%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM571+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 : n017.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 12:15:47 PM UTC 2026
% Result : Theorem 2.77s 6.38s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 8 unt; 3 def)
% Number of atoms : 111 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 35 ~; 37 |; 25 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn 3 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f75,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(f81,axiom,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,X0)) )
=> ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3623) ).
fof(f84,axiom,
( xi != sz00
=> ( ? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xi )
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3702_02) ).
fof(f85,conjecture,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f86,negated_conjecture,
~ ( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(negated_conjecture,[status(cth)],[f85]) ).
fof(f94,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f95,plain,
( aFunction0(xN)
& szDzozmdt0(xN) = szNzAzT0
& sdtlpdtrp0(xN,sz00) = xS
& ! [X0] :
( ( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
( ( ? [X0] :
( aElementOf0(X0,szNzAzT0)
& szszuzczcdt0(X0) = xi )
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) )
| sz00 = xi ),
inference(ennf_transformation,[],[f84]) ).
fof(f99,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(ennf_transformation,[],[f86]) ).
fof(f153,plain,
( ( aElementOf0(sK4,szNzAzT0)
& xi = szszuzczcdt0(sK4)
& aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
& isCountable0(sdtlpdtrp0(xN,xi)) )
| sz00 = xi ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f98]) ).
fof(f182,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f75]) ).
fof(f183,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f75]) ).
fof(f197,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f95]) ).
fof(f203,plain,
( isCountable0(sdtlpdtrp0(xN,xi))
| sz00 = xi ),
inference(cnf_transformation,[],[f153]) ).
fof(f204,plain,
( aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| sz00 = xi ),
inference(cnf_transformation,[],[f153]) ).
fof(f207,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,xi)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f304,definition,
( spl22_1
<=> isCountable0(sdtlpdtrp0(xN,xi)) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f306,plain,
( ~ isCountable0(sdtlpdtrp0(xN,xi))
| spl22_1 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f308,definition,
( spl22_2
<=> aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f310,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),szNzAzT0)
| spl22_2 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
( ~ spl22_1
| ~ spl22_2 ),
inference(avatar_split_clause,[],[f207,f308,f304]) ).
fof(f313,definition,
( spl22_3
<=> sz00 = xi ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
fof(f315,plain,
( sz00 = xi
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f316,plain,
( spl22_3
| spl22_1 ),
inference(avatar_split_clause,[],[f203,f304,f313]) ).
fof(f317,plain,
( spl22_3
| spl22_2 ),
inference(avatar_split_clause,[],[f204,f308,f313]) ).
fof(f386,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sz00))
| spl22_1
| ~ spl22_3 ),
inference(superposition,[],[f306,f315]) ).
fof(f387,plain,
( ~ isCountable0(xS)
| spl22_1
| ~ spl22_3 ),
inference(forward_demodulation,[],[f386,f197]) ).
fof(f388,plain,
( $false
| spl22_1
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f387,f182]) ).
fof(f389,plain,
( spl22_1
| ~ spl22_3 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f391,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szNzAzT0)
| spl22_2
| ~ spl22_3 ),
inference(forward_demodulation,[],[f310,f315]) ).
fof(f393,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| spl22_2
| ~ spl22_3 ),
inference(forward_demodulation,[],[f391,f197]) ).
fof(f394,plain,
( $false
| spl22_2
| ~ spl22_3 ),
inference(forward_subsumption_resolution,[],[f393,f183]) ).
fof(f395,plain,
( spl22_2
| ~ spl22_3 ),
inference(avatar_contradiction_clause,[],[f394]) ).
cnf(s1,plain,
( ~ spl22_1
| ~ spl22_2 ),
inference(sat_conversion,[],[f311]) ).
cnf(s2,plain,
( spl22_1
| spl22_3 ),
inference(sat_conversion,[],[f316]) ).
cnf(s3,plain,
( spl22_2
| spl22_3 ),
inference(sat_conversion,[],[f317]) ).
cnf(s11,plain,
( spl22_1
| ~ spl22_3 ),
inference(sat_conversion,[],[f389]) ).
cnf(s12,plain,
( spl22_2
| ~ spl22_3 ),
inference(sat_conversion,[],[f395]) ).
cnf(s16,plain,
spl22_1,
inference(rat,[],[s2,s11]) ).
cnf(s17,plain,
~ spl22_2,
inference(rat,[],[s1,s16]) ).
cnf(s18,plain,
~ spl22_3,
inference(rat,[],[s12,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s3,s18,s17]) ).
fof(f396,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM571+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.40 % Computer : n017.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Sun Sep 27 20:28:27 UTC 2026
% 0.12/5.40 % CPUTime :
% 0.12/5.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.43 Running first-order theorem proving
% 0.12/5.43 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
% 2.77/6.38 % (2917760)Detected formulas, will run a generic FOF schedule.
% 2.77/6.38 % (2917768)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3085702253:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/6.38 % (2917768)First to succeed.
% 2.77/6.38 % (2917768)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2917760"
% 2.77/6.38 % (2917766)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=3752810619:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/6.38 % (2917770)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=468427533:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/6.38 % (2917767)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=793251114:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/6.38 % (2917769)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=739969111:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/6.38 % (2917765)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=1171889323:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/6.38 % (2917771)dis-21_1_sil=8000:lcm=predicate:random_seed=2966196067: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)
% 2.77/6.38 % (2917769)Also succeeded, but the first one will report.
% 2.77/6.38 % (2917770)Also succeeded, but the first one will report.
% 2.77/6.38 % (2917771)Instruction limit reached!
% 2.77/6.38 % (2917771)------------------------------
% 2.77/6.38 % (2917771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/6.38 % (2917771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/6.38 % (2917771)CaDiCaL version: 2.1.3
% 2.77/6.38 % (2917771)Termination reason: Instruction limit
% 2.77/6.38 % (2917771)Termination phase: Saturation
% 2.77/6.38 % (2917771)Time elapsed: 0.061 s
% 2.77/6.38 % (2917771)Peak memory usage: 88 MB
% 2.77/6.38 % (2917771)Instructions burned: 129 (million)
% 2.77/6.38 % (2917768)Refutation found. Thanks to Tanya!
% 2.77/6.38 % SZS status Theorem for theBenchmark
% 2.77/6.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/6.38 % (2917768)------------------------------
% 2.77/6.38 % (2917768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/6.38 % (2917768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/6.38 % (2917768)CaDiCaL version: 2.1.3
% 2.77/6.38 % (2917768)Termination reason: Refutation
% 2.77/6.38 % (2917768)Time elapsed: 0.005 s
% 2.77/6.38 % (2917768)Peak memory usage: 90 MB
% 2.77/6.38 % (2917768)Instructions burned: 10 (million)
% 2.77/6.38 % (2917768)------------------------------
% 2.77/6.38 % (2917768)------------------------------
% 2.77/6.38 % (2917760)Success in time 0.312 s
% 2.77/6.38 % Vampire exiting
%------------------------------------------------------------------------------