TSTP Solution File: NUN062+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 : Sun May 5 08:45:00 EDT 2024
% Result : Theorem 0.14s 0.32s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 64 ( 13 unt; 0 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 219 ( 72 ~; 51 |; 85 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 181 ( 123 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f326,plain,
$false,
inference(resolution,[],[f317,f306]) ).
fof(f306,plain,
! [X0] : id(sK30,X0),
inference(resolution,[],[f300,f126]) ).
fof(f126,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/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f300,plain,
! [X0] : id(X0,sK30),
inference(resolution,[],[f299,f164]) ).
fof(f164,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| id(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ( r1(X0)
& id(X0,X1) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X1,X0] :
( ( r1(X1)
& id(X1,X0) )
| ~ sP8(X1,X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X1,X0] :
( ( r1(X1)
& id(X1,X0) )
| ~ sP8(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f299,plain,
! [X0] : sP8(X0,sK30),
inference(resolution,[],[f298,f166]) ).
fof(f166,plain,
! [X1] :
( ~ r1(X1)
| sP8(X1,sK30) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X1] :
( ( ~ id(X1,sK30)
& ~ r1(X1) )
| sP8(X1,sK30) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f57,f106]) ).
fof(f106,plain,
( ? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| sP8(X1,X0) )
=> ! [X1] :
( ( ~ id(X1,sK30)
& ~ r1(X1) )
| sP8(X1,sK30) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| sP8(X1,X0) ),
inference(definition_folding,[],[f1,f56]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| ( r1(X1)
& id(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f298,plain,
! [X0] : r1(X0),
inference(subsumption_resolution,[],[f296,f196]) ).
fof(f196,plain,
! [X0] : r1(sK10(X0)),
inference(resolution,[],[f195,f110]) ).
fof(f110,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/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f195,plain,
! [X0,X1] :
( ~ id(sK25(sK9,X0),X1)
| r1(sK10(X0)) ),
inference(resolution,[],[f142,f109]) ).
fof(f109,plain,
! [X2,X3,X1] :
( ~ r3(sK9,X2,X3)
| ~ id(X3,X1)
| r1(sK10(X2)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X1,X2] :
( ! [X3] :
( ~ r3(sK9,X2,X3)
| ~ id(X3,X1) )
| ( r1(sK10(X2))
& id(X2,sK10(X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f39,f59,f58]) ).
fof(f58,plain,
( ? [X0] :
! [X1,X2] :
( ! [X3] :
( ~ r3(X0,X2,X3)
| ~ id(X3,X1) )
| ? [X4] :
( r1(X4)
& id(X2,X4) ) )
=> ! [X2,X1] :
( ! [X3] :
( ~ r3(sK9,X2,X3)
| ~ id(X3,X1) )
| ? [X4] :
( r1(X4)
& id(X2,X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X2] :
( ? [X4] :
( r1(X4)
& id(X2,X4) )
=> ( r1(sK10(X2))
& id(X2,sK10(X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
? [X0] :
! [X1,X2] :
( ! [X3] :
( ~ r3(X0,X2,X3)
| ~ id(X3,X1) )
| ? [X4] :
( r1(X4)
& id(X2,X4) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] :
? [X1,X2] :
( ? [X3] :
( r3(X0,X2,X3)
& id(X3,X1) )
& ! [X4] :
( ~ r1(X4)
| ~ id(X2,X4) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X37] :
? [X45,X62] :
( ? [X46] :
( r3(X37,X62,X46)
& id(X46,X45) )
& ! [X39] :
( ~ r1(X39)
| ~ id(X62,X39) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X37] :
? [X45,X62] :
( ? [X46] :
( r3(X37,X62,X46)
& id(X46,X45) )
& ! [X39] :
( ~ r1(X39)
| ~ id(X62,X39) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(f142,plain,
! [X0,X1] : r3(X0,X1,sK25(X0,X1)),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( r3(X0,X1,sK25(X0,X1))
& r2(sK25(X0,X1),sK24(X0,X1))
& r3(X0,sK27(X0,X1),sK26(X0,X1))
& r2(X1,sK27(X0,X1))
& id(sK26(X0,X1),sK24(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26,sK27])],[f32,f88,f87,f86,f85]) ).
