TSTP Solution File: NUM816^5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---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 THM
% Computer : n018.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 5.28s 2.51s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 9 unt; 0 typ; 1 def)
% Number of atoms : 58 ( 52 equ; 7 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 246 ( 48 ~; 35 |; 6 &; 145 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 4 ^ 34 !; 1 ?; 39 :)
% 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/sandbox2/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(6,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ ( cS @ c0 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
! [A: $i > $o] :
( ~ ( A @ c0 )
| ( A @ ( sk1 @ A ) )
| ( A @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[6]) ).
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(10,plain,
( ( c0 != c0 )
| ( c0
= ( sk1 @ ( (=) @ $i @ c0 ) ) )
| ( c0
= ( cS @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[6:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(12,plain,
( ( c0 != c0 )
| ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(13,plain,
( ( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(simp,[status(thm)],[12]) ).
thf(21,plain,
( ( sk1 @ ( (=) @ $i @ c0 ) )
= c0 ),
inference(simplifyReflect,[status(thm)],[13,20]) ).
thf(102,plain,
! [A: $i > $o] :
( ~ ~ ( A @ c0 )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ~ ( A @ ( cS @ c0 ) ) ),
inference(prim_subst,[status(thm)],[14:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(143,plain,
! [A: $i > $o] :
( ~ ( A @ ( cS @ c0 ) )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ( A @ c0 ) ),
inference(cnf,[status(esa)],[102]) ).
thf(144,plain,
! [A: $i > $o] :
( ~ ( A @ ( cS @ c0 ) )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ( A @ c0 ) ),
inference(simp,[status(thm)],[143]) ).
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(9,plain,
( ( c0 != c0 )
| ( c0
!= ( cS @ ( cS @ ( sk1 @ ( (=) @ $i @ c0 ) ) ) ) )
| ( c0
= ( cS @ c0 ) ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ $i @ c0 ))]]) ).
thf(15,plain,
( ( c0 != c0 )
| ( ( cS @ ( cS @ ( sk1 @ ( (=) @ $i @ c0 ) ) ) )
!= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(16,plain,
( ( ( cS @ ( cS @ ( sk1 @ ( (=) @ $i @ c0 ) ) ) )
!= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(simp,[status(thm)],[15]) ).
thf(22,plain,
( ( ( cS @ ( cS @ c0 ) )
!= c0 )
| ( ( cS @ c0 )
= c0 ) ),
inference(rewrite,[status(thm)],[16,21]) ).
thf(23,plain,
( ( cS @ ( cS @ c0 ) )
!= c0 ),
inference(simplifyReflect,[status(thm)],[22,20]) ).
thf(19,plain,
! [A: $i] :
( ( sk2 @ ( cS @ A ) )
= A ),
introduced(tautology,[new_symbols(inverse(cS),[sk2])]) ).
thf(350,plain,
$false,
inference(e,[status(thm)],[42,14,20,21,144,3,18,11,23,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM816^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.04/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Jun 22 20:42:10 EDT 2024
% 0.13/0.35 % CPUTime :
% 1.10/0.96 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.08 % [INFO] Parsing done (117ms).
% 1.41/1.09 % [INFO] Running in sequential loop mode.
% 1.81/1.31 % [INFO] eprover registered as external prover.
% 1.81/1.31 % [INFO] Scanning for conjecture ...
% 1.97/1.38 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.40 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.40 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.40 % [INFO] Type checking passed.
% 1.97/1.41 % [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 ...
% 5.28/2.50 % External prover 'e' found a proof!
% 5.28/2.50 % [INFO] Killing All external provers ...
% 5.28/2.50 % Time passed: 1928ms (effective reasoning time: 1410ms)
% 5.28/2.50 % 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)>
% 5.28/2.51 % Axioms used in derivation (0):
% 5.28/2.51 % No. of inferences in proof: 30
% 5.28/2.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1928 ms resp. 1410 ms w/o parsing
% 5.74/2.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.74/2.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------