TSTP Solution File: SYO464^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO464^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 09:00:31 EDT 2024
% Result : Theorem 6.47s 2.96s
% Output : Refutation 6.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 14 unt; 14 typ; 6 def)
% Number of atoms : 111 ( 11 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 208 ( 40 ~; 26 |; 2 &; 138 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 9 con; 0-3 aty)
% Number of variables : 38 ( 7 ^ 31 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
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 ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mand @ p @ q ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mimplies @ ( mdia_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mand @ p @ q ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mimplies @ ( mdia_s4 @ p ) @ ( mdia_s4 @ q ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( ~ ( p @ B )
| ~ ( q @ B ) ) )
| ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ~ ( p @ D ) )
| ~ ! [D: $i] :
( ~ ( rel_s4 @ C @ D )
| ~ ( q @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
rel_s4 @ sk2 @ sk3,
inference(cnf,[status(esa)],[5]) ).
thf(4,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(16,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(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( rel_s4 @ A @ C ) ),
inference(cnf,[status(esa)],[16]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ( rel_s4 @ A @ C )
| ( ( rel_s4 @ sk2 @ sk3 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(99,plain,
! [A: $i] :
( ~ ( rel_s4 @ A @ sk2 )
| ( rel_s4 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(10,plain,
rel_s4 @ sk3 @ sk4,
inference(cnf,[status(esa)],[5]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s4 @ A @ B )
| ( rel_s4 @ A @ C )
| ( ( rel_s4 @ sk3 @ sk4 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,17]) ).
thf(93,plain,
! [A: $i] :
( ~ ( rel_s4 @ A @ sk3 )
| ( rel_s4 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(6,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk1 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ~ ( rel_s4 @ A @ sk3 )
| ( q @ B )
| ( ( rel_s4 @ A @ sk4 )
!= ( rel_s4 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[93,6]) ).
thf(134,plain,
( ~ ( rel_s4 @ sk1 @ sk3 )
| ( q @ sk4 ) ),
inference(pattern_uni,[status(thm)],[133:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( q @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(13,plain,
! [A: $i] :
( ~ ( rel_s4 @ sk3 @ A )
| ~ ( q @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(18,plain,
! [A: $i] :
( ~ ( q @ A )
| ( ( rel_s4 @ sk3 @ sk4 )
!= ( rel_s4 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,13]) ).
thf(19,plain,
~ ( q @ sk4 ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk4 ))]]) ).
thf(191,plain,
( ~ ( rel_s4 @ sk1 @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[134,19]) ).
thf(192,plain,
~ ( rel_s4 @ sk1 @ sk3 ),
inference(simp,[status(thm)],[191]) ).
thf(215,plain,
! [A: $i] :
( ~ ( rel_s4 @ A @ sk2 )
| ( ( rel_s4 @ A @ sk3 )
!= ( rel_s4 @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[99,192]) ).
thf(216,plain,
~ ( rel_s4 @ sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( sk1 ))]]) ).
thf(11,plain,
rel_s4 @ sk1 @ sk2,
inference(cnf,[status(esa)],[5]) ).
thf(254,plain,
~ $true,
inference(rewrite,[status(thm)],[216,11]) ).
thf(255,plain,
$false,
inference(simp,[status(thm)],[254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09 % Problem : SYO464^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 10:01:54 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.99/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/1.21 % [INFO] Parsing done (255ms).
% 1.61/1.22 % [INFO] Running in sequential loop mode.
% 2.10/1.59 % [INFO] nitpick registered as external prover.
% 2.10/1.59 % [INFO] Scanning for conjecture ...
% 2.44/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.65/1.80 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.65/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 2.65/1.80 % [INFO] Type checking passed.
% 2.65/1.81 % [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 ...
% 6.47/2.96 % [INFO] Killing All external provers ...
% 6.47/2.96 % Time passed: 2487ms (effective reasoning time: 1731ms)
% 6.47/2.96 % 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)>
% 6.47/2.96 % Axioms used in derivation (1): a2
% 6.47/2.96 % No. of inferences in proof: 26
% 6.47/2.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2487 ms resp. 1731 ms w/o parsing
% 6.47/3.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.47/3.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------