TSTP Solution File: SEU344+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SEU344+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 : n003.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 18:29:04 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 9 unt; 0 def)
% Number of atoms : 230 ( 30 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 252 ( 94 ~; 99 |; 33 &)
% ( 10 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 75 ( 58 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f498,plain,
$false,
inference(avatar_sat_refutation,[],[f371,f381,f398,f406,f461,f489,f495]) ).
fof(f495,plain,
( ~ spl18_1
| spl18_3 ),
inference(avatar_contradiction_clause,[],[f494]) ).
fof(f494,plain,
( $false
| ~ spl18_1
| spl18_3 ),
inference(subsumption_resolution,[],[f464,f392]) ).
fof(f392,plain,
( set_union2(sK7,sK8) != sK8
| spl18_3 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f391,plain,
( spl18_3
<=> set_union2(sK7,sK8) = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f464,plain,
( set_union2(sK7,sK8) = sK8
| ~ spl18_1 ),
inference(resolution,[],[f366,f219]) ).
fof(f219,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| set_union2(X1,X0) = X0 ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| set_union2(X1,X0) = X0 ),
inference(rectify,[],[f107]) ).
fof(f107,plain,
! [X1,X0] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X1,X0] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f366,plain,
( subset(sK7,sK8)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f364,plain,
( spl18_1
<=> subset(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f489,plain,
( spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(avatar_contradiction_clause,[],[f488]) ).
fof(f488,plain,
( $false
| spl18_2
| ~ spl18_3
| ~ spl18_4 ),
inference(subsumption_resolution,[],[f480,f408]) ).
fof(f408,plain,
( sK8 = join(boole_lattice(sK6),sK7,sK8)
| ~ spl18_3 ),
inference(backward_demodulation,[],[f333,f393]) ).
fof(f393,plain,
( set_union2(sK7,sK8) = sK8
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f333,plain,
set_union2(sK7,sK8) = join(boole_lattice(sK6),sK7,sK8),
inference(unit_resulting_resolution,[],[f244,f245,f297]) ).
fof(f297,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(boole_lattice(X1)))
| ~ element(X0,the_carrier(boole_lattice(X1)))
| join(boole_lattice(X1),X0,X2) = set_union2(X0,X2) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0,X1] :
( ! [X2] :
( ~ element(X2,the_carrier(boole_lattice(X1)))
| ( join(boole_lattice(X1),X0,X2) = set_union2(X0,X2)
& meet(boole_lattice(X1),X0,X2) = set_intersection2(X0,X2) ) )
| ~ element(X0,the_carrier(boole_lattice(X1))) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X1,X0] :
( ! [X2] :
( ~ element(X2,the_carrier(boole_lattice(X0)))
| ( join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
& meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2) ) )
| ~ element(X1,the_carrier(boole_lattice(X0))) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( join(boole_lattice(X0),X1,X2) = set_union2(X1,X2)
& meet(boole_lattice(X0),X1,X2) = set_intersection2(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_lattice3) ).
fof(f245,plain,
element(sK7,the_carrier(boole_lattice(sK6))),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
( element(sK7,the_carrier(boole_lattice(sK6)))
& element(sK8,the_carrier(boole_lattice(sK6)))
& ( ~ subset(sK7,sK8)
| ~ below(boole_lattice(sK6),sK7,sK8) )
& ( subset(sK7,sK8)
| below(boole_lattice(sK6),sK7,sK8) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f181,f183,f182]) ).
fof(f182,plain,
( ? [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
& ? [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
& ( ~ subset(X1,X2)
| ~ below(boole_lattice(X0),X1,X2) )
& ( subset(X1,X2)
| below(boole_lattice(X0),X1,X2) ) ) )
=> ( element(sK7,the_carrier(boole_lattice(sK6)))
& ? [X2] :
( element(X2,the_carrier(boole_lattice(sK6)))
& ( ~ subset(sK7,X2)
| ~ below(boole_lattice(sK6),sK7,X2) )
& ( subset(sK7,X2)
| below(boole_lattice(sK6),sK7,X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f183,plain,
( ? [X2] :
( element(X2,the_carrier(boole_lattice(sK6)))
& ( ~ subset(sK7,X2)
| ~ below(boole_lattice(sK6),sK7,X2) )
& ( subset(sK7,X2)
| below(boole_lattice(sK6),sK7,X2) ) )
=> ( element(sK8,the_carrier(boole_lattice(sK6)))
& ( ~ subset(sK7,sK8)
| ~ below(boole_lattice(sK6),sK7,sK8) )
& ( subset(sK7,sK8)
| below(boole_lattice(sK6),sK7,sK8) ) ) ),
introduced(choice_axiom,[]) ).
