TSTP Solution File: SET893+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET893+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 : n028.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 18:26:02 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 8 unt; 0 def)
% Number of atoms : 236 ( 84 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 269 ( 107 ~; 114 |; 35 &)
% ( 10 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 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; 4 con; 0-2 aty)
% Number of variables : 128 ( 105 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f123,plain,
$false,
inference(avatar_sat_refutation,[],[f74,f75,f76,f102,f110,f122]) ).
fof(f122,plain,
( ~ spl7_1
| ~ spl7_2
| spl7_3 ),
inference(avatar_contradiction_clause,[],[f121]) ).
fof(f121,plain,
( $false
| ~ spl7_1
| ~ spl7_2
| spl7_3 ),
inference(subsumption_resolution,[],[f120,f60]) ).
fof(f60,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X3] :
( ( X1 != X3
| ~ in(X3,X0) )
& ( X1 = X3
| in(X3,X0) ) )
=> ( ( sK2(X0,X1) != X1
| ~ in(sK2(X0,X1),X0) )
& ( sK2(X0,X1) = X1
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( X1 != X3
| ~ in(X3,X0) )
& ( X1 = X3
| in(X3,X0) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f120,plain,
( ~ in(sK3,singleton(sK3))
| ~ spl7_1
| ~ spl7_2
| spl7_3 ),
inference(subsumption_resolution,[],[f116,f60]) ).
fof(f116,plain,
( ~ in(sK5,singleton(sK5))
| ~ in(sK3,singleton(sK3))
| ~ spl7_1
| ~ spl7_2
| spl7_3 ),
inference(resolution,[],[f80,f113]) ).
fof(f113,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK5)),cartesian_product2(singleton(sK3),singleton(sK5)))
| ~ spl7_1
| ~ spl7_2
| spl7_3 ),
inference(forward_demodulation,[],[f112,f64]) ).
fof(f64,plain,
( sK4 = sK3
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f63,plain,
( spl7_1
<=> sK4 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f112,plain,
( ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),cartesian_product2(singleton(sK3),singleton(sK5)))
| ~ spl7_2
| spl7_3 ),
inference(forward_demodulation,[],[f111,f68]) ).
fof(f68,plain,
( sK5 = sK6
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl7_2
<=> sK5 = sK6 ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f111,plain,
( ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK6)),cartesian_product2(singleton(sK3),singleton(sK5)))
| spl7_3 ),
inference(forward_demodulation,[],[f73,f47]) ).
fof(f47,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f12]) ).
fof(f12,plain,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f73,plain,
( ~ in(unordered_pair(unordered_pair(sK4,sK6),singleton(sK4)),cartesian_product2(singleton(sK3),singleton(sK5)))
| spl7_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f71,plain,
( spl7_3
<=> in(unordered_pair(unordered_pair(sK4,sK6),singleton(sK4)),cartesian_product2(singleton(sK3),singleton(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f80,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(X1,X0))
| ~ in(X2,X0)
| ~ in(X3,X1) ),
inference(backward_demodulation,[],[f52,f47]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| ~ in(X2,X0)
| in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),cartesian_product2(X1,X0)) ),
inference(definition_unfolding,[],[f40,f41]) ).
fof(f41,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X3,X2),cartesian_product2(X1,X0))
| ~ in(X3,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X3,X2),cartesian_product2(X1,X0))
| ~ in(X3,X1)
| ~ in(X2,X0) )
& ( ( in(X3,X1)
& in(X2,X0) )
| ~ in(ordered_pair(X3,X2),cartesian_product2(X1,X0)) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X3,X1,X2,X0] :
( ( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
| ~ in(X0,X1)
| ~ in(X2,X3) )
& ( ( in(X0,X1)
& in(X2,X3) )
| ~ in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X3,X1,X2,X0] :
( ( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
| ~ in(X0,X1)
| ~ in(X2,X3) )
& ( ( in(X0,X1)
& in(X2,X3) )
| ~ in(ordered_pair(X0,X2),cartesian_product2(X1,X3)) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X3,X1,X2,X0] :
( in(ordered_pair(X0,X2),cartesian_product2(X1,X3))
<=> ( in(X0,X1)
& in(X2,X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X1,X3] :
( ( in(X0,X2)
& in(X1,X3) )
<=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f110,plain,
( spl7_2
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f109,plain,
( $false
| spl7_2
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f107,f69]) ).
fof(f69,plain,
( sK5 != sK6
| spl7_2 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f107,plain,
( sK5 = sK6
| ~ spl7_3 ),
inference(resolution,[],[f92,f61]) ).
fof(f61,plain,
! [X2,X1] :
( ~ in(X2,singleton(X1))
| X1 = X2 ),
inference(equality_resolution,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ in(X2,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f92,plain,
( in(sK6,singleton(sK5))
| ~ spl7_3 ),
inference(resolution,[],[f78,f81]) ).
fof(f81,plain,
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK6)),cartesian_product2(singleton(sK3),singleton(sK5)))
| ~ spl7_3 ),
inference(forward_demodulation,[],[f72,f47]) ).
