%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 12:17:50 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 9 ( 6 unt; 0 def)
% Number of atoms : 13 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : equalish(add(X0,n0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
fof(f2,axiom,
! [X0,X1] : equalish(add(X0,successor(X1)),successor(add(X0,X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',addition) ).
fof(f6,axiom,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(successor(X0),successor(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',successor_substitution) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ equalish(X0,X1)
| ~ equalish(X1,X2)
| equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f11,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',deny_addition_lemma) ).
fof(f20,plain,
! [X0] : equalish(successor(add(X0,n0)),successor(X0)),
inference(resolution,[],[f6,f1]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ equalish(successor(add(X0,X1)),X2)
| equalish(add(X0,successor(X1)),X2) ),
inference(resolution,[],[f9,f2]) ).
fof(f116,plain,
! [X0] : equalish(add(X0,successor(n0)),successor(X0)),
inference(resolution,[],[f34,f20]) ).
fof(f196,plain,
$false,
inference(resolution,[],[f116,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 18:39:45 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (2324731)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2324745)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2152112210:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (2324745) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2324731-2324745"...
% 0.11/0.45 % (2324745)...printing done.
% 0.11/0.45 % (2324745)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2324745)------------------------------
% 0.11/0.45 % (2324745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2324745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2324745)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2324745)Termination reason: Refutation
% 0.11/0.45 % (2324745)Time elapsed: 0.002 s
% 0.11/0.45 % (2324745)Peak memory usage: 11 MB
% 0.11/0.45 % (2324745)Instructions burned: 4 (million)
% 0.11/0.45 % (2324731)Success in time 0.035 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------