fof(f181,plain,
? [X0,X1] :
( element(X1,the_carrier(boole_lattice(X0)))
& ? [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
& ( ~ subset(X1,X2)
| ~ below(boole_lattice(X0),X1,X2) )
& ( subset(X1,X2)
| below(boole_lattice(X0),X1,X2) ) ) ),
inference(rectify,[],[f180]) ).
fof(f180,plain,
? [X1,X0] :
( element(X0,the_carrier(boole_lattice(X1)))
& ? [X2] :
( element(X2,the_carrier(boole_lattice(X1)))
& ( ~ subset(X0,X2)
| ~ below(boole_lattice(X1),X0,X2) )
& ( subset(X0,X2)
| below(boole_lattice(X1),X0,X2) ) ) ),
inference(flattening,[],[f179]) ).
fof(f179,plain,
? [X1,X0] :
( element(X0,the_carrier(boole_lattice(X1)))
& ? [X2] :
( element(X2,the_carrier(boole_lattice(X1)))
& ( ~ subset(X0,X2)
| ~ below(boole_lattice(X1),X0,X2) )
& ( subset(X0,X2)
| below(boole_lattice(X1),X0,X2) ) ) ),
inference(nnf_transformation,[],[f153]) ).
fof(f153,plain,
? [X1,X0] :
( element(X0,the_carrier(boole_lattice(X1)))
& ? [X2] :
( element(X2,the_carrier(boole_lattice(X1)))
& ( below(boole_lattice(X1),X0,X2)
<~> subset(X0,X2) ) ) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
~ ! [X0,X1] :
( element(X0,the_carrier(boole_lattice(X1)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X1)))
=> ( below(boole_lattice(X1),X0,X2)
<=> subset(X0,X2) ) ) ),
inference(rectify,[],[f74]) ).
fof(f74,negated_conjecture,
~ ! [X1,X0] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( subset(X1,X2)
<=> below(boole_lattice(X0),X1,X2) ) ) ),
inference(negated_conjecture,[],[f73]) ).
fof(f73,conjecture,
! [X1,X0] :
( element(X1,the_carrier(boole_lattice(X0)))
=> ! [X2] :
( element(X2,the_carrier(boole_lattice(X0)))
=> ( subset(X1,X2)
<=> below(boole_lattice(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_lattice3) ).
fof(f244,plain,
element(sK8,the_carrier(boole_lattice(sK6))),
inference(cnf_transformation,[],[f184]) ).
fof(f480,plain,
( sK8 != join(boole_lattice(sK6),sK7,sK8)
| spl18_2
| ~ spl18_4 ),
inference(unit_resulting_resolution,[],[f237,f396,f244,f245,f369,f230]) ).
fof(f230,plain,
! [X2,X0,X1] :
( below(X0,X1,X2)
| ~ join_semilatt_str(X0)
| join(X0,X1,X2) != X2
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2) )
& ( below(X0,X1,X2)
| join(X0,X1,X2) != X2 ) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( join(X0,X1,X2) = X2
<=> below(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( join(X0,X1,X2) = X2
<=> below(X0,X1,X2) ) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( join(X0,X1,X2) = X2
<=> below(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).
fof(f369,plain,
( ~ below(boole_lattice(sK6),sK7,sK8)
| spl18_2 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f368,plain,
( spl18_2
<=> below(boole_lattice(sK6),sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f396,plain,
( join_semilatt_str(boole_lattice(sK6))
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f395,plain,
( spl18_4
<=> join_semilatt_str(boole_lattice(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f237,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& ~ empty_carrier(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_lattice3) ).
