TSTP Solution File: SET598+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n002.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 18:25:02 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 87 ( 12 unt; 0 def)
% Number of atoms : 314 ( 47 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 374 ( 147 ~; 151 |; 56 &)
% ( 11 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 92 ( 68 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f472,plain,
$false,
inference(avatar_sat_refutation,[],[f94,f98,f103,f104,f109,f110,f113,f126,f211,f266,f470]) ).
fof(f470,plain,
( ~ spl7_1
| ~ spl7_2
| spl7_4
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f469]) ).
fof(f469,plain,
( $false
| ~ spl7_1
| ~ spl7_2
| spl7_4
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f468,f284]) ).
fof(f284,plain,
( ~ subset(sK1,sF6)
| spl7_4
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f283,f93]) ).
fof(f93,plain,
( sK1 != sF6
| spl7_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f91,plain,
( spl7_4
<=> sK1 = sF6 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f283,plain,
( sK1 = sF6
| ~ subset(sK1,sF6)
| ~ spl7_5 ),
inference(resolution,[],[f281,f46]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f281,plain,
( subset(sF6,sK1)
| ~ spl7_5 ),
inference(subsumption_resolution,[],[f278,f132]) ).
fof(f132,plain,
subset(sF6,sK0),
inference(superposition,[],[f116,f71]) ).
fof(f71,plain,
sF6 = intersection(sK2,sK0),
introduced(function_definition,[]) ).
fof(f116,plain,
! [X0,X1] : subset(intersection(X1,X0),X0),
inference(superposition,[],[f66,f47]) ).
fof(f47,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f66,plain,
! [X0,X1] : subset(intersection(X1,X0),X1),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] : subset(intersection(X1,X0),X1),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] : subset(intersection(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f278,plain,
( ~ subset(sF6,sK0)
| subset(sF6,sK1)
| ~ spl7_5 ),
inference(resolution,[],[f111,f97]) ).
fof(f97,plain,
( ! [X4] :
( ~ subset(X4,sK2)
| ~ subset(X4,sK0)
| subset(X4,sK1) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f96,plain,
( spl7_5
<=> ! [X4] :
( ~ subset(X4,sK2)
| ~ subset(X4,sK0)
| subset(X4,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f111,plain,
subset(sF6,sK2),
inference(superposition,[],[f66,f71]) ).
fof(f468,plain,
( subset(sK1,sF6)
| ~ spl7_1
| ~ spl7_2 ),
inference(subsumption_resolution,[],[f462,f80]) ).
fof(f80,plain,
( subset(sK1,sK0)
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f79,plain,
( spl7_1
<=> subset(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f462,plain,
( ~ subset(sK1,sK0)
| subset(sK1,sF6)
| ~ spl7_2 ),
inference(resolution,[],[f205,f84]) ).
fof(f84,plain,
( subset(sK1,sK2)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f83,plain,
( spl7_2
<=> subset(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f205,plain,
! [X0] :
( ~ subset(X0,sK2)
| subset(X0,sF6)
| ~ subset(X0,sK0) ),
inference(superposition,[],[f59,f71]) ).
fof(f59,plain,
! [X2,X0,X1] :
( subset(X2,intersection(X0,X1))
| ~ subset(X2,X1)
| ~ subset(X2,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ subset(X2,X1)
| ~ subset(X2,X0)
| subset(X2,intersection(X0,X1)) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X2] :
( ~ subset(X2,X0)
| ~ subset(X2,X1)
| subset(X2,intersection(X1,X0)) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X2,X0,X1] :
( subset(X2,intersection(X1,X0))
| ~ subset(X2,X0)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ( subset(X2,X0)
& subset(X2,X1) )
=> subset(X2,intersection(X1,X0)) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).
fof(f266,plain,
( spl7_7
| ~ spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f265,f100,f96,f87,f106]) ).
fof(f106,plain,
( spl7_7
<=> subset(sK3,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f87,plain,
( spl7_3
<=> subset(sK3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f100,plain,
( spl7_6
<=> subset(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f265,plain,
( subset(sK3,sK1)
| ~ spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(subsumption_resolution,[],[f248,f89]) ).
fof(f89,plain,
( subset(sK3,sK0)
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f248,plain,
( subset(sK3,sK1)
| ~ subset(sK3,sK0)
| ~ spl7_5
| ~ spl7_6 ),
inference(resolution,[],[f97,f102]) ).
fof(f102,plain,
( subset(sK3,sK2)
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f211,plain,
( spl7_5
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f208,f91,f96]) ).
fof(f208,plain,
( ! [X7] :
( ~ subset(X7,sK0)
| subset(X7,sK1)
| ~ subset(X7,sK2) )
| ~ spl7_4 ),
inference(superposition,[],[f59,f120]) ).