fof(f85,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) )
& id(X4,X2) ) )
=> ( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK24(X0,X1)) )
& ? [X4] :
( ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) )
& id(X4,sK24(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,sK24(X0,X1)) )
=> ( r3(X0,X1,sK25(X0,X1))
& r2(sK25(X0,X1),sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) )
& id(X4,sK24(X0,X1)) )
=> ( ? [X5] :
( r3(X0,X5,sK26(X0,X1))
& r2(X1,X5) )
& id(sK26(X0,X1),sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X5] :
( r3(X0,X5,sK26(X0,X1))
& r2(X1,X5) )
=> ( r3(X0,sK27(X0,X1),sK26(X0,X1))
& r2(X1,sK27(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r3(X0,X1,X3)
& r2(X3,X2) )
& ? [X4] :
( ? [X5] :
( r3(X0,X5,X4)
& r2(X1,X5) )
& id(X4,X2) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X37,X38] :
? [X39] :
( ? [X42] :
( r3(X37,X38,X42)
& r2(X42,X39) )
& ? [X40] :
( ? [X41] :
( r3(X37,X41,X40)
& r2(X38,X41) )
& id(X40,X39) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f296,plain,
! [X0] :
( r1(X0)
| ~ r1(sK10(X0)) ),
inference(resolution,[],[f272,f128]) ).
fof(f128,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( ~ r1(X0)
& ~ r1(X1) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X1,X0] :
( ( ~ r1(X1)
& ~ r1(X0) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X1,X0] :
( ( ~ r1(X1)
& ~ r1(X0) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f272,plain,
! [X0] :
( sP2(sK10(X0),X0)
| r1(X0) ),
inference(resolution,[],[f129,f201]) ).
fof(f201,plain,
! [X0] : id(X0,sK10(X0)),
inference(resolution,[],[f194,f110]) ).
fof(f194,plain,
! [X0,X1] :
( ~ id(sK25(sK9,X0),X1)
| id(X0,sK10(X0)) ),
inference(resolution,[],[f142,f108]) ).
fof(f108,plain,
! [X2,X3,X1] :
( ~ r3(sK9,X2,X3)
| ~ id(X3,X1)
| id(X2,sK10(X2)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f129,plain,
! [X0,X1] :
( ~ id(X0,X1)
| sP2(X1,X0)
| r1(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( r1(X1)
& r1(X0) )
| sP2(X1,X0)
| ~ id(X0,X1) ),
inference(definition_folding,[],[f28,f44]) ).
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/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f317,plain,
! [X2,X0,X1] : ~ id(X0,sK23(X1,X2)),
inference(resolution,[],[f316,f134]) ).
fof(f134,plain,
! [X0,X1] : r2(X1,sK23(X0,X1)),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( r4(X0,X1,sK21(X0,X1))
& r3(sK21(X0,X1),X0,sK20(X0,X1))
& r4(X0,sK23(X0,X1),sK22(X0,X1))
& r2(X1,sK23(X0,X1))
& id(sK22(X0,X1),sK20(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f31,f83,f82,f81,f80]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) )
& id(X4,X2) ) )
=> ( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK20(X0,X1)) )
& ? [X4] :
( ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) )
& id(X4,sK20(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,sK20(X0,X1)) )
=> ( r4(X0,X1,sK21(X0,X1))
& r3(sK21(X0,X1),X0,sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) )
& id(X4,sK20(X0,X1)) )
=> ( ? [X5] :
( r4(X0,X5,sK22(X0,X1))
& r2(X1,X5) )
& id(sK22(X0,X1),sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X5] :
( r4(X0,X5,sK22(X0,X1))
& r2(X1,X5) )
=> ( r4(X0,sK23(X0,X1),sK22(X0,X1))
& r2(X1,sK23(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r4(X0,X1,X3)
& r3(X3,X0,X2) )
& ? [X4] :
( ? [X5] :
( r4(X0,X5,X4)
& r2(X1,X5) )
& id(X4,X2) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X43,X44] :
? [X45] :
( ? [X48] :
( r4(X43,X44,X48)
& r3(X48,X43,X45) )
& ? [X46] :
( ? [X47] :
( r4(X43,X47,X46)
& r2(X44,X47) )
& id(X46,X45) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f316,plain,
! [X2,X0,X1] :
( ~ r2(X0,X1)
| ~ id(X2,X1) ),
inference(subsumption_resolution,[],[f131,f298]) ).
fof(f131,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/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : NUN062+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.02/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n005.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 18:52:08 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % (22452)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.31 % (22458)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.32 % (22454)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.32 % (22453)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.32 % (22455)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 theBenchmark for (476ds/0Mi)
% 0.14/0.32 % (22457)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.32 % (22459)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 TRYING [1]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 TRYING [2]
% 0.14/0.32 % (22457)First to succeed.
% 0.14/0.32 % (22456)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.32 % (22457)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22452"
% 0.14/0.32 % (22457)Refutation found. Thanks to Tanya!
% 0.14/0.32 % SZS status Theorem for theBenchmark
% 0.14/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.32 % (22457)------------------------------
% 0.14/0.32 % (22457)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.32 % (22457)Termination reason: Refutation
% 0.14/0.32
% 0.14/0.32 % (22457)Memory used [KB]: 929
% 0.14/0.32 % (22457)Time elapsed: 0.006 s
% 0.14/0.32 % (22457)Instructions burned: 9 (million)
% 0.14/0.32 % (22452)Success in time 0.021 s
%------------------------------------------------------------------------------