TSTP Solution File: DAT317^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : DAT317^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 10:30:24 EDT 2024
% Result : Theorem 36.92s 6.75s
% Output : Refutation 37.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 17 unt; 8 typ; 0 def)
% Number of atoms : 70 ( 66 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 457 ( 68 ~; 30 |; 2 &; 350 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 110 ( 18 ^ 86 !; 0 ?; 110 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('\'const/lists/TL\'_type',type,
'\'const/lists/TL\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf('\'const/lists/HD\'_type',type,
'\'const/lists/HD\'':
!>[TA: $tType] : ( ( '\'type/ind_types/list\'' @ TA ) > TA ) ).
thf('\'const/ind_types/NIL\'_type',type,
'\'const/ind_types/NIL\'':
!>[TA: $tType] : ( '\'type/ind_types/list\'' @ TA ) ).
thf('\'const/ind_types/CONS\'_type',type,
'\'const/ind_types/CONS\'':
!>[TA: $tType] : ( TA > ( '\'type/ind_types/list\'' @ TA ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf(skt1_type,type,
skt1: $tType ).
thf(sk1_type,type,
sk1: '\'type/ind_types/list\'' @ skt1 ).
thf(sk2_type,type,
sk2:
!>[TA: $tType] : ( ( ( '\'type/ind_types/list\'' @ TA ) > $o ) > TA ) ).
thf(sk3_type,type,
sk3:
!>[TA: $tType] : ( ( ( '\'type/ind_types/list\'' @ TA ) > $o ) > ( '\'type/ind_types/list\'' @ TA ) ) ).
thf(3,axiom,
! [TA: $tType,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
& ! [B: TA,C: '\'type/ind_types/list\'' @ TA] :
( ( A @ C )
=> ( A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ C ) ) ) )
=> ! [B: '\'type/ind_types/list\'' @ TA] : ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/ind_types/list_INDUCT_') ).
thf(12,plain,
! [TA: $tType,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ( ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
& ! [B: TA,C: '\'type/ind_types/list\'' @ TA] :
( ( A @ C )
=> ( A @ ( '\'const/ind_types/CONS\'' @ TA @ B @ C ) ) ) )
=> ! [B: '\'type/ind_types/list\'' @ TA] : ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: ( '\'type/ind_types/list\'' @ TA ) > $o] :
( ~ ( A @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ( A @ ( '\'const/ind_types/CONS\'' @ TA @ ( sk2 @ TA @ A ) @ ( sk3 @ TA @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[12]) ).
thf(69,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ~ ( B @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ~ ~ ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[13:[bind(A,$thf( ^ [D: '\'type/ind_types/list\'' @ TA] : ~ ( C @ D ) ))]]) ).
thf(92,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( B @ A )
| ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
| ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(93,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( B @ A )
| ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
| ( B @ ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(5620,plain,
! [TA: $tType,B: ( '\'type/ind_types/list\'' @ TA ) > $o,A: '\'type/ind_types/list\'' @ TA] :
( ~ ( B @ A )
| ( B @ ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( B
@ ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) )
@ ( sk3 @ TA
@ ^ [C: '\'type/ind_types/list\'' @ TA] :
~ ( B @ C ) ) ) )
!= ( ~ ( B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[93]) ).
thf(5657,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A != A )
| ( A
= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( A
= ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) )
@ ( sk3 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) ) ) )
!= ( A != A ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[5620:[bind(A,$thf( A )),bind(B,$thf( (=) @ ( '\'type/ind_types/list\'' @ TA ) @ A ))]]) ).
thf(5760,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A != A )
| ( A
= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( ( A
= ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) )
@ ( sk3 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) ) ) )
!= ( A != A ) )
| ~ $true ),
inference(lifteq,[status(thm)],[5657]) ).
thf(6045,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A
= ( '\'const/ind_types/NIL\'' @ TA ) )
| ( A
= ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) )
@ ( sk3 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) ) ) ) ),
inference(simp,[status(thm)],[5760]) ).
thf(8304,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A
= ( '\'const/ind_types/CONS\'' @ TA
@ ( sk2 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) )
@ ( sk3 @ TA
@ ^ [B: '\'type/ind_types/list\'' @ TA] : ( A != B ) ) ) )
| ( A
= ( '\'const/ind_types/NIL\'' @ TA ) ) ),
inference(lifteq,[status(thm)],[6045]) ).
thf(5,axiom,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/HD_') ).
thf(24,plain,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA,B: TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,plain,
! [TA: $tType,B: TA,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [TA: $tType,B: TA,A: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/HD\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ B @ A ) )
= B ),
inference(lifteq,[status(thm)],[25]) ).
thf(4,axiom,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/TL_') ).
thf(21,plain,
! [TA: $tType,A: TA,B: '\'type/ind_types/list\'' @ TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [TA: $tType,B: '\'type/ind_types/list\'' @ TA,A: TA] :
( ( '\'const/lists/TL\'' @ TA @ ( '\'const/ind_types/CONS\'' @ TA @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[22]) ).
