%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE072+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 04:35:39 PM UTC 2026
% Result : Theorem 0.35s 1.62s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 38
% Syntax : Number of formulae : 157 ( 132 unt; 0 def)
% Number of atoms : 190 ( 170 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 69 ( 36 ~; 31 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 230 ( 4 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] : domain(multiplication(addition(X4,X5),domain(X6))) = addition(domain(multiplication(X4,domain(X6))),domain(multiplication(X5,domain(X6)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(domain2,axiom,
! [X4,X5] : domain(multiplication(X4,X5)) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain2) ).
fof(domain5,axiom,
! [X4,X5] : domain(addition(X4,X5)) = addition(domain(X4),domain(X5)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain5) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(domain4,axiom,
domain(zero) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+5.ax',domain4) ).
fof(i_0_18,negated_conjecture,
~ ! [X4,X5,X6] : domain(multiplication(addition(X4,X5),domain(X6))) = addition(domain(multiplication(X4,domain(X6))),domain(multiplication(X5,domain(X6)))),
inference(assume_negation,[status(cth)],[goals]) ).
fof(i_0_19,negated_conjecture,
domain(multiplication(addition(esk1_0,esk2_0),domain(esk3_0))) != addition(domain(multiplication(esk1_0,domain(esk3_0))),domain(multiplication(esk2_0,domain(esk3_0)))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])]) ).
fof(i_0_20,plain,
! [X53,X54,X55] : multiplication(addition(X53,X54),X55) = addition(multiplication(X53,X55),multiplication(X54,X55)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(i_0_21,plain,
! [X50,X51,X52] : multiplication(X50,addition(X51,X52)) = addition(multiplication(X50,X51),multiplication(X50,X52)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(i_0_22,plain,
! [X45,X46,X47] : multiplication(X45,multiplication(X46,X47)) = multiplication(multiplication(X45,X46),X47),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(i_0_23,plain,
! [X40,X41,X42] : addition(X42,addition(X41,X40)) = addition(addition(X42,X41),X40),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(i_0_24,plain,
! [X60] : addition(X60,multiplication(domain(X60),X60)) = multiplication(domain(X60),X60),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(i_0_25,plain,
! [X61,X62] : domain(multiplication(X61,X62)) = domain(multiplication(X61,domain(X62))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(i_0_26,plain,
! [X64,X65] : domain(addition(X64,X65)) = addition(domain(X64),domain(X65)),
inference(variable_rename,[status(thm)],[domain5]) ).
fof(i_0_27,plain,
! [X58,X59] :
( ( ~ leq(X58,X59)
| addition(X58,X59) = X59 )
& ( addition(X58,X59) != X59
| leq(X58,X59) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(i_0_28,plain,
! [X38,X39] : addition(X38,X39) = addition(X39,X38),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(i_0_29,plain,
! [X63] : addition(domain(X63),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(i_0_30,plain,
! [X44] : addition(X44,X44) = X44,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(i_0_31,plain,
! [X49] : multiplication(one,X49) = X49,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(i_0_32,plain,
! [X48] : multiplication(X48,one) = X48,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(i_0_33,plain,
! [X43] : addition(X43,zero) = X43,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(i_0_34,plain,
! [X57] : multiplication(zero,X57) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(i_0_35,plain,
! [X56] : multiplication(X56,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(i_0_36,negated_conjecture,
domain(multiplication(addition(esk1_0,esk2_0),domain(esk3_0))) != addition(domain(multiplication(esk1_0,domain(esk3_0))),domain(multiplication(esk2_0,domain(esk3_0)))),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_37,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_41,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_42,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_43,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_44,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_45,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_46,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_47,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_48,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_49,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_50,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_51,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_52,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_53,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_54,plain,
domain(zero) = zero,
inference(split_conjunct,[status(thm)],[domain4]),
[final] ).
cnf(i_0_55,axiom,
X1 = X1 ).
cnf(i_0_56,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_57,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_58,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_62,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_55_001,axiom,
X1 = X1 ).
cnf(i_0_56_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_57_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_58_004,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_59_005,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_60_006,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_61_007,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_62_008,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_63_009,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_64_010,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_65,plain,
X1 = addition(X1,X1),
inference(scs_inference,[],[i_0_48,i_0_56]) ).
cnf(i_0_66,plain,
leq(X1,X1),
inference(scs_inference,[],[i_0_48,i_0_56,i_0_44]) ).
