TSTP Solution File: SYO451^5 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO451^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 09:00:19 EDT 2024
% Result : Theorem 4.72s 2.05s
% Output : Refutation 4.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 48 ( 14 unt; 13 typ; 6 def)
% Number of atoms : 112 ( 11 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 225 ( 37 ~; 31 |; 2 &; 153 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 36 ( 8 ^ 28 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(mbox_s4_def,definition,
( mbox_s4
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_s4_type,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(mdia_s4_def,definition,
( mdia_s4
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mor @ p @ ( mdia_s4 @ q ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mor @ p @ ( mdia_s4 @ q ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( p @ B )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ~ ( q @ C ) ) )
| ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( q @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
rel_s4 @ sk1 @ sk3,
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( p @ A )
| ( rel_s4 @ A @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(32,plain,
! [A: $i] :
( ( p @ A )
| ( rel_s4 @ A @ ( sk2 @ A ) )
| ( ( rel_s4 @ sk1 @ sk3 )
!= ( rel_s4 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(33,plain,
( ( p @ sk3 )
| ( rel_s4 @ sk3 @ ( sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk3 ))]]) ).
thf(10,plain,
~ ( p @ sk3 ),
inference(cnf,[status(esa)],[5]) ).
thf(105,plain,
( $false
| ( rel_s4 @ sk3 @ ( sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[33,10]) ).
thf(106,plain,
rel_s4 @ sk3 @ ( sk2 @ sk3 ),
inference(simp,[status(thm)],[105]) ).
thf(4,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(14,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s4 @ A @ B )
& ( rel_s4 @ B @ C ) )
=> ( rel_s4 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( rel_s4 @ A @ C ) ),
inference(cnf,[status(esa)],[14]) ).
thf(9,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( p @ A )
| ( q @ ( sk2 @ A ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(20,plain,
! [A: $i] :
( ( p @ A )
| ( q @ ( sk2 @ A ) )
| ( ( rel_s4 @ sk1 @ sk3 )
!= ( rel_s4 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(21,plain,
( ( p @ sk3 )
| ( q @ ( sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk3 ))]]) ).
thf(24,plain,
( $false
| ( q @ ( sk2 @ sk3 ) ) ),
inference(rewrite,[status(thm)],[21,10]) ).
thf(25,plain,
q @ ( sk2 @ sk3 ),
inference(simp,[status(thm)],[24]) ).
thf(8,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ~ ( q @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(11,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ~ ( q @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(27,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( ( q @ ( sk2 @ sk3 ) )
!= ( q @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,11]) ).
thf(28,plain,
~ ( rel_s4 @ sk1 @ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk2 @ sk3 ))]]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( ( rel_s4 @ A @ C )
!= ( rel_s4 @ sk1 @ ( sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,28]) ).
thf(74,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ~ ( rel_s4 @ A @ ( sk2 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk2 @ sk3 ))]]) ).
thf(100,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ~ ( rel_s4 @ A @ ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(128,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( ( rel_s4 @ sk3 @ ( sk2 @ sk3 ) )
!= ( rel_s4 @ A @ ( sk2 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[106,100]) ).
thf(129,plain,
~ ( rel_s4 @ sk1 @ sk3 ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( sk3 ))]]) ).
thf(155,plain,
~ $true,
inference(rewrite,[status(thm)],[129,6]) ).
thf(156,plain,
$false,
inference(simp,[status(thm)],[155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO451^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n022.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 09:34:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.03 % [INFO] Parsing done (153ms).
% 1.39/1.03 % [INFO] Running in sequential loop mode.
% 1.94/1.26 % [INFO] nitpick registered as external prover.
% 1.94/1.26 % [INFO] Scanning for conjecture ...
% 2.22/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.37/1.40 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.37/1.40 % [INFO] Problem is higher-order (TPTP THF).
% 2.37/1.40 % [INFO] Type checking passed.
% 2.37/1.40 % [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 ...
% 4.72/2.05 % [INFO] Killing All external provers ...
% 4.72/2.05 % Time passed: 1516ms (effective reasoning time: 1009ms)
% 4.72/2.05 % 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)>
% 4.72/2.05 % Axioms used in derivation (1): a2
% 4.72/2.05 % No. of inferences in proof: 29
% 4.72/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1516 ms resp. 1009 ms w/o parsing
% 4.72/2.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.72/2.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------