TSTP Solution File: NUN066+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Fri Sep 1 20:50:26 EDT 2023
% Result : Theorem 6.19s 1.35s
% Output : Refutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 17
% Syntax : Number of formulae : 75 ( 12 unt; 0 def)
% Number of atoms : 228 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 247 ( 94 ~; 84 |; 61 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-1 aty)
% Number of variables : 154 (; 116 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41151,plain,
$false,
inference(avatar_sat_refutation,[],[f40888,f41147]) ).
fof(f41147,plain,
~ spl25_222,
inference(avatar_contradiction_clause,[],[f41146]) ).
fof(f41146,plain,
( $false
| ~ spl25_222 ),
inference(subsumption_resolution,[],[f40961,f17439]) ).
fof(f17439,plain,
( ! [X4] : ~ r1(X4)
| ~ spl25_222 ),
inference(avatar_component_clause,[],[f17438]) ).
fof(f17438,plain,
( spl25_222
<=> ! [X4] : ~ r1(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl25_222])]) ).
fof(f40961,plain,
( ! [X13] : r1(X13)
| ~ spl25_222 ),
inference(resolution,[],[f17439,f17734]) ).
fof(f17734,plain,
! [X11] :
( r1(sK8(sK3(X11)))
| r1(X11) ),
inference(resolution,[],[f494,f89]) ).
fof(f89,plain,
! [X0] : id(sK8(X0),X0),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( r3(X0,sK9(X0),sK8(X0))
& r1(sK9(X0))
& id(sK8(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f24,f54,f53]) ).
fof(f53,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) )
=> ( ? [X2] :
( r3(X0,X2,sK8(X0))
& r1(X2) )
& id(sK8(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK8(X0))
& r1(X2) )
=> ( r3(X0,sK9(X0),sK8(X0))
& r1(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X53] :
? [X54] :
( ? [X55] :
( r3(X53,X55,X54)
& r1(X55) )
& id(X54,X53) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_4a) ).
fof(f494,plain,
! [X0,X1] :
( ~ id(X0,sK3(X1))
| r1(X0)
| r1(X1) ),
inference(resolution,[],[f163,f478]) ).
fof(f478,plain,
! [X0] :
( sP0(X0)
| r1(X0) ),
inference(duplicate_literal_removal,[],[f471]) ).
fof(f471,plain,
! [X0] :
( r1(X0)
| sP0(X0)
| sP0(X0) ),
inference(resolution,[],[f164,f82]) ).
fof(f82,plain,
! [X0] :
( id(X0,sK4(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( r1(sK4(X0))
& id(X0,sK4(X0)) )
| sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f41,f48]) ).
fof(f48,plain,
! [X0] :
( ? [X1] :
( r1(X1)
& id(X0,X1) )
=> ( r1(sK4(X0))
& id(X0,sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0] :
( ? [X1] :
( r1(X1)
& id(X0,X1) )
| sP0(X0) ),
inference(definition_folding,[],[f39,f40]) ).
fof(f40,plain,
! [X0] :
( ? [X2] :
( id(X0,X2)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f39,plain,
! [X0] :
( ? [X1] :
( r1(X1)
& id(X0,X1) )
| ? [X2] :
( id(X0,X2)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ? [X0] :
( ! [X1] :
( ~ r1(X1)
| ~ id(X0,X1) )
& ! [X2] :
( ~ id(X0,X2)
| ! [X3] :
( ~ r2(X3,X2)
| ! [X4] :
( ~ r2(X4,X3)
| ~ r1(X4) ) ) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ? [X62] :
( ! [X40] :
( ~ r1(X40)
| ~ id(X62,X40) )
& ! [X45] :
( ~ id(X62,X45)
| ! [X46] :
( ~ r2(X46,X45)
| ! [X39] :
( ~ r2(X39,X46)
| ~ r1(X39) ) ) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
? [X62] :
( ! [X40] :
( ~ r1(X40)
| ~ id(X62,X40) )
& ! [X45] :
( ~ id(X62,X45)
| ! [X46] :
( ~ r2(X46,X45)
| ! [X39] :
( ~ r2(X39,X46)
| ~ r1(X39) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',nonzerononetwoexistid) ).
fof(f164,plain,
! [X2,X3] :
( ~ id(X2,sK4(X3))
| r1(X2)
| sP0(X3) ),
inference(resolution,[],[f102,f83]) ).
