%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM514+3 : 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 : n012.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 12:15:32 PM UTC 2026
% Result : Theorem 2.02s 0.88s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 1 def)
% Number of atoms : 40 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 40 ( 15 ~; 8 |; 14 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f55,axiom,
( aNaturalNumber0(sdtsldt0(xk,xr))
& xk = sdtasdt0(xr,sdtsldt0(xk,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2613) ).
fof(f56,conjecture,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f141,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtasdt0(sdtsldt0(xn,xr),xm) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f142,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtasdt0(sdtsldt0(xn,xr),xm) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(flattening,[],[f141]) ).
fof(f337,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(cnf_transformation,[],[f55]) ).
fof(f341,plain,
aNaturalNumber0(sdtsldt0(xk,xr)),
inference(cnf_transformation,[],[f55]) ).
fof(f345,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtasdt0(sdtsldt0(xn,xr),xm) ),
inference(cnf_transformation,[],[f142]) ).
fof(f358,definition,
! [X0,X1] :
( sQ22_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ22_eqProxy])],[equality_proxy_definition]) ).
fof(f459,plain,
sQ22_eqProxy(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,sdtsldt0(xk,xr))),
inference(equality_proxy_replacement,[],[f337,f358]) ).
fof(f460,plain,
! [X0] :
( ~ sQ22_eqProxy(sdtasdt0(xp,X0),sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f345,f358]) ).
fof(f463,plain,
! [X0,X1] :
( sQ22_eqProxy(X1,X0)
| ~ sQ22_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f358]) ).
fof(f527,plain,
! [X0] :
( ~ sQ22_eqProxy(sdtasdt0(sdtsldt0(xn,xr),xm),sdtasdt0(xp,X0))
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f463,f460]) ).
fof(f621,plain,
~ aNaturalNumber0(sdtsldt0(xk,xr)),
inference(resolution,[],[f459,f527]) ).
fof(f622,plain,
$false,
inference(resolution,[],[f621,f341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM514+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 20:16:49 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 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
% 2.02/0.88 % (2703695)Detected formulas, will run a generic FOF schedule.
% 2.02/0.88 % (2703763)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2675910861:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.02/0.88 % (2703767)dis-21_1_sil=8000:lcm=predicate:random_seed=2200609439: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)
% 2.02/0.88 % (2703758)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=1158775142:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.02/0.88 % (2703761)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=594300247:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.02/0.88 % (2703764)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4272172567:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.02/0.88 % (2703760)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=1361108061:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.02/0.88 % (2703766)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=118368940:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.02/0.88 % (2703767)First to succeed.
% 2.02/0.88 % (2703767)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2703695"
% 2.02/0.88 % (2703764)Also succeeded, but the first one will report.
% 2.02/0.88 % (2703766)Also succeeded, but the first one will report.
% 2.02/0.88 % (2703763)Instruction limit reached!
% 2.02/0.88 % (2703763)------------------------------
% 2.02/0.88 % (2703763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2703763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2703763)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2703763)Termination reason: Instruction limit
% 2.02/0.88 % (2703763)Termination phase: Saturation
% 2.02/0.88 % (2703763)Time elapsed: 0.033 s
% 2.02/0.88 % (2703763)Peak memory usage: 89 MB
% 2.02/0.88 % (2703763)Instructions burned: 109 (million)
% 2.02/0.88 % (2703814)lrs+10_1_sil=8000:sp=occurrence:random_seed=3756263920:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.02/0.88 % (2703814)Also succeeded, but the first one will report.
% 2.02/0.88 % (2703767)Refutation found. Thanks to Tanya!
% 2.02/0.88 % SZS status Theorem for theBenchmark
% 2.02/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 2.02/0.88 % (2703767)------------------------------
% 2.02/0.88 % (2703767)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.02/0.88 % (2703767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.02/0.88 % (2703767)CaDiCaL version: 2.1.3
% 2.02/0.88 % (2703767)Termination reason: Refutation
% 2.02/0.88 % (2703767)Time elapsed: 0.003 s
% 2.02/0.88 % (2703767)Peak memory usage: 88 MB
% 2.02/0.88 % (2703767)Instructions burned: 9 (million)
% 2.02/0.88 % (2703767)------------------------------
% 2.02/0.88 % (2703767)------------------------------
% 2.02/0.88 % (2703695)Success in time 0.253 s
% 2.02/0.88 % Vampire exiting
%------------------------------------------------------------------------------