%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM571+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:09:11 AM UTC 2026
% Result : Theorem 13.42s 3.74s
% Output : Refutation 13.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 14 unt; 0 typ; 3 def)
% Number of atoms : 260 ( 55 equ; 0 cnn)
% Maximal formula atoms : 58 ( 6 avg)
% Number of connectives : 1061 ( 87 ~; 78 |; 97 &; 768 @)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 36 ( 1 ^; 30 !; 2 ?; 36 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtmndt0_decl,type,
sdtmndt0: $i > $i > $i ).
thf(szNzAzT0_decl,type,
szNzAzT0: $i ).
thf(szmzizndt0_decl,type,
szmzizndt0: $i > $i ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(szszuzczcdt0_decl,type,
szszuzczcdt0: $i > $i ).
thf(aFunction0_decl,type,
aFunction0: $i > $o ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xN_decl,type,
xN: $i ).
thf(xi_decl,type,
xi: $i ).
thf(isCountable0_decl,type,
isCountable0: $i > $o ).
thf(sz00_decl,type,
sz00: $i ).
thf(xS_decl,type,
xS: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk43_decl,type,
sk43: $i ).
thf(sk48_decl,type,
sk48: $i > $o ).
thf(sk49_decl,type,
sk49: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( @+[A: $i] :
( ( ( A @ szszuzczcdt0 )
= xi )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( szNzAzT0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(68,axiom,
( ( xi != sz00 )
=> ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
& ? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xi )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3702_02) ).
thf(551,plain,
( ( xi != sz00 )
=> ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
& ? [A: $i] :
( ( ( A @ szszuzczcdt0 )
= xi )
& ( szNzAzT0 @ ( A @ aElementOf0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(552,plain,
! [A: $i] :
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( xi = sz00 ) )
& ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( xi = sz00 ) )
& ( ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
| ( xi = sz00 ) )
& ( ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
| ( xi = sz00 ) )
& ( ( ( sk43 @ szszuzczcdt0 )
= xi )
| ( xi = sz00 ) )
& ( ( szNzAzT0 @ ( sk43 @ aElementOf0 ) )
| ( xi = sz00 ) ) ),
inference(cnf,[status(esa)],[551]) ).
thf(556,plain,
( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( xi = sz00 ) ),
inference(cnfConj,[status(thm)],[552]) ).
thf(564,plain,
( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( sz00 = xi ) ),
inference(lifteq,[status(thm)],[556]) ).
thf(1,conjecture,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(87,plain,
~ ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( ! [A: $i] :
( ( xi @ ( xN @ sdtlpdtrp0 ) @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(88,plain,
( ( ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) )
& ( ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( sk1 @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) )
& ( ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( xi @ ( xN @ sdtlpdtrp0 ) @ ( sk1 @ aElementOf0 ) )
| ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(91,plain,
( ~ ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(cnfConj,[status(thm)],[88]) ).
thf(558,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( xi = sz00 ) ),
inference(cnfConj,[status(thm)],[552]) ).
thf(561,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( sz00 = xi ) ),
inference(lifteq,[status(thm)],[558]) ).
thf(82,axiom,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ) )
=> ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [B: $i] :
( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) )
<=> ( ( B
!= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
& ( B @ aElement0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ aSet0 )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( B @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
thf(639,plain,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ) )
=> ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [B: $i] :
( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
& ! [B: $i] :
( ( ( ( B
!= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
& ( B @ aElement0 ) )
=> ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) )
=> ( ( B
!= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
& ( B @ aElement0 ) ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ aSet0 )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( B @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(640,plain,
( ! [A: $i] :
( ( szNzAzT0 @ ( A @ aElementOf0 ) )
=> ( ( ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ( ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( szNzAzT0 @ ( B @ aElementOf0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ aSet0 ) ) ) )
=> ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
& ! [B: $i] :
( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
& ! [B: $i] :
( ( ( B
!= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
& ( B @ aElement0 ) )
=> ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) ) )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( B @ aElementOf0 ) )
=> ( ( B
!= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
& ( B @ aElement0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ aSet0 )
& ! [B: $i] :
( ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( B @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) ) )
& ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) ) ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
inference(miniscope,[status(thm)],[639]) ).
thf(641,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( E @ aElementOf0 ) )
| ~ ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ ( E @ aElementOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ szszuzczcdt0 @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( D @ aElementOf0 ) )
| ( D
= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ ( D @ aElementOf0 ) )
| ~ ( D @ aElement0 )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( C
!= ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ ( C @ aElementOf0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( C @ aElement0 )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ ( C @ aElementOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ sdtmndt0 ) @ aSet0 )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( B @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ sdtlseqdt0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ ( B @ aElementOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ ( xN @ sdtlpdtrp0 ) @ szmzizndt0 @ aElementOf0 ) )
| ~ ( A @ sk48 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ sk48 )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( A @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ sk48 )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ~ ( szNzAzT0 @ ( A @ sk49 @ aElementOf0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ sk48 )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
| ( A @ ( xN @ sdtlpdtrp0 ) @ ( A @ sk49 @ aElementOf0 ) )
| ~ ( A @ ( xN @ sdtlpdtrp0 ) @ aSet0 )
| ~ ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS )
& ( ( xN @ szDzozmdt0 )
= szNzAzT0 )
& ( xN @ aFunction0 ) ),
inference(cnf,[status(esa)],[640]) ).
