TSTP Solution File: SEU634^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 03:43:05 EDT 2024
% Result : Theorem 13.17s 4.01s
% Output : Refutation 13.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 41 ( 12 unt; 11 typ; 3 def)
% Number of atoms : 80 ( 14 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 302 ( 19 ~; 15 |; 2 &; 249 @)
% ( 0 <=>; 17 =>; 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 : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 49 ( 0 ^ 47 !; 2 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetI2_type,type,
subsetI2: $o ).
thf(subsetI2_def,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(setunionE2_type,type,
setunionE2: $o ).
thf(setunionE2_def,definition,
( setunionE2
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(2,negated_conjecture,
~ ( uniqinunit
=> ( subsetI2
=> ( setunionE2
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) )
=> ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(4,plain,
~ ( subset @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[11,4]) ).
thf(335,plain,
~ ( in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ sk3 ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( setunion @ ( setadjoin @ sk3 @ emptyset ) )),bind(B,$thf( sk3 ))]]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[7]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[13,4]) ).
thf(243,plain,
in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( setunion @ ( setadjoin @ sk3 @ emptyset ) )),bind(B,$thf( sk3 ))]]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ B @ ( sk2 @ B @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ B @ ( sk2 @ B @ A ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(695,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( sk2 @ B @ A ) )
| ( ( in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[243,14]) ).
thf(696,plain,
in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) ),
inference(pattern_uni,[status(thm)],[695:[bind(A,$thf( setadjoin @ sk3 @ emptyset )),bind(B,$thf( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ))]]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk2 @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk2 @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( in @ ( sk2 @ B @ A ) @ A )
| ( ( in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[243,10]) ).
thf(347,plain,
in @ ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( setadjoin @ sk3 @ emptyset )),bind(B,$thf( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(557,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( in @ ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ) )
!= ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[347,12]) ).
thf(558,plain,
( ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) )
= sk3 ),
inference(pattern_uni,[status(thm)],[557:[bind(A,$thf( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) )),bind(B,$thf( sk3 ))]]) ).
thf(1064,plain,
in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ sk3,
inference(rewrite,[status(thm)],[696,558]) ).
thf(1065,plain,
~ $true,
inference(rewrite,[status(thm)],[335,1064]) ).
thf(1066,plain,
$false,
inference(simp,[status(thm)],[1065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08 % Problem : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.10 % Command : run_Leo-III %s %d
% 0.11/0.29 % Computer : n010.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sun May 19 15:27:39 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.89/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.07 % [INFO] Parsing done (151ms).
% 1.28/1.08 % [INFO] Running in sequential loop mode.
% 1.86/1.43 % [INFO] nitpick registered as external prover.
% 1.86/1.44 % [INFO] Scanning for conjecture ...
% 2.06/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.13/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.13/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.59 % [INFO] Type checking passed.
% 2.13/1.59 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 13.17/4.01 % [INFO] Killing All external provers ...
% 13.17/4.01 % Time passed: 3559ms (effective reasoning time: 2922ms)
% 13.17/4.01 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.17/4.01 % Axioms used in derivation (0):
% 13.17/4.01 % No. of inferences in proof: 27
% 13.17/4.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3559 ms resp. 2922 ms w/o parsing
% 13.17/4.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.17/4.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------