fof(f83,plain,
! [X0] :
( r1(sK4(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f102,plain,
! [X0,X1] :
( ~ r1(X1)
| r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| ( ~ r1(X1)
& ~ r1(X0) )
| ~ id(X0,X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X19,X20] :
( ( r1(X20)
& r1(X19) )
| ( ~ r1(X20)
& ~ r1(X19) )
| ~ id(X19,X20) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_8) ).
fof(f163,plain,
! [X0,X1] :
( ~ sP0(X1)
| ~ id(X0,sK3(X1))
| r1(X0) ),
inference(resolution,[],[f102,f78]) ).
fof(f78,plain,
! [X0] :
( r1(sK3(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( id(X0,sK1(X0))
& r2(sK2(X0),sK1(X0))
& r2(sK3(X0),sK2(X0))
& r1(sK3(X0)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f43,f46,f45,f44]) ).
fof(f44,plain,
! [X0] :
( ? [X1] :
( id(X0,X1)
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) )
=> ( id(X0,sK1(X0))
& ? [X2] :
( r2(X2,sK1(X0))
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0] :
( ? [X2] :
( r2(X2,sK1(X0))
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) )
=> ( r2(sK2(X0),sK1(X0))
& ? [X3] :
( r2(X3,sK2(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0] :
( ? [X3] :
( r2(X3,sK2(X0))
& r1(X3) )
=> ( r2(sK3(X0),sK2(X0))
& r1(sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
( ? [X1] :
( id(X0,X1)
& ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r2(X3,X2)
& r1(X3) ) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ? [X2] :
( id(X0,X2)
& ? [X3] :
( r2(X3,X2)
& ? [X4] :
( r2(X4,X3)
& r1(X4) ) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40888,plain,
spl25_222,
inference(avatar_split_clause,[],[f40887,f17438]) ).
fof(f40887,plain,
! [X0] : ~ r1(X0),
inference(subsumption_resolution,[],[f40743,f318]) ).
fof(f318,plain,
! [X2] : ~ r1(sK13(X2)),
inference(resolution,[],[f215,f84]) ).
fof(f84,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] : id(X0,X0),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X13] : id(X13,X13),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_5) ).
fof(f215,plain,
! [X2,X3] :
( ~ id(X2,sK13(X3))
| ~ r1(X2) ),
inference(resolution,[],[f105,f159]) ).
fof(f159,plain,
! [X2] : r2(X2,sK13(X2)),
inference(resolution,[],[f99,f84]) ).
fof(f99,plain,
! [X2,X0] :
( ~ id(X2,sK13(X0))
| r2(X0,X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X2] :
( ( ~ id(X2,sK13(X0))
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,sK13(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f26,f60]) ).
fof(f60,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) )
=> ! [X2] :
( ( ~ id(X2,sK13(X0))
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,sK13(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| ( r2(X0,X2)
& id(X2,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( ~ id(X4,X3)
& ~ r2(X2,X4) )
| ( r2(X2,X4)
& id(X4,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_2) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X2)
| ~ id(X2,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ! [X2] :
( ~ r1(X2)
| ~ id(X2,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X64,X65] :
( ~ r2(X64,X65)
| ! [X66] :
( ~ r1(X66)
| ~ id(X66,X65) ) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_7a) ).
fof(f40743,plain,
! [X0] :
( ~ r1(X0)
| r1(sK13(X0)) ),
inference(resolution,[],[f40742,f555]) ).
fof(f555,plain,
! [X0,X1] :
( ~ id(X0,sK2(X1))
| ~ r1(X0)
| r1(X1) ),
inference(resolution,[],[f219,f478]) ).
fof(f219,plain,
! [X12,X13] :
( ~ sP0(X13)
| ~ id(X12,sK2(X13))
| ~ r1(X12) ),
inference(resolution,[],[f105,f79]) ).
fof(f79,plain,
! [X0] :
( r2(sK3(X0),sK2(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f40742,plain,
! [X2] : id(X2,sK2(sK13(X2))),
inference(subsumption_resolution,[],[f40741,f318]) ).
fof(f40741,plain,
! [X2] :
( id(X2,sK2(sK13(X2)))
| r1(sK13(X2)) ),
inference(subsumption_resolution,[],[f40738,f322]) ).
