%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 08:51:37 AM UTC 2026
% Result : Unsatisfiable 53.66s 58.90s
% Output : Proof 53.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 9 unt; 2 nHn; 15 RR)
% Number of literals : 23 ( 0 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 4 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a2,axiom,
( little_set(X)
| ~ member(X,Y) ),
file('SET003-0.ax',a2) ).
cnf(infinity2,axiom,
member(empty_set,infinity),
file('SET003-0.ax',infinity2) ).
cnf(natural_numbers4,axiom,
( member(empty_set,f44(Z))
| ~ little_set(Z)
| member(Z,natural_numbers) ),
file('NUM003-0.ax',natural_numbers4) ).
cnf(natural_numbers6,axiom,
( ~ member(Z,f44(Z))
| member(Z,natural_numbers) ),
file('NUM003-0.ax',natural_numbers6) ).
cnf(prove_zero_is_a_natural,negated_conjecture,
~ member(empty_set,natural_numbers),
file('theBenchmark.p',prove_zero_is_a_natural) ).
cnf(t1,plain,
~ member(empty_set,natural_numbers),
inference(start,[status(thm),parent(0:0)],[prove_zero_is_a_natural]) ).
cnf(t2,plain,
( ~ little_set(empty_set)
| member(empty_set,f44(empty_set))
| member(empty_set,natural_numbers) ),
inference(extension,[status(thm),parent(t1:1)],[natural_numbers4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( member(empty_set,natural_numbers)
| ~ member(empty_set,f44(empty_set)) ),
inference(extension,[status(thm),parent(t2:2)],[natural_numbers6]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
$false,
inference(reduction,[status(thm),parent(t4:2)],[t4:2,t1:1]) ).
cnf(t7,plain,
( ~ member(empty_set,infinity)
| little_set(empty_set) ),
inference(extension,[status(thm),parent(t2:3)],[a2]) ).
cnf(t8,plain,
$false,
inference(connection,[status(thm),parent(t7:1)],[t7:1,t2:3]) ).
cnf(t9,plain,
member(empty_set,infinity),
inference(extension,[status(thm),parent(t7:2)],[infinity2]) ).
cnf(t10,plain,
$false,
inference(connection,[status(thm),parent(t9:1)],[t9:1,t7:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n014.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sat Sep 19 17:34:28 UTC 2026
% 0.11/5.38 % CPUTime :
% 53.66/58.90 % SZS status Unsatisfiable for theBenchmark
% 53.66/58.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------