%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KLE029+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 : n013.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 04:35:33 PM UTC 2026
% Result : Theorem 6.29s 4.56s
% Output : CNFRefutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 71 ( 24 unt; 0 def)
% Number of atoms : 195 ( 32 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 202 ( 78 ~; 101 |; 16 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 131 ( 4 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(goals,conjecture,
! [X4,X5,X6] :
( ismeet(X4,X5,X6)
<=> ismeetu(X4,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(ismeetu,axiom,
! [X4,X5,X6] :
( ismeetu(X6,X4,X5)
<=> ! [X7] :
( ( leq(X7,X4)
& leq(X7,X5) )
<=> leq(X7,X6) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax',ismeetu) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',order) ).
fof(ismeet,axiom,
! [X4,X5,X6] :
( ismeet(X6,X4,X5)
<=> ( leq(X6,X4)
& leq(X6,X5)
& ! [X7] :
( ( leq(X7,X4)
& leq(X7,X5) )
=> leq(X7,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+3.ax',ismeet) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+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/KLE001+0.ax',additive_associativity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(c_0_7,negated_conjecture,
~ ! [X4,X5,X6] :
( ismeet(X4,X5,X6)
<=> ismeetu(X4,X5,X6) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_8,plain,
! [X71,X72,X73,X74,X75,X76,X77,X78] :
( ( ~ leq(X74,X71)
| ~ leq(X74,X72)
| leq(X74,X73)
| ~ ismeetu(X73,X71,X72) )
& ( leq(X75,X71)
| ~ leq(X75,X73)
| ~ ismeetu(X73,X71,X72) )
& ( leq(X75,X72)
| ~ leq(X75,X73)
| ~ ismeetu(X73,X71,X72) )
& ( ~ leq(esk2_3(X76,X77,X78),X76)
| ~ leq(esk2_3(X76,X77,X78),X77)
| ~ leq(esk2_3(X76,X77,X78),X78)
| ismeetu(X78,X76,X77) )
& ( leq(esk2_3(X76,X77,X78),X76)
| leq(esk2_3(X76,X77,X78),X78)
| ismeetu(X78,X76,X77) )
& ( leq(esk2_3(X76,X77,X78),X77)
| leq(esk2_3(X76,X77,X78),X78)
| ismeetu(X78,X76,X77) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ismeetu])])])])])]) ).
fof(c_0_9,negated_conjecture,
( ( ~ ismeet(esk3_0,esk4_0,esk5_0)
| ~ ismeetu(esk3_0,esk4_0,esk5_0) )
& ( ismeet(esk3_0,esk4_0,esk5_0)
| ismeetu(esk3_0,esk4_0,esk5_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_10,plain,
( leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeetu(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| ismeetu(esk3_0,esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X61,X62] :
( ( ~ leq(X61,X62)
| addition(X61,X62) = X62 )
& ( addition(X61,X62) != X62
| leq(X61,X62) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
fof(c_0_13,plain,
! [X63,X64,X65,X66,X67,X68,X69] :
( ( leq(X65,X63)
| ~ ismeet(X65,X63,X64) )
& ( leq(X65,X64)
| ~ ismeet(X65,X63,X64) )
& ( ~ leq(X66,X63)
| ~ leq(X66,X64)
| leq(X66,X65)
| ~ ismeet(X65,X63,X64) )
& ( leq(esk1_3(X67,X68,X69),X67)
| ~ leq(X69,X67)
| ~ leq(X69,X68)
| ismeet(X69,X67,X68) )
& ( leq(esk1_3(X67,X68,X69),X68)
| ~ leq(X69,X67)
| ~ leq(X69,X68)
| ismeet(X69,X67,X68) )
& ( ~ leq(esk1_3(X67,X68,X69),X69)
| ~ leq(X69,X67)
| ~ leq(X69,X68)
| ismeet(X69,X67,X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ismeet])])])])])]) ).
cnf(c_0_14,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(X1,esk5_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X47] : addition(X47,X47) = X47,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_17,plain,
( leq(X1,X4)
| ~ leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeetu(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( leq(X1,X4)
| ~ leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeet(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeetu(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_20,plain,
! [X43,X44,X45] : addition(X45,addition(X44,X43)) = addition(addition(X45,X44),X43),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_21,plain,
! [X41,X42] : addition(X41,X42) = addition(X42,X41),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
cnf(c_0_22,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(X1,esk5_0)
| addition(X1,esk3_0) != esk3_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( leq(X1,X2)
| ~ ismeet(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
( leq(esk2_3(X1,X2,X3),X2)
| leq(esk2_3(X1,X2,X3),X3)
| ismeetu(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
( leq(X1,esk3_0)
| ~ leq(X1,esk5_0)
| ~ leq(X1,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(X1,esk4_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_28,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,negated_conjecture,
leq(esk3_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_32,plain,
( ismeetu(X1,X2,X1)
| leq(esk2_3(X2,X1,X1),X1) ),
inference(ef,[status(thm)],[c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( leq(X1,esk3_0)
| addition(X1,esk5_0) != esk5_0
| ~ leq(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_34,plain,
( leq(esk1_3(X1,X2,X3),X1)
| ismeet(X3,X1,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(X1,esk4_0)
| addition(X1,esk3_0) != esk3_0 ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_36,plain,
( leq(X1,X2)
| ~ ismeet(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_37,plain,
( ismeetu(X3,X1,X2)
| ~ leq(esk2_3(X1,X2,X3),X1)
| ~ leq(esk2_3(X1,X2,X3),X2)
| ~ leq(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_38,plain,
addition(X1,addition(X2,X3)) = addition(X2,addition(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_28]) ).
