%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM617+3 : 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 : n004.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 12:16:00 PM UTC 2026
% Result : Theorem 2.56s 1.32s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 47 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 41 ( 13 ~; 6 |; 19 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f75,axiom,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f98,axiom,
( ! [X0] :
( aElementOf0(X0,xO)
=> aElementOf0(X0,xS) )
& aSubsetOf0(xO,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
fof(f99,axiom,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xQ)
=> aElementOf0(X0,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5078) ).
fof(f113,axiom,
( aElement0(xx)
& aElementOf0(xx,xQ)
& xx != szmzizndt0(xQ)
& aElementOf0(xx,xP) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f114,conjecture,
aElementOf0(xx,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f115,negated_conjecture,
~ aElementOf0(xx,szNzAzT0),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f131,plain,
~ aElementOf0(xx,szNzAzT0),
inference(flattening,[],[f115]) ).
fof(f139,plain,
( aSet0(xS)
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) )
& aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f167,plain,
( ! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) )
& aSubsetOf0(xO,xS) ),
inference(ennf_transformation,[],[f98]) ).
fof(f168,plain,
( aSet0(xQ)
& ! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(ennf_transformation,[],[f99]) ).
fof(f437,plain,
! [X0] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f139]) ).
fof(f680,plain,
! [X0] :
( aElementOf0(X0,xS)
| ~ aElementOf0(X0,xO) ),
inference(cnf_transformation,[],[f167]) ).
fof(f684,plain,
! [X0] :
( aElementOf0(X0,xO)
| ~ aElementOf0(X0,xQ) ),
inference(cnf_transformation,[],[f168]) ).
fof(f723,plain,
aElementOf0(xx,xQ),
inference(cnf_transformation,[],[f113]) ).
fof(f725,plain,
~ aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f131]) ).
fof(f916,plain,
~ aElementOf0(xx,xS),
inference(resolution,[],[f437,f725]) ).
fof(f922,plain,
~ aElementOf0(xx,xO),
inference(resolution,[],[f680,f916]) ).
fof(f926,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[],[f922,f684]) ).
fof(f927,plain,
$false,
inference(forward_subsumption_resolution,[],[f926,f723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM617+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:46:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.56/1.32 % (3861880)Detected formulas, will run a generic FOF schedule.
% 2.56/1.32 % (3861889)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4035925781:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.56/1.32 % (3861889)First to succeed.
% 2.56/1.32 % (3861889)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3861880"
% 2.56/1.32 % (3861885)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=4223635398:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.56/1.32 % (3861887)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=4223128091:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.56/1.32 % (3861888)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1719633597:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.56/1.32 % (3861886)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=436015972:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.56/1.32 % (3861890)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2641859566:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.56/1.32 % (3861891)dis-21_1_sil=8000:lcm=predicate:random_seed=2056829785: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)
% 2.56/1.32 % (3861891)Also succeeded, but the first one will report.
% 2.56/1.32 % (3861890)Also succeeded, but the first one will report.
% 2.56/1.32 % (3861888)Also succeeded, but the first one will report.
% 2.56/1.32 % (3861889)Refutation found. Thanks to Tanya!
% 2.56/1.32 % SZS status Theorem for theBenchmark
% 2.56/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.32 % (3861889)------------------------------
% 2.56/1.32 % (3861889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.32 % (3861889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.32 % (3861889)CaDiCaL version: 2.1.3
% 2.56/1.32 % (3861889)Termination reason: Refutation
% 2.56/1.32 % (3861889)Time elapsed: 0.007 s
% 2.56/1.32 % (3861889)Peak memory usage: 89 MB
% 2.56/1.32 % (3861889)Instructions burned: 20 (million)
% 2.56/1.32 % (3861889)------------------------------
% 2.56/1.32 % (3861889)------------------------------
% 2.56/1.32 % (3861880)Success in time 0.277 s
% 2.56/1.32 % Vampire exiting
%------------------------------------------------------------------------------