TSTP Solution File: SET755+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 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 : n002.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 18:22:08 EDT 2022
% Result : Theorem 1.35s 0.53s
% Output : Refutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 4 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 154 ( 51 ~; 41 |; 51 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 124 ( 96 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f219,plain,
$false,
inference(subsumption_resolution,[],[f209,f60]) ).
fof(f60,plain,
subset(sK3,sK1),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
( subset(sK1,sK4)
& subset(sK3,sK1)
& ~ subset(inverse_image2(sK2,sK3),inverse_image2(sK2,sK1))
& maps(sK2,sK5,sK4)
& subset(sK3,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5])],[f43,f44]) ).
fof(f44,plain,
( ? [X0,X1,X2,X3,X4] :
( subset(X0,X3)
& subset(X2,X0)
& ~ subset(inverse_image2(X1,X2),inverse_image2(X1,X0))
& maps(X1,X4,X3)
& subset(X2,X3) )
=> ( subset(sK1,sK4)
& subset(sK3,sK1)
& ~ subset(inverse_image2(sK2,sK3),inverse_image2(sK2,sK1))
& maps(sK2,sK5,sK4)
& subset(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
? [X0,X1,X2,X3,X4] :
( subset(X0,X3)
& subset(X2,X0)
& ~ subset(inverse_image2(X1,X2),inverse_image2(X1,X0))
& maps(X1,X4,X3)
& subset(X2,X3) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
? [X2,X0,X4,X3,X1] :
( subset(X2,X3)
& subset(X4,X2)
& ~ subset(inverse_image2(X0,X4),inverse_image2(X0,X2))
& maps(X0,X1,X3)
& subset(X4,X3) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
? [X3,X2,X1,X4,X0] :
( ~ subset(inverse_image2(X0,X4),inverse_image2(X0,X2))
& maps(X0,X1,X3)
& subset(X4,X3)
& subset(X4,X2)
& subset(X2,X3) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X3,X2,X1,X4,X0] :
( ( maps(X0,X1,X3)
& subset(X4,X3)
& subset(X4,X2)
& subset(X2,X3) )
=> subset(inverse_image2(X0,X4),inverse_image2(X0,X2)) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X4,X1,X2] :
( ( subset(X2,X4)
& subset(X2,X1)
& subset(X4,X1)
& maps(X5,X0,X1) )
=> subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X5,X0,X4,X1,X2] :
( ( subset(X2,X4)
& subset(X2,X1)
& subset(X4,X1)
& maps(X5,X0,X1) )
=> subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa05) ).
fof(f209,plain,
~ subset(sK3,sK1),
inference(resolution,[],[f204,f59]) ).
fof(f59,plain,
~ subset(inverse_image2(sK2,sK3),inverse_image2(sK2,sK1)),
inference(cnf_transformation,[],[f45]) ).
fof(f204,plain,
! [X6,X7,X5] :
( subset(inverse_image2(X7,X5),inverse_image2(X7,X6))
| ~ subset(X5,X6) ),
inference(duplicate_literal_removal,[],[f197]) ).
fof(f197,plain,
! [X6,X7,X5] :
( ~ subset(X5,X6)
| subset(inverse_image2(X7,X5),inverse_image2(X7,X6))
| subset(inverse_image2(X7,X5),inverse_image2(X7,X6)) ),
inference(resolution,[],[f191,f66]) ).
fof(f66,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f51,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X0)
& ~ member(X3,X1) )
=> ( member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( member(X3,X0)
& ~ member(X3,X1) ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f191,plain,
! [X21,X24,X22,X23] :
( ~ member(sK7(X21,inverse_image2(X22,X23)),inverse_image2(X22,X24))
| ~ subset(X24,X23)
| subset(X21,inverse_image2(X22,X23)) ),
inference(duplicate_literal_removal,[],[f189]) ).
fof(f189,plain,
! [X21,X24,X22,X23] :
( ~ member(sK7(X21,inverse_image2(X22,X23)),inverse_image2(X22,X24))
| ~ subset(X24,X23)
| ~ member(sK7(X21,inverse_image2(X22,X23)),inverse_image2(X22,X24))
| subset(X21,inverse_image2(X22,X23)) ),
inference(resolution,[],[f91,f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( member(sK6(X2,X0,X1),X3)
| ~ member(X0,inverse_image2(X1,X2))
| ~ subset(X2,X3) ),
inference(resolution,[],[f63,f67]) ).
