TSTP Solution File: SYO572^7 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---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 : n013.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 09:00:58 EDT 2024
% Result : Theorem 5.07s 2.18s
% Output : Refutation 5.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 14 unt; 12 typ; 5 def)
% Number of atoms : 94 ( 10 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 199 ( 34 ~; 19 |; 2 &; 139 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 44 ( 8 ^ 34 !; 2 ?; 44 :)
% 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(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(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > mu ).
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(10,plain,
rel_s4 @ sk1 @ sk2,
inference(cnf,[status(esa)],[7]) ).
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(19,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( exists_in_world @ A @ B )
| ~ ( rel_s4 @ B @ C )
| ( exists_in_world @ A @ C ) ),
inference(cnf,[status(esa)],[18]) ).
thf(101,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( exists_in_world @ A @ B )
| ( exists_in_world @ A @ C )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(102,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ( exists_in_world @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(9,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk2 )
| ( f @ A @ sk2 ) ),
inference(cnf,[status(esa)],[7]) ).
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(13,plain,
! [A: $i] : ( exists_in_world @ ( sk3 @ A ) @ A ),
inference(cnf,[status(esa)],[12]) ).
thf(8,plain,
! [B: $i,A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ~ ( rel_s4 @ sk1 @ B )
| ~ ( f @ A @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(11,plain,
! [B: $i,A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ~ ( rel_s4 @ sk1 @ B )
| ~ ( f @ A @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(22,plain,
! [B: $i,A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ~ ( f @ A @ B )
| ( ( rel_s4 @ sk1 @ sk2 )
!= ( rel_s4 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,11]) ).
thf(23,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ~ ( f @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(34,plain,
! [B: mu,A: $i] :
( ~ ( f @ B @ sk2 )
| ( ( exists_in_world @ ( sk3 @ A ) @ A )
!= ( exists_in_world @ B @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[13,23]) ).
thf(35,plain,
~ ( f @ ( sk3 @ sk1 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(41,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk2 )
| ( ( f @ A @ sk2 )
!= ( f @ ( sk3 @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,35]) ).
thf(42,plain,
~ ( exists_in_world @ ( sk3 @ sk1 ) @ sk2 ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(159,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk1 )
| ( ( exists_in_world @ A @ sk2 )
!= ( exists_in_world @ ( sk3 @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[102,42]) ).
thf(160,plain,
~ ( exists_in_world @ ( sk3 @ sk1 ) @ sk1 ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( sk3 @ sk1 ))]]) ).
thf(191,plain,
~ $true,
inference(rewrite,[status(thm)],[160,13]) ).
thf(192,plain,
$false,
inference(simp,[status(thm)],[191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO572^7 : TPTP v8.2.0. Released v5.5.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 09:42:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.93/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.07 % [INFO] Parsing done (161ms).
% 1.45/1.08 % [INFO] Running in sequential loop mode.
% 1.93/1.29 % [INFO] nitpick registered as external prover.
% 1.93/1.30 % [INFO] Scanning for conjecture ...
% 2.21/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.21/1.42 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.21/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.43 % [INFO] Type checking passed.
% 2.21/1.43 % [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 ...
% 5.07/2.17 % [INFO] Killing All external provers ...
% 5.07/2.18 % Time passed: 1622ms (effective reasoning time: 1088ms)
% 5.07/2.18 % 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)>
% 5.07/2.18 % Axioms used in derivation (2): cumulative_ax, nonempty_ax
% 5.07/2.18 % No. of inferences in proof: 25
% 5.07/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1622 ms resp. 1088 ms w/o parsing
% 5.07/2.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.07/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------