TSTP Solution File: SEV482^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEV482^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 04:11:33 EDT 2024
% Result : Theorem 5.43s 2.19s
% Output : Refutation 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 19 unt; 10 typ; 0 def)
% Number of atoms : 153 ( 22 equ; 0 cnn)
% Maximal formula atoms : 2 ( 7 avg)
% Number of connectives : 479 ( 13 ~; 2 |; 16 &; 430 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 116 ( 18 ^ 93 !; 0 ?; 116 :)
% ( 5 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/sets/IN\'_type',type,
'\'const/sets/IN\'':
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf('\'const/sets/CROSS\'_type',type,
'\'const/sets/CROSS\'':
!>[TA: $tType,TB: $tType] : ( ( TB > $o ) > ( TA > $o ) > ( '\'type/pair/prod\'' @ TB @ TA ) > $o ) ).
thf('\'const/pair/,\'_type',type,
'\'const/pair/,\'':
!>[TA: $tType,TB: $tType] : ( TB > TA > ( '\'type/pair/prod\'' @ TB @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(sk1_type,type,
sk1: ( '\'type/pair/prod\'' @ skt1 @ skt2 ) > $o ).
thf(sk2_type,type,
sk2: skt1 > $o ).
thf(sk3_type,type,
sk3: skt2 > $o ).
thf(sk17_type,type,
sk17: skt1 ).
thf(sk18_type,type,
sk18: skt2 ).
thf(4,axiom,
! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TB @ TA ) > $o] :
( ( ! [B: '\'type/pair/prod\'' @ TB @ TA] : ( A @ B ) )
= ( ! [B: TB,C: TA] : ( A @ ( '\'const/pair/,\'' @ TB @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/pair/FORALL_PAIR_THM_') ).
thf(11,plain,
! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TB @ TA ) > $o] :
( ( ! [B: '\'type/pair/prod\'' @ TB @ TA] : ( A @ B ) )
= ( ! [B: TB,C: TA] : ( A @ ( '\'const/pair/,\'' @ TB @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,plain,
! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TA @ TB ) > $o] :
( ( ! [B: '\'type/pair/prod\'' @ TA @ TB] : ( A @ B ) )
= ( ! [B: TA,C: TB] : ( A @ ( '\'const/pair/,\'' @ TA @ TB @ B @ C ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TA @ TB ) > $o] :
( ( ! [B: '\'type/pair/prod\'' @ TA @ TB] : ( A @ B ) )
= ( ! [B: TA,C: TB] : ( A @ ( '\'const/pair/,\'' @ TA @ TB @ B @ C ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TB @ TA ) > $o,B: TB > $o,C: TA > $o] :
( ( ! [D: '\'type/pair/prod\'' @ TB @ TA] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ D @ ( '\'const/sets/CROSS\'' @ TB @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TB,E: TA] :
( ( ( '\'const/sets/IN\'' @ TB @ D @ B )
& ( '\'const/sets/IN\'' @ TA @ E @ C ) )
=> ( A @ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/FORALL_IN_CROSS_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TB @ TA ) > $o,B: TB > $o,C: TA > $o] :
( ( ! [D: '\'type/pair/prod\'' @ TB @ TA] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ D @ ( '\'const/sets/CROSS\'' @ TB @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TB,E: TA] :
( ( ( '\'const/sets/IN\'' @ TB @ D @ B )
& ( '\'const/sets/IN\'' @ TA @ E @ C ) )
=> ( A @ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TB @ TA ) > $o,B: TB > $o,C: TA > $o] :
( ( ! [D: '\'type/pair/prod\'' @ TB @ TA] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ D @ ( '\'const/sets/CROSS\'' @ TB @ TA @ B @ C ) )
=> ( A @ D ) ) )
= ( ! [D: TB,E: TA] :
( ( ( '\'const/sets/IN\'' @ TB @ D @ B )
& ( '\'const/sets/IN\'' @ TA @ E @ C ) )
=> ( A @ ( '\'const/pair/,\'' @ TB @ TA @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
( ( ! [A: '\'type/pair/prod\'' @ skt1 @ skt2] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ A @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ A ) ) )
!= ( ! [A: skt1,B: skt2] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
( ( ! [A: '\'type/pair/prod\'' @ skt1 @ skt2] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ A @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ A ) ) )
!= ( ! [A: skt1,B: skt2] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(20,plain,
! [TA: $tType,TB: $tType,A: ( '\'type/pair/prod\'' @ TA @ TB ) > $o] :
( ( ( ! [B: TA,C: TB] : ( A @ ( '\'const/pair/,\'' @ TA @ TB @ B @ C ) ) )
!= ( ! [B: skt1,C: skt2] :
( ( ( '\'const/sets/IN\'' @ skt1 @ B @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ C @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ B @ C ) ) ) ) )
| ( ( ! [B: '\'type/pair/prod\'' @ TA @ TB] : ( A @ B ) )
!= ( ! [B: '\'type/pair/prod\'' @ skt1 @ skt2] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ B @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(21,plain,
( ( ! [A: skt1,B: skt2] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) )
!= ( ! [A: skt1,B: skt2] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( ^ [B: '\'type/pair/prod\'' @ skt1 @ skt2] : ( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ B @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) ) => ( sk1 @ B ) ) )),bind_type(TA,$thf( skt1 )),bind_type(TB,$thf( skt2 ))]]) ).
