TSTP Solution File: SEV486^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% 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 : Mon Jun 24 16:00:22 EDT 2024
% Result : Theorem 3.12s 1.71s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 11 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 190 ( 10 ~; 3 |; 5 &; 172 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-4 aty)
% Number of variables : 55 ( 12 ^ 31 !; 12 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
thf('\'const/sets/SETSPEC\'_type',type,
'\'const/sets/SETSPEC\'':
!>[TA: $tType] : ( TA > $o > TA > $o ) ).
thf('\'const/sets/HAS_SIZE\'_type',type,
'\'const/sets/HAS_SIZE\'':
!>[TA: $tType] : ( ( TA > $o ) > '\'type/nums/num\'' > $o ) ).
thf('\'const/sets/GSPEC\'_type',type,
'\'const/sets/GSPEC\'':
!>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).
thf('\'const/sets/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/sets/CARD\'_type',type,
'\'const/sets/CARD\'':
!>[TA: $tType] : ( ( TA > $o ) > '\'type/nums/num\'' ) ).
thf('\'const/arith/<\'_type',type,
'\'const/arith/<\'': '\'type/nums/num\'' > '\'type/nums/num\'' > $o ).
thf(sk1_type,type,
sk1: '\'type/nums/num\'' ).
thf(3,axiom,
! [A: '\'type/nums/num\''] :
( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
@ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_NUMSEG_LT_') ).
thf(7,plain,
! [A: '\'type/nums/num\''] :
( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
@ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,plain,
! [A: '\'type/nums/num\''] :
( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) )
@ A ),
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
= ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/HAS_SIZE_') ).
thf(9,plain,
! [TA: $tType,A: TA > $o,B: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
= ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
= ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) )
= ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ( ( '\'const/sets/CARD\'' @ TA @ A )
= B ) )
| ~ ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B ) ),
inference(bool_ext,[status(thm)],[11]) ).
thf(18,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ~ ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
| ( '\'const/sets/FINITE\'' @ TA @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(1,conjecture,
! [A: '\'type/nums/num\''] :
( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_NUMSEG_LT_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/nums/num\''] :
( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/nums/num\''] :
( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [A: '\'type/nums/num\''] :
? [B: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ A @ ( '\'const/arith/<\'' @ B @ sk1 ) @ B ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(20,plain,
! [TA: $tType,B: '\'type/nums/num\'',A: TA > $o] :
( ~ ( '\'const/sets/HAS_SIZE\'' @ TA @ A @ B )
| ( ( '\'const/sets/FINITE\'' @ TA @ A )
!= ( '\'const/sets/FINITE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [C: '\'type/nums/num\''] :
? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ sk1 ) @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,6]) ).
thf(21,plain,
! [A: '\'type/nums/num\''] :
~ ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ sk1 ) @ C ) )
@ A ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( '\'const/sets/GSPEC\'' @ '\'type/nums/num\'' @ ^ [C: '\'type/nums/num\''] : ? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ sk1 ) @ D ) )),bind(B,$thf( B )),bind_type(TA,$thf( '\'type/nums/num\'' ))]]) ).
thf(26,plain,
! [A: '\'type/nums/num\''] :
~ ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [B: '\'type/nums/num\''] :
? [C: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ B @ ( '\'const/arith/<\'' @ C @ sk1 ) @ C ) )
@ A ),
inference(simp,[status(thm)],[21]) ).
thf(28,plain,
! [B: '\'type/nums/num\'',A: '\'type/nums/num\''] :
( ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [C: '\'type/nums/num\''] :
? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ A ) @ D ) )
@ A )
!= ( '\'const/sets/HAS_SIZE\'' @ '\'type/nums/num\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/nums/num\''
@ ^ [C: '\'type/nums/num\''] :
? [D: '\'type/nums/num\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/nums/num\'' @ C @ ( '\'const/arith/<\'' @ D @ sk1 ) @ D ) )
@ B ) ),
inference(paramod_ordered,[status(thm)],[8,26]) ).
thf(29,plain,
$false,
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEV486^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.11 % Command : run_Leo-III %s %d SAT
% 0.12/0.32 % Computer : n026.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 18:49:55 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (109ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.59/1.18 % [INFO] nitpick registered as external prover.
% 1.59/1.19 % [INFO] Scanning for conjecture ...
% 1.83/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.83/1.26 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.83/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.83/1.27 % [INFO] Type checking passed.
% 1.83/1.28 % [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 ...
% 3.12/1.70 % [INFO] Killing All external provers ...
% 3.12/1.70 % Time passed: 1185ms (effective reasoning time: 721ms)
% 3.12/1.70 % 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)>
% 3.12/1.71 % Axioms used in derivation (2): thm/sets/HAS_SIZE_NUMSEG_LT_, thm/sets/HAS_SIZE_
% 3.12/1.71 % No. of inferences in proof: 18
% 3.12/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1185 ms resp. 721 ms w/o parsing
% 3.12/1.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.12/1.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------