TSTP Solution File: ANA072^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : ANA072^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 2.66s 1.60s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 15 ( 1 unt; 7 typ; 0 def)
% Number of atoms : 40 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 99 ( 7 ~; 0 |; 9 &; 71 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 22 ( 0 ^ 19 !; 0 ?; 22 :)
% ( 3 !>; 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/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_lt\'_type',type,
'\'const/realax/real_lt\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $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\''] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/realax/real_lt\'' @ ( '\'const/sets/sup\'' @ A ) @ B )
= ( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_lt\'' @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LT_FINITE_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/realax/real_lt\'' @ ( '\'const/sets/sup\'' @ A ) @ B )
= ( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_lt\'' @ C @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: '\'type/realax/real\'' > $o,B: '\'type/realax/real\''] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/realax/real_lt\'' @ ( '\'const/sets/sup\'' @ A ) @ B )
= ( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_lt\'' @ C @ B ) ) ) ) ),
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_lt\'' @ B @ C ) )
=> ( '\'const/realax/real_lt\'' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realarith/REAL_LET_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_lt\'' @ B @ C ) )
=> ( '\'const/realax/real_lt\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/sup\'' @ A ) @ A )
& ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_FINITE_') ).
thf(14,plain,
! [A: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ A )
& ( A
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ ( '\'const/sets/sup\'' @ A ) @ A )
& ! [B: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ B @ A )
=> ( '\'const/realax/real_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
$false,
inference(cvc4,[status(thm)],[5,12,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA072^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n004.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 12:44:09 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/1.00 % [INFO] Parsing done (117ms).
% 1.13/1.01 % [INFO] Running in sequential loop mode.
% 1.72/1.20 % [INFO] eprover registered as external prover.
% 1.72/1.20 % [INFO] cvc4 registered as external prover.
% 1.72/1.20 % [INFO] Scanning for conjecture ...
% 1.86/1.26 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.86/1.28 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.86/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.29 % [INFO] Type checking passed.
% 1.86/1.29 % [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 ...
% 2.66/1.60 % External prover 'cvc4' found a proof!
% 2.66/1.60 % [INFO] Killing All external provers ...
% 2.66/1.60 % Time passed: 1054ms (effective reasoning time: 588ms)
% 2.66/1.60 % 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)>
% 2.66/1.60 % Axioms used in derivation (2): thm/realarith/REAL_LET_TRANS_, thm/sets/SUP_FINITE_
% 2.66/1.60 % No. of inferences in proof: 8
% 2.66/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1054 ms resp. 588 ms w/o parsing
% 2.96/1.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.96/1.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------