%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM450+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:08:52 AM UTC 2026
% Result : Theorem 111.79s 57.62s
% Output : Refutation 112.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 19 unt; 0 typ; 10 def)
% Number of atoms : 744 ( 122 equ; 0 cnn)
% Maximal formula atoms : 116 ( 13 avg)
% Number of connectives : 2831 ( 209 ~; 215 |; 344 &;1961 @)
% ( 11 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 6 con; 0-3 aty)
% Number of variables : 211 ( 14 ^; 132 !; 55 ?; 211 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aInteger0_decl,type,
aInteger0: $i > $o ).
thf(aDivisorOf0_decl,type,
aDivisorOf0: $i > $i > $o ).
thf(sz00_decl,type,
sz00: $i ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(sdteqdtlpzmzozddtrp0_decl,type,
sdteqdtlpzmzozddtrp0: $i > $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(smndt0_decl,type,
smndt0: $i > $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sbsmnsldt0_decl,type,
sbsmnsldt0: $i > $i ).
thf(stldt0_decl,type,
stldt0: $i > $i ).
thf(szAzrzSzezqlpdtcmdtrp0_decl,type,
szAzrzSzezqlpdtcmdtrp0: $i > $i > $i ).
thf(isOpen0_decl,type,
isOpen0: $i > $o ).
thf(isClosed0_decl,type,
isClosed0: $i > $o ).
thf(sz10_decl,type,
sz10: $i ).
thf(xS_decl,type,
xS: $i ).
thf(cS2076_decl,type,
cS2076: $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( B @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( A @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( B @ sk6 @ sdtasdt0 ) )
= ( B @ smndt0 @ ( A @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( ( C @ ( B @ sk9 @ sdtasdt0 ) )
= ( B @ smndt0 @ ( A @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(28,axiom,
( ( ( xS @ sbsmnsldt0 @ stldt0 )
= cS2076 )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
<=> ( ( A
= ( sz10 @ smndt0 ) )
| ( A = sz10 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
<=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ stldt0 @ aSet0 )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
<=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2079) ).
thf(338,plain,
( ( ( xS @ sbsmnsldt0 @ stldt0 )
= cS2076 )
& ! [A: $i] :
( ( ( ( A
= ( sz10 @ smndt0 ) )
| ( A = sz10 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ( A
= ( sz10 @ smndt0 ) )
| ( A = sz10 ) ) ) )
& ! [A: $i] :
( ( ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) ) )
& ( xS @ sbsmnsldt0 @ stldt0 @ aSet0 )
& ! [A: $i] :
( ( ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(339,plain,
( ( ( xS @ sbsmnsldt0 @ stldt0 )
= cS2076 )
& ! [A: $i] :
( ( ( A
= ( sz10 @ smndt0 ) )
| ( A = sz10 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ( A
= ( sz10 @ smndt0 ) )
| ( A = sz10 ) ) )
& ! [A: $i] :
( ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ stldt0 @ aSet0 )
& ! [A: $i] :
( ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
inference(miniscope,[status(thm)],[338]) ).
thf(340,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( xS @ sbsmnsldt0 @ stldt0 )
= cS2076 )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( G @ aElementOf0 ) )
| ( G
!= ( sz10 @ smndt0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( G @ aElementOf0 ) )
| ( G != sz10 ) )
& ( ( F
= ( sz10 @ smndt0 ) )
| ( F = sz10 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( E @ aElementOf0 ) )
| ( xS @ sbsmnsldt0 @ ( E @ aElementOf0 ) )
| ~ ( E @ aInteger0 ) )
& ( ~ ( xS @ sbsmnsldt0 @ ( D @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( D @ aElementOf0 ) ) )
& ( ( D @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( D @ aElementOf0 ) ) )
& ( xS @ sbsmnsldt0 @ stldt0 @ aSet0 )
& ( ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
| ~ ( C @ ( B @ aElementOf0 ) )
| ~ ( xS @ ( C @ aElementOf0 ) )
| ~ ( B @ aInteger0 ) )
& ( ( A @ sk17 @ ( A @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ ( A @ sk17 @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
inference(cnf,[status(esa)],[339]) ).
