TSTP Solution File: SET799+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET799+4 : 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 : n015.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 18:22:18 EDT 2022
% Result : Theorem 0.20s 0.54s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 189 ( 46 ~; 31 |; 82 &)
% ( 7 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 146 ( 107 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f99,plain,
$false,
inference(unit_resulting_resolution,[],[f55,f91,f78]) ).
fof(f78,plain,
! [X0] :
( ~ member(X0,sK2)
| apply(sK0,X0,sK4) ),
inference(resolution,[],[f72,f62]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( ~ upper_bound(X1,X0,X2)
| apply(X0,X4,X1)
| ~ member(X4,X2) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( upper_bound(X1,X0,X2)
| ( member(sK6(X0,X1,X2),X2)
& ~ apply(X0,sK6(X0,X1,X2),X1) ) )
& ( ! [X4] :
( ~ member(X4,X2)
| apply(X0,X4,X1) )
| ~ upper_bound(X1,X0,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f47,f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X2)
& ~ apply(X0,X3,X1) )
=> ( member(sK6(X0,X1,X2),X2)
& ~ apply(X0,sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( upper_bound(X1,X0,X2)
| ? [X3] :
( member(X3,X2)
& ~ apply(X0,X3,X1) ) )
& ( ! [X4] :
( ~ member(X4,X2)
| apply(X0,X4,X1) )
| ~ upper_bound(X1,X0,X2) ) ),
inference(rectify,[],[f46]) ).
fof(f46,plain,
! [X0,X2,X1] :
( ( upper_bound(X2,X0,X1)
| ? [X3] :
( member(X3,X1)
& ~ apply(X0,X3,X2) ) )
& ( ! [X3] :
( ~ member(X3,X1)
| apply(X0,X3,X2) )
| ~ upper_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X2,X1] :
( upper_bound(X2,X0,X1)
<=> ! [X3] :
( ~ member(X3,X1)
| apply(X0,X3,X2) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X0,X2] :
( ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) )
<=> upper_bound(X2,X0,X1) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X5,X3,X7] :
( ! [X2] :
( member(X2,X3)
=> apply(X5,X2,X7) )
<=> upper_bound(X7,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_bound) ).
fof(f72,plain,
upper_bound(sK4,sK0,sK2),
inference(resolution,[],[f54,f59]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X2,X3,X1,X0)
| upper_bound(X2,X1,X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ least_upper_bound(X2,X3,X1,X0)
| ( member(X2,X3)
& ! [X4] :
( ~ upper_bound(X4,X1,X3)
| ~ member(X4,X0)
| apply(X1,X2,X4) )
& upper_bound(X2,X1,X3) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X3,X2,X0,X1] :
( ~ least_upper_bound(X0,X1,X2,X3)
| ( member(X0,X1)
& ! [X4] :
( ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X0,X4) )
& upper_bound(X0,X2,X1) ) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X3,X0,X2,X1] :
( ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( apply(X2,X0,X4)
| ~ upper_bound(X4,X2,X1)
| ~ member(X4,X3) ) )
| ~ least_upper_bound(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X3,X0,X2,X1] :
( least_upper_bound(X0,X1,X2,X3)
=> ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( ( upper_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X0,X4) ) ) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f25,plain,
! [X3,X0,X2,X1] :
( least_upper_bound(X0,X1,X2,X3)
<=> ( member(X0,X1)
& upper_bound(X0,X2,X1)
& ! [X4] :
( ( upper_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X0,X4) ) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X0,X2,X5,X3] :
( least_upper_bound(X0,X2,X5,X3)
<=> ( ! [X7] :
( ( upper_bound(X7,X5,X2)
& member(X7,X3) )
=> apply(X5,X0,X7) )
& member(X0,X2)
& upper_bound(X0,X5,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',least_upper_bound) ).
fof(f54,plain,
least_upper_bound(sK4,sK2,sK0,sK1),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
( subset(sK3,sK2)
& subset(sK3,sK1)
& least_upper_bound(sK5,sK3,sK0,sK1)
& ~ apply(sK0,sK5,sK4)
& least_upper_bound(sK4,sK2,sK0,sK1)
& subset(sK2,sK1)
& order(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f40,f43,f42,f41]) ).
