%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG108+4 : 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 : n011.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 08:25:28 AM UTC 2026
% Result : Theorem 199.23s 119.28s
% Output : Refutation 199.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 19 unt; 0 typ; 4 def)
% Number of atoms : 380 ( 116 equ; 0 cnn)
% Maximal formula atoms : 33 ( 5 avg)
% Number of connectives : 997 ( 133 ~; 142 |; 103 &; 591 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 9 con; 0-2 aty)
% Number of variables : 118 ( 4 ^; 77 !; 33 ?; 118 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(sdtpldt1_decl,type,
sdtpldt1: $i > $i > $i ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sdtpldt0_decl,type,
sdtpldt0: $i > $i > $i ).
thf(aIdeal0_decl,type,
aIdeal0: $i > $o ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(sdtasdt0_decl,type,
sdtasdt0: $i > $i > $i ).
thf(sz10_decl,type,
sz10: $i ).
thf(slsdtgt0_decl,type,
slsdtgt0: $i > $i ).
thf(xa_decl,type,
xa: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(xb_decl,type,
xb: $i ).
thf(xI_decl,type,
xI: $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $o ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( B @ ( xb @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( B @ ( A @ sk5 @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) ) ) ).
thf(26,axiom,
( ( xb @ aElement0 )
& ( xa @ aElement0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
thf(186,plain,
( ( xb @ aElement0 )
& ( xa @ aElement0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(187,plain,
( ( xb @ aElement0 )
& ( xa @ aElement0 ) ),
inference(cnf,[status(esa)],[186]) ).
thf(189,plain,
xb @ aElement0,
inference(cnfConj,[status(thm)],[187]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ aElement0 )
=> ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
& ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
thf(71,plain,
! [A: $i] :
( ( A @ aElement0 )
=> ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
& ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(72,plain,
! [A: $i] :
( ( ( sz00
= ( A @ ( sz00 @ sdtasdt0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [A: $i] :
( ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(75,plain,
! [A: $i] :
( ~ ( A @ aElement0 )
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(1194,plain,
! [A: $i] :
( ( ( xb @ aElement0 )
!= ( A @ aElement0 ) )
| ~ $true
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(paramod_ordered,[status(thm)],[189,75]) ).
thf(1195,plain,
! [A: $i] :
( ( ( xb @ aElement0 )
!= ( A @ aElement0 ) )
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1196,plain,
( ( sz00 @ ( xb @ sdtasdt0 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[1195:[bind(A,$thf( xb ))]]) ).
thf(1,conjecture,
( ( ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xb @ sdtasdt0 ) )
= xb )
& ( A @ aElement0 ) ) )
& ( ( xb @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xb @ sdtasdt0 ) )
= sz00 )
& ( A @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( xa @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xa @ sdtasdt0 ) )
= xa )
& ( A @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xa @ sdtasdt0 ) )
= sz00 )
& ( A @ aElement0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xb @ sdtasdt0 ) )
= xb )
& ( A @ aElement0 ) ) )
& ( ( xb @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xb @ sdtasdt0 ) )
= sz00 )
& ( A @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( xa @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xa @ sdtasdt0 ) )
= xa )
& ( A @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xa @ sdtasdt0 ) )
= sz00 )
& ( A @ aElement0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(45,plain,
~ ( ( ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xb @ sdtasdt0 ) )
= xb )
& ( A @ aElement0 ) ) )
& ( ( xb @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xb @ sdtasdt0 ) )
= sz00 )
& ( A @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( xa @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xa @ sdtasdt0 ) )
= xa )
& ( A @ aElement0 ) ) )
& ( ( xa @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| ? [A: $i] :
( ( ( A @ ( xa @ sdtasdt0 ) )
= sz00 )
& ( A @ aElement0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ~ ( xb @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| sk2
| sk1 )
& ( ( ( D @ ( xb @ sdtasdt0 ) )
!= xb )
| ~ ( D @ aElement0 )
| ~ ( xb @ slsdtgt0 @ ( sz00 @ aElementOf0 ) )
| sk2
| sk1 )
& ( ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ( ( C @ ( xb @ sdtasdt0 ) )
!= sz00 )
| ~ ( C @ aElement0 )
| sk2
| sk1 )
& ( ( ( D @ ( xb @ sdtasdt0 ) )
!= xb )
| ~ ( D @ aElement0 )
| ( ( C @ ( xb @ sdtasdt0 ) )
!= sz00 )
| ~ ( C @ aElement0 )
| sk2
| sk1 )
& ( ~ sk2
| ~ ( xa @ slsdtgt0 @ ( xa @ aElementOf0 ) )
| sk1 )
& ( ~ sk2
| ( ( B @ ( xa @ sdtasdt0 ) )
!= xa )
| ~ ( B @ aElement0 )
| sk1 )
& ( ~ sk1
| ~ ( xa @ slsdtgt0 @ ( sz00 @ aElementOf0 ) ) )
& ( ~ sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= sz00 )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(53,plain,
! [A: $i] :
( ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ( ( A @ ( xb @ sdtasdt0 ) )
!= sz00 )
| ~ ( A @ aElement0 )
| sk2
| sk1 ),
inference(cnfConj,[status(thm)],[46]) ).