fof(f120,plain,
( sK1 = intersection(sK0,sK2)
| ~ spl7_4 ),
inference(forward_demodulation,[],[f114,f92]) ).
fof(f92,plain,
( sK1 = sF6
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f114,plain,
sF6 = intersection(sK0,sK2),
inference(superposition,[],[f47,f71]) ).
fof(f126,plain,
( spl7_1
| ~ spl7_4 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f125,plain,
( $false
| spl7_1
| ~ spl7_4 ),
inference(subsumption_resolution,[],[f124,f81]) ).
fof(f81,plain,
( ~ subset(sK1,sK0)
| spl7_1 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f124,plain,
( subset(sK1,sK0)
| ~ spl7_4 ),
inference(superposition,[],[f66,f120]) ).
fof(f113,plain,
( spl7_2
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f112,f91,f83]) ).
fof(f112,plain,
( subset(sK1,sK2)
| ~ spl7_4 ),
inference(forward_demodulation,[],[f111,f92]) ).
fof(f110,plain,
( spl7_4
| spl7_1 ),
inference(avatar_split_clause,[],[f77,f79,f91]) ).
fof(f77,plain,
( subset(sK1,sK0)
| sK1 = sF6 ),
inference(definition_folding,[],[f49,f71]) ).
fof(f49,plain,
( sK1 = intersection(sK2,sK0)
| subset(sK1,sK0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( ( sK1 != intersection(sK2,sK0)
| ~ subset(sK1,sK2)
| ( subset(sK3,sK2)
& ~ subset(sK3,sK1)
& subset(sK3,sK0) )
| ~ subset(sK1,sK0) )
& ( sK1 = intersection(sK2,sK0)
| ( subset(sK1,sK2)
& ! [X4] :
( ~ subset(X4,sK2)
| subset(X4,sK1)
| ~ subset(X4,sK0) )
& subset(sK1,sK0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f27,f29,f28]) ).
fof(f28,plain,
( ? [X0,X1,X2] :
( ( intersection(X2,X0) != X1
| ~ subset(X1,X2)
| ? [X3] :
( subset(X3,X2)
& ~ subset(X3,X1)
& subset(X3,X0) )
| ~ subset(X1,X0) )
& ( intersection(X2,X0) = X1
| ( subset(X1,X2)
& ! [X4] :
( ~ subset(X4,X2)
| subset(X4,X1)
| ~ subset(X4,X0) )
& subset(X1,X0) ) ) )
=> ( ( sK1 != intersection(sK2,sK0)
| ~ subset(sK1,sK2)
| ? [X3] :
( subset(X3,sK2)
& ~ subset(X3,sK1)
& subset(X3,sK0) )
| ~ subset(sK1,sK0) )
& ( sK1 = intersection(sK2,sK0)
| ( subset(sK1,sK2)
& ! [X4] :
( ~ subset(X4,sK2)
| subset(X4,sK1)
| ~ subset(X4,sK0) )
& subset(sK1,sK0) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ? [X3] :
( subset(X3,sK2)
& ~ subset(X3,sK1)
& subset(X3,sK0) )
=> ( subset(sK3,sK2)
& ~ subset(sK3,sK1)
& subset(sK3,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ( intersection(X2,X0) != X1
| ~ subset(X1,X2)
| ? [X3] :
( subset(X3,X2)
& ~ subset(X3,X1)
& subset(X3,X0) )
| ~ subset(X1,X0) )
& ( intersection(X2,X0) = X1
| ( subset(X1,X2)
& ! [X4] :
( ~ subset(X4,X2)
| subset(X4,X1)
| ~ subset(X4,X0) )
& subset(X1,X0) ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
? [X1,X0,X2] :
( ( intersection(X2,X1) != X0
| ~ subset(X0,X2)
| ? [X3] :
( subset(X3,X2)
& ~ subset(X3,X0)
& subset(X3,X1) )
| ~ subset(X0,X1) )
& ( intersection(X2,X1) = X0
| ( subset(X0,X2)
& ! [X3] :
( ~ subset(X3,X2)
| subset(X3,X0)
| ~ subset(X3,X1) )
& subset(X0,X1) ) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
? [X1,X0,X2] :
( ( intersection(X2,X1) != X0
| ~ subset(X0,X2)
| ? [X3] :
( subset(X3,X2)
& ~ subset(X3,X0)
& subset(X3,X1) )
| ~ subset(X0,X1) )
& ( intersection(X2,X1) = X0
| ( subset(X0,X2)
& ! [X3] :
( ~ subset(X3,X2)
| subset(X3,X0)
| ~ subset(X3,X1) )
& subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
? [X1,X0,X2] :
( ( subset(X0,X2)
& ! [X3] :
( ~ subset(X3,X2)
| subset(X3,X0)
| ~ subset(X3,X1) )
& subset(X0,X1) )
<~> intersection(X2,X1) = X0 ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
? [X2,X1,X0] :
( ( subset(X0,X2)
& subset(X0,X1)
& ! [X3] :
( subset(X3,X0)
| ~ subset(X3,X1)
| ~ subset(X3,X2) ) )
<~> intersection(X2,X1) = X0 ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X2,X1,X0] :
( ( subset(X0,X2)
& subset(X0,X1)
& ! [X3] :
( ( subset(X3,X1)
& subset(X3,X2) )
=> subset(X3,X0) ) )
<=> intersection(X2,X1) = X0 ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X2,X1] :
( intersection(X1,X2) = X0
<=> ( subset(X0,X2)
& ! [X3] :
( ( subset(X3,X1)
& subset(X3,X2) )
=> subset(X3,X0) )
& subset(X0,X1) ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X2,X1] :
( intersection(X1,X2) = X0
<=> ( subset(X0,X2)
& ! [X3] :
( ( subset(X3,X1)
& subset(X3,X2) )
=> subset(X3,X0) )
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th57) ).
