TSTP Solution File: SYO412^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO412^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 4.85s 2.17s
% Output : Refutation 4.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 69 ( 12 unt; 15 typ; 5 def)
% Number of atoms : 197 ( 14 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 387 ( 104 ~; 91 |; 0 &; 192 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 12 con; 0-3 aty)
% Number of variables : 37 ( 6 ^ 31 !; 0 ?; 37 :)
% 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_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(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(1,conjecture,
mvalid @ ( mequiv @ ( mdia_k @ ( mimplies @ p @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_k @ ( mimplies @ p @ q ) ) @ ( mimplies @ ( mbox_k @ p ) @ ( mdia_k @ q ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
~ ( ~ ( ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( ~ ( p @ B )
| ( q @ 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 )
| ~ ( q @ B ) ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( ~ ( p @ B )
| ( q @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ~ ( ~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( ~ ( p @ B )
| ( q @ B ) ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( q @ B ) ) )
| ~ ! [A: $i] :
( ~ ( ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ( p @ B ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( q @ B ) ) )
| ~ ! [B: $i] :
( ~ ( rel_k @ A @ B )
| ~ ( ~ ( p @ B )
| ( q @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
( ~ sk1
| ( rel_k @ sk4 @ sk5 )
| ( rel_k @ sk4 @ sk6 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_k @ sk4 @ A )
| ~ ( q @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(15,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_k @ sk4 @ A )
| ~ ( q @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(35,plain,
! [A: $i] :
( ~ sk1
| ( rel_k @ sk4 @ sk5 )
| ~ ( q @ A )
| ( ( rel_k @ sk4 @ sk6 )
!= ( rel_k @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,15]) ).
thf(36,plain,
( ~ sk1
| ( rel_k @ sk4 @ sk5 )
| ~ ( q @ sk6 ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( sk6 ))]]) ).
thf(14,plain,
( ( rel_k @ sk2 @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(11,plain,
! [A: $i] :
( ~ ( rel_k @ sk2 @ A )
| ( p @ A )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(69,plain,
! [A: $i] :
( sk1
| ( p @ A )
| ( ( rel_k @ sk2 @ sk3 )
!= ( rel_k @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(70,plain,
( sk1
| ( p @ sk3 ) ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk3 ))]]) ).
thf(6,plain,
( ~ ( p @ sk3 )
| ( q @ sk3 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(73,plain,
( sk1
| ( q @ sk3 )
| ( ( p @ sk3 )
!= ( p @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[70,6]) ).
thf(74,plain,
( sk1
| ( q @ sk3 ) ),
inference(pattern_uni,[status(thm)],[73:[]]) ).
thf(9,plain,
! [A: $i] :
( ~ ( rel_k @ sk2 @ A )
| ~ ( q @ A )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [A: $i] :
( ~ ( rel_k @ sk2 @ A )
| ~ ( q @ A )
| sk1 ),
inference(simp,[status(thm)],[9]) ).
thf(81,plain,
! [A: $i] :
( sk1
| ~ ( q @ A )
| ( ( rel_k @ sk2 @ sk3 )
!= ( rel_k @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,16]) ).
thf(82,plain,
( sk1
| ~ ( q @ sk3 ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( sk3 ))]]) ).
thf(87,plain,
( sk1
| ( ( q @ sk3 )
!= ( q @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[74,82]) ).
thf(88,plain,
sk1,
inference(pattern_uni,[status(thm)],[87:[]]) ).
thf(93,plain,
( ~ $true
| ( rel_k @ sk4 @ sk5 )
| ~ ( q @ sk6 ) ),
inference(rewrite,[status(thm)],[36,88]) ).
thf(94,plain,
( ( rel_k @ sk4 @ sk5 )
| ~ ( q @ sk6 ) ),
inference(simp,[status(thm)],[93]) ).
