TSTP Solution File: SET921+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n006.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 18:26:06 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 68 ( 6 unt; 0 def)
% Number of atoms : 271 ( 71 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 330 ( 127 ~; 134 |; 52 &)
% ( 13 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 108 ( 86 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f114,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f71,f72,f98,f104,f112]) ).
fof(f112,plain,
( ~ spl9_1
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f111,plain,
( $false
| ~ spl9_1
| ~ spl9_3 ),
inference(subsumption_resolution,[],[f109,f61]) ).
fof(f61,plain,
( in(sK4,sF8)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f59,plain,
( spl9_1
<=> in(sK4,sF8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f109,plain,
( ~ in(sK4,sF8)
| ~ spl9_3 ),
inference(backward_demodulation,[],[f82,f69]) ).
fof(f69,plain,
( sK4 = sK5
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl9_3
<=> sK4 = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f82,plain,
~ in(sK5,sF8),
inference(resolution,[],[f79,f73]) ).
fof(f73,plain,
in(sK5,sF7),
inference(superposition,[],[f51,f53]) ).
fof(f53,plain,
sF7 = singleton(sK5),
introduced(function_definition,[]) ).
fof(f51,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X3,X0] :
( in(X3,X0)
| singleton(X3) != X0 ),
inference(equality_resolution,[],[f41]) ).
fof(f41,plain,
! [X3,X0,X1] :
( in(X3,X0)
| X1 != X3
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ( ( sK3(X0,X1) != X1
| ~ in(sK3(X0,X1),X0) )
& ( sK3(X0,X1) = X1
| in(sK3(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) )
=> ( ( sK3(X0,X1) != X1
| ~ in(sK3(X0,X1),X0) )
& ( sK3(X0,X1) = X1
| in(sK3(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| X1 != X3 )
& ( X1 = X3
| ~ in(X3,X0) ) )
| singleton(X1) != X0 ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( X1 != X2
| ~ in(X2,X0) )
& ( X1 = X2
| in(X2,X0) ) ) )
& ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0,X1] :
( singleton(X1) = X0
<=> ! [X2] :
( in(X2,X0)
<=> X1 = X2 ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f79,plain,
! [X0] :
( ~ in(X0,sF7)
| ~ in(X0,sF8) ),
inference(superposition,[],[f48,f54]) ).
fof(f54,plain,
sF8 = set_difference(sK6,sF7),
introduced(function_definition,[]) ).
fof(f48,plain,
! [X2,X1,X4] :
( ~ in(X4,set_difference(X2,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f33]) ).
fof(f33,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| set_difference(X2,X1) != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( set_difference(X2,X1) = X0
| ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X0) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X2) )
| in(sK1(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) )
& ( ( ~ in(X4,X1)
& in(X4,X2) )
| ~ in(X4,X0) ) )
| set_difference(X2,X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f17,f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) )
=> ( ( in(sK1(X0,X1,X2),X1)
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X0) )
& ( ( ~ in(sK1(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X2) )
| in(sK1(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( set_difference(X2,X1) = X0
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) )
& ( ( ~ in(X4,X1)
& in(X4,X2) )
| ~ in(X4,X0) ) )
| set_difference(X2,X1) != X0 ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( set_difference(X2,X1) = X0
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) ) )
| set_difference(X2,X1) != X0 ) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( set_difference(X2,X1) = X0
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X2)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| in(X3,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) ) )
| set_difference(X2,X1) != X0 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0,X1,X2] :
( set_difference(X2,X1) = X0
<=> ! [X3] :
( in(X3,X0)
<=> ( ~ in(X3,X1)
& in(X3,X2) ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X1,X0] :
( ! [X3] :
( ( ~ in(X3,X1)
& in(X3,X0) )
<=> in(X3,X2) )
<=> set_difference(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f104,plain,
( spl9_2
| ~ spl9_1 ),
inference(avatar_split_clause,[],[f99,f59,f63]) ).
fof(f63,plain,
( spl9_2
<=> in(sK4,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f99,plain,
( in(sK4,sK6)
| ~ spl9_1 ),
inference(resolution,[],[f61,f83]) ).
fof(f83,plain,
! [X0] :
( ~ in(X0,sF8)
| in(X0,sK6) ),
inference(superposition,[],[f49,f54]) ).
fof(f49,plain,
! [X2,X1,X4] :
( ~ in(X4,set_difference(X2,X1))
| in(X4,X2) ),
inference(equality_resolution,[],[f32]) ).
fof(f32,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_difference(X2,X1) != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f98,plain,
( spl9_1
| ~ spl9_2
| spl9_3 ),
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f97,plain,
( $false
| spl9_1
| ~ spl9_2
| spl9_3 ),
inference(subsumption_resolution,[],[f94,f70]) ).
fof(f70,plain,
( sK4 != sK5
| spl9_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f94,plain,
( sK4 = sK5
| spl9_1
| ~ spl9_2 ),
inference(resolution,[],[f92,f78]) ).
fof(f78,plain,
! [X0] :
( ~ in(X0,sF7)
| sK5 = X0 ),
inference(superposition,[],[f52,f53]) ).
