TSTP Solution File: SEU516^1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU516^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 21 03:42:25 EDT 2024
% Result : Theorem 5.50s 2.26s
% Output : Refutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 75
% Syntax : Number of formulae : 95 ( 41 unt; 42 typ; 32 def)
% Number of atoms : 470 ( 102 equ; 0 cnn)
% Maximal formula atoms : 86 ( 8 avg)
% Number of connectives : 1075 ( 39 ~; 32 |; 55 &; 672 @)
% ( 0 <=>; 277 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 43 con; 0-2 aty)
% Number of variables : 325 ( 2 ^ 267 !; 56 ?; 325 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(setextAx_type,type,
setextAx: $o ).
thf(setextAx_def,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
= ( in @ C @ B ) )
=> ( A = B ) ) ) ) ).
thf(emptyset_type,type,
emptyset: $i ).
thf(emptysetAx_type,type,
emptysetAx: $o ).
thf(emptysetAx_def,definition,
( emptysetAx
= ( ! [A: $i] :
~ ( in @ A @ emptyset ) ) ) ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setadjoinAx_type,type,
setadjoinAx: $o ).
thf(setadjoinAx_def,definition,
( setadjoinAx
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
= ( ( C = A )
| ( in @ C @ B ) ) ) ) ) ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(powersetAx_type,type,
powersetAx: $o ).
thf(powersetAx_def,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
= ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ) ) ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(setunionAx_type,type,
setunionAx: $o ).
thf(setunionAx_def,definition,
( setunionAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
= ( ? [C: $i] :
( ( in @ B @ C )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(omega_type,type,
omega: $i ).
thf(omega0Ax_type,type,
omega0Ax: $o ).
thf(omega0Ax_def,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ) ).
thf(omegaSAx_type,type,
omegaSAx: $o ).
thf(omegaSAx_def,definition,
( omegaSAx
= ( ! [A: $i] :
( ( in @ A @ omega )
=> ( in @ ( setadjoin @ A @ A ) @ omega ) ) ) ) ).
thf(omegaIndAx_type,type,
omegaIndAx: $o ).
thf(omegaIndAx_def,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [B: $i] :
( ( ( in @ B @ omega )
& ( in @ B @ A ) )
=> ( in @ ( setadjoin @ B @ B ) @ A ) ) )
=> ! [B: $i] :
( ( in @ B @ omega )
=> ( in @ B @ A ) ) ) ) ) ).
thf(replAx_type,type,
replAx: $o ).
thf(replAx_def,definition,
( replAx
= ( ! [A: $i > $i > $o,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( exu @ ( A @ C ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ B )
& ( A @ E @ D ) ) ) ) ) ) ) ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(foundationAx_def,definition,
( foundationAx
= ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(wellorderingAx_type,type,
wellorderingAx: $o ).
thf(wellorderingAx_def,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ C @ E )
= ( in @ D @ E ) ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ C )
=> ( in @ E @ D ) )
| ! [E: $i] :
( ( in @ E @ D )
=> ( in @ E @ C ) ) ) )
& ! [C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) )
& ? [D: $i] : ( in @ D @ C ) )
=> ? [D: $i,E: $i] :
( ( in @ D @ B )
& ( in @ E @ C )
& ~ ? [F: $i] :
( ( in @ F @ D )
& ( in @ F @ C ) )
& ! [F: $i] :
( ( in @ F @ B )
=> ( ! [G: $i] :
( ( in @ G @ F )
=> ( in @ G @ D ) )
| ( in @ E @ F ) ) ) ) ) ) ) ) ).
thf(descrp_type,type,
descrp: $o ).
thf(descrp_def,definition,
( descrp
= ( ! [A: $i > $o] :
( ( exu @ A )
=> ( A @ ( descr @ A ) ) ) ) ) ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(dsetconstrEL_def,definition,
( dsetconstrEL
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(exuE1_type,type,
exuE1: $o ).
thf(exuE1_def,definition,
( exuE1
= ( ! [A: $i > $o] :
( ( exu @ A )
=> ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) ) ) ) ) ).
thf(prop2setE_type,type,
prop2setE: $o ).
thf(prop2setE_def,definition,
( prop2setE
= ( ! [A: $o,B: $i] :
( ( in @ B @ ( prop2set @ A ) )
=> A ) ) ) ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(emptysetimpfalse_type,type,
emptysetimpfalse: $o ).
thf(emptysetimpfalse_def,definition,
( emptysetimpfalse
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> $false ) ) ) ).
thf(notinemptyset_type,type,
notinemptyset: $o ).
thf(notinemptyset_def,definition,
( notinemptyset
= ( ! [A: $i] :
~ ( in @ A @ emptyset ) ) ) ).
thf(exuE3e_type,type,
exuE3e: $o ).
thf(exuE3e_def,definition,
( exuE3e
= ( ! [A: $i > $o] :
( ( exu @ A )
=> ? [B: $i] : ( A @ B ) ) ) ) ).
