%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM520+3 : 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 : n013.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 12:15:34 PM UTC 2026
% Result : ContradictoryAxioms 2.73s 1.35s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 10 unt; 3 def)
% Number of atoms : 40 ( 13 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 18 ~; 10 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 2 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
fof(f47,axiom,
~ ( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).
fof(f126,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f127,plain,
( sz00 = xk
| sz10 = xk ),
inference(ennf_transformation,[],[f47]) ).
fof(f267,plain,
sz10 != xk,
inference(cnf_transformation,[],[f126]) ).
fof(f268,plain,
sz00 != xk,
inference(cnf_transformation,[],[f126]) ).
fof(f269,plain,
( sz00 = xk
| sz10 = xk ),
inference(cnf_transformation,[],[f127]) ).
fof(f286,definition,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ13_eqProxy])],[equality_proxy_definition]) ).
fof(f361,plain,
~ sQ13_eqProxy(sz00,xk),
inference(equality_proxy_replacement,[],[f268,f286]) ).
fof(f362,plain,
~ sQ13_eqProxy(sz10,xk),
inference(equality_proxy_replacement,[],[f267,f286]) ).
fof(f363,plain,
( sQ13_eqProxy(sz00,xk)
| sQ13_eqProxy(sz10,xk) ),
inference(equality_proxy_replacement,[],[f269,f286,f286]) ).
fof(f370,definition,
( spl14_1
<=> sQ13_eqProxy(sz10,xk) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f371,plain,
( sQ13_eqProxy(sz10,xk)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f373,definition,
( spl14_2
<=> sQ13_eqProxy(sz00,xk) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f374,plain,
( sQ13_eqProxy(sz00,xk)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f375,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f363,f373,f370]) ).
fof(f399,plain,
( $false
| ~ spl14_2 ),
inference(resolution,[],[f361,f374]) ).
fof(f400,plain,
~ spl14_2,
inference(avatar_contradiction_clause,[],[f399]) ).
fof(f401,plain,
( $false
| ~ spl14_1 ),
inference(resolution,[],[f362,f371]) ).
fof(f402,plain,
~ spl14_1,
inference(avatar_contradiction_clause,[],[f401]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f375]) ).
cnf(s6,plain,
~ spl14_2,
inference(sat_conversion,[],[f400]) ).
cnf(s7,plain,
~ spl14_1,
inference(sat_conversion,[],[f402]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s6,s7]) ).
fof(f403,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM520+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:18:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.73/1.35 % (523642)Detected formulas, will run a generic FOF schedule.
% 2.73/1.35 % (523653)dis-21_1_sil=8000:lcm=predicate:random_seed=2730585550: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)
% 2.73/1.35 % (523653)First to succeed.
% 2.73/1.35 % (523653)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-523642"
% 2.73/1.35 % (523649)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=2042253093:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.35 % (523647)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=2844654571:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.35 % (523650)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2401812217:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.35 % (523651)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2662382733:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.35 % (523648)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=694613396:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.35 % (523652)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1072762116:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.35 % (523651)Also succeeded, but the first one will report.
% 2.73/1.35 % (523652)Also succeeded, but the first one will report.
% 2.73/1.35 % (523650)Also succeeded, but the first one will report.
% 2.73/1.35 % (523653)Refutation found. Thanks to Tanya!
% 2.73/1.35 % SZS status ContradictoryAxioms for theBenchmark
% 2.73/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.35 % (523653)------------------------------
% 2.73/1.35 % (523653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.35 % (523653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.35 % (523653)CaDiCaL version: 2.1.3
% 2.73/1.35 % (523653)Termination reason: Refutation
% 2.73/1.35 % (523653)Time elapsed: 0.003 s
% 2.73/1.35 % (523653)Peak memory usage: 89 MB
% 2.73/1.35 % (523653)Instructions burned: 6 (million)
% 2.73/1.35 % (523653)------------------------------
% 2.73/1.35 % (523653)------------------------------
% 2.73/1.35 % (523642)Success in time 0.303 s
% 2.73/1.35 % Vampire exiting
%------------------------------------------------------------------------------