%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE144+2 : 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 : n007.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 04:35:48 PM UTC 2026
% Result : Theorem 5.72s 4.49s
% Output : CNFRefutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 97 ( 66 unt; 0 def)
% Number of atoms : 130 ( 65 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 30 ~; 26 |; 3 &)
% ( 1 <=>; 3 =>; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 147 ( 17 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(star_induction2,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X3,X1),X2),X3)
=> leq(multiplication(X2,star(X1)),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction2) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_associativity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(infty_unfold1,axiom,
! [X1] : strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',infty_unfold1) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_commutativity) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',left_annihilation) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',additive_identity) ).
fof(star_unfold2,axiom,
! [X1] : addition(one,multiplication(star(X1),X1)) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold2) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(star_induction1,axiom,
! [X1,X2,X3] :
( leq(addition(multiplication(X1,X3),X2),X3)
=> leq(multiplication(star(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_induction1) ).
fof(infty_coinduction,axiom,
! [X1,X2,X3] :
( leq(X3,addition(multiplication(X1,X3),X2))
=> leq(X3,multiplication(strong_iteration(X1),X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/KLE004+0.ax',distributivity2) ).
fof(isolation,axiom,
! [X1] : strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',isolation) ).
fof(star_unfold1,axiom,
! [X1] : addition(one,multiplication(X1,star(X1))) = star(X1),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',star_unfold1) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_associativity) ).
fof(goals,conjecture,
! [X4] :
( leq(strong_iteration(star(X4)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_18,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(c_0_19,plain,
! [X50] : multiplication(X50,one) = X50,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_20,plain,
! [X42,X43,X44] : addition(X44,addition(X43,X42)) = addition(addition(X44,X43),X42),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_21,plain,
! [X46] : addition(X46,X46) = X46,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_22,plain,
! [X67] : strong_iteration(X67) = addition(multiplication(X67,strong_iteration(X67)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_23,plain,
! [X40,X41] : addition(X40,X41) = addition(X41,X40),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_24,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X51] : multiplication(one,X51) = X51,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_34,plain,
! [X58] : multiplication(zero,X58) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
fof(c_0_35,plain,
! [X45] : addition(X45,zero) = X45,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_36,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_37,plain,
addition(one,strong_iteration(X1)) = strong_iteration(X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_41,plain,
! [X60] : addition(one,multiplication(star(X60),X60)) = star(X60),
inference(variable_rename,[status(thm)],[star_unfold2]) ).
fof(c_0_42,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])]) ).
cnf(c_0_43,plain,
( leq(star(one),strong_iteration(X1))
| ~ leq(strong_iteration(X1),strong_iteration(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_44,plain,
strong_iteration(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
addition(one,multiplication(star(X1),X1)) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_46,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])]) ).
cnf(c_0_47,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
( leq(star(one),one)
| ~ leq(one,one) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
addition(one,star(X1)) = star(X1),
inference(spm,[status(thm)],[c_0_31,c_0_45]) ).
cnf(c_0_50,plain,
( leq(multiplication(star(X1),X3),X2)
| ~ leq(addition(multiplication(X1,X2),X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,plain,
( star(one) = one
| ~ leq(one,one) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_29]),c_0_49]) ).
cnf(c_0_52,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_53,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])]) ).
cnf(c_0_54,plain,
( leq(multiplication(star(one),X1),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_38]) ).
cnf(c_0_55,plain,
star(one) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_27])]) ).
cnf(c_0_56,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,plain,
( leq(X1,X2)
| ~ leq(addition(X2,X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_38]) ).
cnf(c_0_58,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X1,X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_38]) ).
cnf(c_0_59,plain,
( leq(X1,X2)
| addition(X2,addition(X1,X2)) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_26]) ).
cnf(c_0_60,plain,
addition(X1,addition(X2,addition(X1,X2))) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_61,plain,
leq(X1,multiplication(strong_iteration(one),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_31]),c_0_26]),c_0_60])]) ).
cnf(c_0_62,plain,
leq(X1,strong_iteration(one)),
inference(spm,[status(thm)],[c_0_61,c_0_25]) ).
cnf(c_0_63,plain,
addition(X1,strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_47,c_0_62]) ).
fof(c_0_64,plain,
! [X55,X56,X57] : multiplication(addition(X55,X56),X57) = addition(multiplication(X55,X57),multiplication(X56,X57)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
cnf(c_0_65,plain,
( leq(X1,multiplication(strong_iteration(X2),zero))
| ~ leq(X1,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_56,c_0_40]) ).
