%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM472+2 : 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 12:15:20 PM UTC 2026
% Result : Theorem 4.50s 1.74s
% Output : Refutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 4 unt; 1 def)
% Number of atoms : 22 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 20 ( 9 ~; 5 |; 5 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f39,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = sdtpldt0(xm,xn) )
| sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = sdtpldt0(xm,xn) )
| sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f97,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0) )
& ~ sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f163,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f180,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,xn) != sdtpldt0(xm,X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f191,definition,
! [X0,X1] :
( sQ4_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ4_eqProxy])],[equality_proxy_definition]) ).
fof(f238,plain,
! [X0] :
( ~ sQ4_eqProxy(sdtpldt0(xm,xn),sdtpldt0(xm,X0))
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f180,f191]) ).
fof(f239,plain,
! [X0] : sQ4_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f191]) ).
fof(f256,plain,
~ aNaturalNumber0(xn),
inference(resolution,[],[f239,f238]) ).
fof(f257,plain,
$false,
inference(resolution,[],[f256,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM472+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 20:04:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 4.50/1.74 % (3844621)Detected formulas, will run a generic FOF schedule.
% 4.50/1.74 % (3844643)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=1269345244:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.50/1.74 % (3844649)dis-21_1_sil=8000:lcm=predicate:random_seed=2726070184: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)
% 4.50/1.74 % (3844649)First to succeed.
% 4.50/1.74 % (3844649)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3844621"
% 4.50/1.74 % (3844644)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=1961629974:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.50/1.74 % (3844647)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=954522110:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.50/1.74 % (3844648)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1896055788:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.50/1.74 % (3844646)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2874717927:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.50/1.74 % (3844645)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=3958797987:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.50/1.74 % (3844647)Also succeeded, but the first one will report.
% 4.50/1.74 % (3844648)Also succeeded, but the first one will report.
% 4.50/1.74 % (3844646)Also succeeded, but the first one will report.
% 4.50/1.74 % (3844649)Refutation found. Thanks to Tanya!
% 4.50/1.74 % SZS status Theorem for theBenchmark
% 4.50/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 4.50/1.74 % (3844649)------------------------------
% 4.50/1.74 % (3844649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.74 % (3844649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.74 % (3844649)CaDiCaL version: 2.1.3
% 4.50/1.74 % (3844649)Termination reason: Refutation
% 4.50/1.74 % (3844649)Time elapsed: 0.003 s
% 4.50/1.74 % (3844649)Peak memory usage: 89 MB
% 4.50/1.74 % (3844649)Instructions burned: 3 (million)
% 4.50/1.74 % (3844649)------------------------------
% 4.50/1.74 % (3844649)------------------------------
% 4.50/1.74 % (3844621)Success in time 0.525 s
% 4.50/1.74 % Vampire exiting
%------------------------------------------------------------------------------