TSTP Solution File: SYO414^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO414^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 09:00:10 EDT 2024
% Result : Theorem 3.83s 1.83s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 42 ( 10 unt; 12 typ; 5 def)
% Number of atoms : 139 ( 11 equ; 0 cnn)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 256 ( 62 ~; 46 |; 0 &; 148 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 30 ( 6 ^ 24 !; 0 ?; 30 :)
% 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(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_k_type,type,
rel_k: $i > $i > $o ).
thf(mbox_k_type,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(mbox_k_def,definition,
( mbox_k
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_k @ B @ C )
| ( A @ C ) ) ) ) ).
thf(mdia_k_type,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(mdia_k_def,definition,
( mdia_k
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ A ) ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(r_type,type,
r: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mdia_k @ ( mimplies @ p @ ( mand @ q @ r ) ) ) @ ( mand @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_k @ ( mimplies @ p @ ( mand @ q @ r ) ) ) @ ( mand @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ r ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( ~ ( p @ B )
| ~ ( ~ ( q @ B )
| ~ ( r @ B ) ) ) )
| ~ ( ~ ( ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( q @ B ) ) )
| ~ ( ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( r @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
rel_k @ sk1 @ sk2,
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [B: $i,A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ( p @ A )
| ~ ( rel_k @ sk1 @ B )
| ( p @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ( p @ A )
| ~ ( rel_k @ sk1 @ B )
| ( p @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ( p @ A )
| ( p @ B )
| ( ( rel_k @ sk1 @ B )
!= ( rel_k @ sk1 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[13]) ).
thf(43,plain,
! [A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ( p @ A )
| ( p @ A ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( B ))]]) ).
thf(45,plain,
! [A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[43]) ).
thf(57,plain,
! [A: $i] :
( ( p @ A )
| ( ( rel_k @ sk1 @ sk2 )
!= ( rel_k @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,45]) ).
thf(58,plain,
p @ sk2,
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( sk2 ))]]) ).
thf(9,plain,
( ~ ( p @ sk2 )
| ( r @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
( ~ ( p @ sk2 )
| ( q @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ~ ( q @ A )
| ~ ( rel_k @ sk1 @ B )
| ~ ( r @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ~ ( q @ A )
| ~ ( rel_k @ sk1 @ B )
| ~ ( r @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ~ ( q @ A )
| ~ ( r @ B )
| ( ( rel_k @ sk1 @ sk2 )
!= ( rel_k @ sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7,11]) ).
thf(18,plain,
! [A: $i] :
( ~ ( rel_k @ sk1 @ A )
| ~ ( q @ A )
| ~ ( r @ sk2 ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(32,plain,
! [A: $i] :
( ~ ( q @ A )
| ~ ( r @ sk2 )
| ( ( rel_k @ sk1 @ sk2 )
!= ( rel_k @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,18]) ).
thf(33,plain,
( ~ ( q @ sk2 )
| ~ ( r @ sk2 ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk2 ))]]) ).
thf(34,plain,
( ~ ( p @ sk2 )
| ~ ( r @ sk2 )
| ( ( q @ sk2 )
!= ( q @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10,33]) ).
thf(35,plain,
( ~ ( p @ sk2 )
| ~ ( r @ sk2 ) ),
inference(pattern_uni,[status(thm)],[34:[]]) ).
thf(46,plain,
( ~ ( p @ sk2 )
| ( ( r @ sk2 )
!= ( r @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[9,35]) ).
thf(47,plain,
~ ( p @ sk2 ),
inference(pattern_uni,[status(thm)],[46:[]]) ).
thf(59,plain,
$false,
inference(rewrite,[status(thm)],[58,47]) ).
thf(60,plain,
$false,
inference(simp,[status(thm)],[59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO414^1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n020.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
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 09:59:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.97/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.00 % [INFO] Parsing done (139ms).
% 1.41/1.01 % [INFO] Running in sequential loop mode.
% 1.89/1.21 % [INFO] nitpick registered as external prover.
% 1.89/1.22 % [INFO] Scanning for conjecture ...
% 2.22/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.22/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.22/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.22/1.34 % [INFO] Type checking passed.
% 2.22/1.34 % [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 ...
% 3.83/1.82 % [INFO] Killing All external provers ...
% 3.83/1.83 % Time passed: 1296ms (effective reasoning time: 810ms)
% 3.83/1.83 % 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)>
% 3.83/1.83 % Axioms used in derivation (0):
% 3.83/1.83 % No. of inferences in proof: 25
% 3.83/1.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1296 ms resp. 810 ms w/o parsing
% 3.83/1.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/1.90 % [INFO] Killing All external provers ...
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