TSTP Solution File: SEU534^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 03:42:33 EDT 2024
% Result : Theorem 3.86s 2.22s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 31 ( 14 unt; 8 typ; 2 def)
% Number of atoms : 56 ( 11 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 158 ( 17 ~; 10 |; 4 &; 104 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 0 ^ 38 !; 5 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_type,type,
dsetconstrI: $o ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [A: $i,B: $i > $o] :
( ? [C: $i] :
( ( in @ C @ A )
& ( B @ C ) )
=> ( ( ( dsetconstr @ A @ B )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(2,negated_conjecture,
~ ( dsetconstrI
=> ( emptysetE
=> ! [A: $i,B: $i > $o] :
( ? [C: $i] :
( ( in @ C @ A )
& ( B @ C ) )
=> ( ( ( dsetconstr @ A @ B )
= emptyset )
=> $false ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ! [A: $i,B: $i > $o] :
( ? [C: $i] :
( ( in @ C @ A )
& ( B @ C ) )
=> ( ( dsetconstr @ A @ B )
!= emptyset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ! [A: $i,B: $i > $o] :
( ? [C: $i] :
( ( in @ C @ A )
& ( B @ C ) )
=> ( ( dsetconstr @ A @ B )
!= emptyset ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(9,plain,
sk2 @ sk3,
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
in @ sk3 @ sk1,
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ A )
| ~ ( B @ C )
| ( in @ C @ ( dsetconstr @ A @ B ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(46,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( B @ C )
| ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( in @ sk3 @ sk1 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(47,plain,
! [A: $i > $o] :
( ~ ( A @ sk3 )
| ( in @ sk3 @ ( dsetconstr @ sk1 @ A ) ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(70,plain,
! [A: $i > $o] :
( ~ ( A @ sk3 )
| ( in @ sk3 @ ( dsetconstr @ sk1 @ A ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(92,plain,
! [A: $i > $o] :
( ( in @ sk3 @ ( dsetconstr @ sk1 @ A ) )
| ( ( sk2 @ sk3 )
!= ( A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[9,70]) ).
thf(111,plain,
in @ sk3 @ ( dsetconstr @ sk1 @ sk2 ),
inference(pre_uni,[status(thm)],[92:[bind(A,$thf( sk2 ))]]) ).
thf(5,plain,
( ( dsetconstr @ sk1 @ sk2 )
= emptyset ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
( ( dsetconstr @ sk1 @ sk2 )
= emptyset ),
inference(lifteq,[status(thm)],[5]) ).
thf(134,plain,
in @ sk3 @ emptyset,
inference(rewrite,[status(thm)],[111,10]) ).
thf(6,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(simp,[status(thm)],[6]) ).
thf(16,plain,
! [A: $i] :
( ~ ( in @ A @ emptyset )
| $false ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( A )),bind(B,$thf( $false ))]]) ).
thf(24,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[16]) ).
thf(135,plain,
! [A: $i] :
( ( in @ sk3 @ emptyset )
!= ( in @ A @ emptyset ) ),
inference(paramod_ordered,[status(thm)],[134,24]) ).
thf(136,plain,
$false,
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk3 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU534^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n026.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Sun May 19 15:46:08 EDT 2024
% 0.17/0.38 % CPUTime :
% 1.05/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.06 % [INFO] Parsing done (121ms).
% 1.41/1.07 % [INFO] Running in sequential loop mode.
% 1.80/1.37 % [INFO] nitpick registered as external prover.
% 1.80/1.38 % [INFO] Scanning for conjecture ...
% 2.09/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.49 % [INFO] Type checking passed.
% 2.09/1.49 % [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 ...
% 3.77/2.22 % [INFO] Killing All external provers ...
% 3.86/2.22 % Time passed: 1675ms (effective reasoning time: 1141ms)
% 3.86/2.22 % 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)>
% 3.86/2.22 % Axioms used in derivation (0):
% 3.86/2.22 % No. of inferences in proof: 21
% 3.86/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1675 ms resp. 1141 ms w/o parsing
% 3.87/2.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.87/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------