TSTP Solution File: SYO451^5 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---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 : n028.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 08:56:50 EDT 2024
% Result : Theorem 3.63s 2.30s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 26 ( 9 unt; 11 typ; 7 def)
% Number of atoms : 62 ( 7 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 88 ( 12 ~; 9 |; 2 &; 63 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 23 ( 9 ^ 14 !; 0 ?; 23 :)
% 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(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(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(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(3,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(12,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(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(16,plain,
$false,
inference(e,[status(thm)],[5,12,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO451^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 09:34:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.99/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.60/1.20 % [INFO] Parsing done (216ms).
% 1.60/1.22 % [INFO] Running in sequential loop mode.
% 2.11/1.59 % [INFO] eprover registered as external prover.
% 2.11/1.59 % [INFO] cvc4 registered as external prover.
% 2.11/1.59 % [INFO] Scanning for conjecture ...
% 2.51/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.70/1.80 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.70/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 2.77/1.80 % [INFO] Type checking passed.
% 2.77/1.81 % [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 ...
% 3.63/2.30 % External prover 'e' found a proof!
% 3.63/2.30 % [INFO] Killing All external provers ...
% 3.63/2.30 % Time passed: 1804ms (effective reasoning time: 1075ms)
% 3.63/2.30 % 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)>
% 3.63/2.30 % Axioms used in derivation (2): a1, a2
% 3.63/2.30 % No. of inferences in proof: 8
% 3.63/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1804 ms resp. 1075 ms w/o parsing
% 3.91/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.91/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------