%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE057+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 : n018.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 04:35:37 PM UTC 2026
% Result : Theorem 0.33s 1.61s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 38
% Syntax : Number of formulae : 157 ( 128 unt; 0 def)
% Number of atoms : 194 ( 172 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 48 ~; 32 |; 2 &)
% ( 1 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 264 ( 6 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( domain(X4) = zero
<= X4 = zero ),
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] :
( X4 = zero
=> domain(X4) = zero ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(i_0_19,plain,
! [X50,X51,X52] : multiplication(addition(X50,X51),X52) = addition(multiplication(X50,X52),multiplication(X51,X52)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(i_0_20,plain,
! [X47,X48,X49] : multiplication(X47,addition(X48,X49)) = addition(multiplication(X47,X48),multiplication(X47,X49)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(i_0_21,plain,
! [X42,X43,X44] : multiplication(X42,multiplication(X43,X44)) = multiplication(multiplication(X42,X43),X44),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(i_0_22,plain,
! [X37,X38,X39] : addition(X39,addition(X38,X37)) = addition(addition(X39,X38),X37),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(i_0_23,plain,
! [X57] : addition(X57,multiplication(domain(X57),X57)) = multiplication(domain(X57),X57),
inference(variable_rename,[status(thm)],[domain1]) ).
fof(i_0_24,plain,
! [X58,X59] : domain(multiplication(X58,X59)) = domain(multiplication(X58,domain(X59))),
inference(variable_rename,[status(thm)],[domain2]) ).
fof(i_0_25,plain,
! [X61,X62] : domain(addition(X61,X62)) = addition(domain(X61),domain(X62)),
inference(variable_rename,[status(thm)],[domain5]) ).
fof(i_0_26,plain,
! [X55,X56] :
( ( ~ leq(X55,X56)
| addition(X55,X56) = X56 )
& ( addition(X55,X56) != X56
| leq(X55,X56) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(i_0_27,plain,
! [X35,X36] : addition(X35,X36) = addition(X36,X35),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(i_0_28,plain,
! [X60] : addition(domain(X60),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(i_0_29,plain,
! [X41] : addition(X41,X41) = X41,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(i_0_30,plain,
! [X46] : multiplication(one,X46) = X46,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(i_0_31,plain,
! [X45] : multiplication(X45,one) = X45,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(i_0_32,plain,
! [X40] : addition(X40,zero) = X40,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(i_0_33,plain,
! [X54] : multiplication(zero,X54) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(i_0_34,plain,
! [X53] : multiplication(X53,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
fof(i_0_35,negated_conjecture,
( esk1_0 = zero
& domain(esk1_0) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])]) ).
cnf(i_0_36,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_37,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_41,plain,
domain(multiplication(X1,X2)) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_42,plain,
domain(addition(X1,X2)) = addition(domain(X1),domain(X2)),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_43,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_44,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_45,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_46,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_47,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_48,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_49,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_50,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_51,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_52,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_53,negated_conjecture,
domain(esk1_0) != 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,negated_conjecture,
esk1_0 = zero,
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_56,axiom,
X1 = X1 ).
cnf(i_0_57,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_58,axiom,
( X1 = X2
| X1 != X3
| X3 != 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
| domain(X1) = domain(X2) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_56_001,axiom,
X1 = X1 ).
cnf(i_0_57_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_58_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_59_004,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_60_005,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_61_006,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_62_007,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_63_008,axiom,
( X1 != X2
| domain(X1) = domain(X2) ) ).
cnf(i_0_64_009,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_65_010,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_66,plain,
zero = esk1_0,
inference(scs_inference,[],[i_0_55,i_0_57]) ).
cnf(i_0_67,plain,
leq(X1,X1),
inference(scs_inference,[],[i_0_55,i_0_47,i_0_57,i_0_43]) ).
cnf(i_0_68,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_69,plain,
domain(esk1_0) != esk1_0,
inference(scs_inference,[],[i_0_53,i_0_55,i_0_47,i_0_57,i_0_43,i_0_58]) ).
