%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM587+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 : 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 12:15:52 PM UTC 2026
% Result : Theorem 3.82s 1.52s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 73 ( 3 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 84 ( 34 ~; 28 |; 18 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 26 ( 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f73,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3291) ).
fof(f76,axiom,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(f90,axiom,
( xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi))))
& aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4263) ).
fof(f91,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f92,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f91]) ).
fof(f93,plain,
~ aElementOf0(xx,xT),
inference(flattening,[],[f92]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f202]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f203]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK6(X0,X1),X0)
& aElementOf0(sK6(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f204]) ).
fof(f242,plain,
aSet0(xT),
inference(cnf_transformation,[],[f73]) ).
fof(f246,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(cnf_transformation,[],[f76]) ).
fof(f276,plain,
aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(cnf_transformation,[],[f90]) ).
fof(f277,plain,
xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(cnf_transformation,[],[f90]) ).
fof(f278,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[],[f93]) ).
fof(f286,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f205]) ).
fof(f486,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xT)
| ~ aSet0(xT) ),
inference(resolution,[],[f286,f278]) ).
fof(f495,plain,
! [X0] :
( ~ aSubsetOf0(X0,xT)
| ~ aElementOf0(xx,X0) ),
inference(forward_subsumption_resolution,[],[f486,f242]) ).
fof(f497,plain,
~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(resolution,[],[f495,f246]) ).
fof(f637,plain,
aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(forward_demodulation,[],[f276,f277]) ).
fof(f638,plain,
$false,
inference(forward_subsumption_resolution,[],[f637,f497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM587+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:37:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.82/1.52 % (143218)Detected formulas, will run a generic FOF schedule.
% 3.82/1.52 % (143229)dis-21_1_sil=8000:lcm=predicate:random_seed=4190478545: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)
% 3.82/1.52 % (143227)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2623002942:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.82/1.52 % (143223)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=3501170872:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.82/1.52 % (143228)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3244654832:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.82/1.52 % (143224)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=4012962680:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.82/1.52 % (143225)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=22805914:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.82/1.52 % (143226)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2776768863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.82/1.52 % (143229)Instruction limit reached!
% 3.82/1.52 % (143229)------------------------------
% 3.82/1.52 % (143229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.52 % (143229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.52 % (143229)CaDiCaL version: 2.1.3
% 3.82/1.52 % (143229)Termination reason: Instruction limit
% 3.82/1.52 % (143229)Termination phase: Saturation
% 3.82/1.52 % (143229)Time elapsed: 0.034 s
% 3.82/1.52 % (143229)Peak memory usage: 89 MB
% 3.82/1.52 % (143229)Instructions burned: 132 (million)
% 3.82/1.52 % (143227)First to succeed.
% 3.82/1.52 % (143227)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-143218"
% 3.82/1.52 % (143228)Also succeeded, but the first one will report.
% 3.82/1.52 % (143226)Also succeeded, but the first one will report.
% 3.82/1.52 % (143237)lrs+10_1_sil=8000:sp=occurrence:random_seed=2595412319:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.82/1.52 % (143237)Also succeeded, but the first one will report.
% 3.82/1.52 % (143227)Refutation found. Thanks to Tanya!
% 3.82/1.52 % SZS status Theorem for theBenchmark
% 3.82/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.82/1.52 % (143227)------------------------------
% 3.82/1.52 % (143227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.82/1.52 % (143227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.82/1.52 % (143227)CaDiCaL version: 2.1.3
% 3.82/1.52 % (143227)Termination reason: Refutation
% 3.82/1.52 % (143227)Time elapsed: 0.011 s
% 3.82/1.52 % (143227)Peak memory usage: 88 MB
% 3.82/1.52 % (143227)Instructions burned: 15 (million)
% 3.82/1.52 % (143227)------------------------------
% 3.82/1.52 % (143227)------------------------------
% 3.82/1.52 % (143218)Success in time 0.458 s
% 3.82/1.52 % Vampire exiting
%------------------------------------------------------------------------------