fof(f72,plain,
( in(unordered_pair(unordered_pair(sK4,sK6),singleton(sK4)),cartesian_product2(singleton(sK3),singleton(sK5)))
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f78,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(X1,X0))
| in(X2,X0) ),
inference(backward_demodulation,[],[f54,f47]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),cartesian_product2(X1,X0))
| in(X2,X0) ),
inference(definition_unfolding,[],[f38,f41]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( in(X2,X0)
| ~ in(ordered_pair(X3,X2),cartesian_product2(X1,X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f102,plain,
( spl7_1
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f101,plain,
( $false
| spl7_1
| ~ spl7_3 ),
inference(subsumption_resolution,[],[f99,f65]) ).
fof(f65,plain,
( sK4 != sK3
| spl7_1 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f99,plain,
( sK4 = sK3
| ~ spl7_3 ),
inference(resolution,[],[f89,f61]) ).
fof(f89,plain,
( in(sK4,singleton(sK3))
| ~ spl7_3 ),
inference(resolution,[],[f77,f81]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),cartesian_product2(X1,X0))
| in(X3,X1) ),
inference(backward_demodulation,[],[f53,f47]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),cartesian_product2(X1,X0))
| in(X3,X1) ),
inference(definition_unfolding,[],[f39,f41]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(ordered_pair(X3,X2),cartesian_product2(X1,X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f76,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f58,f67,f71]) ).
fof(f58,plain,
( sK5 = sK6
| in(unordered_pair(unordered_pair(sK4,sK6),singleton(sK4)),cartesian_product2(singleton(sK3),singleton(sK5))) ),
inference(definition_unfolding,[],[f49,f41]) ).
fof(f49,plain,
( sK5 = sK6
| in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( ( sK4 != sK3
| sK5 != sK6
| ~ in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) )
& ( ( sK4 = sK3
& sK5 = sK6 )
| in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f33,f34]) ).
fof(f34,plain,
( ? [X0,X1,X2,X3] :
( ( X0 != X1
| X2 != X3
| ~ in(ordered_pair(X1,X3),cartesian_product2(singleton(X0),singleton(X2))) )
& ( ( X0 = X1
& X2 = X3 )
| in(ordered_pair(X1,X3),cartesian_product2(singleton(X0),singleton(X2))) ) )
=> ( ( sK4 != sK3
| sK5 != sK6
| ~ in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) )
& ( ( sK4 = sK3
& sK5 = sK6 )
| in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( ( X0 != X1
| X2 != X3
| ~ in(ordered_pair(X1,X3),cartesian_product2(singleton(X0),singleton(X2))) )
& ( ( X0 = X1
& X2 = X3 )
| in(ordered_pair(X1,X3),cartesian_product2(singleton(X0),singleton(X2))) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
? [X0,X2,X3,X1] :
( ( X0 != X2
| X1 != X3
| ~ in(ordered_pair(X2,X1),cartesian_product2(singleton(X0),singleton(X3))) )
& ( ( X0 = X2
& X1 = X3 )
| in(ordered_pair(X2,X1),cartesian_product2(singleton(X0),singleton(X3))) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
? [X0,X2,X3,X1] :
( ( X0 != X2
| X1 != X3
| ~ in(ordered_pair(X2,X1),cartesian_product2(singleton(X0),singleton(X3))) )
& ( ( X0 = X2
& X1 = X3 )
| in(ordered_pair(X2,X1),cartesian_product2(singleton(X0),singleton(X3))) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
? [X0,X2,X3,X1] :
( in(ordered_pair(X2,X1),cartesian_product2(singleton(X0),singleton(X3)))
<~> ( X0 = X2
& X1 = X3 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X3,X0,X2] :
( in(ordered_pair(X2,X1),cartesian_product2(singleton(X0),singleton(X3)))
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X2,X1,X0,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3)))
<=> ( X0 = X2
& X1 = X3 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X2,X1,X0,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),singleton(X3)))
<=> ( X0 = X2
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_zfmisc_1) ).
fof(f75,plain,
( spl7_3
| spl7_1 ),
inference(avatar_split_clause,[],[f57,f63,f71]) ).
fof(f57,plain,
( sK4 = sK3
| in(unordered_pair(unordered_pair(sK4,sK6),singleton(sK4)),cartesian_product2(singleton(sK3),singleton(sK5))) ),
inference(definition_unfolding,[],[f50,f41]) ).
fof(f50,plain,
( sK4 = sK3
| in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f74,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f56,f71,f67,f63]) ).
fof(f56,plain,
( ~ in(unordered_pair(unordered_pair(sK4,sK6),singleton(sK4)),cartesian_product2(singleton(sK3),singleton(sK5)))
| sK5 != sK6
| sK4 != sK3 ),
inference(definition_unfolding,[],[f51,f41]) ).
fof(f51,plain,
( sK4 != sK3
| sK5 != sK6
| ~ in(ordered_pair(sK4,sK6),cartesian_product2(singleton(sK3),singleton(sK5))) ),
inference(cnf_transformation,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % 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 : n028.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 14:37:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.46 % (20660)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.48 % (20669)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.49 % (20669)First to succeed.
% 0.20/0.49 % (20669)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (20669)------------------------------
% 0.20/0.49 % (20669)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (20669)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (20669)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (20669)Memory used [KB]: 5500
% 0.20/0.49 % (20669)Time elapsed: 0.084 s
% 0.20/0.49 % (20669)Instructions burned: 4 (million)
% 0.20/0.49 % (20669)------------------------------
% 0.20/0.49 % (20669)------------------------------
% 0.20/0.49 % (20647)Success in time 0.137 s
%------------------------------------------------------------------------------