%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE139+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:35:47 PM UTC 2026
% Result : Theorem 117.14s 84.89s
% Output : CNFRefutation 119.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 30
% Syntax : Number of formulae : 227 ( 198 unt; 0 def)
% Number of atoms : 261 ( 219 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 32 ~; 27 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 540 ( 4 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(X4),addition(multiplication(strong_iteration(X4),X4),one))
& leq(addition(multiplication(strong_iteration(X4),X4),one),strong_iteration(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(star_induction1,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X3),X2),X3)
=> leq(multiplication(star(X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_coinduction) ).
fof(distributivity2,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(distributivity1,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',distributivity1) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(i_0_19,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(X4),addition(multiplication(strong_iteration(X4),X4),one))
& leq(addition(multiplication(strong_iteration(X4),X4),one),strong_iteration(X4)) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(i_0_20,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(multiplication(strong_iteration(esk1_0),esk1_0),one))
| ~ leq(addition(multiplication(strong_iteration(esk1_0),esk1_0),one),strong_iteration(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])])]) ).
fof(i_0_21,plain,
! [X61,X62,X63] :
( ~ leq(addition(multiplication(X61,X63),X62),X63)
| leq(multiplication(star(X61),X62),X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction1])]) ).
fof(i_0_22,plain,
! [X64,X65,X66] :
( ~ leq(addition(multiplication(X66,X64),X65),X66)
| leq(multiplication(X65,star(X64)),X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction2])]) ).
fof(i_0_23,plain,
! [X68,X69,X70] :
( ~ leq(X70,addition(multiplication(X68,X70),X69))
| leq(X70,multiplication(strong_iteration(X68),X69)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(i_0_24,plain,
! [X55,X56,X57] : multiplication(addition(X55,X56),X57) = addition(multiplication(X55,X57),multiplication(X56,X57)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(i_0_25,plain,
! [X52,X53,X54] : multiplication(X52,addition(X53,X54)) = addition(multiplication(X52,X53),multiplication(X52,X54)),
inference(variable_rename,[status(thm)],[distributivity1]) ).
fof(i_0_26,plain,
! [X47,X48,X49] : multiplication(X47,multiplication(X48,X49)) = multiplication(multiplication(X47,X48),X49),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(i_0_27,plain,
! [X42,X43,X44] : addition(X44,addition(X43,X42)) = addition(addition(X44,X43),X42),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(i_0_28,plain,
! [X71] : strong_iteration(X71) = addition(star(X71),multiplication(strong_iteration(X71),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
fof(i_0_29,plain,
! [X60] : addition(one,multiplication(star(X60),X60)) = star(X60),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(i_0_30,plain,
! [X59] : addition(one,multiplication(X59,star(X59))) = star(X59),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
fof(i_0_31,plain,
! [X67] : strong_iteration(X67) = addition(multiplication(X67,strong_iteration(X67)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(i_0_32,plain,
! [X72,X73] :
( ( ~ leq(X72,X73)
| addition(X72,X73) = X73 )
& ( addition(X72,X73) != X73
| leq(X72,X73) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(i_0_33,plain,
! [X40,X41] : addition(X40,X41) = addition(X41,X40),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(i_0_34,plain,
! [X46] : addition(X46,X46) = X46,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(i_0_35,plain,
! [X51] : multiplication(one,X51) = X51,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(i_0_36,plain,
! [X50] : multiplication(X50,one) = X50,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(i_0_37,plain,
! [X45] : addition(X45,zero) = X45,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(i_0_38,plain,
! [X58] : multiplication(zero,X58) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(i_0_39,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(multiplication(strong_iteration(esk1_0),esk1_0),one))
| ~ leq(addition(multiplication(strong_iteration(esk1_0),esk1_0),one),strong_iteration(esk1_0)) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_40,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_41,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_42,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_43,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_44,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_45,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_46,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_47,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_48,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_49,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_50,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_51,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_52,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_53,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_54,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_55,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_56,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_57,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_58,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_59,axiom,
X1 = X1 ).
cnf(i_0_60,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_61,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_62,axiom,
( X1 != X2
| strong_iteration(X1) = strong_iteration(X2) ) ).
cnf(i_0_63,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_64,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_65,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_66,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_67,axiom,
( X1 != X2
| star(X1) = star(X2) ) ).
cnf(i_0_68,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_69,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_70,plain,
leq(X1,X1),
inference(scs_inference,[],[i_0_54,i_0_51]) ).
cnf(i_0_72,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(scs_inference,[],[i_0_43,i_0_54,i_0_51,i_0_60]) ).
cnf(i_0_73,plain,
multiplication(addition(X1,X1),X2) = multiplication(X1,X2),
inference(scs_inference,[],[i_0_43,i_0_54,i_0_51,i_0_60,i_0_61]) ).
cnf(i_0_74,plain,
addition(X1,X1) = X1,
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_75,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_78,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_82,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_83,plain,
X1 = multiplication(one,X1),
inference(scs_inference,[],[i_0_55,i_0_60]) ).
cnf(i_0_84,plain,
multiplication(multiplication(one,X1),one) = X1,
inference(scs_inference,[],[i_0_55,i_0_56,i_0_60,i_0_61]) ).
cnf(i_0_85,plain,
multiplication(X1,one) = X1,
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_91,plain,
addition(X1,zero) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_92,plain,
addition(X1,X2) = addition(X2,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_103,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_109,plain,
multiplication(X1,one) = X1,
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_114,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_122,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_44,i_0_60]) ).
