TSTP Solution File: ANA091^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ANA091^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 May 20 18:39:16 EDT 2024
% Result : Theorem 3.00s 1.73s
% Output : Refutation 3.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 15 ( 3 unt; 5 typ; 0 def)
% Number of atoms : 48 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 135 ( 6 ~; 0 |; 12 &; 99 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-3 aty)
% Number of variables : 41 ( 0 ^ 35 !; 4 ?; 41 :)
% ( 2 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'const/sets/inf\'_type',type,
'\'const/sets/inf\'': ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/realax/real_le\'_type',type,
'\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).
thf(1,conjecture,
! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\'',C: '\'type/realax/real\'',D: '\'type/realax/real\''] :
( ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ A )
& ( '\'const/realax/real_le\'' @ D @ C )
& ! [E: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ E @ A )
=> ( '\'const/realax/real_le\'' @ B @ E ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\'',C: '\'type/realax/real\'',D: '\'type/realax/real\''] :
( ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ A )
& ( '\'const/realax/real_le\'' @ D @ C )
& ! [E: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ E @ A )
=> ( '\'const/realax/real_le\'' @ B @ E ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\'',C: '\'type/realax/real\'',D: '\'type/realax/real\''] :
( ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ D @ A )
& ( '\'const/realax/real_le\'' @ D @ C )
& ! [E: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ E @ A )
=> ( '\'const/realax/real_le\'' @ B @ E ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(12,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
= ( A
!= ( '\'const/sets/EMPTY\'' @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).
thf(14,plain,
! [TA: $tType,A: TA > $o] :
( ( ? [B: TA] : ( '\'const/sets/IN\'' @ TA @ B @ A ) )
= ( A
!= ( '\'const/sets/EMPTY\'' @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: '\'type/realax/real\'' > $o] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [B: '\'type/realax/real\''] :
! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) ) )
=> ( ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
& ! [B: '\'type/realax/real\''] :
( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(17,plain,
! [A: '\'type/realax/real\'' > $o] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
& ? [B: '\'type/realax/real\''] :
! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) ) )
=> ( ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/inf\'' @ A ) @ B ) )
& ! [B: '\'type/realax/real\''] :
( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ B @ C ) )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[6,12,14,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA091^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n021.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 07:46:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.93/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.03 % [INFO] Parsing done (117ms).
% 1.24/1.04 % [INFO] Running in sequential loop mode.
% 1.74/1.23 % [INFO] eprover registered as external prover.
% 1.74/1.24 % [INFO] cvc4 registered as external prover.
% 1.74/1.24 % [INFO] Scanning for conjecture ...
% 1.86/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.86/1.32 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.86/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.33 % [INFO] Type checking passed.
% 1.86/1.34 % [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 ...
% 3.00/1.73 % External prover 'e' found a proof!
% 3.00/1.73 % [INFO] Killing All external provers ...
% 3.00/1.73 % Time passed: 1184ms (effective reasoning time: 689ms)
% 3.00/1.73 % 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)>
% 3.00/1.73 % Axioms used in derivation (3): thm/realax/REAL_LE_TRANS_, thm/sets/MEMBER_NOT_EMPTY_, thm/sets/INF_
% 3.00/1.73 % No. of inferences in proof: 10
% 3.00/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1184 ms resp. 689 ms w/o parsing
% 3.24/1.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.24/1.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------