%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM482+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 : n007.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 12:24:29 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 11 unt; 2 def)
% Number of atoms : 211 ( 82 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 259 ( 84 ~; 76 |; 88 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 32 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox/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/sandbox/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(f46,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(f60,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f111,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,[],[f46]) ).
fof(f112,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,[],[f111]) ).
fof(f115,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(f116,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,[],[f112,f115]) ).
fof(f134,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,[],[f115]) ).
fof(f135,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,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK7(X0)
& sK7(X0) != X0
& aNaturalNumber0(sK7(X0))
& aNaturalNumber0(sK8(X0))
& sdtasdt0(sK7(X0),sK8(X0)) = X0
& doDivides0(sK7(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f135]) ).
fof(f137,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,[],[f116]) ).
fof(f140,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f150,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f203,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f216,plain,
! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f223,plain,
isPrime0(xk),
inference(cnf_transformation,[],[f137]) ).
fof(f227,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) != xk
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f243,definition,
( spl9_1
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f244,plain,
( aNaturalNumber0(sz10)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f260,plain,
spl9_1,
inference(avatar_split_clause,[],[f140,f243]) ).
fof(f271,plain,
xk = sdtasdt0(xk,sz10),
inference(resolution,[],[f150,f203]) ).
fof(f285,plain,
( xk != xk
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sP1(xk) ),
inference(superposition,[],[f227,f271]) ).
fof(f286,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xk)
| sP1(xk) ),
inference(trivial_inequality_removal,[],[f285]) ).
fof(f287,plain,
( ~ aNaturalNumber0(xk)
| sP1(xk)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f286,f244]) ).
fof(f288,plain,
( sP1(xk)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f287,f203]) ).
fof(f297,plain,
( ~ isPrime0(xk)
| ~ spl9_1 ),
inference(resolution,[],[f288,f216]) ).
fof(f298,plain,
( $false
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f297,f223]) ).
fof(f299,plain,
~ spl9_1,
inference(avatar_contradiction_clause,[],[f298]) ).
cnf(s3,plain,
spl9_1,
inference(sat_conversion,[],[f260]) ).
cnf(s5,plain,
~ spl9_1,
inference(sat_conversion,[],[f299]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s5]) ).
fof(f300,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 20:05:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (1748038)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1748046)dis+10_1_sil=32000:sp=arity:random_seed=627473154:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (1748046) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1748038-1748046"...
% 0.10/0.45 % (1748044)% WARNING: option uhcvi not known.
% 0.10/0.45 % (1748046)...printing done.
% 0.10/0.45 % (1748046)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1748046)------------------------------
% 0.10/0.45 % (1748046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1748046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1748046)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1748046)Termination reason: Refutation
% 0.10/0.45 % (1748046)Time elapsed: 0.003 s
% 0.10/0.45 % (1748046)Peak memory usage: 12 MB
% 0.10/0.45 % (1748046)Instructions burned: 6 (million)
% 0.10/0.45 % (1748038)Success in time 0.042 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------