TSTP Solution File: SYO462^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO462^2 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 09:00:28 EDT 2024
% Result : Theorem 5.30s 2.66s
% Output : Refutation 5.30s
% 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_d_type,type,
rel_d: $i > $i > $o ).
thf(mbox_d_type,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(mbox_d_def,definition,
( mbox_d
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_d @ 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_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_d @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_d @ p ) @ ( mbox_d @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_d @ A @ B )
| ~ ( ~ ( ~ ( p @ B )
| ( q @ B ) )
| ~ ( ~ ( q @ B )
| ( p @ B ) ) ) )
| ~ ( ~ ( ~ ! [B: $i] :
( ~ ( rel_d @ A @ B )
| ( p @ B ) )
| ! [B: $i] :
( ~ ( rel_d @ A @ B )
| ( q @ B ) ) )
| ~ ( ~ ! [B: $i] :
( ~ ( rel_d @ A @ B )
| ( q @ B ) )
| ! [B: $i] :
( ~ ( rel_d @ A @ B )
| ( p @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( rel_d @ sk1 @ sk3 )
| sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [A: $i] :
( ~ ( rel_d @ sk1 @ A )
| ~ ( p @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
! [A: $i] :
( sk2
| ~ ( p @ A )
| ( q @ A )
| ( ( rel_d @ sk1 @ sk3 )
!= ( rel_d @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,6]) ).
thf(26,plain,
( sk2
| ~ ( p @ sk3 )
| ( q @ sk3 ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( sk3 ))]]) ).
thf(9,plain,
( ~ ( q @ sk3 )
| sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(64,plain,
( sk2
| ~ ( p @ sk3 )
| ( ( q @ sk3 )
!= ( q @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[26,9]) ).
thf(65,plain,
( sk2
| ~ ( p @ sk3 ) ),
inference(pattern_uni,[status(thm)],[64:[]]) ).
thf(5,plain,
( ~ sk2
| ( rel_d @ sk1 @ sk4 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [A: $i] :
( ~ sk2
| ~ ( rel_d @ sk1 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [A: $i] :
( ~ sk2
| ~ ( rel_d @ sk1 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(17,plain,
! [A: $i] :
( ~ sk2
| ( q @ A )
| ( ( rel_d @ sk1 @ sk4 )
!= ( rel_d @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,13]) ).
thf(18,plain,
( ~ sk2
| ( q @ sk4 ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk4 ))]]) ).
thf(7,plain,
! [A: $i] :
( ~ ( rel_d @ sk1 @ A )
| ~ ( q @ A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(31,plain,
! [A: $i] :
( ~ sk2
| ~ ( q @ A )
| ( p @ A )
| ( ( rel_d @ sk1 @ sk4 )
!= ( rel_d @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,7]) ).
thf(32,plain,
( ~ sk2
| ~ ( q @ sk4 )
| ( p @ sk4 ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( sk4 ))]]) ).
thf(59,plain,
( ~ sk2
| ( p @ sk4 )
| ( ( q @ sk4 )
!= ( q @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[18,32]) ).
thf(60,plain,
( ~ sk2
| ( p @ sk4 ) ),
inference(pattern_uni,[status(thm)],[59:[]]) ).
thf(10,plain,
( ~ sk2
| ~ ( p @ sk4 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(73,plain,
( ~ sk2
| ( ( p @ sk4 )
!= ( p @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[60,10]) ).
thf(74,plain,
~ sk2,
inference(pattern_uni,[status(thm)],[73:[]]) ).
thf(82,plain,
( ( rel_d @ sk1 @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[8,74]) ).
thf(83,plain,
rel_d @ sk1 @ sk3,
inference(simp,[status(thm)],[82]) ).
thf(11,plain,
! [A: $i] :
( ~ ( rel_d @ sk1 @ A )
| ( p @ A )
| sk2 ),
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
! [A: $i] :
( ~ ( rel_d @ sk1 @ A )
| ( p @ A )
| sk2 ),
inference(simp,[status(thm)],[11]) ).
thf(84,plain,
! [A: $i] :
( ~ ( rel_d @ sk1 @ A )
| ( p @ A )
| $false ),
inference(rewrite,[status(thm)],[14,74]) ).
thf(85,plain,
! [A: $i] :
( ~ ( rel_d @ sk1 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[84]) ).
thf(92,plain,
! [A: $i] :
( ( p @ A )
| ( ( rel_d @ sk1 @ sk3 )
!= ( rel_d @ sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[83,85]) ).
thf(93,plain,
p @ sk3,
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk3 ))]]) ).
thf(108,plain,
( $false
| ~ $true ),
inference(rewrite,[status(thm)],[65,74,93]) ).
thf(109,plain,
$false,
inference(simp,[status(thm)],[108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO462^2 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon May 20 10:26:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.98/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.13 % [INFO] Parsing done (184ms).
% 1.28/1.15 % [INFO] Running in sequential loop mode.
% 2.09/1.51 % [INFO] nitpick registered as external prover.
% 2.09/1.51 % [INFO] Scanning for conjecture ...
% 2.40/1.68 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.52/1.71 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.52/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.52/1.72 % [INFO] Type checking passed.
% 2.52/1.72 % [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 ...
% 5.30/2.65 % [INFO] Killing All external provers ...
% 5.30/2.66 % Time passed: 2177ms (effective reasoning time: 1500ms)
% 5.30/2.66 % 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)>
% 5.30/2.66 % Axioms used in derivation (0):
% 5.30/2.66 % No. of inferences in proof: 33
% 5.30/2.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2177 ms resp. 1500 ms w/o parsing
% 5.30/2.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.30/2.71 % [INFO] Killing All external provers ...
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