thf(346,plain,
! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
| ( A != sz10 ) ),
inference(cnfConj,[status(thm)],[340]) ).
thf(359,plain,
! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
| ( A != sz10 ) ),
inference(lifteq,[status(thm)],[346]) ).
thf(360,plain,
xS @ sbsmnsldt0 @ stldt0 @ ( sz10 @ aElementOf0 ),
inference(simp,[status(thm)],[359]) ).
thf(344,plain,
( ( xS @ sbsmnsldt0 @ stldt0 )
= cS2076 ),
inference(cnfConj,[status(thm)],[340]) ).
thf(354,plain,
( ( xS @ sbsmnsldt0 @ stldt0 )
= cS2076 ),
inference(lifteq,[status(thm)],[344]) ).
thf(975,plain,
cS2076 @ ( sz10 @ aElementOf0 ),
inference(rewrite,[status(thm)],[360,354]) ).
thf(11,axiom,
( ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
<=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
<=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 )
& ( xS @ sbsmnsldt0 @ isClosed0 )
& ( xS @ sbsmnsldt0 @ stldt0 @ isOpen0 )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
<=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
<=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
thf(130,plain,
( ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) )
& ! [A: $i] :
( ( ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) ) )
& ! [A: $i] :
( ( ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 )
& ( xS @ sbsmnsldt0 @ isClosed0 )
& ( xS @ sbsmnsldt0 @ stldt0 @ isOpen0 )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) )
& ! [A: $i] :
( ( ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) ) )
& ! [A: $i] :
( ( ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(131,plain,
( ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) )
& ! [A: $i] :
( ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) )
& ! [A: $i] :
( ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 )
& ( xS @ sbsmnsldt0 @ isClosed0 )
& ( xS @ sbsmnsldt0 @ stldt0 @ isOpen0 )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
| ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) ) )
& ( C @ aInteger0 ) )
=> ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) ) )
& ! [C: $i] :
( ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
=> ( ( B @ ( A @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
& ( A @ smndt0 @ ( C @ sdtpldt0 ) @ ( B @ aDivisorOf0 ) )
& ? [D: $i] :
( ( ( D @ ( B @ sdtasdt0 ) )
= ( A @ smndt0 @ ( C @ sdtpldt0 ) ) )
& ( D @ aInteger0 ) )
& ( C @ aInteger0 ) ) )
& ( B @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
& ( B != sz00 )
& ( B @ aInteger0 ) ) )
& ! [A: $i] :
( ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
& ( A @ aInteger0 ) ) )
& ! [A: $i] :
( ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) )
=> ( ? [B: $i] :
( ( B @ ( A @ aElementOf0 ) )
& ( xS @ ( B @ aElementOf0 ) ) )
& ( A @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
inference(miniscope,[status(thm)],[130]) ).
