TSTP Solution File: ANA068^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ANA068^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 7 07:27:49 EDT 2024
% Result : Theorem 3.49s 1.68s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 20 ( 3 unt; 8 typ; 0 def)
% Number of atoms : 31 ( 2 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 69 ( 6 ~; 0 |; 2 &; 59 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 26 ( 2 ^ 16 !; 2 ?; 26 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'const/sets/UNIV\'_type',type,
'\'const/sets/UNIV\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/sets/SUBSET\'_type',type,
'\'const/sets/SUBSET\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf('\'const/sets/SETSPEC\'_type',type,
'\'const/sets/SETSPEC\'':
!>[TA: $tType] : ( TA > $o > TA > $o ) ).
thf('\'const/sets/INFINITE\'_type',type,
'\'const/sets/INFINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $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/realax/real_le\'_type',type,
'\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).
thf(5,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/sets/FINITE\'' @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_') ).
thf(13,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ B )
& ( '\'const/sets/SUBSET\'' @ TA @ A @ B ) )
=> ( '\'const/sets/FINITE\'' @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
'\'const/sets/INFINITE\'' @ '\'type/realax/real\'' @ ( '\'const/sets/UNIV\'' @ '\'type/realax/real\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/real_INFINITE_') ).
thf(2,negated_conjecture,
~ ( '\'const/sets/INFINITE\'' @ '\'type/realax/real\'' @ ( '\'const/sets/UNIV\'' @ '\'type/realax/real\'' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( '\'const/sets/INFINITE\'' @ '\'type/realax/real\'' @ ( '\'const/sets/UNIV\'' @ '\'type/realax/real\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o] : ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNIV_') ).
thf(11,plain,
! [TA: $tType,A: TA > $o] : ( '\'const/sets/SUBSET\'' @ TA @ A @ ( '\'const/sets/UNIV\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: '\'type/realax/real\''] :
~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/realax/real\''
@ ^ [B: '\'type/realax/real\''] :
? [C: '\'type/realax/real\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/realax/real\'' @ B @ ( '\'const/realax/real_le\'' @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_REAL_INTERVAL_1') ).
thf(8,plain,
! [A: '\'type/realax/real\''] :
~ ( '\'const/sets/FINITE\'' @ '\'type/realax/real\''
@ ( '\'const/sets/GSPEC\'' @ '\'type/realax/real\''
@ ^ [B: '\'type/realax/real\''] :
? [C: '\'type/realax/real\''] : ( '\'const/sets/SETSPEC\'' @ '\'type/realax/real\'' @ B @ ( '\'const/realax/real_le\'' @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INFINITE\'' @ TA @ A )
= ( ~ ( '\'const/sets/FINITE\'' @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INFINITE_') ).
thf(15,plain,
! [TA: $tType,A: TA > $o] :
( ( '\'const/sets/INFINITE\'' @ TA @ A )
= ( ~ ( '\'const/sets/FINITE\'' @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[13,7,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : ANA068^1 : TPTP v8.1.2. Released v7.0.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n009.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 : Mon May 6 12:46:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.89/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.95 % [INFO] Parsing done (110ms).
% 1.24/0.96 % [INFO] Running in sequential loop mode.
% 1.66/1.16 % [INFO] eprover registered as external prover.
% 1.66/1.16 % [INFO] cvc4 registered as external prover.
% 1.66/1.17 % [INFO] Scanning for conjecture ...
% 1.77/1.21 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.77/1.23 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.77/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.77/1.25 % [INFO] Type checking passed.
% 1.77/1.25 % [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 ...
% 3.49/1.68 % External prover 'e' found a proof!
% 3.49/1.68 % [INFO] Killing All external provers ...
% 3.49/1.68 % Time passed: 1139ms (effective reasoning time: 719ms)
% 3.49/1.68 % 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)>
% 3.49/1.68 % Axioms used in derivation (4): thm/sets/FINITE_SUBSET_, thm/sets/SUBSET_UNIV_, thm/sets/FINITE_REAL_INTERVAL_1, thm/sets/INFINITE_
% 3.49/1.68 % No. of inferences in proof: 12
% 3.49/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1139 ms resp. 719 ms w/o parsing
% 3.49/1.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.49/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------