thf(56,plain,
! [A: $i] :
( ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| sk2
| sk1
| ( ( A @ ( xb @ sdtasdt0 ) )
!= sz00 ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(57,plain,
! [A: $i] :
( ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| sk2
| sk1
| ( ( A @ ( xb @ sdtasdt0 ) )
!= sz00 ) ),
inference(simp,[status(thm)],[56]) ).
thf(1475,plain,
! [A: $i] :
( ( ( sz00 @ ( xb @ sdtasdt0 ) )
!= ( A @ ( xb @ sdtasdt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| sk2
| sk1
| ( sz00 != sz00 ) ),
inference(paramod_ordered,[status(thm)],[1196,57]) ).
thf(1476,plain,
! [A: $i] :
( ( ( sz00 @ ( xb @ sdtasdt0 ) )
!= ( A @ ( xb @ sdtasdt0 ) ) )
| ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ~ ( A @ aElement0 )
| sk2
| sk1 ),
inference(simp,[status(thm)],[1475]) ).
thf(1477,plain,
( ~ ( xb @ slsdtgt0 @ ( xb @ aElementOf0 ) )
| ~ ( sz00 @ aElement0 )
| sk2
| sk1 ),
inference(pattern_uni,[status(thm)],[1476:[bind(A,$thf( sz00 ))]]) ).
thf(30,axiom,
sz00 @ aElement0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
thf(219,plain,
sz00 @ aElement0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(52,plain,
! [A: $i] :
( ~ sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= sz00 )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(55,plain,
! [A: $i] :
( ~ sk1
| ~ ( A @ aElement0 )
| ( ( A @ ( xa @ sdtasdt0 ) )
!= sz00 ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(397,plain,
! [A: $i] :
( ( ( sz00 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ sk1
| ~ $true
| ( ( A @ ( xa @ sdtasdt0 ) )
!= sz00 ) ),
inference(paramod_ordered,[status(thm)],[219,55]) ).
thf(398,plain,
! [A: $i] :
( ( ( sz00 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= sz00 ) ),
inference(simp,[status(thm)],[397]) ).
thf(399,plain,
( ~ sk1
| ( ( sz00 @ ( xa @ sdtasdt0 ) )
!= sz00 ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( sz00 ))]]) ).
thf(188,plain,
xa @ aElement0,
inference(cnfConj,[status(thm)],[187]) ).
thf(1219,plain,
! [A: $i] :
( ( ( xa @ aElement0 )
!= ( A @ aElement0 ) )
| ~ $true
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(paramod_ordered,[status(thm)],[188,75]) ).
thf(1220,plain,
! [A: $i] :
( ( ( xa @ aElement0 )
!= ( A @ aElement0 ) )
| ( ( sz00 @ ( A @ sdtasdt0 ) )
= sz00 ) ),
inference(simp,[status(thm)],[1219]) ).
thf(1221,plain,
( ( sz00 @ ( xa @ sdtasdt0 ) )
= sz00 ),
inference(pattern_uni,[status(thm)],[1220:[bind(A,$thf( xa ))]]) ).
thf(1552,plain,
( ~ sk1
| ( sz00 != sz00 ) ),
inference(rewrite,[status(thm)],[399,1221]) ).
thf(1553,plain,
~ sk1,
inference(simp,[status(thm)],[1552]) ).