thf(13,plain,
( ~ sk1
| ( rel_k @ sk4 @ sk5 )
| ( q @ sk6 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(91,plain,
( ~ $true
| ( rel_k @ sk4 @ sk5 )
| ( q @ sk6 ) ),
inference(rewrite,[status(thm)],[13,88]) ).
thf(92,plain,
( ( rel_k @ sk4 @ sk5 )
| ( q @ sk6 ) ),
inference(simp,[status(thm)],[91]) ).
thf(8,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_k @ sk4 @ A )
| ( p @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [A: $i] :
( ~ sk1
| ~ ( rel_k @ sk4 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(106,plain,
! [A: $i] :
( ~ $true
| ~ ( rel_k @ sk4 @ A )
| ( p @ A ) ),
inference(rewrite,[status(thm)],[17,88]) ).
thf(107,plain,
! [A: $i] :
( ~ ( rel_k @ sk4 @ A )
| ( p @ A ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [A: $i] :
( ( q @ sk6 )
| ( p @ A )
| ( ( rel_k @ sk4 @ sk5 )
!= ( rel_k @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[92,107]) ).
thf(109,plain,
( ( q @ sk6 )
| ( p @ sk5 ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( sk5 ))]]) ).
thf(12,plain,
( ~ sk1
| ~ ( p @ sk5 )
| ( q @ sk6 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
( ~ sk1
| ~ ( p @ sk5 )
| ( rel_k @ sk4 @ sk6 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(23,plain,
! [A: $i] :
( ~ sk1
| ~ ( p @ sk5 )
| ~ ( q @ A )
| ( ( rel_k @ sk4 @ sk6 )
!= ( rel_k @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,15]) ).
thf(24,plain,
( ~ sk1
| ~ ( p @ sk5 )
| ~ ( q @ sk6 ) ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk6 ))]]) ).
thf(26,plain,
( ~ sk1
| ~ ( p @ sk5 )
| ( ( q @ sk6 )
!= ( q @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[12,24]) ).
thf(27,plain,
( ~ sk1
| ~ ( p @ sk5 ) ),
inference(pattern_uni,[status(thm)],[26:[]]) ).
thf(99,plain,
( ~ $true
| ~ ( p @ sk5 ) ),
inference(rewrite,[status(thm)],[27,88]) ).
thf(100,plain,
~ ( p @ sk5 ),
inference(simp,[status(thm)],[99]) ).
thf(112,plain,
( ( q @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[109,100]) ).
thf(113,plain,
q @ sk6,
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
( ( rel_k @ sk4 @ sk5 )
| ~ $true ),
inference(rewrite,[status(thm)],[94,113]) ).
thf(115,plain,
rel_k @ sk4 @ sk5,
inference(simp,[status(thm)],[114]) ).
thf(118,plain,
! [A: $i] :
( ( p @ A )
| ( ( rel_k @ sk4 @ sk5 )
!= ( rel_k @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[115,107]) ).
thf(119,plain,
p @ sk5,
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( sk5 ))]]) ).
thf(120,plain,
$false,
inference(rewrite,[status(thm)],[119,100]) ).
thf(121,plain,
$false,
inference(simp,[status(thm)],[120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYO412^1 : TPTP v8.2.0. Released v4.0.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n021.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 10:59:39 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.05 % [INFO] Parsing done (161ms).
% 1.39/1.06 % [INFO] Running in sequential loop mode.
% 1.88/1.30 % [INFO] nitpick registered as external prover.
% 1.88/1.30 % [INFO] Scanning for conjecture ...
% 2.20/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.44 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.44 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.44 % [INFO] Type checking passed.
% 2.20/1.45 % [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 ...
% 4.85/2.16 % [INFO] Killing All external provers ...
% 4.85/2.16 % Time passed: 1625ms (effective reasoning time: 1096ms)
% 4.85/2.16 % 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)>
% 4.85/2.17 % Axioms used in derivation (0):
% 4.85/2.17 % No. of inferences in proof: 49
% 4.85/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1625 ms resp. 1096 ms w/o parsing
% 4.85/2.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.85/2.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------