%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE037+1 : 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 : n004.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 04:35:34 PM UTC 2026
% Result : Theorem 1.35s 1.74s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 49 unt; 0 def)
% Number of atoms : 124 ( 50 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 40 ~; 37 |; 1 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 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 : 108 ( 8 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
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(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',left_annihilation) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_right_identity) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',order) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',right_annihilation) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
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(goals,conjecture,
! [X4] : leq(one,star(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_12,plain,
! [X41] : addition(X41,zero) = X41,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_13,plain,
! [X36,X37] : addition(X36,X37) = addition(X37,X36),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_14,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(c_0_15,plain,
! [X55] : multiplication(zero,X55) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_16,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X46] : multiplication(X46,one) = X46,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_19,plain,
! [X58] : leq(addition(one,multiplication(X58,star(X58))),star(X58)),
inference(variable_rename,[status(thm)],[star_unfold_right]) ).
fof(c_0_20,plain,
! [X47] : multiplication(one,X47) = X47,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_21,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])]) ).
cnf(c_0_22,plain,
( leq(multiplication(X3,star(X2)),X1)
| ~ leq(addition(multiplication(X1,X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
leq(addition(one,multiplication(X1,star(X1))),star(X1)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( leq(multiplication(X1,star(X2)),zero)
| ~ leq(X1,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X2,X1),X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
leq(one,star(zero)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_16]) ).
fof(c_0_32,plain,
! [X54] : multiplication(X54,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_33,plain,
( leq(multiplication(X1,star(X2)),one)
| ~ leq(addition(X2,X1),one) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_34,plain,
( multiplication(X1,star(X2)) = zero
| ~ leq(X1,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_16]) ).
cnf(c_0_35,plain,
( leq(multiplication(X1,star(one)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_36,plain,
addition(one,star(zero)) = star(zero),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_37,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( leq(star(X1),one)
| ~ leq(addition(X1,one),one) ),
inference(spm,[status(thm)],[c_0_33,c_0_27]) ).
cnf(c_0_39,plain,
( leq(one,star(X1))
| ~ leq(X1,zero) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_16]) ).
cnf(c_0_40,plain,
( leq(star(one),star(zero))
| ~ leq(star(zero),star(zero)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27]) ).
fof(c_0_41,plain,
! [X42] : addition(X42,X42) = X42,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_42,plain,
( leq(multiplication(X1,star(zero)),X2)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_24]) ).
cnf(c_0_43,plain,
( addition(one,star(X1)) = one
| ~ leq(addition(X1,one),one) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_17]) ).
cnf(c_0_44,plain,
( addition(one,star(X1)) = star(X1)
| ~ leq(X1,zero) ),
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
cnf(c_0_45,plain,
( addition(star(zero),star(one)) = star(zero)
| ~ leq(star(zero),star(zero)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_40]),c_0_17]) ).
cnf(c_0_46,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_47,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( leq(star(zero),X1)
| ~ leq(one,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_27]) ).
fof(c_0_49,plain,
! [X38,X39,X40] : addition(X40,addition(X39,X38)) = addition(addition(X40,X39),X38),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_50,plain,
( star(X1) = one
| ~ leq(addition(X1,one),one)
| ~ leq(X1,zero) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
( leq(zero,X1)
| ~ leq(multiplication(X1,X2),X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_23]) ).
cnf(c_0_52,plain,
addition(star(zero),star(one)) = star(zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]) ).
cnf(c_0_53,plain,
( addition(star(zero),X1) = X1
| ~ leq(one,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_54,plain,
leq(addition(one,star(one)),star(one)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_55,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( leq(one,one)
| ~ leq(addition(X1,one),one)
| ~ leq(X1,zero) ),
inference(spm,[status(thm)],[c_0_38,c_0_50]) ).
cnf(c_0_57,plain,
( leq(zero,X1)
| ~ leq(X1,X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_25]) ).
cnf(c_0_58,plain,
( star(one) = star(zero)
| ~ leq(one,star(one)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
addition(one,star(one)) = star(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_54]),c_0_55]),c_0_47]) ).
cnf(c_0_60,plain,
( addition(X1,star(zero)) = X1
| ~ leq(one,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_53]) ).
cnf(c_0_61,plain,
( leq(one,one)
| addition(X1,one) != one
| ~ leq(X1,zero) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_46]),c_0_55]),c_0_47]) ).
cnf(c_0_62,plain,
leq(zero,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_46]),c_0_47])]) ).
cnf(c_0_63,plain,
( leq(multiplication(X1,star(X2)),X3)
| ~ leq(addition(X1,multiplication(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_64,plain,
star(one) = star(zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_46]),c_0_59])]) ).
cnf(c_0_65,plain,
( star(zero) = one
| ~ leq(one,one) ),
inference(spm,[status(thm)],[c_0_36,c_0_60]) ).
cnf(c_0_66,plain,
leq(one,one),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_24]),c_0_62])]) ).
cnf(c_0_67,plain,
( leq(multiplication(X1,star(zero)),X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_25]),c_0_64]) ).
cnf(c_0_68,plain,
star(zero) = one,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_69,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_25]) ).
cnf(c_0_70,plain,
addition(X1,addition(X2,X3)) = addition(X3,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_55]) ).
cnf(c_0_71,plain,
( leq(addition(X1,X2),X3)
| ~ leq(addition(X1,addition(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_69,c_0_55]) ).
cnf(c_0_72,plain,
addition(X1,addition(X2,X1)) = addition(X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_47]) ).
cnf(c_0_73,plain,
( leq(addition(X1,X2),X1)
| ~ leq(addition(X2,X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_47]),c_0_55]),c_0_72]) ).
cnf(c_0_74,plain,
( leq(addition(X1,X2),X1)
| addition(X2,X1) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_46]),c_0_55]),c_0_47]) ).
fof(c_0_75,negated_conjecture,
~ ! [X4] : leq(one,star(X4)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_76,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_47]) ).
cnf(c_0_77,plain,
leq(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_74]),c_0_47])]) ).
fof(c_0_78,negated_conjecture,
~ leq(one,star(esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])]) ).
cnf(c_0_79,plain,
leq(X1,addition(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_76]),c_0_77])]) ).
cnf(c_0_80,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_28,c_0_26]),c_0_55]),c_0_17]) ).
cnf(c_0_81,negated_conjecture,
~ leq(one,star(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,plain,
leq(one,star(X1)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KLE037+1 : 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
% 0.13/0.32 % Computer : n004.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 20:26:03 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.35/1.74 % Version : CSE_E---1.7
% 1.35/1.74 % Problem : theBenchmark.p
% 1.35/1.74 % SZS status Theorem for theBenchmark.p
% 1.35/1.74 % SZS output start CNFRefutation
% See solution above
% 1.35/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------