TSTP Solution File: SET975+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET975+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 : n006.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 18:22:55 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 3 unt; 0 def)
% Number of atoms : 178 ( 52 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 208 ( 79 ~; 82 |; 35 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 69 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,plain,
$false,
inference(avatar_sat_refutation,[],[f55,f57,f76,f90]) ).
fof(f90,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f89]) ).
fof(f89,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(subsumption_resolution,[],[f80,f78]) ).
fof(f78,plain,
( ~ in(sK0,singleton(sK3))
| spl5_2 ),
inference(unit_resulting_resolution,[],[f53,f45]) ).
fof(f45,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) )
=> ( ( sK4(X0,X1) != X0
| ~ in(sK4(X0,X1),X1) )
& ( sK4(X0,X1) = X0
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( X0 != X3
| ~ in(X3,X1) )
& ( X0 = X3
| in(X3,X1) ) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [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,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f53,plain,
( sK0 != sK3
| spl5_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f52,plain,
( spl5_2
<=> sK0 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f80,plain,
( in(sK0,singleton(sK3))
| ~ spl5_1 ),
inference(unit_resulting_resolution,[],[f50,f40]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
| in(X2,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
| ~ in(X3,X0)
| ~ in(X2,X1) )
& ( ( in(X3,X0)
& in(X2,X1) )
| ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0)) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X2,X3,X1,X0] :
( ( in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X2,X3,X1,X0] :
( ( in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X2,X3,X1,X0] :
( in(ordered_pair(X1,X0),cartesian_product2(X3,X2))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0,X3,X2] :
( ( in(X1,X3)
& in(X0,X2) )
<=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f50,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f48,plain,
( spl5_1
<=> in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f76,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f75]) ).
fof(f75,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f68,f46]) ).
fof(f46,plain,
in(sK1,sK2),
inference(subsumption_resolution,[],[f32,f41]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
| in(X3,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f32,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| in(sK1,sK2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| ~ in(sK1,sK2)
| sK0 != sK3 )
& ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| ( in(sK1,sK2)
& sK0 = sK3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
| ~ in(X1,X2)
| X0 != X3 )
& ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
| ( in(X1,X2)
& X0 = X3 ) ) )
=> ( ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| ~ in(sK1,sK2)
| sK0 != sK3 )
& ( in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| ( in(sK1,sK2)
& sK0 = sK3 ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
| ~ in(X1,X2)
| X0 != X3 )
& ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X3),X2))
| ( in(X1,X2)
& X0 = X3 ) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
? [X1,X2,X3,X0] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
| ~ in(X2,X3)
| X0 != X1 )
& ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
| ( in(X2,X3)
& X0 = X1 ) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
? [X1,X2,X3,X0] :
( ( ~ in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
| ~ in(X2,X3)
| X0 != X1 )
& ( in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
| ( in(X2,X3)
& X0 = X1 ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
? [X1,X2,X3,X0] :
( ( in(X2,X3)
& X0 = X1 )
<~> in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),cartesian_product2(singleton(X0),X3))
<=> ( in(X2,X3)
& X0 = X1 ) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X2,X0,X1,X3] :
( ( in(X1,X3)
& X0 = X2 )
<=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X2,X0,X1,X3] :
( ( in(X1,X3)
& X0 = X2 )
<=> in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f68,plain,
( ~ in(sK1,sK2)
| spl5_1
| ~ spl5_2 ),
inference(unit_resulting_resolution,[],[f44,f58,f42]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
| ~ in(X2,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f58,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK0),sK2))
| spl5_1
| ~ spl5_2 ),
inference(backward_demodulation,[],[f49,f54]) ).
fof(f54,plain,
( sK0 = sK3
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f49,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| spl5_1 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f44,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( in(X2,X1)
| X0 != X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f57,plain,
( ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f56,f48,f52]) ).
fof(f56,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2))
| sK0 != sK3 ),
inference(subsumption_resolution,[],[f33,f46]) ).
fof(f33,plain,
( ~ in(sK1,sK2)
| sK0 != sK3
| ~ in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f31,f52,f48]) ).
fof(f31,plain,
( sK0 = sK3
| in(ordered_pair(sK0,sK1),cartesian_product2(singleton(sK3),sK2)) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % 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 : n006.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 14:31:55 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.49 % (13580)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)
% 0.20/0.49 % (13561)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 % (13561)First to succeed.
% 0.20/0.50 % (13572)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50 % (13561)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (13561)------------------------------
% 0.20/0.50 % (13561)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (13561)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (13561)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (13561)Memory used [KB]: 6012
% 0.20/0.50 % (13561)Time elapsed: 0.098 s
% 0.20/0.50 % (13561)Instructions burned: 3 (million)
% 0.20/0.50 % (13561)------------------------------
% 0.20/0.50 % (13561)------------------------------
% 0.20/0.50 % (13552)Success in time 0.155 s
%------------------------------------------------------------------------------