thf(32,axiom,
sz10 @ aElement0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
thf(222,plain,
sz10 @ aElement0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(47,plain,
! [A: $i] :
( ~ sk2
| ( ( A @ ( xa @ sdtasdt0 ) )
!= xa )
| ~ ( A @ aElement0 )
| sk1 ),
inference(cnfConj,[status(thm)],[46]) ).
thf(60,plain,
! [A: $i] :
( ~ sk2
| ~ ( A @ aElement0 )
| sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(61,plain,
! [A: $i] :
( ~ sk2
| ~ ( A @ aElement0 )
| sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(simp,[status(thm)],[60]) ).
thf(561,plain,
! [A: $i] :
( ( ( sz10 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ sk2
| ~ $true
| sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(paramod_ordered,[status(thm)],[222,61]) ).
thf(562,plain,
! [A: $i] :
( ( ( sz10 @ aElement0 )
!= ( A @ aElement0 ) )
| ~ sk2
| sk1
| ( ( A @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(simp,[status(thm)],[561]) ).
thf(563,plain,
( ~ sk2
| sk1
| ( ( sz10 @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(pattern_uni,[status(thm)],[562:[bind(A,$thf( sz10 ))]]) ).
thf(1684,plain,
( ~ sk2
| $false
| ( ( sz10 @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(rewrite,[status(thm)],[563,1553]) ).
thf(1685,plain,
( ~ sk2
| ( ( sz10 @ ( xa @ sdtasdt0 ) )
!= xa ) ),
inference(simp,[status(thm)],[1684]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ aElement0 )
=> ( ( A
= ( A @ ( sz10 @ sdtasdt0 ) ) )
& ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
thf(213,plain,
! [A: $i] :
( ( A @ aElement0 )
=> ( ( A
= ( A @ ( sz10 @ sdtasdt0 ) ) )
& ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(214,plain,
! [A: $i] :
( ( ( A
= ( A @ ( sz10 @ sdtasdt0 ) ) )
| ~ ( A @ aElement0 ) )
& ( ( ( sz10 @ ( A @ sdtasdt0 ) )
= A )
| ~ ( A @ aElement0 ) ) ),
inference(cnf,[status(esa)],[213]) ).
thf(215,plain,
! [A: $i] :
( ( ( sz10 @ ( A @ sdtasdt0 ) )
= A )
| ~ ( A @ aElement0 ) ),
inference(cnfConj,[status(thm)],[214]) ).
thf(217,plain,
! [A: $i] :
( ~ ( A @ aElement0 )
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(lifteq,[status(thm)],[215]) ).
thf(57647,plain,
! [A: $i] :
( ( ( xa @ aElement0 )
!= ( A @ aElement0 ) )
| ~ $true
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[188,217]) ).
thf(57648,plain,
! [A: $i] :
( ( ( xa @ aElement0 )
!= ( A @ aElement0 ) )
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(simp,[status(thm)],[57647]) ).
thf(57649,plain,
( ( sz10 @ ( xa @ sdtasdt0 ) )
= xa ),
inference(pattern_uni,[status(thm)],[57648:[bind(A,$thf( xa ))]]) ).
thf(59059,plain,
( ~ sk2
| ( xa != xa ) ),
inference(rewrite,[status(thm)],[1685,57649]) ).
thf(59060,plain,
~ sk2,
inference(simp,[status(thm)],[59059]) ).