thf(132,plain,
! [T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( T @ aElementOf0 ) )
| ~ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( T @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( R @ aElementOf0 ) )
| ~ ( P @ sk9 @ ( P @ ( R @ sdteqdtlpzmzozddtrp0 ) ) )
| ~ ( R @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( R @ aElementOf0 ) )
| ~ ( P @ smndt0 @ ( R @ sdtpldt0 ) @ ( P @ sk9 @ aDivisorOf0 ) )
| ~ ( R @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( R @ aElementOf0 ) )
| ( ( S @ ( P @ sk9 @ sdtasdt0 ) )
!= ( P @ smndt0 @ ( R @ sdtpldt0 ) ) )
| ~ ( S @ aInteger0 )
| ~ ( R @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ sk9 @ ( P @ ( Q @ sdteqdtlpzmzozddtrp0 ) ) )
| ~ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( Q @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ smndt0 @ ( Q @ sdtpldt0 ) @ ( P @ sk9 @ aDivisorOf0 ) )
| ~ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( Q @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( ( P @ ( Q @ sk10 ) @ ( P @ sk9 @ sdtasdt0 ) )
= ( P @ smndt0 @ ( Q @ sdtpldt0 ) ) )
| ~ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( Q @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ ( Q @ sk10 ) @ aInteger0 )
| ~ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( Q @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( Q @ aInteger0 )
| ~ ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ ( Q @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ sk9 @ ( P @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( ( P @ sk9 )
!= sz00 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( P @ sk9 @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( P @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( O @ aElementOf0 ) )
| ( xS @ sbsmnsldt0 @ ( O @ aElementOf0 ) )
| ~ ( O @ aInteger0 ) )
& ( ~ ( xS @ sbsmnsldt0 @ ( N @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( N @ aElementOf0 ) ) )
& ( ( N @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( N @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ ( L @ aElementOf0 ) )
| ~ ( M @ ( L @ aElementOf0 ) )
| ~ ( xS @ ( M @ aElementOf0 ) )
| ~ ( L @ aInteger0 ) )
& ( ( K @ sk8 @ ( K @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( K @ aElementOf0 ) ) )
& ( ( xS @ ( K @ sk8 @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( K @ aElementOf0 ) ) )
& ( ( K @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ ( K @ aElementOf0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 )
& ( xS @ sbsmnsldt0 @ isClosed0 )
& ( xS @ sbsmnsldt0 @ stldt0 @ isOpen0 )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( J @ aElementOf0 ) )
| ~ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( J @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( H @ aElementOf0 ) )
| ~ ( F @ sk6 @ ( F @ ( H @ sdteqdtlpzmzozddtrp0 ) ) )
| ~ ( H @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( H @ aElementOf0 ) )
| ~ ( F @ smndt0 @ ( H @ sdtpldt0 ) @ ( F @ sk6 @ aDivisorOf0 ) )
| ~ ( H @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( H @ aElementOf0 ) )
| ( ( I @ ( F @ sk6 @ sdtasdt0 ) )
!= ( F @ smndt0 @ ( H @ sdtpldt0 ) ) )
| ~ ( I @ aInteger0 )
| ~ ( H @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ sk6 @ ( F @ ( G @ sdteqdtlpzmzozddtrp0 ) ) )
| ~ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( G @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ smndt0 @ ( G @ sdtpldt0 ) @ ( F @ sk6 @ aDivisorOf0 ) )
| ~ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( G @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( ( F @ ( G @ sk7 ) @ ( F @ sk6 @ sdtasdt0 ) )
= ( F @ smndt0 @ ( G @ sdtpldt0 ) ) )
| ~ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( G @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ ( G @ sk7 ) @ aInteger0 )
| ~ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( G @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( G @ aInteger0 )
| ~ ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ ( G @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ sk6 @ ( F @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( ( F @ sk6 )
!= sz00 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( F @ sk6 @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( F @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( E @ aElementOf0 ) )
| ( xS @ sbsmnsldt0 @ ( E @ aElementOf0 ) )
| ~ ( E @ aInteger0 ) )
& ( ~ ( xS @ sbsmnsldt0 @ ( D @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( D @ aElementOf0 ) ) )
& ( ( D @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( D @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
| ~ ( C @ ( B @ aElementOf0 ) )
| ~ ( xS @ ( C @ aElementOf0 ) )
| ~ ( B @ aInteger0 ) )
& ( ( A @ sk5 @ ( A @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( xS @ ( A @ sk5 @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( ( A @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ ( A @ aElementOf0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) ),
inference(cnf,[status(esa)],[131]) ).