cnf(i_0_67,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_68,plain,
domain(multiplication(addition(esk1_0,esk2_0),domain(esk3_0))) != addition(domain(multiplication(esk2_0,domain(esk3_0))),domain(multiplication(esk1_0,domain(esk3_0)))),
inference(scs_inference,[],[i_0_36,i_0_48,i_0_46,i_0_56,i_0_44,i_0_57]) ).
cnf(i_0_69,plain,
addition(X1,X2) = addition(X2,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_70,plain,
leq(X1,multiplication(domain(X1),X1)),
inference(scs_inference,[],[i_0_41,i_0_44]) ).
cnf(i_0_71,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_72,plain,
X1 = multiplication(one,X1),
inference(scs_inference,[],[i_0_49,i_0_41,i_0_44,i_0_56]) ).
cnf(i_0_73,plain,
multiplication(one,X1) = addition(X1,X1),
inference(scs_inference,[],[i_0_65,i_0_49,i_0_41,i_0_44,i_0_56,i_0_57]) ).
cnf(i_0_74,plain,
X1 = addition(X1,X1),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_75,plain,
leq(domain(X1),one),
inference(scs_inference,[],[i_0_47,i_0_44]) ).
cnf(i_0_76,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_77,plain,
addition(X1,X1) = multiplication(one,X1),
inference(scs_inference,[],[i_0_73,i_0_47,i_0_44,i_0_56]) ).
cnf(i_0_78,plain,
X1 = multiplication(one,addition(X1,X1)),
inference(scs_inference,[],[i_0_72,i_0_65,i_0_73,i_0_47,i_0_44,i_0_56,i_0_57]) ).
cnf(i_0_79,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_80,plain,
multiplication(one,addition(X1,X1)) = X1,
inference(scs_inference,[],[i_0_78,i_0_56]) ).
cnf(i_0_81,plain,
addition(X1,X1) = multiplication(one,multiplication(one,X1)),
inference(scs_inference,[],[i_0_77,i_0_72,i_0_78,i_0_56,i_0_57]) ).
cnf(i_0_82,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_83,plain,
multiplication(one,multiplication(one,X1)) = addition(X1,X1),
inference(scs_inference,[],[i_0_81,i_0_56]) ).
cnf(i_0_84,plain,
multiplication(one,addition(addition(X1,X1),addition(X1,X1))) = multiplication(one,X1),
inference(scs_inference,[],[i_0_80,i_0_77,i_0_81,i_0_56,i_0_57]) ).
cnf(i_0_85,plain,
multiplication(one,addition(X1,X1)) = X1,
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_86,plain,
multiplication(one,X1) = multiplication(one,addition(addition(X1,X1),addition(X1,X1))),
inference(scs_inference,[],[i_0_84,i_0_56]) ).
cnf(i_0_87,plain,
multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))) = addition(X1,X1),
inference(scs_inference,[],[i_0_83,i_0_80,i_0_84,i_0_56,i_0_57]) ).
cnf(i_0_88,plain,
multiplication(one,addition(X1,X1)) = X1,
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_89,plain,
addition(X1,X1) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_87,i_0_56]) ).
cnf(i_0_90,plain,
addition(multiplication(one,X1),multiplication(one,X1)) = addition(X1,X1),
inference(scs_inference,[],[i_0_83,i_0_77,i_0_87,i_0_56,i_0_57]) ).
cnf(i_0_91,plain,
addition(X1,X1) = multiplication(one,X1),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_92,plain,
addition(X1,X1) = addition(multiplication(one,X1),multiplication(one,X1)),
inference(scs_inference,[],[i_0_90,i_0_56]) ).
cnf(i_0_93,plain,
X1 = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_89,i_0_65,i_0_90,i_0_56,i_0_57]) ).
cnf(i_0_94,plain,
addition(X1,X1) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_95,plain,
multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))) = X1,
inference(scs_inference,[],[i_0_93,i_0_56]) ).
cnf(i_0_96,plain,
multiplication(one,addition(addition(X1,X1),addition(X1,X1))) = addition(multiplication(one,X1),multiplication(one,X1)),
inference(scs_inference,[],[i_0_92,i_0_80,i_0_93,i_0_56,i_0_57]) ).
cnf(i_0_97,plain,
multiplication(one,addition(X1,X1)) = X1,
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_98,plain,
addition(multiplication(one,X1),multiplication(one,X1)) = multiplication(one,addition(addition(X1,X1),addition(X1,X1))),
inference(scs_inference,[],[i_0_96,i_0_56]) ).
cnf(i_0_99,plain,
multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))) = multiplication(one,X1),
inference(scs_inference,[],[i_0_95,i_0_72,i_0_96,i_0_56,i_0_57]) ).
