TSTP Solution File: SYO497^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO497^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 09:00:42 EDT 2024
% Result : Theorem 4.51s 2.27s
% Output : Refutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of formulae : 57 ( 19 unt; 16 typ; 9 def)
% Number of atoms : 144 ( 14 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 305 ( 57 ~; 38 |; 2 &; 204 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 69 ( 14 ^ 53 !; 2 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
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(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] : ( 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(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ 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_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( 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: mu ).
thf(sk4_type,type,
sk4: $i ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(1,conjecture,
( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( f @ A ) @ ( mbox_s5 @ ( f @ A ) ) ) ) )
@ ( mdia_s5 @ ( mexists_ind @ f ) ) )
@ ( mbox_s5 @ ( mexists_ind @ f ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mand
@ ( mbox_s5
@ ( mforall_ind
@ ^ [A: mu] : ( mimplies @ ( f @ A ) @ ( mbox_s5 @ ( f @ A ) ) ) ) )
@ ( mdia_s5 @ ( mexists_ind @ f ) ) )
@ ( mbox_s5 @ ( mexists_ind @ f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: mu] :
( ~ ( f @ C @ B )
| ! [D: $i] :
( ~ ( rel_s5 @ B @ D )
| ( f @ C @ D ) ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: mu] :
~ ( f @ C @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: mu] :
~ ( f @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: mu] :
( ~ ( f @ C @ B )
| ! [D: $i] :
( ~ ( rel_s5 @ B @ D )
| ( f @ C @ D ) ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ? [C: mu] : ( f @ C @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ~ ? [C: mu] : ( f @ C @ B ) ) ),
inference(miniscope,[status(thm)],[6]) ).
thf(9,plain,
rel_s5 @ sk1 @ sk4,
inference(cnf,[status(esa)],[7]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(16,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s5 @ A @ B )
& ( rel_s5 @ B @ C ) )
=> ( rel_s5 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C ) ),
inference(cnf,[status(esa)],[16]) ).
thf(11,plain,
f @ sk3 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ~ ( f @ B @ A )
| ~ ( rel_s5 @ A @ C )
| ( f @ B @ C ) ),
inference(cnf,[status(esa)],[7]) ).
thf(31,plain,
! [C: $i,B: mu,A: $i] :
( ~ ( rel_s5 @ sk1 @ A )
| ~ ( rel_s5 @ A @ C )
| ( f @ B @ C )
| ( ( f @ sk3 @ sk2 )
!= ( f @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(32,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk1 @ sk2 )
| ~ ( rel_s5 @ sk2 @ A )
| ( f @ sk3 @ A ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(39,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk1 @ sk2 )
| ~ ( rel_s5 @ sk2 @ A )
| ( f @ sk3 @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(8,plain,
rel_s5 @ sk1 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(51,plain,
! [A: $i] :
( ~ $true
| ~ ( rel_s5 @ sk2 @ A )
| ( f @ sk3 @ A ) ),
inference(rewrite,[status(thm)],[39,8]) ).
thf(52,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ( f @ sk3 @ A ) ),
inference(simp,[status(thm)],[51]) ).
thf(10,plain,
! [A: mu] :
~ ( f @ A @ sk4 ),
inference(cnf,[status(esa)],[7]) ).
thf(13,plain,
! [A: mu] :
~ ( f @ A @ sk4 ),
inference(simp,[status(thm)],[10]) ).
thf(54,plain,
! [B: mu,A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ( ( f @ sk3 @ A )
!= ( f @ B @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[52,13]) ).
thf(55,plain,
~ ( rel_s5 @ sk2 @ sk4 ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( ( rel_s5 @ A @ C )
!= ( rel_s5 @ sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[17,55]) ).
thf(89,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ~ ( rel_s5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(104,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ~ ( rel_s5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[89]) ).
thf(112,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ( ( rel_s5 @ sk1 @ sk4 )
!= ( rel_s5 @ A @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[9,104]) ).
thf(113,plain,
~ ( rel_s5 @ sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( sk1 ))]]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( ( rel_s5 @ B @ A )
!= ( rel_s5 @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19,113]) ).
thf(197,plain,
~ ( rel_s5 @ sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(247,plain,
~ $true,
inference(rewrite,[status(thm)],[197,8]) ).
thf(248,plain,
$false,
inference(simp,[status(thm)],[247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO497^6 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n028.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 20 09:40:39 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.04 % [INFO] Parsing done (161ms).
% 1.41/1.05 % [INFO] Running in sequential loop mode.
% 2.00/1.28 % [INFO] nitpick registered as external prover.
% 2.00/1.28 % [INFO] Scanning for conjecture ...
% 2.44/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.44/1.42 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.44/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.44/1.42 % [INFO] Type checking passed.
% 2.44/1.42 % [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 ...
% 4.51/2.26 % [INFO] Killing All external provers ...
% 4.51/2.27 % Time passed: 1726ms (effective reasoning time: 1214ms)
% 4.51/2.27 % 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)>
% 4.51/2.27 % Axioms used in derivation (2): a3, a2
% 4.51/2.27 % No. of inferences in proof: 32
% 4.51/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1726 ms resp. 1214 ms w/o parsing
% 4.59/2.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.59/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------