cnf(c_0_66,plain,
leq(X1,multiplication(strong_iteration(X2),strong_iteration(one))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_63]),c_0_62])]) ).
cnf(c_0_67,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
fof(c_0_68,plain,
! [X71] : strong_iteration(X71) = addition(star(X71),multiplication(strong_iteration(X71),zero)),
inference(variable_rename,[status(thm)],[isolation]) ).
cnf(c_0_69,plain,
leq(strong_iteration(one),multiplication(strong_iteration(strong_iteration(X1)),zero)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
addition(strong_iteration(one),X1) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_29,c_0_63]) ).
fof(c_0_71,plain,
! [X59] : addition(one,multiplication(X59,star(X59))) = star(X59),
inference(variable_rename,[status(thm)],[star_unfold1]) ).
fof(c_0_72,plain,
! [X47,X48,X49] : multiplication(X47,multiplication(X48,X49)) = multiplication(multiplication(X47,X48),X49),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
cnf(c_0_73,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_38]),c_0_29]) ).
cnf(c_0_74,plain,
strong_iteration(X1) = addition(star(X1),multiplication(strong_iteration(X1),zero)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
multiplication(strong_iteration(strong_iteration(X1)),zero) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_69]),c_0_70]) ).
fof(c_0_76,negated_conjecture,
~ ! [X4] :
( leq(strong_iteration(star(X4)),strong_iteration(one))
& leq(strong_iteration(one),strong_iteration(star(X4))) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_77,plain,
( leq(X1,multiplication(strong_iteration(one),X2))
| ~ leq(X1,addition(X2,X1)) ),
inference(spm,[status(thm)],[c_0_58,c_0_29]) ).
cnf(c_0_78,plain,
addition(one,multiplication(X1,star(X1))) = star(X1),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_79,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_80,plain,
multiplication(addition(X1,one),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_70,c_0_73]) ).
cnf(c_0_81,plain,
strong_iteration(strong_iteration(X1)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_63]) ).
fof(c_0_82,negated_conjecture,
( ~ leq(strong_iteration(star(esk1_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(esk1_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_76])])]) ).
cnf(c_0_83,plain,
( leq(strong_iteration(X1),strong_iteration(one))
| ~ leq(strong_iteration(X1),strong_iteration(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_37]),c_0_25]) ).
cnf(c_0_84,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_56,c_0_29]) ).
cnf(c_0_85,plain,
addition(one,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))) = star(multiplication(X1,X2)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_86,plain,
multiplication(addition(one,X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_80,c_0_29]) ).
cnf(c_0_87,plain,
multiplication(strong_iteration(one),zero) = strong_iteration(one),
inference(rw,[status(thm)],[c_0_75,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( ~ leq(strong_iteration(star(esk1_0)),strong_iteration(one))
| ~ leq(strong_iteration(one),strong_iteration(star(esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_89,plain,
leq(strong_iteration(X1),strong_iteration(one)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_52]),c_0_27])]) ).
cnf(c_0_90,plain,
( leq(multiplication(X1,star(multiplication(X2,X1))),strong_iteration(X2))
| ~ leq(multiplication(X1,star(multiplication(X2,X1))),star(multiplication(X2,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_25]) ).
cnf(c_0_91,plain,
multiplication(star(X1),strong_iteration(one)) = strong_iteration(one),
inference(spm,[status(thm)],[c_0_86,c_0_49]) ).
cnf(c_0_92,plain,
star(strong_iteration(one)) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_75]),c_0_39]),c_0_75]),c_0_37]) ).
cnf(c_0_93,plain,
multiplication(strong_iteration(one),X1) = strong_iteration(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_87]),c_0_39]),c_0_87]) ).
cnf(c_0_94,negated_conjecture,
~ leq(strong_iteration(one),strong_iteration(star(esk1_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
cnf(c_0_95,plain,
leq(strong_iteration(one),strong_iteration(star(X1))),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),c_0_93]),c_0_92]),c_0_93]),c_0_92]),c_0_89])]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE144+2 : 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
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:31:09 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.72/4.49 % Version : CSE_E---1.7
% 5.72/4.49 % Problem : theBenchmark.p
% 5.72/4.49 % SZS status Theorem for theBenchmark.p
% 5.72/4.49 % SZS output start CNFRefutation
% See solution above
% 5.82/4.50 % Total time : 3.372s
%------------------------------------------------------------------------------