TSTP Solution File: SET754+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET754+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 : n025.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 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 10 unt; 0 def)
% Number of atoms : 214 ( 7 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 241 ( 78 ~; 66 |; 68 &)
% ( 9 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 181 ( 145 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,plain,
$false,
inference(subsumption_resolution,[],[f89,f87]) ).
fof(f87,plain,
~ member(sK7(sK1,sK2,sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3)),image2(sK2,sK3)),
inference(unit_resulting_resolution,[],[f76,f85,f71]) ).
fof(f71,plain,
! [X2,X3,X0,X1] :
( ~ apply(X1,X2,X3)
| ~ member(X3,X0)
| member(X2,inverse_image2(X1,X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X1,X0))
| ! [X3] :
( ~ apply(X1,X2,X3)
| ~ member(X3,X0) ) )
& ( ( apply(X1,X2,sK6(X0,X1,X2))
& member(sK6(X0,X1,X2),X0) )
| ~ member(X2,inverse_image2(X1,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f54,f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X1,X2,X4)
& member(X4,X0) )
=> ( apply(X1,X2,sK6(X0,X1,X2))
& member(sK6(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X1,X0))
| ! [X3] :
( ~ apply(X1,X2,X3)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( apply(X1,X2,X4)
& member(X4,X0) )
| ~ member(X2,inverse_image2(X1,X0)) ) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
! [X1,X0,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X5,X1,X2] :
( member(X2,inverse_image2(X5,X1))
<=> ? [X4] :
( member(X4,X1)
& apply(X5,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).
fof(f85,plain,
apply(sK2,sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3),sK7(sK1,sK2,sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3))),
inference(unit_resulting_resolution,[],[f77,f63,f73]) ).
fof(f73,plain,
! [X2,X0,X1,X6] :
( ~ maps(X2,X1,X0)
| apply(X2,X6,sK7(X0,X2,X6))
| ~ member(X6,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( ~ member(X5,X0)
| ~ member(X3,X0)
| X3 = X5
| ~ member(X4,X1)
| ~ apply(X2,X4,X3)
| ~ apply(X2,X4,X5) )
& ! [X6] :
( ~ member(X6,X1)
| ( apply(X2,X6,sK7(X0,X2,X6))
& member(sK7(X0,X2,X6),X0) ) ) )
| ~ maps(X2,X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f57,f58]) ).
fof(f58,plain,
! [X0,X2,X6] :
( ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) )
=> ( apply(X2,X6,sK7(X0,X2,X6))
& member(sK7(X0,X2,X6),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( ~ member(X5,X0)
| ~ member(X3,X0)
| X3 = X5
| ~ member(X4,X1)
| ~ apply(X2,X4,X3)
| ~ apply(X2,X4,X5) )
& ! [X6] :
( ~ member(X6,X1)
| ? [X7] :
( apply(X2,X6,X7)
& member(X7,X0) ) ) )
| ~ maps(X2,X1,X0) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ( ! [X7,X5,X6] :
( ~ member(X6,X2)
| ~ member(X7,X2)
| X6 = X7
| ~ member(X5,X0)
| ~ apply(X1,X5,X7)
| ~ apply(X1,X5,X6) )
& ! [X3] :
( ~ member(X3,X0)
| ? [X4] :
( apply(X1,X3,X4)
& member(X4,X2) ) ) )
| ~ maps(X1,X0,X2) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ~ member(X3,X0)
| ? [X4] :
( apply(X1,X3,X4)
& member(X4,X2) ) )
& ! [X5,X6,X7] :
( X6 = X7
| ~ apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ member(X7,X2)
| ~ member(X5,X0)
| ~ member(X6,X2) ) )
| ~ maps(X1,X0,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X1,X0,X2] :
( maps(X1,X0,X2)
=> ( ! [X3] :
( member(X3,X0)
=> ? [X4] :
( apply(X1,X3,X4)
& member(X4,X2) ) )
& ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X5,X0)
& member(X6,X2) )
=> ( ( apply(X1,X5,X7)
& apply(X1,X5,X6) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f34,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( member(X3,X0)
=> ? [X4] :
( apply(X1,X3,X4)
& member(X4,X2) ) )
& ! [X5,X6,X7] :
( ( member(X7,X2)
& member(X5,X0)
& member(X6,X2) )
=> ( ( apply(X1,X5,X7)
& apply(X1,X5,X6) )
=> X6 = X7 ) ) )
<=> maps(X1,X0,X2) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X5,X1] :
( ( ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) )
& ! [X2,X7,X6] :
( ( member(X7,X1)
& member(X2,X0)
& member(X6,X1) )
=> ( ( apply(X5,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) ) )
<=> maps(X5,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps) ).
