%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM531+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 : n001.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 12:15:37 PM UTC 2026
% Result : Theorem 2.74s 1.34s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 12 unt; 2 def)
% Number of atoms : 57 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 21 ~; 13 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 8 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEmpFin) ).
fof(f8,axiom,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> ~ isFinite0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCountNFin) ).
fof(f9,conjecture,
! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> X0 != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( aSet0(X0)
& isCountable0(X0) )
=> X0 != slcrc0 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f17,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ aSet0(X0)
| ~ isCountable0(X0) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0] :
( slcrc0 = X0
& aSet0(X0)
& isCountable0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f20,plain,
? [X0] :
( slcrc0 = X0
& aSet0(X0)
& isCountable0(X0) ),
inference(flattening,[],[f19]) ).
fof(f25,plain,
( slcrc0 = sK1
& aSet0(sK1)
& isCountable0(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f20]) ).
fof(f29,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0] :
( ~ isCountable0(X0)
| ~ aSet0(X0)
| ~ isFinite0(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
isCountable0(sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f32,plain,
aSet0(sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f33,plain,
slcrc0 = sK1,
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
isFinite0(sK1),
inference(definition_unfolding,[],[f29,f33]) ).
fof(f44,plain,
( ~ aSet0(sK1)
| ~ isFinite0(sK1) ),
inference(resolution,[],[f30,f31]) ).
fof(f46,definition,
( spl3_1
<=> isFinite0(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f47,plain,
( ~ isFinite0(sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,definition,
( spl3_2
<=> aSet0(sK1) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f50,plain,
( ~ aSet0(sK1)
| spl3_2 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f44,f49,f46]) ).
fof(f52,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f47,f37]) ).
fof(f53,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f52]) ).
fof(f54,plain,
( $false
| spl3_2 ),
inference(resolution,[],[f50,f32]) ).
fof(f55,plain,
spl3_2,
inference(avatar_contradiction_clause,[],[f54]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
spl3_1,
inference(sat_conversion,[],[f53]) ).
cnf(s3,plain,
spl3_2,
inference(sat_conversion,[],[f55]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f56,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM531+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 20:27:46 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.74/1.34 % (3927740)Detected formulas, will run a generic FOF schedule.
% 2.74/1.34 % (3927751)dis-21_1_sil=8000:lcm=predicate:random_seed=1703211061: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)
% 2.74/1.34 % (3927751)First to succeed.
% 2.74/1.34 % (3927751)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3927740"
% 2.74/1.34 % (3927745)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=2576753704:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.34 % (3927749)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3279538987:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.34 % (3927746)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=3986278241:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.34 % (3927747)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=1934928570:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.34 % (3927748)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3822612534:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.34 % (3927750)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2103873974:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.34 % (3927749)Also succeeded, but the first one will report.
% 2.74/1.34 % (3927748)Also succeeded, but the first one will report.
% 2.74/1.34 % (3927750)Also succeeded, but the first one will report.
% 2.74/1.34 % (3927751)Refutation found. Thanks to Tanya!
% 2.74/1.34 % SZS status Theorem for theBenchmark
% 2.74/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.34 % (3927751)------------------------------
% 2.74/1.34 % (3927751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.34 % (3927751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.34 % (3927751)CaDiCaL version: 2.1.3
% 2.74/1.34 % (3927751)Termination reason: Refutation
% 2.74/1.34 % (3927751)Time elapsed: 0.002 s
% 2.74/1.34 % (3927751)Peak memory usage: 89 MB
% 2.74/1.34 % (3927751)Instructions burned: 1 (million)
% 2.74/1.34 % (3927751)------------------------------
% 2.74/1.34 % (3927751)------------------------------
% 2.74/1.34 % (3927740)Success in time 0.301 s
% 2.74/1.34 % Vampire exiting
%------------------------------------------------------------------------------