TSTP Solution File: LCL542+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : LCL542+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_uns --cores 0 -t %d %s
% Computer : n017.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 17:43:04 EDT 2022
% Result : Theorem 0.19s 0.50s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 108 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 40 ~; 35 |; 0 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f517,plain,
$false,
inference(avatar_sat_refutation,[],[f274,f291,f325,f383,f393,f394,f481,f487,f516]) ).
fof(f516,plain,
( ~ spl2_7
| spl2_11
| ~ spl2_19
| ~ spl2_33 ),
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f515,plain,
( $false
| ~ spl2_7
| spl2_11
| ~ spl2_19
| ~ spl2_33 ),
inference(subsumption_resolution,[],[f514,f269]) ).
fof(f269,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl2_7
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f514,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| spl2_11
| ~ spl2_19
| ~ spl2_33 ),
inference(resolution,[],[f493,f286]) ).
fof(f286,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| spl2_11 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f284,plain,
( spl2_11
<=> is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f493,plain,
( ! [X4,X5] :
( is_a_theorem(strict_implies(X4,X5))
| ~ is_a_theorem(implies(X4,X5)) )
| ~ spl2_19
| ~ spl2_33 ),
inference(superposition,[],[f378,f320]) ).
fof(f320,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f319,plain,
( spl2_19
<=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f378,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f377,plain,
( spl2_33
<=> ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f487,plain,
spl2_34,
inference(avatar_split_clause,[],[f223,f380]) ).
fof(f380,plain,
( spl2_34
<=> necessitation ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f223,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f481,plain,
spl2_8,
inference(avatar_split_clause,[],[f203,f271]) ).
fof(f271,plain,
( spl2_8
<=> and_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f203,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f394,plain,
~ spl2_12,
inference(avatar_split_clause,[],[f222,f288]) ).
fof(f288,plain,
( spl2_12
<=> axiom_m2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f222,plain,
~ axiom_m2,
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
~ axiom_m2,
inference(flattening,[],[f90]) ).
fof(f90,negated_conjecture,
~ axiom_m2,
inference(negated_conjecture,[],[f89]) ).
fof(f89,conjecture,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f393,plain,
spl2_20,
inference(avatar_split_clause,[],[f232,f322]) ).
fof(f322,plain,
( spl2_20
<=> op_strict_implies ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f232,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f383,plain,
( spl2_33
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f216,f380,f377]) ).
fof(f216,plain,
! [X0] :
( ~ necessitation
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f127]) ).
fof(f127,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/sandbox/benchmark/theBenchmark.p',necessitation) ).
fof(f325,plain,
( spl2_19
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f218,f322,f319]) ).
fof(f218,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f291,plain,
( ~ spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f215,f288,f284]) ).
fof(f215,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f147,f177]) ).
fof(f177,plain,
( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),X0))
=> ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
( axiom_m2
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
=> axiom_m2 ),
inference(unused_predicate_definition_removal,[],[f64]) ).
fof(f64,axiom,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
<=> axiom_m2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
fof(f274,plain,
( spl2_7
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f227,f271,f268]) ).
fof(f227,plain,
! [X0,X1] :
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(rectify,[],[f157]) ).
fof(f157,plain,
( ! [X1,X0] : is_a_theorem(implies(and(X1,X0),X1))
| ~ and_1 ),
inference(ennf_transformation,[],[f136]) ).
fof(f136,plain,
( and_1
=> ! [X1,X0] : is_a_theorem(implies(and(X1,X0),X1)) ),
inference(unused_predicate_definition_removal,[],[f91]) ).
fof(f91,plain,
( and_1
<=> ! [X1,X0] : is_a_theorem(implies(and(X1,X0),X1)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
( ! [X1,X0] : is_a_theorem(implies(and(X0,X1),X0))
<=> and_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL542+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 01:31:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (15386)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.49 % (15375)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.49 % (15375)Refutation not found, incomplete strategy% (15375)------------------------------
% 0.19/0.49 % (15375)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (15375)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (15375)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.49
% 0.19/0.49 % (15375)Memory used [KB]: 6012
% 0.19/0.49 % (15375)Time elapsed: 0.003 s
% 0.19/0.49 % (15375)------------------------------
% 0.19/0.49 % (15375)------------------------------
% 0.19/0.49 % (15371)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50 % (15371)First to succeed.
% 0.19/0.50 % (15390)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.50 % (15392)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.50 % (15390)Refutation not found, incomplete strategy% (15390)------------------------------
% 0.19/0.50 % (15390)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15381)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.50 % (15390)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (15381)Refutation not found, incomplete strategy% (15381)------------------------------
% 0.19/0.50 % (15381)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15390)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (15390)Memory used [KB]: 6012
% 0.19/0.50 % (15390)Time elapsed: 0.003 s
% 0.19/0.50 % (15390)Instructions burned: 1 (million)
% 0.19/0.50 % (15390)------------------------------
% 0.19/0.50 % (15390)------------------------------
% 0.19/0.50 % (15374)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (15377)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50 % (15374)Refutation not found, incomplete strategy% (15374)------------------------------
% 0.19/0.50 % (15374)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15374)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (15374)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (15374)Memory used [KB]: 6012
% 0.19/0.50 % (15374)Time elapsed: 0.002 s
% 0.19/0.50 % (15374)------------------------------
% 0.19/0.50 % (15374)------------------------------
% 0.19/0.50 % (15372)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50 % (15377)Refutation not found, incomplete strategy% (15377)------------------------------
% 0.19/0.50 % (15377)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15381)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (15377)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (15377)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (15377)Memory used [KB]: 6012
% 0.19/0.50 % (15377)Time elapsed: 0.001 s
% 0.19/0.50 % (15377)------------------------------
% 0.19/0.50 % (15377)------------------------------
% 0.19/0.50 % (15381)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (15381)Memory used [KB]: 6012
% 0.19/0.50 % (15381)Time elapsed: 0.005 s
% 0.19/0.50 % (15381)Instructions burned: 2 (million)
% 0.19/0.50 % (15381)------------------------------
% 0.19/0.50 % (15381)------------------------------
% 0.19/0.50 % (15372)Refutation not found, incomplete strategy% (15372)------------------------------
% 0.19/0.50 % (15372)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15372)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (15372)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50
% 0.19/0.50 % (15372)Memory used [KB]: 6012
% 0.19/0.50 % (15372)Time elapsed: 0.001 s
% 0.19/0.50 % (15372)------------------------------
% 0.19/0.50 % (15372)------------------------------
% 0.19/0.50 % (15383)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.50 % (15386)Instruction limit reached!
% 0.19/0.50 % (15386)------------------------------
% 0.19/0.50 % (15386)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15371)Refutation found. Thanks to Tanya!
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (15371)------------------------------
% 0.19/0.50 % (15371)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (15371)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (15371)Termination reason: Refutation
% 0.19/0.50
% 0.19/0.50 % (15371)Memory used [KB]: 6268
% 0.19/0.50 % (15371)Time elapsed: 0.096 s
% 0.19/0.50 % (15371)Instructions burned: 6 (million)
% 0.19/0.50 % (15371)------------------------------
% 0.19/0.50 % (15371)------------------------------
% 0.19/0.50 % (15365)Success in time 0.155 s
%------------------------------------------------------------------------------