TSTP Solution File: SEU159+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU159+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 : n026.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 18:32:13 EDT 2022
% Result : Theorem 1.33s 0.52s
% Output : Refutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 71 ( 3 unt; 0 def)
% Number of atoms : 267 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 309 ( 113 ~; 129 |; 46 &)
% ( 15 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 108 ( 89 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f118,plain,
$false,
inference(avatar_sat_refutation,[],[f64,f65,f66,f96,f101,f103,f111,f117]) ).
fof(f117,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f116]) ).
fof(f116,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_5 ),
inference(subsumption_resolution,[],[f115,f58]) ).
fof(f58,plain,
( in(sK4,sK2)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl5_2
<=> in(sK4,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f115,plain,
( ~ in(sK4,sK2)
| spl5_1
| ~ spl5_5 ),
inference(subsumption_resolution,[],[f114,f55]) ).
fof(f55,plain,
( ~ subset(unordered_pair(sK3,sK4),sK2)
| spl5_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl5_1
<=> subset(unordered_pair(sK3,sK4),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f114,plain,
( subset(unordered_pair(sK3,sK4),sK2)
| ~ in(sK4,sK2)
| ~ spl5_5 ),
inference(superposition,[],[f41,f95]) ).
fof(f95,plain,
( sK1(unordered_pair(sK3,sK4),sK2) = sK4
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f93,plain,
( spl5_5
<=> sK1(unordered_pair(sK3,sK4),sK2) = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& ~ in(X3,X1) )
=> ( in(sK1(X0,X1),X0)
& ~ in(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( in(X3,X0)
& ~ in(X3,X1) ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f111,plain,
( spl5_1
| ~ spl5_3
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f110,plain,
( $false
| spl5_1
| ~ spl5_3
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f109,f55]) ).
fof(f109,plain,
( subset(unordered_pair(sK3,sK4),sK2)
| ~ spl5_3
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f108,f62]) ).
fof(f62,plain,
( in(sK3,sK2)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f61,plain,
( spl5_3
<=> in(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f108,plain,
( ~ in(sK3,sK2)
| subset(unordered_pair(sK3,sK4),sK2)
| ~ spl5_4 ),
inference(superposition,[],[f41,f91]) ).
fof(f91,plain,
( sK1(unordered_pair(sK3,sK4),sK2) = sK3
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f89,plain,
( spl5_4
<=> sK1(unordered_pair(sK3,sK4),sK2) = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f103,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f102]) ).
fof(f102,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(subsumption_resolution,[],[f98,f59]) ).
fof(f59,plain,
( ~ in(sK4,sK2)
| spl5_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f98,plain,
( in(sK4,sK2)
| ~ spl5_1 ),
inference(resolution,[],[f97,f49]) ).
fof(f49,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f48]) ).
fof(f48,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f33]) ).
fof(f33,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 ) )
& ( in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0 ) ) )
& ( ! [X4] :
( ( X1 = X4
| X0 = X4
| ~ in(X4,X2) )
& ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f19,f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( in(X3,X2)
| X1 = X3
| X0 = X3 ) )
=> ( ( ~ in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X0 ) )
& ( in(sK0(X0,X1,X2),X2)
| sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( in(X3,X2)
| X1 = X3
| X0 = X3 ) ) )
& ( ! [X4] :
( ( X1 = X4
| X0 = X4
| ~ in(X4,X2) )
& ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X2,X1,X0] :
( ( unordered_pair(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( X1 != X3
& X2 != X3 ) )
& ( in(X3,X0)
| X1 = X3
| X2 = X3 ) ) )
& ( ! [X3] :
( ( X1 = X3
| X2 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( X1 != X3
& X2 != X3 ) ) )
| unordered_pair(X2,X1) != X0 ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X2,X1,X0] :
( ( unordered_pair(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( X1 != X3
& X2 != X3 ) )
& ( in(X3,X0)
| X1 = X3
| X2 = X3 ) ) )
& ( ! [X3] :
( ( X1 = X3
| X2 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( X1 != X3
& X2 != X3 ) ) )
| unordered_pair(X2,X1) != X0 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X2,X1,X0] :
( unordered_pair(X2,X1) = X0
<=> ! [X3] :
( ( X1 = X3
| X2 = X3 )
<=> in(X3,X0) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X1,X0] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X0 = X3
| X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f97,plain,
( ! [X0] :
( ~ in(X0,unordered_pair(sK3,sK4))
| in(X0,sK2) )
| ~ spl5_1 ),
inference(resolution,[],[f54,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
( subset(unordered_pair(sK3,sK4),sK2)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f101,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f100,plain,
( $false
| ~ spl5_1
| spl5_3 ),
inference(subsumption_resolution,[],[f99,f63]) ).
fof(f63,plain,
( ~ in(sK3,sK2)
| spl5_3 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f99,plain,
( in(sK3,sK2)
| ~ spl5_1 ),
inference(resolution,[],[f97,f51]) ).
