%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 08:51:39 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 8 ( 6 unt; 0 nHn; 7 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 2 ( 1 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 : 4 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(adding_zero,axiom,
equalish(add(A,n0),A),
file('NUM001-0.ax',adding_zero) ).
cnf(smaller_number,axiom,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('NUM001-1.ax',smaller_number) ).
cnf(prove_zero_is_less_than_all_successors,negated_conjecture,
~ less(n0,successor(a)),
file('theBenchmark.p',prove_zero_is_less_than_all_successors) ).
cnf(t1,plain,
~ less(n0,successor(a)),
inference(start,[status(thm),parent(0:0)],[prove_zero_is_less_than_all_successors]) ).
cnf(t2,plain,
( ~ equalish(add(successor(a),n0),successor(a))
| less(n0,successor(a)) ),
inference(extension,[status(thm),parent(t1:1)],[smaller_number]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
equalish(add(successor(a),n0),successor(a)),
inference(extension,[status(thm),parent(t2:2)],[adding_zero]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM023-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.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 : Sat Sep 19 17:30:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------