TSTP Solution File: SEU633^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : n029.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 03:38:43 EDT 2024
% Result : Theorem 3.72s 1.87s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 4 unt; 6 typ; 1 def)
% Number of atoms : 60 ( 17 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 161 ( 32 ~; 18 |; 3 &; 94 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 27 ( 0 ^ 24 !; 3 ?; 27 :)
% 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/sandbox/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(6,plain,
in @ sk3 @ ( setunion @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
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(13,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( ( in @ sk3 @ A )
!= ( in @ A @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(16,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( sk3 != A )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[13]) ).
thf(17,plain,
( ~ ( in @ sk3 @ sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16]) ).
thf(11,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(12,plain,
~ ( in @ ( setunion @ sk2 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( setunion @ sk2 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ ( in @ sk3 @ A )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(14,plain,
! [A: $i] :
( ~ ( in @ sk3 @ A )
| ( sk3 != A )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[10]) ).
thf(18,plain,
( ~ ( in @ sk3 @ sk3 )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[14]) ).
thf(21,plain,
( ( sk3 != sk2 )
| ( ( in @ sk3 @ ( setunion @ sk2 ) )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[6,17]) ).
thf(22,plain,
( ( sk3 != sk2 )
| ( sk3 != sk3 )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
( ( sk3 != sk2 )
| ( ( setunion @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[22]) ).
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(101,plain,
$false,
inference(e,[status(thm)],[6,9,17,12,3,18,23,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU633^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 16:50:39 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (102ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.46/1.17 % [INFO] eprover registered as external prover.
% 1.46/1.17 % [INFO] cvc4 registered as external prover.
% 1.46/1.18 % [INFO] Scanning for conjecture ...
% 1.77/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.86/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.86/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.26 % [INFO] Type checking passed.
% 1.86/1.26 % [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 ...
% 3.72/1.87 % External prover 'e' found a proof!
% 3.72/1.87 % [INFO] Killing All external provers ...
% 3.72/1.87 % Time passed: 1353ms (effective reasoning time: 904ms)
% 3.72/1.87 % 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)>
% 3.72/1.87 % Axioms used in derivation (0):
% 3.72/1.87 % No. of inferences in proof: 19
% 3.72/1.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1353 ms resp. 904 ms w/o parsing
% 3.72/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.72/1.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------