thf(139,plain,
! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ sk6 @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(215,plain,
! [A: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ sk6 @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(125708,plain,
! [A: $i] :
( ( cS2076 @ ( A @ sk6 @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( cS2076 @ ( A @ aElementOf0 ) ) ),
inference(rewrite,[status(thm)],[215,354]) ).
thf(125811,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ aElementOf0 ) )
!= ( cS2076 @ ( A @ aElementOf0 ) ) )
| ( cS2076 @ ( A @ sk6 @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[975,125708]) ).
thf(125812,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ aElementOf0 ) )
!= ( cS2076 @ ( A @ aElementOf0 ) ) )
| ( cS2076 @ ( A @ sk6 @ ( A @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) ) ),
inference(simp,[status(thm)],[125811]) ).
thf(125813,plain,
cS2076 @ ( sz10 @ sk6 @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ),
inference(pattern_uni,[status(thm)],[125812:[bind(A,$thf( sz10 ))]]) ).
thf(1,conjecture,
? [A: $i] :
( ( ( ! [B: $i] :
( ( ( ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
| ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
| ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) )
& ( B @ aInteger0 ) )
=> ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
& ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) )
& ( B @ aInteger0 ) ) ) )
& ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 ) )
=> ( ( ! [B: $i] :
( ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
<=> ( ? [C: $i] :
( ( C @ ( B @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) )
& ( B @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) )
=> ( ! [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) )
<=> ( ~ ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
& ( B @ aInteger0 ) ) )
=> ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ! [B: $i] :
( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) ) ) ) ) )
& ( A != sz00 )
& ( A @ aInteger0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( ( ! [B: $i] :
( ( ( ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
| ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
| ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) )
& ( B @ aInteger0 ) )
=> ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
& ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) )
& ( B @ aInteger0 ) ) ) )
& ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 ) )
=> ( ( ! [B: $i] :
( ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
<=> ( ? [C: $i] :
( ( C @ ( B @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) )
& ( B @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) )
=> ( ! [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) )
<=> ( ~ ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
& ( B @ aInteger0 ) ) )
=> ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ! [B: $i] :
( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) ) ) ) ) )
& ( A != sz00 )
& ( A @ aInteger0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ? [A: $i] :
( ( ( ! [B: $i] :
( ( ( ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
| ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
| ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) )
& ( B @ aInteger0 ) )
=> ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
& ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) )
& ( B @ aInteger0 ) ) ) )
& ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 ) )
=> ( ( ! [B: $i] :
( ( ( ? [C: $i] :
( ( C @ ( B @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) )
& ( B @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
=> ( ? [C: $i] :
( ( C @ ( B @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) )
& ( B @ aInteger0 ) ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) )
=> ( ! [B: $i] :
( ( ( ~ ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
& ( B @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
& ( B @ aInteger0 ) ) ) )
=> ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ! [B: $i] :
( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) ) ) ) ) )
& ( A != sz00 )
& ( A @ aInteger0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
~ ? [A: $i] :
( ( ( ! [B: $i] :
( ( ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
| ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
| ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) ) )
& ( B @ aInteger0 ) )
=> ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) ) )
& ! [B: $i] :
( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
& ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
& ? [C: $i] :
( ( ( C @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
& ( C @ aInteger0 ) )
& ( B @ aInteger0 ) ) )
& ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 ) )
=> ( ( ! [B: $i] :
( ( ? [C: $i] :
( ( C @ ( B @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) )
& ( B @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) ) )
& ! [B: $i] :
( ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
=> ( ? [C: $i] :
( ( C @ ( B @ aElementOf0 ) )
& ( xS @ ( C @ aElementOf0 ) ) )
& ( B @ aInteger0 ) ) )
& ( xS @ sbsmnsldt0 @ aSet0 ) )
=> ( ( ! [B: $i] :
( ( ~ ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
& ( B @ aInteger0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) )
& ! [B: $i] :
( ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) )
=> ( ~ ( xS @ sbsmnsldt0 @ ( B @ aElementOf0 ) )
& ( B @ aInteger0 ) ) ) )
=> ( ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ! [B: $i] :
( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
=> ( xS @ sbsmnsldt0 @ stldt0 @ ( B @ aElementOf0 ) ) ) ) ) ) )
& ( A != sz00 )
& ( A @ aInteger0 ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ sk3 @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( A @ sk3 @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( xS @ sbsmnsldt0 @ stldt0 @ ( I @ aElementOf0 ) )
| ( xS @ sbsmnsldt0 @ ( I @ aElementOf0 ) )
| ~ ( I @ aInteger0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ~ ( xS @ sbsmnsldt0 @ ( H @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( H @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( H @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( H @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( xS @ sbsmnsldt0 @ ( F @ aElementOf0 ) )
| ~ ( G @ ( F @ aElementOf0 ) )
| ~ ( xS @ ( G @ aElementOf0 ) )
| ~ ( F @ aInteger0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( E @ sk2 ) @ ( E @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( E @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( xS @ ( A @ ( E @ sk2 ) @ aElementOf0 ) )
| ~ ( xS @ sbsmnsldt0 @ ( E @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( E @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ ( E @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( xS @ sbsmnsldt0 @ aSet0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
| ~ ( A @ ( sz10 @ ( C @ sdteqdtlpzmzozddtrp0 ) ) )
| ~ ( C @ aInteger0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
| ~ ( sz10 @ smndt0 @ ( C @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
| ~ ( C @ aInteger0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( C @ aElementOf0 ) )
| ( ( D @ ( A @ sdtasdt0 ) )
!= ( sz10 @ smndt0 @ ( C @ sdtpldt0 ) ) )
| ~ ( D @ aInteger0 )
| ~ ( C @ aInteger0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( sz10 @ ( B @ sdteqdtlpzmzozddtrp0 ) ) )
| ~ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) @ ( A @ aDivisorOf0 ) )
| ~ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( ( A @ ( B @ sk1 ) @ ( A @ sdtasdt0 ) )
= ( sz10 @ smndt0 @ ( B @ sdtpldt0 ) ) )
| ~ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( B @ sk1 ) @ aInteger0 )
| ~ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( B @ aInteger0 )
| ~ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ ( B @ aElementOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) )
& ( ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSet0 )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ( A = sz00 )
| ~ ( A @ aInteger0 ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(97,plain,
! [A: $i] :
( ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( A @ aInteger0 )
| ( A = sz00 ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(23016,plain,
! [A: $i] :
( ~ ( cS2076 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
| ~ ( A @ aInteger0 )
| ( A = sz00 ) ),
inference(rewrite,[status(thm)],[97,354]) ).
thf(126241,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ sk6 @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
!= ( cS2076 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) ) )
| ~ $true
| ~ ( A @ aInteger0 )
| ( A = sz00 ) ),
inference(paramod_ordered,[status(thm)],[125813,23016]) ).
thf(126242,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ sk6 @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) )
!= ( cS2076 @ ( A @ ( sz10 @ szAzrzSzezqlpdtcmdtrp0 ) @ aSubsetOf0 ) ) )
| ~ ( A @ aInteger0 )
| ( A = sz00 ) ),
inference(simp,[status(thm)],[126241]) ).
thf(126243,plain,
( ~ ( sz10 @ sk6 @ aInteger0 )
| ( ( sz10 @ sk6 )
= sz00 ) ),
inference(pattern_uni,[status(thm)],[126242:[bind(A,$thf( sz10 @ sk6 ))]]) ).
thf(158,plain,
! [A: $i] :
( ( A @ sk6 @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(213,plain,
! [A: $i] :
( ( A @ sk6 @ aInteger0 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(121715,plain,
! [A: $i] :
( ( A @ sk6 @ aInteger0 )
| ~ ( cS2076 @ ( A @ aElementOf0 ) ) ),
inference(rewrite,[status(thm)],[213,354]) ).
