%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:24:53 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 : 35 ( 10 unt; 2 def)
% Number of atoms : 92 ( 25 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 106 ( 49 ~; 35 |; 11 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f84,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3856) ).
fof(f85,axiom,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3856_02) ).
fof(f86,conjecture,
( ! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X0),X1)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( xi != xj
=> szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f87,negated_conjecture,
~ ( ! [X0,X1] :
( ( aElementOf0(X0,szNzAzT0)
& aElementOf0(X1,szNzAzT0) )
=> ( sdtlseqdt0(szszuzczcdt0(X0),X1)
=> ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X0)) ) ) )
=> ( xi != xj
=> szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj)) ) ),
inference(negated_conjecture,[status(cth)],[f86]) ).
fof(f205,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(ennf_transformation,[],[f85]) ).
fof(f206,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(flattening,[],[f205]) ).
fof(f207,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [X0,X1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(ennf_transformation,[],[f87]) ).
fof(f208,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj))
& xi != xj
& ! [X0,X1] :
( ( aSubsetOf0(sdtlpdtrp0(xN,X1),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& szmzizndt0(sdtlpdtrp0(xN,X1)) != szmzizndt0(sdtlpdtrp0(xN,X0)) )
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ) ),
inference(flattening,[],[f207]) ).
fof(f370,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f371,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f372,plain,
( xi = xj
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ),
inference(cnf_transformation,[],[f206]) ).
fof(f373,plain,
! [X0,X1] :
( ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f208]) ).
fof(f375,plain,
xi != xj,
inference(cnf_transformation,[],[f208]) ).
fof(f376,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f208]) ).
fof(f424,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi) ),
inference(forward_subsumption_resolution,[],[f372,f375]) ).
fof(f443,definition,
( spl21_4
<=> sdtlseqdt0(szszuzczcdt0(xj),xi) ),
introduced(definition,[new_symbols(definition,[spl21_4])],[avatar_definition]) ).
fof(f445,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f447,definition,
( spl21_5
<=> sdtlseqdt0(szszuzczcdt0(xi),xj) ),
introduced(definition,[new_symbols(definition,[spl21_5])],[avatar_definition]) ).
fof(f449,plain,
( sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f450,plain,
( spl21_4
| spl21_5 ),
inference(avatar_split_clause,[],[f424,f447,f443]) ).
fof(f453,plain,
( ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ spl21_5 ),
inference(resolution,[],[f373,f449]) ).
fof(f454,plain,
( ~ aElementOf0(xj,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f453,f371]) ).
fof(f455,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f454,f370]) ).
fof(f456,plain,
( $false
| ~ spl21_5 ),
inference(forward_subsumption_resolution,[],[f455,f376]) ).
fof(f457,plain,
~ spl21_5,
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f458,plain,
( ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ spl21_4 ),
inference(resolution,[],[f445,f373]) ).
fof(f459,plain,
( ~ aElementOf0(xi,szNzAzT0)
| szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ spl21_4 ),
inference(forward_subsumption_resolution,[],[f458,f370]) ).
fof(f460,plain,
( szmzizndt0(sdtlpdtrp0(xN,xi)) != szmzizndt0(sdtlpdtrp0(xN,xj))
| ~ spl21_4 ),
inference(forward_subsumption_resolution,[],[f459,f371]) ).
fof(f461,plain,
( $false
| ~ spl21_4 ),
inference(forward_subsumption_resolution,[],[f460,f376]) ).
fof(f462,plain,
~ spl21_4,
inference(avatar_contradiction_clause,[],[f461]) ).
cnf(s4,plain,
( spl21_4
| spl21_5 ),
inference(sat_conversion,[],[f450]) ).
cnf(s5,plain,
~ spl21_5,
inference(sat_conversion,[],[f457]) ).
cnf(s6,plain,
~ spl21_4,
inference(sat_conversion,[],[f462]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s5,s6]) ).
fof(f463,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n009.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 20:34:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (2376563)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2376572)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=382404374:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2376569)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2376572) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2376563-2376572"...
% 0.11/0.45 % (2376568)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3528557937_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (2376569)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1586019757:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % (2376570)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=671134927:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (2376572)...printing done.
% 0.11/0.45 % (2376571)dis+10_1_sil=32000:sp=arity:random_seed=108708213:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (2376573)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2983572442:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (2376574)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2737232987:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (2376572)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 % (2376572)------------------------------
% 0.11/0.45 % (2376572)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2376572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2376572)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2376572)Termination reason: Refutation
% 0.11/0.45 % (2376572)Time elapsed: 0.006 s
% 0.11/0.45 % (2376572)Peak memory usage: 12 MB
% 0.11/0.45 % (2376572)Instructions burned: 17 (million)
% 0.11/0.45 % (2376563)Success in time 0.038 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------