TSTP Solution File: NUN081+2 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUN081+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 : n015.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 18:08:08 EDT 2022
% Result : Theorem 1.46s 0.58s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 182 ( 40 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 199 ( 71 ~; 44 |; 73 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 151 ( 97 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f171,plain,
$false,
inference(resolution,[],[f148,f100]) ).
fof(f100,plain,
r1(sK0),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X1] :
( ( sK0 != X1
& ~ r1(X1) )
| ( sK0 = X1
& r1(X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1,f26]) ).
fof(f26,plain,
( ? [X0] :
! [X1] :
( ( X0 != X1
& ~ r1(X1) )
| ( X0 = X1
& r1(X1) ) )
=> ! [X1] :
( ( sK0 != X1
& ~ r1(X1) )
| ( sK0 = X1
& r1(X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1,axiom,
? [X0] :
! [X1] :
( ( X0 != X1
& ~ r1(X1) )
| ( X0 = X1
& r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f148,plain,
! [X2] : ~ r1(X2),
inference(resolution,[],[f143,f135]) ).
fof(f135,plain,
! [X3,X4] :
( sP20(sK19(X3,X4))
| ~ r1(X3) ),
inference(resolution,[],[f110,f93]) ).
fof(f93,plain,
! [X0,X1] : r2(X0,sK19(X0,X1)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( r4(X1,X0,sK17(X0,X1))
& r3(sK17(X0,X1),X1,sK16(X0,X1))
& r2(X0,sK19(X0,X1))
& r4(X1,sK19(X0,X1),sK18(X0,X1))
& sK18(X0,X1) = sK16(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f17,f54,f53,f52,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( r4(X1,X0,X3)
& r3(X3,X1,X2) )
& ? [X4] :
( ? [X5] :
( r2(X0,X5)
& r4(X1,X5,X4) )
& X2 = X4 ) )
=> ( ? [X3] :
( r4(X1,X0,X3)
& r3(X3,X1,sK16(X0,X1)) )
& ? [X4] :
( ? [X5] :
( r2(X0,X5)
& r4(X1,X5,X4) )
& sK16(X0,X1) = X4 ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1] :
( ? [X3] :
( r4(X1,X0,X3)
& r3(X3,X1,sK16(X0,X1)) )
=> ( r4(X1,X0,sK17(X0,X1))
& r3(sK17(X0,X1),X1,sK16(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f53,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( r2(X0,X5)
& r4(X1,X5,X4) )
& sK16(X0,X1) = X4 )
=> ( ? [X5] :
( r2(X0,X5)
& r4(X1,X5,sK18(X0,X1)) )
& sK18(X0,X1) = sK16(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1] :
( ? [X5] :
( r2(X0,X5)
& r4(X1,X5,sK18(X0,X1)) )
=> ( r2(X0,sK19(X0,X1))
& r4(X1,sK19(X0,X1),sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1] :
? [X2] :
( ? [X3] :
( r4(X1,X0,X3)
& r3(X3,X1,X2) )
& ? [X4] :
( ? [X5] :
( r2(X0,X5)
& r4(X1,X5,X4) )
& X2 = X4 ) ),
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/sandbox/benchmark/theBenchmark.p',axiom_2a) ).
fof(f110,plain,
! [X6,X5] :
( ~ r2(X6,X5)
| ~ r1(X6)
| sP20(X5) ),
inference(cnf_transformation,[],[f110_D]) ).
fof(f110_D,plain,
! [X5] :
( ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) )
<=> ~ sP20(X5) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP20])]) ).
fof(f143,plain,
! [X0] : ~ sP20(X0),
inference(resolution,[],[f142,f136]) ).
fof(f136,plain,
! [X0] :
( sP21(sK15(X0))
| ~ sP20(X0) ),
inference(resolution,[],[f112,f109]) ).
fof(f109,plain,
! [X0] : r2(X0,sK15(X0)),
inference(equality_resolution,[],[f87]) ).
fof(f87,plain,
! [X2,X0] :
( r2(X0,X2)
| sK15(X0) != X2 ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X2] :
( ( sK15(X0) = X2
& r2(X0,X2) )
| ( ~ r2(X0,X2)
& sK15(X0) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f16,f49]) ).
fof(f49,plain,
! [X0] :
( ? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( ~ r2(X0,X2)
& X1 != X2 ) )
=> ! [X2] :
( ( sK15(X0) = X2
& r2(X0,X2) )
| ( ~ r2(X0,X2)
& sK15(X0) != X2 ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0] :
? [X1] :
! [X2] :
( ( X1 = X2
& r2(X0,X2) )
| ( ~ r2(X0,X2)
& X1 != X2 ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2] :
? [X3] :
! [X4] :
( ( X3 = X4
& r2(X2,X4) )
| ( ~ r2(X2,X4)
& X3 != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f112,plain,
! [X4,X5] :
( ~ r2(X5,X4)
| sP21(X4)
| ~ sP20(X5) ),
inference(cnf_transformation,[],[f112_D]) ).
fof(f112_D,plain,
! [X4] :
( ! [X5] :
( ~ r2(X5,X4)
| ~ sP20(X5) )
<=> ~ sP21(X4) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP21])]) ).
fof(f142,plain,
! [X0] : ~ sP21(X0),
inference(resolution,[],[f139,f130]) ).
fof(f130,plain,
! [X0] : ~ sP22(X0),
inference(resolution,[],[f115,f121]) ).
