%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET801+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n029.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 05:08:31 PM UTC 2026
% Result : Theorem 1.98s 1.90s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 152 ( 55 ~; 65 |; 20 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 93 ( 3 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV13,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( greatest(X8,X6,X3)
<=> ( member(X8,X3)
& least_upper_bound(X8,X3,X6,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV13) ).
fof(greatest,axiom,
! [X6,X4,X8] :
( greatest(X8,X6,X4)
<=> ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest) ).
fof(upper_bound,axiom,
! [X6,X4,X8] :
( upper_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',upper_bound) ).
fof(least_upper_bound,axiom,
! [X1,X3,X6,X4] :
( least_upper_bound(X1,X3,X6,X4)
<=> ( member(X1,X3)
& upper_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X1,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( greatest(X8,X6,X3)
<=> ( member(X8,X3)
& least_upper_bound(X8,X3,X6,X4) ) ) ) ),
inference(assume_negation,[status(cth)],[thIV13]) ).
fof(c_0_5,plain,
! [X150,X151,X152,X153,X154,X155,X156] :
( ( member(X152,X151)
| ~ greatest(X152,X150,X151) )
& ( ~ member(X153,X151)
| apply(X150,X153,X152)
| ~ greatest(X152,X150,X151) )
& ( member(esk8_3(X154,X155,X156),X155)
| ~ member(X156,X155)
| greatest(X156,X154,X155) )
& ( ~ apply(X154,esk8_3(X154,X155,X156),X156)
| ~ member(X156,X155)
| greatest(X156,X154,X155) ) ),
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)],[greatest])])])])])]) ).
fof(c_0_6,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& ( ~ greatest(esk17_0,esk14_0,esk16_0)
| ~ member(esk17_0,esk16_0)
| ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0) )
& ( member(esk17_0,esk16_0)
| greatest(esk17_0,esk14_0,esk16_0) )
& ( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| greatest(esk17_0,esk14_0,esk16_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,plain,
( apply(X3,X1,X4)
| ~ member(X1,X2)
| ~ greatest(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| greatest(esk17_0,esk14_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X134,X135,X136,X137,X138,X139,X140] :
( ( ~ upper_bound(X136,X134,X135)
| ~ member(X137,X135)
| apply(X134,X137,X136) )
& ( member(esk6_3(X138,X139,X140),X139)
| upper_bound(X140,X138,X139) )
& ( ~ apply(X138,esk6_3(X138,X139,X140),X140)
| upper_bound(X140,X138,X139) ) ),
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)],[upper_bound])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| apply(esk14_0,X1,esk17_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( member(esk6_3(X1,X2,X3),X2)
| upper_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X182,X183,X184,X185,X186,X187,X188,X189,X190] :
( ( member(X182,X183)
| ~ least_upper_bound(X182,X183,X184,X185) )
& ( upper_bound(X182,X184,X183)
| ~ least_upper_bound(X182,X183,X184,X185) )
& ( ~ member(X186,X185)
| ~ upper_bound(X186,X184,X183)
| apply(X184,X182,X186)
| ~ least_upper_bound(X182,X183,X184,X185) )
& ( member(esk12_4(X187,X188,X189,X190),X190)
| ~ member(X187,X188)
| ~ upper_bound(X187,X189,X188)
| least_upper_bound(X187,X188,X189,X190) )
& ( upper_bound(esk12_4(X187,X188,X189,X190),X189,X188)
| ~ member(X187,X188)
| ~ upper_bound(X187,X189,X188)
| least_upper_bound(X187,X188,X189,X190) )
& ( ~ apply(X189,X187,esk12_4(X187,X188,X189,X190))
| ~ member(X187,X188)
| ~ upper_bound(X187,X189,X188)
| least_upper_bound(X187,X188,X189,X190) ) ),
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)],[least_upper_bound])])])])])]) ).
cnf(c_0_13,plain,
( upper_bound(X3,X1,X2)
| ~ apply(X1,esk6_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| upper_bound(X1,X2,esk16_0)
| apply(esk14_0,esk6_3(X2,esk16_0,X1),esk17_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( upper_bound(X1,X2,X3)
| ~ least_upper_bound(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( apply(X2,X4,X1)
| ~ upper_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
upper_bound(esk17_0,esk14_0,esk16_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( member(X1,X2)
| ~ greatest(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( member(esk17_0,esk16_0)
| greatest(esk17_0,esk14_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( greatest(X3,X1,X2)
| ~ apply(X1,esk8_3(X1,X2,X3),X3)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( apply(esk14_0,X1,esk17_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ greatest(esk17_0,esk14_0,esk16_0)
| ~ member(esk17_0,esk16_0)
| ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
member(esk17_0,esk16_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( greatest(esk17_0,esk14_0,X1)
| ~ member(esk8_3(esk14_0,X1,esk17_0),esk16_0)
| ~ member(esk17_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( member(esk8_3(X1,X2,X3),X2)
| greatest(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,plain,
( upper_bound(esk12_4(X1,X2,X3,X4),X3,X2)
| least_upper_bound(X1,X2,X3,X4)
| ~ member(X1,X2)
| ~ upper_bound(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| ~ greatest(esk17_0,esk14_0,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
greatest(esk17_0,esk14_0,esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]) ).
cnf(c_0_29,plain,
( least_upper_bound(X2,X3,X1,X4)
| ~ apply(X1,X2,esk12_4(X2,X3,X1,X4))
| ~ member(X2,X3)
| ~ upper_bound(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,plain,
( least_upper_bound(X1,X2,X3,X4)
| apply(X3,X5,esk12_4(X1,X2,X3,X4))
| ~ upper_bound(X1,X3,X2)
| ~ member(X5,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_32,plain,
( least_upper_bound(X1,X2,X3,X4)
| ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET801+4 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.32 % Computer : n029.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 : Tue May 5 02:36:14 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.98/1.90 % Version : CSE_E---1.7
% 1.98/1.90 % Problem : theBenchmark.p
% 1.98/1.90 % SZS status Theorem for theBenchmark.p
% 1.98/1.90 % SZS output start CNFRefutation
% See solution above
% 1.98/1.90 % Total time : 1.372s
%------------------------------------------------------------------------------