TSTP Solution File: SET931+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET931+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 : n027.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 18:22:46 EDT 2022
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 9 unt; 0 def)
% Number of atoms : 299 ( 187 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 353 ( 137 ~; 148 |; 53 &)
% ( 13 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 71 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[f60,f65,f70,f75,f76,f101,f104,f109,f123,f147]) ).
fof(f147,plain,
( ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(avatar_contradiction_clause,[],[f146]) ).
fof(f146,plain,
( $false
| ~ spl5_1
| spl5_2
| spl5_3
| spl5_4
| spl5_5 ),
inference(subsumption_resolution,[],[f145,f73]) ).
fof(f73,plain,
( empty_set != sK4
| spl5_5 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f72,plain,
( spl5_5
<=> empty_set = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f145,plain,
( empty_set = sK4
| ~ spl5_1
| spl5_2
| spl5_3
| spl5_4 ),
inference(subsumption_resolution,[],[f144,f69]) ).
fof(f69,plain,
( singleton(sK2) != sK4
| spl5_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl5_4
<=> singleton(sK2) = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f144,plain,
( singleton(sK2) = sK4
| empty_set = sK4
| ~ spl5_1
| spl5_2
| spl5_3 ),
inference(subsumption_resolution,[],[f143,f64]) ).
fof(f64,plain,
( unordered_pair(sK2,sK3) != sK4
| spl5_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f62,plain,
( spl5_3
<=> unordered_pair(sK2,sK3) = sK4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f143,plain,
( unordered_pair(sK2,sK3) = sK4
| singleton(sK2) = sK4
| empty_set = sK4
| ~ spl5_1
| spl5_2 ),
inference(subsumption_resolution,[],[f142,f59]) ).
fof(f59,plain,
( sK4 != singleton(sK3)
| spl5_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f57,plain,
( spl5_2
<=> sK4 = singleton(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f142,plain,
( sK4 = singleton(sK3)
| unordered_pair(sK2,sK3) = sK4
| empty_set = sK4
| singleton(sK2) = sK4
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f141]) ).
fof(f141,plain,
( singleton(sK2) = sK4
| unordered_pair(sK2,sK3) = sK4
| empty_set != empty_set
| empty_set = sK4
| sK4 = singleton(sK3)
| ~ spl5_1 ),
inference(superposition,[],[f129,f54]) ).
fof(f54,plain,
( empty_set = set_difference(sK4,unordered_pair(sK2,sK3))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f53,plain,
( spl5_1
<=> empty_set = set_difference(sK4,unordered_pair(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f129,plain,
! [X2,X3,X4] :
( empty_set != set_difference(X3,unordered_pair(X2,X4))
| singleton(X2) = X3
| singleton(X4) = X3
| unordered_pair(X2,X4) = X3
| empty_set = X3 ),
inference(resolution,[],[f38,f32]) ).
fof(f32,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
& ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( ( subset(X1,X0)
| empty_set != set_difference(X1,X0) )
& ( empty_set = set_difference(X1,X0)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X1,X0] :
( subset(X1,X0)
<=> empty_set = set_difference(X1,X0) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> empty_set = set_difference(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ subset(X2,unordered_pair(X0,X1))
| singleton(X0) = X2
| empty_set = X2
| unordered_pair(X0,X1) = X2
| singleton(X1) = X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| empty_set = X2
| singleton(X1) = X2
| singleton(X0) = X2
| ~ subset(X2,unordered_pair(X0,X1)) )
& ( subset(X2,unordered_pair(X0,X1))
| ( unordered_pair(X0,X1) != X2
& empty_set != X2
& singleton(X1) != X2
& singleton(X0) != X2 ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0,X2] :
( ( unordered_pair(X1,X0) = X2
| empty_set = X2
| singleton(X0) = X2
| singleton(X1) = X2
| ~ subset(X2,unordered_pair(X1,X0)) )
& ( subset(X2,unordered_pair(X1,X0))
| ( unordered_pair(X1,X0) != X2
& empty_set != X2
& singleton(X0) != X2
& singleton(X1) != X2 ) ) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( ( unordered_pair(X1,X0) = X2
| empty_set = X2
| singleton(X0) = X2
| singleton(X1) = X2
| ~ subset(X2,unordered_pair(X1,X0)) )
& ( subset(X2,unordered_pair(X1,X0))
| ( unordered_pair(X1,X0) != X2
& empty_set != X2
& singleton(X0) != X2
& singleton(X1) != X2 ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0,X2] :
( ( unordered_pair(X1,X0) = X2
| empty_set = X2
| singleton(X0) = X2
| singleton(X1) = X2 )
<=> subset(X2,unordered_pair(X1,X0)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X2,X1,X0] :
( ~ ( singleton(X0) != X2
& empty_set != X2
& singleton(X1) != X2
& unordered_pair(X1,X0) != X2 )
<=> subset(X2,unordered_pair(X1,X0)) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X1,X0] :
( ~ ( empty_set != X0
& singleton(X2) != X0
& singleton(X1) != X0
& unordered_pair(X1,X2) != X0 )
<=> subset(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f123,plain,
( spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f122,plain,
( $false
| spl5_1
| ~ spl5_4 ),
inference(trivial_inequality_removal,[],[f121]) ).