thf(setext_type,type,
setext: $o ).
thf(setext_def,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) ) ) ) ).
thf(emptyI_type,type,
emptyI: $o ).
thf(emptyI_def,definition,
( emptyI
= ( ! [A: $i] :
( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = emptyset ) ) ) ) ).
thf(noeltsimpempty_type,type,
noeltsimpempty: $o ).
thf(noeltsimpempty_def,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = emptyset ) ) ) ) ).
thf(setbeta_type,type,
setbeta: $o ).
thf(setbeta_def,definition,
( setbeta
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( dsetconstr @ A @ B ) )
= ( B @ C ) ) ) ) ) ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(nonemptyE1_def,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] : ( in @ B @ A ) ) ) ) ).
thf(nonemptyI_type,type,
nonemptyI: $o ).
thf(nonemptyI_def,definition,
( nonemptyI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( nonempty @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(nonemptyI1_type,type,
nonemptyI1: $o ).
thf(nonemptyI1_def,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( nonempty @ A ) ) ) ) ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(setadjoinIL_def,definition,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).
thf(emptyinunitempty_type,type,
emptyinunitempty: $o ).
thf(emptyinunitempty_def,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
thf(setadjoinIR_type,type,
setadjoinIR: $o ).
thf(setadjoinIR_def,definition,
( setadjoinIR
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ B )
=> ( in @ C @ ( setadjoin @ A @ B ) ) ) ) ) ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(setadjoinE_def,definition,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ).
thf(sk21_type,type,
sk21: $i ).
thf(sk22_type,type,
sk22: $i ).
thf(sk23_type,type,
sk23: $i ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ( ( C = A )
| ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(2,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ( ( C = A )
| ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
= ( in @ C @ B ) )
=> ( A = B ) )
=> ( ! [A: $i] :
~ ( in @ A @ emptyset )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
= ( ( C = A )
| ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
= ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
= ( ? [C: $i] :
( ( in @ B @ C )
& ( in @ C @ A ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [A: $i] :
( ( in @ A @ omega )
=> ( in @ ( setadjoin @ A @ A ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [B: $i] :
( ( ( in @ B @ omega )
& ( in @ B @ A ) )
=> ( in @ ( setadjoin @ B @ B ) @ A ) ) )
=> ! [B: $i] :
( ( in @ B @ omega )
=> ( in @ B @ A ) ) )
=> ( ! [A: $i > $i > $o,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( A @ C @ D )
& ! [E: $i] :
( ( A @ C @ E )
=> ( D = E ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ B )
& ( A @ E @ D ) ) ) ) )
=> ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ C @ E )
= ( in @ D @ E ) ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ C )
=> ( in @ E @ D ) )
| ! [E: $i] :
( ( in @ E @ D )
=> ( in @ E @ C ) ) ) )
& ! [C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) )
& ? [D: $i] : ( in @ D @ C ) )
=> ? [D: $i,E: $i] :
( ( in @ D @ B )
& ( in @ E @ C )
& ~ ? [F: $i] :
( ( in @ F @ D )
& ( in @ F @ C ) )
& ! [F: $i] :
( ( in @ F @ B )
=> ( ! [G: $i] :
( ( in @ G @ F )
=> ( in @ G @ D ) )
| ( in @ E @ F ) ) ) ) ) )
=> ( ! [A: $i > $o] :
( ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) )
=> ( A @ ( descr @ A ) ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $o,B: $i] :
( ( in @ B
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [C: $i] : A ) )
=> A )
=> ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i] :
~ ( in @ A @ emptyset )
=> ( ! [A: $i] :
~ ( in @ A @ emptyset )
=> ( ! [A: $i > $o] :
( ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) )
=> ? [B: $i] : ( A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( dsetconstr @ A @ B ) )
= ( B @ C ) ) )
=> ( ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ( dsetconstr @ A @ B )
!= emptyset ) ) )
=> ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) )
=> ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ B )
=> ( in @ C @ ( setadjoin @ A @ B ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ( ( C = A )
| ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
= ( in @ C @ B ) )
=> ( A = B ) )
=> ( ~ ? [A: $i] : ( in @ A @ emptyset )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
= ( ( C = A )
| ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
= ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
= ( ? [C: $i] :
( ( in @ B @ C )
& ( in @ C @ A ) ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [A: $i] :
( ( in @ A @ omega )
=> ( in @ ( setadjoin @ A @ A ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [B: $i] :
( ( ( in @ B @ omega )
& ( in @ B @ A ) )
=> ( in @ ( setadjoin @ B @ B ) @ A ) ) )
=> ! [B: $i] :
( ( in @ B @ omega )
=> ( in @ B @ A ) ) )