fof(f109,plain,
( ~ spl7_2
| ~ spl7_4
| ~ spl7_1
| ~ spl7_7 ),
inference(avatar_split_clause,[],[f73,f106,f79,f91,f83]) ).
fof(f73,plain,
( ~ subset(sK3,sK1)
| ~ subset(sK1,sK0)
| sK1 != sF6
| ~ subset(sK1,sK2) ),
inference(definition_folding,[],[f53,f71]) ).
fof(f53,plain,
( sK1 != intersection(sK2,sK0)
| ~ subset(sK1,sK2)
| ~ subset(sK3,sK1)
| ~ subset(sK1,sK0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f104,plain,
( spl7_4
| spl7_2 ),
inference(avatar_split_clause,[],[f75,f83,f91]) ).
fof(f75,plain,
( subset(sK1,sK2)
| sK1 = sF6 ),
inference(definition_folding,[],[f51,f71]) ).
fof(f51,plain,
( sK1 = intersection(sK2,sK0)
| subset(sK1,sK2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f103,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_2
| spl7_6 ),
inference(avatar_split_clause,[],[f72,f100,f83,f91,f79]) ).
fof(f72,plain,
( subset(sK3,sK2)
| ~ subset(sK1,sK2)
| sK1 != sF6
| ~ subset(sK1,sK0) ),
inference(definition_folding,[],[f54,f71]) ).
fof(f54,plain,
( sK1 != intersection(sK2,sK0)
| ~ subset(sK1,sK2)
| subset(sK3,sK2)
| ~ subset(sK1,sK0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f98,plain,
( spl7_4
| spl7_5 ),
inference(avatar_split_clause,[],[f76,f96,f91]) ).
fof(f76,plain,
! [X4] :
( ~ subset(X4,sK2)
| sK1 = sF6
| subset(X4,sK1)
| ~ subset(X4,sK0) ),
inference(definition_folding,[],[f50,f71]) ).
fof(f50,plain,
! [X4] :
( sK1 = intersection(sK2,sK0)
| ~ subset(X4,sK2)
| subset(X4,sK1)
| ~ subset(X4,sK0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f94,plain,
( ~ spl7_1
| ~ spl7_2
| spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f74,f91,f87,f83,f79]) ).
fof(f74,plain,
( sK1 != sF6
| subset(sK3,sK0)
| ~ subset(sK1,sK2)
| ~ subset(sK1,sK0) ),
inference(definition_folding,[],[f52,f71]) ).
fof(f52,plain,
( sK1 != intersection(sK2,sK0)
| ~ subset(sK1,sK2)
| subset(sK3,sK0)
| ~ subset(sK1,sK0) ),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % 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 : n002.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 14:14:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (5565)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.50 % (5557)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.50 % (5548)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (5557)First to succeed.
% 0.19/0.52 % (5551)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52 % (5566)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 (2999ds/498Mi)
% 0.19/0.52 % (5565)Also succeeded, but the first one will report.
% 0.19/0.52 % (5570)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 % (5557)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (5557)------------------------------
% 0.19/0.52 % (5557)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (5557)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (5557)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (5557)Memory used [KB]: 5628
% 0.19/0.52 % (5557)Time elapsed: 0.114 s
% 0.19/0.52 % (5557)Instructions burned: 10 (million)
% 0.19/0.52 % (5557)------------------------------
% 0.19/0.52 % (5557)------------------------------
% 0.19/0.52 % (5543)Success in time 0.174 s
%------------------------------------------------------------------------------