fof(f67,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X0)
| ~ member(X1,inverse_image2(X2,X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( member(X1,inverse_image2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ apply(X2,X1,X3) ) )
& ( ( member(sK6(X0,X1,X2),X0)
& apply(X2,X1,sK6(X0,X1,X2)) )
| ~ member(X1,inverse_image2(X2,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f47,f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& apply(X2,X1,X4) )
=> ( member(sK6(X0,X1,X2),X0)
& apply(X2,X1,sK6(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( member(X1,inverse_image2(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ apply(X2,X1,X3) ) )
& ( ? [X4] :
( member(X4,X0)
& apply(X2,X1,X4) )
| ~ member(X1,inverse_image2(X2,X0)) ) ),
inference(rectify,[],[f46]) ).
fof(f46,plain,
! [X1,X0,X2] :
( ( member(X0,inverse_image2(X2,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X2,X0,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X2,X0,X3) )
| ~ member(X0,inverse_image2(X2,X1)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( member(X0,inverse_image2(X2,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X2,X0,X3) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X2,X1,X5] :
( ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) )
<=> member(X2,inverse_image2(X5,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
fof(f91,plain,
! [X2,X3,X0,X1] :
( ~ member(sK6(X0,sK7(X1,inverse_image2(X2,X3)),X2),X3)
| ~ member(sK7(X1,inverse_image2(X2,X3)),inverse_image2(X2,X0))
| subset(X1,inverse_image2(X2,X3)) ),
inference(resolution,[],[f75,f62]) ).
fof(f62,plain,
! [X2,X0,X1] :
( apply(X2,X1,sK6(X0,X1,X2))
| ~ member(X1,inverse_image2(X2,X0)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f75,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,sK7(X1,inverse_image2(X0,X2)),X3)
| ~ member(X3,X2)
| subset(X1,inverse_image2(X0,X2)) ),
inference(resolution,[],[f64,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f64,plain,
! [X2,X3,X0,X1] :
( member(X1,inverse_image2(X2,X0))
| ~ apply(X2,X1,X3)
| ~ member(X3,X0) ),
inference(cnf_transformation,[],[f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET755+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 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 : n002.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 14:30:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50 % (5487)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 % (5479)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)
% 0.20/0.51 % (5479)Instruction limit reached!
% 0.20/0.51 % (5479)------------------------------
% 0.20/0.51 % (5479)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (5479)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (5479)Termination reason: Unknown
% 0.20/0.51 % (5479)Termination phase: Property scanning
% 0.20/0.51
% 0.20/0.51 % (5479)Memory used [KB]: 1535
% 0.20/0.51 % (5479)Time elapsed: 0.005 s
% 0.20/0.51 % (5479)Instructions burned: 3 (million)
% 0.20/0.51 % (5479)------------------------------
% 0.20/0.51 % (5479)------------------------------
% 0.20/0.51 % (5471)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)
% 0.20/0.51 % (5472)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)
% 0.20/0.52 % (5468)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)
% 0.20/0.52 % (5471)First to succeed.
% 1.35/0.53 % (5467)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)
% 1.35/0.53 % (5467)Instruction limit reached!
% 1.35/0.53 % (5467)------------------------------
% 1.35/0.53 % (5467)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (5467)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (5467)Termination reason: Unknown
% 1.35/0.53 % (5467)Termination phase: Saturation
% 1.35/0.53
% 1.35/0.53 % (5467)Memory used [KB]: 1535
% 1.35/0.53 % (5467)Time elapsed: 0.003 s
% 1.35/0.53 % (5467)Instructions burned: 4 (million)
% 1.35/0.53 % (5467)------------------------------
% 1.35/0.53 % (5467)------------------------------
% 1.35/0.53 % (5469)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)
% 1.35/0.53 % (5470)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)
% 1.35/0.53 % (5471)Refutation found. Thanks to Tanya!
% 1.35/0.53 % SZS status Theorem for theBenchmark
% 1.35/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 1.35/0.53 % (5471)------------------------------
% 1.35/0.53 % (5471)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53 % (5471)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53 % (5471)Termination reason: Refutation
% 1.35/0.53
% 1.35/0.53 % (5471)Memory used [KB]: 6012
% 1.35/0.53 % (5471)Time elapsed: 0.077 s
% 1.35/0.53 % (5471)Instructions burned: 17 (million)
% 1.35/0.53 % (5471)------------------------------
% 1.35/0.53 % (5471)------------------------------
% 1.35/0.53 % (5464)Success in time 0.178 s
%------------------------------------------------------------------------------