%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:23 PM UTC 2026
% Result : Theorem 2.54s 1.34s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 1 def)
% Number of atoms : 201 ( 83 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 254 ( 81 ~; 75 |; 88 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 35 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(f41,conjecture,
( ( ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) ) )
=> ( X0 = sz10
| X0 = xk ) )
& isPrime0(xk) )
=> ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) )
| isPrime0(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f42,negated_conjecture,
~ ( ( ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) ) )
=> ( X0 = sz10
| X0 = xk ) )
& isPrime0(xk) )
=> ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) )
| isPrime0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f44,plain,
~ ( ( ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) ) )
=> ( X0 = sz10
| X0 = xk ) )
& isPrime0(xk) )
=> ? [X2] :
( aNaturalNumber0(X2)
& ( ? [X3] :
( aNaturalNumber0(X3)
& xk = sdtasdt0(X2,X3) )
| doDivides0(X2,xk) )
& ( ( sz00 != X2
& sz10 != X2
& ! [X4] :
( ( aNaturalNumber0(X4)
& ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X4,X5) = X2 )
& doDivides0(X4,X2) )
=> ( sz10 = X4
| X2 = X4 ) ) )
| isPrime0(X2) ) ) ),
inference(rectify,[],[f42]) ).
fof(f49,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| xk != sdtasdt0(X2,X3) )
& ~ doDivides0(X2,xk) )
| ( ( sz00 = X2
| sz10 = X2
| ? [X4] :
( sz10 != X4
& X2 != X4
& aNaturalNumber0(X4)
& ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X4,X5) = X2 )
& doDivides0(X4,X2) ) )
& ~ isPrime0(X2) ) )
& ! [X0] :
( X0 = sz10
| X0 = xk
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) ) )
& isPrime0(xk) ),
inference(ennf_transformation,[],[f44]) ).
fof(f50,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| xk != sdtasdt0(X2,X3) )
& ~ doDivides0(X2,xk) )
| ( ( sz00 = X2
| sz10 = X2
| ? [X4] :
( sz10 != X4
& X2 != X4
& aNaturalNumber0(X4)
& ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X4,X5) = X2 )
& doDivides0(X4,X2) ) )
& ~ isPrime0(X2) ) )
& ! [X0] :
( X0 = sz10
| X0 = xk
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) ) )
& isPrime0(xk) ),
inference(flattening,[],[f49]) ).
fof(f53,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f109,definition,
! [X2] :
( ( ( sz00 = X2
| sz10 = X2
| ? [X4] :
( sz10 != X4
& X2 != X4
& aNaturalNumber0(X4)
& ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X4,X5) = X2 )
& doDivides0(X4,X2) ) )
& ~ isPrime0(X2) )
| ~ sP1(X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f110,plain,
( ! [X2] :
( ~ aNaturalNumber0(X2)
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| xk != sdtasdt0(X2,X3) )
& ~ doDivides0(X2,xk) )
| sP1(X2) )
& ! [X0] :
( X0 = sz10
| X0 = xk
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) ) )
& isPrime0(xk) ),
inference(definition_folding,[],[f50,f109]) ).
fof(f114,plain,
! [X2] :
( ( ( sz00 = X2
| sz10 = X2
| ? [X4] :
( sz10 != X4
& X2 != X4
& aNaturalNumber0(X4)
& ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X4,X5) = X2 )
& doDivides0(X4,X2) ) )
& ~ isPrime0(X2) )
| ~ sP1(X2) ),
inference(nnf_transformation,[],[f109]) ).
fof(f115,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK4(X0)
& sK4(X0) != X0
& aNaturalNumber0(sK4(X0))
& aNaturalNumber0(sK5(X0))
& sdtasdt0(sK4(X0),sK5(X0)) = X0
& doDivides0(sK4(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0))],[f115]) ).
fof(f117,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| sP1(X0) )
& ! [X2] :
( sz10 = X2
| xk = X2
| ~ aNaturalNumber0(X2)
| ( ! [X3] :
( ~ aNaturalNumber0(X3)
| xk != sdtasdt0(X2,X3) )
& ~ doDivides0(X2,xk) ) )
& isPrime0(xk) ),
inference(rectify,[],[f110]) ).
fof(f128,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f141,plain,
! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f148,plain,
isPrime0(xk),
inference(cnf_transformation,[],[f117]) ).
fof(f152,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f157,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f159,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f228,plain,
! [X0] :
( xk != X0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| sP1(X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f152,f157]) ).
fof(f229,plain,
! [X0] :
( xk != X0
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(duplicate_literal_removal,[],[f228]) ).
fof(f231,plain,
! [X0] :
( xk != X0
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(forward_subsumption_resolution,[],[f229,f159]) ).
fof(f232,plain,
( ~ aNaturalNumber0(xk)
| sP1(xk) ),
inference(equality_resolution,[],[f231]) ).
fof(f233,plain,
sP1(xk),
inference(forward_subsumption_resolution,[],[f232,f128]) ).
fof(f238,plain,
~ isPrime0(xk),
inference(resolution,[],[f233,f141]) ).
fof(f239,plain,
$false,
inference(forward_subsumption_resolution,[],[f238,f148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n016.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Sun Sep 27 20:11:33 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.54/1.34 % (2960840)Detected formulas, will run a generic FOF schedule.
% 2.54/1.34 % (2960849)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3852661051:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.34 % (2960849)First to succeed.
% 2.54/1.34 % (2960849)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2960840"
% 2.54/1.34 % (2960850)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3229359834:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.34 % (2960850)Also succeeded, but the first one will report.
% 2.54/1.34 % (2960848)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=647456044:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.34 % (2960847)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1930837969:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.34 % (2960846)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3154413716:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.34 % (2960845)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3645025903:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.34 % (2960848)Also succeeded, but the first one will report.
% 2.54/1.34 % (2960851)dis-21_1_sil=8000:lcm=predicate:random_seed=893081698:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.54/1.34 % (2960851)Also succeeded, but the first one will report.
% 2.54/1.34 % (2960849)Refutation found. Thanks to Tanya!
% 2.54/1.34 % SZS status Theorem for theBenchmark
% 2.54/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.34 % (2960849)------------------------------
% 2.54/1.34 % (2960849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.34 % (2960849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.34 % (2960849)CaDiCaL version: 2.1.3
% 2.54/1.34 % (2960849)Termination reason: Refutation
% 2.54/1.34 % (2960849)Time elapsed: 0.002 s
% 2.54/1.34 % (2960849)Peak memory usage: 88 MB
% 2.54/1.34 % (2960849)Instructions burned: 5 (million)
% 2.54/1.34 % (2960849)------------------------------
% 2.54/1.34 % (2960849)------------------------------
% 2.54/1.34 % (2960840)Success in time 0.275 s
% 2.54/1.34 % Vampire exiting
%------------------------------------------------------------------------------