TSTP Solution File: SYN045^7 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYN045^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 08:09:58 EDT 2024
% Result : Theorem 3.24s 1.74s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 25
% Syntax : Number of formulae : 32 ( 11 unt; 13 typ; 7 def)
% Number of atoms : 157 ( 7 equ; 0 cnn)
% Maximal formula atoms : 44 ( 8 avg)
% Number of connectives : 252 ( 34 ~; 31 |; 4 &; 179 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 10 ^ 34 !; 2 ?; 46 :)
% 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(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(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
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(r_type,type,
r: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(p_type,type,
p: $i > $o ).
thf(6,axiom,
! [A: mu,B: $i,C: $i] :
( ( ( exists_in_world @ A @ B )
& ( rel_s4 @ B @ C ) )
=> ( exists_in_world @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax) ).
thf(38,plain,
! [A: mu,B: $i,C: $i] :
( ( ( exists_in_world @ A @ B )
& ( rel_s4 @ B @ C ) )
=> ( exists_in_world @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel13) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i] :
~ ( ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( p @ C ) )
| ~ ( ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( q @ C ) )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( r @ C ) ) ) )
| ~ ( ~ ( ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( p @ C ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( q @ C ) ) )
| ~ ( ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( p @ C ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( r @ C ) ) ) ) )
| ~ ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ( ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( p @ C ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( q @ C ) ) )
| ~ ( ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( p @ C ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( r @ C ) ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( p @ C ) )
| ~ ( ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( q @ C ) )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( r @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(36,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)],[5]) ).
thf(3,axiom,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(32,plain,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(34,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,plain,
$false,
inference(cvc4,[status(thm)],[38,7,36,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN045^7 : TPTP v8.2.0. Released v5.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 14:07:09 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (140ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 1.88/1.21 % [INFO] eprover registered as external prover.
% 1.88/1.21 % [INFO] cvc4 registered as external prover.
% 1.88/1.22 % [INFO] Scanning for conjecture ...
% 2.24/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.24/1.34 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.24/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.35 % [INFO] Type checking passed.
% 2.24/1.35 % [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 ...
% 3.24/1.74 % External prover 'cvc4' found a proof!
% 3.24/1.74 % [INFO] Killing All external provers ...
% 3.24/1.74 % Time passed: 1209ms (effective reasoning time: 723ms)
% 3.24/1.74 % 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)>
% 3.24/1.74 % Axioms used in derivation (4): cumulative_ax, a2, nonempty_ax, a1
% 3.24/1.74 % No. of inferences in proof: 12
% 3.24/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1209 ms resp. 723 ms w/o parsing
% 3.58/1.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.58/1.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------