%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM561+2 : 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 : n002.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 12:15:45 PM UTC 2026
% Result : Theorem 2.62s 1.34s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 5 unt; 1 def)
% Number of atoms : 18 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 5 |; 3 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 3 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2911_02) ).
fof(f71,conjecture,
( ? [X0] :
( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = sdtlpdtrp0(xF,xx) )
| aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f72,negated_conjecture,
~ ( ? [X0] :
( aElementOf0(X0,szDzozmdt0(xF))
& sdtlpdtrp0(xF,X0) = sdtlpdtrp0(xF,xx) )
| aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
inference(negated_conjecture,[status(cth)],[f71]) ).
fof(f78,plain,
( ! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
| sdtlpdtrp0(xF,X0) != sdtlpdtrp0(xF,xx) )
& ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
inference(ennf_transformation,[],[f72]) ).
fof(f79,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f81,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
| sdtlpdtrp0(xF,X0) != sdtlpdtrp0(xF,xx) ),
inference(cnf_transformation,[],[f78]) ).
fof(f82,definition,
~ sP0(sdtlpdtrp0(xF,xx)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f83,plain,
! [X0] :
( ~ aElementOf0(X0,szDzozmdt0(xF))
| sP0(sdtlpdtrp0(xF,X0)) ),
inference(inequality_splitting,[],[f81,f82]) ).
fof(f84,plain,
sP0(sdtlpdtrp0(xF,xx)),
inference(resolution,[],[f79,f83]) ).
fof(f85,plain,
$false,
inference(forward_subsumption_resolution,[],[f84,f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM561+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:32:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.62/1.34 % (3855734)Detected formulas, will run a generic FOF schedule.
% 2.62/1.34 % (3855742)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3594422103:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.34 % (3855742)First to succeed.
% 2.62/1.34 % (3855742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3855734"
% 2.62/1.34 % (3855739)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=3753839672:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.34 % (3855741)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=1087889625:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.34 % (3855740)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=375163694:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.34 % (3855743)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=509510853:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.34 % (3855745)dis-21_1_sil=8000:lcm=predicate:random_seed=775128241: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)
% 2.62/1.34 % (3855744)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1586744671:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.34 % (3855743)Also succeeded, but the first one will report.
% 2.62/1.34 % (3855745)Also succeeded, but the first one will report.
% 2.62/1.34 % (3855744)Also succeeded, but the first one will report.
% 2.62/1.34 % (3855742)Refutation found. Thanks to Tanya!
% 2.62/1.34 % SZS status Theorem for theBenchmark
% 2.62/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.34 % (3855742)------------------------------
% 2.62/1.34 % (3855742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.34 % (3855742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.34 % (3855742)CaDiCaL version: 2.1.3
% 2.62/1.34 % (3855742)Termination reason: Refutation
% 2.62/1.34 % (3855742)Time elapsed: 0.001 s
% 2.62/1.34 % (3855742)Peak memory usage: 88 MB
% 2.62/1.34 % (3855742)------------------------------
% 2.62/1.34 % (3855742)------------------------------
% 2.62/1.34 % (3855734)Success in time 0.284 s
% 2.62/1.34 % Vampire exiting
%------------------------------------------------------------------------------