cnf(i_0_70,plain,
leq(X1,multiplication(domain(X1),X1)),
inference(scs_inference,[],[i_0_40,i_0_43]) ).
cnf(i_0_71,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_72,plain,
X1 = multiplication(one,X1),
inference(scs_inference,[],[i_0_48,i_0_40,i_0_43,i_0_57]) ).
cnf(i_0_73,plain,
domain(esk1_0) != multiplication(one,zero),
inference(scs_inference,[],[i_0_53,i_0_48,i_0_40,i_0_43,i_0_57,i_0_58]) ).
cnf(i_0_74,plain,
multiplication(one,X1) = X1,
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_75,plain,
leq(domain(X1),one),
inference(scs_inference,[],[i_0_46,i_0_43]) ).
cnf(i_0_76,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_77,plain,
X1 = multiplication(X1,one),
inference(scs_inference,[],[i_0_49,i_0_46,i_0_43,i_0_57]) ).
cnf(i_0_78,plain,
domain(esk1_0) != multiplication(zero,one),
inference(scs_inference,[],[i_0_53,i_0_49,i_0_46,i_0_43,i_0_57,i_0_58]) ).
cnf(i_0_79,plain,
multiplication(X1,one) = X1,
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_80,plain,
X1 = addition(X1,zero),
inference(scs_inference,[],[i_0_50,i_0_57]) ).
cnf(i_0_81,plain,
domain(esk1_0) != addition(zero,zero),
inference(scs_inference,[],[i_0_53,i_0_50,i_0_57,i_0_58]) ).
cnf(i_0_82,plain,
addition(X1,zero) = X1,
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_83,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(scs_inference,[],[i_0_36,i_0_57]) ).
cnf(i_0_84,plain,
addition(X1,X2) = addition(multiplication(X1,one),multiplication(X2,one)),
inference(scs_inference,[],[i_0_77,i_0_36,i_0_57,i_0_58]) ).
cnf(i_0_85,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_86,plain,
X1 = multiplication(X1,one),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_87,plain,
addition(multiplication(X1,one),multiplication(X2,one)) = addition(X1,X2),
inference(scs_inference,[],[i_0_84,i_0_57]) ).
cnf(i_0_88,plain,
X1 = addition(multiplication(X1,one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_80,i_0_84,i_0_57,i_0_58]) ).
cnf(i_0_89,plain,
addition(X1,X2) = addition(multiplication(X1,one),multiplication(X2,one)),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_90,plain,
addition(multiplication(X1,one),multiplication(zero,one)) = X1,
inference(scs_inference,[],[i_0_88,i_0_57]) ).
cnf(i_0_91,plain,
addition(multiplication(multiplication(X1,X2),one),multiplication(multiplication(X3,X2),one)) = multiplication(addition(X1,X3),X2),
inference(scs_inference,[],[i_0_83,i_0_87,i_0_88,i_0_57,i_0_58]) ).
cnf(i_0_92,plain,
addition(multiplication(X1,one),multiplication(X2,one)) = addition(X1,X2),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_93,plain,
leq(multiplication(multiplication(zero,one),one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_83,i_0_87,i_0_88,i_0_57,i_0_58,i_0_43]) ).
cnf(i_0_94,plain,
( addition(X1,X2) != X2
| leq(X1,X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_95,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(multiplication(X1,X3),one),multiplication(multiplication(X2,X3),one)),
inference(scs_inference,[],[i_0_91,i_0_57]) ).
cnf(i_0_96,plain,
domain(esk1_0) != addition(multiplication(zero,one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_53,i_0_90,i_0_91,i_0_57,i_0_58]) ).
cnf(i_0_97,plain,
addition(multiplication(X1,one),multiplication(zero,one)) = X1,
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_98,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_37,i_0_57]) ).
