%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM584+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n013.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 04:57:55 PM UTC 2026
% Result : Theorem 2.53s 2.32s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 112 ( 20 equ)
% Maximal formula atoms : 22 ( 8 avg)
% Number of connectives : 132 ( 34 ~; 39 |; 44 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 18 !; 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) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',m__4007) ).
fof(m__4024,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)) ) ) )
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
=> aElementOf0(X1,xS) )
& aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4024) ).
fof(c_0_3,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) )
& sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK )
| aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_4,negated_conjecture,
! [X406,X407] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X406,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X406) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X407)
| ~ aElementOf0(X407,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X407,xQ)
| X407 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X407,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X407,xQ)
| ~ aElement0(X407)
| aElementOf0(X407,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X407 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X407)
| aElementOf0(X407,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK )
& ( ~ aElementOf0(esk33_0,xS)
| sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK )
& ( ~ aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS)
| sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK )
& ~ aElementOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),slbdtsldtrb0(xS,xK)) ),
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,hypothesis,
! [X401,X402] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X401,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X401) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X402)
| ~ aElementOf0(X402,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X402,xQ)
| X402 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X402,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X402,xQ)
| ~ aElement0(X402)
| aElementOf0(X402,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X402 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X402)
| aElementOf0(X402,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_6,hypothesis,
! [X403,X404,X405] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X403,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X403) )
& aSet0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& ( aElement0(X404)
| ~ aElementOf0(X404,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( aElementOf0(X404,xQ)
| X404 = szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X404,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X404,xQ)
| ~ aElement0(X404)
| aElementOf0(X404,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( X404 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElement0(X404)
| aElementOf0(X404,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& ( ~ aElementOf0(X405,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| aElementOf0(X405,xS) )
& aSubsetOf0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))),xS) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4024])])])]) ).
cnf(c_0_7,negated_conjecture,
( aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
| sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,hypothesis,
sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) = xK,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
( ~ aElementOf0(esk33_0,xS)
| sbrdtbr0(sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) != xK ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
aElementOf0(esk33_0,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8])]) ).
cnf(c_0_12,negated_conjecture,
~ aElementOf0(esk33_0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_8])]) ).
cnf(c_0_13,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM584+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.15/0.33 % Computer : n013.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 00:47:26 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.53/2.32 % Version : CSE_E---1.7
% 2.53/2.32 % Problem : theBenchmark.p
% 2.53/2.32 % SZS status Theorem for theBenchmark.p
% 2.53/2.32 % SZS output start CNFRefutation
% See solution above
% 2.53/2.33 % Total time : 1.773s
%------------------------------------------------------------------------------