cnf(i_0_100,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_101,plain,
multiplication(one,X1) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_99,i_0_56]) ).
cnf(i_0_102,plain,
addition(X1,X1) = multiplication(one,addition(multiplication(one,multiplication(one,multiplication(one,X1))),multiplication(one,multiplication(one,multiplication(one,X1))))),
inference(scs_inference,[],[i_0_92,i_0_89,i_0_99,i_0_56,i_0_57]) ).
cnf(i_0_103,plain,
addition(X1,X1) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_104,plain,
multiplication(one,addition(multiplication(one,multiplication(one,multiplication(one,X1))),multiplication(one,multiplication(one,multiplication(one,X1))))) = addition(X1,X1),
inference(scs_inference,[],[i_0_102,i_0_56]) ).
cnf(i_0_105,plain,
addition(multiplication(one,X1),multiplication(one,X1)) = addition(multiplication(one,addition(addition(X1,X1),addition(X1,X1))),multiplication(one,addition(addition(X1,X1),addition(X1,X1)))),
inference(scs_inference,[],[i_0_98,i_0_65,i_0_102,i_0_56,i_0_57]) ).
cnf(i_0_106,plain,
X1 = addition(X1,X1),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_107,plain,
addition(multiplication(one,addition(addition(X1,X1),addition(X1,X1))),multiplication(one,addition(addition(X1,X1),addition(X1,X1)))) = addition(multiplication(one,X1),multiplication(one,X1)),
inference(scs_inference,[],[i_0_105,i_0_56]) ).
cnf(i_0_108,plain,
multiplication(one,X1) = addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1))),
inference(scs_inference,[],[i_0_86,i_0_105,i_0_73,i_0_56,i_0_57]) ).
cnf(i_0_109,plain,
multiplication(one,X1) = addition(X1,X1),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_110,plain,
addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1))) = multiplication(one,X1),
inference(scs_inference,[],[i_0_108,i_0_56]) ).
cnf(i_0_111,plain,
addition(multiplication(one,addition(addition(X1,X1),addition(X1,X1))),multiplication(one,addition(addition(X1,X1),addition(X1,X1)))) = addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))),
inference(scs_inference,[],[i_0_107,i_0_92,i_0_108,i_0_56,i_0_57]) ).
cnf(i_0_112,plain,
addition(X1,X1) = addition(multiplication(one,X1),multiplication(one,X1)),
inference(rename_variables,[],[i_0_92]) ).
cnf(i_0_113,plain,
addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))) = addition(multiplication(one,addition(addition(X1,X1),addition(X1,X1))),multiplication(one,addition(addition(X1,X1),addition(X1,X1)))),
inference(scs_inference,[],[i_0_111,i_0_56]) ).
cnf(i_0_114,plain,
addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1))) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_110,i_0_101,i_0_111,i_0_56,i_0_57]) ).
cnf(i_0_115,plain,
multiplication(one,X1) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_116,plain,
multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))) = addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1))),
inference(scs_inference,[],[i_0_114,i_0_56]) ).
cnf(i_0_117,plain,
addition(addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1))),addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1)))) = addition(X1,X1),
inference(scs_inference,[],[i_0_110,i_0_83,i_0_114,i_0_56,i_0_57]) ).
cnf(i_0_118,plain,
addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1))) = multiplication(one,X1),
inference(rename_variables,[],[i_0_110]) ).
cnf(i_0_119,plain,
addition(X1,X1) = addition(addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1))),addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1)))),
inference(scs_inference,[],[i_0_117,i_0_56]) ).
cnf(i_0_120,plain,
addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))) = multiplication(one,multiplication(one,addition(addition(X1,X1),addition(X1,X1)))),
inference(scs_inference,[],[i_0_113,i_0_77,i_0_117,i_0_56,i_0_57]) ).
cnf(i_0_121,plain,
addition(X1,X1) = multiplication(one,X1),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_122,plain,
multiplication(one,multiplication(one,addition(addition(X1,X1),addition(X1,X1)))) = addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))),
inference(scs_inference,[],[i_0_120,i_0_56]) ).
cnf(i_0_123,plain,
addition(X1,X1) = multiplication(one,addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1)))),
inference(scs_inference,[],[i_0_119,i_0_77,i_0_120,i_0_56,i_0_57]) ).
cnf(i_0_124,plain,
addition(X1,X1) = multiplication(one,X1),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_125,plain,
multiplication(one,addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1)))) = addition(X1,X1),
inference(scs_inference,[],[i_0_123,i_0_56]) ).
