TSTP Solution File: NUN085+2 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% 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 : n018.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 18:08:09 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 86 ( 43 unt; 0 def)
% Number of atoms : 246 ( 76 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 225 ( 65 ~; 41 |; 105 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 178 ( 115 !; 63 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f193,plain,
$false,
inference(subsumption_resolution,[],[f191,f138]) ).
fof(f138,plain,
! [X0] : ~ r2(X0,sK11),
inference(resolution,[],[f123,f119]) ).
fof(f119,plain,
r1(sK11),
inference(equality_resolution,[],[f85]) ).
fof(f85,plain,
! [X1] :
( sK11 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X1] :
( ( ~ r1(X1)
& sK11 != X1 )
| ( sK11 = X1
& r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f1,f44]) ).
fof(f44,plain,
( ? [X0] :
! [X1] :
( ( ~ r1(X1)
& X0 != X1 )
| ( X0 = X1
& r1(X1) ) )
=> ! [X1] :
( ( ~ r1(X1)
& sK11 != X1 )
| ( sK11 = X1
& r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X0 != X1 )
| ( X0 = X1
& r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f123,plain,
! [X2,X0] :
( ~ r1(X2)
| ~ r2(X0,X2) ),
inference(equality_resolution,[],[f94]) ).
fof(f94,plain,
! [X2,X0,X1] :
( X1 != X2
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ! [X2] :
( X1 != X2
| ~ r1(X2) )
| ~ r2(X0,X1) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X40,X41] :
( ! [X42] :
( ~ r1(X42)
| X41 != X42 )
| ~ r2(X40,X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f191,plain,
r2(sK11,sK11),
inference(superposition,[],[f116,f177]) ).
fof(f177,plain,
sK10(sK11) = sK11,
inference(backward_demodulation,[],[f176,f164]) ).
fof(f164,plain,
! [X0] : sK0(sK11,X0) = X0,
inference(resolution,[],[f66,f134]) ).
fof(f134,plain,
! [X0] : r3(X0,sK11,X0),
inference(backward_demodulation,[],[f124,f125]) ).
fof(f125,plain,
! [X0] : sK5(X0) = sK11,
inference(resolution,[],[f88,f74]) ).
fof(f74,plain,
! [X0] : r1(sK5(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( sK4(X0) = X0
& r1(sK5(X0))
& r3(X0,sK5(X0),sK4(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f18,f34,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( X0 = X1
& ? [X2] :
( r1(X2)
& r3(X0,X2,X1) ) )
=> ( sK4(X0) = X0
& ? [X2] :
( r1(X2)
& r3(X0,X2,sK4(X0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,sK4(X0)) )
=> ( r1(sK5(X0))
& r3(X0,sK5(X0),sK4(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0] :
? [X1] :
( X0 = X1
& ? [X2] :
( r1(X2)
& r3(X0,X2,X1) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( ? [X31] :
( r1(X31)
& r3(X29,X31,X30) )
& X29 = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f88,plain,
! [X1] :
( ~ r1(X1)
| sK11 = X1 ),
inference(cnf_transformation,[],[f45]) ).
fof(f124,plain,
! [X0] : r3(X0,sK5(X0),X0),
inference(backward_demodulation,[],[f73,f75]) ).
fof(f75,plain,
! [X0] : sK4(X0) = X0,
inference(cnf_transformation,[],[f35]) ).
fof(f73,plain,
! [X0] : r3(X0,sK5(X0),sK4(X0)),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X3,X0,X1] :
( ~ r3(X1,X0,X3)
| sK0(X0,X1) = X3 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X3] :
( ( r3(X1,X0,X3)
& sK0(X0,X1) = X3 )
| ( ~ r3(X1,X0,X3)
& sK0(X0,X1) != X3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f20,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( r3(X1,X0,X3)
& X2 = X3 )
| ( ~ r3(X1,X0,X3)
& X2 != X3 ) )
=> ! [X3] :
( ( r3(X1,X0,X3)
& sK0(X0,X1) = X3 )
| ( ~ r3(X1,X0,X3)
& sK0(X0,X1) != X3 ) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
? [X2] :
! [X3] :
( ( r3(X1,X0,X3)
& X2 = X3 )
| ( ~ r3(X1,X0,X3)
& X2 != X3 ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X6,X5] :
? [X7] :
! [X8] :
( ( X7 != X8
& ~ r3(X5,X6,X8) )
| ( r3(X5,X6,X8)
& X7 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f176,plain,
sK10(sK0(sK11,sK11)) = sK11,
inference(forward_demodulation,[],[f168,f175]) ).
