TSTP Solution File: ANA086^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ANA086^1 : TPTP v8.2.0. 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 : Mon May 20 18:39:43 EDT 2024
% Result : Theorem 6.29s 2.25s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 3 unt; 10 typ; 0 def)
% Number of atoms : 159 ( 19 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 358 ( 41 ~; 46 |; 7 &; 248 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 56 ( 0 ^ 52 !; 2 ?; 56 :)
% ( 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(sk1_type,type,
sk1: '\'type/realax/real\'' > $o ).
thf(sk2_type,type,
sk2: '\'type/realax/real\'' ).
thf(sk3_type,type,
sk3: ( '\'type/realax/real\'' > $o ) > $o ).
thf(sk4_type,type,
sk4: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(sk5_type,type,
sk5: '\'type/realax/real\'' > ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf(3,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(9,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)],[3]) ).
thf(12,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(18,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'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/REAL_LE_INF_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'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(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
( ( ( A
!= ( '\'const/sets/EMPTY\'' @ '\'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)],[2]) ).
thf(6,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( '\'const/realax/real_le\'' @ sk2 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk5 @ B @ A ) )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(32,plain,
! [C: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o,A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ~ ( sk3 @ B )
| ( '\'const/realax/real_le\'' @ C @ ( '\'const/sets/inf\'' @ B ) )
| ( ( '\'const/realax/real_le\'' @ sk2 @ A )
!= ( '\'const/realax/real_le\'' @ C @ ( sk5 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,15]) ).
thf(33,plain,
! [A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ sk2 @ A ) @ sk1 )
| ~ ( sk3 @ A )
| ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk5 @ sk2 @ E )),bind(B,$thf( E )),bind(C,$thf( sk2 ))]]) ).
thf(36,plain,
! [A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ sk2 @ A ) @ sk1 )
| ~ ( sk3 @ A )
| ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ A ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(274,plain,
! [C: '\'type/realax/real\'' > $o,B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( sk3 @ A )
| ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/inf\'' @ A ) )
| ~ ( sk3 @ C )
| ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ C ) )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ B @ A ) @ A )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk5 @ sk2 @ C ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[18,36]) ).
thf(275,plain,
( ~ ( sk3 @ sk1 )
| ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) )
| ~ ( sk3 @ sk1 )
| ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).
thf(287,plain,
( ~ ( sk3 @ sk1 )
| ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(5,plain,
~ ( '\'const/realax/real_le\'' @ sk2 @ ( '\'const/sets/inf\'' @ sk1 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(19,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
| ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(14,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(16,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(7,plain,
( sk1
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
( sk1
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(65,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ~ ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ A ) )
| ( sk3 @ A )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16,8]) ).
thf(66,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ ( sk4 @ A @ sk1 ) )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( sk1 )),bind(B,$thf( B ))]]) ).
thf(79,plain,
! [A: '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ A @ ( sk4 @ A @ sk1 ) )
| ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[66]) ).
thf(92,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ sk1 )
| ( sk3 @ sk1 )
| ( ( '\'const/realax/real_le\'' @ sk2 @ A )
!= ( '\'const/realax/real_le\'' @ B @ ( sk4 @ B @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,79]) ).
thf(93,plain,
( ~ ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ sk2 @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk4 @ sk2 @ sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(222,plain,
! [B: '\'type/realax/real\'',A: '\'type/realax/real\'' > $o] :
( ( A
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( sk3 @ A )
| ( sk3 @ sk1 )
| ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ B @ A ) @ A )
!= ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( sk4 @ sk2 @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,93]) ).
thf(223,plain,
( ( sk1
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( sk3 @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(233,plain,
( ( sk1
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
| ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[223]) ).
thf(234,plain,
sk3 @ sk1,
inference(simplifyReflect,[status(thm)],[233,8]) ).
thf(310,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[287,5,234]) ).
thf(311,plain,
$false,
inference(simp,[status(thm)],[310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA086^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n009.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 07:58:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.95 % [INFO] Parsing done (104ms).
% 1.18/0.96 % [INFO] Running in sequential loop mode.
% 1.51/1.16 % [INFO] nitpick registered as external prover.
% 1.51/1.16 % [INFO] Scanning for conjecture ...
% 1.67/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.67/1.24 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.67/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.67/1.25 % [INFO] Type checking passed.
% 1.67/1.25 % [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 ...
% 6.29/2.24 % [INFO] Killing All external provers ...
% 6.29/2.24 % Time passed: 1721ms (effective reasoning time: 1276ms)
% 6.29/2.24 % 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)>
% 6.29/2.25 % Axioms used in derivation (1): thm/sets/INF_
% 6.29/2.25 % No. of inferences in proof: 34
% 6.29/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1721 ms resp. 1276 ms w/o parsing
% 6.29/2.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.29/2.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------