TSTP Solution File: NUN059+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 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 18:08:01 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 166 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 152 ( 36 ~; 23 |; 83 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 152 ( 84 !; 68 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f129,plain,
$false,
inference(resolution,[],[f128,f124]) ).
fof(f124,plain,
! [X0] : ~ r4(X0,X0,sK3),
inference(resolution,[],[f123,f70]) ).
fof(f70,plain,
! [X0,X1] : r4(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( sK4(X0,X1) = sK5(X0,X1)
& r4(X0,sK6(X0,X1),sK5(X0,X1))
& r2(X1,sK6(X0,X1))
& r3(sK7(X0,X1),X0,sK4(X0,X1))
& r4(X0,X1,sK7(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f33,f37,f36,f35,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) ) )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) )
=> ( ? [X3] :
( sK4(X0,X1) = X3
& ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) ) )
& ? [X5] :
( r3(X5,X0,sK4(X0,X1))
& r4(X0,X1,X5) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X3] :
( sK4(X0,X1) = X3
& ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) ) )
=> ( sK4(X0,X1) = sK5(X0,X1)
& ? [X4] :
( r4(X0,X4,sK5(X0,X1))
& r2(X1,X4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X4] :
( r4(X0,X4,sK5(X0,X1))
& r2(X1,X4) )
=> ( r4(X0,sK6(X0,X1),sK5(X0,X1))
& r2(X1,sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X5] :
( r3(X5,X0,sK4(X0,X1))
& r4(X0,X1,X5) )
=> ( r3(sK7(X0,X1),X0,sK4(X0,X1))
& r4(X0,X1,sK7(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r4(X0,X4,X3)
& r2(X1,X4) ) )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
? [X2] :
( ? [X4] :
( X2 = X4
& ? [X5] :
( r4(X1,X5,X4)
& r2(X0,X5) ) )
& ? [X3] :
( r3(X3,X1,X2)
& r4(X1,X0,X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X20,X19] :
? [X21] :
( ? [X24] :
( r3(X24,X19,X21)
& r4(X19,X20,X24) )
& ? [X22] :
( ? [X23] :
( r2(X20,X23)
& r4(X19,X23,X22) )
& X21 = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ r4(X0,X0,sK7(X1,X1))
| ~ r4(X2,X2,sK3) ),
inference(resolution,[],[f70,f122]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( ~ r4(X1,X1,X2)
| ~ r4(X3,X3,X2)
| ~ r4(X0,X0,sK3) ),
inference(resolution,[],[f121,f106]) ).
fof(f106,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ r3(X5,X4,X6)
| ~ r4(X1,X1,X4)
| ~ r4(X2,X2,X6)
| ~ r4(X3,X3,X5) ),
inference(equality_resolution,[],[f75]) ).
fof(f75,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r4(X1,X1,X4)
| ~ r3(X5,X4,X0)
| ~ r4(X3,X3,X5)
| ~ r4(X2,X2,X6)
| X0 != X6 ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( ~ r4(X1,X1,X4)
| ! [X5] :
( ~ r3(X5,X4,X0)
| ~ r4(X3,X3,X5) ) )
| ! [X6] :
( ~ r4(X2,X2,X6)
| X0 != X6 ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ! [X5] :
( ~ r4(X3,X3,X5)
| ! [X6] :
( ~ r3(X6,X5,X2)
| ~ r4(X1,X1,X6) ) )
| ! [X4] :
( ~ r4(X0,X0,X4)
| X2 != X4 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
~ ? [X1,X0,X2,X3] :
( ? [X4] :
( X2 = X4
& r4(X0,X0,X4) )
& ? [X5] :
( r4(X3,X3,X5)
& ? [X6] :
( r3(X6,X5,X2)
& r4(X1,X1,X6) ) ) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X21,X38,X15,X22] :
( ? [X16] :
( X15 = X16
& r4(X21,X21,X16) )
& ? [X24] :
( ? [X18] :
( r3(X18,X24,X15)
& r4(X38,X38,X18) )
& r4(X22,X22,X24) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X21,X38,X15,X22] :
( ? [X16] :
( X15 = X16
& r4(X21,X21,X16) )
& ? [X24] :
( ? [X18] :
( r3(X18,X24,X15)
& r4(X38,X38,X18) )
& r4(X22,X22,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwo) ).
fof(f121,plain,
! [X0] : r3(X0,sK3,X0),
inference(forward_demodulation,[],[f120,f112]) ).