cnf(i_0_99,plain,
multiplication(addition(X1,X2),X3) = multiplication(addition(multiplication(X1,X3),multiplication(X2,X3)),one),
inference(scs_inference,[],[i_0_95,i_0_83,i_0_37,i_0_57,i_0_58]) ).
cnf(i_0_100,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_101,plain,
multiplication(addition(multiplication(X1,X2),multiplication(X3,X2)),one) = multiplication(addition(X1,X3),X2),
inference(scs_inference,[],[i_0_99,i_0_57]) ).
cnf(i_0_102,plain,
addition(multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one),multiplication(zero,one)) = multiplication(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_98,i_0_90,i_0_99,i_0_57,i_0_58]) ).
cnf(i_0_103,plain,
addition(multiplication(X1,one),multiplication(zero,one)) = X1,
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_104,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_102,i_0_57]) ).
cnf(i_0_105,plain,
addition(multiplication(multiplication(X1,X2),one),multiplication(multiplication(X1,X3),one)) = multiplication(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_98,i_0_87,i_0_102,i_0_57,i_0_58]) ).
cnf(i_0_106,plain,
addition(multiplication(X1,one),multiplication(X2,one)) = addition(X1,X2),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_107,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(multiplication(X1,X2),one),multiplication(multiplication(X1,X3),one)),
inference(scs_inference,[],[i_0_105,i_0_57]) ).
cnf(i_0_108,plain,
addition(X1,X2) = addition(multiplication(addition(multiplication(one,X1),multiplication(one,X2)),one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_104,i_0_72,i_0_105,i_0_57,i_0_58]) ).
cnf(i_0_109,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one),multiplication(zero,one)),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_110,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_111,plain,
addition(multiplication(addition(multiplication(one,X1),multiplication(one,X2)),one),multiplication(zero,one)) = addition(X1,X2),
inference(scs_inference,[],[i_0_108,i_0_57]) ).
cnf(i_0_112,plain,
multiplication(X1,addition(X2,X3)) = multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one),
inference(scs_inference,[],[i_0_107,i_0_83,i_0_108,i_0_57,i_0_58]) ).
cnf(i_0_113,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_114,plain,
multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one) = multiplication(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_112,i_0_57]) ).
cnf(i_0_115,plain,
domain(esk1_0) != addition(multiplication(addition(multiplication(one,zero),multiplication(one,zero)),one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_111,i_0_112,i_0_81,i_0_57,i_0_58]) ).
cnf(i_0_116,plain,
addition(multiplication(addition(multiplication(one,X1),multiplication(one,X2)),one),multiplication(zero,one)) = addition(X1,X2),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_117,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(scs_inference,[],[i_0_38,i_0_57]) ).
cnf(i_0_118,plain,
domain(esk1_0) != multiplication(one,addition(zero,zero)),
inference(scs_inference,[],[i_0_104,i_0_115,i_0_38,i_0_57,i_0_58]) ).
cnf(i_0_119,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one),multiplication(zero,one)),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_120,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_39,i_0_57]) ).
cnf(i_0_121,plain,
domain(esk1_0) != multiplication(addition(multiplication(one,zero),multiplication(one,zero)),one),
inference(scs_inference,[],[i_0_114,i_0_118,i_0_39,i_0_57,i_0_58]) ).
cnf(i_0_122,plain,
multiplication(addition(multiplication(X1,X2),multiplication(X1,X3)),one) = multiplication(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_123,plain,
addition(domain(X1),domain(X2)) = domain(addition(X1,X2)),
inference(scs_inference,[],[i_0_42,i_0_57]) ).
cnf(i_0_124,plain,
multiplication(X1,X2) = multiplication(X1,multiplication(X2,one)),
inference(scs_inference,[],[i_0_117,i_0_77,i_0_42,i_0_57,i_0_58]) ).
cnf(i_0_125,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(rename_variables,[],[i_0_117]) ).
