TSTP Solution File: SET791+4 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET791+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 : 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 18:22:16 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 202 ( 18 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 229 ( 70 ~; 59 |; 65 &)
% ( 6 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 140 ( 124 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f61,plain,
$false,
inference(subsumption_resolution,[],[f60,f57]) ).
fof(f57,plain,
apply(sK2,sK3(sK2,sK0,sK1),sK1),
inference(unit_resulting_resolution,[],[f40,f51,f39]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ greatest(X1,X2,X0)
| apply(X2,X3,X1)
| ~ member(X3,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( apply(X2,X3,X1)
| ~ member(X3,X0) )
& member(X1,X0) )
| ~ greatest(X1,X2,X0) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( apply(X2,X3,X0)
| ~ member(X3,X1) )
& member(X0,X1) )
| ~ greatest(X0,X2,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( greatest(X0,X2,X1)
=> ( member(X0,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X2,X3,X0) ) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] :
( greatest(X0,X2,X1)
<=> ( member(X0,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X2,X3,X0) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X5,X1,X0] :
( ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X5) )
& member(X5,X1) )
<=> greatest(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest) ).
fof(f51,plain,
member(sK3(sK2,sK0,sK1),sK0),
inference(unit_resulting_resolution,[],[f42,f46,f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(sK3(X0,X1,X2),X1)
| max(X2,X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( member(sK3(X0,X1,X2),X1)
& apply(X0,X2,sK3(X0,X1,X2))
& sK3(X0,X1,X2) != X2 )
| max(X2,X0,X1)
| ~ member(X2,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f32,f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3)
& X2 != X3 )
=> ( member(sK3(X0,X1,X2),X1)
& apply(X0,X2,sK3(X0,X1,X2))
& sK3(X0,X1,X2) != X2 ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ? [X3] :
( member(X3,X1)
& apply(X0,X2,X3)
& X2 != X3 )
| max(X2,X0,X1)
| ~ member(X2,X1) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ? [X3] :
( member(X3,X0)
& apply(X2,X1,X3)
& X1 != X3 )
| max(X1,X2,X0)
| ~ member(X1,X0) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X1,X2,X0] :
( max(X1,X2,X0)
| ? [X3] :
( X1 != X3
& member(X3,X0)
& apply(X2,X1,X3) )
| ~ member(X1,X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ( member(X3,X0)
& apply(X2,X1,X3) )
=> X1 = X3 )
& member(X1,X0) )
=> max(X1,X2,X0) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,plain,
! [X1,X2,X0] :
( max(X1,X2,X0)
<=> ( ! [X3] :
( ( member(X3,X0)
& apply(X2,X1,X3) )
=> X1 = X3 )
& member(X1,X0) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X5,X0] :
( max(X5,X0,X1)
<=> ( ! [X2] :
( ( apply(X0,X5,X2)
& member(X2,X1) )
=> X2 = X5 )
& member(X5,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max) ).
fof(f46,plain,
member(sK1,sK0),
inference(unit_resulting_resolution,[],[f40,f38]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ greatest(X1,X2,X0)
| member(X1,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
~ max(sK1,sK2,sK0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ~ max(sK1,sK2,sK0)
& order(sK2,sK0)
& greatest(sK1,sK2,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1,X2] :
( ~ max(X1,X2,X0)
& order(X2,X0)
& greatest(X1,X2,X0) )
=> ( ~ max(sK1,sK2,sK0)
& order(sK2,sK0)
& greatest(sK1,sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ~ max(X1,X2,X0)
& order(X2,X0)
& greatest(X1,X2,X0) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
? [X0,X2,X1] :
( ~ max(X2,X1,X0)
& order(X1,X0)
& greatest(X2,X1,X0) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
? [X1,X0,X2] :
( ~ max(X2,X1,X0)
& greatest(X2,X1,X0)
& order(X1,X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
~ ! [X1,X0,X2] :
( ( greatest(X2,X1,X0)
& order(X1,X0) )
=> max(X2,X1,X0) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X1,X0,X5] :
( ( order(X0,X1)
& greatest(X5,X0,X1) )
=> max(X5,X0,X1) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X1,X0,X5] :
( ( order(X0,X1)
& greatest(X5,X0,X1) )
=> max(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV3) ).
