%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM609+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 : n014.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 12:15:58 PM UTC 2026
% Result : Theorem 2.67s 1.34s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 4 unt; 0 def)
% Number of atoms : 66 ( 12 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 74 ( 22 ~; 14 |; 31 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f104,axiom,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X0] :
( aElementOf0(X0,xP)
<=> ( aElement0(X0)
& aElementOf0(X0,xQ)
& X0 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(f107,conjecture,
( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xQ) )
| aSubsetOf0(xP,xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f108,negated_conjecture,
~ ( ! [X0] :
( aElementOf0(X0,xP)
=> aElementOf0(X0,xQ) )
| aSubsetOf0(xP,xQ) ),
inference(negated_conjecture,[status(cth)],[f107]) ).
fof(f123,plain,
( aSet0(xP)
& ! [X0] :
( aElementOf0(X0,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X0) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(rectify,[],[f104]) ).
fof(f166,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(ennf_transformation,[],[f123]) ).
fof(f167,plain,
( ? [X0] :
( ~ aElementOf0(X0,xQ)
& aElementOf0(X0,xP) )
& ~ aSubsetOf0(xP,xQ) ),
inference(ennf_transformation,[],[f108]) ).
fof(f377,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(nnf_transformation,[],[f166]) ).
fof(f378,plain,
( aSet0(xP)
& ! [X0] :
( sdtlseqdt0(szmzizndt0(xQ),X0)
| ~ aElementOf0(X0,xQ) )
& ! [X1] :
( ( aElementOf0(X1,xP)
| ~ aElement0(X1)
| ~ aElementOf0(X1,xQ)
| szmzizndt0(xQ) = X1 )
& ( ( aElement0(X1)
& aElementOf0(X1,xQ)
& szmzizndt0(xQ) != X1 )
| ~ aElementOf0(X1,xP) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(flattening,[],[f377]) ).
fof(f380,plain,
( ~ aElementOf0(sK54,xQ)
& aElementOf0(sK54,xP)
& ~ aSubsetOf0(xP,xQ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X0,sK54)],[f167]) ).
fof(f693,plain,
! [X1] :
( aElementOf0(X1,xQ)
| ~ aElementOf0(X1,xP) ),
inference(cnf_transformation,[],[f378]) ).
fof(f702,plain,
aElementOf0(sK54,xP),
inference(cnf_transformation,[],[f380]) ).
fof(f703,plain,
~ aElementOf0(sK54,xQ),
inference(cnf_transformation,[],[f380]) ).
fof(f911,plain,
~ aElementOf0(sK54,xP),
inference(resolution,[],[f693,f703]) ).
fof(f915,plain,
$false,
inference(forward_subsumption_resolution,[],[f911,f702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM609+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 20:44:31 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 2.67/1.34 % (1144207)Detected formulas, will run a generic FOF schedule.
% 2.67/1.34 % (1144216)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2783224335:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.34 % (1144216)First to succeed.
% 2.67/1.34 % (1144216)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1144207"
% 2.67/1.34 % (1144213)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=290081534:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.34 % (1144214)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=880868623:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.34 % (1144212)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=3069293145:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.34 % (1144215)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3291124305:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.34 % (1144218)dis-21_1_sil=8000:lcm=predicate:random_seed=3455881080: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)
% 2.67/1.34 % (1144217)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1245851497:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.34 % (1144218)Also succeeded, but the first one will report.
% 2.67/1.34 % (1144217)Also succeeded, but the first one will report.
% 2.67/1.34 % (1144215)Also succeeded, but the first one will report.
% 2.67/1.34 % (1144216)Refutation found. Thanks to Tanya!
% 2.67/1.34 % SZS status Theorem for theBenchmark
% 2.67/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.34 % (1144216)------------------------------
% 2.67/1.34 % (1144216)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.34 % (1144216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.34 % (1144216)CaDiCaL version: 2.1.3
% 2.67/1.34 % (1144216)Termination reason: Refutation
% 2.67/1.34 % (1144216)Time elapsed: 0.007 s
% 2.67/1.34 % (1144216)Peak memory usage: 89 MB
% 2.67/1.34 % (1144216)Instructions burned: 20 (million)
% 2.67/1.34 % (1144216)------------------------------
% 2.67/1.34 % (1144216)------------------------------
% 2.67/1.34 % (1144207)Success in time 0.298 s
% 2.67/1.34 % Vampire exiting
%------------------------------------------------------------------------------