%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM568+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:15:46 PM UTC 2026
% Result : Theorem 3.48s 1.47s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 10 unt; 2 def)
% Number of atoms : 55 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 49 ( 19 ~; 23 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 17 ( 12 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3418) ).
fof(f78,axiom,
xK != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3462) ).
fof(f80,conjecture,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xK ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f81,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xK ),
inference(negated_conjecture,[status(cth)],[f80]) ).
fof(f90,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xK ),
inference(ennf_transformation,[],[f81]) ).
fof(f121,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f122,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f121]) ).
fof(f147,plain,
! [X0] :
( X0 = sz00
| ( aElementOf0(sK10(X0),szNzAzT0)
& szszuzczcdt0(sK10(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f122]) ).
fof(f151,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f161,plain,
sz00 != xK,
inference(cnf_transformation,[],[f78]) ).
fof(f163,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xK ),
inference(cnf_transformation,[],[f90]) ).
fof(f205,plain,
! [X0] :
( szszuzczcdt0(sK10(X0)) = X0
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f206,plain,
! [X0] :
( aElementOf0(sK10(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f216,definition,
~ sP11(sz00),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f217,plain,
sP11(xK),
inference(inequality_splitting,[],[f161,f216]) ).
fof(f220,definition,
~ sP13(xK),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f221,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sP13(szszuzczcdt0(X0)) ),
inference(inequality_splitting,[],[f163,f220]) ).
fof(f241,plain,
! [X0] :
( sP13(szszuzczcdt0(sK10(X0)))
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(resolution,[],[f221,f206]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f241,f205]) ).
fof(f245,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sz00 = X0
| sP13(X0) ),
inference(duplicate_literal_removal,[],[f244]) ).
fof(f283,plain,
( sz00 = xK
| sP13(xK) ),
inference(resolution,[],[f151,f245]) ).
fof(f287,plain,
sz00 = xK,
inference(forward_subsumption_resolution,[],[f283,f220]) ).
fof(f317,plain,
sP11(sz00),
inference(superposition,[],[f217,f287]) ).
fof(f319,plain,
$false,
inference(forward_subsumption_resolution,[],[f317,f216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:36:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.48/1.47 % (1989248)Detected formulas, will run a generic FOF schedule.
% 3.48/1.47 % (1989259)dis-21_1_sil=8000:lcm=predicate:random_seed=853178550: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)
% 3.48/1.47 % (1989259)Instruction limit reached!
% 3.48/1.47 % (1989259)------------------------------
% 3.48/1.47 % (1989259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (1989259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (1989259)CaDiCaL version: 2.1.3
% 3.48/1.47 % (1989259)Termination reason: Instruction limit
% 3.48/1.47 % (1989259)Termination phase: Saturation
% 3.48/1.47 % (1989259)Time elapsed: 0.035 s
% 3.48/1.47 % (1989259)Peak memory usage: 89 MB
% 3.48/1.47 % (1989259)Instructions burned: 136 (million)
% 3.48/1.47 % (1989254)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=1661946277:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.48/1.47 % (1989256)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=106658893:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.48/1.47 % (1989255)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=2569317143:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.48/1.47 % (1989253)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=1539342582:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.48/1.47 % (1989258)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4018127078:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.48/1.47 % (1989256)First to succeed.
% 3.48/1.47 % (1989256)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1989248"
% 3.48/1.47 % (1989257)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=622165732:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.48/1.47 % (1989258)Also succeeded, but the first one will report.
% 3.48/1.47 % (1989257)Also succeeded, but the first one will report.
% 3.48/1.47 % (1989266)lrs+10_1_sil=8000:sp=occurrence:random_seed=2870415947:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.48/1.47 % (1989266)Also succeeded, but the first one will report.
% 3.48/1.47 % (1989256)Refutation found. Thanks to Tanya!
% 3.48/1.47 % SZS status Theorem for theBenchmark
% 3.48/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.47 % (1989256)------------------------------
% 3.48/1.47 % (1989256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.47 % (1989256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.47 % (1989256)CaDiCaL version: 2.1.3
% 3.48/1.47 % (1989256)Termination reason: Refutation
% 3.48/1.47 % (1989256)Time elapsed: 0.007 s
% 3.48/1.47 % (1989256)Peak memory usage: 89 MB
% 3.48/1.47 % (1989256)Instructions burned: 9 (million)
% 3.48/1.47 % (1989256)------------------------------
% 3.48/1.47 % (1989256)------------------------------
% 3.48/1.47 % (1989248)Success in time 0.412 s
% 3.48/1.47 % Vampire exiting
%------------------------------------------------------------------------------