fof(f40,plain,
greatest(sK1,sK2,sK0),
inference(cnf_transformation,[],[f31]) ).
fof(f60,plain,
~ apply(sK2,sK3(sK2,sK0,sK1),sK1),
inference(unit_resulting_resolution,[],[f41,f46,f51,f49,f50,f35]) ).
fof(f35,plain,
! [X0,X1,X6,X7] :
( ~ apply(X0,X7,X6)
| ~ apply(X0,X6,X7)
| ~ member(X7,X1)
| X6 = X7
| ~ member(X6,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ~ order(X0,X1)
| ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4,X5] :
( ~ member(X3,X1)
| ~ apply(X0,X5,X3)
| ~ member(X5,X1)
| ~ apply(X0,X3,X4)
| ~ member(X4,X1)
| apply(X0,X5,X4) )
& ! [X6,X7] :
( ~ apply(X0,X6,X7)
| ~ apply(X0,X7,X6)
| ~ member(X6,X1)
| X6 = X7
| ~ member(X7,X1) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X1,X0] :
( ~ order(X1,X0)
| ( ! [X5] :
( apply(X1,X5,X5)
| ~ member(X5,X0) )
& ! [X4,X3,X2] :
( ~ member(X4,X0)
| ~ apply(X1,X2,X4)
| ~ member(X2,X0)
| ~ apply(X1,X4,X3)
| ~ member(X3,X0)
| apply(X1,X2,X3) )
& ! [X6,X7] :
( ~ apply(X1,X6,X7)
| ~ apply(X1,X7,X6)
| ~ member(X6,X0)
| X6 = X7
| ~ member(X7,X0) ) ) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X5] :
( apply(X1,X5,X5)
| ~ member(X5,X0) )
& ! [X3,X4,X2] :
( apply(X1,X2,X3)
| ~ apply(X1,X2,X4)
| ~ apply(X1,X4,X3)
| ~ member(X4,X0)
| ~ member(X3,X0)
| ~ member(X2,X0) )
& ! [X7,X6] :
( X6 = X7
| ~ apply(X1,X7,X6)
| ~ apply(X1,X6,X7)
| ~ member(X6,X0)
| ~ member(X7,X0) ) )
| ~ order(X1,X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( order(X1,X0)
=> ( ! [X5] :
( member(X5,X0)
=> apply(X1,X5,X5) )
& ! [X3,X4,X2] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X2,X4)
& apply(X1,X4,X3) )
=> apply(X1,X2,X3) ) )
& ! [X7,X6] :
( ( member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X7,X6)
& apply(X1,X6,X7) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( order(X1,X0)
<=> ( ! [X5] :
( member(X5,X0)
=> apply(X1,X5,X5) )
& ! [X3,X4,X2] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X2,X4)
& apply(X1,X4,X3) )
=> apply(X1,X2,X3) ) )
& ! [X7,X6] :
( ( member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X7,X6)
& apply(X1,X6,X7) )
=> X6 = X7 ) ) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( order(X0,X1)
<=> ( ! [X2,X4,X3] :
( ( member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X3,X2)
& apply(X0,X2,X3) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f50,plain,
apply(sK2,sK1,sK3(sK2,sK0,sK1)),
inference(unit_resulting_resolution,[],[f42,f46,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( apply(X0,X2,sK3(X0,X1,X2))
| max(X2,X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
sK1 != sK3(sK2,sK0,sK1),
inference(unit_resulting_resolution,[],[f42,f46,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( sK3(X0,X1,X2) != X2
| max(X2,X0,X1)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f41,plain,
order(sK2,sK0),
inference(cnf_transformation,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.34 % Computer : n001.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 14:41:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % (22023)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.50 % (22023)First to succeed.
% 0.20/0.50 % (22023)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (22023)------------------------------
% 0.20/0.50 % (22023)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (22023)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (22023)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (22023)Memory used [KB]: 6012
% 0.20/0.50 % (22023)Time elapsed: 0.083 s
% 0.20/0.50 % (22023)Instructions burned: 2 (million)
% 0.20/0.50 % (22023)------------------------------
% 0.20/0.50 % (22023)------------------------------
% 0.20/0.50 % (22013)Success in time 0.15 s
%------------------------------------------------------------------------------