TSTP Solution File: NUM500+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n023.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 18:00:08 EDT 2022
% Result : Theorem 1.66s 0.61s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 219 ( 80 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 247 ( 76 ~; 75 |; 88 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 31 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f652,plain,
$false,
inference(subsumption_resolution,[],[f651,f519]) ).
fof(f519,plain,
isPrime0(sK8(xk)),
inference(subsumption_resolution,[],[f518,f388]) ).
fof(f388,plain,
~ sQ16_eqProxy(sz00,xk),
inference(equality_proxy_replacement,[],[f274,f350]) ).
fof(f350,plain,
! [X0,X1] :
( sQ16_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ16_eqProxy])]) ).
fof(f274,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
( sz00 != xk
& sz10 != xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(f518,plain,
( isPrime0(sK8(xk))
| sQ16_eqProxy(sz00,xk) ),
inference(subsumption_resolution,[],[f504,f225]) ).
fof(f225,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
& aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f504,plain,
( ~ aNaturalNumber0(xk)
| sQ16_eqProxy(sz00,xk)
| isPrime0(sK8(xk)) ),
inference(resolution,[],[f352,f399]) ).
fof(f399,plain,
! [X0] :
( sQ16_eqProxy(sz10,X0)
| ~ aNaturalNumber0(X0)
| isPrime0(sK8(X0))
| sQ16_eqProxy(sz00,X0) ),
inference(equality_proxy_replacement,[],[f287,f350,f350]) ).
fof(f287,plain,
! [X0] :
( isPrime0(sK8(X0))
| sz00 = X0
| sz10 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ( isPrime0(sK8(X0))
& aNaturalNumber0(sK8(X0))
& doDivides0(sK8(X0),X0) )
| sz00 = X0
| sz10 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f147,f178]) ).
fof(f178,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( isPrime0(sK8(X0))
& aNaturalNumber0(sK8(X0))
& doDivides0(sK8(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f147,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aNaturalNumber0(X1)
& doDivides0(X1,X0) )
| sz00 = X0
| sz10 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aNaturalNumber0(X1)
& doDivides0(X1,X0) )
| sz00 = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0 ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( sz00 != X0
& aNaturalNumber0(X0)
& sz10 != X0 )
=> ? [X1] :
( isPrime0(X1)
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f352,plain,
~ sQ16_eqProxy(sz10,xk),
inference(equality_proxy_replacement,[],[f219,f350]) ).
fof(f219,plain,
sz10 != xk,
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( sz10 != xk
& sz00 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
~ ( sz00 = xk
| sz10 = xk ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(f651,plain,
~ isPrime0(sK8(xk)),
inference(resolution,[],[f646,f237]) ).
fof(f237,plain,
! [X0] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( sz10 = X0
| sz00 = X0
| ( doDivides0(sK3(X0),X0)
& sK3(X0) != X0
& sz10 != sK3(X0)
& aNaturalNumber0(sK3(X0))
& aNaturalNumber0(sK4(X0))
& sdtasdt0(sK3(X0),sK4(X0)) = X0 ) ) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f156,f158,f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( doDivides0(X1,X0)
& X0 != X1
& sz10 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) )
=> ( doDivides0(sK3(X0),X0)
& sK3(X0) != X0
& sz10 != sK3(X0)
& aNaturalNumber0(sK3(X0))
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(sK3(X0),X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(sK3(X0),X2) = X0 )
=> ( aNaturalNumber0(sK4(X0))
& sdtasdt0(sK3(X0),sK4(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( sz10 = X0
| sz00 = X0
| ? [X1] :
( doDivides0(X1,X0)
& X0 != X1
& sz10 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( sz10 = X0
| sz00 = X0
| ? [X1] :
( doDivides0(X1,X0)
& X0 != X1
& sz10 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f646,plain,
sP0(sK8(xk)),
inference(subsumption_resolution,[],[f633,f523]) ).
fof(f523,plain,
aNaturalNumber0(sK8(xk)),
inference(subsumption_resolution,[],[f522,f225]) ).
fof(f522,plain,
( aNaturalNumber0(sK8(xk))
| ~ aNaturalNumber0(xk) ),
inference(subsumption_resolution,[],[f505,f388]) ).
fof(f505,plain,
( aNaturalNumber0(sK8(xk))
| sQ16_eqProxy(sz00,xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f352,f400]) ).
fof(f400,plain,
! [X0] :
( sQ16_eqProxy(sz10,X0)
| sQ16_eqProxy(sz00,X0)
| aNaturalNumber0(sK8(X0))
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f286,f350,f350]) ).
fof(f286,plain,
! [X0] :
( aNaturalNumber0(sK8(X0))
| sz00 = X0
| sz10 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f633,plain,
( sP0(sK8(xk))
| ~ aNaturalNumber0(sK8(xk)) ),
inference(resolution,[],[f521,f238]) ).
fof(f238,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| sP0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] :
( sP0(X0)
| ( ! [X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1) )
& ~ doDivides0(X0,xk) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f149]) ).
fof(f149,plain,
! [X0] :
( sP0(X0)
| ( ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) )
& ~ doDivides0(X0,xk) )
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f120,f148]) ).
