TSTP Solution File: SYO309^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO309^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 21 08:59:52 EDT 2024
% Result : Theorem 19.29s 4.19s
% Output : Refutation 19.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 12 unt; 6 typ; 0 def)
% Number of atoms : 90 ( 22 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 519 ( 96 ~; 34 |; 0 &; 386 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 30 ^ 61 !; 17 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(cS_type,type,
cS: $i > $i ).
thf(cQ_type,type,
cQ: $i > $i ).
thf(cR_type,type,
cR: $i > $i > $o ).
thf(sk1_type,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(1,conjecture,
( ! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
= ( ~ ( A @ ( cS @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEO1) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
= ( ~ ( A @ ( cS @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) )
=> ? [A: $i > $o] :
! [B: $i] :
( ( A @ B )
= ( ~ ( A @ ( cS @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i > $o] :
( ( A @ ( sk1 @ A ) )
!= ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [A: $i > $o] :
( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ ( sk1 @ A ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
! [A: $i > $o] :
( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(9,plain,
! [A: $i > $o] :
( ~ ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ~ ( A @ ( sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(11,plain,
! [A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
| ( A @ ( cS @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(5,plain,
! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [A: $i] :
( ( ? [B: $i] : ( cR @ A @ ( cQ @ B ) ) )
= ( ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(14,plain,
! [A: $i] :
( ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
| ~ ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(28,plain,
! [A: $i] :
( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
| ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(13,plain,
! [A: $i] :
( ~ ? [B: $i] : ( cR @ A @ ( cQ @ B ) )
| ~ ? [B: $i] : ( cR @ ( cS @ A ) @ ( cQ @ B ) ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ A ) @ ( cQ @ C ) )
| ~ ( cR @ A @ ( cQ @ B ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ~ ( cR @ B @ ( cQ @ C ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
!= ( cR @ ( cS @ B ) @ ( cQ @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,27]) ).
thf(589,plain,
! [B: $i,A: $i] :
( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
| ~ ( cR @ B @ ( cQ @ A ) ) ),
inference(pattern_uni,[status(thm)],[588:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( C )),bind(D,$thf( sk3 @ E ))]]) ).
thf(619,plain,
! [B: $i,A: $i] :
( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
| ~ ( cR @ B @ ( cQ @ A ) ) ),
inference(simp,[status(thm)],[589]) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ( cR @ C @ ( cQ @ ( sk2 @ C ) ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk3 @ A ) ) )
!= ( cR @ C @ ( cQ @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,619]) ).
thf(754,plain,
! [A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[753:[bind(A,$thf( E )),bind(B,$thf( sk3 @ E )),bind(C,$thf( cS @ E ))]]) ).
thf(798,plain,
! [A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) ) ),
inference(simp,[status(thm)],[754]) ).
thf(10,plain,
! [A: $i > $o] :
( ~ ( A @ ( cS @ ( sk1 @ A ) ) )
| ( A @ ( sk1 @ A ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(12,plain,
! [A: $i > $o] :
( ( A @ ( sk1 @ A ) )
| ~ ( A @ ( cS @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(216,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ~ ~ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) ),
inference(prim_subst,[status(thm)],[12:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(243,plain,
! [A: $i > $o] :
( ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[216]) ).
thf(244,plain,
! [A: $i > $o] :
( ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) )
| ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(355,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) )
!= ( ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[244]) ).
thf(408,plain,
! [A: $i > $o] :
( ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) )
| ( ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) )
!= ( ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ( A @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(542,plain,
! [A: $i > $o] :
( ~ ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ~ ( A @ B ) ) )
| ( ( ~ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ~ ( A @ B ) ) ) ) )
!= ( ~ ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ~ ( A @ B ) ) ) ) ) ),
inference(prim_subst,[status(thm)],[408:[bind(A,$thf( ^ [C: $i] : ~ ( B @ C ) ))]]) ).
