TSTP Solution File: SYO457^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO457^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 09:00:24 EDT 2024
% Result : Theorem 3.55s 2.19s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 32 ( 12 unt; 11 typ; 5 def)
% Number of atoms : 64 ( 7 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 95 ( 20 ~; 11 |; 0 &; 64 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 19 ( 5 ^ 14 !; 0 ?; 19 :)
% 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(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
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(q_type,type,
q: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mdia_s5 @ ( mimplies @ q @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mdia_s5 @ ( mimplies @ q @ 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 )
| ~ ( ~ ( q @ B )
| ( p @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
rel_s5 @ sk1 @ sk2,
inference(cnf,[status(esa)],[6]) ).
thf(8,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ~ ( p @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ~ ( p @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(24,plain,
! [A: $i] :
( ~ ( p @ A )
| ( ( rel_s5 @ sk1 @ sk2 )
!= ( rel_s5 @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,12]) ).
thf(25,plain,
~ ( p @ sk2 ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk2 ))]]) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(13,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(cnf,[status(esa)],[13]) ).
thf(9,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( p @ B )
| ( ( rel_s5 @ A @ A )
!= ( rel_s5 @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,9]) ).
thf(21,plain,
p @ sk2,
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(30,plain,
~ $true,
inference(rewrite,[status(thm)],[25,21]) ).
thf(31,plain,
$false,
inference(simp,[status(thm)],[30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO457^6 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 09:21:09 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.85/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.14 % [INFO] Parsing done (238ms).
% 1.51/1.16 % [INFO] Running in sequential loop mode.
% 1.91/1.49 % [INFO] nitpick registered as external prover.
% 1.91/1.50 % [INFO] Scanning for conjecture ...
% 2.40/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.46/1.69 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.46/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.70 % [INFO] Type checking passed.
% 2.46/1.70 % [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 ...
% 3.55/2.18 % [INFO] Killing All external provers ...
% 3.55/2.18 % Time passed: 1731ms (effective reasoning time: 1021ms)
% 3.55/2.18 % 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)>
% 3.55/2.19 % Axioms used in derivation (1): a1
% 3.55/2.19 % No. of inferences in proof: 16
% 3.55/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1731 ms resp. 1021 ms w/o parsing
% 3.55/2.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.55/2.23 % [INFO] Killing All external provers ...
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