%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM027-1 : 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 : n019.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 08:51:40 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(adding_zero,axiom,
equalish(add(A,n0),A),
file('NUM001-0.ax',adding_zero) ).
cnf(addition,axiom,
equalish(add(A,successor(B)),successor(add(A,B))),
file('NUM001-0.ax',addition) ).
cnf(times_zero,axiom,
equalish(multiply(A,n0),n0),
file('NUM001-0.ax',times_zero) ).
cnf(times,axiom,
equalish(multiply(A,successor(B)),add(multiply(A,B),A)),
file('NUM001-0.ax',times) ).
cnf(successor_equality1,axiom,
( equalish(A,B)
| ~ equalish(successor(A),successor(B)) ),
file('NUM001-0.ax',successor_equality1) ).
cnf(successor_substitution,axiom,
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
file('NUM001-0.ax',successor_substitution) ).
cnf(transitivity_of_less,axiom,
( less(C,B)
| ~ less(C,A)
| ~ less(A,B) ),
file('NUM001-1.ax',transitivity_of_less) ).
cnf(smaller_number,axiom,
( less(B,C)
| ~ equalish(add(successor(A),B),C) ),
file('NUM001-1.ax',smaller_number) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(B,A)),A),B)
| ~ less(A,B) ),
file('NUM001-1.ax',less_lemma) ).
cnf(reflexivity,axiom,
equalish(X,X),
file('theBenchmark.p',reflexivity) ).
cnf(symmetry,axiom,
( equalish(Y,X)
| ~ equalish(X,Y) ),
file('theBenchmark.p',symmetry) ).
cnf(transitivity,axiom,
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',transitivity) ).
cnf(equality_preserved_over_times,axiom,
( equalish(multiply(A,C),multiply(B,C))
| ~ equalish(A,B) ),
file('theBenchmark.p',equality_preserved_over_times) ).
cnf(not_less_and_equal,axiom,
( ~ equalish(A,B)
| ~ less(A,B) ),
file('theBenchmark.p',not_less_and_equal) ).
cnf(numbers_either_less_or_equal,axiom,
( less(B,A)
| equalish(B,A)
| less(A,B) ),
file('theBenchmark.p',numbers_either_less_or_equal) ).
cnf(number_not_less_than_itself,axiom,
~ less(A,A),
file('theBenchmark.p',number_not_less_than_itself) ).
cnf(zero_is_the_first_number,axiom,
~ equalish(successor(A),n0),
file('theBenchmark.p',zero_is_the_first_number) ).
cnf(multiply_lemma,axiom,
( less(multiply(A,C),multiply(B,C))
| equalish(C,n0)
| ~ less(A,B) ),
file('theBenchmark.p',multiply_lemma) ).
cnf(b_not_less_than_a,hypothesis,
~ less(b,a),
file('theBenchmark.p',b_not_less_than_a) ).
cnf(b_times_c_less_than_a_times_c,hypothesis,
less(multiply(b,c),multiply(a,c)),
file('theBenchmark.p',b_times_c_less_than_a_times_c) ).
cnf(prove_c_is_0,negated_conjecture,
~ equalish(c,n0),
file('theBenchmark.p',prove_c_is_0) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM027-1 : 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
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 17:36:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------