%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM630+1 : 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 : 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 12:16:04 PM UTC 2026
% Result : Theorem 2.86s 11.35s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 20 unt; 1 def)
% Number of atoms : 66 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 17 |; 16 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f86,axiom,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( aFunction0(sdtlpdtrp0(xC,X0))
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( ( aSet0(X1)
& aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0)))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4151) ).
fof(f103,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f111,axiom,
( aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5309) ).
fof(f114,axiom,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5585) ).
fof(f115,axiom,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5599) ).
fof(f116,conjecture,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f117,negated_conjecture,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(negated_conjecture,[status(cth)],[f116]) ).
fof(f118,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(flattening,[],[f117]) ).
fof(f136,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,X0))
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(ennf_transformation,[],[f86]) ).
fof(f137,plain,
( aFunction0(xC)
& szDzozmdt0(xC) = szNzAzT0
& ! [X0] :
( ( aFunction0(sdtlpdtrp0(xC,X0))
& szDzozmdt0(sdtlpdtrp0(xC,X0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)
& ! [X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk)) ) )
| ~ aElementOf0(X0,szNzAzT0) ) ),
inference(flattening,[],[f136]) ).
fof(f313,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sdtlpdtrp0(xc,sdtpldt0(X1,szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ aSet0(X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))),xk))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f348,plain,
xp = szmzizndt0(xQ),
inference(cnf_transformation,[],[f103]) ).
fof(f349,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(cnf_transformation,[],[f104]) ).
fof(f350,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f358,plain,
aElementOf0(xn,szNzAzT0),
inference(cnf_transformation,[],[f111]) ).
fof(f362,plain,
xD = sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),
inference(cnf_transformation,[],[f114]) ).
fof(f363,plain,
aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(cnf_transformation,[],[f115]) ).
fof(f364,plain,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) != sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(cnf_transformation,[],[f118]) ).
fof(f486,definition,
~ sP28(sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))),
introduced(definition,[new_symbols(definition,[sP28])],[inequality_splitting_name_introduction]) ).
fof(f487,plain,
sP28(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP)),
inference(inequality_splitting,[],[f364,f486]) ).
fof(f531,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(forward_demodulation,[],[f350,f349]) ).
fof(f542,plain,
aSet0(sdtmndt0(xQ,xp)),
inference(forward_demodulation,[],[f531,f348]) ).
fof(f2765,plain,
( ~ sP28(sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP))
| ~ aSet0(xP)
| ~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(superposition,[],[f486,f313]) ).
fof(f2775,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk))
| ~ aElementOf0(xn,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f2765,f487]) ).
fof(f2787,plain,
( ~ aSet0(xP)
| ~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
inference(forward_subsumption_resolution,[],[f2775,f358]) ).
fof(f2794,plain,
( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
inference(forward_demodulation,[],[f2787,f349]) ).
fof(f2796,plain,
( ~ aSet0(sdtmndt0(xQ,xp))
| ~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)) ),
inference(forward_demodulation,[],[f2794,f348]) ).
fof(f2797,plain,
~ aElementOf0(xP,slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN,xn),szmzizndt0(sdtlpdtrp0(xN,xn))),xk)),
inference(forward_subsumption_resolution,[],[f2796,f542]) ).
fof(f2798,plain,
~ aElementOf0(xP,slbdtsldtrb0(xD,xk)),
inference(forward_demodulation,[],[f2797,f362]) ).
fof(f2799,plain,
$false,
inference(forward_subsumption_resolution,[],[f2798,f363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM630+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.40 % Computer : n002.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Sun Sep 27 20:53:32 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/10.44 Running first-order theorem proving
% 0.11/10.44 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
% 2.86/11.35 % (3863602)Detected formulas, will run a generic FOF schedule.
% 2.86/11.35 % (3863610)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2443943520:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.86/11.35 % (3863610)First to succeed.
% 2.86/11.35 % (3863610)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3863602"
% 2.86/11.35 % (3863607)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=402988120:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.86/11.35 % (3863612)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3544823789:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.86/11.35 % (3863609)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=1046098626:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.86/11.35 % (3863611)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3149561646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.86/11.35 % (3863613)dis-21_1_sil=8000:lcm=predicate:random_seed=2541023633: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)
% 2.86/11.35 % (3863608)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=2027735014:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.86/11.35 % (3863612)Also succeeded, but the first one will report.
% 2.86/11.35 % (3863611)Also succeeded, but the first one will report.
% 2.86/11.35 % (3863613)Instruction limit reached!
% 2.86/11.35 % (3863613)------------------------------
% 2.86/11.35 % (3863613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/11.35 % (3863613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/11.35 % (3863613)CaDiCaL version: 2.1.3
% 2.86/11.35 % (3863613)Termination reason: Instruction limit
% 2.86/11.35 % (3863613)Termination phase: Saturation
% 2.86/11.35 % (3863613)Time elapsed: 0.075 s
% 2.86/11.35 % (3863613)Peak memory usage: 91 MB
% 2.86/11.35 % (3863613)Instructions burned: 129 (million)
% 2.86/11.35 % (3863610)Refutation found. Thanks to Tanya!
% 2.86/11.35 % SZS status Theorem for theBenchmark
% 2.86/11.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/11.35 % (3863610)------------------------------
% 2.86/11.35 % (3863610)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/11.35 % (3863610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/11.35 % (3863610)CaDiCaL version: 2.1.3
% 2.86/11.35 % (3863610)Termination reason: Refutation
% 2.86/11.35 % (3863610)Time elapsed: 0.036 s
% 2.86/11.35 % (3863610)Peak memory usage: 90 MB
% 2.86/11.35 % (3863610)Instructions burned: 99 (million)
% 2.86/11.35 % (3863610)------------------------------
% 2.86/11.35 % (3863610)------------------------------
% 2.86/11.35 % (3863602)Success in time 0.328 s
% 2.86/11.35 % Vampire exiting
%------------------------------------------------------------------------------