fof(f121,plain,
( empty_set != empty_set
| spl5_1
| ~ spl5_4 ),
inference(superposition,[],[f55,f112]) ).
fof(f112,plain,
( ! [X0] : empty_set = set_difference(sK4,unordered_pair(sK2,X0))
| ~ spl5_4 ),
inference(resolution,[],[f110,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f110,plain,
( ! [X0] : subset(sK4,unordered_pair(sK2,X0))
| ~ spl5_4 ),
inference(superposition,[],[f51,f68]) ).
fof(f68,plain,
( singleton(sK2) = sK4
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f51,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,[],[f22]) ).
fof(f55,plain,
( empty_set != set_difference(sK4,unordered_pair(sK2,sK3))
| spl5_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f109,plain,
( spl5_1
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f108]) ).
fof(f108,plain,
( $false
| spl5_1
| ~ spl5_5 ),
inference(subsumption_resolution,[],[f107,f90]) ).
fof(f90,plain,
! [X2,X1] : empty_set = set_difference(empty_set,unordered_pair(X1,X2)),
inference(resolution,[],[f31,f49]) ).
fof(f49,plain,
! [X0,X1] : subset(empty_set,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f36]) ).
fof(f36,plain,
! [X2,X0,X1] :
( subset(X2,unordered_pair(X0,X1))
| empty_set != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f107,plain,
( empty_set != set_difference(empty_set,unordered_pair(sK2,sK3))
| spl5_1
| ~ spl5_5 ),
inference(forward_demodulation,[],[f55,f74]) ).
fof(f74,plain,
( empty_set = sK4
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f104,plain,
( spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f103]) ).
fof(f103,plain,
( $false
| spl5_1
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f102,f89]) ).
fof(f89,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(resolution,[],[f31,f40]) ).
fof(f40,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f102,plain,
( empty_set != set_difference(sK4,sK4)
| spl5_1
| ~ spl5_3 ),
inference(backward_demodulation,[],[f55,f63]) ).
fof(f63,plain,
( unordered_pair(sK2,sK3) = sK4
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f101,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f100]) ).
fof(f100,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f99]) ).
fof(f99,plain,
( empty_set != empty_set
| spl5_1
| ~ spl5_2 ),
inference(superposition,[],[f55,f93]) ).
fof(f93,plain,
( ! [X7] : empty_set = set_difference(sK4,unordered_pair(X7,sK3))
| ~ spl5_2 ),
inference(resolution,[],[f31,f77]) ).
fof(f77,plain,
( ! [X0] : subset(sK4,unordered_pair(X0,sK3))
| ~ spl5_2 ),
inference(superposition,[],[f50,f58]) ).
fof(f58,plain,
( sK4 = singleton(sK3)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f50,plain,
! [X0,X1] : subset(singleton(X1),unordered_pair(X0,X1)),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X2,X0,X1] :
( subset(X2,unordered_pair(X0,X1))
| singleton(X1) != X2 ),
inference(cnf_transformation,[],[f22]) ).
fof(f76,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f45,f72,f53]) ).
fof(f45,plain,
( empty_set != sK4
| empty_set != set_difference(sK4,unordered_pair(sK2,sK3)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( ( ( sK4 != singleton(sK3)
& singleton(sK2) != sK4
& empty_set != sK4
& unordered_pair(sK2,sK3) != sK4 )
| empty_set != set_difference(sK4,unordered_pair(sK2,sK3)) )
& ( sK4 = singleton(sK3)
| singleton(sK2) = sK4
| empty_set = sK4
| unordered_pair(sK2,sK3) = sK4
| empty_set = set_difference(sK4,unordered_pair(sK2,sK3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f28,f29]) ).
