%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:15:49 PM UTC 2026
% Result : Theorem 3.48s 1.46s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 50 ( 16 unt; 6 def)
% Number of atoms : 123 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 132 ( 59 ~; 47 |; 11 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f84,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3856) ).
fof(f85,axiom,
( xi != xj
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
file('/export/starexec/sandbox/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/sandbox/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(f201,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(ennf_transformation,[],[f85]) ).
fof(f202,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(flattening,[],[f201]) ).
fof(f203,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(f204,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,[],[f203]) ).
fof(f438,plain,
aElementOf0(xj,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f439,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[],[f84]) ).
fof(f440,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| xi = xj ),
inference(cnf_transformation,[],[f202]) ).
fof(f441,plain,
! [X0,X1] :
( szmzizndt0(sdtlpdtrp0(xN,X0)) != szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f443,plain,
xi != xj,
inference(cnf_transformation,[],[f204]) ).
fof(f444,plain,
szmzizndt0(sdtlpdtrp0(xN,xi)) = szmzizndt0(sdtlpdtrp0(xN,xj)),
inference(cnf_transformation,[],[f204]) ).
fof(f482,definition,
! [X0,X1] :
( sQ25_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ25_eqProxy])],[equality_proxy_definition]) ).
fof(f552,plain,
( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| sQ25_eqProxy(xi,xj) ),
inference(equality_proxy_replacement,[],[f440,f482]) ).
fof(f553,plain,
sQ25_eqProxy(szmzizndt0(sdtlpdtrp0(xN,xi)),szmzizndt0(sdtlpdtrp0(xN,xj))),
inference(equality_proxy_replacement,[],[f444,f482]) ).
fof(f554,plain,
~ sQ25_eqProxy(xi,xj),
inference(equality_proxy_replacement,[],[f443,f482]) ).
fof(f555,plain,
! [X0,X1] :
( ~ sQ25_eqProxy(szmzizndt0(sdtlpdtrp0(xN,X0)),szmzizndt0(sdtlpdtrp0(xN,X1)))
| ~ sdtlseqdt0(szszuzczcdt0(X0),X1)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_proxy_replacement,[],[f441,f482]) ).
fof(f557,plain,
! [X0,X1] :
( sQ25_eqProxy(X1,X0)
| ~ sQ25_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f482]) ).
fof(f560,definition,
( spl26_1
<=> sQ25_eqProxy(xi,xj) ),
introduced(definition,[new_symbols(definition,[spl26_1])],[avatar_definition]) ).
fof(f561,plain,
( sQ25_eqProxy(xi,xj)
| ~ spl26_1 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f563,definition,
( spl26_2
<=> sdtlseqdt0(szszuzczcdt0(xi),xj) ),
introduced(definition,[new_symbols(definition,[spl26_2])],[avatar_definition]) ).
fof(f566,definition,
( spl26_3
<=> sdtlseqdt0(szszuzczcdt0(xj),xi) ),
introduced(definition,[new_symbols(definition,[spl26_3])],[avatar_definition]) ).
fof(f568,plain,
( spl26_1
| spl26_2
| spl26_3 ),
inference(avatar_split_clause,[],[f552,f566,f563,f560]) ).
fof(f580,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szNzAzT0)
| ~ aElementOf0(xj,szNzAzT0) ),
inference(resolution,[],[f555,f553]) ).
fof(f582,definition,
( spl26_7
<=> aElementOf0(xj,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl26_7])],[avatar_definition]) ).
fof(f583,plain,
( ~ aElementOf0(xj,szNzAzT0)
| spl26_7 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f585,definition,
( spl26_8
<=> aElementOf0(xi,szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl26_8])],[avatar_definition]) ).
fof(f586,plain,
( ~ aElementOf0(xi,szNzAzT0)
| spl26_8 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f588,plain,
( ~ spl26_7
| ~ spl26_8
| ~ spl26_2 ),
inference(avatar_split_clause,[],[f580,f563,f585,f582]) ).
