TSTP Solution File: SEU820^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 03:43:57 EDT 2024
% Result : Theorem 6.27s 2.64s
% Output : Refutation 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 64 ( 14 unt; 16 typ; 4 def)
% Number of atoms : 146 ( 21 equ; 0 cnn)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 275 ( 47 ~; 55 |; 7 &; 140 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 15 con; 0-2 aty)
% Number of variables : 39 ( 1 ^ 37 !; 1 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf(vacuousDall_def,definition,
( vacuousDall
= ( ! [A: $i > $o,B: $i] :
( ( in @ B @ emptyset )
=> ( A @ B ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf(subsetemptysetimpeq_def,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf(powersetE1_type,type,
powersetE1: $o ).
thf(powersetE1_def,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ) ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(ordinal_def,definition,
( ordinal
= ( ^ [A: $i] :
( ( transitiveset @ A )
& ( wellorderedByIn @ A ) ) ) ) ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: $o ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(1,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetOrdinal) ).
thf(2,negated_conjecture,
~ ( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o,B: $i] :
( ( in @ B @ emptyset )
=> ( A @ B ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ( subset @ A @ emptyset ) )
& ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ! [C: $i] :
( ( in @ C @ emptyset )
=> ( ( ( in @ A @ B )
& ( in @ B @ C ) )
=> ( in @ A @ C ) ) ) ) )
& ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $i] :
( ( in @ B @ emptyset )
=> ( ( A = B )
| ( in @ A @ B )
| ( in @ B @ A ) ) ) )
& ! [A: $i] :
( ( in @ A @ emptyset )
=> ~ ( in @ A @ A ) )
& ! [A: $i] :
( ( in @ A @ ( powerset @ emptyset ) )
=> ( ( A != emptyset )
=> ? [B: $i] :
( ( in @ B @ A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( B = C )
| ( in @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
( sk1
| sk3
| ( in @ sk11 @ ( powerset @ emptyset ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
( ( in @ sk2 @ emptyset )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(25,plain,
! [B: $i,A: $i > $o] :
( ~ ( in @ B @ emptyset )
| ( A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(58,plain,
! [B: $i,A: $i > $o] :
( ~ sk1
| ( A @ B )
| ( ( in @ sk2 @ emptyset )
!= ( in @ B @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[16,25]) ).
thf(59,plain,
! [A: $i > $o] :
( ~ sk1
| ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(11,plain,
( ~ ( subset @ sk2 @ emptyset )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(147,plain,
! [A: $i > $o] :
( ~ sk1
| ( ( A @ sk2 )
!= ( subset @ sk2 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[59,11]) ).
thf(162,plain,
~ sk1,
inference(pre_uni,[status(thm)],[147:[bind(A,$thf( ^ [B: $i] : ( subset @ sk2 @ emptyset ) ))]]) ).
thf(183,plain,
( $false
| sk3
| ( in @ sk11 @ ( powerset @ emptyset ) ) ),
inference(rewrite,[status(thm)],[24,162]) ).
thf(184,plain,
( sk3
| ( in @ sk11 @ ( powerset @ emptyset ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(22,plain,
( sk1
| sk4
| ( in @ sk8 @ emptyset )
| ( in @ sk10 @ emptyset )
| ~ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(76,plain,
! [A: $i] :
( ~ ( in @ A @ emptyset )
| $false ),
inference(prim_subst,[status(thm)],[25:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(99,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[76]) ).
thf(322,plain,
( $false
| sk4
| $false
| $false
| ~ sk3 ),
inference(rewrite,[status(thm)],[22,162,99]) ).
thf(323,plain,
( sk4
| ~ sk3 ),
inference(simp,[status(thm)],[322]) ).
thf(6,plain,
( sk1
| ( in @ sk7 @ emptyset )
| ~ sk4
| ~ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(226,plain,
( $false
| ( in @ sk7 @ emptyset )
| ~ sk4
| ~ sk3 ),
inference(rewrite,[status(thm)],[6,162]) ).
thf(227,plain,
( ( in @ sk7 @ emptyset )
| ~ sk4
| ~ sk3 ),
inference(simp,[status(thm)],[226]) ).
thf(246,plain,
( $false
| ~ sk4
| ~ sk3 ),
inference(rewrite,[status(thm)],[227,99]) ).
thf(247,plain,
( ~ sk4
| ~ sk3 ),
inference(simp,[status(thm)],[246]) ).
thf(324,plain,
( ~ sk3
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[323,247]) ).
thf(325,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[324:[]]) ).
thf(328,plain,
( $false
| ( in @ sk11 @ ( powerset @ emptyset ) ) ),
inference(rewrite,[status(thm)],[184,325]) ).
thf(329,plain,
in @ sk11 @ ( powerset @ emptyset ),
inference(simp,[status(thm)],[328]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( subset @ B @ A )
| ( ( in @ sk11 @ ( powerset @ emptyset ) )
!= ( in @ B @ ( powerset @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[329,32]) ).
thf(463,plain,
subset @ sk11 @ emptyset,
inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( emptyset )),bind(B,$thf( sk11 ))]]) ).
thf(23,plain,
! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(38,plain,
! [A: $i] :
( ( A = emptyset )
| ~ ( subset @ A @ emptyset ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(39,plain,
! [A: $i] :
( ( A = emptyset )
| ~ ( subset @ A @ emptyset ) ),
inference(simp,[status(thm)],[38]) ).
thf(5,plain,
( sk1
| sk3
| ( sk11 != emptyset ) ),
inference(cnf,[status(esa)],[3]) ).
thf(30,plain,
( ( sk11 != emptyset )
| sk1
| sk3 ),
inference(lifteq,[status(thm)],[5]) ).
thf(273,plain,
( ( sk11 != emptyset )
| $false
| sk3 ),
inference(rewrite,[status(thm)],[30,162]) ).
thf(274,plain,
( ( sk11 != emptyset )
| sk3 ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [A: $i] :
( ~ ( subset @ A @ emptyset )
| sk3
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[39,274]) ).
thf(276,plain,
( ~ ( subset @ sk11 @ emptyset )
| sk3 ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk11 ))]]) ).
thf(326,plain,
( ~ ( subset @ sk11 @ emptyset )
| $false ),
inference(rewrite,[status(thm)],[276,325]) ).
thf(327,plain,
~ ( subset @ sk11 @ emptyset ),
inference(simp,[status(thm)],[326]) ).
thf(485,plain,
$false,
inference(rewrite,[status(thm)],[463,327]) ).
thf(486,plain,
$false,
inference(simp,[status(thm)],[485]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SEU820^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.17 % Command : run_Leo-III %s %d
% 0.17/0.39 % Computer : n028.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Sun May 19 17:12:39 EDT 2024
% 0.17/0.39 % CPUTime :
% 0.99/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.05 % [INFO] Parsing done (127ms).
% 1.29/1.06 % [INFO] Running in sequential loop mode.
% 1.76/1.35 % [INFO] nitpick registered as external prover.
% 1.76/1.36 % [INFO] Scanning for conjecture ...
% 1.88/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.49 % [INFO] Type checking passed.
% 2.24/1.50 % [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 ...
% 6.27/2.63 % [INFO] Killing All external provers ...
% 6.27/2.64 % Time passed: 2070ms (effective reasoning time: 1571ms)
% 6.27/2.64 % 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)>
% 6.27/2.64 % Axioms used in derivation (0):
% 6.27/2.64 % No. of inferences in proof: 44
% 6.27/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2070 ms resp. 1571 ms w/o parsing
% 6.27/2.68 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.27/2.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------