TSTP Solution File: LCL536+1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 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 : Wed Aug 31 17:48:39 EDT 2022
% Result : Theorem 0.19s 0.54s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 53 ( 15 unt; 0 def)
% Number of atoms : 106 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 92 ( 39 ~; 34 |; 0 &)
% ( 11 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f501,plain,
$false,
inference(avatar_sat_refutation,[],[f354,f365,f418,f427,f445,f463,f470,f473,f500]) ).
fof(f500,plain,
( ~ spl1_27
| spl1_30
| ~ spl1_42
| ~ spl1_47 ),
inference(avatar_contradiction_clause,[],[f499]) ).
fof(f499,plain,
( $false
| ~ spl1_27
| spl1_30
| ~ spl1_42
| ~ spl1_47 ),
inference(subsumption_resolution,[],[f498,f349]) ).
fof(f349,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ spl1_27 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f348,plain,
( spl1_27
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f498,plain,
( ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0))))
| spl1_30
| ~ spl1_42
| ~ spl1_47 ),
inference(resolution,[],[f494,f364]) ).
fof(f364,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| spl1_30 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f362,plain,
( spl1_30
<=> is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f494,plain,
( ! [X2,X3] :
( is_a_theorem(strict_implies(X2,X3))
| ~ is_a_theorem(implies(X2,X3)) )
| ~ spl1_42
| ~ spl1_47 ),
inference(superposition,[],[f417,f440]) ).
fof(f440,plain,
( ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0))
| ~ spl1_47 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f439,plain,
( spl1_47
<=> ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_47])]) ).
fof(f417,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f416,plain,
( spl1_42
<=> ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
fof(f473,plain,
spl1_28,
inference(avatar_split_clause,[],[f223,f351]) ).
fof(f351,plain,
( spl1_28
<=> axiom_5 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f223,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f470,plain,
spl1_48,
inference(avatar_split_clause,[],[f211,f442]) ).
fof(f442,plain,
( spl1_48
<=> op_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
fof(f211,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f463,plain,
~ spl1_29,
inference(avatar_split_clause,[],[f217,f358]) ).
fof(f358,plain,
( spl1_29
<=> axiom_m10 ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f217,plain,
~ axiom_m10,
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
~ axiom_m10,
inference(flattening,[],[f89]) ).
fof(f89,negated_conjecture,
~ axiom_m10,
inference(negated_conjecture,[],[f88]) ).
fof(f88,conjecture,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(f445,plain,
( spl1_47
| ~ spl1_48 ),
inference(avatar_split_clause,[],[f203,f442,f439]) ).
fof(f203,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,plain,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X1,X0) = necessarily(implies(X1,X0)) ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X1,X0] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f427,plain,
spl1_41,
inference(avatar_split_clause,[],[f215,f412]) ).
fof(f412,plain,
( spl1_41
<=> necessitation ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
fof(f215,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f418,plain,
( ~ spl1_41
| spl1_42 ),
inference(avatar_split_clause,[],[f196,f416,f412]) ).
fof(f196,plain,
! [X0] :
( ~ is_a_theorem(X0)
| ~ necessitation
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
( ~ necessitation
| ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f365,plain,
( spl1_29
| ~ spl1_30 ),
inference(avatar_split_clause,[],[f219,f362,f358]) ).
fof(f219,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f161,f181]) ).
fof(f181,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
| axiom_m10 ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_m10 ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f72,axiom,
( axiom_m10
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m10) ).
fof(f354,plain,
( spl1_27
| ~ spl1_28 ),
inference(avatar_split_clause,[],[f218,f351,f348]) ).
fof(f218,plain,
! [X0] :
( ~ axiom_5
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
( ~ axiom_5
| ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f58,axiom,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
<=> axiom_5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 02:06:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.51 % (3495)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52 % (3495)First to succeed.
% 0.19/0.52 % (3517)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.52 % (3516)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.52 % (3494)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (3500)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (3499)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.54 % (3494)Also succeeded, but the first one will report.
% 0.19/0.54 % (3495)Refutation found. Thanks to Tanya!
% 0.19/0.54 % SZS status Theorem for theBenchmark
% 0.19/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.54 % (3495)------------------------------
% 0.19/0.54 % (3495)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (3495)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (3495)Termination reason: Refutation
% 0.19/0.54
% 0.19/0.54 % (3495)Memory used [KB]: 5756
% 0.19/0.54 % (3495)Time elapsed: 0.119 s
% 0.19/0.54 % (3495)Instructions burned: 6 (million)
% 0.19/0.54 % (3495)------------------------------
% 0.19/0.54 % (3495)------------------------------
% 0.19/0.54 % (3483)Success in time 0.189 s
%------------------------------------------------------------------------------