thf(658,plain,
( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS ),
inference(cnfConj,[status(thm)],[641]) ).
thf(667,plain,
( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
= xS ),
inference(lifteq,[status(thm)],[658]) ).
thf(10,axiom,
( ( xS @ isCountable0 )
& ( szNzAzT0 @ ( xS @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xS @ aSet0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
thf(106,plain,
( ( xS @ isCountable0 )
& ( szNzAzT0 @ ( xS @ aSubsetOf0 ) )
& ! [A: $i] :
( ( xS @ ( A @ aElementOf0 ) )
=> ( szNzAzT0 @ ( A @ aElementOf0 ) ) )
& ( xS @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(107,plain,
! [A: $i] :
( ( xS @ isCountable0 )
& ( szNzAzT0 @ ( xS @ aSubsetOf0 ) )
& ( ( szNzAzT0 @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( xS @ aSet0 ) ),
inference(cnf,[status(esa)],[106]) ).
thf(110,plain,
szNzAzT0 @ ( xS @ aSubsetOf0 ),
inference(cnfConj,[status(thm)],[107]) ).
thf(111,plain,
xS @ isCountable0,
inference(cnfConj,[status(thm)],[107]) ).
thf(688,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
!= ( xS @ isCountable0 ) )
| ~ $true
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(paramod_ordered,[status(thm)],[111,91]) ).
thf(689,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0 )
!= ( xS @ isCountable0 ) )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(simp,[status(thm)],[688]) ).
thf(690,plain,
( ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS )
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(simp,[status(thm)],[689]) ).
thf(753,plain,
( ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
!= ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[110,690]) ).
thf(754,plain,
( ( ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) )
!= ( szNzAzT0 @ ( xS @ aSubsetOf0 ) ) )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS ) ),
inference(simp,[status(thm)],[753]) ).
thf(759,plain,
( ( szNzAzT0 != szNzAzT0 )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS )
| ( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS ) ),
inference(simp,[status(thm)],[754]) ).
thf(762,plain,
( ( xi @ ( xN @ sdtlpdtrp0 ) )
!= xS ),
inference(simp,[status(thm)],[759]) ).
thf(897,plain,
( ( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) ) )
| ( xS != xS ) ),
inference(paramod_ordered,[status(thm)],[667,762]) ).
thf(898,plain,
( ( sz00 @ ( xN @ sdtlpdtrp0 ) )
!= ( xi @ ( xN @ sdtlpdtrp0 ) ) ),
inference(simp,[status(thm)],[897]) ).
thf(911,plain,
( ( sz00 != xi )
| ( xN != xN ) ),
inference(simp,[status(thm)],[898]) ).
thf(923,plain,
sz00 != xi,
inference(simp,[status(thm)],[911]) ).
thf(1110,plain,
xi @ ( xN @ sdtlpdtrp0 ) @ isCountable0,
inference(simplifyReflect,[status(thm)],[561,923]) ).
thf(1115,plain,
( ~ $true
| ~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ) ),
inference(rewrite,[status(thm)],[91,1110]) ).
thf(1116,plain,
~ ( szNzAzT0 @ ( xi @ ( xN @ sdtlpdtrp0 ) @ aSubsetOf0 ) ),
inference(simp,[status(thm)],[1115]) ).
thf(1405,plain,
( $false
| ( sz00 = xi ) ),
inference(rewrite,[status(thm)],[564,1116]) ).
thf(1406,plain,
sz00 = xi,
inference(simp,[status(thm)],[1405]) ).
thf(1407,plain,
$false,
inference(simplifyReflect,[status(thm)],[1406,923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM571+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.41 % Computer : n003.cluster.edu
% 0.13/0.41 % Model : x86_64 x86_64
% 0.13/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.41 % Memory : 8046.5625MB
% 0.13/0.41 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 03:18:08 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.68/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.90/0.88 % [INFO] Parsing done (153ms).
% 0.90/0.89 % [INFO] Running in sequential loop mode.
% 1.76/1.10 % [INFO] eprover registered as external prover.
% 1.76/1.10 % [INFO] Scanning for conjecture ...
% 2.04/1.13 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.14 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.16 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.18 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.26/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 84 axioms. Running axiom selection ...
% 2.26/1.27 % [INFO] Axiom selection finished. Selected 84 axioms (removed 0 axioms).
% 2.26/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.32 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.33 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.34 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.58/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.58/1.36 % [INFO] Type checking passed.
% 2.58/1.36 % [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 ...
% 13.42/3.74 % [INFO] Killing All external provers ...
% 13.42/3.74 % Time passed: 3224ms (effective reasoning time: 2846ms)
% 13.42/3.74 % 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)>
% 13.42/3.74 % Axioms used in derivation (3): m__3702_02, m__3623, m__3435
% 13.42/3.74 % No. of inferences in proof: 40
% 13.42/3.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3224 ms resp. 2846 ms w/o parsing
% 13.96/3.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.96/3.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------