fof(f63,plain,
maps(sK2,sK4,sK1),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( ~ subset(sK3,inverse_image2(sK2,image2(sK2,sK3)))
& subset(sK3,sK4)
& maps(sK2,sK4,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f46,f47]) ).
fof(f47,plain,
( ? [X0,X1,X2,X3] :
( ~ subset(X2,inverse_image2(X1,image2(X1,X2)))
& subset(X2,X3)
& maps(X1,X3,X0) )
=> ( ~ subset(sK3,inverse_image2(sK2,image2(sK2,sK3)))
& subset(sK3,sK4)
& maps(sK2,sK4,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0,X1,X2,X3] :
( ~ subset(X2,inverse_image2(X1,image2(X1,X2)))
& subset(X2,X3)
& maps(X1,X3,X0) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
? [X1,X3,X2,X0] :
( ~ subset(X2,inverse_image2(X3,image2(X3,X2)))
& subset(X2,X0)
& maps(X3,X0,X1) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
? [X3,X0,X2,X1] :
( ~ subset(X2,inverse_image2(X3,image2(X3,X2)))
& maps(X3,X0,X1)
& subset(X2,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
~ ! [X3,X0,X2,X1] :
( ( maps(X3,X0,X1)
& subset(X2,X0) )
=> subset(X2,inverse_image2(X3,image2(X3,X2))) ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X10,X5] :
( ( maps(X5,X0,X1)
& subset(X10,X0) )
=> subset(X10,inverse_image2(X5,image2(X5,X10))) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X1,X10,X5] :
( ( maps(X5,X0,X1)
& subset(X10,X0) )
=> subset(X10,inverse_image2(X5,image2(X5,X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa04) ).
fof(f77,plain,
member(sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3),sK4),
inference(unit_resulting_resolution,[],[f64,f75,f60]) ).
fof(f60,plain,
! [X3,X0,X1] :
( ~ member(X3,X1)
| member(X3,X0)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ( ~ member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1) )
| ~ subset(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f43,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) )
=> ( ~ member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1) )
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X1,X0)
<=> ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X1,X0] :
( 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(f75,plain,
member(sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3),sK3),
inference(unit_resulting_resolution,[],[f65,f61]) ).
fof(f61,plain,
! [X0,X1] :
( member(sK0(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f65,plain,
~ subset(sK3,inverse_image2(sK2,image2(sK2,sK3))),
inference(cnf_transformation,[],[f48]) ).
fof(f64,plain,
subset(sK3,sK4),
inference(cnf_transformation,[],[f48]) ).
fof(f76,plain,
~ member(sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3),inverse_image2(sK2,image2(sK2,sK3))),
inference(unit_resulting_resolution,[],[f65,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
member(sK7(sK1,sK2,sK0(inverse_image2(sK2,image2(sK2,sK3)),sK3)),image2(sK2,sK3)),
inference(unit_resulting_resolution,[],[f75,f85,f68]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ apply(X1,X3,X2)
| member(X2,image2(X1,X0))
| ~ member(X3,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X1,X0))
| ! [X3] :
( ~ apply(X1,X3,X2)
| ~ member(X3,X0) ) )
& ( ( apply(X1,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X0) )
| ~ member(X2,image2(X1,X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f50,f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X1,X4,X2)
& member(X4,X0) )
=> ( apply(X1,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X1,X0))
| ! [X3] :
( ~ apply(X1,X3,X2)
| ~ member(X3,X0) ) )
& ( ? [X4] :
( apply(X1,X4,X2)
& member(X4,X0) )
| ~ member(X2,image2(X1,X0)) ) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X1,X0,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X1,X0,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET754+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n025.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 14:28:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (14949)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)
% 0.19/0.50 % (14972)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)
% 0.19/0.51 % (14960)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.51 % (14953)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)
% 0.19/0.51 % (14954)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)
% 0.19/0.51 % (14962)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (14955)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)
% 0.19/0.51 % (14962)First to succeed.
% 0.19/0.51 % (14971)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)
% 0.19/0.52 % (14962)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (14962)------------------------------
% 0.19/0.52 % (14962)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (14962)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (14962)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (14962)Memory used [KB]: 6012
% 0.19/0.52 % (14962)Time elapsed: 0.107 s
% 0.19/0.52 % (14962)Instructions burned: 3 (million)
% 0.19/0.52 % (14962)------------------------------
% 0.19/0.52 % (14962)------------------------------
% 0.19/0.52 % (14942)Success in time 0.165 s
%------------------------------------------------------------------------------