%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM592+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 : n021.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 04:57:57 PM UTC 2026
% Result : Theorem 50.86s 29.04s
% Output : CNFRefutation 50.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 7 unt; 0 def)
% Number of atoms : 477 ( 65 equ)
% Maximal formula atoms : 304 ( 15 avg)
% Number of connectives : 639 ( 192 ~; 295 |; 124 &)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__4448_02,hypothesis,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
& aSet0(xY)
& ! [X1] :
( aElementOf0(X1,xY)
<=> ( aElement0(X1)
& aElementOf0(X1,sdtlpdtrp0(xN,xi))
& X1 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
fof(m__4545,hypothesis,
( aElementOf0(xu,xT)
& aSet0(xX)
& ! [X1] :
( aElementOf0(X1,xX)
=> aElementOf0(X1,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [X1] :
( ( aSet0(X1)
& ( ( ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,xX) )
| aSubsetOf0(X1,xX) )
& sbrdtbr0(X1) = xk )
| aElementOf0(X1,slbdtsldtrb0(xX,xk)) ) )
=> sdtlpdtrp0(xd,X1) = xu ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4545) ).
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,xT)
& ? [X2] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X3) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& X3 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X2)
& ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xk
& aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X3) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(c_0_3,plain,
! [X1] :
( epred4_1(X1)
<=> ? [X2] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X3) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& X3 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X2)
& ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xk
& aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X3) = X1 ) ) ),
introduced(definition) ).
fof(c_0_4,plain,
! [X1] :
( ? [X2] :
( ( ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,xi))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X3) ) )
=> ( ( aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& ! [X3] :
( aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> ( aElement0(X3)
& aElementOf0(X3,sdtlpdtrp0(xN,xi))
& X3 != szmzizndt0(sdtlpdtrp0(xN,xi)) ) ) )
=> ( ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) )
| aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ) )
& isCountable0(X2)
& ! [X3] :
( ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
=> aElementOf0(X4,X2) )
& aSubsetOf0(X3,X2)
& sbrdtbr0(X3) = xk
& aElementOf0(X3,slbdtsldtrb0(X2,xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,xi),X3) = X1 ) )
=> epred4_1(X1) ),
inference(split_equiv,[status(thm)],[c_0_3]) ).
fof(c_0_5,plain,
! [X503,X504,X505,X506,X507,X510] :
( ( aSet0(esk43_2(X503,X504))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| ~ aElementOf0(X505,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X505)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| ~ aElementOf0(X505,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X505)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| ~ aElementOf0(X505,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X505)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| ~ aElementOf0(X505,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X505)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| ~ aElementOf0(X505,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X505)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| ~ aElementOf0(X505,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X505)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| aSet0(sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| aElement0(X506)
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| aElement0(X506)
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| aElement0(X506)
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| aElement0(X506)
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| aElement0(X506)
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| aElement0(X506)
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| aElementOf0(X506,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| aElementOf0(X506,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| aElementOf0(X506,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| aElementOf0(X506,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| aElementOf0(X506,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| aElementOf0(X506,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| X506 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| X506 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| X506 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| X506 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| X506 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| X506 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X506,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| ~ aElement0(X507)
| ~ aElementOf0(X507,sdtlpdtrp0(xN,xi))
| X507 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X507,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| ~ aElement0(X507)
| ~ aElementOf0(X507,sdtlpdtrp0(xN,xi))
| X507 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X507,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| ~ aElement0(X507)
| ~ aElementOf0(X507,sdtlpdtrp0(xN,xi))
| X507 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X507,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| ~ aElement0(X507)
| ~ aElementOf0(X507,sdtlpdtrp0(xN,xi))
| X507 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X507,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| ~ aElement0(X507)
| ~ aElementOf0(X507,sdtlpdtrp0(xN,xi))
| X507 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X507,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| ~ aElement0(X507)
| ~ aElementOf0(X507,sdtlpdtrp0(xN,xi))
| X507 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X507,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| aElementOf0(esk42_2(X503,X504),X504)
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| aElementOf0(esk42_2(X503,X504),X504)
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| aElementOf0(esk42_2(X503,X504),X504)
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| aElementOf0(esk42_2(X503,X504),X504)
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| aElementOf0(esk42_2(X503,X504),X504)
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| aElementOf0(esk42_2(X503,X504),X504)
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| ~ aElementOf0(esk42_2(X503,X504),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| ~ aElementOf0(esk42_2(X503,X504),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| ~ aElementOf0(esk42_2(X503,X504),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| ~ aElementOf0(esk42_2(X503,X504),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| ~ aElementOf0(esk42_2(X503,X504),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| ~ aElementOf0(esk42_2(X503,X504),sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ aSet0(X504)
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSet0(esk43_2(X503,X504))
| ~ aSubsetOf0(X504,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( ~ aElementOf0(X510,esk43_2(X503,X504))
| aElementOf0(X510,X504)
| ~ aSubsetOf0(X504,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aSubsetOf0(esk43_2(X503,X504),X504)
| ~ aSubsetOf0(X504,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sbrdtbr0(esk43_2(X503,X504)) = xk
| ~ aSubsetOf0(X504,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( aElementOf0(esk43_2(X503,X504),slbdtsldtrb0(X504,xk))
| ~ aSubsetOf0(X504,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) )
& ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X503,X504)) != X503
| ~ aSubsetOf0(X504,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X504)
| epred4_1(X503) ) ),
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)],[c_0_4])])])])])]) ).