fof(f322,plain,
! [X3] : sP0(sK13(X3)),
inference(subsumption_resolution,[],[f319,f83]) ).
fof(f319,plain,
! [X3] :
( ~ r1(sK4(sK13(X3)))
| sP0(sK13(X3)) ),
inference(resolution,[],[f215,f147]) ).
fof(f147,plain,
! [X2] :
( id(sK4(X2),X2)
| sP0(X2) ),
inference(resolution,[],[f100,f82]) ).
fof(f100,plain,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X14,X15] :
( id(X15,X14)
| ~ id(X14,X15) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_6) ).
fof(f40738,plain,
! [X2] :
( id(X2,sK2(sK13(X2)))
| ~ sP0(sK13(X2))
| r1(sK13(X2)) ),
inference(resolution,[],[f3161,f479]) ).
fof(f479,plain,
! [X0] :
( id(X0,sK1(X0))
| r1(X0) ),
inference(resolution,[],[f478,f81]) ).
fof(f81,plain,
! [X0] :
( ~ sP0(X0)
| id(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f3161,plain,
! [X50,X49] :
( ~ id(sK13(X49),sK1(X50))
| id(X49,sK2(X50))
| ~ sP0(X50) ),
inference(resolution,[],[f309,f80]) ).
fof(f80,plain,
! [X0] :
( r2(sK2(X0),sK1(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f309,plain,
! [X3,X4,X5] :
( ~ r2(X3,X4)
| id(X5,X3)
| ~ id(sK13(X5),X4) ),
inference(resolution,[],[f106,f159]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,X3)
| ~ r2(X1,X2)
| id(X0,X1)
| ~ id(X3,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( id(X0,X1)
| ! [X2] :
( ~ r2(X1,X2)
| ! [X3] :
( ~ r2(X0,X3)
| ~ id(X3,X2) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X49,X50] :
( id(X49,X50)
| ! [X51] :
( ~ r2(X50,X51)
| ! [X52] :
( ~ r2(X49,X52)
| ~ id(X52,X51) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.aK3I1bSKeR/Vampire---4.8_14673',axiom_3a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN066+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n001.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 16:49:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.41 % (14883)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41 % (14902)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on Vampire---4 for (1451ds/0Mi)
% 0.21/0.41 % (14903)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on Vampire---4 for (569ds/0Mi)
% 0.21/0.41 % (14904)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on Vampire---4 for (476ds/0Mi)
% 0.21/0.41 % (14906)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on Vampire---4 for (396ds/0Mi)
% 0.21/0.41 % (14905)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on Vampire---4 for (470ds/0Mi)
% 0.21/0.41 % (14907)dis+11_4:5_nm=4_216 on Vampire---4 for (216ds/0Mi)
% 0.21/0.41 % (14908)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on Vampire---4 for (1451ds/0Mi)
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [3]
% 0.21/0.42 TRYING [3]
% 0.21/0.42 TRYING [3]
% 0.21/0.42 TRYING [3]
% 0.21/0.43 TRYING [4]
% 0.21/0.43 TRYING [4]
% 0.21/0.45 TRYING [5]
% 0.21/0.45 TRYING [5]
% 0.21/0.46 TRYING [4]
% 0.21/0.47 TRYING [4]
% 0.21/0.50 TRYING [6]
% 0.21/0.52 TRYING [6]
% 0.21/0.61 TRYING [7]
% 0.21/0.62 TRYING [5]
% 0.21/0.68 TRYING [5]
% 0.21/0.70 TRYING [7]
% 5.69/1.23 TRYING [8]
% 6.19/1.34 % (14907)First to succeed.
% 6.19/1.35 % (14907)Refutation found. Thanks to Tanya!
% 6.19/1.35 % SZS status Theorem for Vampire---4
% 6.19/1.35 % SZS output start Proof for Vampire---4
% See solution above
% 6.19/1.35 % (14907)------------------------------
% 6.19/1.35 % (14907)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 6.19/1.35 % (14907)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 6.19/1.35 % (14907)Termination reason: Refutation
% 6.19/1.35
% 6.19/1.35 % (14907)Memory used [KB]: 25202
% 6.19/1.35 % (14907)Time elapsed: 0.935 s
% 6.19/1.35 % (14907)------------------------------
% 6.19/1.35 % (14907)------------------------------
% 6.19/1.35 % (14883)Success in time 0.981 s
% 6.19/1.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------