecture,
( ~ product(X1,e_3,e_3)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_99,c_0_163]),
[final] ).
cnf(c_0_255,negated_conjecture,
( product(X1,X2,e_3)
| ~ product(X2,e_3,e_4)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_206,c_0_204]),
[final] ).
cnf(c_0_256,negated_conjecture,
( ~ product(X1,e_4,e_2)
| ~ product(X1,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_102,c_0_163]),
[final] ).
cnf(c_0_257,negated_conjecture,
( product(X1,X2,e_2)
| ~ product(X2,e_2,e_3)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_207,c_0_203]),
[final] ).
cnf(c_0_258,negated_conjecture,
( product(X1,X2,e_2)
| ~ product(X2,e_2,e_1)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_202]),
[final] ).
cnf(c_0_259,negated_conjecture,
( product(X1,X2,e_1)
| ~ product(X2,e_2,e_3)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_203]),
[final] ).
cnf(c_0_260,negated_conjecture,
( product(X1,X2,e_1)
| ~ product(X2,e_3,e_4)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_204]),
[final] ).
cnf(c_0_261,negated_conjecture,
( product(X1,X2,e_4)
| ~ product(X2,e_2,e_1)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_185]),
[final] ).
cnf(c_0_262,negated_conjecture,
( product(X1,X2,e_2)
| ~ product(X2,e_2,e_4)
| ~ product(X1,e_3,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_208]),
[final] ).
cnf(c_0_263,negated_conjecture,
( product(X1,e_3,e_4)
| ~ product(X1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_209,c_0_187]),
[final] ).
cnf(c_0_264,negated_conjecture,
( product(X1,e_2,e_3)
| ~ product(X1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_210,c_0_188]),
[final] ).
cnf(c_0_265,negated_conjecture,
( product(X1,e_2,e_1)
| ~ product(X1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_48,c_0_143]),
[final] ).
cnf(c_0_266,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_101,c_0_199]),
[final] ).
cnf(c_0_267,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_101,c_0_211]),
[final] ).
cnf(c_0_268,negated_conjecture,
( ~ product(e_2,e_4,e_3)
| ~ product(X1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_101,c_0_144]),
[final] ).
cnf(c_0_269,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_81,c_0_212]),
[final] ).
cnf(c_0_270,plain,
( ~ product(e_4,e_2,e_4)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_212]),
[final] ).
cnf(c_0_271,plain,
( ~ product(e_4,e_2,e_4)
| ~ product(e_3,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_113,c_0_195]),
[final] ).
cnf(c_0_272,plain,
( ~ product(e_3,e_3,e_4)
| ~ product(e_4,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_81,c_0_194]),
[final] ).
cnf(c_0_273,negated_conjecture,
( ~ product(e_4,e_2,e_4)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_113,c_0_213]),
[final] ).
cnf(c_0_274,negated_conjecture,
( ~ product(e_3,e_3,e_4)
| ~ product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_81,c_0_214]),
[final] ).
cnf(c_0_275,negated_conjecture,
( product(e_4,e_3,e_4)
| ~ product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_121]),
[final] ).
cnf(c_0_276,negated_conjecture,
( ~ product(e_3,e_2,e_4)
| ~ product(X1,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_150]),c_0_106]),
[final] ).
cnf(c_0_277,negated_conjecture,
( ~ product(e_3,e_3,e_4)
| ~ product(X1,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_215]),c_0_106]),
[final] ).
cnf(c_0_278,negated_conjecture,
( ~ product(e_3,e_4,e_4)
| ~ product(X1,e_1,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_216]),c_0_106]),
[final] ).
cnf(c_0_279,negated_conjecture,
( product(e_3,e_4,e_3)
| ~ product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_75,c_0_96]),
[final] ).
cnf(c_0_280,negated_conjecture,
( product(e_3,e_4,e_3)
| ~ product(e_4,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_106,c_0_96]),
[final] ).
cnf(c_0_281,negated_conjecture,
( product(e_3,e_4,e_3)
| ~ product(e_4,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_65,c_0_96]),
[final] ).
cnf(c_0_282,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_181,c_0_150]),
[final] ).
cnf(c_0_283,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_217,c_0_150]),
[final] ).
cnf(c_0_284,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_181,c_0_215]),
[final] ).
cnf(c_0_285,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_217,c_0_215]),
[final] ).
cnf(c_0_286,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_181,c_0_216]),
[final] ).
cnf(c_0_287,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_217,c_0_216]),
[final] ).
cnf(c_0_288,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_3,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_75,c_0_216]),
[final] ).
cnf(c_0_289,negated_conjecture,
( product(e_2,e_1,e_2)
| ~ product(e_4,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_102,c_0_88]),
[final] ).
cnf(c_0_290,negated_conjecture,
( ~ product(e_4,e_2,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_94]),
[final] ).
cnf(c_0_291,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_106,c_0_94]),
[final] ).
