TSTP Solution File: SET884+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET884+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 : n014.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 18:26:00 EDT 2022
% Result : Theorem 0.22s 0.55s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 11 unt; 3 typ; 0 def)
% Number of atoms : 192 ( 113 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 240 ( 92 ~; 80 |; 51 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 4 ( 0 usr; 3 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 89 !; 16 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_5,type,
sQ8_eqProxy: ( $int * $int ) > $o ).
tff(pred_def_6,type,
sQ9_eqProxy: ( $rat * $rat ) > $o ).
tff(pred_def_7,type,
sQ10_eqProxy: ( $real * $real ) > $o ).
fof(f185,plain,
$false,
inference(subsumption_resolution,[],[f184,f83]) ).
fof(f83,plain,
sK3 != sK4,
inference(literal_reordering,[],[f51]) ).
fof(f51,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( sK3 != sK2
& sK3 != sK4
& subset(singleton(sK3),unordered_pair(sK2,sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f30,f31]) ).
fof(f31,plain,
( ? [X0,X1,X2] :
( X0 != X1
& X1 != X2
& subset(singleton(X1),unordered_pair(X0,X2)) )
=> ( sK3 != sK2
& sK3 != sK4
& subset(singleton(sK3),unordered_pair(sK2,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1,X2] :
( X0 != X1
& X1 != X2
& subset(singleton(X1),unordered_pair(X0,X2)) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
? [X1,X2,X0] :
( X1 != X2
& X0 != X2
& subset(singleton(X2),unordered_pair(X1,X0)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X0,X2] :
~ ( X1 != X2
& X0 != X2
& subset(singleton(X2),unordered_pair(X1,X0)) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X2,X1,X0] :
~ ( X0 != X1
& subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X2 ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X2,X1,X0] :
~ ( X0 != X1
& subset(singleton(X0),unordered_pair(X1,X2))
& X0 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).
fof(f184,plain,
sK3 = sK4,
inference(subsumption_resolution,[],[f182,f70]) ).
fof(f70,plain,
sK3 != sK2,
inference(literal_reordering,[],[f52]) ).
fof(f52,plain,
sK3 != sK2,
inference(cnf_transformation,[],[f32]) ).
fof(f182,plain,
( sK3 = sK2
| sK3 = sK4 ),
inference(resolution,[],[f160,f67]) ).
fof(f67,plain,
! [X2,X0,X4] :
( ~ in(X4,unordered_pair(X2,X0))
| X0 = X4
| X2 = X4 ),
inference(literal_reordering,[],[f64]) ).
fof(f64,plain,
! [X2,X0,X4] :
( X2 = X4
| ~ in(X4,unordered_pair(X2,X0))
| X0 = X4 ),
inference(equality_resolution,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( X2 = X4
| X0 = X4
| ~ in(X4,X1)
| unordered_pair(X2,X0) != X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( unordered_pair(X2,X0) = X1
| ( ( ( sK1(X0,X1,X2) != X2
& sK1(X0,X1,X2) != X0 )
| ~ in(sK1(X0,X1,X2),X1) )
& ( sK1(X0,X1,X2) = X2
| sK1(X0,X1,X2) = X0
| in(sK1(X0,X1,X2),X1) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| ( X2 != X4
& X0 != X4 ) )
& ( X2 = X4
| X0 = X4
| ~ in(X4,X1) ) )
| unordered_pair(X2,X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) )
=> ( ( ( sK1(X0,X1,X2) != X2
& sK1(X0,X1,X2) != X0 )
| ~ in(sK1(X0,X1,X2),X1) )
& ( sK1(X0,X1,X2) = X2
| sK1(X0,X1,X2) = X0
| in(sK1(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( unordered_pair(X2,X0) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| ( X2 != X4
& X0 != X4 ) )
& ( X2 = X4
| X0 = X4
| ~ in(X4,X1) ) )
| unordered_pair(X2,X0) != X1 ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( unordered_pair(X2,X0) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( X2 = X3
| X0 = X3
| ~ in(X3,X1) ) )
| unordered_pair(X2,X0) != X1 ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( unordered_pair(X2,X0) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( X2 = X3
| X0 = X3
| ~ in(X3,X1) ) )
| unordered_pair(X2,X0) != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2] :
( unordered_pair(X2,X0) = X1
<=> ! [X3] :
( in(X3,X1)
<=> ( X2 = X3
| X0 = X3 ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X0] :
( ! [X3] :
( ( X0 = X3
| X1 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f160,plain,
in(sK3,unordered_pair(sK2,sK4)),
inference(resolution,[],[f133,f82]) ).
