%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET797+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 : n010.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 05:08:30 PM UTC 2026
% Result : Theorem 1.20s 1.86s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 59 ( 18 ~; 18 |; 13 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV9,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3,X5] :
( ( subset(X3,X4)
& subset(X5,X4)
& subset(X3,X5) )
=> ! [X8] :
( upper_bound(X8,X6,X5)
=> upper_bound(X8,X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV9) ).
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(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(c_0_3,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X3,X5] :
( ( subset(X3,X4)
& subset(X5,X4)
& subset(X3,X5) )
=> ! [X8] :
( upper_bound(X8,X6,X5)
=> upper_bound(X8,X6,X3) ) ) ),
inference(assume_negation,[status(cth)],[thIV9]) ).
fof(c_0_4,plain,
! [X135,X136,X137,X138,X139,X140,X141] :
( ( ~ upper_bound(X137,X135,X136)
| ~ member(X138,X136)
| apply(X135,X138,X137) )
& ( member(esk6_3(X139,X140,X141),X140)
| upper_bound(X141,X139,X140) )
& ( ~ apply(X139,esk6_3(X139,X140,X141),X141)
| upper_bound(X141,X139,X140) ) ),
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])])])])])]) ).
fof(c_0_5,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& subset(esk17_0,esk15_0)
& subset(esk16_0,esk17_0)
& upper_bound(esk18_0,esk14_0,esk17_0)
& ~ upper_bound(esk18_0,esk14_0,esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( apply(X2,X4,X1)
| ~ upper_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
upper_bound(esk18_0,esk14_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X88,X89,X90,X91,X92] :
( ( ~ subset(X88,X89)
| ~ member(X90,X88)
| member(X90,X89) )
& ( member(esk1_2(X91,X92),X91)
| subset(X91,X92) )
& ( ~ member(esk1_2(X91,X92),X92)
| subset(X91,X92) ) ),
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_9,plain,
( upper_bound(X3,X1,X2)
| ~ apply(X1,esk6_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( apply(esk14_0,X1,esk18_0)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
subset(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( upper_bound(esk18_0,esk14_0,X1)
| ~ member(esk6_3(esk14_0,X1,esk18_0),esk17_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk17_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( upper_bound(esk18_0,esk14_0,X1)
| ~ member(esk6_3(esk14_0,X1,esk18_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( member(esk6_3(X1,X2,X3),X2)
| upper_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
~ upper_bound(esk18_0,esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20 % Problem : SET797+4 : TPTP v9.2.1. Released v3.2.0.
% 0.02/0.20 % 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
% 0.13/0.42 % Computer : n010.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8042.1875MB
% 0.13/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Tue May 5 02:35:51 EDT 2026
% 0.13/0.43 % CPUTime :
% 0.16/0.45 % start to proof: theBenchmark
% 1.20/1.86 % Version : CSE_E---1.7
% 1.20/1.86 % Problem : theBenchmark.p
% 1.20/1.86 % SZS status Theorem for theBenchmark.p
% 1.20/1.86 % SZS output start CNFRefutation
% See solution above
% 1.20/1.86 % Total time : 1.384s
%------------------------------------------------------------------------------