%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:24:33 PM UTC 2026
% Result : Theorem 0.31s 0.46s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 7 unt; 1 def)
% Number of atoms : 184 ( 85 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 213 ( 64 ~; 69 |; 76 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 44 ( 22 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f38,axiom,
! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f46,axiom,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(f48,conjecture,
? [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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ? [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)],[f48]) ).
fof(f55,plain,
~ ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) )
=> ( sz10 = X2
| X0 = X2 ) ) )
| isPrime0(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f118,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(ennf_transformation,[],[f38]) ).
fof(f119,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(flattening,[],[f118]) ).
fof(f126,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f127,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f128,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) ) ),
inference(flattening,[],[f127]) ).
fof(f132,definition,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| sP2(X0) ),
inference(definition_folding,[],[f128,f132]) ).
fof(f148,plain,
! [X0] :
( ( aNaturalNumber0(sK6(X0))
& doDivides0(sK6(X0),X0)
& isPrime0(sK6(X0)) )
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f119]) ).
fof(f159,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f132]) ).
fof(f160,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) )
| ~ sP2(X0) ),
inference(rectify,[],[f159]) ).
fof(f161,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK14(X0)
& sK14(X0) != X0
& aNaturalNumber0(sK14(X0))
& aNaturalNumber0(sK15(X0))
& sdtasdt0(sK14(X0),sK15(X0)) = X0
& doDivides0(sK14(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP2(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0))],[f160]) ).
fof(f227,plain,
! [X0] :
( isPrime0(sK6(X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f228,plain,
! [X0] :
( doDivides0(sK6(X0),X0)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f229,plain,
! [X0] :
( aNaturalNumber0(sK6(X0))
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f271,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f272,plain,
sz10 != xk,
inference(cnf_transformation,[],[f126]) ).
fof(f273,plain,
sz00 != xk,
inference(cnf_transformation,[],[f126]) ).
fof(f276,plain,
! [X0] :
( ~ sP2(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f283,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f666,plain,
( ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk
| ~ aNaturalNumber0(sK6(xk))
| sP2(sK6(xk)) ),
inference(resolution,[],[f228,f283]) ).
fof(f669,plain,
( ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk
| sP2(sK6(xk)) ),
inference(forward_subsumption_resolution,[],[f666,f229]) ).
fof(f671,plain,
( sz00 = xk
| sz10 = xk
| sP2(sK6(xk)) ),
inference(forward_subsumption_resolution,[],[f669,f271]) ).
fof(f673,plain,
( sz10 = xk
| sP2(sK6(xk)) ),
inference(forward_subsumption_resolution,[],[f671,f273]) ).
fof(f675,plain,
sP2(sK6(xk)),
inference(forward_subsumption_resolution,[],[f673,f272]) ).
fof(f685,plain,
~ isPrime0(sK6(xk)),
inference(resolution,[],[f675,f276]) ).
fof(f716,plain,
( ~ aNaturalNumber0(xk)
| sz00 = xk
| sz10 = xk ),
inference(resolution,[],[f685,f227]) ).
fof(f717,plain,
( sz00 = xk
| sz10 = xk ),
inference(forward_subsumption_resolution,[],[f716,f271]) ).
fof(f718,plain,
sz10 = xk,
inference(forward_subsumption_resolution,[],[f717,f273]) ).
fof(f719,plain,
$false,
inference(forward_subsumption_resolution,[],[f718,f272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM500+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n008.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:14:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.46 % (1570802)Will run a generic schedule for satisfiability detection.
% 0.31/0.46 % (1570812)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=431519163:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.46 % (1570808)% WARNING: option uhcvi not known.
% 0.31/0.46 % (1570807)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1754338803_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.46 % (1570813)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3317009506:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.46 % (1570808)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2949752385:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.46 % (1570809)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3057794158:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.46 % (1570810)dis+10_1_sil=32000:sp=arity:random_seed=183688651:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.46 % (1570811)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3917271770:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.46 % Detected minimum model sizes of [3]
% 0.31/0.46 % Detected maximum model sizes of [max]
% 0.31/0.46 % TRYING [3]
% 0.31/0.46 % (1570810) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1570802-1570810"...
% 0.31/0.46 % (1570810)...printing done.
% 0.31/0.46 % (1570810)Refutation found. Thanks to Tanya!
% 0.31/0.46 % SZS status Theorem for theBenchmark
% 0.31/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.46 % (1570810)------------------------------
% 0.31/0.46 % (1570810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.46 % (1570810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.46 % (1570810)CaDiCaL version: 2.1.3
% 0.31/0.46 % (1570810)Termination reason: Refutation
% 0.31/0.46 % (1570810)Time elapsed: 0.013 s
% 0.31/0.46 % (1570810)Peak memory usage: 12 MB
% 0.31/0.46 % (1570810)Instructions burned: 19 (million)
% 0.31/0.46 % (1570802)Success in time 0.05 s
% 0.31/0.46 % Vampire exiting
%------------------------------------------------------------------------------