fof(f121,plain,
! [X0] : r3(X0,sK0,X0),
inference(backward_demodulation,[],[f116,f118]) ).
fof(f118,plain,
! [X0] : sK0 = sK8(X0),
inference(resolution,[],[f57,f77]) ).
fof(f77,plain,
! [X0] : r1(sK8(X0)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( r3(X0,sK8(X0),sK7(X0))
& r1(sK8(X0))
& sK7(X0) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f22,f39,f38]) ).
fof(f38,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& X0 = X1 )
=> ( ? [X2] :
( r3(X0,X2,sK7(X0))
& r1(X2) )
& sK7(X0) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0] :
( ? [X2] :
( r3(X0,X2,sK7(X0))
& r1(X2) )
=> ( r3(X0,sK8(X0),sK7(X0))
& r1(sK8(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0] :
? [X1] :
( ? [X2] :
( r3(X0,X2,X1)
& r1(X2) )
& X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X29] :
? [X30] :
( X29 = X30
& ? [X31] :
( r1(X31)
& r3(X29,X31,X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f57,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f116,plain,
! [X0] : r3(X0,sK8(X0),X0),
inference(backward_demodulation,[],[f78,f76]) ).
fof(f76,plain,
! [X0] : sK7(X0) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f78,plain,
! [X0] : r3(X0,sK8(X0),sK7(X0)),
inference(cnf_transformation,[],[f40]) ).
fof(f115,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| ~ sP22(X3) ),
inference(general_splitting,[],[f113,f114_D]) ).
fof(f114,plain,
! [X3,X4] :
( ~ r2(X4,X3)
| ~ sP21(X4)
| sP22(X3) ),
inference(cnf_transformation,[],[f114_D]) ).
fof(f114_D,plain,
! [X3] :
( ! [X4] :
( ~ r2(X4,X3)
| ~ sP21(X4) )
<=> ~ sP22(X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP22])]) ).
fof(f113,plain,
! [X3,X0,X1,X4] :
( ~ r3(X0,X1,X3)
| ~ r2(X4,X3)
| ~ sP21(X4) ),
inference(general_splitting,[],[f111,f112_D]) ).
fof(f111,plain,
! [X3,X0,X1,X4,X5] :
( ~ r3(X0,X1,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ sP20(X5) ),
inference(general_splitting,[],[f101,f110_D]) ).
fof(f101,plain,
! [X3,X0,X1,X6,X4,X5] :
( ~ r3(X0,X1,X3)
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X6) ),
inference(equality_resolution,[],[f60]) ).
fof(f60,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ r3(X0,X1,X2)
| X2 != X3
| ~ r2(X4,X3)
| ~ r2(X5,X4)
| ~ r2(X6,X5)
| ~ r1(X6) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ r3(X0,X1,X2)
| ! [X3] :
( X2 != X3
| ! [X4] :
( ~ r2(X4,X3)
| ! [X5] :
( ~ r2(X5,X4)
| ! [X6] :
( ~ r2(X6,X5)
| ~ r1(X6) ) ) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
~ ? [X1,X2,X0] :
( ? [X3] :
( X2 = X3
& ? [X4] :
( r2(X4,X3)
& ? [X5] :
( r2(X5,X4)
& ? [X6] :
( r1(X6)
& r2(X6,X5) ) ) ) )
& r3(X0,X1,X2) ),
inference(rectify,[],[f13]) ).
fof(f13,negated_conjecture,
~ ? [X38,X21,X22] :
( r3(X38,X21,X22)
& ? [X15] :
( ? [X16] :
( ? [X24] :
( ? [X18] :
( r2(X18,X24)
& r1(X18) )
& r2(X24,X16) )
& r2(X16,X15) )
& X15 = X22 ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
? [X38,X21,X22] :
( r3(X38,X21,X22)
& ? [X15] :
( ? [X16] :
( ? [X24] :
( ? [X18] :
( r2(X18,X24)
& r1(X18) )
& r2(X24,X16) )
& r2(X16,X15) )
& X15 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplusyeqthree) ).
fof(f139,plain,
! [X0] :
( sP22(sK15(X0))
| ~ sP21(X0) ),
inference(resolution,[],[f114,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUN081+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 10:01:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.55 % (1202)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.56 % (1206)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.56 TRYING [1]
% 0.20/0.57 % (1210)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)
% 0.20/0.57 TRYING [2]
% 0.20/0.57 TRYING [3]
% 1.46/0.57 % (1206)First to succeed.
% 1.46/0.57 % (1197)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.46/0.57 TRYING [4]
% 1.46/0.57 % (1218)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)
% 1.46/0.57 % (1198)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.46/0.58 % (1206)Refutation found. Thanks to Tanya!
% 1.46/0.58 % SZS status Theorem for theBenchmark
% 1.46/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.46/0.58 % (1206)------------------------------
% 1.46/0.58 % (1206)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.46/0.58 % (1206)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.46/0.58 % (1206)Termination reason: Refutation
% 1.46/0.58
% 1.46/0.58 % (1206)Memory used [KB]: 5500
% 1.46/0.58 % (1206)Time elapsed: 0.142 s
% 1.46/0.58 % (1206)Instructions burned: 5 (million)
% 1.46/0.58 % (1206)------------------------------
% 1.46/0.58 % (1206)------------------------------
% 1.46/0.58 % (1195)Success in time 0.221 s
%------------------------------------------------------------------------------