thf(9,axiom,
( ( xI
= ( xb @ slsdtgt0 @ ( xa @ slsdtgt0 @ sdtpldt1 ) ) )
& ! [A: $i] :
( ( xI @ ( A @ aElementOf0 ) )
<=> ? [B: $i,C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) )
& ! [A: $i] :
( ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) )
<=> ? [B: $i] :
( ( ( B @ ( xb @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) )
& ! [A: $i] :
( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
<=> ? [B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) )
& ( xI @ aIdeal0 )
& ! [A: $i] :
( ( xI @ ( A @ aElementOf0 ) )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( xI @ ( A @ ( B @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [B: $i] :
( ( xI @ ( B @ aElementOf0 ) )
=> ( xI @ ( B @ ( A @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( xI @ aSet0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
thf(77,plain,
( ( xI
= ( xb @ slsdtgt0 @ ( xa @ slsdtgt0 @ sdtpldt1 ) ) )
& ! [A: $i] :
( ( ? [B: $i,C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) )
=> ( xI @ ( A @ aElementOf0 ) ) )
& ( ( xI @ ( A @ aElementOf0 ) )
=> ? [B: $i,C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) ) )
& ! [A: $i] :
( ( ? [B: $i] :
( ( ( B @ ( xb @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) )
=> ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) ) )
& ( ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xb @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) ) )
& ! [A: $i] :
( ( ? [B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) )
=> ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) )
& ( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) ) )
& ( xI @ aIdeal0 )
& ! [A: $i] :
( ( xI @ ( A @ aElementOf0 ) )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( xI @ ( A @ ( B @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [B: $i] :
( ( xI @ ( B @ aElementOf0 ) )
=> ( xI @ ( B @ ( A @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( xI @ aSet0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(78,plain,
( ( xI
= ( xb @ slsdtgt0 @ ( xa @ slsdtgt0 @ sdtpldt1 ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) )
=> ( xI @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xI @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ? [C: $i] :
( ( ( C @ ( B @ sdtpldt0 ) )
= A )
& ( xb @ slsdtgt0 @ ( C @ aElementOf0 ) ) )
& ( xa @ slsdtgt0 @ ( B @ aElementOf0 ) ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( ( B @ ( xb @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) )
=> ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xb @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) )
& ! [A: $i] :
( ? [B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) )
=> ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) ) )
& ! [A: $i] :
( ( xa @ slsdtgt0 @ ( A @ aElementOf0 ) )
=> ? [B: $i] :
( ( ( B @ ( xa @ sdtasdt0 ) )
= A )
& ( B @ aElement0 ) ) )
& ( xI @ aIdeal0 )
& ! [A: $i] :
( ( xI @ ( A @ aElementOf0 ) )
=> ( ! [B: $i] :
( ( B @ aElement0 )
=> ( xI @ ( A @ ( B @ sdtasdt0 ) @ aElementOf0 ) ) )
& ! [B: $i] :
( ( xI @ ( B @ aElementOf0 ) )
=> ( xI @ ( B @ ( A @ sdtpldt0 ) @ aElementOf0 ) ) ) ) )
& ( xI @ aSet0 ) ),
inference(miniscope,[status(thm)],[77]) ).
thf(79,plain,
! [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] :
( ( xI
= ( xb @ slsdtgt0 @ ( xa @ slsdtgt0 @ sdtpldt1 ) ) )
& ( ( xI @ ( K @ aElementOf0 ) )
| ( ( M @ ( L @ sdtpldt0 ) )
!= K )
| ~ ( xb @ slsdtgt0 @ ( M @ aElementOf0 ) )
| ~ ( xa @ slsdtgt0 @ ( L @ aElementOf0 ) ) )
& ( ( ( J @ sk6 @ ( J @ sk5 @ sdtpldt0 ) )
= J )
| ~ ( xI @ ( J @ aElementOf0 ) ) )
& ( ( xb @ slsdtgt0 @ ( J @ sk6 @ aElementOf0 ) )
| ~ ( xI @ ( J @ aElementOf0 ) ) )
& ( ( xa @ slsdtgt0 @ ( J @ sk5 @ aElementOf0 ) )
| ~ ( xI @ ( J @ aElementOf0 ) ) )
& ( ( xb @ slsdtgt0 @ ( H @ aElementOf0 ) )
| ( ( I @ ( xb @ sdtasdt0 ) )
!= H )
| ~ ( I @ aElement0 ) )
& ( ( ( G @ sk4 @ ( xb @ sdtasdt0 ) )
= G )
| ~ ( xb @ slsdtgt0 @ ( G @ aElementOf0 ) ) )
& ( ( G @ sk4 @ aElement0 )
| ~ ( xb @ slsdtgt0 @ ( G @ aElementOf0 ) ) )
& ( ( xa @ slsdtgt0 @ ( E @ aElementOf0 ) )
| ( ( F @ ( xa @ sdtasdt0 ) )
!= E )
| ~ ( F @ aElement0 ) )
& ( ( ( D @ sk3 @ ( xa @ sdtasdt0 ) )
= D )
| ~ ( xa @ slsdtgt0 @ ( D @ aElementOf0 ) ) )
& ( ( D @ sk3 @ aElement0 )
| ~ ( xa @ slsdtgt0 @ ( D @ aElementOf0 ) ) )
& ( xI @ aIdeal0 )
& ( ( xI @ ( A @ ( C @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( C @ aElement0 )
| ~ ( xI @ ( A @ aElementOf0 ) ) )
& ( ( xI @ ( B @ ( A @ sdtpldt0 ) @ aElementOf0 ) )
| ~ ( xI @ ( B @ aElementOf0 ) )
| ~ ( xI @ ( A @ aElementOf0 ) ) )
& ( xI @ aSet0 ) ),
inference(cnf,[status(esa)],[78]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ( ( B @ ( xb @ sdtasdt0 ) )
!= A )
| ~ ( B @ aElement0 ) ),
inference(cnfConj,[status(thm)],[79]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( xb @ slsdtgt0 @ ( A @ aElementOf0 ) )
| ~ ( B @ aElement0 )
| ( ( B @ ( xb @ sdtasdt0 ) )
!= A ) ),
inference(lifteq,[status(thm)],[81]) ).