fof(f112,plain,
! [X0] : sK3 = sK1(X0),
inference(resolution,[],[f67,f59]) ).
fof(f59,plain,
! [X0] : r1(sK1(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( r3(X0,sK1(X0),sK0(X0))
& r1(sK1(X0))
& sK0(X0) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f27,f26]) ).
fof(f26,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& X0 = X1 )
=> ( ? [X2] :
( r3(X0,X2,sK0(X0))
& r1(X2) )
& sK0(X0) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK0(X0))
& r1(X2) )
=> ( r3(X0,sK1(X0),sK0(X0))
& r1(sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( ? [X31] :
( r3(X29,X31,X30)
& r1(X31) )
& X29 = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f67,plain,
! [X1] :
( ~ r1(X1)
| sK3 = X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1] :
( ( r1(X1)
& sK3 = X1 )
| ( ~ r1(X1)
& sK3 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1,f31]) ).
fof(f31,plain,
( ? [X0] :
! [X1] :
( ( r1(X1)
& X0 = X1 )
| ( ~ r1(X1)
& X0 != X1 ) )
=> ! [X1] :
( ( r1(X1)
& sK3 = X1 )
| ( ~ r1(X1)
& sK3 != X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( r1(X1)
& X0 = X1 )
| ( ~ r1(X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f120,plain,
! [X0] : r3(X0,sK1(X0),X0),
inference(forward_demodulation,[],[f60,f58]) ).
fof(f58,plain,
! [X0] : sK0(X0) = X0,
inference(cnf_transformation,[],[f28]) ).
fof(f60,plain,
! [X0] : r3(X0,sK1(X0),sK0(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f128,plain,
! [X0] : r4(X0,sK3,sK3),
inference(forward_demodulation,[],[f127,f114]) ).
fof(f114,plain,
! [X1] : sK3 = sK10(X1),
inference(resolution,[],[f67,f83]) ).
fof(f83,plain,
! [X0] : r1(sK10(X0)),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( r1(sK10(X0))
& r4(X0,sK10(X0),sK9(X0))
& r1(sK11(X0))
& sK9(X0) = sK11(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f21,f44,f43,f42]) ).
fof(f42,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) )
=> ( ? [X2] :
( r1(X2)
& r4(X0,X2,sK9(X0)) )
& ? [X3] :
( r1(X3)
& sK9(X0) = X3 ) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,sK9(X0)) )
=> ( r1(sK10(X0))
& r4(X0,sK10(X0),sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0] :
( ? [X3] :
( r1(X3)
& sK9(X0) = X3 )
=> ( r1(sK11(X0))
& sK9(X0) = sK11(X0) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X32] :
? [X33] :
( ? [X34] :
( r4(X32,X34,X33)
& r1(X34) )
& ? [X35] :
( X33 = X35
& r1(X35) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f127,plain,
! [X0] : r4(X0,sK10(X0),sK3),
inference(forward_demodulation,[],[f99,f115]) ).
fof(f115,plain,
! [X2] : sK3 = sK11(X2),
inference(resolution,[],[f67,f81]) ).
fof(f81,plain,
! [X0] : r1(sK11(X0)),
inference(cnf_transformation,[],[f45]) ).
fof(f99,plain,
! [X0] : r4(X0,sK10(X0),sK11(X0)),
inference(definition_unfolding,[],[f82,f80]) ).
fof(f80,plain,
! [X0] : sK9(X0) = sK11(X0),
inference(cnf_transformation,[],[f45]) ).
fof(f82,plain,
! [X0] : r4(X0,sK10(X0),sK9(X0)),
inference(cnf_transformation,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN059+2 : TPTP v8.1.0. Bugfixed v7.4.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Aug 30 09:47:10 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.20/0.48 % (20460)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.48 % (20469)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.48 % (20469)First to succeed.
% 0.20/0.49 % (20469)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 % (20469)------------------------------
% 0.20/0.49 % (20469)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (20469)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (20469)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (20469)Memory used [KB]: 1023
% 0.20/0.49 % (20469)Time elapsed: 0.073 s
% 0.20/0.49 % (20469)Instructions burned: 3 (million)
% 0.20/0.49 % (20469)------------------------------
% 0.20/0.49 % (20469)------------------------------
% 0.20/0.49 % (20442)Success in time 0.136 s
%------------------------------------------------------------------------------