TSTP Solution File: SYO572^7 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO572^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 08:57:24 EDT 2024
% Result : Theorem 3.35s 1.73s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 30 ( 11 unt; 11 typ; 7 def)
% Number of atoms : 63 ( 7 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 97 ( 7 ~; 3 |; 4 &; 76 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 10 ^ 22 !; 2 ?; 34 :)
% 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(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mforall_ind_def,definition,
( mforall_ind
= ( ^ [A: mu > $i > $o,B: $i] :
! [C: mu] :
( ( exists_in_world @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).
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(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(f_type,type,
f: mu > $i > $o ).
thf(4,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(14,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty_ax) ).
thf(12,plain,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( mvalid
@ ( mimplies @ ( mdia_s4 @ ( mforall_ind @ f ) )
@ ( mexists_ind
@ ^ [A: mu] : ( mdia_s4 @ ( f @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mimplies @ ( mdia_s4 @ ( mforall_ind @ f ) )
@ ( mexists_ind
@ ^ [A: mu] : ( mdia_s4 @ ( f @ A ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ! [C: mu] :
( ( exists_in_world @ C @ B )
=> ( f @ C @ B ) ) )
| ~ ! [B: mu] :
( ( exists_in_world @ B @ A )
=> ! [C: $i] :
( ~ ( rel_s4 @ A @ C )
| ~ ( f @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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/sandbox/benchmark/theBenchmark.p',cumulative_ax) ).
thf(18,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(5,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(16,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(20,plain,
$false,
inference(e,[status(thm)],[14,12,7,18,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO572^7 : TPTP v8.2.0. Released v5.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n015.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 09:42:39 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.02 % [INFO] Parsing done (152ms).
% 1.39/1.02 % [INFO] Running in sequential loop mode.
% 1.94/1.23 % [INFO] eprover registered as external prover.
% 1.94/1.23 % [INFO] cvc4 registered as external prover.
% 1.94/1.24 % [INFO] Scanning for conjecture ...
% 2.27/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.27/1.36 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.36/1.37 % [INFO] Problem is higher-order (TPTP THF).
% 2.36/1.37 % [INFO] Type checking passed.
% 2.36/1.37 % [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 ...
% 3.35/1.72 % External prover 'e' found a proof!
% 3.35/1.72 % [INFO] Killing All external provers ...
% 3.35/1.72 % Time passed: 1197ms (effective reasoning time: 698ms)
% 3.35/1.72 % 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)>
% 3.35/1.73 % Axioms used in derivation (4): a1, nonempty_ax, cumulative_ax, a2
% 3.35/1.73 % No. of inferences in proof: 12
% 3.35/1.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1197 ms resp. 698 ms w/o parsing
% 3.47/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.47/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------