thf(1,conjecture,
! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A
!= ( '\'const/ind_types/NIL\'' @ TA ) )
=> ( A
= ( '\'const/ind_types/CONS\'' @ TA @ ( '\'const/lists/HD\'' @ TA @ A ) @ ( '\'const/lists/TL\'' @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/CONS_HD_TL_') ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A
!= ( '\'const/ind_types/NIL\'' @ TA ) )
=> ( A
= ( '\'const/ind_types/CONS\'' @ TA @ ( '\'const/lists/HD\'' @ TA @ A ) @ ( '\'const/lists/TL\'' @ TA @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [TA: $tType,A: '\'type/ind_types/list\'' @ TA] :
( ( A
!= ( '\'const/ind_types/NIL\'' @ TA ) )
=> ( A
= ( '\'const/ind_types/CONS\'' @ TA @ ( '\'const/lists/HD\'' @ TA @ A ) @ ( '\'const/lists/TL\'' @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( sk1
!= ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ ( '\'const/lists/TL\'' @ skt1 @ sk1 ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
( ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ ( '\'const/lists/TL\'' @ skt1 @ sk1 ) )
!= sk1 ),
inference(lifteq,[status(thm)],[8]) ).
thf(30,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ B )
!= sk1 )
| ( ( '\'const/lists/TL\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B ) )
!= ( '\'const/lists/TL\'' @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,10]) ).
thf(31,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ B )
!= sk1 )
| ( ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
! [B: '\'type/ind_types/list\'' @ skt1,A: skt1] :
( ( ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ B )
!= sk1 )
| ( ( '\'const/ind_types/CONS\'' @ skt1 @ A @ B )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ B ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[31]) ).
thf(33,plain,
! [A: '\'type/ind_types/list\'' @ skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( '\'const/lists/HD\'' @ skt1 @ sk1 )),bind(B,$thf( B ))]]) ).
thf(34,plain,
! [A: '\'type/ind_types/list\'' @ skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ ( '\'const/lists/HD\'' @ skt1 @ sk1 ) @ A )
!= sk1 ),
inference(simp,[status(thm)],[33]) ).
thf(114,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: '\'type/ind_types/list\'' @ skt1] :
( ( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ C )
!= sk1 )
| ( ( '\'const/lists/HD\'' @ skt1 @ ( '\'const/ind_types/CONS\'' @ skt1 @ B @ A ) )
!= ( '\'const/lists/HD\'' @ skt1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[26,34]) ).
thf(121,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: '\'type/ind_types/list\'' @ skt1] :
( ( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ C )
!= sk1 )
| ( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[114]) ).
thf(135,plain,
! [C: '\'type/ind_types/list\'' @ skt1,B: skt1,A: '\'type/ind_types/list\'' @ skt1] :
( ( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ C )
!= sk1 )
| ( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ A )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ B @ C ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[121]) ).
thf(136,plain,
! [B: skt1,A: '\'type/ind_types/list\'' @ skt1] :
( ( '\'const/ind_types/CONS\'' @ skt1 @ B @ A )
!= sk1 ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A ))]]) ).
thf(8367,plain,
! [C: skt1,B: '\'type/ind_types/list\'' @ skt1,A: '\'type/ind_types/list\'' @ skt1] :
( ( A
= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( A != sk1 )
| ( ( '\'const/ind_types/CONS\'' @ skt1
@ ( sk2 @ skt1
@ ^ [D: '\'type/ind_types/list\'' @ skt1] : ( A != D ) )
@ ( sk3 @ skt1
@ ^ [D: '\'type/ind_types/list\'' @ skt1] : ( A != D ) ) )
!= ( '\'const/ind_types/CONS\'' @ skt1 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8304,136]) ).
thf(8368,plain,
! [A: '\'type/ind_types/list\'' @ skt1] :
( ( A
= ( '\'const/ind_types/NIL\'' @ skt1 ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[8367:[bind(A,$thf( A )),bind(B,$thf( sk3 @ skt1 @ ^ [D: '\'type/ind_types/list\'' @ skt1] : ( A != D ) )),bind(C,$thf( sk2 @ skt1 @ ^ [D: '\'type/ind_types/list\'' @ skt1] : ( A != D ) ))]]) ).
thf(8697,plain,
( sk1
= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(simp,[status(thm)],[8368]) ).
thf(9,plain,
( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
( sk1
!= ( '\'const/ind_types/NIL\'' @ skt1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(8731,plain,
$false,
inference(simplifyReflect,[status(thm)],[8697,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT317^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 18:44:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.99/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.98 % [INFO] Parsing done (121ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.65/1.19 % [INFO] nitpick registered as external prover.
% 1.65/1.19 % [INFO] Scanning for conjecture ...
% 1.81/1.25 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.81/1.27 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.81/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.81/1.28 % [INFO] Type checking passed.
% 1.81/1.29 % [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 ...
% 36.92/6.75 % [INFO] Killing All external provers ...
% 36.92/6.75 % Time passed: 6222ms (effective reasoning time: 5764ms)
% 36.92/6.75 % 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)>
% 36.92/6.75 % Axioms used in derivation (3): thm/ind_types/list_INDUCT_, thm/lists/HD_, thm/lists/TL_
% 36.92/6.75 % No. of inferences in proof: 39
% 36.92/6.75 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6222 ms resp. 5764 ms w/o parsing
% 37.05/6.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.05/6.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------