fof(f29,plain,
( ? [X0,X1,X2] :
( ( ( singleton(X1) != X2
& singleton(X0) != X2
& empty_set != X2
& unordered_pair(X0,X1) != X2 )
| empty_set != set_difference(X2,unordered_pair(X0,X1)) )
& ( singleton(X1) = X2
| singleton(X0) = X2
| empty_set = X2
| unordered_pair(X0,X1) = X2
| empty_set = set_difference(X2,unordered_pair(X0,X1)) ) )
=> ( ( ( sK4 != singleton(sK3)
& singleton(sK2) != sK4
& empty_set != sK4
& unordered_pair(sK2,sK3) != sK4 )
| empty_set != set_difference(sK4,unordered_pair(sK2,sK3)) )
& ( sK4 = singleton(sK3)
| singleton(sK2) = sK4
| empty_set = sK4
| unordered_pair(sK2,sK3) = sK4
| empty_set = set_difference(sK4,unordered_pair(sK2,sK3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ( ( singleton(X1) != X2
& singleton(X0) != X2
& empty_set != X2
& unordered_pair(X0,X1) != X2 )
| empty_set != set_difference(X2,unordered_pair(X0,X1)) )
& ( singleton(X1) = X2
| singleton(X0) = X2
| empty_set = X2
| unordered_pair(X0,X1) = X2
| empty_set = set_difference(X2,unordered_pair(X0,X1)) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
? [X0,X2,X1] :
( ( ( singleton(X2) != X1
& singleton(X0) != X1
& empty_set != X1
& unordered_pair(X0,X2) != X1 )
| empty_set != set_difference(X1,unordered_pair(X0,X2)) )
& ( singleton(X2) = X1
| singleton(X0) = X1
| empty_set = X1
| unordered_pair(X0,X2) = X1
| empty_set = set_difference(X1,unordered_pair(X0,X2)) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0,X2,X1] :
( ( ( singleton(X2) != X1
& singleton(X0) != X1
& empty_set != X1
& unordered_pair(X0,X2) != X1 )
| empty_set != set_difference(X1,unordered_pair(X0,X2)) )
& ( singleton(X2) = X1
| singleton(X0) = X1
| empty_set = X1
| unordered_pair(X0,X2) = X1
| empty_set = set_difference(X1,unordered_pair(X0,X2)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X0,X2,X1] :
( empty_set = set_difference(X1,unordered_pair(X0,X2))
<~> ( singleton(X2) = X1
| singleton(X0) = X1
| empty_set = X1
| unordered_pair(X0,X2) = X1 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
~ ! [X2,X0,X1] :
( ~ ( empty_set != X1
& singleton(X2) != X1
& singleton(X0) != X1
& unordered_pair(X0,X2) != X1 )
<=> empty_set = set_difference(X1,unordered_pair(X0,X2)) ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X1,X0,X2] :
( ~ ( singleton(X2) != X0
& unordered_pair(X1,X2) != X0
& empty_set != X0
& singleton(X1) != X0 )
<=> empty_set = set_difference(X0,unordered_pair(X1,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X1,X0,X2] :
( ~ ( singleton(X2) != X0
& unordered_pair(X1,X2) != X0
& empty_set != X0
& singleton(X1) != X0 )
<=> empty_set = set_difference(X0,unordered_pair(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
fof(f75,plain,
( spl5_3
| spl5_4
| spl5_1
| spl5_5
| spl5_2 ),
inference(avatar_split_clause,[],[f43,f57,f72,f53,f67,f62]) ).
fof(f43,plain,
( sK4 = singleton(sK3)
| empty_set = sK4
| empty_set = set_difference(sK4,unordered_pair(sK2,sK3))
| singleton(sK2) = sK4
| unordered_pair(sK2,sK3) = sK4 ),
inference(cnf_transformation,[],[f30]) ).
fof(f70,plain,
( ~ spl5_4
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f46,f53,f67]) ).
fof(f46,plain,
( empty_set != set_difference(sK4,unordered_pair(sK2,sK3))
| singleton(sK2) != sK4 ),
inference(cnf_transformation,[],[f30]) ).
fof(f65,plain,
( ~ spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f44,f53,f62]) ).
fof(f44,plain,
( empty_set != set_difference(sK4,unordered_pair(sK2,sK3))
| unordered_pair(sK2,sK3) != sK4 ),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f47,f57,f53]) ).
fof(f47,plain,
( sK4 != singleton(sK3)
| empty_set != set_difference(sK4,unordered_pair(sK2,sK3)) ),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET931+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:46:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.48 % (20243)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)
% 0.21/0.49 % (20219)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.49 % (20219)Refutation not found, incomplete strategy% (20219)------------------------------
% 0.21/0.49 % (20219)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (20219)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (20219)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.49
% 0.21/0.49 % (20219)Memory used [KB]: 5884
% 0.21/0.49 % (20219)Time elapsed: 0.067 s
% 0.21/0.49 % (20219)Instructions burned: 3 (million)
% 0.21/0.49 % (20219)------------------------------
% 0.21/0.49 % (20219)------------------------------
% 0.21/0.49 % (20243)First to succeed.
% 0.21/0.49 % (20243)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (20243)------------------------------
% 0.21/0.49 % (20243)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49 % (20243)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49 % (20243)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (20243)Memory used [KB]: 6012
% 0.21/0.49 % (20243)Time elapsed: 0.056 s
% 0.21/0.49 % (20243)Instructions burned: 6 (million)
% 0.21/0.49 % (20243)------------------------------
% 0.21/0.49 % (20243)------------------------------
% 0.21/0.49 % (20217)Success in time 0.142 s
%------------------------------------------------------------------------------