%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE044+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 : n015.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 04:35:35 PM UTC 2026
% Result : Theorem 217.68s 92.76s
% Output : CNFRefutation 219.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 222 ( 191 unt; 0 def)
% Number of atoms : 258 ( 173 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 36 ~; 30 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 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 : 427 ( 9 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4] :
( leq(star(addition(one,X4)),star(X4))
& leq(star(X4),star(addition(one,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(star_induction_left,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X2)
=> leq(multiplication(star(X1),X3),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_left) ).
fof(star_induction_right,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X2),X3),X1)
=> leq(multiplication(X3,star(X2)),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_induction_right) ).
fof(star_unfold_left,axiom,
! [X1] : leq(addition(one,multiplication(star(X1),X1)),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_left) ).
fof(star_unfold_right,axiom,
! [X1] : leq(addition(one,multiplication(X1,star(X1))),star(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+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/sandbox2/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+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/KLE002+0.ax',additive_associativity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_annihilation) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_annihilation) ).
fof(i_0_17,negated_conjecture,
~ ! [X4] :
( leq(star(addition(one,X4)),star(X4))
& leq(star(X4),star(addition(one,X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(i_0_18,negated_conjecture,
( ~ leq(star(addition(one,esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(addition(one,esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])])]) ).
fof(i_0_19,plain,
! [X60,X61,X62] :
( ~ leq(addition(multiplication(X60,X61),X62),X61)
| leq(multiplication(star(X60),X62),X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_left])]) ).
fof(i_0_20,plain,
! [X63,X64,X65] :
( ~ leq(addition(multiplication(X63,X64),X65),X63)
| leq(multiplication(X65,star(X64)),X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[star_induction_right])]) ).
fof(i_0_21,plain,
! [X59] : leq(addition(one,multiplication(star(X59),X59)),star(X59)),
inference(variable_rename,[status(thm)],[star_unfold_left]) ).
fof(i_0_22,plain,
! [X58] : leq(addition(one,multiplication(X58,star(X58))),star(X58)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(i_0_23,plain,
! [X51,X52,X53] : multiplication(addition(X51,X52),X53) = addition(multiplication(X51,X53),multiplication(X52,X53)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(i_0_24,plain,
! [X48,X49,X50] : multiplication(X48,addition(X49,X50)) = addition(multiplication(X48,X49),multiplication(X48,X50)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(i_0_25,plain,
! [X43,X44,X45] : multiplication(X43,multiplication(X44,X45)) = multiplication(multiplication(X43,X44),X45),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(i_0_26,plain,
! [X38,X39,X40] : addition(X40,addition(X39,X38)) = addition(addition(X40,X39),X38),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(i_0_27,plain,
! [X56,X57] :
( ( ~ leq(X56,X57)
| addition(X56,X57) = X57 )
& ( addition(X56,X57) != X57
| leq(X56,X57) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(i_0_28,plain,
! [X36,X37] : addition(X36,X37) = addition(X37,X36),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(i_0_29,plain,
! [X42] : addition(X42,X42) = X42,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(i_0_30,plain,
! [X47] : multiplication(one,X47) = X47,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(i_0_31,plain,
! [X46] : multiplication(X46,one) = X46,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(i_0_32,plain,
! [X41] : addition(X41,zero) = X41,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(i_0_33,plain,
! [X55] : multiplication(zero,X55) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(i_0_34,plain,
! [X54] : multiplication(X54,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(i_0_35,negated_conjecture,
( ~ leq(star(addition(one,esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(addition(one,esk1_0))) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_36,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_37,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_41,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_42,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_43,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
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(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,axiom,
X1 = X1 ).
cnf(i_0_54,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_55,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_56,axiom,
( X1 != X2
| addition(X1,X3) = addition(X2,X3) ) ).
cnf(i_0_57,axiom,
( X1 != X2
| addition(X3,X1) = addition(X3,X2) ) ).
cnf(i_0_58,axiom,
( X1 != X2
| multiplication(X1,X3) = multiplication(X2,X3) ) ).
cnf(i_0_59,axiom,
( X1 != X2
| multiplication(X3,X1) = multiplication(X3,X2) ) ).
cnf(i_0_60,axiom,
( X1 != X2
| ~ leq(X1,X3)
| leq(X2,X3) ) ).
cnf(i_0_61,axiom,
( X1 != X2
| ~ leq(X3,X1)
| leq(X3,X2) ) ).
cnf(i_0_62,plain,
leq(X1,X1),
inference(scs_inference,[],[i_0_47,i_0_44]) ).
cnf(i_0_64,plain,
X1 = addition(X1,X1),
inference(scs_inference,[],[i_0_47,i_0_44,i_0_54]) ).
cnf(i_0_65,plain,
addition(multiplication(one,X1),multiplication(one,X1)) = X1,
inference(scs_inference,[],[i_0_47,i_0_48,i_0_44,i_0_54,i_0_55]) ).
