%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM025-2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 08:51:39 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 11 unt; 4 nHn; 14 RR)
% Number of literals : 25 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
( ~ greater_or_equalish(C,B)
| greater_or_equalish(C,A)
| greater_or_equalish(A,B) ),
file('theBenchmark.p',transitivity_of_less) ).
cnf(smaller_number,axiom,
( ~ greater_or_equalish(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('theBenchmark.p',smaller_number) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| greater_or_equalish(A,B) ),
file('theBenchmark.p',less_lemma) ).
cnf(no_number_less_than_itself,axiom,
greater_or_equalish(A,A),
file('theBenchmark.p',no_number_less_than_itself) ).
cnf(a_less_than_b,hypothesis,
~ greater_or_equalish(a,b),
file('theBenchmark.p',a_less_than_b) ).
cnf(prove_b_not_less_than_a,negated_conjecture,
~ greater_or_equalish(b,a),
file('theBenchmark.p',prove_b_not_less_than_a) ).
cnf(t1,plain,
( ~ greater_or_equalish(b,a)
| ~ equalish(add(successor(predecessor_of_1st_minus_2nd(a,b)),b),a) ),
inference(start,[status(thm),parent(0:0)],[smaller_number]) ).
cnf(t2,plain,
( greater_or_equalish(b,a)
| equalish(add(successor(predecessor_of_1st_minus_2nd(a,b)),b),a) ),
inference(extension,[status(thm),parent(t1:1)],[less_lemma]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
~ greater_or_equalish(b,a),
inference(extension,[status(thm),parent(t2:2)],[prove_b_not_less_than_a]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ greater_or_equalish(b,b)
| greater_or_equalish(a,b)
| greater_or_equalish(b,a) ),
inference(extension,[status(thm),parent(t1:2)],[transitivity_of_less]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:2]) ).
cnf(t8,plain,
~ greater_or_equalish(a,b),
inference(extension,[status(thm),parent(t6:2)],[a_less_than_b]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
greater_or_equalish(b,b),
inference(extension,[status(thm),parent(t6:3)],[no_number_less_than_itself]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM025-2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_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
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 17:35:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------