cnf(i_0_129,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_136,plain,
multiplication(zero,X1) = zero,
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_143,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_146,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_150,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_153,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_173,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_182,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_193,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_201,plain,
addition(X1,zero) = X1,
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_208,plain,
addition(X1,X2) = addition(X2,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_218,plain,
star(X1) = addition(one,multiplication(X1,star(X1))),
inference(scs_inference,[],[i_0_49,i_0_60]) ).
cnf(i_0_226,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_235,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_236,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(scs_inference,[],[i_0_45,i_0_60]) ).
cnf(i_0_245,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_249,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_260,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_266,plain,
addition(X1,X1) = X1,
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_272,plain,
multiplication(one,X1) = X1,
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_278,plain,
multiplication(X1,one) = X1,
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_283,plain,
star(X1) = addition(one,multiplication(star(X1),X1)),
inference(scs_inference,[],[i_0_48,i_0_60]) ).
cnf(i_0_302,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_314,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_318,plain,
X1 = addition(X1,zero),
inference(scs_inference,[],[i_0_57,i_0_60]) ).
cnf(i_0_340,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_344,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_383,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_398,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_404,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_413,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_417,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_46,i_0_60]) ).
cnf(i_0_433,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_437,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_441,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_445,plain,
zero = multiplication(zero,X1),
inference(scs_inference,[],[i_0_58,i_0_60]) ).
cnf(i_0_448,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_452,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_474,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_478,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_526,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_543,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_562,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_583,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_587,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_600,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_671,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_694,plain,
addition(star(X1),multiplication(strong_iteration(X1),zero)) = strong_iteration(X1),
inference(scs_inference,[],[i_0_47,i_0_60]) ).
cnf(i_0_713,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_717,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_729,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_769,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_777,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_780,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_796,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_799,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_808,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_813,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_816,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_819,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_848,plain,
addition(multiplication(X1,strong_iteration(X1)),one) = strong_iteration(X1),
inference(scs_inference,[],[i_0_50,i_0_60]) ).
cnf(i_0_864,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_867,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_876,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_886,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_891,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_894,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_897,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_900,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_903,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_908,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_913,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_920,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_926,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_929,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_951,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_976,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_994,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_997,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1011,plain,
X1 = addition(X1,X1),
inference(scs_inference,[],[i_0_54,i_0_60]) ).
cnf(i_0_1023,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1046,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1049,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1056,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1066,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1089,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_1113,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1116,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1119,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1122,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1128,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1134,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1137,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1140,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1164,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1167,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1170,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1173,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1179,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1182,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1185,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1189,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1196,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1203,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1210,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1223,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1227,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1230,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1240,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1278,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1285,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1288,plain,
multiplication(one,X1) = X1,
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_1304,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1312,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1330,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1353,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1361,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1373,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1382,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1411,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1596,plain,
star(multiplication(addition(X1,X2),X3)) = star(addition(multiplication(X1,X3),multiplication(X2,X3))),
inference(scs_inference,[],[i_0_43,i_0_62,i_0_63,i_0_64,i_0_65,i_0_66,i_0_67]) ).
cnf(i_0_1648,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1652,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1705,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1727,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1851,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1958,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_43]) ).
cnf(c_0_455,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
i_0_46 ).
cnf(c_0_456,plain,
star(X1) = addition(one,multiplication(star(X1),X1)),
i_0_283 ).
cnf(c_0_457,plain,
addition(one,addition(multiplication(star(X1),X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_455,c_0_456]) ).
cnf(c_0_458,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
i_0_43 ).
cnf(c_0_459,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(multiplication(strong_iteration(esk1_0),esk1_0),one))
| ~ leq(addition(multiplication(strong_iteration(esk1_0),esk1_0),one),strong_iteration(esk1_0)) ),
i_0_39 ).
cnf(c_0_460,plain,
addition(X1,X2) = addition(X2,X1),
i_0_53 ).
cnf(c_0_461,plain,
addition(one,multiplication(addition(star(X1),X2),X1)) = addition(star(X1),multiplication(X2,X1)),
inference(spm,[status(thm)],[c_0_457,c_0_458]) ).
cnf(c_0_462,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
i_0_47 ).
cnf(c_0_463,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
i_0_45 ).
cnf(c_0_464,plain,
zero = multiplication(zero,X1),
i_0_445 ).
cnf(c_0_465,negated_conjecture,
( ~ leq(strong_iteration(esk1_0),addition(one,multiplication(strong_iteration(esk1_0),esk1_0)))
| ~ leq(addition(one,multiplication(strong_iteration(esk1_0),esk1_0)),strong_iteration(esk1_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_459,c_0_460]),c_0_460]) ).
cnf(c_0_466,plain,
addition(one,multiplication(strong_iteration(X1),X1)) = strong_iteration(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_461,c_0_462]),c_0_463]),c_0_464]),c_0_462]) ).
cnf(c_0_467,plain,
leq(X1,X1),
i_0_70 ).
cnf(c_0_468,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_465,c_0_466]),c_0_467]),c_0_466]),c_0_467])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE139+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 20:31:00 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 117.14/84.89 % Version : CSE_E---1.7
% 117.14/84.89 % Problem : theBenchmark.p
% 117.14/84.89 % SZS status Theorem for theBenchmark.p
% 117.14/84.89 % SZS output start CNFRefutation
% See solution above
% 119.14/86.89 % Total time : 84.300s
%------------------------------------------------------------------------------