cnf(i_0_66,plain,
addition(X1,X1) = X1,
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_72,plain,
addition(X1,zero) = X1,
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_80,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_81,plain,
addition(X1,X2) = addition(X2,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_84,plain,
addition(X1,zero) = X1,
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_103,plain,
multiplication(X1,zero) = zero,
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_104,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_115,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_119,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_164,plain,
X1 = multiplication(one,X1),
inference(scs_inference,[],[i_0_48,i_0_54]) ).
cnf(i_0_182,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_185,plain,
multiplication(X1,zero) = zero,
inference(rename_variables,[],[i_0_52]) ).
cnf(i_0_198,plain,
X1 = multiplication(X1,one),
inference(scs_inference,[],[i_0_49,i_0_54]) ).
cnf(i_0_210,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(scs_inference,[],[i_0_40,i_0_54]) ).
cnf(i_0_218,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_41,i_0_54]) ).
cnf(i_0_234,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(scs_inference,[],[i_0_42,i_0_54]) ).
cnf(i_0_259,plain,
X1 = addition(X1,zero),
inference(scs_inference,[],[i_0_50,i_0_54]) ).
cnf(i_0_401,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(scs_inference,[],[i_0_43,i_0_54]) ).
cnf(i_0_593,plain,
multiplication(zero,X1) = zero,
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_628,plain,
zero = multiplication(X1,zero),
inference(scs_inference,[],[i_0_52,i_0_54]) ).
cnf(i_0_733,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_750,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_759,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_786,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_796,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_800,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_816,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_857,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_861,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_874,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_878,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_889,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_901,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_959,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_972,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1018,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1035,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1039,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1049,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1062,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1067,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1070,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1184,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_1212,plain,
addition(X1,X2) = addition(X2,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_1422,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_1524,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_1548,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_1560,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1562,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1570,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1579,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1581,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1588,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(rename_variables,[],[i_0_40]) ).
cnf(i_0_1600,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1603,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1606,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1621,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1630,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1632,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1639,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1651,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1654,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_1658,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1667,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1669,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1676,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1686,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1689,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1691,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1695,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(rename_variables,[],[i_0_42]) ).
cnf(i_0_1705,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1713,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_1715,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_67,plain,
X1 = addition(multiplication(one,X1),multiplication(one,X1)),
inference(scs_inference,[],[i_0_65,i_0_54]) ).
cnf(i_0_68,plain,
addition(multiplication(one,X1),multiplication(one,X1)) = addition(X1,X1),
inference(scs_inference,[],[i_0_64,i_0_65,i_0_54,i_0_55]) ).
cnf(i_0_69,plain,
X1 = addition(X1,X1),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_100,plain,
X1 = addition(X1,X1),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_170,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_188,plain,
X1 = multiplication(one,X1),
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_215,plain,
X1 = multiplication(X1,one),
inference(rename_variables,[],[i_0_198]) ).
cnf(i_0_224,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_218]) ).
cnf(i_0_228,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_218]) ).
cnf(i_0_241,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(rename_variables,[],[i_0_234]) ).
cnf(i_0_250,plain,
addition(multiplication(X1,X2),multiplication(X3,X2)) = multiplication(addition(X1,X3),X2),
inference(rename_variables,[],[i_0_210]) ).
cnf(i_0_256,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(rename_variables,[],[i_0_234]) ).
cnf(i_0_264,plain,
X1 = addition(X1,zero),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_406,plain,
X1 = addition(X1,zero),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_409,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_401]) ).
cnf(i_0_465,plain,
addition(multiplication(X1,X2),multiplication(X1,X3)) = multiplication(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_218]) ).
cnf(i_0_552,plain,
multiplication(multiplication(X1,X2),X3) = multiplication(X1,multiplication(X2,X3)),
inference(rename_variables,[],[i_0_234]) ).
cnf(i_0_555,plain,
addition(addition(X1,X2),X3) = addition(X1,addition(X2,X3)),
inference(rename_variables,[],[i_0_401]) ).
cnf(i_0_1016,plain,
multiplication(addition(one,one),X1) = X1,
inference(scs_inference,[],[i_0_40,i_0_65,i_0_55]) ).
cnf(i_0_1017,plain,
addition(multiplication(one,X1),multiplication(one,X1)) = X1,
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_1019,plain,
X1 = multiplication(addition(one,one),X1),
inference(scs_inference,[],[i_0_40,i_0_65,i_0_55,i_0_54]) ).
cnf(i_0_1079,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1081,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1122,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1124,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1148,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1162,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1164,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1178,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1180,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1230,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1232,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1246,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1266,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1278,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1280,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1303,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1320,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1322,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1351,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_1377,plain,
leq(X1,X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(c_0_212,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(multiplication(X3,X2),X1),X3) ),
i_0_37 ).
cnf(c_0_213,plain,
X1 = multiplication(X1,one),
i_0_198 ).
cnf(c_0_214,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_212,c_0_213]) ).
cnf(c_0_215,plain,
X1 = addition(X1,X1),
i_0_64 ).
cnf(c_0_216,plain,
leq(X1,X1),
i_0_62 ).
cnf(c_0_217,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
i_0_39 ).
cnf(c_0_218,plain,
X1 = multiplication(one,X1),
i_0_164 ).
cnf(c_0_219,plain,
leq(multiplication(X1,star(one)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_216])]) ).
