TSTP Solution File: NUN076+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 08:45:05 EDT 2024
% Result : Theorem 4.54s 1.01s
% Output : Refutation 4.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 81 ( 22 unt; 0 def)
% Number of atoms : 239 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 259 ( 101 ~; 74 |; 77 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 192 ( 140 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52448,plain,
$false,
inference(resolution,[],[f52221,f191]) ).
fof(f191,plain,
r1(sK28),
inference(resolution,[],[f188,f161]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| r1(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( r1(X0)
& id(X0,X1) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f101]) ).
fof(f101,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(f188,plain,
sP8(sK28,sK28),
inference(resolution,[],[f163,f106]) ).
fof(f106,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/benchmark/theBenchmark.p',axiom_5) ).
fof(f163,plain,
! [X1] :
( ~ id(X1,sK28)
| sP8(X1,sK28) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X1] :
( ( ~ id(X1,sK28)
& ~ r1(X1) )
| sP8(X1,sK28) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f57,f103]) ).
fof(f103,plain,
( ? [X0] :
! [X1] :
( ( ~ id(X1,X0)
& ~ r1(X1) )
| sP8(X1,X0) )
=> ! [X1] :
( ( ~ id(X1,sK28)
& ~ r1(X1) )
| sP8(X1,sK28) ) ),
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/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f52221,plain,
! [X0] : ~ r1(X0),
inference(subsumption_resolution,[],[f52182,f4376]) ).
fof(f4376,plain,
! [X0,X1] : id(sK14(X0),sK16(X1)),
inference(resolution,[],[f690,f487]) ).
fof(f487,plain,
! [X0] : id(sK14(X0),sK28),
inference(resolution,[],[f478,f160]) ).
fof(f160,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| id(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f478,plain,
! [X0] : sP8(sK14(X0),sK28),
inference(resolution,[],[f476,f162]) ).
fof(f162,plain,
! [X1] :
( ~ r1(X1)
| sP8(X1,sK28) ),
inference(cnf_transformation,[],[f104]) ).
fof(f476,plain,
! [X0] : r1(sK14(X0)),
inference(subsumption_resolution,[],[f474,f117]) ).
fof(f117,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( r1(sK15(X0))
& id(sK14(X0),sK15(X0))
& r4(X0,sK16(X0),sK14(X0))
& r1(sK16(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f25,f69,f68,f67]) ).
fof(f67,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& id(X1,X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) )
=> ( ? [X2] :
( r1(X2)
& id(sK14(X0),X2) )
& ? [X3] :
( r4(X0,X3,sK14(X0))
& r1(X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0] :
( ? [X2] :
( r1(X2)
& id(sK14(X0),X2) )
=> ( r1(sK15(X0))
& id(sK14(X0),sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ? [X3] :
( r4(X0,X3,sK14(X0))
& r1(X3) )
=> ( r4(X0,sK16(X0),sK14(X0))
& r1(sK16(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& id(X1,X2) )
& ? [X3] :
( r4(X0,X3,X1)
& r1(X3) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X56] :
? [X57] :
( ? [X59] :
( r1(X59)
& id(X57,X59) )
& ? [X58] :
( r4(X56,X58,X57)
& r1(X58) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f474,plain,
! [X0] :
( r1(sK14(X0))
| ~ r1(sK15(X0)) ),
inference(resolution,[],[f238,f124]) ).
fof(f124,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ~ r1(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( ~ r1(X0)
& ~ r1(X1) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f75]) ).
fof(f75,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(f238,plain,
! [X0] :
( sP2(sK15(X0),sK14(X0))
| r1(sK14(X0)) ),
inference(resolution,[],[f125,f116]) ).
fof(f116,plain,
! [X0] : id(sK14(X0),sK15(X0)),
inference(cnf_transformation,[],[f70]) ).
fof(f125,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/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f690,plain,
! [X0,X1] :
( ~ id(X0,sK28)
| id(X0,sK16(X1)) ),
inference(resolution,[],[f147,f180]) ).
fof(f180,plain,
! [X0] : id(sK28,sK16(X0)),
inference(resolution,[],[f177,f122]) ).
fof(f122,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/benchmark/theBenchmark.p',axiom_6) ).
fof(f177,plain,
! [X0] : id(sK16(X0),sK28),
inference(resolution,[],[f160,f165]) ).
fof(f165,plain,
! [X0] : sP8(sK16(X0),sK28),
inference(resolution,[],[f162,f114]) ).
fof(f114,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f70]) ).
fof(f147,plain,
! [X2,X0,X1] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ id(X1,X2)
| id(X0,X2)
| ~ id(X0,X1) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X16,X17,X18] :
( ~ id(X17,X18)
| id(X16,X18)
| ~ id(X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f52182,plain,
! [X0] :
( ~ r1(X0)
| ~ id(sK14(sK17(sK17(X0))),sK16(sK17(sK17(X0)))) ),
inference(resolution,[],[f52179,f111]) ).
fof(f111,plain,
! [X0] : id(sK12(X0),X0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( r3(X0,sK13(X0),sK12(X0))
& r1(sK13(X0))
& id(sK12(X0),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f24,f65,f64]) ).
fof(f64,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& id(X1,X0) )
=> ( ? [X2] :
( r3(X0,X2,sK12(X0))
& r1(X2) )
& id(sK12(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK12(X0))
& r1(X2) )
=> ( r3(X0,sK13(X0),sK12(X0))
& r1(sK13(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/benchmark/theBenchmark.p',axiom_4a) ).
