TSTP Solution File: SET962+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : n020.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 18:22:52 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 3 unt; 0 def)
% Number of atoms : 182 ( 35 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 208 ( 88 ~; 87 |; 17 &)
% ( 8 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 76 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f121,plain,
$false,
inference(avatar_sat_refutation,[],[f57,f70,f81,f108,f112,f120]) ).
fof(f120,plain,
( ~ spl5_1
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f119]) ).
fof(f119,plain,
( $false
| ~ spl5_1
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f117,f31]) ).
fof(f31,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( cartesian_product2(sK1,sK1) = cartesian_product2(sK0,sK0)
& sK0 != sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
& X0 != X1 )
=> ( cartesian_product2(sK1,sK1) = cartesian_product2(sK0,sK0)
& sK0 != sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
& X0 != X1 ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
? [X1,X0] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
& X0 != X1 ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X0] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X1,X0] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X1,X0] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f117,plain,
( sK0 = sK1
| ~ spl5_1
| ~ spl5_3 ),
inference(resolution,[],[f111,f65]) ).
fof(f65,plain,
( ! [X7] : ~ in(X7,sK1)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl5_3
<=> ! [X7] : ~ in(X7,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f111,plain,
( ! [X1] :
( in(sK2(X1,sK0),X1)
| sK0 = X1 )
| ~ spl5_1 ),
inference(resolution,[],[f52,f37]) ).
fof(f37,plain,
! [X0,X1] :
( in(sK2(X0,X1),X1)
| X0 = X1
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( in(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ in(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( in(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X1)
<~> in(X2,X0) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f52,plain,
( ! [X9] : ~ in(X9,sK0)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f51,plain,
( spl5_1
<=> ! [X9] : ~ in(X9,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f112,plain,
( ~ spl5_1
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f109,plain,
( $false
| ~ spl5_1
| ~ spl5_4 ),
inference(resolution,[],[f52,f94]) ).
fof(f94,plain,
( in(sK2(sK0,sK1),sK0)
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f93,f31]) ).
fof(f93,plain,
( in(sK2(sK0,sK1),sK0)
| sK0 = sK1
| ~ spl5_4 ),
inference(factoring,[],[f82]) ).
fof(f82,plain,
( ! [X0] :
( in(sK2(X0,sK1),sK0)
| sK1 = X0
| in(sK2(X0,sK1),X0) )
| ~ spl5_4 ),
inference(resolution,[],[f68,f37]) ).
fof(f68,plain,
( ! [X6] :
( ~ in(X6,sK1)
| in(X6,sK0) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f67,plain,
( spl5_4
<=> ! [X6] :
( ~ in(X6,sK1)
| in(X6,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f108,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_contradiction_clause,[],[f107]) ).
fof(f107,plain,
( $false
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f106,f86]) ).
fof(f86,plain,
( in(sK2(sK1,sK0),sK1)
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f85,f31]) ).
fof(f85,plain,
( sK0 = sK1
| in(sK2(sK1,sK0),sK1)
| ~ spl5_2 ),
inference(factoring,[],[f72]) ).
fof(f72,plain,
( ! [X2] :
( in(sK2(X2,sK0),sK1)
| in(sK2(X2,sK0),X2)
| sK0 = X2 )
| ~ spl5_2 ),
inference(resolution,[],[f37,f55]) ).
fof(f55,plain,
( ! [X8] :
( ~ in(X8,sK0)
| in(X8,sK1) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f54,plain,
( spl5_2
<=> ! [X8] :
( ~ in(X8,sK0)
| in(X8,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f106,plain,
( ~ in(sK2(sK1,sK0),sK1)
| ~ spl5_2
| ~ spl5_4 ),
inference(subsumption_resolution,[],[f100,f31]) ).
fof(f100,plain,
( sK0 = sK1
| ~ in(sK2(sK1,sK0),sK1)
| ~ spl5_2
| ~ spl5_4 ),
inference(resolution,[],[f38,f87]) ).
fof(f87,plain,
( in(sK2(sK1,sK0),sK0)
| ~ spl5_2
| ~ spl5_4 ),
inference(resolution,[],[f86,f68]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f81,plain,
( ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f80]) ).
fof(f80,plain,
( $false
| ~ spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f79,f31]) ).
fof(f79,plain,
( sK0 = sK1
| ~ spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f77,f65]) ).
fof(f77,plain,
( in(sK2(sK0,sK1),sK1)
| sK0 = sK1
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f73,f55]) ).
fof(f73,plain,
( ! [X3] :
( in(sK2(X3,sK1),X3)
| sK1 = X3 )
| ~ spl5_3 ),
inference(resolution,[],[f37,f65]) ).
fof(f70,plain,
( spl5_4
| spl5_3 ),
inference(avatar_split_clause,[],[f60,f64,f67]) ).
fof(f60,plain,
! [X4,X5] :
( ~ in(X4,sK1)
| ~ in(X5,sK1)
| in(X5,sK0) ),
inference(resolution,[],[f49,f35]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
| in(X3,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
| ~ in(X3,X2)
| ~ in(X1,X0) )
& ( ( in(X3,X2)
& in(X1,X0) )
| ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2)) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X3,X2,X1] :
( ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
| ~ in(X1,X2)
| ~ in(X3,X0) )
& ( ( in(X1,X2)
& in(X3,X0) )
| ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X0,X3,X2,X1] :
( ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
| ~ in(X1,X2)
| ~ in(X3,X0) )
& ( ( in(X1,X2)
& in(X3,X0) )
| ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X3,X2,X1] :
( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
<=> ( in(X1,X2)
& in(X3,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X1,X3,X0] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f49,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
| ~ in(X0,sK1)
| ~ in(X1,sK1) ),
inference(superposition,[],[f36,f32]) ).
fof(f32,plain,
cartesian_product2(sK1,sK1) = cartesian_product2(sK0,sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
| ~ in(X3,X2)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f57,plain,
( spl5_2
| spl5_1 ),
inference(avatar_split_clause,[],[f47,f51,f54]) ).
fof(f47,plain,
! [X10,X11] :
( ~ in(X10,sK0)
| ~ in(X11,sK0)
| in(X11,sK1) ),
inference(resolution,[],[f36,f42]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK0))
| in(X0,sK1) ),
inference(superposition,[],[f34,f32]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X1,X3),cartesian_product2(X0,X2))
| in(X1,X0) ),
inference(cnf_transformation,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.04/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 14:34:30 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.49 % (27103)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.50 % (27087)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 % (27087)First to succeed.
% 0.20/0.51 % (27087)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 % (27087)------------------------------
% 0.20/0.51 % (27087)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (27087)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (27087)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (27087)Memory used [KB]: 6012
% 0.20/0.51 % (27087)Time elapsed: 0.041 s
% 0.20/0.51 % (27087)Instructions burned: 4 (million)
% 0.20/0.51 % (27087)------------------------------
% 0.20/0.51 % (27087)------------------------------
% 0.20/0.51 % (27080)Success in time 0.149 s
%------------------------------------------------------------------------------