%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM458+1 : 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 : n015.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 12:24:23 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 87 ( 16 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 102 ( 44 ~; 39 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 33 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f20,axiom,
aNaturalNumber0(xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__718) ).
fof(f21,conjecture,
sdtlseqdt0(xm,xm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ sdtlseqdt0(xm,xm),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
~ sdtlseqdt0(xm,xm),
inference(flattening,[],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f26,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f25]) ).
fof(f33,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f50,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f54,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f55]) ).
fof(f59,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f67,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f89,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f20]) ).
fof(f90,plain,
~ sdtlseqdt0(xm,xm),
inference(cnf_transformation,[],[f24]) ).
fof(f91,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f85]) ).
fof(f113,plain,
xm = sdtpldt0(xm,sz00),
inference(resolution,[],[f67,f89]) ).
fof(f270,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f91,f62]) ).
fof(f323,plain,
( sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f270,f113]) ).
fof(f326,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f323,f90]) ).
fof(f330,plain,
~ aNaturalNumber0(xm),
inference(forward_subsumption_resolution,[],[f326,f59]) ).
fof(f332,plain,
$false,
inference(forward_subsumption_resolution,[],[f330,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM458+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 20:03:46 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 Running first-order model finding
% 0.13/0.38 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
% 0.13/0.42 % (1979004)Will run a generic schedule for satisfiability detection.
% 0.13/0.42 % (1979011)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=957970338:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.42 % (1979010)% WARNING: option uhcvi not known.
% 0.13/0.42 % (1979011) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1979004-1979011"...
% 0.13/0.42 % (1979011)...printing done.
% 0.13/0.42 % (1979011)Refutation found. Thanks to Tanya!
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.42 % (1979011)------------------------------
% 0.13/0.42 % (1979011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.42 % (1979011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.42 % (1979011)CaDiCaL version: 2.1.3
% 0.13/0.42 % (1979011)Termination reason: Refutation
% 0.13/0.42 % (1979011)Time elapsed: 0.004 s
% 0.13/0.42 % (1979011)Peak memory usage: 12 MB
% 0.13/0.42 % (1979011)Instructions burned: 8 (million)
% 0.13/0.42 % (1979004)Success in time 0.028 s
% 0.13/0.42 % Vampire exiting
%------------------------------------------------------------------------------