%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM695_8 : TPTP v9.3.1. Released v8.0.0.
% 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 12:16:33 PM UTC 2026
% Result : Theorem 2.35s 0.92s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 2 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
nat: $tType ).
tff(func_def_0,type,
x: nat ).
tff(func_def_1,type,
suc: nat > nat ).
tff(func_def_2,type,
n_1: nat ).
tff(func_def_3,type,
pl: ( nat * nat ) > nat ).
tff(func_def_6,type,
sK0: nat > nat ).
tff(pred_def_1,type,
more: ( nat * nat ) > $o ).
tff(f4,axiom,
! [X0: nat,X1: nat] : more(pl(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz18) ).
tff(f5,axiom,
! [X0: nat] : ( suc(X0) = pl(n_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz4g) ).
tff(f6,conjecture,
more(suc(x),n_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz24b) ).
tff(f7,negated_conjecture,
~ more(suc(x),n_1),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f10,plain,
~ more(suc(x),n_1),
inference(flattening,[],[f7]) ).
tff(f13,plain,
~ more(suc(x),n_1),
inference(cnf_transformation,[],[f10]) ).
tff(f14,plain,
! [X0: nat,X1: nat] : more(pl(X0,X1),X0),
inference(cnf_transformation,[],[f4]) ).
tff(f17,plain,
! [X0: nat] : ( suc(X0) = pl(n_1,X0) ),
inference(cnf_transformation,[],[f5]) ).
tff(f18,plain,
~ more(pl(n_1,x),n_1),
inference(definition_unfolding,[],[f13,f17]) ).
tff(f21,plain,
$false,
inference(resolution,[],[f14,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM695_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 21:06:49 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 2.35/0.92 % (2741356)Detected formulas, will run a generic FOF schedule.
% 2.35/0.92 % (2741367)dis-21_1_sil=8000:lcm=predicate:random_seed=2701139365: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)
% 2.35/0.92 % (2741364)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3837394541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.35/0.92 % (2741363)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=151923694:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.35/0.92 % (2741366)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=792581773:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.35/0.92 % (2741361)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=990187970:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.35/0.92 % (2741362)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=2455636928:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.35/0.92 % (2741365)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=555711357:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.35/0.92 % (2741364)Refutation not found, incomplete strategy
% 2.35/0.92 % (2741364)------------------------------
% 2.35/0.92 % (2741364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.92 % (2741367)Also succeeded, but the first one will report.
% 2.35/0.92 % (2741365)First to succeed.
% 2.35/0.92 % (2741364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.92 % (2741364)CaDiCaL version: 2.1.3
% 2.35/0.92 % (2741364)Termination reason: Refutation not found, incomplete strategy
% 2.35/0.92 % (2741364)Time elapsed: 0.001 s
% 2.35/0.92 % (2741364)Peak memory usage: 88 MB
% 2.35/0.92 % (2741366)Also succeeded, but the first one will report.
% 2.35/0.92 % (2741365)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2741356"
% 2.35/0.92 % (2741364)------------------------------
% 2.35/0.92 % (2741364)------------------------------
% 2.35/0.92 % (2741365)Refutation found. Thanks to Tanya!
% 2.35/0.92 % SZS status Theorem for theBenchmark
% 2.35/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.92 % (2741365)------------------------------
% 2.35/0.92 % (2741365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.92 % (2741365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.92 % (2741365)CaDiCaL version: 2.1.3
% 2.35/0.92 % (2741365)Termination reason: Refutation
% 2.35/0.92 % (2741365)Time elapsed: 0.001 s
% 2.35/0.92 % (2741365)Peak memory usage: 88 MB
% 2.35/0.92 % (2741365)------------------------------
% 2.35/0.92 % (2741365)------------------------------
% 2.35/0.92 % (2741356)Success in time 0.299 s
% 2.35/0.92 % Vampire exiting
%------------------------------------------------------------------------------