fof(f41,plain,
( ? [X0,X1] :
( ? [X2,X3] :
( subset(X3,X2)
& subset(X3,X1)
& ? [X4,X5] :
( least_upper_bound(X5,X3,X0,X1)
& ~ apply(X0,X5,X4)
& least_upper_bound(X4,X2,X0,X1) )
& subset(X2,X1) )
& order(X0,X1) )
=> ( ? [X3,X2] :
( subset(X3,X2)
& subset(X3,sK1)
& ? [X5,X4] :
( least_upper_bound(X5,X3,sK0,sK1)
& ~ apply(sK0,X5,X4)
& least_upper_bound(X4,X2,sK0,sK1) )
& subset(X2,sK1) )
& order(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
( ? [X3,X2] :
( subset(X3,X2)
& subset(X3,sK1)
& ? [X5,X4] :
( least_upper_bound(X5,X3,sK0,sK1)
& ~ apply(sK0,X5,X4)
& least_upper_bound(X4,X2,sK0,sK1) )
& subset(X2,sK1) )
=> ( subset(sK3,sK2)
& subset(sK3,sK1)
& ? [X5,X4] :
( least_upper_bound(X5,sK3,sK0,sK1)
& ~ apply(sK0,X5,X4)
& least_upper_bound(X4,sK2,sK0,sK1) )
& subset(sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
( ? [X5,X4] :
( least_upper_bound(X5,sK3,sK0,sK1)
& ~ apply(sK0,X5,X4)
& least_upper_bound(X4,sK2,sK0,sK1) )
=> ( least_upper_bound(sK5,sK3,sK0,sK1)
& ~ apply(sK0,sK5,sK4)
& least_upper_bound(sK4,sK2,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0,X1] :
( ? [X2,X3] :
( subset(X3,X2)
& subset(X3,X1)
& ? [X4,X5] :
( least_upper_bound(X5,X3,X0,X1)
& ~ apply(X0,X5,X4)
& least_upper_bound(X4,X2,X0,X1) )
& subset(X2,X1) )
& order(X0,X1) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
? [X1,X0] :
( ? [X3,X2] :
( subset(X2,X3)
& subset(X2,X0)
& ? [X5,X4] :
( least_upper_bound(X4,X2,X1,X0)
& ~ apply(X1,X4,X5)
& least_upper_bound(X5,X3,X1,X0) )
& subset(X3,X0) )
& order(X1,X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
? [X1,X0] :
( ? [X3,X2] :
( ? [X4,X5] :
( ~ apply(X1,X4,X5)
& least_upper_bound(X5,X3,X1,X0)
& least_upper_bound(X4,X2,X1,X0) )
& subset(X2,X3)
& subset(X3,X0)
& subset(X2,X0) )
& order(X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
~ ! [X1,X0] :
( order(X1,X0)
=> ! [X3,X2] :
( ( subset(X2,X3)
& subset(X3,X0)
& subset(X2,X0) )
=> ! [X4,X5] :
( ( least_upper_bound(X5,X3,X1,X0)
& least_upper_bound(X4,X2,X1,X0) )
=> apply(X1,X4,X5) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,negated_conjecture,
~ ! [X3,X5] :
( order(X5,X3)
=> ! [X8,X9] :
( ( subset(X8,X9)
& subset(X8,X3)
& subset(X9,X3) )
=> ! [X10,X11] :
( ( least_upper_bound(X10,X8,X5,X3)
& least_upper_bound(X11,X9,X5,X3) )
=> apply(X5,X10,X11) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
! [X3,X5] :
( order(X5,X3)
=> ! [X8,X9] :
( ( subset(X8,X9)
& subset(X8,X3)
& subset(X9,X3) )
=> ! [X10,X11] :
( ( least_upper_bound(X10,X8,X5,X3)
& least_upper_bound(X11,X9,X5,X3) )
=> apply(X5,X10,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV11) ).
fof(f91,plain,
member(sK5,sK2),
inference(resolution,[],[f77,f58]) ).
fof(f58,plain,
subset(sK3,sK2),
inference(cnf_transformation,[],[f44]) ).
fof(f77,plain,
! [X0] :
( ~ subset(sK3,X0)
| member(sK5,X0) ),
inference(resolution,[],[f74,f68]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subset(X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X1,X0)
=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X1,X0)
<=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f74,plain,
member(sK5,sK3),
inference(resolution,[],[f56,f61]) ).
fof(f61,plain,
! [X2,X3,X0,X1] :
( ~ least_upper_bound(X2,X3,X1,X0)
| member(X2,X3) ),
inference(cnf_transformation,[],[f45]) ).
fof(f56,plain,
least_upper_bound(sK5,sK3,sK0,sK1),
inference(cnf_transformation,[],[f44]) ).
fof(f55,plain,
~ apply(sK0,sK5,sK4),
inference(cnf_transformation,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET799+4 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:32:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.52 % (26464)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)
% 0.20/0.52 % (26460)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.52 % (26482)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.53 % (26478)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.53 % (26465)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.53 % (26487)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.53 % (26481)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)
% 0.20/0.53 % (26482)First to succeed.
% 0.20/0.53 % (26479)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.20/0.53 % (26475)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (26460)Instruction limit reached!
% 0.20/0.53 % (26460)------------------------------
% 0.20/0.53 % (26460)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (26460)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (26460)Termination reason: Unknown
% 0.20/0.53 % (26460)Termination phase: Saturation
% 0.20/0.53
% 0.20/0.53 % (26460)Memory used [KB]: 6012
% 0.20/0.53 % (26460)Time elapsed: 0.129 s
% 0.20/0.53 % (26460)Instructions burned: 4 (million)
% 0.20/0.53 % (26460)------------------------------
% 0.20/0.53 % (26460)------------------------------
% 0.20/0.54 % (26462)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.54 % (26463)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.54 % (26479)Also succeeded, but the first one will report.
% 0.20/0.54 % (26459)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.54 % (26482)Refutation found. Thanks to Tanya!
% 0.20/0.54 % SZS status Theorem for theBenchmark
% 0.20/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54 % (26482)------------------------------
% 0.20/0.54 % (26482)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (26482)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (26482)Termination reason: Refutation
% 0.20/0.54
% 0.20/0.54 % (26482)Memory used [KB]: 1535
% 0.20/0.54 % (26482)Time elapsed: 0.075 s
% 0.20/0.54 % (26482)Instructions burned: 5 (million)
% 0.20/0.54 % (26482)------------------------------
% 0.20/0.54 % (26482)------------------------------
% 0.20/0.54 % (26452)Success in time 0.181 s
%------------------------------------------------------------------------------