TSTP Solution File: SYN367^7 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYN367^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 08:11:46 EDT 2024
% Result : Theorem 9.81s 3.32s
% Output : Refutation 9.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 36 ( 13 unt; 15 typ; 9 def)
% Number of atoms : 118 ( 9 equ; 0 cnn)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 203 ( 23 ~; 18 |; 4 &; 150 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 2 con; 0-3 aty)
% Number of variables : 55 ( 20 ^ 33 !; 2 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: $i > $o,B: $i] :
~ ( A @ B ) ) ) ).
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(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(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(big_r_type,type,
big_r: mu > $i > $o ).
thf(big_q_type,type,
big_q: mu > $i > $o ).
thf(4,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
thf(28,plain,
! [A: $i] : ( rel_s4 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(32,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
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ A ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ A ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_q @ A ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_r @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2118) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ A ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ A ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_q @ A ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] : ( mbox_s4 @ ( big_r @ A ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: mu] :
( ( exists_in_world @ D @ C )
=> ( ~ ( ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( p @ E ) )
| ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( big_q @ D @ E ) ) )
| ~ ( ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ~ ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( p @ F ) ) )
| ~ ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( big_r @ D @ E ) ) ) ) ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: mu] :
( ( exists_in_world @ D @ C )
=> ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( big_q @ D @ E ) ) ) )
| ! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ! [D: mu] :
( ( exists_in_world @ D @ C )
=> ! [E: $i] :
( ~ ( rel_s4 @ C @ E )
| ( big_r @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax) ).
thf(26,plain,
! [A: $i] :
? [B: mu] : ( exists_in_world @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(30,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(770,plain,
$false,
inference(e,[status(thm)],[28,32,7,26,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SYN367^7 : TPTP v8.2.0. Released v5.5.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n008.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon May 20 14:28:24 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.96/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/1.15 % [INFO] Parsing done (233ms).
% 1.33/1.16 % [INFO] Running in sequential loop mode.
% 2.08/1.50 % [INFO] eprover registered as external prover.
% 2.08/1.51 % [INFO] cvc4 registered as external prover.
% 2.15/1.51 % [INFO] Scanning for conjecture ...
% 2.39/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.60/1.71 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.60/1.72 % [INFO] Problem is higher-order (TPTP THF).
% 2.60/1.72 % [INFO] Type checking passed.
% 2.60/1.73 % [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 ...
% 9.71/3.31 % External prover 'e' found a proof!
% 9.71/3.31 % [INFO] Killing All external provers ...
% 9.71/3.32 % Time passed: 2860ms (effective reasoning time: 2149ms)
% 9.71/3.32 % 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)>
% 9.81/3.32 % Axioms used in derivation (4): a1, cumulative_ax, nonempty_ax, a2
% 9.81/3.32 % No. of inferences in proof: 12
% 9.81/3.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2860 ms resp. 2149 ms w/o parsing
% 9.81/3.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.81/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------