TSTP Solution File: NUM816^5 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n020.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 13:06:29 EDT 2024
% Result : Theorem 10.39s 2.89s
% Output : Refutation 10.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 60 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 271 ( 54 ~; 33 |; 6 &; 166 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 13 ^ 34 !; 1 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(c0_type,type,
c0: $i ).
thf(cS_type,type,
cS: $i > $i ).
thf(cODD1_type,type,
cODD1: $i > $o ).
thf(cODD1_def,definition,
( cODD1
= ( ^ [A: $i] :
~ ( cEVEN1 @ A ) ) ) ).
thf(sk1_type,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM406) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ( cODD1 @ ( cS @ c0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ ( cS @ B ) ) ) ) )
=> ( A @ ( cS @ c0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ~ ? [A: $i] :
( ( cS @ A )
= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $o] :
( ( ( A @ c0 )
& ! [B: $i] :
( ( A @ B )
=> ( A @ ( cS @ ( cS @ B ) ) ) ) )
=> ( A @ ( cS @ c0 ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
| ( A @ ( cS @ c0 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ~ ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
| ( A @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(26,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( cS @ c0 ) )
| ( ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(41,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( cS @ c0 ) )
| ( ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[26:[]]) ).
thf(42,plain,
! [A: $i > $o] :
( ( A @ ( cS @ c0 ) )
| ~ ( A @ c0 )
| ( ( A @ ( cS @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ c0 ) ) ),
inference(pre_uni,[status(thm)],[41:[]]) ).
thf(64,plain,
! [A: $i > $o] :
( ~ ( A @ ( cS @ c0 ) )
| ~ ~ ( A @ c0 )
| ( ( ~ ( A
@ ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) ) )
!= ( ~ ( A @ c0 ) ) ) ),
inference(prim_subst,[status(thm)],[42:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(80,plain,
! [A: $i > $o] :
( ( ( ~ ( A
@ ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) ) )
!= ( ~ ( A @ c0 ) ) )
| ( A @ c0 )
| ~ ( A @ ( cS @ c0 ) ) ),
inference(cnf,[status(esa)],[64]) ).
thf(81,plain,
! [A: $i > $o] :
( ( ( A
@ ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) )
!= ( A @ c0 ) )
| ( A @ c0 )
| ~ ( A @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(225,plain,
! [A: $i > $o] :
( ( A @ c0 )
| ~ ( A @ ( cS @ c0 ) )
| ( A
@ ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) )
| ( A @ c0 ) ),
inference(bool_ext,[status(thm)],[81]) ).
thf(234,plain,
( ( ( cS @ c0 )
= c0 )
| ( ( cS @ c0 )
!= ( cS @ c0 ) )
| ( ( cS @ c0 )
= ( cS
@ ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) ) ) )
| ( ( cS @ c0 )
= c0 ) ),
inference(replace_leibeq,[status(thm)],[225:[bind(A,$thf( (=) @ $i @ ( cS @ c0 ) ))]]) ).
thf(239,plain,
( ( ( cS @ c0 )
= c0 )
| ( ( cS @ c0 )
!= ( cS @ c0 ) )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) ) )
= ( cS @ c0 ) )
| ( ( cS @ c0 )
= c0 ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(248,plain,
( ( ( cS @ c0 )
= c0 )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) ) )
= ( cS @ c0 ) )
| ( ( cS @ c0 )
= c0 ) ),
inference(pattern_uni,[status(thm)],[239:[]]) ).
thf(260,plain,
( ( ( cS @ c0 )
= c0 )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) ) )
= ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(8,plain,
! [A: $i] :
( ( cS @ A )
!= c0 ),
inference(cnf,[status(esa)],[4]) ).
thf(20,plain,
! [A: $i] :
( ( cS @ A )
!= c0 ),
inference(lifteq,[status(thm)],[8]) ).
thf(840,plain,
( ( cS
@ ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) ) )
= ( cS @ c0 ) ),
inference(simplifyReflect,[status(thm)],[260,20]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( cS @ A )
!= ( cS @ B ) )
| ( A = B ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
! [A: $i] :
( ( sk2 @ ( cS @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(cS),[sk2])]) ).
thf(854,plain,
! [A: $i] :
( ( ( sk2 @ ( cS @ c0 ) )
= A )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] :
( ( cS @ c0 )
!= B ) ) ) )
!= ( cS @ A ) ) ),
inference(paramod_ordered,[status(thm)],[840,19]) ).
thf(855,plain,
( ( sk2 @ ( cS @ c0 ) )
= ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) ) ),
inference(pattern_uni,[status(thm)],[854:[bind(A,$thf( cS @ ( sk1 @ ^ [B: $i] : ( ( cS @ c0 ) != B ) ) ))]]) ).
thf(1270,plain,
( ( cS
@ ( sk1
@ ^ [A: $i] :
( ( cS @ c0 )
!= A ) ) )
= c0 ),
inference(rewrite,[status(thm)],[855,19]) ).
thf(1271,plain,
$false,
inference(simplifyReflect,[status(thm)],[1270,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.12 % Command : run_Leo-III %s %d SAT
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Jun 22 20:42:10 EDT 2024
% 0.19/0.33 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (102ms).
% 1.18/0.96 % [INFO] Running in sequential loop mode.
% 1.47/1.17 % [INFO] nitpick registered as external prover.
% 1.47/1.17 % [INFO] Scanning for conjecture ...
% 1.77/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.82/1.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.82/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.82/1.26 % [INFO] Type checking passed.
% 1.82/1.26 % [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 ...
% 10.39/2.88 % [INFO] Killing All external provers ...
% 10.39/2.88 % Time passed: 2358ms (effective reasoning time: 1913ms)
% 10.39/2.88 % 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)>
% 10.39/2.88 % Axioms used in derivation (0):
% 10.39/2.88 % No. of inferences in proof: 28
% 10.39/2.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2358 ms resp. 1913 ms w/o parsing
% 10.39/2.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.39/2.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------