fof(f51,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f32]) ).
fof(f32,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f96,plain,
( spl5_4
| spl5_5
| spl5_1 ),
inference(avatar_split_clause,[],[f85,f53,f93,f89]) ).
fof(f85,plain,
( sK1(unordered_pair(sK3,sK4),sK2) = sK4
| sK1(unordered_pair(sK3,sK4),sK2) = sK3
| spl5_1 ),
inference(resolution,[],[f47,f79]) ).
fof(f79,plain,
( in(sK1(unordered_pair(sK3,sK4),sK2),unordered_pair(sK3,sK4))
| spl5_1 ),
inference(resolution,[],[f42,f55]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X0 = X4
| X1 = X4 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| X0 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f21]) ).
fof(f66,plain,
( spl5_2
| spl5_1 ),
inference(avatar_split_clause,[],[f45,f53,f57]) ).
fof(f45,plain,
( subset(unordered_pair(sK3,sK4),sK2)
| in(sK4,sK2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ( ~ subset(unordered_pair(sK3,sK4),sK2)
| ~ in(sK4,sK2)
| ~ in(sK3,sK2) )
& ( subset(unordered_pair(sK3,sK4),sK2)
| ( in(sK4,sK2)
& in(sK3,sK2) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1,X2] :
( ( ~ subset(unordered_pair(X1,X2),X0)
| ~ in(X2,X0)
| ~ in(X1,X0) )
& ( subset(unordered_pair(X1,X2),X0)
| ( in(X2,X0)
& in(X1,X0) ) ) )
=> ( ( ~ subset(unordered_pair(sK3,sK4),sK2)
| ~ in(sK4,sK2)
| ~ in(sK3,sK2) )
& ( subset(unordered_pair(sK3,sK4),sK2)
| ( in(sK4,sK2)
& in(sK3,sK2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ subset(unordered_pair(X1,X2),X0)
| ~ in(X2,X0)
| ~ in(X1,X0) )
& ( subset(unordered_pair(X1,X2),X0)
| ( in(X2,X0)
& in(X1,X0) ) ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ subset(unordered_pair(X1,X2),X0)
| ~ in(X2,X0)
| ~ in(X1,X0) )
& ( subset(unordered_pair(X1,X2),X0)
| ( in(X2,X0)
& in(X1,X0) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( in(X2,X0)
& in(X1,X0) )
<~> subset(unordered_pair(X1,X2),X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
~ ! [X1,X0,X2] :
( subset(unordered_pair(X1,X2),X0)
<=> ( in(X2,X0)
& in(X1,X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X0,X2)
& in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f65,plain,
( spl5_1
| spl5_3 ),
inference(avatar_split_clause,[],[f44,f61,f53]) ).
fof(f44,plain,
( in(sK3,sK2)
| subset(unordered_pair(sK3,sK4),sK2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f64,plain,
( ~ spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f46,f61,f57,f53]) ).
fof(f46,plain,
( ~ in(sK3,sK2)
| ~ in(sK4,sK2)
| ~ subset(unordered_pair(sK3,sK4),sK2) ),
inference(cnf_transformation,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU159+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
% 0.13/0.34 % Computer : n026.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 14:56:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (30253)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.50 % (30248)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.50 % (30242)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/191324Mi)
% 0.20/0.50 TRYING [1]
% 0.20/0.50 % (30247)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 (3000ds/48Mi)
% 0.20/0.51 % (30256)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 (3000ds/68Mi)
% 0.20/0.51 TRYING [2]
% 0.20/0.51 TRYING [3]
% 0.20/0.51 TRYING [4]
% 0.20/0.51 % (30262)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/176Mi)
% 0.20/0.51 % (30262)First to succeed.
% 0.20/0.51 % (30265)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.20/0.51 % (30263)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.20/0.52 % (30245)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.52 % (30257)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.20/0.52 TRYING [5]
% 0.20/0.52 % (30269)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/177Mi)
% 0.20/0.52 % (30264)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 1.33/0.52 % (30244)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 1.33/0.52 % (30262)Refutation found. Thanks to Tanya!
% 1.33/0.52 % SZS status Theorem for theBenchmark
% 1.33/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.52 % (30262)------------------------------
% 1.33/0.52 % (30262)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.52 % (30262)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.52 % (30262)Termination reason: Refutation
% 1.33/0.52
% 1.33/0.52 % (30262)Memory used [KB]: 5500
% 1.33/0.52 % (30262)Time elapsed: 0.115 s
% 1.33/0.52 % (30262)Instructions burned: 4 (million)
% 1.33/0.52 % (30262)------------------------------
% 1.33/0.52 % (30262)------------------------------
% 1.33/0.52 % (30239)Success in time 0.172 s
%------------------------------------------------------------------------------