TSTP Solution File: SEU633^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU633^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 03:43:04 EDT 2024
% Result : Theorem 4.24s 2.00s
% Output : Refutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 7 unt; 6 typ; 1 def)
% Number of atoms : 56 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 175 ( 17 ~; 15 |; 3 &; 126 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 0 ^ 31 !; 3 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(setunionE_type,type,
setunionE: $o ).
thf(setunionE_def,definition,
( setunionE
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) ) ) ) ).
thf(sk1_type,type,
sk1: $o > $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( setunionE
=> ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(2,negated_conjecture,
~ ( setunionE
=> ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) )
=> ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ? [C: $i] :
( ( in @ C @ A )
& ( in @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ B @ ( sk1 @ C @ B @ A ) )
| C ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
in @ sk3 @ ( setunion @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A )
| C ),
inference(cnf,[status(esa)],[3]) ).
thf(27,plain,
! [C: $o,B: $i,A: $i] :
( ( in @ ( sk1 @ C @ B @ A ) @ A )
| C
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ B @ ( setunion @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,4]) ).
thf(28,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ sk3 @ sk2 ) @ sk2 )
| A ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(59,plain,
! [A: $o] :
( ( in @ ( sk1 @ A @ sk3 @ sk2 ) @ sk2 )
| A ),
inference(simp,[status(thm)],[28]) ).
thf(110,plain,
( ( in @ ( sk1 @ $false @ sk3 @ sk2 ) @ sk2 )
| $false ),
inference(prim_subst,[status(thm)],[59:[bind(A,$thf( $false ))]]) ).
thf(123,plain,
in @ ( sk1 @ $false @ sk3 @ sk2 ) @ sk2,
inference(simp,[status(thm)],[110]) ).
thf(8,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ sk3 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ sk3 @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(135,plain,
! [A: $i] :
( ~ ( in @ sk3 @ A )
| ( ( in @ ( sk1 @ $false @ sk3 @ sk2 ) @ sk2 )
!= ( in @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[123,9]) ).
thf(136,plain,
~ ( in @ sk3 @ ( sk1 @ $false @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk1 @ $false @ sk3 @ sk2 ))]]) ).
thf(153,plain,
! [C: $o,B: $i,A: $i] :
( ~ ( in @ B @ ( setunion @ A ) )
| C
| ( ( in @ B @ ( sk1 @ C @ B @ A ) )
!= ( in @ sk3 @ ( sk1 @ $false @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5,136]) ).
thf(154,plain,
( ~ ( in @ sk3 @ ( setunion @ sk2 ) )
| $false ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( $false ))]]) ).
thf(165,plain,
~ ( in @ sk3 @ ( setunion @ sk2 ) ),
inference(simp,[status(thm)],[154]) ).
thf(166,plain,
~ $true,
inference(rewrite,[status(thm)],[165,6]) ).
thf(167,plain,
$false,
inference(simp,[status(thm)],[166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU633^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n025.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 : Sun May 19 16:50:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.02 % [INFO] Parsing done (112ms).
% 1.27/1.03 % [INFO] Running in sequential loop mode.
% 1.66/1.25 % [INFO] nitpick registered as external prover.
% 1.66/1.25 % [INFO] Scanning for conjecture ...
% 1.66/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.93/1.33 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.93/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.33 % [INFO] Type checking passed.
% 1.93/1.33 % [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 ...
% 4.24/2.00 % [INFO] Killing All external provers ...
% 4.24/2.00 % Time passed: 1489ms (effective reasoning time: 966ms)
% 4.24/2.00 % 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)>
% 4.24/2.00 % Axioms used in derivation (0):
% 4.24/2.00 % No. of inferences in proof: 20
% 4.24/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1489 ms resp. 966 ms w/o parsing
% 4.24/2.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.24/2.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------