TSTP Solution File: SYO462^5 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO462^5 : 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 08:56:59 EDT 2024
% Result : Theorem 3.34s 2.22s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 24 ( 8 unt; 10 typ; 6 def)
% Number of atoms : 63 ( 6 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 104 ( 19 ~; 13 |; 2 &; 68 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 7 ^ 15 !; 0 ?; 22 :)
% 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(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ 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(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(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( ~ ( ~ ( p @ B )
| ( q @ B ) )
| ~ ( ~ ( q @ B )
| ( p @ B ) ) ) )
| ~ ( ~ ( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( q @ B ) ) )
| ~ ( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( q @ B ) )
| ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(16,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(18,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(20,plain,
$false,
inference(e,[status(thm)],[5,16,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYO462^5 : TPTP v8.2.0. Released v4.0.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.10/0.31 % Computer : n027.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 09:57:09 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.93/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.15 % [INFO] Parsing done (218ms).
% 1.60/1.18 % [INFO] Running in sequential loop mode.
% 2.12/1.53 % [INFO] eprover registered as external prover.
% 2.12/1.54 % [INFO] cvc4 registered as external prover.
% 2.12/1.54 % [INFO] Scanning for conjecture ...
% 2.51/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.51/1.74 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.51/1.74 % [INFO] Problem is higher-order (TPTP THF).
% 2.51/1.75 % [INFO] Type checking passed.
% 2.51/1.75 % [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 ...
% 3.34/2.22 % External prover 'e' found a proof!
% 3.34/2.22 % [INFO] Killing All external provers ...
% 3.34/2.22 % Time passed: 1762ms (effective reasoning time: 1037ms)
% 3.34/2.22 % 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)>
% 3.34/2.22 % Axioms used in derivation (2): a1, a2
% 3.34/2.22 % No. of inferences in proof: 8
% 3.34/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1762 ms resp. 1037 ms w/o parsing
% 3.75/2.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.75/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------