fof(f120,plain,
! [X0] :
( ( ~ isPrime0(X0)
& ( sz10 = X0
| sz00 = X0
| ? [X1] :
( doDivides0(X1,X0)
& X0 != X1
& sz10 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) )
| ( ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) )
& ~ doDivides0(X0,xk) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ( ( sz00 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& doDivides0(X1,X0)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X1) )
| sz10 = X0 )
& ~ isPrime0(X0) )
| ( ! [X3] :
( xk != sdtasdt0(X0,X3)
| ~ aNaturalNumber0(X3) )
& ~ doDivides0(X0,xk) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
~ ? [X0] :
( ( ( sz00 != X0
& ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X1) )
=> ( sz10 = X1
| X0 = X1 ) )
& sz10 != X0 )
| isPrime0(X0) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& xk = sdtasdt0(X0,X3) )
| doDivides0(X0,xk) )
& aNaturalNumber0(X0) ),
inference(rectify,[],[f49]) ).
fof(f49,negated_conjecture,
~ ? [X0] :
( aNaturalNumber0(X0)
& ( ( sz00 != X0
& ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X1) )
=> ( sz10 = X1
| X0 = X1 ) )
& sz10 != X0 )
| isPrime0(X0) )
& ( ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) )
| doDivides0(X0,xk) ) ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
? [X0] :
( aNaturalNumber0(X0)
& ( ( sz00 != X0
& ! [X1] :
( ( doDivides0(X1,X0)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& aNaturalNumber0(X1) )
=> ( sz10 = X1
| X0 = X1 ) )
& sz10 != X0 )
| isPrime0(X0) )
& ( ? [X1] :
( sdtasdt0(X0,X1) = xk
& aNaturalNumber0(X1) )
| doDivides0(X0,xk) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f521,plain,
doDivides0(sK8(xk),xk),
inference(subsumption_resolution,[],[f520,f388]) ).
fof(f520,plain,
( doDivides0(sK8(xk),xk)
| sQ16_eqProxy(sz00,xk) ),
inference(subsumption_resolution,[],[f506,f225]) ).
fof(f506,plain,
( ~ aNaturalNumber0(xk)
| doDivides0(sK8(xk),xk)
| sQ16_eqProxy(sz00,xk) ),
inference(resolution,[],[f352,f401]) ).
fof(f401,plain,
! [X0] :
( sQ16_eqProxy(sz10,X0)
| ~ aNaturalNumber0(X0)
| sQ16_eqProxy(sz00,X0)
| doDivides0(sK8(X0),X0) ),
inference(equality_proxy_replacement,[],[f285,f350,f350]) ).
fof(f285,plain,
! [X0] :
( doDivides0(sK8(X0),X0)
| sz00 = X0
| sz10 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM500+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n023.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 07:08:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.56 % (17485)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.56 % (17508)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.56 % (17500)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.57 % (17491)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.57 % (17495)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.58 % (17503)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.58 % (17500)Instruction limit reached!
% 0.19/0.58 % (17500)------------------------------
% 0.19/0.58 % (17500)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59 % (17500)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59 % (17500)Termination reason: Unknown
% 0.19/0.59 % (17500)Termination phase: Naming
% 0.19/0.59 % (17497)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.59
% 0.19/0.59 % (17500)Memory used [KB]: 1535
% 0.19/0.59 % (17500)Time elapsed: 0.005 s
% 0.19/0.59 % (17500)Instructions burned: 3 (million)
% 0.19/0.59 % (17500)------------------------------
% 0.19/0.59 % (17500)------------------------------
% 0.19/0.59 % (17482)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.59 % (17497)Instruction limit reached!
% 0.19/0.59 % (17497)------------------------------
% 0.19/0.59 % (17497)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.59 % (17497)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.59 % (17497)Termination reason: Unknown
% 0.19/0.59 % (17497)Termination phase: Property scanning
% 0.19/0.59
% 0.19/0.59 % (17497)Memory used [KB]: 1535
% 0.19/0.59 % (17497)Time elapsed: 0.004 s
% 0.19/0.59 % (17497)Instructions burned: 4 (million)
% 0.19/0.59 % (17497)------------------------------
% 0.19/0.59 % (17497)------------------------------
% 1.66/0.60 % (17486)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.66/0.60 % (17487)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.66/0.60 % (17483)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.66/0.60 % (17488)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.66/0.60 % (17502)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.66/0.61 % (17495)First to succeed.
% 1.66/0.61 % (17506)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.66/0.61 % (17495)Refutation found. Thanks to Tanya!
% 1.66/0.61 % SZS status Theorem for theBenchmark
% 1.66/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.66/0.61 % (17495)------------------------------
% 1.66/0.61 % (17495)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.66/0.61 % (17495)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.66/0.61 % (17495)Termination reason: Refutation
% 1.66/0.61
% 1.66/0.61 % (17495)Memory used [KB]: 1918
% 1.66/0.61 % (17495)Time elapsed: 0.164 s
% 1.66/0.61 % (17495)Instructions burned: 14 (million)
% 1.66/0.61 % (17495)------------------------------
% 1.66/0.61 % (17495)------------------------------
% 1.66/0.61 % (17481)Success in time 0.252 s
%------------------------------------------------------------------------------