fof(f592,plain,
( $false
| spl26_7 ),
inference(resolution,[],[f438,f583]) ).
fof(f593,plain,
spl26_7,
inference(avatar_contradiction_clause,[],[f592]) ).
fof(f598,plain,
( $false
| spl26_8 ),
inference(resolution,[],[f439,f586]) ).
fof(f599,plain,
spl26_8,
inference(avatar_contradiction_clause,[],[f598]) ).
fof(f605,plain,
( $false
| ~ spl26_1 ),
inference(resolution,[],[f561,f554]) ).
fof(f606,plain,
~ spl26_1,
inference(avatar_contradiction_clause,[],[f605]) ).
fof(f631,plain,
! [X0,X1] :
( ~ sQ25_eqProxy(szmzizndt0(sdtlpdtrp0(xN,X0)),szmzizndt0(sdtlpdtrp0(xN,X1)))
| ~ sdtlseqdt0(szszuzczcdt0(X1),X0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f557,f555]) ).
fof(f635,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[],[f631,f553]) ).
fof(f640,plain,
( ~ spl26_8
| ~ spl26_7
| ~ spl26_3 ),
inference(avatar_split_clause,[],[f635,f566,f582,f585]) ).
cnf(s1,plain,
( spl26_1
| spl26_2
| spl26_3 ),
inference(sat_conversion,[],[f568]) ).
cnf(s4,plain,
( ~ spl26_2
| ~ spl26_7
| ~ spl26_8 ),
inference(sat_conversion,[],[f588]) ).
cnf(s6,plain,
spl26_7,
inference(sat_conversion,[],[f593]) ).
cnf(s8,plain,
spl26_8,
inference(sat_conversion,[],[f599]) ).
cnf(s10,plain,
~ spl26_1,
inference(sat_conversion,[],[f606]) ).
cnf(s13,plain,
( ~ spl26_3
| ~ spl26_7
| ~ spl26_8 ),
inference(sat_conversion,[],[f640]) ).
cnf(s15,plain,
~ spl26_3,
inference(rat,[],[s13,s8,s6]) ).
cnf(s16,plain,
~ spl26_2,
inference(rat,[],[s4,s8,s6]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s15,s16,s10]) ).
fof(f641,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM578+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:35:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.46 % (1580052)Detected formulas, will run a generic FOF schedule.
% 3.48/1.46 % (1580057)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=781702851:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.46 % (1580063)dis-21_1_sil=8000:lcm=predicate:random_seed=2979995730:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.48/1.46 % (1580061)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2849688010:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.46 % (1580058)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1215242437:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.46 % (1580060)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1459287030:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.46 % (1580059)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3091613493:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.46 % (1580062)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3456058710:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.46 % (1580063)First to succeed.
% 3.48/1.46 % (1580063)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1580052"
% 3.48/1.46 % (1580062)Also succeeded, but the first one will report.
% 3.48/1.46 % (1580061)Also succeeded, but the first one will report.
% 3.48/1.46 % (1580060)Also succeeded, but the first one will report.
% 3.48/1.46 % (1580063)Refutation found. Thanks to Tanya!
% 3.48/1.46 % SZS status Theorem for theBenchmark
% 3.48/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.46 % (1580063)------------------------------
% 3.48/1.46 % (1580063)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.46 % (1580063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.46 % (1580063)CaDiCaL version: 2.1.3
% 3.48/1.46 % (1580063)Termination reason: Refutation
% 3.48/1.46 % (1580063)Time elapsed: 0.008 s
% 3.48/1.46 % (1580063)Peak memory usage: 89 MB
% 3.48/1.46 % (1580063)Instructions burned: 11 (million)
% 3.48/1.46 % (1580063)------------------------------
% 3.48/1.46 % (1580063)------------------------------
% 3.48/1.46 % (1580052)Success in time 0.413 s
% 3.48/1.46 % Vampire exiting
%------------------------------------------------------------------------------