cnf(c_0_39,negated_conjecture,
addition(esk3_0,esk5_0) = esk5_0,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( addition(X1,esk2_3(X2,X1,X1)) = X1
| ismeetu(X1,X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_29]) ).
cnf(c_0_41,plain,
( ismeet(X3,X1,X2)
| ~ leq(esk1_3(X1,X2,X3),X3)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_42,negated_conjecture,
( ismeet(X1,esk4_0,X2)
| leq(esk1_3(esk4_0,X2,X1),esk3_0)
| addition(esk5_0,esk1_3(esk4_0,X2,X1)) != esk5_0
| ~ leq(X1,esk4_0)
| ~ leq(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_29]) ).
cnf(c_0_43,negated_conjecture,
leq(esk3_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_36]) ).
cnf(c_0_44,plain,
( leq(esk1_3(X1,X2,X3),X2)
| ismeet(X3,X1,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_45,plain,
( ismeetu(X1,X2,X1)
| ~ leq(esk2_3(X2,X1,X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_32]) ).
cnf(c_0_46,negated_conjecture,
addition(esk3_0,addition(X1,esk5_0)) = addition(X1,esk5_0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
( addition(X1,addition(esk2_3(X2,X1,X1),X3)) = addition(X1,X3)
| ismeetu(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ismeet(esk3_0,esk4_0,X1)
| addition(esk5_0,esk1_3(esk4_0,X1,esk3_0)) != esk5_0
| ~ leq(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]) ).
cnf(c_0_49,plain,
( addition(X1,esk1_3(X2,X1,X3)) = X1
| ismeet(X3,X2,X1)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_44]),c_0_29]) ).
cnf(c_0_50,plain,
( ismeetu(X1,X2,X1)
| addition(X2,esk2_3(X2,X1,X1)) != X2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_15]),c_0_29]) ).
cnf(c_0_51,negated_conjecture,
( addition(esk5_0,esk2_3(X1,esk3_0,esk3_0)) = esk5_0
| ismeetu(esk3_0,X1,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_39]),c_0_29]) ).
cnf(c_0_52,negated_conjecture,
( ismeetu(X1,X2,esk5_0)
| leq(esk2_3(X2,esk5_0,X1),esk3_0)
| leq(esk2_3(X2,esk5_0,X1),X1)
| ~ leq(esk2_3(X2,esk5_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_53,plain,
( leq(esk2_3(X1,X2,X3),X1)
| leq(esk2_3(X1,X2,X3),X3)
| ismeetu(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_54,negated_conjecture,
( ~ ismeet(esk3_0,esk4_0,esk5_0)
| ~ ismeetu(esk3_0,esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_55,negated_conjecture,
ismeet(esk3_0,esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_31]),c_0_43])]) ).
cnf(c_0_56,negated_conjecture,
ismeetu(esk3_0,esk5_0,esk3_0),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
addition(esk3_0,esk4_0) = esk4_0,
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
cnf(c_0_58,negated_conjecture,
( ismeetu(X1,esk4_0,esk5_0)
| leq(esk2_3(esk4_0,esk5_0,X1),esk3_0)
| leq(esk2_3(esk4_0,esk5_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
~ ismeetu(esk3_0,esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_60,negated_conjecture,
( leq(X1,esk5_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_61,negated_conjecture,
addition(esk3_0,addition(X1,esk4_0)) = addition(X1,esk4_0),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
leq(esk2_3(esk4_0,esk5_0,esk3_0),esk3_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_58]),c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( addition(X1,esk5_0) = esk5_0
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( addition(esk4_0,esk2_3(X1,esk3_0,esk3_0)) = esk4_0
| ismeetu(esk3_0,X1,esk3_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_57]),c_0_29]) ).
cnf(c_0_65,negated_conjecture,
( ~ leq(esk2_3(esk4_0,esk5_0,esk3_0),esk5_0)
| ~ leq(esk2_3(esk4_0,esk5_0,esk3_0),esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_62]),c_0_59]) ).
cnf(c_0_66,negated_conjecture,
addition(esk5_0,esk2_3(esk4_0,esk5_0,esk3_0)) = esk5_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_62]),c_0_29]) ).
cnf(c_0_67,negated_conjecture,
ismeetu(esk3_0,esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_50,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
~ leq(esk2_3(esk4_0,esk5_0,esk3_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_15]),c_0_29]),c_0_66])]) ).
cnf(c_0_69,negated_conjecture,
( leq(X1,esk4_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE029+1 : 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
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:26:11 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 6.29/4.56 % Version : CSE_E---1.7
% 6.29/4.56 % Problem : theBenchmark.p
% 6.29/4.56 % SZS status Theorem for theBenchmark.p
% 6.29/4.56 % SZS output start CNFRefutation
% See solution above
% 6.29/4.58 % Total time : 3.368s
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