TSTP Solution File: SET901+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET901+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_uns --cores 0 -t %d %s
% Computer : n025.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 18:22:42 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 8 unt; 0 def)
% Number of atoms : 218 ( 123 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 265 ( 106 ~; 99 |; 48 &)
% ( 10 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 64 ( 49 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f89,plain,
$false,
inference(avatar_sat_refutation,[],[f48,f53,f58,f63,f65,f71,f74,f82,f87]) ).
fof(f87,plain,
( spl3_2
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f86]) ).
fof(f86,plain,
( $false
| spl3_2
| ~ spl3_5 ),
inference(subsumption_resolution,[],[f83,f37]) ).
fof(f37,plain,
! [X0,X1] : subset(empty_set,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f33]) ).
fof(f33,plain,
! [X2,X0,X1] :
( subset(X2,unordered_pair(X0,X1))
| empty_set != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( singleton(X0) = X2
| empty_set = X2
| singleton(X1) = X2
| unordered_pair(X0,X1) = X2
| ~ subset(X2,unordered_pair(X0,X1)) )
& ( subset(X2,unordered_pair(X0,X1))
| ( singleton(X0) != X2
& empty_set != X2
& singleton(X1) != X2
& unordered_pair(X0,X1) != X2 ) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X2,X0] :
( ( singleton(X1) = X0
| empty_set = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| ~ subset(X0,unordered_pair(X1,X2)) )
& ( subset(X0,unordered_pair(X1,X2))
| ( singleton(X1) != X0
& empty_set != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 ) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X1,X2,X0] :
( ( singleton(X1) = X0
| empty_set = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| ~ subset(X0,unordered_pair(X1,X2)) )
& ( subset(X0,unordered_pair(X1,X2))
| ( singleton(X1) != X0
& empty_set != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X1,X2,X0] :
( ( singleton(X1) = X0
| empty_set = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 )
<=> subset(X0,unordered_pair(X1,X2)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X2,X1,X0] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( singleton(X2) != X0
& empty_set != X0
& unordered_pair(X1,X2) != X0
& singleton(X1) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f83,plain,
( ~ subset(empty_set,unordered_pair(sK1,sK2))
| spl3_2
| ~ spl3_5 ),
inference(backward_demodulation,[],[f47,f61]) ).
fof(f61,plain,
( empty_set = sK0
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f60,plain,
( spl3_5
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f47,plain,
( ~ subset(sK0,unordered_pair(sK1,sK2))
| spl3_2 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f45,plain,
( spl3_2
<=> subset(sK0,unordered_pair(sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f82,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f79]) ).
fof(f79,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(unit_resulting_resolution,[],[f47,f76]) ).
fof(f76,plain,
( ! [X1] : subset(sK0,unordered_pair(X1,sK2))
| ~ spl3_1 ),
inference(superposition,[],[f38,f42]) ).
fof(f42,plain,
( singleton(sK2) = sK0
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f41,plain,
( spl3_1
<=> singleton(sK2) = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f38,plain,
! [X0,X1] : subset(singleton(X1),unordered_pair(X0,X1)),
inference(equality_resolution,[],[f32]) ).
fof(f32,plain,
! [X2,X0,X1] :
( subset(X2,unordered_pair(X0,X1))
| singleton(X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f74,plain,
( spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f73]) ).
fof(f73,plain,
( $false
| spl3_2
| ~ spl3_4 ),
inference(subsumption_resolution,[],[f72,f24]) ).
fof(f24,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f10,plain,
! [X1] : subset(X1,X1),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f72,plain,
( ~ subset(sK0,sK0)
| spl3_2
| ~ spl3_4 ),
inference(backward_demodulation,[],[f47,f56]) ).
fof(f56,plain,
( unordered_pair(sK1,sK2) = sK0
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f55,plain,
( spl3_4
<=> unordered_pair(sK1,sK2) = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f71,plain,
( spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f68]) ).
fof(f68,plain,
( $false
| spl3_2
| ~ spl3_3 ),
inference(unit_resulting_resolution,[],[f47,f66]) ).
fof(f66,plain,
( ! [X0] : subset(sK0,unordered_pair(sK1,X0))
| ~ spl3_3 ),
inference(superposition,[],[f36,f51]) ).
fof(f51,plain,
( singleton(sK1) = sK0
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f50,plain,
( spl3_3
<=> singleton(sK1) = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f36,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X2,X0,X1] :
( subset(X2,unordered_pair(X0,X1))
| singleton(X0) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f65,plain,
( spl3_3
| spl3_5
| spl3_1
| spl3_4 ),
inference(avatar_split_clause,[],[f64,f55,f41,f60,f50]) ).
