TSTP Solution File: SEU805^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:43:52 EDT 2024
% Result : Theorem 27.58s 5.64s
% Output : Refutation 27.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 51 ( 14 unt; 11 typ; 4 def)
% Number of atoms : 108 ( 35 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 299 ( 39 ~; 25 |; 9 &; 208 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 1 ^ 48 !; 13 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(foundationAx_type,type,
foundationAx: $o ).
thf(foundationAx_def,definition,
( foundationAx
= ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(nonempty_type,type,
nonempty: $i > $o ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(nonemptyE1_type,type,
nonemptyE1: $o ).
thf(nonemptyE1_def,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] : ( in @ B @ A ) ) ) ) ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(disjointsetsI1_type,type,
disjointsetsI1: $o ).
thf(disjointsetsI1_def,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ( ( binintersect @ B @ A )
= emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundation2) ).
thf(2,negated_conjecture,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ( ( binintersect @ B @ A )
= emptyset ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) )
=> ( ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] :
( ( in @ B @ A )
& ( ( binintersect @ B @ A )
= emptyset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( in @ ( sk3 @ B @ A ) @ A )
| ( ( binintersect @ A @ B )
= emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( ( binintersect @ A @ B )
= emptyset )
| ( in @ ( sk3 @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( ( binintersect @ A @ B )
= emptyset )
| ( in @ ( sk3 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[11]) ).
thf(10,plain,
! [A: $i] :
( ( A = emptyset )
| ( in @ ( sk2 @ A ) @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [A: $i] :
( ( A = emptyset )
| ( in @ ( sk2 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(14,plain,
! [A: $i] :
( ( A = emptyset )
| ( in @ ( sk2 @ A ) @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(6,plain,
sk4 != emptyset,
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
sk4 != emptyset,
inference(lifteq,[status(thm)],[6]) ).
thf(30,plain,
! [A: $i] :
( ( in @ ( sk2 @ A ) @ A )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[14,15]) ).
thf(31,plain,
in @ ( sk2 @ sk4 ) @ sk4,
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk4 ))]]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( in @ ( sk1 @ A ) @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ A ) @ A )
| ( ( in @ ( sk2 @ sk4 ) @ sk4 )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,4]) ).
thf(97,plain,
in @ ( sk1 @ sk4 ) @ sk4,
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 @ sk4 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( in @ A @ sk4 )
| ( ( binintersect @ A @ sk4 )
!= emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [A: $i] :
( ( ( binintersect @ A @ sk4 )
!= emptyset )
| ~ ( in @ A @ sk4 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(19,plain,
! [A: $i] :
( ( ( binintersect @ A @ sk4 )
!= emptyset )
| ~ ( in @ A @ sk4 ) ),
inference(simp,[status(thm)],[18]) ).
thf(120,plain,
! [A: $i] :
( ( ( binintersect @ A @ sk4 )
!= emptyset )
| ( ( in @ ( sk1 @ sk4 ) @ sk4 )
!= ( in @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[97,19]) ).
thf(121,plain,
( ( binintersect @ ( sk1 @ sk4 ) @ sk4 )
!= emptyset ),
inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk1 @ sk4 ))]]) ).
thf(284,plain,
! [B: $i,A: $i] :
( ( in @ ( sk3 @ B @ A ) @ A )
| ( ( binintersect @ A @ B )
!= ( binintersect @ ( sk1 @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[12,121]) ).
thf(285,plain,
in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ ( sk1 @ sk4 ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ A )
| ~ ( in @ C @ ( sk1 @ A ) )
| ~ ( in @ C @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( sk1 @ A ) )
| ~ ( in @ C @ A )
| ( ( in @ ( sk2 @ sk4 ) @ sk4 )
!= ( in @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,7]) ).
thf(61,plain,
! [A: $i] :
( ~ ( in @ A @ ( sk1 @ sk4 ) )
| ~ ( in @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 @ sk4 )),bind(C,$thf( C ))]]) ).
thf(82,plain,
! [A: $i] :
( ~ ( in @ A @ ( sk1 @ sk4 ) )
| ~ ( in @ A @ sk4 ) ),
inference(simp,[status(thm)],[61]) ).
thf(2383,plain,
! [A: $i] :
( ~ ( in @ A @ sk4 )
| ( ( in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ ( sk1 @ sk4 ) )
!= ( in @ A @ ( sk1 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,82]) ).
thf(2384,plain,
~ ( in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ sk4 ),
inference(pattern_uni,[status(thm)],[2383:[bind(A,$thf( sk3 @ sk4 @ ( sk1 @ sk4 ) ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( in @ ( sk3 @ B @ A ) @ B )
| ( ( binintersect @ A @ B )
= emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [B: $i,A: $i] :
( ( ( binintersect @ A @ B )
= emptyset )
| ( in @ ( sk3 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( binintersect @ A @ B )
= emptyset )
| ( in @ ( sk3 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[16]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( in @ ( sk3 @ B @ A ) @ B )
| ( ( binintersect @ A @ B )
!= ( binintersect @ ( sk1 @ sk4 ) @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17,121]) ).
thf(449,plain,
in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ sk4,
inference(pattern_uni,[status(thm)],[448:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( sk4 ))]]) ).
thf(2921,plain,
~ $true,
inference(rewrite,[status(thm)],[2384,449]) ).
thf(2922,plain,
$false,
inference(simp,[status(thm)],[2921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.11 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n015.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 18:16:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.89/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.08 % [INFO] Parsing done (164ms).
% 1.30/1.10 % [INFO] Running in sequential loop mode.
% 1.82/1.45 % [INFO] nitpick registered as external prover.
% 1.82/1.45 % [INFO] Scanning for conjecture ...
% 2.08/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.60 % [INFO] Type checking passed.
% 2.08/1.60 % [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 ...
% 26.82/5.62 % [INFO] Killing All external provers ...
% 27.58/5.63 % Time passed: 5167ms (effective reasoning time: 4525ms)
% 27.58/5.63 % 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)>
% 27.58/5.63 % Axioms used in derivation (0):
% 27.58/5.63 % No. of inferences in proof: 36
% 27.58/5.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5167 ms resp. 4525 ms w/o parsing
% 27.74/5.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.74/5.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------