%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 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 12:24:07 PM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 32 ~; 25 |; 9 &)
% ( 2 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
? [X1] :
! [X2] :
( in(X2,X1)
<=> ( in(X2,X0)
& ordinal(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
fof(f29,axiom,
! [X0] :
~ ! [X1] :
( in(X1,X0)
<=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(f30,conjecture,
! [X0] :
~ ! [X1] :
( ordinal(X1)
=> in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
~ ! [X1] :
( ordinal(X1)
=> in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f56,plain,
! [X0] :
? [X1] :
( in(X1,X0)
<~> ordinal(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f57,plain,
? [X0] :
! [X1] :
( in(X1,X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f75,plain,
! [X0] :
? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& ( ( in(X2,X0)
& ordinal(X2) )
| ~ in(X2,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f76,plain,
! [X0] :
? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& ( ( in(X2,X0)
& ordinal(X2) )
| ~ in(X2,X1) ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X2] :
( ( in(X2,sK14(X0))
| ~ in(X2,X0)
| ~ ordinal(X2) )
& ( ( in(X2,X0)
& ordinal(X2) )
| ~ in(X2,sK14(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f76]) ).
fof(f78,plain,
! [X0] :
? [X1] :
( ( ~ ordinal(X1)
| ~ in(X1,X0) )
& ( ordinal(X1)
| in(X1,X0) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f79,plain,
! [X0] :
( ( ~ ordinal(sK15(X0))
| ~ in(sK15(X0),X0) )
& ( ordinal(sK15(X0))
| in(sK15(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f78]) ).
fof(f80,plain,
! [X1] :
( in(X1,sK16)
| ~ ordinal(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f57]) ).
fof(f135,plain,
! [X2,X0] :
( ~ in(X2,sK14(X0))
| ordinal(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f137,plain,
! [X2,X0] :
( in(X2,sK14(X0))
| ~ in(X2,X0)
| ~ ordinal(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f140,plain,
! [X0] :
( in(sK15(X0),X0)
| ordinal(sK15(X0)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f141,plain,
! [X0] :
( ~ in(sK15(X0),X0)
| ~ ordinal(sK15(X0)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f142,plain,
! [X1] :
( in(X1,sK16)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f214,plain,
! [X0] :
( ordinal(sK15(sK14(X0)))
| ordinal(sK15(sK14(X0))) ),
inference(resolution,[],[f140,f135]) ).
fof(f215,plain,
! [X0] : ordinal(sK15(sK14(X0))),
inference(duplicate_literal_removal,[],[f214]) ).
fof(f232,plain,
! [X0] :
( ~ in(sK15(sK14(X0)),X0)
| ~ ordinal(sK15(sK14(X0)))
| ~ ordinal(sK15(sK14(X0))) ),
inference(resolution,[],[f137,f141]) ).
fof(f233,plain,
! [X0] :
( ~ in(sK15(sK14(X0)),X0)
| ~ ordinal(sK15(sK14(X0))) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f294,plain,
! [X0] : ~ in(sK15(sK14(X0)),X0),
inference(forward_subsumption_resolution,[],[f233,f215]) ).
fof(f295,plain,
~ ordinal(sK15(sK14(sK16))),
inference(resolution,[],[f294,f142]) ).
fof(f298,plain,
$false,
inference(forward_subsumption_resolution,[],[f295,f215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 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 19:47:40 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.11/0.44 % (1554752)Will run a generic schedule for satisfiability detection.
% 0.11/0.44 % (1554760)dis+10_1_sil=32000:sp=arity:random_seed=3922638174:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.44 % (1554760) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1554752-1554760"...
% 0.11/0.44 % (1554760)...printing done.
% 0.11/0.44 % (1554760)Refutation found. Thanks to Tanya!
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.44 % (1554760)------------------------------
% 0.11/0.44 % (1554760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.44 % (1554760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.44 % (1554760)CaDiCaL version: 2.1.3
% 0.11/0.44 % (1554760)Termination reason: Refutation
% 0.11/0.44 % (1554760)Time elapsed: 0.003 s
% 0.11/0.44 % (1554760)Peak memory usage: 12 MB
% 0.11/0.44 % (1554760)Instructions burned: 6 (million)
% 0.11/0.44 % (1554752)Success in time 0.03 s
% 0.11/0.44 % Vampire exiting
%------------------------------------------------------------------------------