TSTP Solution File: SEV492^1 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV492^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% 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 Jun 24 15:59:10 EDT 2024
% Result : Theorem 3.21s 1.94s
% Output : Refutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 21 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 143 ( 9 ~; 0 |; 16 &; 104 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 33 ( 0 ^ 31 !; 2 ?; 33 :)
% 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_le\'_type',type,
'\'const/realax/real_le\'': '\'type/realax/real\'' > '\'type/realax/real\'' > $o ).
thf(7,axiom,
! [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_le\'' @ ( '\'const/sets/sup\'' @ A ) @ B )
= ( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LE_FINITE_') ).
thf(25,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_le\'' @ ( '\'const/sets/sup\'' @ A ) @ B )
= ( ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
=> ( '\'const/realax/real_le\'' @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,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/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_ANTISYM_') ).
thf(14,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)],[3]) ).
thf(6,axiom,
! [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_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) )
= ( ? [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
& ( '\'const/realax/real_le\'' @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_FINITE_') ).
thf(21,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_le\'' @ B @ ( '\'const/sets/sup\'' @ A ) )
= ( ? [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ A )
& ( '\'const/realax/real_le\'' @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,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(17,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)],[4]) ).
thf(1,conjecture,
! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
& ( B
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( ( '\'const/sets/sup\'' @ B )
= A )
= ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ B )
& ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ B )
=> ( '\'const/realax/real_le\'' @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUP_UNIQUE_FINITE_') ).
thf(2,negated_conjecture,
~ ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
& ( B
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( ( '\'const/sets/sup\'' @ B )
= A )
= ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ B )
& ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ B )
=> ( '\'const/realax/real_le\'' @ C @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: '\'type/realax/real\'',B: '\'type/realax/real\'' > $o] :
( ( ( '\'const/sets/FINITE\'' @ '\'type/realax/real\'' @ B )
& ( B
!= ( '\'const/sets/EMPTY\'' @ '\'type/realax/real\'' ) ) )
=> ( ( ( '\'const/sets/sup\'' @ B )
= A )
= ( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ A @ B )
& ! [C: '\'type/realax/real\''] :
( ( '\'const/sets/IN\'' @ '\'type/realax/real\'' @ C @ B )
=> ( '\'const/realax/real_le\'' @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: '\'type/realax/real\''] : ( '\'const/realax/real_le\'' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realax/REAL_LE_REFL_') ).
thf(19,plain,
! [A: '\'type/realax/real\''] : ( '\'const/realax/real_le\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
$false,
inference(e,[status(thm)],[25,14,21,17,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEV492^1 : TPTP v8.2.0. Released v7.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.09/0.28 % Computer : n021.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Fri Jun 21 18:48:25 EDT 2024
% 0.09/0.28 % CPUTime :
% 1.00/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.11 % [INFO] Parsing done (159ms).
% 1.33/1.12 % [INFO] Running in sequential loop mode.
% 1.82/1.37 % [INFO] eprover registered as external prover.
% 1.82/1.37 % [INFO] Scanning for conjecture ...
% 2.03/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.03/1.46 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.19/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.49 % [INFO] Type checking passed.
% 2.19/1.49 % [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 ...
% 3.21/1.94 % External prover 'e' found a proof!
% 3.21/1.94 % [INFO] Killing All external provers ...
% 3.21/1.94 % Time passed: 1449ms (effective reasoning time: 817ms)
% 3.21/1.94 % 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)>
% 3.21/1.94 % Axioms used in derivation (5): thm/sets/REAL_LE_SUP_FINITE_, thm/realax/REAL_LE_TRANS_, thm/sets/REAL_SUP_LE_FINITE_, thm/realax/REAL_LE_ANTISYM_, thm/realax/REAL_LE_REFL_
% 3.21/1.94 % No. of inferences in proof: 14
% 3.21/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1449 ms resp. 817 ms w/o parsing
% 3.27/1.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.27/1.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------