fof(f52,plain,
! [X3,X1] :
( ~ in(X3,singleton(X1))
| X1 = X3 ),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X3,X0,X1] :
( X1 = X3
| ~ in(X3,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f25]) ).
fof(f92,plain,
( in(sK4,sF7)
| spl9_1
| ~ spl9_2 ),
inference(subsumption_resolution,[],[f91,f60]) ).
fof(f60,plain,
( ~ in(sK4,sF8)
| spl9_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f91,plain,
( in(sK4,sF8)
| in(sK4,sF7)
| ~ spl9_2 ),
inference(superposition,[],[f84,f54]) ).
fof(f84,plain,
( ! [X0] :
( in(sK4,set_difference(sK6,X0))
| in(sK4,X0) )
| ~ spl9_2 ),
inference(resolution,[],[f47,f65]) ).
fof(f65,plain,
( in(sK4,sK6)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f47,plain,
! [X2,X1,X4] :
( ~ in(X4,X2)
| in(X4,X1)
| in(X4,set_difference(X2,X1)) ),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| set_difference(X2,X1) != X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f72,plain,
( spl9_3
| ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f55,f63,f59,f68]) ).
fof(f55,plain,
( ~ in(sK4,sK6)
| ~ in(sK4,sF8)
| sK4 = sK5 ),
inference(definition_folding,[],[f46,f54,f53]) ).
fof(f46,plain,
( ~ in(sK4,set_difference(sK6,singleton(sK5)))
| sK4 = sK5
| ~ in(sK4,sK6) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( ( ~ in(sK4,set_difference(sK6,singleton(sK5)))
| sK4 = sK5
| ~ in(sK4,sK6) )
& ( in(sK4,set_difference(sK6,singleton(sK5)))
| ( sK4 != sK5
& in(sK4,sK6) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f28,f29]) ).
fof(f29,plain,
( ? [X0,X1,X2] :
( ( ~ in(X0,set_difference(X2,singleton(X1)))
| X0 = X1
| ~ in(X0,X2) )
& ( in(X0,set_difference(X2,singleton(X1)))
| ( X0 != X1
& in(X0,X2) ) ) )
=> ( ( ~ in(sK4,set_difference(sK6,singleton(sK5)))
| sK4 = sK5
| ~ in(sK4,sK6) )
& ( in(sK4,set_difference(sK6,singleton(sK5)))
| ( sK4 != sK5
& in(sK4,sK6) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ~ in(X0,set_difference(X2,singleton(X1)))
| X0 = X1
| ~ in(X0,X2) )
& ( in(X0,set_difference(X2,singleton(X1)))
| ( X0 != X1
& in(X0,X2) ) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X0,X2,X1] :
( ( ~ in(X0,set_difference(X1,singleton(X2)))
| X0 = X2
| ~ in(X0,X1) )
& ( in(X0,set_difference(X1,singleton(X2)))
| ( X0 != X2
& in(X0,X1) ) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0,X2,X1] :
( ( ~ in(X0,set_difference(X1,singleton(X2)))
| X0 = X2
| ~ in(X0,X1) )
& ( in(X0,set_difference(X1,singleton(X2)))
| ( X0 != X2
& in(X0,X1) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X2,X1] :
( ( X0 != X2
& in(X0,X1) )
<~> in(X0,set_difference(X1,singleton(X2))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X0,X2,X1] :
( ( X0 != X2
& in(X0,X1) )
<=> in(X0,set_difference(X1,singleton(X2))) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X0,X2,X1] :
( ( X0 != X2
& in(X0,X1) )
<=> in(X0,set_difference(X1,singleton(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
fof(f71,plain,
( spl9_1
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f56,f68,f59]) ).
fof(f56,plain,
( sK4 != sK5
| in(sK4,sF8) ),
inference(definition_folding,[],[f45,f54,f53]) ).
fof(f45,plain,
( in(sK4,set_difference(sK6,singleton(sK5)))
| sK4 != sK5 ),
inference(cnf_transformation,[],[f30]) ).
fof(f66,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f57,f63,f59]) ).
fof(f57,plain,
( in(sK4,sK6)
| in(sK4,sF8) ),
inference(definition_folding,[],[f44,f54,f53]) ).
fof(f44,plain,
( in(sK4,set_difference(sK6,singleton(sK5)))
| in(sK4,sK6) ),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n006.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 14:29:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % (3801)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)
% 0.19/0.50 % (3800)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.50 % (3806)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.19/0.50 % (3798)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)
% 0.19/0.50 % (3810)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)
% 0.19/0.51 % (3800)First to succeed.
% 0.19/0.51 % (3810)Also succeeded, but the first one will report.
% 0.19/0.51 % (3800)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (3800)------------------------------
% 0.19/0.51 % (3800)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (3800)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (3800)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (3800)Memory used [KB]: 5500
% 0.19/0.51 % (3800)Time elapsed: 0.104 s
% 0.19/0.51 % (3800)Instructions burned: 3 (million)
% 0.19/0.51 % (3800)------------------------------
% 0.19/0.51 % (3800)------------------------------
% 0.19/0.51 % (3792)Success in time 0.161 s
%------------------------------------------------------------------------------