fof(f175,plain,
! [X6,X5] : sK10(sK0(X5,X6)) = sK0(sK10(X5),X6),
inference(forward_demodulation,[],[f167,f169]) ).
fof(f169,plain,
! [X0,X1] : sK10(sK0(X0,X1)) = sK22(X0,X1),
inference(backward_demodulation,[],[f148,f165]) ).
fof(f165,plain,
! [X2,X1] : sK24(X1,X2) = sK0(X1,X2),
inference(resolution,[],[f66,f105]) ).
fof(f105,plain,
! [X0,X1] : r3(X1,X0,sK24(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( sK21(X0,X1) = sK22(X0,X1)
& r2(X0,sK23(X0,X1))
& r3(X1,sK23(X0,X1),sK22(X0,X1))
& r2(sK24(X0,X1),sK21(X0,X1))
& r3(X1,X0,sK24(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24])],[f21,f63,f62,f61,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r2(X0,X4)
& r3(X1,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X1,X0,X5) ) )
=> ( ? [X3] :
( sK21(X0,X1) = X3
& ? [X4] :
( r2(X0,X4)
& r3(X1,X4,X3) ) )
& ? [X5] :
( r2(X5,sK21(X0,X1))
& r3(X1,X0,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X3] :
( sK21(X0,X1) = X3
& ? [X4] :
( r2(X0,X4)
& r3(X1,X4,X3) ) )
=> ( sK21(X0,X1) = sK22(X0,X1)
& ? [X4] :
( r2(X0,X4)
& r3(X1,X4,sK22(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X1] :
( ? [X4] :
( r2(X0,X4)
& r3(X1,X4,sK22(X0,X1)) )
=> ( r2(X0,sK23(X0,X1))
& r3(X1,sK23(X0,X1),sK22(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0,X1] :
( ? [X5] :
( r2(X5,sK21(X0,X1))
& r3(X1,X0,X5) )
=> ( r2(sK24(X0,X1),sK21(X0,X1))
& r3(X1,X0,sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r2(X0,X4)
& r3(X1,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X1,X0,X5) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X14,X13] :
? [X15] :
( ? [X16] :
( ? [X17] :
( r2(X14,X17)
& r3(X13,X17,X16) )
& X15 = X16 )
& ? [X18] :
( r2(X18,X15)
& r3(X13,X14,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f148,plain,
! [X0,X1] : sK10(sK24(X0,X1)) = sK22(X0,X1),
inference(resolution,[],[f113,f83]) ).
fof(f83,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK10(X0) = X2 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK10(X0) != X2 )
| ( r2(X0,X2)
& sK10(X0) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f16,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X1 != X2 )
| ( r2(X0,X2)
& X1 = X2 ) )
=> ! [X2] :
( ( ~ r2(X0,X2)
& sK10(X0) != X2 )
| ( r2(X0,X2)
& sK10(X0) = X2 ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X1 != X2 )
| ( r2(X0,X2)
& X1 = X2 ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( r2(X2,X4)
& X3 = X4 )
| ( ~ r2(X2,X4)
& X3 != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f113,plain,
! [X0,X1] : r2(sK24(X0,X1),sK22(X0,X1)),
inference(definition_unfolding,[],[f106,f109]) ).
fof(f109,plain,
! [X0,X1] : sK21(X0,X1) = sK22(X0,X1),
inference(cnf_transformation,[],[f64]) ).
fof(f106,plain,
! [X0,X1] : r2(sK24(X0,X1),sK21(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
fof(f167,plain,
! [X6,X5] : sK22(X5,X6) = sK0(sK10(X5),X6),
inference(resolution,[],[f66,f144]) ).
fof(f144,plain,
! [X0,X1] : r3(X1,sK10(X0),sK22(X0,X1)),
inference(backward_demodulation,[],[f107,f140]) ).
fof(f140,plain,
! [X2,X1] : sK10(X1) = sK23(X1,X2),
inference(resolution,[],[f83,f108]) ).
fof(f108,plain,
! [X0,X1] : r2(X0,sK23(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
fof(f107,plain,
! [X0,X1] : r3(X1,sK23(X0,X1),sK22(X0,X1)),
inference(cnf_transformation,[],[f64]) ).
fof(f168,plain,
sK0(sK10(sK11),sK11) = sK11,
inference(resolution,[],[f66,f142]) ).
fof(f142,plain,
r3(sK11,sK10(sK11),sK11),
inference(backward_demodulation,[],[f136,f141]) ).
fof(f141,plain,
sK10(sK11) = sK17,
inference(resolution,[],[f83,f132]) ).
