TSTP Solution File: SET890+1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 7 10:50:48 EDT 2024
% Result : Theorem 98.29s 14.86s
% Output : Refutation 98.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 67 ( 17 unt; 7 typ; 0 def)
% Number of atoms : 190 ( 56 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 607 ( 53 ~; 43 |; 30 &; 436 @)
% ( 6 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 0 ^ 123 !; 9 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(sk5_type,type,
sk5: $i > $i > $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk4 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[51]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[22]) ).
thf(1,conjecture,
! [A: $i] :
( ( union @ ( singleton @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( union @ ( singleton @ A ) )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(12,plain,
~ ! [A: $i] :
( ( union @ ( singleton @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
( ( union @ ( singleton @ sk1 ) )
!= sk1 ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
( ( union @ ( singleton @ sk1 ) )
!= sk1 ),
inference(lifteq,[status(thm)],[13]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != sk1 )
| ( A
!= ( union @ ( singleton @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,14]) ).
thf(100,plain,
! [A: $i] :
( ~ ( subset @ ( union @ ( singleton @ sk1 ) ) @ A )
| ~ ( subset @ A @ ( union @ ( singleton @ sk1 ) ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( union @ ( singleton @ sk1 ) )),bind(B,$thf( B ))]]) ).
thf(125,plain,
( ~ ( subset @ ( union @ ( singleton @ sk1 ) ) @ sk1 )
| ~ ( subset @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ( B
= ( singleton @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,plain,
( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( in @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(miniscope,[status(thm)],[28]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ( C != A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[29]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ( C != A )
| ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(47,plain,
! [A: $i] : ( in @ A @ ( singleton @ A ) ),
inference(simp,[status(thm)],[46]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ),
inference(cnf,[status(esa)],[81]) ).
thf(16535,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ ( union @ C ) )
| ( ( in @ A @ ( singleton @ A ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[47,82]) ).
thf(16536,plain,
! [A: $i] : ( subset @ A @ ( union @ ( singleton @ A ) ) ),
inference(pattern_uni,[status(thm)],[16535:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( singleton @ D ))]]) ).
thf(16570,plain,
! [A: $i] : ( subset @ A @ ( union @ ( singleton @ A ) ) ),
inference(simp,[status(thm)],[16536]) ).
thf(20451,plain,
( ~ ( subset @ ( union @ ( singleton @ sk1 ) ) @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[125,16570]) ).
thf(20452,plain,
~ ( subset @ ( union @ ( singleton @ sk1 ) ) @ sk1 ),
inference(simp,[status(thm)],[20451]) ).
thf(20622,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk4 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ ( union @ ( singleton @ sk1 ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[54,20452]) ).
thf(20623,plain,
~ ( in @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ sk1 ),
inference(pattern_uni,[status(thm)],[20622:[bind(A,$thf( union @ ( singleton @ sk1 ) )),bind(B,$thf( sk1 ))]]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( in @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[49]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( in @ ( sk4 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[50]) ).
thf(20619,plain,
! [B: $i,A: $i] :
( ( in @ ( sk4 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ ( union @ ( singleton @ sk1 ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[53,20452]) ).
thf(20620,plain,
in @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ),
inference(pattern_uni,[status(thm)],[20619:[bind(A,$thf( union @ ( singleton @ sk1 ) )),bind(B,$thf( sk1 ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( ( B
= ( union @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( union @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,plain,
( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( union @ A ) ) ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( union @ A ) )
| ~ ( in @ C @ B )
| ( in @ C @ ( sk5 @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( union @ A ) )
| ~ ( in @ C @ B )
| ( in @ C @ ( sk5 @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( union @ A ) )
| ( in @ B @ ( sk5 @ B @ ( union @ A ) @ A ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(21666,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( sk5 @ B @ ( union @ A ) @ A ) )
| ( ( in @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) )
!= ( in @ B @ ( union @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[20620,78]) ).
thf(21667,plain,
in @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( sk5 @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ) ),
inference(pattern_uni,[status(thm)],[21666:[bind(A,$thf( singleton @ sk1 )),bind(B,$thf( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ))]]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( union @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( sk5 @ C @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[56]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( union @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( sk5 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( union @ A ) )
| ( in @ ( sk5 @ B @ ( union @ A ) @ A ) @ A ) ),
inference(simp,[status(thm)],[69]) ).
thf(21677,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ B @ ( union @ A ) @ A ) @ A )
| ( ( in @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) )
!= ( in @ B @ ( union @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[20620,70]) ).
thf(21678,plain,
in @ ( sk5 @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ),
inference(pattern_uni,[status(thm)],[21677:[bind(A,$thf( singleton @ sk1 )),bind(B,$thf( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ))]]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ~ ( in @ C @ B )
| ( C = A ) ),
inference(cnf,[status(esa)],[29]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ( C = A )
| ~ ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( in @ B @ ( singleton @ A ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(25046,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( in @ ( sk5 @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ) )
!= ( in @ B @ ( singleton @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[21678,37]) ).
thf(25047,plain,
( ( sk5 @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[25046:[bind(A,$thf( sk1 )),bind(B,$thf( sk5 @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ ( union @ ( singleton @ sk1 ) ) @ ( singleton @ sk1 ) ))]]) ).
thf(37175,plain,
in @ ( sk4 @ sk1 @ ( union @ ( singleton @ sk1 ) ) ) @ sk1,
inference(rewrite,[status(thm)],[21667,25047]) ).
thf(37176,plain,
~ $true,
inference(rewrite,[status(thm)],[20623,37175]) ).
thf(37177,plain,
$false,
inference(simp,[status(thm)],[37176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET890+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n004.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 20:52:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.88/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (105ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.47/1.16 % [INFO] nitpick registered as external prover.
% 1.47/1.16 % [INFO] Scanning for conjecture ...
% 1.67/1.21 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.78/1.23 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.84/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.84/1.26 % [INFO] Type checking passed.
% 1.84/1.26 % [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 ...
% 98.29/14.85 % [INFO] Killing All external provers ...
% 98.29/14.85 % Time passed: 14322ms (effective reasoning time: 13885ms)
% 98.29/14.85 % 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)>
% 98.29/14.85 % Axioms used in derivation (5): d1_tarski, l50_zfmisc_1, d4_tarski, d3_tarski, d10_xboole_0
% 98.29/14.85 % No. of inferences in proof: 60
% 98.29/14.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14322 ms resp. 13885 ms w/o parsing
% 98.29/14.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 98.29/14.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------