%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET803+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 : n017.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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 9 unt; 0 def)
% Number of atoms : 80 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 90 ( 34 ~; 30 |; 18 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 50 ( 2 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV15,conjecture,
! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( max(X8,X1,X2)
& max(X9,X1,X2)
& X8 != X9 )
=> ~ ? [X6] : greatest(X6,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV15) ).
fof(max,axiom,
! [X1,X2,X6] :
( max(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X6,X3) )
=> X6 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',max) ).
fof(greatest,axiom,
! [X1,X2,X6] :
( greatest(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( order(X1,X2)
=> ! [X8,X9] :
( ( max(X8,X1,X2)
& max(X9,X1,X2)
& X8 != X9 )
=> ~ ? [X6] : greatest(X6,X1,X2) ) ),
inference(assume_negation,[status(cth)],[thIV15]) ).
fof(c_0_4,plain,
! [X103,X104,X105,X106,X107,X108,X109] :
( ( member(X105,X104)
| ~ max(X105,X103,X104) )
& ( ~ member(X106,X104)
| ~ apply(X103,X105,X106)
| X105 = X106
| ~ max(X105,X103,X104) )
& ( member(esk7_3(X107,X108,X109),X108)
| ~ member(X109,X108)
| max(X109,X107,X108) )
& ( apply(X107,X109,esk7_3(X107,X108,X109))
| ~ member(X109,X108)
| max(X109,X107,X108) )
& ( X109 != esk7_3(X107,X108,X109)
| ~ member(X109,X108)
| max(X109,X107,X108) ) ),
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)],[max])])])])])]) ).
fof(c_0_5,negated_conjecture,
( order(esk11_0,esk12_0)
& max(esk13_0,esk11_0,esk12_0)
& max(esk14_0,esk11_0,esk12_0)
& esk13_0 != esk14_0
& greatest(esk15_0,esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,plain,
! [X87,X88,X89,X90,X91,X92,X93] :
( ( member(X89,X88)
| ~ greatest(X89,X87,X88) )
& ( ~ member(X90,X88)
| apply(X87,X90,X89)
| ~ greatest(X89,X87,X88) )
& ( member(esk5_3(X91,X92,X93),X92)
| ~ member(X93,X92)
| greatest(X93,X91,X92) )
& ( ~ apply(X91,esk5_3(X91,X92,X93),X93)
| ~ member(X93,X92)
| greatest(X93,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)],[greatest])])])])])]) ).
cnf(c_0_7,plain,
( X4 = X1
| ~ member(X1,X2)
| ~ apply(X3,X4,X1)
| ~ max(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
max(esk14_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( apply(X3,X1,X4)
| ~ member(X1,X2)
| ~ greatest(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
greatest(esk15_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ greatest(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ max(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
( X1 = esk14_0
| ~ apply(esk11_0,esk14_0,X1)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( apply(esk11_0,X1,esk15_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
member(esk15_0,esk12_0),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
member(esk14_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_17,negated_conjecture,
max(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
esk15_0 = esk14_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
( X1 = esk13_0
| ~ apply(esk11_0,esk13_0,X1)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( apply(esk11_0,X1,esk14_0)
| ~ member(X1,esk12_0) ),
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk13_0 != esk14_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET803+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 : n017.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 02:34:28 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------