thf(121774,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ aElementOf0 ) )
!= ( cS2076 @ ( A @ aElementOf0 ) ) )
| ( A @ sk6 @ aInteger0 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[975,121715]) ).
thf(121775,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ aElementOf0 ) )
!= ( cS2076 @ ( A @ aElementOf0 ) ) )
| ( A @ sk6 @ aInteger0 ) ),
inference(simp,[status(thm)],[121774]) ).
thf(121776,plain,
sz10 @ sk6 @ aInteger0,
inference(pattern_uni,[status(thm)],[121775:[bind(A,$thf( sz10 ))]]) ).
thf(127854,plain,
( ~ $true
| ( ( sz10 @ sk6 )
= sz00 ) ),
inference(rewrite,[status(thm)],[126243,121776]) ).
thf(127855,plain,
( ( sz10 @ sk6 )
= sz00 ),
inference(simp,[status(thm)],[127854]) ).
thf(135,plain,
! [A: $i] :
( ( ( A @ sk6 )
!= sz00 )
| ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(205,plain,
! [A: $i] :
( ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
| ( ( A @ sk6 )
!= sz00 ) ),
inference(lifteq,[status(thm)],[135]) ).
thf(206,plain,
! [A: $i] :
( ~ ( xS @ sbsmnsldt0 @ stldt0 @ ( A @ aElementOf0 ) )
| ( ( A @ sk6 )
!= sz00 ) ),
inference(simp,[status(thm)],[205]) ).
thf(956,plain,
! [A: $i] :
( ~ ( cS2076 @ ( A @ aElementOf0 ) )
| ( ( A @ sk6 )
!= sz00 ) ),
inference(rewrite,[status(thm)],[206,354]) ).
thf(979,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ aElementOf0 ) )
!= ( cS2076 @ ( A @ aElementOf0 ) ) )
| ~ $true
| ( ( A @ sk6 )
!= sz00 ) ),
inference(paramod_ordered,[status(thm)],[975,956]) ).
thf(980,plain,
! [A: $i] :
( ( ( cS2076 @ ( sz10 @ aElementOf0 ) )
!= ( cS2076 @ ( A @ aElementOf0 ) ) )
| ( ( A @ sk6 )
!= sz00 ) ),
inference(simp,[status(thm)],[979]) ).
thf(981,plain,
( ( sz10 @ sk6 )
!= sz00 ),
inference(pattern_uni,[status(thm)],[980:[bind(A,$thf( sz10 ))]]) ).
thf(127856,plain,
$false,
inference(simplifyReflect,[status(thm)],[127855,981]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM450+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/5.42 % Computer : n001.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Sat Sep 26 02:53:02 UTC 2026
% 0.14/5.43 % CPUTime :
% 0.14/5.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/6.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/6.28 % [INFO] Parsing done (248ms).
% 1.32/6.29 % [INFO] Running in sequential loop mode.
% 2.14/6.68 % [INFO] eprover registered as external prover.
% 2.14/6.69 % [INFO] Scanning for conjecture ...
% 2.34/6.78 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.34/6.79 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.80 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.81 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.82 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.52/6.89 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 2.73/7.01 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 3.04/7.05 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.06 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.08 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.09 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.10 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.04/7.10 % [INFO] Problem is first-order (TPTP FOF).
% 3.04/7.11 % [INFO] Type checking passed.
% 3.04/7.12 % [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 ...
% 111.79/57.62 % [INFO] Killing All external provers ...
% 111.79/57.62 % Time passed: 52045ms (effective reasoning time: 51317ms)
% 111.79/57.62 % 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)>
% 111.79/57.62 % Axioms used in derivation (2): m__2079, m__2144
% 111.79/57.62 % No. of inferences in proof: 47
% 111.79/57.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 52045 ms resp. 51317 ms w/o parsing
% 112.11/57.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 112.11/57.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------