cnf(c_0_220,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
i_0_45 ).
cnf(c_0_221,plain,
leq(addition(one,star(one)),star(one)),
inference(spm,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_222,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
i_0_43 ).
cnf(c_0_223,plain,
leq(star(one),one),
inference(spm,[status(thm)],[c_0_219,c_0_218]) ).
cnf(c_0_224,plain,
addition(X1,X2) = addition(X2,X1),
i_0_46 ).
cnf(c_0_225,plain,
addition(one,star(one)) = star(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_222]),c_0_215]) ).
cnf(c_0_226,plain,
star(one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_223]),c_0_224]),c_0_225]) ).
cnf(c_0_227,plain,
addition(one,addition(star(one),X1)) = addition(star(one),X1),
inference(spm,[status(thm)],[c_0_222,c_0_225]) ).
cnf(c_0_228,plain,
( leq(X1,X2)
| ~ leq(addition(X2,X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_214,c_0_226]),c_0_213]) ).
cnf(c_0_229,plain,
addition(one,addition(X1,star(one))) = addition(X1,star(one)),
inference(spm,[status(thm)],[c_0_227,c_0_224]) ).
cnf(c_0_230,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_228,c_0_224]) ).
cnf(c_0_231,plain,
addition(one,addition(X1,one)) = addition(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_229,c_0_226]),c_0_226]) ).
cnf(c_0_232,plain,
leq(one,addition(X1,one)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_216])]) ).
cnf(c_0_233,plain,
leq(one,addition(one,X1)),
inference(spm,[status(thm)],[c_0_232,c_0_224]) ).
cnf(c_0_234,plain,
addition(one,addition(star(X1),multiplication(X1,star(X1)))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_217]),c_0_222]),c_0_224]) ).
cnf(c_0_235,plain,
leq(one,star(X1)),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_236,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
i_0_44 ).
cnf(c_0_237,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_224,c_0_222]) ).
cnf(c_0_238,plain,
leq(addition(one,multiplication(star(X1),X1)),star(X1)),
i_0_38 ).
cnf(c_0_239,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_220,c_0_235]) ).
cnf(c_0_240,plain,
( leq(multiplication(X1,star(X2)),X3)
| addition(X3,addition(multiplication(X3,X2),X1)) != X3 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_236]),c_0_222]),c_0_237]) ).
cnf(c_0_241,plain,
addition(one,addition(star(X1),multiplication(star(X1),X1))) = star(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_238]),c_0_222]),c_0_224]) ).
cnf(c_0_242,plain,
addition(one,addition(star(X1),X2)) = addition(star(X1),X2),
inference(spm,[status(thm)],[c_0_222,c_0_239]) ).
cnf(c_0_243,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
i_0_41 ).
cnf(c_0_244,negated_conjecture,
( ~ leq(star(addition(one,esk1_0)),star(esk1_0))
| ~ leq(star(esk1_0),star(addition(one,esk1_0))) ),
i_0_35 ).
cnf(c_0_245,plain,
( leq(star(X1),X2)
| addition(X2,addition(one,multiplication(X2,X1))) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_218]),c_0_224]) ).
cnf(c_0_246,plain,
addition(star(X1),multiplication(star(X1),X1)) = star(X1),
inference(rw,[status(thm)],[c_0_241,c_0_242]) ).
cnf(c_0_247,plain,
addition(one,addition(star(addition(X1,X2)),addition(multiplication(star(addition(X1,X2)),X1),multiplication(star(addition(X1,X2)),X2)))) = star(addition(X1,X2)),
inference(spm,[status(thm)],[c_0_241,c_0_243]) ).
cnf(c_0_248,negated_conjecture,
~ leq(star(esk1_0),star(addition(one,esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_243]),c_0_213]),c_0_246]),c_0_239]),c_0_215])]) ).
cnf(c_0_249,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_224]),c_0_222]) ).
cnf(c_0_250,plain,
addition(star(addition(X1,X2)),addition(multiplication(star(addition(X1,X2)),X1),multiplication(star(addition(X1,X2)),X2))) = star(addition(X1,X2)),
inference(rw,[status(thm)],[c_0_247,c_0_242]) ).
cnf(c_0_251,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_222,c_0_215]) ).
cnf(c_0_252,plain,
addition(star(addition(one,esk1_0)),multiplication(star(addition(one,esk1_0)),esk1_0)) != star(addition(one,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_245]),c_0_249]),c_0_242]) ).
cnf(c_0_253,plain,
addition(star(addition(one,X1)),multiplication(star(addition(one,X1)),X1)) = star(addition(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_213]),c_0_251]) ).
cnf(c_0_254,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_252,c_0_253])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE044+2 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.14/0.32 % Computer : n015.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 20:27:32 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 217.68/92.76 % Version : CSE_E---1.7
% 217.68/92.76 % Problem : theBenchmark.p
% 217.68/92.76 % SZS status Theorem for theBenchmark.p
% 217.68/92.76 % SZS output start CNFRefutation
% See solution above
% 219.18/94.24 % Total time : 90.511s
%------------------------------------------------------------------------------