%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE140+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 41.11s 24.58s
% Output : CNFRefutation 41.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 30 unt; 0 def)
% Number of atoms : 56 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 8 |; 2 &)
% ( 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 1 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_left_identity) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',order) ).
fof(goals,conjecture,
! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',multiplicative_right_identity) ).
fof(idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE004+0.ax',idempotence) ).
fof(c_0_10,plain,
! [X69] : strong_iteration(X69) = addition(multiplication(X69,strong_iteration(X69)),one),
inference(variable_rename,[status(thm)],[infty_unfold1]) ).
fof(c_0_11,plain,
! [X42,X43] : addition(X42,X43) = addition(X43,X42),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_12,plain,
! [X70,X71,X72] :
( ~ leq(X72,addition(multiplication(X70,X72),X71))
| leq(X72,multiplication(strong_iteration(X70),X71)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[infty_coinduction])]) ).
fof(c_0_13,plain,
! [X44,X45,X46] : addition(X46,addition(X45,X44)) = addition(addition(X46,X45),X44),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
cnf(c_0_14,plain,
strong_iteration(X1) = addition(multiplication(X1,strong_iteration(X1)),one),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X57,X58,X59] : multiplication(addition(X57,X58),X59) = addition(multiplication(X57,X59),multiplication(X58,X59)),
inference(variable_rename,[status(thm)],[distributivity2]) ).
fof(c_0_17,plain,
! [X53] : multiplication(one,X53) = X53,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_18,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(multiplication(X2,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X74,X75] :
( ( ~ leq(X74,X75)
| addition(X74,X75) = X75 )
& ( addition(X74,X75) != X75
| leq(X74,X75) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_20,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
addition(one,multiplication(X1,strong_iteration(X1))) = strong_iteration(X1),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_24,negated_conjecture,
~ ! [X4,X5] :
( leq(X4,X5)
=> leq(strong_iteration(X4),strong_iteration(X5)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_25,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| ~ leq(X1,addition(X3,multiplication(X2,X1))) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_26,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
addition(one,addition(multiplication(X1,strong_iteration(X1)),X2)) = addition(strong_iteration(X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_15]) ).
fof(c_0_29,plain,
! [X52] : multiplication(X52,one) = X52,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_30,plain,
! [X48] : addition(X48,X48) = X48,
inference(variable_rename,[status(thm)],[idempotence]) ).
fof(c_0_31,negated_conjecture,
( leq(esk1_0,esk2_0)
& ~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).
cnf(c_0_32,plain,
( leq(X1,multiplication(strong_iteration(X2),X3))
| addition(X1,addition(X3,multiplication(X2,X1))) != addition(X3,multiplication(X2,X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
addition(one,multiplication(addition(X1,X2),strong_iteration(X1))) = multiplication(addition(X2,one),strong_iteration(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_22]),c_0_28]) ).
cnf(c_0_34,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_37,negated_conjecture,
leq(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
leq(strong_iteration(X1),strong_iteration(addition(X1,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_28]),c_0_20]),c_0_35])]) ).
cnf(c_0_39,negated_conjecture,
addition(esk1_0,esk2_0) = esk2_0,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ leq(strong_iteration(esk1_0),strong_iteration(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : KLE140+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.05/0.24 % Computer : n024.cluster.edu
% 0.05/0.24 % Model : x86_64 x86_64
% 0.05/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.24 % Memory : 8042.1875MB
% 0.05/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.05/0.24 % CPULimit : 300
% 0.05/0.24 % WCLimit : 300
% 0.05/0.24 % DateTime : Mon May 4 15:30:56 EDT 2026
% 0.05/0.24 % CPUTime :
% 0.05/0.24 % start to proof: theBenchmark
% 41.11/24.58 % Version : CSE_E---1.7
% 41.11/24.58 % Problem : theBenchmark.p
% 41.11/24.58 % SZS status Theorem for theBenchmark.p
% 41.11/24.58 % SZS output start CNFRefutation
% See solution above
% 41.31/24.75 % Total time : 18.381s
%------------------------------------------------------------------------------