TSTP Solution File: SYO495^6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO495^6 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 09:00:41 EDT 2024
% Result : Theorem 241.26s 131.12s
% Output : Refutation 241.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 32 ( 11 unt; 12 typ; 5 def)
% Number of atoms : 77 ( 8 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 142 ( 16 ~; 20 |; 0 &; 106 @)
% ( 0 <=>; 0 =>; 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 : 15 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 32 ( 12 ^ 20 !; 0 ?; 32 :)
% 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(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(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(f_type,type,
f: mu > $i > $o ).
thf(g_type,type,
g: mu > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: mu ).
thf(1,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [A: mu] : ( mor @ ( mbox_s5 @ ( f @ A ) ) @ ( mbox_s5 @ ( g @ A ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [A: mu] : ( mor @ ( f @ A ) @ ( g @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [A: mu] : ( mor @ ( mbox_s5 @ ( f @ A ) ) @ ( mbox_s5 @ ( g @ A ) ) ) )
@ ( mbox_s5
@ ( mforall_ind
@ ^ [A: mu] : ( mor @ ( f @ A ) @ ( g @ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ~ ! [B: mu] :
( ! [C: $i] :
( ~ ( rel_s5 @ A @ C )
| ( f @ B @ C ) )
| ! [C: $i] :
( ~ ( rel_s5 @ A @ C )
| ( g @ B @ C ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: mu] :
( ( f @ C @ B )
| ( g @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
rel_s5 @ sk1 @ sk2,
inference(cnf,[status(esa)],[6]) ).
thf(10,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( rel_s5 @ sk1 @ B )
| ( f @ A @ B )
| ~ ( rel_s5 @ sk1 @ C )
| ( g @ A @ C ) ),
inference(cnf,[status(esa)],[6]) ).
thf(138,plain,
! [C: $i,B: $i,A: mu] :
( ~ ( rel_s5 @ sk1 @ B )
| ( f @ A @ B )
| ( g @ A @ C )
| ( ( rel_s5 @ sk1 @ sk2 )
!= ( rel_s5 @ sk1 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[9,10]) ).
thf(139,plain,
! [B: $i,A: mu] :
( ~ ( rel_s5 @ sk1 @ B )
| ( f @ A @ B )
| ( g @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(5170,plain,
! [B: $i,A: mu] :
( ( f @ A @ B )
| ( g @ A @ sk2 )
| ( ( rel_s5 @ sk1 @ sk2 )
!= ( rel_s5 @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,139]) ).
thf(5171,plain,
! [A: mu] :
( ( f @ A @ sk2 )
| ( g @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[5170:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(7,plain,
~ ( g @ sk3 @ sk2 ),
inference(cnf,[status(esa)],[6]) ).
thf(48156,plain,
! [A: mu] :
( ( f @ A @ sk2 )
| ( ( g @ A @ sk2 )
!= ( g @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5171,7]) ).
thf(48157,plain,
f @ sk3 @ sk2,
inference(pattern_uni,[status(thm)],[48156:[bind(A,$thf( sk3 ))]]) ).
thf(8,plain,
~ ( f @ sk3 @ sk2 ),
inference(cnf,[status(esa)],[6]) ).
thf(48158,plain,
$false,
inference(rewrite,[status(thm)],[48157,8]) ).
thf(48159,plain,
$false,
inference(simp,[status(thm)],[48158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO495^6 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n005.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 09:29:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.93/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.07 % [INFO] Parsing done (155ms).
% 1.55/1.08 % [INFO] Running in sequential loop mode.
% 1.93/1.29 % [INFO] nitpick registered as external prover.
% 1.93/1.29 % [INFO] Scanning for conjecture ...
% 2.22/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.22/1.41 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.22/1.41 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.42 % [INFO] Type checking passed.
% 2.22/1.42 % [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 ...
% 241.26/131.11 % [INFO] Killing All external provers ...
% 241.26/131.11 % Time passed: 130556ms (effective reasoning time: 130026ms)
% 241.26/131.11 % 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)>
% 241.26/131.11 % Axioms used in derivation (0):
% 241.26/131.11 % No. of inferences in proof: 15
% 241.26/131.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 130556 ms resp. 130026 ms w/o parsing
% 241.26/131.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 241.26/131.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------