thf(105,plain,
! [A: $i] :
( ( xb @ slsdtgt0 @ ( A @ ( xb @ sdtasdt0 ) @ aElementOf0 ) )
| ~ ( A @ aElement0 ) ),
inference(simp,[status(thm)],[104]) ).
thf(5905,plain,
! [A: $i] :
( ( ( sz10 @ aElement0 )
!= ( A @ aElement0 ) )
| ( xb @ slsdtgt0 @ ( A @ ( xb @ sdtasdt0 ) @ aElementOf0 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[222,105]) ).
thf(5906,plain,
! [A: $i] :
( ( ( sz10 @ aElement0 )
!= ( A @ aElement0 ) )
| ( xb @ slsdtgt0 @ ( A @ ( xb @ sdtasdt0 ) @ aElementOf0 ) ) ),
inference(simp,[status(thm)],[5905]) ).
thf(5907,plain,
xb @ slsdtgt0 @ ( sz10 @ ( xb @ sdtasdt0 ) @ aElementOf0 ),
inference(pattern_uni,[status(thm)],[5906:[bind(A,$thf( sz10 ))]]) ).
thf(57538,plain,
! [A: $i] :
( ( ( xb @ aElement0 )
!= ( A @ aElement0 ) )
| ~ $true
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[189,217]) ).
thf(57539,plain,
! [A: $i] :
( ( ( xb @ aElement0 )
!= ( A @ aElement0 ) )
| ( ( sz10 @ ( A @ sdtasdt0 ) )
= A ) ),
inference(simp,[status(thm)],[57538]) ).
thf(57540,plain,
( ( sz10 @ ( xb @ sdtasdt0 ) )
= xb ),
inference(pattern_uni,[status(thm)],[57539:[bind(A,$thf( xb ))]]) ).
thf(58342,plain,
xb @ slsdtgt0 @ ( xb @ aElementOf0 ),
inference(rewrite,[status(thm)],[5907,57540]) ).
thf(278846,plain,
( ~ $true
| ~ $true
| $false
| $false ),
inference(rewrite,[status(thm)],[1477,1553,59060,58342,219]) ).
thf(278847,plain,
$false,
inference(simp,[status(thm)],[278846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.16/0.41 % Computer : n011.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 06:07:13 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.22 % [INFO] Parsing done (232ms).
% 1.46/1.23 % [INFO] Running in sequential loop mode.
% 2.25/1.63 % [INFO] eprover registered as external prover.
% 2.25/1.64 % [INFO] Scanning for conjecture ...
% 2.47/1.73 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.74 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.75 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.76 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.47/1.77 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.73/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.95/1.90 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 2.95/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.93 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.95 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.95/1.98 % [INFO] Problem is first-order (TPTP FOF).
% 2.95/1.99 % [INFO] Type checking passed.
% 2.95/2.00 % [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 ...
% 199.23/119.27 % [INFO] Killing All external provers ...
% 199.23/119.28 % Time passed: 118724ms (effective reasoning time: 118038ms)
% 199.23/119.28 % 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)>
% 199.23/119.28 % Axioms used in derivation (6): mSortsC, mMulZero, m__2174, mSortsC_01, m__2091, mMulUnit
% 199.23/119.28 % No. of inferences in proof: 71
% 199.23/119.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 118724 ms resp. 118038 ms w/o parsing
% 199.36/119.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 199.36/119.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------