fof(f461,plain,
( spl18_1
| ~ spl18_3 ),
inference(avatar_contradiction_clause,[],[f460]) ).
fof(f460,plain,
( $false
| spl18_1
| ~ spl18_3 ),
inference(subsumption_resolution,[],[f457,f365]) ).
fof(f365,plain,
( ~ subset(sK7,sK8)
| spl18_1 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f457,plain,
( subset(sK7,sK8)
| ~ spl18_3 ),
inference(superposition,[],[f302,f393]) ).
fof(f302,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f406,plain,
spl18_4,
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f405,plain,
( $false
| spl18_4 ),
inference(subsumption_resolution,[],[f401,f247]) ).
fof(f247,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f401,plain,
( ~ latt_str(boole_lattice(sK6))
| spl18_4 ),
inference(resolution,[],[f397,f283]) ).
fof(f283,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ( join_semilatt_str(X0)
& meet_semilatt_str(X0) )
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f397,plain,
( ~ join_semilatt_str(boole_lattice(sK6))
| spl18_4 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f398,plain,
( spl18_3
| ~ spl18_4
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f376,f368,f395,f391]) ).
fof(f376,plain,
( ~ join_semilatt_str(boole_lattice(sK6))
| set_union2(sK7,sK8) = sK8
| ~ spl18_2 ),
inference(forward_demodulation,[],[f375,f333]) ).
fof(f375,plain,
( ~ join_semilatt_str(boole_lattice(sK6))
| sK8 = join(boole_lattice(sK6),sK7,sK8)
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f374,f244]) ).
fof(f374,plain,
( ~ element(sK8,the_carrier(boole_lattice(sK6)))
| sK8 = join(boole_lattice(sK6),sK7,sK8)
| ~ join_semilatt_str(boole_lattice(sK6))
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f373,f245]) ).
fof(f373,plain,
( ~ join_semilatt_str(boole_lattice(sK6))
| sK8 = join(boole_lattice(sK6),sK7,sK8)
| ~ element(sK7,the_carrier(boole_lattice(sK6)))
| ~ element(sK8,the_carrier(boole_lattice(sK6)))
| ~ spl18_2 ),
inference(subsumption_resolution,[],[f372,f237]) ).
fof(f372,plain,
( empty_carrier(boole_lattice(sK6))
| sK8 = join(boole_lattice(sK6),sK7,sK8)
| ~ element(sK7,the_carrier(boole_lattice(sK6)))
| ~ element(sK8,the_carrier(boole_lattice(sK6)))
| ~ join_semilatt_str(boole_lattice(sK6))
| ~ spl18_2 ),
inference(resolution,[],[f370,f231]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ below(X0,X1,X2)
| empty_carrier(X0)
| join(X0,X1,X2) = X2
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ element(X2,the_carrier(X0)) ),
inference(cnf_transformation,[],[f171]) ).
fof(f370,plain,
( below(boole_lattice(sK6),sK7,sK8)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f381,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f243,f368,f364]) ).
fof(f243,plain,
( ~ below(boole_lattice(sK6),sK7,sK8)
| ~ subset(sK7,sK8) ),
inference(cnf_transformation,[],[f184]) ).
fof(f371,plain,
( spl18_1
| spl18_2 ),
inference(avatar_split_clause,[],[f242,f368,f364]) ).
fof(f242,plain,
( below(boole_lattice(sK6),sK7,sK8)
| subset(sK7,sK8) ),
inference(cnf_transformation,[],[f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU344+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % 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 : n003.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 15:16:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47 % (8302)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.47 % (8294)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.48 % (8294)First to succeed.
% 0.19/0.49 % (8294)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50 % (8294)------------------------------
% 0.19/0.50 % (8294)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (8294)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50 % (8294)Termination reason: Refutation
% 0.19/0.50
% 0.19/0.50 % (8294)Memory used [KB]: 6268
% 0.19/0.50 % (8294)Time elapsed: 0.080 s
% 0.19/0.50 % (8294)Instructions burned: 14 (million)
% 0.19/0.50 % (8294)------------------------------
% 0.19/0.50 % (8294)------------------------------
% 0.19/0.50 % (8272)Success in time 0.145 s
%------------------------------------------------------------------------------