TSTP Solution File: SYN357^7 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 08:18:12 EDT 2024
% Result : Theorem 4.00s 2.00s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 19
% Syntax : Number of formulae : 33 ( 9 unt; 13 typ; 5 def)
% Number of atoms : 74 ( 8 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 152 ( 23 ~; 16 |; 0 &; 110 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 28 ( 11 ^ 17 !; 0 ?; 28 :)
% 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(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
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] :
( ( exists_in_world @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mexists_ind_def,definition,
( mexists_ind
= ( ^ [A: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [B: mu] : ( mnot @ ( A @ B ) ) ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(mbox_s4_def,definition,
( mbox_s4
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s4 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(big_p_type,type,
big_p: mu > $i > $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: mu ).
thf(sk4_type,type,
sk4: mu > $i ).
thf(sk5_type,type,
sk5: mu > $i ).
thf(1,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mexists_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ A ) ) @ ( mbox_s4 @ ( big_p @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2108) ).
thf(2,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mexists_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( big_p @ A ) ) @ ( mbox_s4 @ ( big_p @ B ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ~ ( rel_s4 @ A @ B )
| ! [C: mu] :
( ( exists_in_world @ C @ B )
=> ~ ! [D: mu] :
( ( exists_in_world @ D @ B )
=> ~ ! [E: $i] :
( ~ ( rel_s4 @ B @ E )
| ~ ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( big_p @ C @ F ) )
| ! [F: $i] :
( ~ ( rel_s4 @ E @ F )
| ( big_p @ D @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
exists_in_world @ sk3 @ sk2,
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk2 )
| ( rel_s4 @ ( sk4 @ A ) @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(92,plain,
! [A: mu] :
( ( rel_s4 @ ( sk4 @ A ) @ ( sk5 @ A ) )
| ( ( exists_in_world @ sk3 @ sk2 )
!= ( exists_in_world @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(93,plain,
rel_s4 @ ( sk4 @ sk3 ) @ ( sk5 @ sk3 ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk3 ))]]) ).
thf(9,plain,
! [B: $i,A: mu] :
( ~ ( exists_in_world @ A @ sk2 )
| ~ ( rel_s4 @ ( sk4 @ A ) @ B )
| ( big_p @ sk3 @ B ) ),
inference(cnf,[status(esa)],[7]) ).
thf(97,plain,
! [B: $i,A: mu] :
( ~ ( exists_in_world @ A @ sk2 )
| ( big_p @ sk3 @ B )
| ( ( rel_s4 @ ( sk4 @ sk3 ) @ ( sk5 @ sk3 ) )
!= ( rel_s4 @ ( sk4 @ A ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[93,9]) ).
thf(98,plain,
( ~ ( exists_in_world @ sk3 @ sk2 )
| ( big_p @ sk3 @ ( sk5 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( sk3 )),bind(B,$thf( sk5 @ sk3 ))]]) ).
thf(8,plain,
! [A: mu] :
( ~ ( exists_in_world @ A @ sk2 )
| ~ ( big_p @ A @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(22,plain,
! [A: mu] :
( ~ ( big_p @ A @ ( sk5 @ A ) )
| ( ( exists_in_world @ sk3 @ sk2 )
!= ( exists_in_world @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,8]) ).
thf(23,plain,
~ ( big_p @ sk3 @ ( sk5 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( sk3 ))]]) ).
thf(101,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[98,23,11]) ).
thf(102,plain,
$false,
inference(simp,[status(thm)],[101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN357^7 : TPTP v8.2.0. Released v5.5.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 13:42:39 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.02 % [INFO] Parsing done (153ms).
% 1.50/1.03 % [INFO] Running in sequential loop mode.
% 1.78/1.22 % [INFO] nitpick registered as external prover.
% 1.78/1.23 % [INFO] Scanning for conjecture ...
% 2.14/1.33 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.14/1.35 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.14/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.35 % [INFO] Type checking passed.
% 2.14/1.36 % [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 ...
% 4.00/2.00 % [INFO] Killing All external provers ...
% 4.00/2.00 % Time passed: 1461ms (effective reasoning time: 965ms)
% 4.00/2.00 % 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)>
% 4.00/2.00 % Axioms used in derivation (0):
% 4.00/2.00 % No. of inferences in proof: 15
% 4.00/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1461 ms resp. 965 ms w/o parsing
% 4.00/2.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.00/2.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------