%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET800+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 : n022.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 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 95 ( 29 ~; 30 |; 24 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 62 ( 3 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV12,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X9,X10] :
( ( subset(X9,X4)
& subset(X10,X4)
& subset(X9,X10) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X11,X9,X6,X4)
& greatest_lower_bound(X12,X10,X6,X4) )
=> apply(X6,X12,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV12) ).
fof(greatest_lower_bound,axiom,
! [X1,X3,X6,X4] :
( greatest_lower_bound(X1,X3,X6,X4)
<=> ( member(X1,X3)
& lower_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X9,X10] :
( ( subset(X9,X4)
& subset(X10,X4)
& subset(X9,X10) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X11,X9,X6,X4)
& greatest_lower_bound(X12,X10,X6,X4) )
=> apply(X6,X12,X11) ) ) ),
inference(assume_negation,[status(cth)],[thIV12]) ).
fof(c_0_5,plain,
! [X198,X199,X200,X201,X202,X203,X204,X205,X206] :
( ( member(X198,X199)
| ~ greatest_lower_bound(X198,X199,X200,X201) )
& ( lower_bound(X198,X200,X199)
| ~ greatest_lower_bound(X198,X199,X200,X201) )
& ( ~ member(X202,X201)
| ~ lower_bound(X202,X200,X199)
| apply(X200,X202,X198)
| ~ greatest_lower_bound(X198,X199,X200,X201) )
& ( member(esk13_4(X203,X204,X205,X206),X206)
| ~ member(X203,X204)
| ~ lower_bound(X203,X205,X204)
| greatest_lower_bound(X203,X204,X205,X206) )
& ( lower_bound(esk13_4(X203,X204,X205,X206),X205,X204)
| ~ member(X203,X204)
| ~ lower_bound(X203,X205,X204)
| greatest_lower_bound(X203,X204,X205,X206) )
& ( ~ apply(X205,esk13_4(X203,X204,X205,X206),X203)
| ~ member(X203,X204)
| ~ lower_bound(X203,X205,X204)
| greatest_lower_bound(X203,X204,X205,X206) ) ),
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_lower_bound])])])])])]) ).
fof(c_0_6,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& subset(esk17_0,esk15_0)
& subset(esk16_0,esk17_0)
& greatest_lower_bound(esk18_0,esk16_0,esk14_0,esk15_0)
& greatest_lower_bound(esk19_0,esk17_0,esk14_0,esk15_0)
& ~ apply(esk14_0,esk19_0,esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X93,X94,X95,X96,X97] :
( ( ~ subset(X93,X94)
| ~ member(X95,X93)
| member(X95,X94) )
& ( member(esk1_2(X96,X97),X96)
| subset(X96,X97) )
& ( ~ member(esk1_2(X96,X97),X97)
| subset(X96,X97) ) ),
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)],[subset])])])])])]) ).
cnf(c_0_8,plain,
( member(X1,X2)
| ~ greatest_lower_bound(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
greatest_lower_bound(esk18_0,esk16_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X148,X149,X150,X151,X152,X153,X154] :
( ( ~ lower_bound(X150,X148,X149)
| ~ member(X151,X149)
| apply(X148,X150,X151) )
& ( member(esk7_3(X152,X153,X154),X153)
| lower_bound(X154,X152,X153) )
& ( ~ apply(X152,X154,esk7_3(X152,X153,X154))
| lower_bound(X154,X152,X153) ) ),
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)],[lower_bound])])])])])]) ).
cnf(c_0_11,plain,
( lower_bound(X1,X2,X3)
| ~ greatest_lower_bound(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
greatest_lower_bound(esk19_0,esk17_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
member(esk18_0,esk16_0),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
lower_bound(esk19_0,esk14_0,esk17_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( member(esk18_0,X1)
| ~ subset(esk16_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
subset(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
~ apply(esk14_0,esk19_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk14_0,esk19_0,X1)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
member(esk18_0,esk17_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET800+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
% 0.16/0.33 % Computer : n022.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 : Tue May 5 02:35:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------