cnf(i_0_126,plain,
X1 = multiplication(X1,one),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_127,plain,
multiplication(X1,multiplication(X2,one)) = multiplication(X1,X2),
inference(scs_inference,[],[i_0_124,i_0_57]) ).
cnf(i_0_128,plain,
domain(esk1_0) != addition(multiplication(one,zero),multiplication(one,zero)),
inference(scs_inference,[],[i_0_98,i_0_124,i_0_118,i_0_57,i_0_58]) ).
cnf(i_0_129,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_130,plain,
zero = multiplication(zero,X1),
inference(scs_inference,[],[i_0_51,i_0_57]) ).
cnf(i_0_131,plain,
domain(esk1_0) != multiplication(addition(multiplication(one,zero),multiplication(one,zero)),multiplication(one,one)),
inference(scs_inference,[],[i_0_127,i_0_121,i_0_51,i_0_57,i_0_58]) ).
cnf(i_0_132,plain,
multiplication(X1,multiplication(X2,one)) = multiplication(X1,X2),
inference(rename_variables,[],[i_0_127]) ).
cnf(i_0_133,plain,
zero = multiplication(X1,zero),
inference(scs_inference,[],[i_0_52,i_0_57]) ).
cnf(i_0_134,plain,
domain(esk1_0) != multiplication(addition(multiplication(one,zero),multiplication(one,zero)),multiplication(multiplication(one,one),one)),
inference(scs_inference,[],[i_0_127,i_0_131,i_0_52,i_0_57,i_0_58]) ).
cnf(i_0_135,plain,
multiplication(X1,multiplication(X2,one)) = multiplication(X1,X2),
inference(rename_variables,[],[i_0_127]) ).
cnf(i_0_136,plain,
zero = domain(zero),
inference(scs_inference,[],[i_0_54,i_0_57]) ).
cnf(i_0_137,plain,
domain(esk1_0) != multiplication(multiplication(addition(multiplication(one,zero),multiplication(one,zero)),multiplication(one,one)),one),
inference(scs_inference,[],[i_0_117,i_0_134,i_0_54,i_0_57,i_0_58]) ).
cnf(i_0_138,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(rename_variables,[],[i_0_117]) ).
cnf(i_0_139,plain,
domain(multiplication(X1,domain(X2))) = domain(multiplication(X1,X2)),
inference(scs_inference,[],[i_0_41,i_0_57]) ).
cnf(i_0_140,plain,
esk1_0 = domain(zero),
inference(scs_inference,[],[i_0_136,i_0_55,i_0_41,i_0_57,i_0_58]) ).
cnf(i_0_141,plain,
domain(zero) = esk1_0,
inference(scs_inference,[],[i_0_140,i_0_57]) ).
cnf(i_0_142,plain,
addition(multiplication(zero,one),multiplication(zero,one)) = domain(zero),
inference(scs_inference,[],[i_0_136,i_0_90,i_0_140,i_0_57,i_0_58]) ).
cnf(i_0_143,plain,
addition(multiplication(X1,one),multiplication(zero,one)) = X1,
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_144,plain,
domain(zero) = addition(multiplication(zero,one),multiplication(zero,one)),
inference(scs_inference,[],[i_0_142,i_0_57]) ).
cnf(i_0_145,plain,
domain(esk1_0) != domain(zero),
inference(scs_inference,[],[i_0_141,i_0_142,i_0_69,i_0_57,i_0_58]) ).
cnf(i_0_146,plain,
$false,
inference(scs_inference,[],[i_0_141,i_0_55,i_0_142,i_0_69,i_0_57,i_0_58,i_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE057+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
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 20:29:32 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.33/1.61 % Version : CSE_E---1.7
% 0.33/1.61 % Problem : theBenchmark.p
% 0.33/1.61 % SZS status Theorem for theBenchmark.p
% 0.33/1.61 % SZS output start CNFRefutation
% See solution above
% 0.45/1.74 % Total time : 1.271s
%------------------------------------------------------------------------------