%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM568+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 : n005.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 3.52s 1.41s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 45 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 45 ( 19 ~; 19 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 15 ( 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNatExtra) ).
fof(f74,axiom,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
fof(f78,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
fof(f80,conjecture,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f81,negated_conjecture,
~ ? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xK ),
inference(negated_conjecture,[status(cth)],[f80]) ).
fof(f99,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(X0) != xK ),
inference(ennf_transformation,[],[f81]) ).
fof(f135,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f136,plain,
! [X0] :
( X0 = sz00
| ? [X1] :
( aElementOf0(X1,szNzAzT0)
& X0 = szszuzczcdt0(X1) )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(flattening,[],[f135]) ).
fof(f192,plain,
! [X0] :
( X0 = sz00
| ( aElementOf0(sK23(X0),szNzAzT0)
& szszuzczcdt0(sK23(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X1,sK23(X0))],[f136]) ).
fof(f201,plain,
aElementOf0(xK,szNzAzT0),
inference(cnf_transformation,[],[f74]) ).
fof(f252,plain,
sz00 != xK,
inference(cnf_transformation,[],[f78]) ).
fof(f254,plain,
! [X0] :
( szszuzczcdt0(X0) != xK
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f301,plain,
! [X0] :
( szszuzczcdt0(sK23(X0)) = X0
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f302,plain,
! [X0] :
( aElementOf0(sK23(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f412,plain,
! [X0] :
( xK != X0
| ~ aElementOf0(sK23(X0),szNzAzT0)
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[],[f254,f301]) ).
fof(f423,plain,
! [X0] :
( xK != X0
| sz00 = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f412,f302]) ).
fof(f424,plain,
( sz00 = xK
| ~ aElementOf0(xK,szNzAzT0) ),
inference(equality_resolution,[],[f423]) ).
fof(f425,plain,
~ aElementOf0(xK,szNzAzT0),
inference(forward_subsumption_resolution,[],[f424,f252]) ).
fof(f426,plain,
$false,
inference(forward_subsumption_resolution,[],[f425,f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM568+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n005.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Sun Sep 27 20:32:18 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 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
% 3.52/1.41 % (141999)Detected formulas, will run a generic FOF schedule.
% 3.52/1.41 % (142004)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=473658840:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.52/1.41 % (142008)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=477916008:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.52/1.41 % (142009)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2199114833:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.52/1.41 % (142007)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1039243067:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.52/1.41 % (142006)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=30474550:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.52/1.41 % (142010)dis-21_1_sil=8000:lcm=predicate:random_seed=2980433877: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)
% 3.52/1.41 % (142005)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=4096569662:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.52/1.41 % (142008)First to succeed.
% 3.52/1.41 % (142008)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-141999"
% 3.52/1.41 % (142007)Also succeeded, but the first one will report.
% 3.52/1.41 % (142009)Also succeeded, but the first one will report.
% 3.52/1.41 % (142010)Instruction limit reached!
% 3.52/1.41 % (142010)------------------------------
% 3.52/1.41 % (142010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.41 % (142010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.41 % (142010)CaDiCaL version: 2.1.3
% 3.52/1.41 % (142010)Termination reason: Instruction limit
% 3.52/1.41 % (142010)Termination phase: Saturation
% 3.52/1.41 % (142010)Time elapsed: 0.062 s
% 3.52/1.41 % (142010)Peak memory usage: 89 MB
% 3.52/1.41 % (142010)Instructions burned: 129 (million)
% 3.52/1.41 % (142018)lrs+10_1_sil=8000:sp=occurrence:random_seed=2776060238:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.52/1.41 % (142018)Also succeeded, but the first one will report.
% 3.52/1.41 % (142008)Refutation found. Thanks to Tanya!
% 3.52/1.41 % SZS status Theorem for theBenchmark
% 3.52/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.41 % (142008)------------------------------
% 3.52/1.41 % (142008)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.41 % (142008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.41 % (142008)CaDiCaL version: 2.1.3
% 3.52/1.41 % (142008)Termination reason: Refutation
% 3.52/1.41 % (142008)Time elapsed: 0.007 s
% 3.52/1.41 % (142008)Peak memory usage: 88 MB
% 3.52/1.41 % (142008)Instructions burned: 9 (million)
% 3.52/1.41 % (142008)------------------------------
% 3.52/1.41 % (142008)------------------------------
% 3.52/1.41 % (141999)Success in time 0.42 s
% 3.52/1.41 % Vampire exiting
%------------------------------------------------------------------------------