TSTP Solution File: SEV510^1 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV510^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n024.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 16:00:26 EDT 2024
% Result : Theorem 16.96s 3.77s
% Output : Refutation 16.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 9 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 441 ( 26 ~; 20 |; 5 &; 378 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 78 ( 16 ^ 62 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'type/realax/real\'_type',type,
'\'type/realax/real\'': $tType ).
thf('\'type/nums/num\'_type',type,
'\'type/nums/num\'': $tType ).
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/CARD\'_type',type,
'\'const/sets/CARD\'':
!>[TA: $tType] : ( ( TA > $o ) > '\'type/nums/num\'' ) ).
thf('\'const/realax/real_of_num\'_type',type,
'\'const/realax/real_of_num\'': '\'type/nums/num\'' > '\'type/realax/real\'' ).
thf('\'const/realax/real_mul\'_type',type,
'\'const/realax/real_mul\'': '\'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/iterate/sum\'_type',type,
'\'const/iterate/sum\'':
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/realax/real\'' ) > '\'type/realax/real\'' ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: skt1 > $o ).
thf(sk2_type,type,
sk2: skt1 > '\'type/realax/real\'' ).
thf(sk3_type,type,
sk3: '\'type/realax/real\'' ).
thf(sk4_type,type,
sk4:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > '\'type/realax/real\'' ) > ( TA > '\'type/realax/real\'' ) > TA ) ).
thf(3,axiom,
! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ C )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ C )
=> ( '\'const/realax/real_le\'' @ ( A @ D ) @ ( B @ D ) ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_LE_') ).
thf(9,plain,
! [TA: $tType,A: TA > '\'type/realax/real\'',B: TA > '\'type/realax/real\'',C: TA > $o] :
( ( ( '\'const/sets/FINITE\'' @ TA @ C )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ C )
=> ( '\'const/realax/real_le\'' @ ( A @ D ) @ ( B @ D ) ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
| ( '\'const/sets/IN\'' @ TA @ ( sk4 @ TA @ C @ B @ A ) @ C )
| ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(4,axiom,
! [TA: $tType,A: '\'type/realax/real\'',B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ B )
=> ( ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : A )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_CONST_') ).
thf(12,plain,
! [TA: $tType,A: '\'type/realax/real\'',B: TA > $o] :
( ( '\'const/sets/FINITE\'' @ TA @ B )
=> ( ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : A )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [TA: $tType,B: TA > $o,A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
| ( ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : A )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ B ) ) @ A ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(14,plain,
! [TA: $tType,B: TA > $o,A: '\'type/realax/real\''] :
( ( ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : A )
= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ B ) ) @ A ) )
| ~ ( '\'const/sets/FINITE\'' @ TA @ B ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o,B: TA > '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ A )
=> ( '\'const/realax/real_le\'' @ ( B @ D ) @ C ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ A @ B ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/SUM_BOUND_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o,B: TA > '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ A )
=> ( '\'const/realax/real_le\'' @ ( B @ D ) @ C ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ A @ B ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ A ) ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [TA: $tType,A: TA > $o,B: TA > '\'type/realax/real\'',C: '\'type/realax/real\''] :
( ( ( '\'const/sets/FINITE\'' @ TA @ A )
& ! [D: TA] :
( ( '\'const/sets/IN\'' @ TA @ D @ A )
=> ( '\'const/realax/real_le\'' @ ( B @ D ) @ C ) ) )
=> ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ A @ B ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
~ ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 ) @ ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ skt1 @ sk1 ) ) @ sk3 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(18,plain,
! [TA: $tType,B: TA > $o,A: '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ B )
| ~ ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 )
@ ( '\'const/iterate/sum\'' @ TA @ B
@ ^ [C: TA] : A ) )
| ( ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ TA @ B ) ) @ A )
!= ( '\'const/realax/real_mul\'' @ ( '\'const/realax/real_of_num\'' @ ( '\'const/sets/CARD\'' @ skt1 @ sk1 ) ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,6]) ).
thf(19,plain,
( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ~ ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 )
@ ( '\'const/iterate/sum\'' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(8,plain,
'\'const/sets/FINITE\'' @ skt1 @ sk1,
inference(cnf,[status(esa)],[5]) ).
thf(22,plain,
( ~ $true
| ~ ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 )
@ ( '\'const/iterate/sum\'' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ) ),
inference(rewrite,[status(thm)],[19,8]) ).
thf(23,plain,
~ ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 )
@ ( '\'const/iterate/sum\'' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ),
inference(simp,[status(thm)],[22]) ).
thf(198,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
| ( '\'const/sets/IN\'' @ TA @ ( sk4 @ TA @ C @ B @ A ) @ C )
| ( ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) )
!= ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 )
@ ( '\'const/iterate/sum\'' @ skt1 @ sk1
@ ^ [D: skt1] : sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,23]) ).
