%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:11:36 PM UTC 2026
% Result : Unsatisfiable 3.59s 1.48s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of formulae : 5 ( 4 unt; 0 def)
% Number of atoms : 6 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 3 ( 2 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : equalish(add(X0,n0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adding_zero) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ equalish(add(successor(X0),X1),X2)
| less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',smaller_number) ).
fof(f15,negated_conjecture,
~ less(n0,successor(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_is_less_than_all_successors) ).
fof(f29,plain,
! [X0] : less(n0,successor(X0)),
inference(resolution,[],[f8,f1]) ).
fof(f33,plain,
$false,
inference(resolution,[],[f29,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 18:40:01 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.59/1.48 % (1096580)Input is clausal, will run a generic CNF schedule.
% 3.59/1.48 % (1096587)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1210626359:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.59/1.48 % (1096585)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=2125336850:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.59/1.48 % (1096586)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2176413332:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.59/1.48 % (1096589)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1639345926:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.59/1.48 % (1096588)lrs+10_1_sil=8000:sp=occurrence:random_seed=2268766230:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.59/1.48 % (1096591)dis-21_1_sil=8000:lcm=predicate:random_seed=348095333:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.59/1.48 % (1096590)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2998137339:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.59/1.48 % (1096589)Also succeeded, but the first one will report.
% 3.59/1.48 % (1096588)First to succeed.
% 3.59/1.48 % (1096590)Also succeeded, but the first one will report.
% 3.59/1.48 % (1096591)Also succeeded, but the first one will report.
% 3.59/1.48 % (1096588)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1096580"
% 3.59/1.48 % (1096588)Refutation found. Thanks to Tanya!
% 3.59/1.48 % SZS status Unsatisfiable for theBenchmark
% 3.59/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.48 % (1096588)------------------------------
% 3.59/1.48 % (1096588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.48 % (1096588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.48 % (1096588)CaDiCaL version: 2.1.3
% 3.59/1.48 % (1096588)Termination reason: Refutation
% 3.59/1.48 % (1096588)Time elapsed: 0.002 s
% 3.59/1.48 % (1096588)Peak memory usage: 88 MB
% 3.59/1.48 % (1096588)Instructions burned: 1 (million)
% 3.59/1.48 % (1096588)------------------------------
% 3.59/1.48 % (1096588)------------------------------
% 3.59/1.48 % (1096580)Success in time 0.436 s
% 3.59/1.48 % Vampire exiting
%------------------------------------------------------------------------------