%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM457+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 : n020.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 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 82 ( 49 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 94 ( 40 ~; 37 |; 10 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f17,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__624) ).
fof(f18,conjecture,
( sdtasdt0(xm,xn) = sz00
=> ( xm = sz00
| xn = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
~ ( sdtasdt0(xm,xn) = sz00
=> ( xm = sz00
| xn = sz00 ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f35,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f40,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f41,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f40]) ).
fof(f44,plain,
( sz00 != xm
& sz00 != xn
& sdtasdt0(xm,xn) = sz00 ),
inference(ennf_transformation,[],[f19]) ).
fof(f45,plain,
( sz00 != xm
& sz00 != xn
& sdtasdt0(xm,xn) = sz00 ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f59,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f69,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f17]) ).
fof(f70,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f17]) ).
fof(f71,plain,
sz00 = sdtasdt0(xm,xn),
inference(cnf_transformation,[],[f45]) ).
fof(f72,plain,
sz00 != xn,
inference(cnf_transformation,[],[f45]) ).
fof(f73,plain,
sz00 != xm,
inference(cnf_transformation,[],[f45]) ).
fof(f93,plain,
sz00 = sdtasdt0(sz00,xn),
inference(resolution,[],[f59,f69]) ).
fof(f143,plain,
! [X0] :
( sz00 != sdtasdt0(X0,xn)
| sz00 = xn
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| xm = X0 ),
inference(superposition,[],[f65,f71]) ).
fof(f146,plain,
! [X0] :
( sz00 != sdtasdt0(X0,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| xm = X0 ),
inference(forward_subsumption_resolution,[],[f143,f72]) ).
fof(f148,plain,
! [X0] :
( sz00 != sdtasdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| xm = X0 ),
inference(forward_subsumption_resolution,[],[f146,f70]) ).
fof(f150,plain,
! [X0] :
( sz00 != sdtasdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| xm = X0 ),
inference(forward_subsumption_resolution,[],[f148,f69]) ).
fof(f236,plain,
( sz00 != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = xm ),
inference(superposition,[],[f150,f93]) ).
fof(f239,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = xm ),
inference(trivial_inequality_removal,[],[f236]) ).
fof(f242,plain,
sz00 = xm,
inference(forward_subsumption_resolution,[],[f239,f46]) ).
fof(f245,plain,
$false,
inference(forward_subsumption_resolution,[],[f242,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM457+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n020.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 20:01:04 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
% 0.11/0.41 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
% 0.11/0.45 % (3708621)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (3708626)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4051773445_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (3708629)dis+10_1_sil=32000:sp=arity:random_seed=3975371767:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (3708628)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=206327152:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (3708630)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=253527181:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (3708631)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3205409664:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (3708632)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1740697692:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (3708627)% WARNING: option uhcvi not known.
% 0.11/0.45 % TRYING [1]
% 0.11/0.45 % TRYING [2]
% 0.11/0.45 % (3708627)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2437399042:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % TRYING [3]
% 0.11/0.45 % (3708627) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3708621-3708627"...
% 0.11/0.45 % (3708629) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3708621-3708629"...
% 0.11/0.45 % (3708627)...printing done.
% 0.11/0.45 % (3708629)...printing done.
% 0.11/0.45 % (3708627)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3708627)------------------------------
% 0.11/0.45 % (3708627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3708627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3708627)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3708627)Termination reason: Refutation
% 0.11/0.45 % (3708627)Time elapsed: 0.003 s
% 0.11/0.45 % (3708627)Peak memory usage: 12 MB
% 0.11/0.45 % (3708627)Instructions burned: 9 (million)
% 0.11/0.45 % (3708621)Success in time 0.037 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------