cnf(c_0_292,negated_conjecture,
( ~ product(e_4,e_4,e_2)
| ~ product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_94]),
[final] ).
cnf(c_0_293,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_112]),
[final] ).
cnf(c_0_294,negated_conjecture,
( ~ product(e_4,e_2,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_112]),
[final] ).
cnf(c_0_295,negated_conjecture,
( ~ product(e_4,e_4,e_2)
| ~ product(e_4,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_112]),
[final] ).
cnf(c_0_296,negated_conjecture,
( ~ product(e_3,e_1,e_1)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_218,c_0_115]),
[final] ).
cnf(c_0_297,negated_conjecture,
( ~ product(e_3,e_1,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_81,c_0_115]),
[final] ).
cnf(c_0_298,negated_conjecture,
( ~ product(e_4,e_2,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_75,c_0_115]),
[final] ).
cnf(c_0_299,negated_conjecture,
( ~ product(e_4,e_3,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_106,c_0_115]),
[final] ).
cnf(c_0_300,negated_conjecture,
( product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_219]),c_0_48]),
[final] ).
cnf(c_0_301,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_3,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_68,c_0_219]),
[final] ).
cnf(c_0_302,negated_conjecture,
( product(e_1,e_4,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| ~ product(e_4,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_44,c_0_219]),
[final] ).
cnf(c_0_303,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_54]),c_0_220]),
[final] ).
cnf(c_0_304,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_54]),c_0_218]),
[final] ).
cnf(c_0_305,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| ~ product(e_1,e_2,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_113]),
[final] ).
cnf(c_0_306,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_2,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_55,c_0_168]),
[final] ).
cnf(c_0_307,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_3,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_68,c_0_168]),
[final] ).
cnf(c_0_308,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| ~ product(e_4,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_44,c_0_168]),
[final] ).
cnf(c_0_309,negated_conjecture,
( product(X1,e_1,e_3)
| ~ product(e_2,e_1,e_1)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_197]),
[final] ).
cnf(c_0_310,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_197]),
[final] ).
cnf(c_0_311,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_197]),
[final] ).
cnf(c_0_312,negated_conjecture,
( product(X1,e_1,e_3)
| ~ product(e_3,e_1,e_1)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_198]),
[final] ).
cnf(c_0_313,negated_conjecture,
( product(X1,e_1,e_3)
| ~ product(e_4,e_1,e_1)
| ~ product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_48,c_0_196]),
[final] ).
cnf(c_0_314,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_198]),
[final] ).
cnf(c_0_315,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_198]),
[final] ).
cnf(c_0_316,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_196]),
[final] ).
cnf(c_0_317,negated_conjecture,
( ~ product(e_3,e_2,e_3)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_196]),
[final] ).
cnf(c_0_318,negated_conjecture,
( product(e_1,e_2,e_3)
| ~ product(e_1,e_4,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_193]),c_0_223]),
[final] ).
cnf(c_0_319,negated_conjecture,
( ~ product(e_2,e_2,e_3)
| ~ product(X1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_199]),c_0_75]),
[final] ).
cnf(c_0_320,negated_conjecture,
( ~ product(e_2,e_3,e_3)
| ~ product(X1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_211]),c_0_75]),
[final] ).
cnf(c_0_321,negated_conjecture,
( ~ product(e_2,e_4,e_3)
| ~ product(X1,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_144]),c_0_75]),
[final] ).
cnf(c_0_322,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_2,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_199]),
[final] ).
cnf(c_0_323,negated_conjecture,
( ~ product(e_2,e_4,e_2)
| ~ product(e_2,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_65,c_0_211]),
[final] ).
cnf(c_0_324,negated_conjecture,
( ~ product(e_2,e_3,e_2)
| ~ product(e_2,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_106,c_0_144]),
[final] ).
cnf(c_0_325,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_60]),
[final] ).
cnf(c_0_326,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_60]),
[final] ).
cnf(c_0_327,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_60]),
[final] ).
cnf(c_0_328,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_72]),
[final] ).
cnf(c_0_329,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_72]),
[final] ).
cnf(c_0_330,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_49]),
[final] ).
cnf(c_0_331,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_49]),
[final] ).
cnf(c_0_332,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_4,e_1,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_49]),
[final] ).
cnf(c_0_333,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_139]),
[final] ).
cnf(c_0_334,plain,
( ~ product(e_1,e_4,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_65,c_0_139]),
[final] ).
cnf(c_0_335,plain,
( ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_55,c_0_192]),
[final] ).
cnf(c_0_336,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_192]),
[final] ).
cnf(c_0_337,negated_conjecture,
( ~ product(e_1,e_2,e_1)
| ~ product(X1,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_139]),c_0_50]),
[final] ).
cnf(c_0_338,negated_conjecture,
( ~ product(e_1,e_3,e_1)
| ~ product(X1,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_192]),c_0_50]),
[final] ).
