TSTP Solution File: SET791+4 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n017.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 18:25:39 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 7 unt; 0 def)
% Number of atoms : 264 ( 24 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 309 ( 106 ~; 101 |; 65 &)
% ( 8 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 151 ( 135 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f113,plain,
$false,
inference(avatar_sat_refutation,[],[f94,f99,f112]) ).
fof(f112,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f111]) ).
fof(f111,plain,
( $false
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f110,f47]) ).
fof(f47,plain,
~ max(sK1,sK2,sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
( greatest(sK1,sK2,sK0)
& ~ max(sK1,sK2,sK0)
& order(sK2,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f35,f36]) ).
fof(f36,plain,
( ? [X0,X1,X2] :
( greatest(X1,X2,X0)
& ~ max(X1,X2,X0)
& order(X2,X0) )
=> ( greatest(sK1,sK2,sK0)
& ~ max(sK1,sK2,sK0)
& order(sK2,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
? [X0,X1,X2] :
( greatest(X1,X2,X0)
& ~ max(X1,X2,X0)
& order(X2,X0) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
? [X2,X0,X1] :
( greatest(X0,X1,X2)
& ~ max(X0,X1,X2)
& order(X1,X2) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
? [X1,X0,X2] :
( ~ max(X0,X1,X2)
& order(X1,X2)
& greatest(X0,X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X1,X0,X2] :
( ( order(X1,X2)
& greatest(X0,X1,X2) )
=> max(X0,X1,X2) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X5,X0,X1] :
( ( greatest(X5,X0,X1)
& order(X0,X1) )
=> max(X5,X0,X1) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X5,X0,X1] :
( ( greatest(X5,X0,X1)
& order(X0,X1) )
=> max(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV3) ).
fof(f110,plain,
( max(sK1,sK2,sK0)
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f109,f52]) ).
fof(f52,plain,
member(sK1,sK0),
inference(resolution,[],[f44,f48]) ).
fof(f48,plain,
greatest(sK1,sK2,sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ greatest(X0,X2,X1)
| member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( apply(X2,X3,X0)
| ~ member(X3,X1) )
& member(X0,X1) )
| ~ greatest(X0,X2,X1) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( apply(X1,X3,X2)
| ~ member(X3,X0) )
& member(X2,X0) )
| ~ greatest(X2,X1,X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X1,X0] :
( greatest(X2,X1,X0)
=> ( ! [X3] :
( member(X3,X0)
=> apply(X1,X3,X2) )
& member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f16,plain,
! [X2,X1,X0] :
( greatest(X2,X1,X0)
<=> ( ! [X3] :
( member(X3,X0)
=> apply(X1,X3,X2) )
& member(X2,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0,X5] :
( ( member(X5,X1)
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X5) ) )
<=> greatest(X5,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest) ).
fof(f109,plain,
( ~ member(sK1,sK0)
| max(sK1,sK2,sK0)
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f108]) ).
fof(f108,plain,
( max(sK1,sK2,sK0)
| sK1 != sK1
| ~ member(sK1,sK0)
| ~ spl4_1 ),
inference(superposition,[],[f51,f90]) ).
fof(f90,plain,
( sK1 = sK3(sK0,sK2,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f88,plain,
( spl4_1
<=> sK1 = sK3(sK0,sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f51,plain,
! [X2,X0,X1] :
( sK3(X0,X1,X2) != X2
| max(X2,X1,X0)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| max(X2,X1,X0)
| ( sK3(X0,X1,X2) != X2
& member(sK3(X0,X1,X2),X0)
& apply(X1,X2,sK3(X0,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f38,f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X3] :
( X2 != X3
& member(X3,X0)
& apply(X1,X2,X3) )
=> ( sK3(X0,X1,X2) != X2
& member(sK3(X0,X1,X2),X0)
& apply(X1,X2,sK3(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X2,X0)
| max(X2,X1,X0)
| ? [X3] :
( X2 != X3
& member(X3,X0)
& apply(X1,X2,X3) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X2,X0] :
( ~ member(X0,X1)
| max(X0,X2,X1)
| ? [X3] :
( X0 != X3
& member(X3,X1)
& apply(X2,X0,X3) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( max(X0,X2,X1)
| ? [X3] :
( X0 != X3
& member(X3,X1)
& apply(X2,X0,X3) )
| ~ member(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( member(X3,X1)
& apply(X2,X0,X3) )
=> X0 = X3 )
& member(X0,X1) )
=> max(X0,X2,X1) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( max(X0,X2,X1)
<=> ( ! [X3] :
( ( member(X3,X1)
& apply(X2,X0,X3) )
=> X0 = X3 )
& member(X0,X1) ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X5,X1,X0] :
( max(X5,X0,X1)
<=> ( ! [X2] :
( ( member(X2,X1)
& apply(X0,X5,X2) )
=> X2 = X5 )
& member(X5,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max) ).
fof(f99,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f98,plain,
( $false
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f97,f47]) ).
fof(f97,plain,
( max(sK1,sK2,sK0)
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f96,f52]) ).
fof(f96,plain,
( ~ member(sK1,sK0)
| max(sK1,sK2,sK0)
| ~ spl4_2 ),
inference(subsumption_resolution,[],[f95,f46]) ).
fof(f46,plain,
order(sK2,sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f95,plain,
( ~ order(sK2,sK0)
| ~ member(sK1,sK0)
| max(sK1,sK2,sK0)
| ~ spl4_2 ),
inference(resolution,[],[f93,f57]) ).
