TSTP Solution File: SET766+4 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 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 : n001.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 18:22:10 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 158 ( 49 ~; 40 |; 45 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 80 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,plain,
$false,
inference(subsumption_resolution,[],[f44,f34]) ).
fof(f34,plain,
~ member(sK2,equivalence_class(sK2,sK0,sK1)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
( member(sK2,sK0)
& ~ member(sK2,equivalence_class(sK2,sK0,sK1))
& equivalence(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f28]) ).
fof(f28,plain,
( ? [X0,X1,X2] :
( member(X2,X0)
& ~ member(X2,equivalence_class(X2,X0,X1))
& equivalence(X1,X0) )
=> ( member(sK2,sK0)
& ~ member(sK2,equivalence_class(sK2,sK0,sK1))
& equivalence(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1,X2] :
( member(X2,X0)
& ~ member(X2,equivalence_class(X2,X0,X1))
& equivalence(X1,X0) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
? [X1,X2,X0] :
( member(X0,X1)
& ~ member(X0,equivalence_class(X0,X1,X2))
& equivalence(X2,X1) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
? [X1,X2,X0] :
( ~ member(X0,equivalence_class(X0,X1,X2))
& member(X0,X1)
& equivalence(X2,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X1,X2,X0] :
( ( member(X0,X1)
& equivalence(X2,X1) )
=> member(X0,equivalence_class(X0,X1,X2)) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X0,X3,X6] :
( ( member(X0,X3)
& equivalence(X6,X3) )
=> member(X0,equivalence_class(X0,X3,X6)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X0,X3,X6] :
( ( member(X0,X3)
& equivalence(X6,X3) )
=> member(X0,equivalence_class(X0,X3,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII02) ).
fof(f44,plain,
member(sK2,equivalence_class(sK2,sK0,sK1)),
inference(unit_resulting_resolution,[],[f35,f42,f38]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( member(X1,equivalence_class(X0,X3,X2))
| ~ member(X1,X3)
| ~ apply(X2,X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ( member(X1,equivalence_class(X0,X3,X2))
| ~ apply(X2,X0,X1)
| ~ member(X1,X3) )
& ( ( apply(X2,X0,X1)
& member(X1,X3) )
| ~ member(X1,equivalence_class(X0,X3,X2)) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ( member(X1,equivalence_class(X0,X3,X2))
| ~ apply(X2,X0,X1)
| ~ member(X1,X3) )
& ( ( apply(X2,X0,X1)
& member(X1,X3) )
| ~ member(X1,equivalence_class(X0,X3,X2)) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( member(X1,equivalence_class(X0,X3,X2))
<=> ( apply(X2,X0,X1)
& member(X1,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X2,X6,X3] :
( ( member(X2,X3)
& apply(X6,X0,X2) )
<=> member(X2,equivalence_class(X0,X3,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).
fof(f42,plain,
apply(sK1,sK2,sK2),
inference(unit_resulting_resolution,[],[f33,f35,f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ equivalence(X0,X1)
| ~ member(X2,X1)
| apply(X0,X2,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4,X5] :
( ~ apply(X0,X3,X4)
| ~ member(X3,X1)
| apply(X0,X3,X5)
| ~ member(X4,X1)
| ~ apply(X0,X4,X5)
| ~ member(X5,X1) )
& ! [X6,X7] :
( ~ member(X7,X1)
| ~ apply(X0,X7,X6)
| ~ member(X6,X1)
| apply(X0,X6,X7) ) )
| ~ equivalence(X0,X1) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( ! [X5] :
( apply(X1,X5,X5)
| ~ member(X5,X0) )
& ! [X3,X4,X2] :
( ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| apply(X1,X3,X2)
| ~ member(X4,X0)
| ~ apply(X1,X4,X2)
| ~ member(X2,X0) )
& ! [X7,X6] :
( ~ member(X6,X0)
| ~ apply(X1,X6,X7)
| ~ member(X7,X0)
| apply(X1,X7,X6) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( ( ! [X7,X6] :
( apply(X1,X7,X6)
| ~ apply(X1,X6,X7)
| ~ member(X7,X0)
| ~ member(X6,X0) )
& ! [X2,X4,X3] :
( apply(X1,X3,X2)
| ~ apply(X1,X4,X2)
| ~ apply(X1,X3,X4)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X5] :
( apply(X1,X5,X5)
| ~ member(X5,X0) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( equivalence(X1,X0)
=> ( ! [X7,X6] :
( ( member(X7,X0)
& member(X6,X0) )
=> ( apply(X1,X6,X7)
=> apply(X1,X7,X6) ) )
& ! [X2,X4,X3] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X4,X2)
& apply(X1,X3,X4) )
=> apply(X1,X3,X2) ) )
& ! [X5] :
( member(X5,X0)
=> apply(X1,X5,X5) ) ) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( equivalence(X1,X0)
<=> ( ! [X7,X6] :
( ( member(X7,X0)
& member(X6,X0) )
=> ( apply(X1,X6,X7)
=> apply(X1,X7,X6) ) )
& ! [X2,X4,X3] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X4,X2)
& apply(X1,X3,X4) )
=> apply(X1,X3,X2) ) )
& ! [X5] :
( member(X5,X0)
=> apply(X1,X5,X5) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X6] :
( ( ! [X5,X2,X4] :
( ( member(X2,X0)
& member(X4,X0)
& member(X5,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) )
& ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) ) )
<=> equivalence(X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence) ).
fof(f33,plain,
equivalence(sK1,sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f35,plain,
member(sK2,sK0),
inference(cnf_transformation,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET766+4 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.13/0.33 % Computer : n001.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 30 14:40:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.47 % (18208)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.19/0.47 % (18184)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)
% 0.19/0.48 % (18184)First to succeed.
% 0.19/0.48 % (18184)Refutation found. Thanks to Tanya!
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (18184)------------------------------
% 0.19/0.48 % (18184)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (18184)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (18184)Termination reason: Refutation
% 0.19/0.48
% 0.19/0.48 % (18184)Memory used [KB]: 6012
% 0.19/0.48 % (18184)Time elapsed: 0.100 s
% 0.19/0.48 % (18184)Instructions burned: 2 (million)
% 0.19/0.48 % (18184)------------------------------
% 0.19/0.48 % (18184)------------------------------
% 0.19/0.48 % (18180)Success in time 0.138 s
%------------------------------------------------------------------------------