%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET731+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 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 : n007.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 05:08:24 PM UTC 2026
% Result : Theorem 18.07s 11.51s
% Output : CNFRefutation 18.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 80 ( 4 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 88 ( 30 ~; 29 |; 20 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-4 aty)
% Number of variables : 58 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII22,conjecture,
! [X6,X10,X1,X2,X11] :
( ( maps(X6,X1,X2)
& subset(X11,X2)
& image2(X6,X1) = X11
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X11) )
=> ( apply(X10,X3,X5)
<=> apply(X6,X3,X5) ) ) )
=> surjective(X10,X1,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII22) ).
fof(surjective,axiom,
! [X6,X1,X2] :
( surjective(X6,X1,X2)
<=> ! [X5] :
( member(X5,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X6,X4,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(image2,axiom,
! [X6,X1,X5] :
( member(X5,image2(X6,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(c_0_3,negated_conjecture,
~ ! [X6,X10,X1,X2,X11] :
( ( maps(X6,X1,X2)
& subset(X11,X2)
& image2(X6,X1) = X11
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X11) )
=> ( apply(X10,X3,X5)
<=> apply(X6,X3,X5) ) ) )
=> surjective(X10,X1,X11) ),
inference(assume_negation,[status(cth)],[thII22]) ).
fof(c_0_4,negated_conjecture,
! [X396,X397] :
( maps(esk41_0,esk43_0,esk44_0)
& subset(esk45_0,esk44_0)
& image2(esk41_0,esk43_0) = esk45_0
& ( ~ apply(esk42_0,X396,X397)
| apply(esk41_0,X396,X397)
| ~ member(X396,esk43_0)
| ~ member(X397,esk45_0) )
& ( ~ apply(esk41_0,X396,X397)
| apply(esk42_0,X396,X397)
| ~ member(X396,esk43_0)
| ~ member(X397,esk45_0) )
& ~ surjective(esk42_0,esk43_0,esk45_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
fof(c_0_5,plain,
! [X271,X272,X273,X274,X276,X277,X278,X280] :
( ( member(esk21_4(X271,X272,X273,X274),X272)
| ~ member(X274,X273)
| ~ surjective(X271,X272,X273) )
& ( apply(X271,esk21_4(X271,X272,X273,X274),X274)
| ~ member(X274,X273)
| ~ surjective(X271,X272,X273) )
& ( member(esk22_3(X276,X277,X278),X278)
| surjective(X276,X277,X278) )
& ( ~ member(X280,X277)
| ~ apply(X276,X280,esk22_3(X276,X277,X278))
| surjective(X276,X277,X278) ) ),
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)],[surjective])])])])])]) ).
fof(c_0_6,plain,
! [X301,X302,X303,X305,X306,X307,X308] :
( ( member(esk25_3(X301,X302,X303),X302)
| ~ member(X303,image2(X301,X302)) )
& ( apply(X301,esk25_3(X301,X302,X303),X303)
| ~ member(X303,image2(X301,X302)) )
& ( ~ member(X308,X306)
| ~ apply(X305,X308,X307)
| member(X307,image2(X305,X306)) ) ),
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)],[image2])])])])])]) ).
cnf(c_0_7,negated_conjecture,
~ surjective(esk42_0,esk43_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( member(esk22_3(X1,X2,X3),X3)
| surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(esk25_3(X1,X2,X3),X2)
| ~ member(X3,image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
image2(esk41_0,esk43_0) = esk45_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
( apply(X1,esk25_3(X1,X2,X3),X3)
| ~ member(X3,image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,negated_conjecture,
( apply(esk42_0,X1,X2)
| ~ apply(esk41_0,X1,X2)
| ~ member(X1,esk43_0)
| ~ member(X2,esk45_0) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
member(esk22_3(esk42_0,esk43_0,esk45_0),esk45_0),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( member(esk25_3(esk41_0,esk43_0,X1),esk43_0)
| ~ member(X1,esk45_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( apply(esk41_0,esk25_3(esk41_0,esk43_0,X1),X1)
| ~ member(X1,esk45_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( apply(esk42_0,X1,esk22_3(esk42_0,esk43_0,esk45_0))
| ~ apply(esk41_0,X1,esk22_3(esk42_0,esk43_0,esk45_0))
| ~ member(X1,esk43_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
member(esk25_3(esk41_0,esk43_0,esk22_3(esk42_0,esk43_0,esk45_0)),esk43_0),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
apply(esk41_0,esk25_3(esk41_0,esk43_0,esk22_3(esk42_0,esk43_0,esk45_0)),esk22_3(esk42_0,esk43_0,esk45_0)),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_19,plain,
( surjective(X3,X2,X4)
| ~ member(X1,X2)
| ~ apply(X3,X1,esk22_3(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,negated_conjecture,
apply(esk42_0,esk25_3(esk41_0,esk43_0,esk22_3(esk42_0,esk43_0,esk45_0)),esk22_3(esk42_0,esk43_0,esk45_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17])]),c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET731+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n007.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:32:24 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 18.07/11.51 % Version : CSE_E---1.7
% 18.07/11.51 % Problem : theBenchmark.p
% 18.07/11.51 % SZS status Theorem for theBenchmark.p
% 18.07/11.51 % SZS output start CNFRefutation
% See solution above
% 18.07/11.58 % Total time : 8.385s
%------------------------------------------------------------------------------