TSTP Solution File: NUM812^5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : NUM812^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n025.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 13:02:38 EDT 2024
% Result : Theorem 15.06s 4.22s
% Output : Refutation 15.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 45 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 131 ( 40 ~; 25 |; 2 &; 57 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 9 ^ 29 !; 3 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(c0_type,type,
c0: $i ).
thf(cS_type,type,
cS: $i > $i ).
thf(cIND_type,type,
cIND: $o ).
thf(cIND_def,definition,
( cIND
= ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( cIND
=> ! [A: $i] :
( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM578) ).
thf(2,negated_conjecture,
~ ( cIND
=> ! [A: $i] :
( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ B ) ) ) )
=> ! [B: $i] : ( A @ B ) )
=> ! [A: $i] :
( ( A = c0 )
| ? [B: $i] :
( A
= ( cS @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(35,plain,
! [B: $i > $o,A: $i] :
( ~ ~ ( B @ c0 )
| ~ ~ ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[6:[bind(A,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(59,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ( B @ c0 ) ),
inference(cnf,[status(esa)],[35]) ).
thf(60,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
| ( B @ c0 ) ),
inference(simp,[status(thm)],[59]) ).
thf(3087,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ( B @ c0 )
| ( ( B
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C ) ) ) )
!= ( ~ ( B @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[60]) ).
thf(3108,plain,
! [A: $i] :
( ( A != A )
| ( A = c0 )
| ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A != A ) )
| ~ $true ),
inference(replace_leibeq,[status(thm)],[3087:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).
thf(3127,plain,
! [A: $i] :
( ( A != A )
| ( A = c0 )
| ( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
!= ( A != A ) )
| ~ $true ),
inference(lifteq,[status(thm)],[3108]) ).
thf(3224,plain,
! [A: $i] :
( ( A = c0 )
| ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) ) ),
inference(simp,[status(thm)],[3127]) ).
thf(4741,plain,
! [A: $i] :
( ( A
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B ) ) ) )
| ( A = c0 ) ),
inference(lifteq,[status(thm)],[3224]) ).
thf(4,plain,
! [A: $i] :
( sk2
!= ( cS @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: $i] :
( ( cS @ A )
!= sk2 ),
inference(lifteq,[status(thm)],[4]) ).
thf(16,plain,
! [A: $i] :
( ( cS @ A )
!= sk2 ),
inference(simp,[status(thm)],[15]) ).
thf(4833,plain,
! [B: $i,A: $i] :
( ( A = c0 )
| ( A != sk2 )
| ( ( cS
@ ( sk1
@ ^ [C: $i] : ( A != C ) ) )
!= ( cS @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4741,16]) ).
thf(4834,plain,
! [A: $i] :
( ( A = c0 )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[4833:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ^ [C: $i] : ( A != C ) ))]]) ).
thf(4985,plain,
sk2 = c0,
inference(simp,[status(thm)],[4834]) ).
thf(5,plain,
sk2 != c0,
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
sk2 != c0,
inference(lifteq,[status(thm)],[5]) ).
thf(4988,plain,
$false,
inference(simplifyReflect,[status(thm)],[4985,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM812^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Jun 23 04:03:25 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.97/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (106ms).
% 1.20/0.99 % [INFO] Running in sequential loop mode.
% 1.67/1.27 % [INFO] eprover registered as external prover.
% 1.67/1.27 % [INFO] Scanning for conjecture ...
% 1.86/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.86/1.36 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.86/1.36 % [INFO] Problem is higher-order (TPTP THF).
% 1.86/1.36 % [INFO] Type checking passed.
% 1.86/1.36 % [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 ...
% 15.06/4.22 % [INFO] Killing All external provers ...
% 15.06/4.22 % Time passed: 3698ms (effective reasoning time: 3223ms)
% 15.06/4.22 % 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)>
% 15.06/4.22 % Axioms used in derivation (0):
% 15.06/4.22 % No. of inferences in proof: 21
% 15.06/4.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3698 ms resp. 3223 ms w/o parsing
% 15.06/4.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.06/4.24 % [INFO] Killing All external provers ...
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