fof(f64,plain,
( unordered_pair(sK1,sK2) = sK0
| singleton(sK2) = sK0
| empty_set = sK0
| singleton(sK1) = sK0 ),
inference(subsumption_resolution,[],[f26,f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ subset(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = X2
| empty_set = X2
| singleton(X1) = X2
| singleton(X0) = X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f26,plain,
( singleton(sK2) = sK0
| subset(sK0,unordered_pair(sK1,sK2))
| empty_set = sK0
| singleton(sK1) = sK0
| unordered_pair(sK1,sK2) = sK0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ( ~ subset(sK0,unordered_pair(sK1,sK2))
| ( singleton(sK1) != sK0
& unordered_pair(sK1,sK2) != sK0
& empty_set != sK0
& singleton(sK2) != sK0 ) )
& ( subset(sK0,unordered_pair(sK1,sK2))
| singleton(sK1) = sK0
| unordered_pair(sK1,sK2) = sK0
| empty_set = sK0
| singleton(sK2) = sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( ( ~ subset(X0,unordered_pair(X1,X2))
| ( singleton(X1) != X0
& unordered_pair(X1,X2) != X0
& empty_set != X0
& singleton(X2) != X0 ) )
& ( subset(X0,unordered_pair(X1,X2))
| singleton(X1) = X0
| unordered_pair(X1,X2) = X0
| empty_set = X0
| singleton(X2) = X0 ) )
=> ( ( ~ subset(sK0,unordered_pair(sK1,sK2))
| ( singleton(sK1) != sK0
& unordered_pair(sK1,sK2) != sK0
& empty_set != sK0
& singleton(sK2) != sK0 ) )
& ( subset(sK0,unordered_pair(sK1,sK2))
| singleton(sK1) = sK0
| unordered_pair(sK1,sK2) = sK0
| empty_set = sK0
| singleton(sK2) = sK0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( ~ subset(X0,unordered_pair(X1,X2))
| ( singleton(X1) != X0
& unordered_pair(X1,X2) != X0
& empty_set != X0
& singleton(X2) != X0 ) )
& ( subset(X0,unordered_pair(X1,X2))
| singleton(X1) = X0
| unordered_pair(X1,X2) = X0
| empty_set = X0
| singleton(X2) = X0 ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
? [X0,X2,X1] :
( ( ~ subset(X0,unordered_pair(X2,X1))
| ( singleton(X2) != X0
& unordered_pair(X2,X1) != X0
& empty_set != X0
& singleton(X1) != X0 ) )
& ( subset(X0,unordered_pair(X2,X1))
| singleton(X2) = X0
| unordered_pair(X2,X1) = X0
| empty_set = X0
| singleton(X1) = X0 ) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X2,X1] :
( ( ~ subset(X0,unordered_pair(X2,X1))
| ( singleton(X2) != X0
& unordered_pair(X2,X1) != X0
& empty_set != X0
& singleton(X1) != X0 ) )
& ( subset(X0,unordered_pair(X2,X1))
| singleton(X2) = X0
| unordered_pair(X2,X1) = X0
| empty_set = X0
| singleton(X1) = X0 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
? [X0,X2,X1] :
( ( singleton(X2) = X0
| unordered_pair(X2,X1) = X0
| empty_set = X0
| singleton(X1) = X0 )
<~> subset(X0,unordered_pair(X2,X1)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
~ ! [X2,X0,X1] :
( ~ ( singleton(X2) != X0
& singleton(X1) != X0
& empty_set != X0
& unordered_pair(X2,X1) != X0 )
<=> subset(X0,unordered_pair(X2,X1)) ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X0,X2,X1] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( singleton(X1) != X0
& unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& empty_set != X0 ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X0,X2,X1] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( singleton(X1) != X0
& unordered_pair(X1,X2) != X0
& singleton(X2) != X0
& empty_set != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
fof(f63,plain,
( ~ spl3_5
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f28,f45,f60]) ).
fof(f28,plain,
( ~ subset(sK0,unordered_pair(sK1,sK2))
| empty_set != sK0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f58,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f29,f55,f45]) ).
fof(f29,plain,
( unordered_pair(sK1,sK2) != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f53,plain,
( ~ spl3_3
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f30,f45,f50]) ).
fof(f30,plain,
( ~ subset(sK0,unordered_pair(sK1,sK2))
| singleton(sK1) != sK0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f27,f45,f41]) ).
fof(f27,plain,
( ~ subset(sK0,unordered_pair(sK1,sK2))
| singleton(sK2) != sK0 ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n025.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 14:37:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (18007)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)
% 0.20/0.50 % (18012)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50 % (18027)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.50 % (18004)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)
% 0.20/0.50 % (18004)First to succeed.
% 0.20/0.50 % (18010)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.50 % (18012)Also succeeded, but the first one will report.
% 0.20/0.51 % (18004)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (18004)------------------------------
% 0.20/0.51 % (18004)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (18004)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (18004)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (18004)Memory used [KB]: 6012
% 0.20/0.51 % (18004)Time elapsed: 0.102 s
% 0.20/0.51 % (18004)Instructions burned: 3 (million)
% 0.20/0.51 % (18004)------------------------------
% 0.20/0.51 % (18004)------------------------------
% 0.20/0.51 % (17996)Success in time 0.154 s
%------------------------------------------------------------------------------