%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET798+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n025.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 1.30s 1.73s
% Output : CNFRefutation 1.30s
% 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(thIV10,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3,X5] :
( ( subset(X3,X4)
& subset(X5,X4)
& subset(X3,X5) )
=> ! [X8] :
( lower_bound(X8,X6,X5)
=> lower_bound(X8,X6,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV10) ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/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] :
( lower_bound(X8,X6,X5)
=> lower_bound(X8,X6,X3) ) ) ),
inference(assume_negation,[status(cth)],[thIV10]) ).
fof(c_0_4,plain,
! [X143,X144,X145,X146,X147,X148,X149] :
( ( ~ lower_bound(X145,X143,X144)
| ~ member(X146,X144)
| apply(X143,X145,X146) )
& ( member(esk7_3(X147,X148,X149),X148)
| lower_bound(X149,X147,X148) )
& ( ~ apply(X147,X149,esk7_3(X147,X148,X149))
| lower_bound(X149,X147,X148) ) ),
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])])])])])]) ).
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)
& lower_bound(esk18_0,esk14_0,esk17_0)
& ~ lower_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,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
lower_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,
( lower_bound(X2,X1,X3)
| ~ apply(X1,X2,esk7_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( apply(esk14_0,esk18_0,X1)
| ~ 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,
( lower_bound(esk18_0,esk14_0,X1)
| ~ member(esk7_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,
( lower_bound(esk18_0,esk14_0,X1)
| ~ member(esk7_3(esk14_0,X1,esk18_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( member(esk7_3(X1,X2,X3),X2)
| lower_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
~ lower_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
% 0.00/0.11 % Problem : SET798+4 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n025.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 02:36:13 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------