fof(f132,plain,
r2(sK11,sK17),
inference(backward_demodulation,[],[f103,f127]) ).
fof(f127,plain,
sK18 = sK11,
inference(resolution,[],[f88,f104]) ).
fof(f104,plain,
r1(sK18),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
( r1(sK18)
& r2(sK18,sK17)
& r1(sK19)
& r3(sK19,sK17,sK16)
& r1(sK20)
& sK16 = sK20 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20])],[f53,f58,f57,f56,f55,f54]) ).
fof(f54,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& ? [X3] :
( r1(X3)
& r3(X3,X1,X0) ) )
& ? [X4] :
( r1(X4)
& X0 = X4 ) )
=> ( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& ? [X3] :
( r1(X3)
& r3(X3,X1,sK16) ) )
& ? [X4] :
( r1(X4)
& sK16 = X4 ) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& ? [X3] :
( r1(X3)
& r3(X3,X1,sK16) ) )
=> ( ? [X2] :
( r1(X2)
& r2(X2,sK17) )
& ? [X3] :
( r1(X3)
& r3(X3,sK17,sK16) ) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
( ? [X2] :
( r1(X2)
& r2(X2,sK17) )
=> ( r1(sK18)
& r2(sK18,sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
( ? [X3] :
( r1(X3)
& r3(X3,sK17,sK16) )
=> ( r1(sK19)
& r3(sK19,sK17,sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
( ? [X4] :
( r1(X4)
& sK16 = X4 )
=> ( r1(sK20)
& sK16 = sK20 ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& ? [X3] :
( r1(X3)
& r3(X3,X1,X0) ) )
& ? [X4] :
( r1(X4)
& X0 = X4 ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
? [X0] :
( ? [X1] :
( ? [X3] :
( r1(X3)
& r2(X3,X1) )
& ? [X2] :
( r1(X2)
& r3(X2,X1,X0) ) )
& ? [X4] :
( r1(X4)
& X0 = X4 ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
~ ! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r3(X2,X1,X0) )
| ! [X3] :
( ~ r2(X3,X1)
| ~ r1(X3) ) )
| ! [X4] :
( ~ r1(X4)
| X0 != X4 ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X38] :
( ! [X21] :
( ! [X22] :
( ~ r1(X22)
| ~ r3(X22,X21,X38) )
| ! [X15] :
( ~ r2(X15,X21)
| ~ r1(X15) ) )
| ! [X16] :
( ~ r1(X16)
| X16 != X38 ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X38] :
( ! [X21] :
( ! [X22] :
( ~ r1(X22)
| ~ r3(X22,X21,X38) )
| ! [X15] :
( ~ r2(X15,X21)
| ~ r1(X15) ) )
| ! [X16] :
( ~ r1(X16)
| X16 != X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplusoneidzero) ).
fof(f103,plain,
r2(sK18,sK17),
inference(cnf_transformation,[],[f59]) ).
fof(f136,plain,
r3(sK11,sK17,sK11),
inference(backward_demodulation,[],[f131,f128]) ).
fof(f128,plain,
sK19 = sK11,
inference(resolution,[],[f88,f102]) ).
fof(f102,plain,
r1(sK19),
inference(cnf_transformation,[],[f59]) ).
fof(f131,plain,
r3(sK19,sK17,sK11),
inference(backward_demodulation,[],[f112,f129]) ).
fof(f129,plain,
sK20 = sK11,
inference(resolution,[],[f88,f100]) ).
fof(f100,plain,
r1(sK20),
inference(cnf_transformation,[],[f59]) ).
fof(f112,plain,
r3(sK19,sK17,sK20),
inference(definition_unfolding,[],[f101,f99]) ).
fof(f99,plain,
sK16 = sK20,
inference(cnf_transformation,[],[f59]) ).
fof(f101,plain,
r3(sK19,sK17,sK16),
inference(cnf_transformation,[],[f59]) ).
fof(f116,plain,
! [X0] : r2(X0,sK10(X0)),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X2,X0] :
( sK10(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN085+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n018.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 09:55:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.50 % (8976)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.51 % (8971)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (8984)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.51 % (8984)First to succeed.
% 0.19/0.52 % (8967)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52 % (8984)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (8984)------------------------------
% 0.19/0.52 % (8984)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (8984)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (8984)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (8984)Memory used [KB]: 5500
% 0.19/0.52 % (8984)Time elapsed: 0.110 s
% 0.19/0.52 % (8984)Instructions burned: 5 (million)
% 0.19/0.52 % (8984)------------------------------
% 0.19/0.52 % (8984)------------------------------
% 0.19/0.52 % (8959)Success in time 0.169 s
%------------------------------------------------------------------------------