cnf(i_0_126,plain,
multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))) = multiplication(one,addition(addition(X1,X1),addition(X1,X1))),
inference(scs_inference,[],[i_0_116,i_0_77,i_0_123,i_0_56,i_0_57]) ).
cnf(i_0_127,plain,
addition(X1,X1) = multiplication(one,X1),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_128,plain,
multiplication(one,addition(addition(X1,X1),addition(X1,X1))) = multiplication(one,addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_126,i_0_56]) ).
cnf(i_0_129,plain,
multiplication(one,addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1)))) = multiplication(one,addition(X1,X1)),
inference(scs_inference,[],[i_0_125,i_0_72,i_0_126,i_0_56,i_0_57]) ).
cnf(i_0_130,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_131,plain,
multiplication(one,addition(X1,X1)) = multiplication(one,addition(addition(multiplication(one,X1),multiplication(one,X1)),addition(multiplication(one,X1),multiplication(one,X1)))),
inference(scs_inference,[],[i_0_129,i_0_56]) ).
cnf(i_0_132,plain,
multiplication(one,addition(addition(X1,X1),addition(X1,X1))) = addition(multiplication(one,multiplication(one,multiplication(one,X1))),multiplication(one,multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_128,i_0_129,i_0_38,i_0_56,i_0_57]) ).
cnf(i_0_133,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_134,plain,
addition(multiplication(one,multiplication(one,multiplication(one,X1))),multiplication(one,multiplication(one,multiplication(one,X1)))) = multiplication(one,addition(addition(X1,X1),addition(X1,X1))),
inference(scs_inference,[],[i_0_132,i_0_56]) ).
cnf(i_0_135,plain,
multiplication(one,addition(X1,X1)) = addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))),
inference(scs_inference,[],[i_0_131,i_0_132,i_0_96,i_0_56,i_0_57]) ).
cnf(i_0_136,plain,
multiplication(one,addition(addition(X1,X1),addition(X1,X1))) = addition(multiplication(one,X1),multiplication(one,X1)),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_137,plain,
addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))) = multiplication(one,addition(X1,X1)),
inference(scs_inference,[],[i_0_135,i_0_56]) ).
cnf(i_0_138,plain,
addition(multiplication(one,multiplication(one,multiplication(one,X1))),multiplication(one,multiplication(one,multiplication(one,X1)))) = multiplication(one,X1),
inference(scs_inference,[],[i_0_134,i_0_135,i_0_84,i_0_56,i_0_57]) ).
cnf(i_0_139,plain,
multiplication(one,addition(addition(X1,X1),addition(X1,X1))) = multiplication(one,X1),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_140,plain,
multiplication(one,X1) = addition(multiplication(one,multiplication(one,multiplication(one,X1))),multiplication(one,multiplication(one,multiplication(one,X1)))),
inference(scs_inference,[],[i_0_138,i_0_56]) ).
cnf(i_0_141,plain,
addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))) = multiplication(one,addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1)))),
inference(scs_inference,[],[i_0_137,i_0_86,i_0_138,i_0_56,i_0_57]) ).
cnf(i_0_142,plain,
multiplication(one,X1) = multiplication(one,addition(addition(X1,X1),addition(X1,X1))),
inference(rename_variables,[],[i_0_86]) ).
cnf(i_0_143,plain,
multiplication(one,addition(addition(addition(X1,X1),addition(X1,X1)),addition(addition(X1,X1),addition(X1,X1)))) = addition(multiplication(one,multiplication(one,X1)),multiplication(one,multiplication(one,X1))),
inference(scs_inference,[],[i_0_141,i_0_56]) ).
cnf(i_0_144,plain,
domain(multiplication(addition(esk1_0,esk2_0),domain(esk3_0))) != domain(addition(multiplication(esk1_0,domain(esk3_0)),multiplication(esk2_0,domain(esk3_0)))),
inference(scs_inference,[],[i_0_36,i_0_141,i_0_43,i_0_56,i_0_57]) ).
cnf(i_0_145,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_146,plain,
$false,
inference(scs_inference,[],[i_0_36,i_0_141,i_0_37,i_0_43,i_0_56,i_0_57,i_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE072+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.33 % Computer : n003.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 20:28:11 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 0.35/1.62 % Version : CSE_E---1.7
% 0.35/1.62 % Problem : theBenchmark.p
% 0.35/1.62 % SZS status Theorem for theBenchmark.p
% 0.35/1.62 % SZS output start CNFRefutation
% See solution above
% 0.46/1.75 % Total time : 1.271s
%------------------------------------------------------------------------------