fof(f82,plain,
! [X3] : in(X3,singleton(X3)),
inference(literal_reordering,[],[f59]) ).
fof(f59,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X3,X0] :
( in(X3,X0)
| singleton(X3) != X0 ),
inference(equality_resolution,[],[f39]) ).
fof(f39,plain,
! [X3,X0,X1] :
( in(X3,X0)
| X1 != X3
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ( ( ~ in(sK0(X0,X1),X0)
| sK0(X0,X1) != X1 )
& ( in(sK0(X0,X1),X0)
| sK0(X0,X1) = X1 ) ) )
& ( ! [X3] :
( ( X1 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| X1 != X3 ) )
| singleton(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) )
=> ( ( ~ in(sK0(X0,X1),X0)
| sK0(X0,X1) != X1 )
& ( in(sK0(X0,X1),X0)
| sK0(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) ) )
& ( ! [X3] :
( ( X1 = X3
| ~ in(X3,X0) )
& ( in(X3,X0)
| X1 != X3 ) )
| singleton(X1) != X0 ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( singleton(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) ) )
& ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( singleton(X1) = X0
<=> ! [X2] :
( X1 = X2
<=> in(X2,X0) ) ),
inference(rectify,[],[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(f133,plain,
! [X2] :
( ~ in(X2,singleton(sK3))
| in(X2,unordered_pair(sK2,sK4)) ),
inference(resolution,[],[f80,f81]) ).
fof(f81,plain,
subset(singleton(sK3),unordered_pair(sK2,sK4)),
inference(literal_reordering,[],[f50]) ).
fof(f50,plain,
subset(singleton(sK3),unordered_pair(sK2,sK4)),
inference(cnf_transformation,[],[f32]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| ~ in(X2,X1)
| in(X2,X0) ),
inference(literal_reordering,[],[f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X0] :
( subset(X1,X0)
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET884+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 30 14:29:03 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.22/0.53 % (11443)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.22/0.54 TRYING [1]
% 0.22/0.54 % (11449)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.54 % (11450)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.54 % (11460)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.22/0.54 % (11457)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 (2999ds/68Mi)
% 0.22/0.54 % (11452)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.54 % (11455)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.22/0.54 TRYING [1]
% 0.22/0.54 % (11458)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.22/0.54 % (11467)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.22/0.54 % (11457)First to succeed.
% 0.22/0.54 % (11444)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.22/0.54 % (11469)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 (2999ds/68Mi)
% 0.22/0.55 TRYING [2]
% 0.22/0.55 TRYING [1]
% 0.22/0.55 TRYING [2]
% 0.22/0.55 TRYING [3]
% 0.22/0.55 TRYING [3]
% 0.22/0.55 % (11458)Also succeeded, but the first one will report.
% 0.22/0.55 % (11463)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.22/0.55 % (11457)Refutation found. Thanks to Tanya!
% 0.22/0.55 % SZS status Theorem for theBenchmark
% 0.22/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.55 % (11457)------------------------------
% 0.22/0.55 % (11457)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.55 % (11457)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.55 % (11457)Termination reason: Refutation
% 0.22/0.55
% 0.22/0.55 % (11457)Memory used [KB]: 5756
% 0.22/0.55 % (11457)Time elapsed: 0.006 s
% 0.22/0.55 % (11457)Instructions burned: 6 (million)
% 0.22/0.55 % (11457)------------------------------
% 0.22/0.55 % (11457)------------------------------
% 0.22/0.55 % (11442)Success in time 0.183 s
%------------------------------------------------------------------------------