thf(579,plain,
! [A: $i > $o] :
( ( ( ~ ( A
@ ( cS
@ ( sk1
@ ^ [B: $i] :
~ ~ ( A @ B ) ) ) ) )
!= ( ~ ~ ( A
@ ( sk1
@ ^ [B: $i] :
~ ~ ( A @ B ) ) ) ) )
| ( A
@ ( sk1
@ ^ [B: $i] :
~ ~ ( A @ B ) ) ) ),
inference(cnf,[status(esa)],[542]) ).
thf(580,plain,
! [A: $i > $o] :
( ( ( ~ ( A @ ( cS @ ( sk1 @ A ) ) ) )
!= ( A @ ( sk1 @ A ) ) )
| ( A @ ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[579]) ).
thf(1507,plain,
! [B: $i > $o,A: $i] :
( ( cR @ A @ ( cQ @ ( sk2 @ A ) ) )
| ( B @ ( sk1 @ B ) )
| ( ( cR @ ( cS @ A ) @ ( cQ @ ( sk2 @ ( cS @ A ) ) ) )
!= ( B @ ( cS @ ( sk1 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[798,580]) ).
thf(1545,plain,
( ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) )
| ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1507:[bind(A,$thf( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )),bind(B,$thf( ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ))]]) ).
thf(1578,plain,
( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[1545]) ).
thf(756,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( cR @ B @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ D ) )
| ( ( cR @ B @ ( cQ @ ( sk2 @ B ) ) )
!= ( cR @ ( cS @ C ) @ ( cQ @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[619,27]) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ B ) ) ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( A )),bind(B,$thf( cS @ H )),bind(C,$thf( H )),bind(D,$thf( D )),bind(E,$thf( sk2 @ ( cS @ H ) ))]]) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ~ ( cR @ C @ ( cQ @ B ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(1638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( cR @ ( cS @ C ) @ ( cQ @ A ) )
| ( ( cR
@ ( sk1
@ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) ) ) )
!= ( cR @ C @ ( cQ @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1578,801]) ).
thf(1639,plain,
! [A: $i] :
~ ( cR
@ ( cS
@ ( sk1
@ ^ [B: $i] : ( cR @ B @ ( cQ @ ( sk2 @ B ) ) ) ) )
@ ( cQ @ A ) ),
inference(pattern_uni,[status(thm)],[1638:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ) )),bind(C,$thf( sk1 @ ^ [D: $i] : ( cR @ D @ ( cQ @ ( sk2 @ D ) ) ) ))]]) ).
thf(1656,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
| ( ( A @ ( cS @ ( sk1 @ A ) ) )
!= ( cR
@ ( cS
@ ( sk1
@ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) )
@ ( cQ @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,1639]) ).
thf(1664,plain,
~ ( cR
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) )
@ ( cQ
@ ( sk2
@ ( sk1
@ ^ [A: $i] : ( cR @ A @ ( cQ @ ( sk2 @ A ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[1656:[bind(A,$thf( ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) )),bind(B,$thf( sk2 @ ( cS @ ( sk1 @ ^ [C: $i] : ( cR @ C @ ( cQ @ ( sk2 @ C ) ) ) ) ) ))]]) ).
thf(1729,plain,
~ $true,
inference(rewrite,[status(thm)],[1664,1578]) ).
thf(1730,plain,
$false,
inference(simp,[status(thm)],[1729]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SYO309^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Mon May 20 09:29:24 EDT 2024
% 0.15/0.38 % CPUTime :
% 0.97/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.00 % [INFO] Parsing done (103ms).
% 1.19/1.00 % [INFO] Running in sequential loop mode.
% 1.58/1.23 % [INFO] nitpick registered as external prover.
% 1.58/1.23 % [INFO] Scanning for conjecture ...
% 1.75/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.75/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.90/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.31 % [INFO] Type checking passed.
% 1.90/1.31 % [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 ...
% 19.29/4.18 % [INFO] Killing All external provers ...
% 19.29/4.18 % Time passed: 3638ms (effective reasoning time: 3173ms)
% 19.29/4.18 % 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)>
% 19.29/4.18 % Axioms used in derivation (0):
% 19.29/4.18 % No. of inferences in proof: 42
% 19.29/4.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3638 ms resp. 3173 ms w/o parsing
% 19.49/4.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.49/4.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------