fof(f52179,plain,
! [X0,X1] :
( ~ id(sK12(sK16(sK17(sK17(X0)))),X1)
| ~ r1(X0)
| ~ id(sK14(sK17(sK17(X0))),X1) ),
inference(resolution,[],[f52170,f508]) ).
fof(f508,plain,
! [X0] : r2(X0,sK17(X0)),
inference(resolution,[],[f484,f119]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| r2(X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( r2(X1,X0)
& id(X0,X2) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ( r2(X0,X2)
& id(X2,X1) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ( r2(X0,X2)
& id(X2,X1) )
| ~ sP1(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f484,plain,
! [X0] : sP1(sK17(X0),X0,sK17(X0)),
inference(resolution,[],[f121,f106]) ).
fof(f121,plain,
! [X2,X0] :
( ~ id(X2,sK17(X0))
| sP1(X2,X0,sK17(X0)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X2] :
( ( ~ id(X2,sK17(X0))
& ~ r2(X0,X2) )
| sP1(X2,X0,sK17(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f43,f73]) ).
fof(f73,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| sP1(X2,X0,X1) )
=> ! [X2] :
( ( ~ id(X2,sK17(X0))
& ~ r2(X0,X2) )
| sP1(X2,X0,sK17(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ id(X2,X1)
& ~ r2(X0,X2) )
| sP1(X2,X0,X1) ),
inference(definition_folding,[],[f26,f42]) ).
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/benchmark/theBenchmark.p',axiom_2) ).
fof(f52170,plain,
! [X2,X0,X1] :
( ~ r2(sK17(X0),X1)
| ~ r1(X0)
| ~ id(sK12(sK16(X1)),X2)
| ~ id(sK14(X1),X2) ),
inference(resolution,[],[f5435,f508]) ).
fof(f5435,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X0)
| ~ r2(X1,X2)
| ~ id(sK12(sK16(X2)),X3)
| ~ id(sK14(X2),X3) ),
inference(resolution,[],[f778,f113]) ).
fof(f113,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f66]) ).
fof(f778,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r3(sK16(X4),X5,X0)
| ~ r2(X2,X3)
| ~ r1(X2)
| ~ r2(X3,X4)
| ~ id(X0,X1)
| ~ id(sK14(X4),X1) ),
inference(resolution,[],[f105,f115]) ).
fof(f115,plain,
! [X0] : r4(X0,sK16(X0),sK14(X0)),
inference(cnf_transformation,[],[f70]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r4(X5,X1,X4)
| ~ id(X3,X0)
| ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r3(X1,X2,X3)
| ~ id(X4,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ! [X3] :
( ~ r3(X1,X2,X3)
| ~ id(X3,X0) )
| ! [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( ~ r2(X7,X6)
| ~ r1(X7) )
| ~ r2(X6,X5) )
| ~ r4(X5,X1,X4) )
| ~ id(X4,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ? [X0,X1,X2] :
( ? [X3] :
( r3(X1,X2,X3)
& id(X3,X0) )
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& r4(X5,X1,X4) )
& id(X4,X0) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ? [X62,X45,X46] :
( ? [X40] :
( r3(X45,X46,X40)
& id(X40,X62) )
& ? [X39] :
( ? [X48] :
( ? [X42] :
( ? [X57] :
( r2(X57,X42)
& r1(X57) )
& r2(X42,X48) )
& r4(X48,X45,X39) )
& id(X39,X62) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
? [X62,X45,X46] :
( ? [X40] :
( r3(X45,X46,X40)
& id(X40,X62) )
& ? [X39] :
( ? [X48] :
( ? [X42] :
( ? [X57] :
( r2(X57,X42)
& r1(X57) )
& r2(X42,X48) )
& r4(X48,X45,X39) )
& id(X39,X62) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thereexistsanevennumberid) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUN076+1 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 18:54:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (22012)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (22014)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (22015)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)
% 0.15/0.38 % (22017)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38 % (22018)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38 % (22016)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38 % (22019)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)
% 0.15/0.38 % (22013)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.15/0.39 TRYING [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [3]
% 0.22/0.40 TRYING [4]
% 0.22/0.40 TRYING [4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.22/0.42 TRYING [5]
% 0.22/0.42 TRYING [5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 0.22/0.43 TRYING [4]
% 0.22/0.43 TRYING [4]
% 0.22/0.47 TRYING [6]
% 0.22/0.47 TRYING [6,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 1.34/0.56 TRYING [7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 1.34/0.56 TRYING [7]
% 1.34/0.58 TRYING [5]
% 1.34/0.61 TRYING [5]
% 4.13/0.96 TRYING [8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
% 4.54/1.00 TRYING [8]
% 4.54/1.01 % (22017)First to succeed.
% 4.54/1.01 % (22017)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-22012"
% 4.54/1.01 % (22017)Refutation found. Thanks to Tanya!
% 4.54/1.01 % SZS status Theorem for theBenchmark
% 4.54/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 4.54/1.01 % (22017)------------------------------
% 4.54/1.01 % (22017)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.54/1.01 % (22017)Termination reason: Refutation
% 4.54/1.01
% 4.54/1.01 % (22017)Memory used [KB]: 16510
% 4.54/1.01 % (22017)Time elapsed: 0.628 s
% 4.54/1.01 % (22017)Instructions burned: 2255 (million)
% 4.54/1.01 % (22012)Success in time 0.63 s
%------------------------------------------------------------------------------