%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM583+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n016.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 04:57:54 PM UTC 2026
% Result : Theorem 4.05s 3.35s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 124 ( 16 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 134 ( 32 ~; 36 |; 50 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__4037,hypothesis,
( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> aElementOf0(X1,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4037) ).
fof(m__3989_02,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3989_02) ).
fof(m__4007,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4007) ).
fof(c_0_4,negated_conjecture,
~ ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) ) )
=> ( ( aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
| aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_5,hypothesis,
! [X401] :
( ( ~ aElementOf0(X401,sdtlpdtrp0(xN,xi))
| aElementOf0(X401,xS) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),xS) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4037])])]) ).
fof(c_0_6,hypothesis,
! [X396,X397,X398] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X396,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X396) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X397)
| ~ aElementOf0(X397,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X397,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X397,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X397 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X397,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElement0(X397)
| ~ aElementOf0(X397,sdtlpdtrp0(xN,xi))
| X397 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X397,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSet0(xQ)
& ( ~ aElementOf0(X398,xQ)
| aElementOf0(X398,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aSubsetOf0(xQ,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),xk)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__3989_02])])])]) ).
fof(c_0_7,hypothesis,
! [X399,X400] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X399,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X399) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X400)
| ~ aElementOf0(X400,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X400,xQ)
| X400 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X400,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X400,xQ)
| ~ aElement0(X400)
| aElementOf0(X400,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X400 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X400)
| aElementOf0(X400,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4007])])])]) ).
fof(c_0_8,negated_conjecture,
! [X402,X403] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X402,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X402) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X403)
| ~ aElementOf0(X403,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X403,xQ)
| X403 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X403,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X403,xQ)
| ~ aElement0(X403)
| aElementOf0(X403,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X403 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X403)
| aElementOf0(X403,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ~ aElementOf0(esk33_0,xS)
& ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
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_4])])])])]) ).
cnf(c_0_9,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( aElementOf0(X1,xQ)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),xS),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = esk33_0
| aElementOf0(esk33_0,xQ) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
~ aElementOf0(esk33_0,xS),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,hypothesis,
aElementOf0(esk33_0,xQ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,hypothesis,
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,hypothesis,
aElementOf0(esk33_0,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,hypothesis,
aElementOf0(esk33_0,sdtlpdtrp0(xN,xi)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_20]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM583+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:49:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 4.05/3.35 % Version : CSE_E---1.7
% 4.05/3.35 % Problem : theBenchmark.p
% 4.05/3.35 % SZS status Theorem for theBenchmark.p
% 4.05/3.35 % SZS output start CNFRefutation
% See solution above
% 4.05/3.36 % Total time : 2.757s
%------------------------------------------------------------------------------