cnf(c_0_339,negated_conjecture,
( ~ product(e_1,e_4,e_1)
| ~ product(X1,e_1,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_193]),c_0_50]),
[final] ).
cnf(c_0_340,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_68,c_0_193]),
[final] ).
cnf(c_0_341,plain,
( ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_4,e_1) ),
inference(spm,[status(thm)],[c_0_75,c_0_193]),
[final] ).
cnf(c_0_342,plain,
( product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_89,c_0_160]),
[final] ).
cnf(c_0_343,plain,
( product(e_2,e_4,e_4)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| ~ product(e_2,e_3,e_1) ),
inference(spm,[status(thm)],[c_0_99,c_0_140]),
[final] ).
cnf(c_0_344,plain,
( ~ product(X1,e_1,e_2)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_224]),
[final] ).
cnf(c_0_345,plain,
( ~ product(X1,e_1,e_3)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_225]),
[final] ).
cnf(c_0_346,plain,
( ~ product(X1,e_1,e_4)
| ~ next(X1,e_1) ),
inference(spm,[status(thm)],[c_0_31,c_0_226]),
[final] ).
cnf(c_0_347,negated_conjecture,
~ product(e_3,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_187]),c_0_119])]),
[final] ).
cnf(c_0_348,negated_conjecture,
~ product(e_4,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_187]),c_0_119])]),
[final] ).
cnf(c_0_349,negated_conjecture,
~ product(e_1,e_3,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_204]),c_0_143])]),
[final] ).
cnf(c_0_350,negated_conjecture,
~ product(e_3,e_3,e_4),
inference(spm,[status(thm)],[c_0_106,c_0_189]),
[final] ).
cnf(c_0_351,negated_conjecture,
~ product(e_3,e_1,e_3),
inference(spm,[status(thm)],[c_0_205,c_0_189]),
[final] ).
cnf(c_0_352,negated_conjecture,
~ product(e_1,e_3,e_3),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_227]),c_0_154]),c_0_155]),c_0_156]),c_0_157]),
[final] ).
cnf(c_0_353,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_81,c_0_167]),
[final] ).
cnf(c_0_354,negated_conjecture,
~ product(e_2,e_3,e_1),
inference(spm,[status(thm)],[c_0_99,c_0_143]),
[final] ).
cnf(c_0_355,negated_conjecture,
~ product(e_4,e_2,e_4),
inference(spm,[status(thm)],[c_0_135,c_0_163]),
[final] ).
cnf(c_0_356,negated_conjecture,
~ product(e_2,e_3,e_2),
inference(spm,[status(thm)],[c_0_122,c_0_130]),
[final] ).
cnf(c_0_357,plain,
~ product(e_4,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_228,c_0_130])]),
[final] ).
cnf(c_0_358,plain,
~ product(e_3,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_130])]),
[final] ).
cnf(c_0_359,negated_conjecture,
~ product(e_4,e_1,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_230,c_0_151])]),
[final] ).
cnf(c_0_360,negated_conjecture,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_111,c_0_211]),
[final] ).
cnf(c_0_361,negated_conjecture,
~ product(e_4,e_2,e_2),
inference(spm,[status(thm)],[c_0_75,c_0_107]),
[final] ).
cnf(c_0_362,plain,
~ product(e_1,e_4,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_231,c_0_107])]),
[final] ).
cnf(c_0_363,plain,
~ product(e_1,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_232,c_0_107])]),
[final] ).
cnf(c_0_364,negated_conjecture,
~ product(e_2,e_1,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_88]),c_0_50]),
[final] ).
cnf(c_0_365,negated_conjecture,
~ product(e_3,e_1,e_1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_88]),c_0_183]),
[final] ).
cnf(c_0_366,axiom,
~ equalish(e_3,e_4),
e_3_is_not_e_4,
[final] ).
cnf(c_0_367,axiom,
~ equalish(e_2,e_4),
e_2_is_not_e_4,
[final] ).
cnf(c_0_368,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3,
[final] ).
cnf(c_0_369,axiom,
~ equalish(e_1,e_4),
e_1_is_not_e_4,
[final] ).
cnf(c_0_370,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3,
[final] ).
cnf(c_0_371,axiom,
~ equalish(e_1,e_2),
e_1_is_not_e_2,
[final] ).
cnf(c_0_372,plain,
product(e_2,e_2,e_2),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_235,c_0_236]),c_0_237]),c_0_238]),
[final] ).
cnf(c_0_373,plain,
product(e_3,e_3,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_239]),c_0_130])]),
[final] ).
cnf(c_0_374,axiom,
next(e_3,e_4),
e_3_then_e_4,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP128-2.004 : 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 : n004.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 18:23:17 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Satisfiable for theBenchmark.p
% 1.30/1.74 % SZS output start Saturation
% See solution above
% 1.30/1.74 % Total time : 1.369s
%------------------------------------------------------------------------------