fof(f57,plain,
! [X0] :
( member(sK3(sK0,X0,sK1),sK0)
| max(sK1,X0,sK0) ),
inference(resolution,[],[f50,f52]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| max(X2,X1,X0)
| member(sK3(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f93,plain,
( ! [X0] :
( ~ member(sK3(sK0,sK2,sK1),X0)
| ~ member(sK1,X0)
| ~ order(sK2,X0) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f92,plain,
( spl4_2
<=> ! [X0] :
( ~ member(sK1,X0)
| ~ member(sK3(sK0,sK2,sK1),X0)
| ~ order(sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f94,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f86,f92,f88]) ).
fof(f86,plain,
! [X0] :
( ~ member(sK1,X0)
| sK1 = sK3(sK0,sK2,sK1)
| ~ order(sK2,X0)
| ~ member(sK3(sK0,sK2,sK1),X0) ),
inference(subsumption_resolution,[],[f85,f47]) ).
fof(f85,plain,
! [X0] :
( max(sK1,sK2,sK0)
| ~ member(sK3(sK0,sK2,sK1),X0)
| ~ order(sK2,X0)
| ~ member(sK1,X0)
| sK1 = sK3(sK0,sK2,sK1) ),
inference(duplicate_literal_removal,[],[f84]) ).
fof(f84,plain,
! [X0] :
( sK1 = sK3(sK0,sK2,sK1)
| max(sK1,sK2,sK0)
| ~ member(sK1,X0)
| ~ order(sK2,X0)
| max(sK1,sK2,sK0)
| ~ member(sK3(sK0,sK2,sK1),X0) ),
inference(resolution,[],[f67,f58]) ).
fof(f58,plain,
! [X0] :
( apply(sK2,sK3(sK0,X0,sK1),sK1)
| max(sK1,X0,sK0) ),
inference(resolution,[],[f57,f55]) ).
fof(f55,plain,
! [X0] :
( ~ member(X0,sK0)
| apply(sK2,X0,sK1) ),
inference(resolution,[],[f45,f48]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ greatest(X0,X2,X1)
| ~ member(X3,X1)
| apply(X2,X3,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f67,plain,
! [X6,X5] :
( ~ apply(X5,sK3(sK0,X5,sK1),sK1)
| ~ order(X5,X6)
| ~ member(sK3(sK0,X5,sK1),X6)
| max(sK1,X5,sK0)
| ~ member(sK1,X6)
| sK1 = sK3(sK0,X5,sK1) ),
inference(resolution,[],[f41,f61]) ).
fof(f61,plain,
! [X0] :
( apply(X0,sK1,sK3(sK0,X0,sK1))
| max(sK1,X0,sK0) ),
inference(resolution,[],[f49,f52]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| apply(X1,X2,sK3(X0,X1,X2))
| max(X2,X1,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f41,plain,
! [X0,X1,X6,X7] :
( ~ apply(X1,X6,X7)
| ~ member(X7,X0)
| ~ apply(X1,X7,X6)
| ~ member(X6,X0)
| ~ order(X1,X0)
| X6 = X7 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ order(X1,X0)
| ( ! [X2,X3,X4] :
( ~ apply(X1,X3,X2)
| ~ apply(X1,X2,X4)
| apply(X1,X3,X4)
| ~ member(X4,X0)
| ~ member(X2,X0)
| ~ member(X3,X0) )
& ! [X5] :
( ~ member(X5,X0)
| apply(X1,X5,X5) )
& ! [X6,X7] :
( ~ apply(X1,X7,X6)
| ~ apply(X1,X6,X7)
| ~ member(X6,X0)
| ~ member(X7,X0)
| X6 = X7 ) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ~ order(X0,X1)
| ( ! [X3,X4,X5] :
( ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X5)
| apply(X0,X4,X5)
| ~ member(X5,X1)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) )
& ! [X7,X6] :
( ~ apply(X0,X6,X7)
| ~ apply(X0,X7,X6)
| ~ member(X7,X1)
| ~ member(X6,X1)
| X6 = X7 ) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) )
& ! [X4,X5,X3] :
( apply(X0,X4,X5)
| ~ apply(X0,X3,X5)
| ~ apply(X0,X4,X3)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1) )
& ! [X6,X7] :
( X6 = X7
| ~ apply(X0,X6,X7)
| ~ apply(X0,X7,X6)
| ~ member(X7,X1)
| ~ member(X6,X1) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( order(X0,X1)
=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X4,X5,X3] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X4,X3) )
=> apply(X0,X4,X5) ) )
& ! [X6,X7] :
( ( member(X7,X1)
& member(X6,X1) )
=> ( ( apply(X0,X6,X7)
& apply(X0,X7,X6) )
=> X6 = X7 ) ) ) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X4,X5,X3] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X4,X3) )
=> apply(X0,X4,X5) ) )
& ! [X6,X7] :
( ( member(X7,X1)
& member(X6,X1) )
=> ( ( apply(X0,X6,X7)
& apply(X0,X7,X6) )
=> X6 = X7 ) ) )
<=> order(X0,X1) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X2,X4] :
( ( member(X3,X1)
& member(X2,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) )
<=> order(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET791+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 13:44:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % (19122)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.48 % (19122)First to succeed.
% 0.20/0.49 % (19122)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (19122)------------------------------
% 0.20/0.49 % (19122)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (19122)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (19122)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (19122)Memory used [KB]: 5500
% 0.20/0.49 % (19122)Time elapsed: 0.109 s
% 0.20/0.49 % (19122)Instructions burned: 5 (million)
% 0.20/0.49 % (19122)------------------------------
% 0.20/0.49 % (19122)------------------------------
% 0.20/0.49 % (19117)Success in time 0.141 s
%------------------------------------------------------------------------------