TSTP Solution File: SYO462^4 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO462^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 09:00:29 EDT 2024
% Result : Theorem 3.59s 2.02s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 17
% Syntax : Number of formulae : 49 ( 8 unt; 12 typ; 4 def)
% Number of atoms : 136 ( 11 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 236 ( 57 ~; 55 |; 0 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 24 ( 5 ^ 19 !; 0 ?; 24 :)
% 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(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_b_type,type,
rel_b: $i > $i > $o ).
thf(mbox_b_type,type,
mbox_b: ( $i > $o ) > $i > $o ).
thf(mbox_b_def,definition,
( mbox_b
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_b @ B @ C )
| ( A @ C ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_b @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_b @ p ) @ ( mbox_b @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_b @ A @ B )
| ~ ( ~ ( ~ ( p @ B )
| ( q @ B ) )
| ~ ( ~ ( q @ B )
| ( p @ B ) ) ) )
| ~ ( ~ ( ~ ! [B: $i] :
( ~ ( rel_b @ A @ B )
| ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_b @ A @ B )
| ( q @ B ) ) )
| ~ ( ~ ! [B: $i] :
( ~ ( rel_b @ A @ B )
| ( q @ B ) )
| ! [B: $i] :
( ~ ( rel_b @ A @ B )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( rel_b @ sk1 @ sk3 )
| sk2 ),
inference(cnf,[status(esa)],[5]) ).
thf(7,plain,
! [A: $i] :
( ~ ( rel_b @ sk1 @ A )
| ~ ( p @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(30,plain,
! [A: $i] :
( sk2
| ~ ( p @ A )
| ( q @ A )
| ( ( rel_b @ sk1 @ sk3 )
!= ( rel_b @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,7]) ).
thf(31,plain,
( sk2
| ~ ( p @ sk3 )
| ( q @ sk3 ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk3 ))]]) ).
thf(10,plain,
( ~ ( q @ sk3 )
| sk2 ),
inference(cnf,[status(esa)],[5]) ).
thf(66,plain,
( sk2
| ~ ( p @ sk3 )
| ( ( q @ sk3 )
!= ( q @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31,10]) ).
thf(67,plain,
( sk2
| ~ ( p @ sk3 ) ),
inference(pattern_uni,[status(thm)],[66:[]]) ).
thf(6,plain,
( ~ sk2
| ( rel_b @ sk1 @ sk4 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(13,plain,
! [A: $i] :
( ~ sk2
| ~ ( rel_b @ sk1 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
! [A: $i] :
( ~ sk2
| ~ ( rel_b @ sk1 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(20,plain,
! [A: $i] :
( ~ sk2
| ( q @ A )
| ( ( rel_b @ sk1 @ sk4 )
!= ( rel_b @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,14]) ).
thf(21,plain,
( ~ sk2
| ( q @ sk4 ) ),
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk4 ))]]) ).
thf(8,plain,
! [A: $i] :
( ~ ( rel_b @ sk1 @ A )
| ~ ( q @ A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(34,plain,
! [A: $i] :
( ~ sk2
| ~ ( q @ A )
| ( p @ A )
| ( ( rel_b @ sk1 @ sk4 )
!= ( rel_b @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(35,plain,
( ~ sk2
| ~ ( q @ sk4 )
| ( p @ sk4 ) ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( sk4 ))]]) ).
thf(60,plain,
( ~ sk2
| ( p @ sk4 )
| ( ( q @ sk4 )
!= ( q @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[21,35]) ).
thf(61,plain,
( ~ sk2
| ( p @ sk4 ) ),
inference(pattern_uni,[status(thm)],[60:[]]) ).
thf(11,plain,
( ~ sk2
| ~ ( p @ sk4 ) ),
inference(cnf,[status(esa)],[5]) ).
thf(77,plain,
( ~ sk2
| ( ( p @ sk4 )
!= ( p @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[61,11]) ).
thf(78,plain,
~ sk2,
inference(pattern_uni,[status(thm)],[77:[]]) ).
thf(83,plain,
( ( rel_b @ sk1 @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[9,78]) ).
thf(84,plain,
rel_b @ sk1 @ sk3,
inference(simp,[status(thm)],[83]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_b @ sk1 @ A )
| ( p @ A )
| sk2 ),
inference(cnf,[status(esa)],[5]) ).
thf(15,plain,
! [A: $i] :
( ~ ( rel_b @ sk1 @ A )
| ( p @ A )
| sk2 ),
inference(simp,[status(thm)],[12]) ).
thf(87,plain,
! [A: $i] :
( ~ ( rel_b @ sk1 @ A )
| ( p @ A )
| $false ),
inference(rewrite,[status(thm)],[15,78]) ).
thf(88,plain,
! [A: $i] :
( ~ ( rel_b @ sk1 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[87]) ).
thf(103,plain,
! [A: $i] :
( ( p @ A )
| ( ( rel_b @ sk1 @ sk3 )
!= ( rel_b @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[84,88]) ).
thf(104,plain,
p @ sk3,
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( sk3 ))]]) ).
thf(109,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[67,104,78]) ).
thf(110,plain,
$false,
inference(simp,[status(thm)],[109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SYO462^4 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n002.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 09:05:53 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.81/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (151ms).
% 1.32/0.96 % [INFO] Running in sequential loop mode.
% 1.75/1.21 % [INFO] nitpick registered as external prover.
% 1.75/1.21 % [INFO] Scanning for conjecture ...
% 2.09/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.09/1.35 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.09/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.35 % [INFO] Type checking passed.
% 2.09/1.36 % [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 ...
% 3.59/2.01 % [INFO] Killing All external provers ...
% 3.59/2.02 % Time passed: 1567ms (effective reasoning time: 1050ms)
% 3.59/2.02 % 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)>
% 3.59/2.02 % Axioms used in derivation (0):
% 3.59/2.02 % No. of inferences in proof: 33
% 3.59/2.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1567 ms resp. 1050 ms w/o parsing
% 3.80/2.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.80/2.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------