TSTP Solution File: SYO471^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO471^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 09:00:36 EDT 2024
% Result : Theorem 5.10s 2.16s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 47 ( 16 unt; 13 typ; 6 def)
% Number of atoms : 97 ( 12 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 185 ( 30 ~; 20 |; 2 &; 129 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 41 ( 6 ^ 35 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ) ).
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_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mdia_s5 @ ( mdia_s5 @ p ) ) @ ( mbox_s5 @ ( mdia_s5 @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mdia_s5 @ p ) ) @ ( mbox_s5 @ ( mdia_s5 @ p ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ( p @ C ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
rel_s5 @ sk2 @ sk3,
inference(cnf,[status(esa)],[6]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(14,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s5 @ A @ B )
& ( rel_s5 @ B @ C ) )
=> ( rel_s5 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C ) ),
inference(cnf,[status(esa)],[14]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,15]) ).
thf(56,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk2 )
| ( rel_s5 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(9,plain,
p @ sk3,
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ~ ( p @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(18,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( ( p @ sk3 )
!= ( p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(19,plain,
~ ( rel_s5 @ sk4 @ sk3 ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk3 ))]]) ).
thf(234,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk2 )
| ( ( rel_s5 @ A @ sk3 )
!= ( rel_s5 @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[56,19]) ).
thf(235,plain,
~ ( rel_s5 @ sk4 @ sk2 ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( sk4 ))]]) ).
thf(8,plain,
rel_s5 @ sk1 @ sk4,
inference(cnf,[status(esa)],[6]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ A ) ),
inference(cnf,[status(esa)],[16]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk1 @ sk4 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,17]) ).
thf(120,plain,
rel_s5 @ sk4 @ sk1,
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(7,plain,
rel_s5 @ sk1 @ sk2,
inference(cnf,[status(esa)],[6]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk1 @ sk2 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7,15]) ).
thf(52,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk1 )
| ( rel_s5 @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(164,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk2 )
| ( ( rel_s5 @ sk4 @ sk1 )
!= ( rel_s5 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[120,52]) ).
thf(165,plain,
rel_s5 @ sk4 @ sk2,
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( sk4 ))]]) ).
thf(290,plain,
~ $true,
inference(rewrite,[status(thm)],[235,165]) ).
thf(291,plain,
$false,
inference(simp,[status(thm)],[290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO471^6 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 10:57:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (153ms).
% 1.25/1.02 % [INFO] Running in sequential loop mode.
% 1.92/1.23 % [INFO] nitpick registered as external prover.
% 1.92/1.24 % [INFO] Scanning for conjecture ...
% 2.13/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.31/1.37 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.31/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.31/1.37 % [INFO] Type checking passed.
% 2.31/1.38 % [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 ...
% 5.10/2.16 % [INFO] Killing All external provers ...
% 5.10/2.16 % Time passed: 1637ms (effective reasoning time: 1137ms)
% 5.10/2.16 % 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)>
% 5.10/2.16 % Axioms used in derivation (2): a2, a3
% 5.10/2.16 % No. of inferences in proof: 28
% 5.10/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1637 ms resp. 1137 ms w/o parsing
% 5.10/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.10/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------