TSTP Solution File: SYO450^3 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n022.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 : Mon Jun 24 20:51:29 EDT 2024
% Result : Theorem 3.10s 1.76s
% Output : Refutation 3.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 66 ( 5 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 92 ( 19 ~; 11 |; 0 &; 62 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 14 ( 5 ^ 9 !; 0 ?; 14 :)
% 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_m_type,type,
rel_m: $i > $i > $o ).
thf(mbox_m_type,type,
mbox_m: ( $i > $o ) > $i > $o ).
thf(mbox_m_def,definition,
( mbox_m
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_m @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_m_type,type,
mdia_m: ( $i > $o ) > $i > $o ).
thf(mdia_m_def,definition,
( mdia_m
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_m @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(r_type,type,
r: $i > $o ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mbox_m @ ( mimplies @ p @ ( mdia_m @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_m @ ( mimplies @ q @ ( mimplies @ ( mbox_m @ p ) @ ( mdia_m @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mimplies @ p @ ( mdia_m @ ( mimplies @ q @ r ) ) ) ) @ ( mdia_m @ ( mimplies @ q @ ( mimplies @ ( mbox_m @ p ) @ ( mdia_m @ r ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_m @ A @ B )
| ~ ( p @ B )
| ~ ! [C: $i] :
( ~ ( rel_m @ B @ C )
| ~ ( ~ ( q @ C )
| ( r @ C ) ) ) )
| ~ ! [B: $i] :
( ~ ( rel_m @ A @ B )
| ~ ( ~ ( q @ B )
| ~ ! [C: $i] :
( ~ ( rel_m @ B @ C )
| ( p @ C ) )
| ~ ! [C: $i] :
( ~ ( rel_m @ B @ C )
| ~ ( r @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
mreflexive @ rel_m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(13,plain,
! [A: $i] : ( rel_m @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
$false,
inference(e,[status(thm)],[4,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO450^3 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n022.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 : Sun Jun 23 09:37:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.95/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.07 % [INFO] Parsing done (162ms).
% 1.43/1.08 % [INFO] Running in sequential loop mode.
% 1.92/1.28 % [INFO] eprover registered as external prover.
% 1.92/1.29 % [INFO] Scanning for conjecture ...
% 2.27/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.27/1.41 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.27/1.41 % [INFO] Problem is higher-order (TPTP THF).
% 2.27/1.42 % [INFO] Type checking passed.
% 2.27/1.42 % [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 ...
% 3.10/1.75 % External prover 'e' found a proof!
% 3.10/1.75 % [INFO] Killing All external provers ...
% 3.10/1.75 % Time passed: 1235ms (effective reasoning time: 674ms)
% 3.10/1.75 % 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)>
% 3.10/1.76 % Axioms used in derivation (1): a1
% 3.10/1.76 % No. of inferences in proof: 6
% 3.10/1.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1235 ms resp. 674 ms w/o parsing
% 3.34/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.34/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------