%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM588+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 : 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 04:57:56 PM UTC 2026
% Result : Theorem 2.79s 2.40s
% Output : CNFRefutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 4 unt; 0 def)
% Number of atoms : 116 ( 11 equ)
% Maximal formula atoms : 44 ( 12 avg)
% Number of connectives : 134 ( 27 ~; 22 |; 61 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 9 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& X3 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) )
& aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(X2) )
=> ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xk
& aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X4) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtlpdtrp0(xN,X1))
& X4 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
| aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X3) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,X1))
& X3 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) )
& aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
& aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& isCountable0(X2) )
=> ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xk
& aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
=> ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X1)),sdtlpdtrp0(xN,X1))
& ! [X4] :
( aElementOf0(X4,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X1)),X4) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
& ! [X4] :
( aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
<=> ( aElement0(X4)
& aElementOf0(X4,sdtlpdtrp0(xN,X1))
& X4 != szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1)))) )
| aSubsetOf0(X3,sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))))
| aElementOf0(X3,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X1),szmzizndt0(sdtlpdtrp0(xN,X1))),xk)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_2,negated_conjecture,
! [X431,X432,X433,X435,X436,X437] :
( aElementOf0(esk34_0,szNzAzT0)
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),sdtlpdtrp0(xN,esk34_0))
& ( ~ aElementOf0(X431,sdtlpdtrp0(xN,esk34_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),X431) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
& ( aElement0(X432)
| ~ aElementOf0(X432,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& ( aElementOf0(X432,sdtlpdtrp0(xN,esk34_0))
| ~ aElementOf0(X432,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& ( X432 != szmzizndt0(sdtlpdtrp0(xN,esk34_0))
| ~ aElementOf0(X432,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& ( ~ aElement0(X432)
| ~ aElementOf0(X432,sdtlpdtrp0(xN,esk34_0))
| X432 = szmzizndt0(sdtlpdtrp0(xN,esk34_0))
| aElementOf0(X432,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& aSet0(esk35_0)
& ( ~ aElementOf0(X433,esk35_0)
| aElementOf0(X433,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& aSubsetOf0(esk35_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
& isCountable0(esk35_0)
& aSet0(esk36_0)
& ( ~ aElementOf0(X435,esk36_0)
| aElementOf0(X435,esk35_0) )
& aSubsetOf0(esk36_0,esk35_0)
& sbrdtbr0(esk36_0) = xk
& aElementOf0(esk36_0,slbdtsldtrb0(esk35_0,xk))
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),sdtlpdtrp0(xN,esk34_0))
& ( ~ aElementOf0(X436,sdtlpdtrp0(xN,esk34_0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,esk34_0)),X436) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
& ( aElement0(X437)
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& ( aElementOf0(X437,sdtlpdtrp0(xN,esk34_0))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& ( X437 != szmzizndt0(sdtlpdtrp0(xN,esk34_0))
| ~ aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& ( ~ aElement0(X437)
| ~ aElementOf0(X437,sdtlpdtrp0(xN,esk34_0))
| X437 = szmzizndt0(sdtlpdtrp0(xN,esk34_0))
| aElementOf0(X437,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))) )
& aElementOf0(esk37_0,esk36_0)
& ~ aElementOf0(esk37_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
& ~ aSubsetOf0(esk36_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
& ~ aElementOf0(esk36_0,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))),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_1])])])])]) ).
cnf(c_0_3,negated_conjecture,
( aElementOf0(X1,esk35_0)
| ~ aElementOf0(X1,esk36_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
aElementOf0(esk37_0,esk36_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
( aElementOf0(X1,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0))))
| ~ aElementOf0(X1,esk35_0) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
aElementOf0(esk37_0,esk35_0),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_7,negated_conjecture,
~ aElementOf0(esk37_0,sdtmndt0(sdtlpdtrp0(xN,esk34_0),szmzizndt0(sdtlpdtrp0(xN,esk34_0)))),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_8,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM588+3 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % 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
% 0.17/0.33 % Computer : n007.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 00:46:24 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 2.79/2.40 % Version : CSE_E---1.7
% 2.79/2.40 % Problem : theBenchmark.p
% 2.79/2.40 % SZS status Theorem for theBenchmark.p
% 2.79/2.40 % SZS output start CNFRefutation
% See solution above
% 2.79/2.40 % Total time : 1.769s
%------------------------------------------------------------------------------