TSTP Solution File: NUM817^5 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM817^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 10:45:49 EDT 2024
% Result : Theorem 29.13s 5.40s
% Output : Refutation 29.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 11 unt; 5 typ; 1 def)
% Number of atoms : 75 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 275 ( 61 ~; 43 |; 6 &; 153 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 75 ( 13 ^ 58 !; 4 ?; 75 :)
% 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 > $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 ) ) )
=> ? [A: $i] : ( cODD1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM405) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cS @ A )
!= c0 )
& ! [A: $i,B: $i] :
( ( ( cS @ A )
= ( cS @ B ) )
=> ( A = B ) ) )
=> ? [A: $i] : ( cODD1 @ A ) ),
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] :
~ ! [B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ),
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,B: $i > $o] :
( ( ( B @ c0 )
& ! [C: $i] :
( ( B @ C )
=> ( B @ ( cS @ ( cS @ C ) ) ) ) )
=> ( B @ A ) ) ),
inference(miniscope,[status(thm)],[3]) ).
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(5,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ~ ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(25,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ A )
| ( ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
!= ( B @ c0 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(41,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ c0 )
| ( B @ A )
| ( ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
!= ( B @ c0 ) ) ),
inference(pre_uni,[status(thm)],[25:[]]) ).
thf(42,plain,
! [B: $i > $o,A: $i] :
( ( B @ A )
| ~ ( B @ c0 )
| ( ( B @ ( cS @ ( cS @ ( sk1 @ B @ A ) ) ) )
!= ( B @ c0 ) ) ),
inference(pre_uni,[status(thm)],[41:[]]) ).
thf(63,plain,
! [B: $i > $o,A: $i] :
( ~ ( B @ A )
| ~ ~ ( B @ c0 )
| ( ( ~ ( B
@ ( cS
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ) ) ) )
!= ( ~ ( B @ c0 ) ) ) ),
inference(prim_subst,[status(thm)],[42:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( C @ D ) ))]]) ).
thf(90,plain,
! [B: $i > $o,A: $i] :
( ( ( ~ ( B
@ ( cS
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ) ) ) )
!= ( ~ ( B @ c0 ) ) )
| ( B @ c0 )
| ~ ( B @ A ) ),
inference(cnf,[status(esa)],[63]) ).
thf(91,plain,
! [B: $i > $o,A: $i] :
( ( ( B
@ ( cS
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ) ) )
!= ( B @ c0 ) )
| ( B @ c0 )
| ~ ( B @ A ) ),
inference(simp,[status(thm)],[90]) ).
thf(231,plain,
! [B: $i > $o,A: $i] :
( ( B @ c0 )
| ~ ( B @ A )
| ( B
@ ( cS
@ ( cS
@ ( sk1
@ ^ [C: $i] :
~ ( B @ C )
@ A ) ) ) )
| ( B @ c0 ) ),
inference(bool_ext,[status(thm)],[91]) ).
thf(243,plain,
! [A: $i] :
( ( A = c0 )
| ( A != A )
| ( A
= ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B )
@ A ) ) ) )
| ( A = c0 ) ),
inference(replace_leibeq,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( (=) @ $i @ A ))]]) ).
thf(245,plain,
! [A: $i] :
( ( A = c0 )
| ( A != A )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B )
@ A ) ) )
= A )
| ( A = c0 ) ),
inference(lifteq,[status(thm)],[243]) ).
thf(252,plain,
! [A: $i] :
( ( A = c0 )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B )
@ A ) ) )
= A )
| ( A = c0 ) ),
inference(pattern_uni,[status(thm)],[245:[]]) ).
thf(263,plain,
! [A: $i] :
( ( A = c0 )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B )
@ A ) ) )
= A ) ),
inference(simp,[status(thm)],[252]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( A = c0 )
| ( ( sk2 @ A )
= B )
| ( ( cS
@ ( cS
@ ( sk1
@ ^ [C: $i] : ( A != C )
@ A ) ) )
!= ( cS @ B ) ) ),
inference(paramod_ordered,[status(thm)],[263,19]) ).
thf(273,plain,
! [A: $i] :
( ( A = c0 )
| ( ( sk2 @ A )
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B )
@ A ) ) ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( E )),bind(B,$thf( cS @ ( sk1 @ ^ [D: $i] : ( E != D ) @ E ) ))]]) ).
thf(288,plain,
! [A: $i] :
( ( A = c0 )
| ( ( sk2 @ A )
= ( cS
@ ( sk1
@ ^ [B: $i] : ( A != B )
@ A ) ) ) ),
inference(simp,[status(thm)],[273]) ).
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(5310,plain,
! [B: $i,A: $i] :
( ( A = c0 )
| ( ( sk2 @ A )
!= c0 )
| ( ( cS
@ ( sk1
@ ^ [C: $i] : ( A != C )
@ A ) )
!= ( cS @ B ) ) ),
inference(paramod_ordered,[status(thm)],[288,20]) ).
thf(5311,plain,
! [A: $i] :
( ( A = c0 )
| ( ( sk2 @ A )
!= c0 ) ),
inference(pattern_uni,[status(thm)],[5310:[bind(A,$thf( D )),bind(B,$thf( sk1 @ ^ [D: $i] : ( D != D ) @ D ))]]) ).
thf(5509,plain,
! [A: $i] :
( ( A = c0 )
| ( ( sk2 @ A )
!= c0 ) ),
inference(simp,[status(thm)],[5311]) ).
thf(5525,plain,
! [B: $i,A: $i] :
( ( B = c0 )
| ( A != c0 )
| ( ( sk2 @ ( cS @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,5509]) ).
thf(5526,plain,
! [A: $i] :
( ( ( cS @ A )
= c0 )
| ( A != c0 ) ),
inference(pattern_uni,[status(thm)],[5525:[bind(A,$thf( C )),bind(B,$thf( cS @ C ))]]) ).
thf(5536,plain,
( ( cS @ c0 )
= c0 ),
inference(simp,[status(thm)],[5526]) ).
thf(5541,plain,
$false,
inference(simplifyReflect,[status(thm)],[5536,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM817^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.10/0.10 % Command : run_Leo-III %s %d
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Mon May 6 19:37:24 EDT 2024
% 0.10/0.29 % CPUTime :
% 0.73/0.73 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.82/0.85 % [INFO] Parsing done (125ms).
% 0.82/0.86 % [INFO] Running in sequential loop mode.
% 1.25/1.06 % [INFO] nitpick registered as external prover.
% 1.25/1.06 % [INFO] Scanning for conjecture ...
% 1.38/1.12 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.38/1.13 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.38/1.14 % [INFO] Problem is higher-order (TPTP THF).
% 1.38/1.14 % [INFO] Type checking passed.
% 1.38/1.14 % [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 ...
% 29.13/5.39 % [INFO] Killing All external provers ...
% 29.13/5.39 % Time passed: 4985ms (effective reasoning time: 4524ms)
% 29.13/5.39 % 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)>
% 29.13/5.40 % Axioms used in derivation (0):
% 29.13/5.40 % No. of inferences in proof: 33
% 29.13/5.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4985 ms resp. 4524 ms w/o parsing
% 29.13/5.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.13/5.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------