fof(c_0_6,hypothesis,
! [X449,X450] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi))
& ( ~ aElementOf0(X449,sdtlpdtrp0(xN,xi))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X449) )
& aSet0(xY)
& ( aElement0(X450)
| ~ aElementOf0(X450,xY) )
& ( aElementOf0(X450,sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X450,xY) )
& ( X450 != szmzizndt0(sdtlpdtrp0(xN,xi))
| ~ aElementOf0(X450,xY) )
& ( ~ aElement0(X450)
| ~ aElementOf0(X450,sdtlpdtrp0(xN,xi))
| X450 = szmzizndt0(sdtlpdtrp0(xN,xi))
| aElementOf0(X450,xY) )
& xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
& xd = sdtlpdtrp0(xC,xi) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4448_02])])])]) ).
cnf(c_0_7,plain,
( aElementOf0(esk43_2(X1,X2),slbdtsldtrb0(X2,xk))
| epred4_1(X1)
| ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,hypothesis,
! [X461,X462] :
( aElementOf0(xu,xT)
& aSet0(xX)
& ( ~ aElementOf0(X461,xX)
| aElementOf0(X461,xY) )
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ( aElementOf0(esk36_1(X462),X462)
| sbrdtbr0(X462) != xk
| ~ aSet0(X462)
| sdtlpdtrp0(xd,X462) = xu )
& ( ~ aElementOf0(esk36_1(X462),xX)
| sbrdtbr0(X462) != xk
| ~ aSet0(X462)
| sdtlpdtrp0(xd,X462) = xu )
& ( ~ aSubsetOf0(X462,xX)
| sbrdtbr0(X462) != xk
| ~ aSet0(X462)
| sdtlpdtrp0(xd,X462) = xu )
& ( ~ aElementOf0(X462,slbdtsldtrb0(xX,xk))
| ~ aSet0(X462)
| sdtlpdtrp0(xd,X462) = xu ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4545])])])])]) ).
cnf(c_0_10,plain,
( aSet0(esk43_2(X1,X2))
| epred4_1(X1)
| ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( epred4_1(X1)
| sdtlpdtrp0(sdtlpdtrp0(xC,xi),esk43_2(X1,X2)) != X1
| ~ aSubsetOf0(X2,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,hypothesis,
xd = sdtlpdtrp0(xC,xi),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( epred4_1(X1)
| aElementOf0(esk43_2(X1,X2),slbdtsldtrb0(X2,xk))
| ~ aSubsetOf0(X2,xY)
| ~ isCountable0(X2) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,hypothesis,
aSubsetOf0(xX,xY),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
isCountable0(xX),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( epred4_1(X1)
| aSet0(esk43_2(X1,X2))
| ~ aSubsetOf0(X2,xY)
| ~ isCountable0(X2) ),
inference(rw,[status(thm)],[c_0_10,c_0_8]) ).
fof(c_0_17,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,xT)
& epred4_1(X1) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[m__]),c_0_3]) ).
cnf(c_0_18,plain,
( epred4_1(X1)
| sdtlpdtrp0(xd,esk43_2(X1,X2)) != X1
| ~ aSubsetOf0(X2,xY)
| ~ isCountable0(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_8]) ).
cnf(c_0_19,hypothesis,
( sdtlpdtrp0(xd,X1) = xu
| ~ aElementOf0(X1,slbdtsldtrb0(xX,xk))
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,hypothesis,
( epred4_1(X1)
| aElementOf0(esk43_2(X1,xX),slbdtsldtrb0(xX,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_21,hypothesis,
( epred4_1(X1)
| aSet0(esk43_2(X1,xX)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15])]) ).
fof(c_0_22,negated_conjecture,
! [X464] :
( ~ aElementOf0(X464,xT)
| ~ epred4_1(X464) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
cnf(c_0_23,hypothesis,
( epred4_1(X1)
| sdtlpdtrp0(xd,esk43_2(X1,xX)) != X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_14]),c_0_15])]) ).
cnf(c_0_24,hypothesis,
( sdtlpdtrp0(xd,esk43_2(X1,xX)) = xu
| epred4_1(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ aElementOf0(X1,xT)
| ~ epred4_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,hypothesis,
aElementOf0(xu,xT),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,hypothesis,
( epred4_1(X1)
| xu != X1 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
~ epred4_1(xu),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_27]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM592+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
% 0.16/0.32 % Computer : n021.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 00:48:55 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 50.86/29.04 % Version : CSE_E---1.7
% 50.86/29.04 % Problem : theBenchmark.p
% 50.86/29.04 % SZS status Theorem for theBenchmark.p
% 50.86/29.04 % SZS output start CNFRefutation
% See solution above
% 50.96/29.17 % Total time : 23.820s
%------------------------------------------------------------------------------