TSTP Solution File: SEV464^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV464^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 21 04:10:36 EDT 2024
% Result : Theorem 10.97s 3.83s
% Output : Refutation 10.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 25 ( 15 unt; 10 typ; 0 def)
% Number of atoms : 63 ( 24 equ; 0 cnn)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 173 ( 5 ~; 0 |; 2 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 2 con; 0-6 aty)
% Number of variables : 64 ( 0 ^ 56 !; 2 ?; 64 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/trivia/o\'_type',type,
'\'const/trivia/o\'':
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TC > TA ) > ( TB > TC ) > TB > TA ) ).
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/IMAGE\'_type',type,
'\'const/sets/IMAGE\'':
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TB > $o ) > TA > $o ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(skt3_type,type,
skt3: $tType ).
thf(sk1_type,type,
sk1: skt2 > skt1 ).
thf(sk2_type,type,
sk2: skt3 > skt2 ).
thf(sk3_type,type,
sk3: skt3 > $o ).
thf(sk4_type,type,
sk4: skt1 ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > $o] :
( ( '\'const/sets/IMAGE\'' @ TA @ TC @ ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B ) @ C )
= ( '\'const/sets/IMAGE\'' @ TB @ TC @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IMAGE_o_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > $o] :
( ( '\'const/sets/IMAGE\'' @ TA @ TC @ ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B ) @ C )
= ( '\'const/sets/IMAGE\'' @ TB @ TC @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA > $o] :
( ( '\'const/sets/IMAGE\'' @ TA @ TC @ ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B ) @ C )
= ( '\'const/sets/IMAGE\'' @ TB @ TC @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA > $o,C: TA > TB] :
( ( '\'const/sets/IN\'' @ TB @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ C @ B ) )
= ( ? [D: TA] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TA @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_IMAGE_') ).
thf(9,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA > $o,C: TA > TB] :
( ( '\'const/sets/IN\'' @ TB @ A @ ( '\'const/sets/IMAGE\'' @ TA @ TB @ C @ B ) )
= ( ? [D: TA] :
( ( A
= ( C @ D ) )
& ( '\'const/sets/IN\'' @ TA @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,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(15,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)],[5]) ).
thf(16,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( A = B )
= ( ! [C: TA] :
( ( '\'const/sets/IN\'' @ TA @ C @ A )
= ( '\'const/sets/IN\'' @ TA @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(4,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA] :
( ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B @ C )
= ( A @ ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/trivia/o_THM_') ).
thf(12,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TB > TC,B: TA > TB,C: TA] :
( ( '\'const/trivia/o\'' @ TB @ TA @ TC @ A @ B @ C )
= ( A @ ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(7,plain,
( ( '\'const/sets/IMAGE\'' @ skt3 @ skt1 @ ( '\'const/trivia/o\'' @ skt2 @ skt3 @ skt1 @ sk1 @ sk2 ) @ sk3 )
!= ( '\'const/sets/IMAGE\'' @ skt2 @ skt1 @ sk1 @ ( '\'const/sets/IMAGE\'' @ skt3 @ skt2 @ sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
( ( '\'const/sets/IMAGE\'' @ skt3 @ skt1 @ ( '\'const/trivia/o\'' @ skt2 @ skt3 @ skt1 @ sk1 @ sk2 ) @ sk3 )
!= ( '\'const/sets/IMAGE\'' @ skt2 @ skt1 @ sk1 @ ( '\'const/sets/IMAGE\'' @ skt3 @ skt2 @ sk2 @ sk3 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
( ( '\'const/sets/IMAGE\'' @ skt3 @ skt1 @ ( '\'const/trivia/o\'' @ skt2 @ skt3 @ skt1 @ sk1 @ sk2 ) @ sk3 @ sk4 )
!= ( '\'const/sets/IMAGE\'' @ skt2 @ skt1 @ sk1 @ ( '\'const/sets/IMAGE\'' @ skt3 @ skt2 @ sk2 @ sk3 ) @ sk4 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(122,plain,
$false,
inference(cvc4,[status(thm)],[6,9,17,12,18,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEV464^1 : TPTP v8.2.0. Released v7.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.11/0.33 % Computer : n003.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sun May 19 18:35:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.99/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.11 % [INFO] Parsing done (162ms).
% 1.27/1.13 % [INFO] Running in sequential loop mode.
% 1.86/1.48 % [INFO] eprover registered as external prover.
% 1.86/1.49 % [INFO] cvc4 registered as external prover.
% 1.86/1.49 % [INFO] Scanning for conjecture ...
% 2.03/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.03/1.62 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.24/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.65 % [INFO] Type checking passed.
% 2.24/1.65 % [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 ...
% 10.97/3.82 % External prover 'cvc4' found a proof!
% 10.97/3.82 % [INFO] Killing All external provers ...
% 10.97/3.82 % Time passed: 3345ms (effective reasoning time: 2692ms)
% 10.97/3.82 % 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)>
% 10.97/3.83 % Axioms used in derivation (3): thm/sets/IN_IMAGE_, thm/sets/EXTENSION_, thm/trivia/o_THM_
% 10.97/3.83 % No. of inferences in proof: 15
% 10.97/3.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3345 ms resp. 2692 ms w/o parsing
% 10.97/3.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.97/3.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------