thf(32,plain,
( ( ^ [A: skt1] :
! [B: skt2] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) )
!= ( ^ [A: skt1] :
! [B: skt2] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(44,plain,
( ( ^ [A: skt1,B: skt2] :
( ( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) )
!= ( ^ [A: skt1,B: skt2] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) )
=> ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(97,plain,
( ( ( ^ [A: skt1,B: skt2] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) ) )
!= ( ^ [A: skt1,B: skt2] : ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) ) ) )
| ( ( ^ [A: skt1,B: skt2] : ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) )
!= ( ^ [A: skt1,B: skt2] : ( sk1 @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(99,plain,
( ( ^ [A: skt1,B: skt2] :
( ( '\'const/sets/IN\'' @ skt1 @ A @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ B @ sk3 ) ) )
!= ( ^ [A: skt1,B: skt2] : ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ A @ B ) @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(100,plain,
( ( ( '\'const/sets/IN\'' @ skt1 @ sk17 @ sk2 )
& ( '\'const/sets/IN\'' @ skt2 @ sk18 @ sk3 ) )
!= ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ skt1 @ skt2 ) @ ( '\'const/pair/,\'' @ skt1 @ skt2 @ sk17 @ sk18 ) @ ( '\'const/sets/CROSS\'' @ skt1 @ skt2 @ sk2 @ sk3 ) ) ),
inference(func_ext,[status(esa)],[99]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB > $o,D: TA > $o] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ ( '\'const/pair/,\'' @ TB @ TA @ A @ B ) @ ( '\'const/sets/CROSS\'' @ TB @ TA @ C @ D ) )
= ( ( '\'const/sets/IN\'' @ TB @ A @ C )
& ( '\'const/sets/IN\'' @ TA @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/IN_CROSS_') ).
thf(8,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA,C: TB > $o,D: TA > $o] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TB @ TA ) @ ( '\'const/pair/,\'' @ TB @ TA @ A @ B ) @ ( '\'const/sets/CROSS\'' @ TB @ TA @ C @ D ) )
= ( ( '\'const/sets/IN\'' @ TB @ A @ C )
& ( '\'const/sets/IN\'' @ TA @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TA > $o,B: TB,A: TA] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TA @ TB ) @ ( '\'const/pair/,\'' @ TA @ TB @ A @ B ) @ ( '\'const/sets/CROSS\'' @ TA @ TB @ C @ D ) )
= ( ( '\'const/sets/IN\'' @ TA @ A @ C )
& ( '\'const/sets/IN\'' @ TB @ B @ D ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [TA: $tType,TB: $tType,D: TB > $o,C: TA > $o,B: TB,A: TA] :
( ( '\'const/sets/IN\'' @ ( '\'type/pair/prod\'' @ TA @ TB ) @ ( '\'const/pair/,\'' @ TA @ TB @ A @ B ) @ ( '\'const/sets/CROSS\'' @ TA @ TB @ C @ D ) )
= ( ( '\'const/sets/IN\'' @ TA @ A @ C )
& ( '\'const/sets/IN\'' @ TB @ B @ D ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(101,plain,
$false,
inference(simplifyReflect,[status(thm)],[100,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV482^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n026.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 : Sun May 19 19:07:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.12/0.98 % [INFO] Parsing done (111ms).
% 1.12/0.99 % [INFO] Running in sequential loop mode.
% 1.64/1.20 % [INFO] nitpick registered as external prover.
% 1.64/1.20 % [INFO] Scanning for conjecture ...
% 1.81/1.27 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.81/1.29 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.81/1.30 % [INFO] Problem is higher-order (TPTP THF).
% 1.81/1.31 % [INFO] Type checking passed.
% 1.81/1.31 % [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 ...
% 5.43/2.18 % [INFO] Killing All external provers ...
% 5.43/2.19 % Time passed: 1652ms (effective reasoning time: 1191ms)
% 5.43/2.19 % 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)>
% 5.43/2.19 % Axioms used in derivation (2): thm/pair/FORALL_PAIR_THM_, thm/sets/IN_CROSS_
% 5.43/2.19 % No. of inferences in proof: 21
% 5.43/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1652 ms resp. 1191 ms w/o parsing
% 5.43/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.43/2.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------