=> ( ! [A: $i > $i > $o,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( A @ C @ D )
& ! [E: $i] :
( ( A @ C @ E )
=> ( D = E ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ B )
& ( A @ E @ D ) ) ) ) )
=> ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ A )
& ( in @ D @ A ) )
=> ( ! [E: $i] :
( ( in @ E @ B )
=> ( ( in @ C @ E )
= ( in @ D @ E ) ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [E: $i] :
( ( in @ E @ C )
=> ( in @ E @ D ) )
| ! [E: $i] :
( ( in @ E @ D )
=> ( in @ E @ C ) ) ) )
& ! [C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( in @ D @ A ) )
& ? [D: $i] : ( in @ D @ C ) )
=> ? [D: $i] :
( ( in @ D @ B )
& ? [E: $i] :
( ( in @ E @ C )
& ~ ? [F: $i] :
( ( in @ F @ D )
& ( in @ F @ C ) )
& ! [F: $i] :
( ( in @ F @ B )
=> ( ! [G: $i] :
( ( in @ G @ F )
=> ( in @ G @ D ) )
| ( in @ E @ F ) ) ) ) ) ) )
=> ( ! [A: $i > $o] :
( ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) )
=> ( A @ ( descr @ A ) ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $o] :
( ? [B: $i] :
( in @ B
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [C: $i] : A ) )
=> A )
=> ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ~ ? [A: $i] : ( in @ A @ emptyset )
=> ( ~ ? [A: $i] : ( in @ A @ emptyset )
=> ( ! [A: $i > $o] :
( ? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) )
=> ? [B: $i] : ( A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ~ ? [B: $i] : ( in @ B @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ~ ? [B: $i] : ( in @ B @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( in @ C @ ( dsetconstr @ A @ B ) )
= ( B @ C ) ) )
=> ( ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ( dsetconstr @ A @ B )
!= emptyset ) ) )
=> ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) )
=> ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ B )
=> ( in @ C @ ( setadjoin @ A @ B ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ( ( C = A )
| ( in @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(25,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(cnf,[status(esa)],[4]) ).
thf(70,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[25]) ).
thf(51,plain,
in @ sk23 @ ( setadjoin @ sk21 @ sk22 ),
inference(cnf,[status(esa)],[4]) ).
thf(5,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( C = A )
| ( in @ C @ B )
| D ),
inference(cnf,[status(esa)],[4]) ).
thf(61,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( in @ C @ B )
| D ),
inference(lifteq,[status(thm)],[5]) ).
thf(62,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( in @ C @ B )
| D ),
inference(simp,[status(thm)],[61]) ).
thf(248,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ( in @ C @ B )
| D
| ( ( in @ sk23 @ ( setadjoin @ sk21 @ sk22 ) )
!= ( in @ C @ ( setadjoin @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,62]) ).
thf(249,plain,
! [A: $o] :
( ( sk23 = sk21 )
| ( in @ sk23 @ sk22 )
| A ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( sk21 )),bind(B,$thf( sk22 )),bind(C,$thf( sk23 ))]]) ).
thf(311,plain,
! [A: $o] :
( ( sk23 = sk21 )
| ( in @ sk23 @ sk22 )
| A ),
inference(simp,[status(thm)],[249]) ).
thf(42,plain,
~ ( in @ sk23 @ sk22 ),
inference(cnf,[status(esa)],[4]) ).
thf(374,plain,
! [A: $o] :
( ( sk23 = sk21 )
| $false
| A ),
inference(rewrite,[status(thm)],[311,42]) ).
thf(375,plain,
! [A: $o] :
( ( sk23 = sk21 )
| A ),
inference(simp,[status(thm)],[374]) ).
thf(17,plain,
sk23 != sk21,
inference(cnf,[status(esa)],[4]) ).
thf(96,plain,
sk23 != sk21,
inference(lifteq,[status(thm)],[17]) ).
thf(376,plain,
! [A: $o] : A,
inference(simplifyReflect,[status(thm)],[375,96]) ).
thf(379,plain,
~ $true,
inference(rewrite,[status(thm)],[70,376]) ).
thf(380,plain,
$false,
inference(simp,[status(thm)],[379]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU516^1 : TPTP v8.2.0. Released v3.7.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 15:48:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.92/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.02 % [INFO] Parsing done (151ms).
% 1.27/1.02 % [INFO] Running in sequential loop mode.
% 1.80/1.22 % [INFO] nitpick registered as external prover.
% 1.80/1.23 % [INFO] Scanning for conjecture ...
% 2.31/1.36 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.31/1.39 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.31/1.39 % [INFO] Problem is higher-order (TPTP THF).
% 2.31/1.39 % [INFO] Type checking passed.
% 2.31/1.40 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.50/2.25 % [INFO] Killing All external provers ...
% 5.50/2.25 % Time passed: 1723ms (effective reasoning time: 1225ms)
% 5.50/2.26 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.50/2.26 % Axioms used in derivation (0):
% 5.50/2.26 % No. of inferences in proof: 21
% 5.50/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1723 ms resp. 1225 ms w/o parsing
% 5.50/2.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.50/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------