TSTP Solution File: SET879+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET879+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 : n008.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 18:25:59 EDT 2022
% Result : Theorem 1.67s 0.57s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 7 unt; 3 typ; 0 def)
% Number of atoms : 118 ( 83 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 135 ( 56 ~; 52 |; 16 &)
% ( 8 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 4 ( 0 usr; 3 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 51 !; 9 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_4,type,
sQ6_eqProxy: ( $int * $int ) > $o ).
tff(pred_def_5,type,
sQ7_eqProxy: ( $rat * $rat ) > $o ).
tff(pred_def_6,type,
sQ8_eqProxy: ( $real * $real ) > $o ).
fof(f130,plain,
$false,
inference(subsumption_resolution,[],[f129,f43]) ).
fof(f43,plain,
! [X2] : in(X2,singleton(X2)),
inference(literal_reordering,[],[f38]) ).
fof(f38,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f37]) ).
fof(f37,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f28]) ).
fof(f28,plain,
! [X2,X0,X1] :
( in(X2,X1)
| X0 != X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( ~ in(sK1(X0,X1),X1)
| sK1(X0,X1) != X0 )
& ( in(sK1(X0,X1),X1)
| sK1(X0,X1) = X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f16,f17]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X1)
| X0 != X3 )
& ( in(X3,X1)
| X0 = X3 ) )
=> ( ( ~ in(sK1(X0,X1),X1)
| sK1(X0,X1) != X0 )
& ( in(sK1(X0,X1),X1)
| sK1(X0,X1) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| X0 != X3 )
& ( in(X3,X1)
| X0 = X3 ) ) ) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
! [X1,X0] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
! [X1,X0] :
( ! [X2] :
( X1 = X2
<=> in(X2,X0) )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f129,plain,
~ in(sK3,singleton(sK3)),
inference(trivial_inequality_removal,[],[f128]) ).
fof(f128,plain,
( ~ in(sK3,singleton(sK3))
| singleton(sK3) != singleton(sK3) ),
inference(superposition,[],[f45,f126]) ).
fof(f126,plain,
singleton(sK3) = set_difference(singleton(sK3),singleton(sK3)),
inference(forward_demodulation,[],[f124,f103]) ).
fof(f103,plain,
sK3 = sK2,
inference(trivial_inequality_removal,[],[f102]) ).
fof(f102,plain,
( singleton(sK3) != singleton(sK3)
| sK3 = sK2 ),
inference(duplicate_literal_removal,[],[f100]) ).
fof(f100,plain,
( sK3 = sK2
| sK3 = sK2
| singleton(sK3) != singleton(sK3) ),
inference(superposition,[],[f42,f88]) ).
fof(f88,plain,
! [X2,X3] :
( singleton(X2) = set_difference(singleton(X2),singleton(X3))
| X2 = X3 ),
inference(resolution,[],[f39,f40]) ).
fof(f40,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(literal_reordering,[],[f36]) ).
fof(f36,plain,
! [X2,X0] :
( X0 = X2
| ~ in(X2,singleton(X0)) ),
inference(equality_resolution,[],[f29]) ).
fof(f29,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X0,X1] :
( in(X0,X1)
| singleton(X0) = set_difference(singleton(X0),X1) ),
inference(literal_reordering,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X0) = set_difference(singleton(X0),X1)
| in(X0,X1) )
& ( ~ in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),X1)
<=> ~ in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(f42,plain,
( singleton(sK3) != set_difference(singleton(sK3),singleton(sK2))
| sK3 = sK2 ),
inference(literal_reordering,[],[f31]) ).
fof(f31,plain,
( sK3 = sK2
| singleton(sK3) != set_difference(singleton(sK3),singleton(sK2)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
( ( sK3 = sK2
| singleton(sK3) != set_difference(singleton(sK3),singleton(sK2)) )
& ( sK3 != sK2
| singleton(sK3) = set_difference(singleton(sK3),singleton(sK2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f19,f20]) ).
fof(f20,plain,
( ? [X0,X1] :
( ( X0 = X1
| singleton(X1) != set_difference(singleton(X1),singleton(X0)) )
& ( X0 != X1
| singleton(X1) = set_difference(singleton(X1),singleton(X0)) ) )
=> ( ( sK3 = sK2
| singleton(sK3) != set_difference(singleton(sK3),singleton(sK2)) )
& ( sK3 != sK2
| singleton(sK3) = set_difference(singleton(sK3),singleton(sK2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0,X1] :
( ( X0 = X1
| singleton(X1) != set_difference(singleton(X1),singleton(X0)) )
& ( X0 != X1
| singleton(X1) = set_difference(singleton(X1),singleton(X0)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
? [X0,X1] :
( singleton(X1) = set_difference(singleton(X1),singleton(X0))
<~> X0 != X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
~ ! [X1,X0] :
( singleton(X1) = set_difference(singleton(X1),singleton(X0))
<=> X0 != X1 ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X1,X0] :
( singleton(X0) = set_difference(singleton(X0),singleton(X1))
<=> X0 != X1 ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X1,X0] :
( singleton(X0) = set_difference(singleton(X0),singleton(X1))
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f124,plain,
singleton(sK3) = set_difference(singleton(sK3),singleton(sK2)),
inference(subsumption_resolution,[],[f49,f103]) ).
fof(f49,plain,
( sK3 != sK2
| singleton(sK3) = set_difference(singleton(sK3),singleton(sK2)) ),
inference(literal_reordering,[],[f30]) ).
fof(f30,plain,
( sK3 != sK2
| singleton(sK3) = set_difference(singleton(sK3),singleton(sK2)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( singleton(X0) != set_difference(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(literal_reordering,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) != set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET879+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_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n008.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 14:31:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.56 % (11207)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.20/0.56 % (11207)First to succeed.
% 1.67/0.57 % (11199)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 1.67/0.57 % (11207)Refutation found. Thanks to Tanya!
% 1.67/0.57 % SZS status Theorem for theBenchmark
% 1.67/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.67/0.57 % (11207)------------------------------
% 1.67/0.57 % (11207)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.67/0.57 % (11207)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.67/0.57 % (11207)Termination reason: Refutation
% 1.67/0.57
% 1.67/0.57 % (11207)Memory used [KB]: 5756
% 1.67/0.57 % (11207)Time elapsed: 0.009 s
% 1.67/0.57 % (11207)Instructions burned: 4 (million)
% 1.67/0.57 % (11207)------------------------------
% 1.67/0.57 % (11207)------------------------------
% 1.67/0.57 % (11192)Success in time 0.224 s
%------------------------------------------------------------------------------