thf(199,plain,
( ~ ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
| ( '\'const/sets/IN\'' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [A: skt1] : sk3
@ sk2 )
@ sk1 ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( sk2 )),bind(B,$thf( ^ [D: skt1] : sk3 )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(225,plain,
( ~ $true
| ( '\'const/sets/IN\'' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [A: skt1] : sk3
@ sk2 )
@ sk1 ) ),
inference(rewrite,[status(thm)],[199,8]) ).
thf(226,plain,
( '\'const/sets/IN\'' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [A: skt1] : sk3
@ sk2 )
@ sk1 ),
inference(simp,[status(thm)],[225]) ).
thf(7,plain,
! [A: skt1] :
( ~ ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 )
| ( '\'const/realax/real_le\'' @ ( sk2 @ A ) @ sk3 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(227,plain,
! [A: skt1] :
( ( '\'const/realax/real_le\'' @ ( sk2 @ A ) @ sk3 )
| ( ( '\'const/sets/IN\'' @ skt1
@ ( sk4 @ skt1 @ sk1
@ ^ [B: skt1] : sk3
@ sk2 )
@ sk1 )
!= ( '\'const/sets/IN\'' @ skt1 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[226,7]) ).
thf(228,plain,
( '\'const/realax/real_le\''
@ ( sk2
@ ( sk4 @ skt1 @ sk1
@ ^ [A: skt1] : sk3
@ sk2 ) )
@ sk3 ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( sk4 @ skt1 @ sk1 @ ^ [B: skt1] : sk3 @ sk2 ))]]) ).
thf(10,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/sets/FINITE\'' @ TA @ C )
| ~ ( '\'const/realax/real_le\'' @ ( A @ ( sk4 @ TA @ C @ B @ A ) ) @ ( B @ ( sk4 @ TA @ C @ B @ A ) ) )
| ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(91,plain,
! [TA: $tType,C: TA > $o,B: TA > '\'type/realax/real\'',A: TA > '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ ( A @ ( sk4 @ TA @ C @ B @ A ) ) @ ( B @ ( sk4 @ TA @ C @ B @ A ) ) )
| ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ TA @ C @ A ) @ ( '\'const/iterate/sum\'' @ TA @ C @ B ) )
| ( ( '\'const/sets/FINITE\'' @ skt1 @ sk1 )
!= ( '\'const/sets/FINITE\'' @ TA @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8,10]) ).
thf(92,plain,
! [B: skt1 > '\'type/realax/real\'',A: skt1 > '\'type/realax/real\''] :
( ~ ( '\'const/realax/real_le\'' @ ( A @ ( sk4 @ skt1 @ sk1 @ B @ A ) ) @ ( B @ ( sk4 @ skt1 @ sk1 @ B @ A ) ) )
| ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ A ) @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ B ) ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind_type(TA,$thf( skt1 ))]]) ).
thf(921,plain,
! [B: skt1 > '\'type/realax/real\'',A: skt1 > '\'type/realax/real\''] :
( ( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ A ) @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ B ) )
| ( ( '\'const/realax/real_le\''
@ ( sk2
@ ( sk4 @ skt1 @ sk1
@ ^ [C: skt1] : sk3
@ sk2 ) )
@ sk3 )
!= ( '\'const/realax/real_le\'' @ ( A @ ( sk4 @ skt1 @ sk1 @ B @ A ) ) @ ( B @ ( sk4 @ skt1 @ sk1 @ B @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[228,92]) ).
thf(947,plain,
( '\'const/realax/real_le\'' @ ( '\'const/iterate/sum\'' @ skt1 @ sk1 @ sk2 )
@ ( '\'const/iterate/sum\'' @ skt1 @ sk1
@ ^ [A: skt1] : sk3 ) ),
inference(pre_uni,[status(thm)],[921:[bind(A,$thf( sk2 )),bind(B,$thf( ^ [C: skt1] : sk3 ))]]) ).
thf(975,plain,
$false,
inference(rewrite,[status(thm)],[947,23]) ).
thf(976,plain,
$false,
inference(simp,[status(thm)],[975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV510^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 19:40:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (116ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.18 % [INFO] nitpick registered as external prover.
% 1.63/1.19 % [INFO] Scanning for conjecture ...
% 1.76/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.87/1.27 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.87/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.87/1.28 % [INFO] Type checking passed.
% 1.87/1.29 % [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 ...
% 16.96/3.76 % [INFO] Killing All external provers ...
% 16.96/3.77 % Time passed: 3241ms (effective reasoning time: 2779ms)
% 16.96/3.77 % 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)>
% 16.96/3.77 % Axioms used in derivation (2): thm/iterate/SUM_LE_, thm/iterate/SUM_CONST_
% 16.96/3.77 % No. of inferences in proof: 30
% 16.96/3.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3241 ms resp. 2779 ms w/o parsing
% 16.96/3.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.96/3.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------