TSTP Solution File: ANA090^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ANA090^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 63.89s 10.14s
% Output : Refutation 63.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 39 ( 11 unt; 13 typ; 0 def)
% Number of atoms : 132 ( 42 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 309 ( 11 ~; 2 |; 15 &; 251 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-4 aty)
% Number of variables : 85 ( 0 ^ 70 !; 10 ?; 85 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'const/sets/sup\'_type',type,
'\'const/sets/sup\'': ( '\'type/realax/real\'' > $o ) > '\'type/realax/real\'' ).
thf('\'const/sets/INSERT\'_type',type,
'\'const/sets/INSERT\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > TA > $o ) ).
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/FINITE\'_type',type,
'\'const/sets/FINITE\'':
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf('\'const/sets/EMPTY\'_type',type,
'\'const/sets/EMPTY\'':
!>[TA: $tType] : ( TA > $o ) ).
thf('\'const/realax/real_neg\'_type',type,
'\'const/realax/real_neg\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_min\'_type',type,
'\'const/realax/real_min\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_max\'_type',type,
'\'const/realax/real_max\'': '\'type/realax/real\'' > '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_le\'_type',type,
'\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).
thf('\'const/realax/real_abs\'_type',type,
'\'const/realax/real_abs\'': '\'type/realax/real\'' > '\'type/realax/real\'' ).
thf('\'const/class/COND\'_type',type,
'\'const/class/COND\'':
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(5,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
=> ( ( '\'const/sets/sup\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
= ( '\'const/class/COND\'' @ '\'type/realax/real\''
@ ( B
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
@ A
@ ( '\'const/realax/real_max\'' @ A @ ( '\'const/sets/sup\'' @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_INSERT_FINITE_') ).
thf(25,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
=> ( ( '\'const/sets/sup\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
= ( '\'const/class/COND\'' @ '\'type/realax/real\''
@ ( B
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
@ A
@ ( '\'const/realax/real_max\'' @ A @ ( '\'const/sets/sup\'' @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [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\'' @ ( '\'const/realax/real_abs\'' @ C ) @ B ) ) )
=> ( ( ( '\'const/sets/sup\'' @ A )
= ( '\'const/sets/inf\'' @ A ) )
= ( ? [B: '\'type/realax/real\''] :
( A
= ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ B @ ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_EQ_INF_') ).
thf(2,negated_conjecture,
~ ! [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\'' @ ( '\'const/realax/real_abs\'' @ C ) @ B ) ) )
=> ( ( ( '\'const/sets/sup\'' @ A )
= ( '\'const/sets/inf\'' @ A ) )
= ( ? [B: '\'type/realax/real\''] :
( A
= ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ B @ ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,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\'' @ ( '\'const/realax/real_abs\'' @ C ) @ B ) ) )
=> ( ( ( '\'const/sets/sup\'' @ A )
= ( '\'const/sets/inf\'' @ A ) )
= ( ? [B: '\'type/realax/real\''] :
( A
= ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ B @ ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
=> ( ( '\'const/sets/inf\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
= ( '\'const/class/COND\'' @ '\'type/realax/real\''
@ ( B
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
@ A
@ ( '\'const/realax/real_min\'' @ A @ ( '\'const/sets/inf\'' @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_INSERT_FINITE_') ).
thf(20,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
=> ( ( '\'const/sets/inf\'' @ ( '\'const/sets/INSERT\'' @ '\'type/realax/real\'' @ A @ B ) )
= ( '\'const/class/COND\'' @ '\'type/realax/real\''
@ ( B
= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) )
@ A
@ ( '\'const/realax/real_min\'' @ A @ ( '\'const/sets/inf\'' @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,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\'' @ C @ B ) ) )
=> ( ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) )
& ! [B: '\'type/realax/real\''] :
( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ C @ B ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/sup\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_') ).
thf(53,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\'' @ C @ B ) ) )
=> ( ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) )
& ! [B: '\'type/realax/real\''] :
( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ C @ B ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/sets/sup\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ A ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(64,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( ( '\'const/realax/real_le\'' @ A @ B )
& ( '\'const/realax/real_le\'' @ B @ A ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_') ).
thf(39,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)],[10]) ).
thf(11,axiom,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ A ) @ B )
= ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A )
& ( '\'const/realax/real_le\'' @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/real/REAL_ABS_BOUNDS_') ).
thf(50,plain,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_abs\'' @ A ) @ B )
= ( ( '\'const/realax/real_le\'' @ ( '\'const/realax/real_neg\'' @ B ) @ A )
& ( '\'const/realax/real_le\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [TA: $tType] : ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/EMPTY\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FINITE_EMPTY_') ).
thf(23,plain,
! [TA: $tType] : ( '\'const/sets/FINITE\'' @ TA @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/NOT_IN_EMPTY_') ).
thf(28,plain,
! [TA: $tType,A: TA] :
~ ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/EMPTY\'' @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_') ).
thf(33,plain,
! [TA: $tType,A: TA > $o,B: TA] :
( ( '\'const/sets/IN\'' @ TA @ B @ A )
= ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/EXTENSION_') ).
thf(36,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
= ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_INSERT_') ).
thf(30,plain,
! [TA: $tType,A: TA,B: TA,C: TA > $o] :
( ( '\'const/sets/IN\'' @ TA @ A @ ( '\'const/sets/INSERT\'' @ TA @ B @ C ) )
= ( ( A = B )
| ( '\'const/sets/IN\'' @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9159,plain,
$false,
inference(e,[status(thm)],[25,14,20,53,64,39,50,23,28,33,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA090^1 : TPTP v8.2.0. Released v7.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n029.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 07:43:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (123ms).
% 1.44/1.01 % [INFO] Running in sequential loop mode.
% 1.79/1.23 % [INFO] eprover registered as external prover.
% 1.79/1.23 % [INFO] cvc4 registered as external prover.
% 1.79/1.23 % [INFO] Scanning for conjecture ...
% 1.90/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.90/1.32 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.17/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.17/1.35 % [INFO] Type checking passed.
% 2.17/1.36 % [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 ...
% 63.89/10.14 % External prover 'e' found a proof!
% 63.89/10.14 % [INFO] Killing All external provers ...
% 63.89/10.14 % Time passed: 9611ms (effective reasoning time: 9130ms)
% 63.89/10.14 % 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)>
% 63.89/10.14 % Axioms used in derivation (11): thm/sets/IN_INSERT_, thm/real/REAL_ABS_BOUNDS_, thm/sets/EXTENSION_, thm/sets/SUP_, thm/sets/IN_, thm/sets/SUP_INSERT_FINITE_, thm/sets/NOT_IN_EMPTY_, thm/sets/INF_INSERT_FINITE_, thm/sets/INF_, thm/realax/REAL_LE_ANTISYM_, thm/sets/FINITE_EMPTY_
% 63.89/10.14 % No. of inferences in proof: 26
% 63.89/10.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9611 ms resp. 9130 ms w/o parsing
% 63.99/10.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.99/10.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------