%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM020-1 : 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 : n020.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 0.11s 0.44s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 14 unt; 0 nHn; 16 RR)
% Number of literals : 27 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 1 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 : 9 ( 0 sgn)
% 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(successor_substitution,axiom,
( equalish(successor(A),successor(B))
| ~ equalish(A,B) ),
file('NUM001-0.ax',successor_substitution) ).
cnf(reflexivity,axiom,
equalish(X,X),
file('theBenchmark.p',reflexivity) ).
cnf(transitivity,axiom,
( equalish(X,Z)
| ~ equalish(Y,Z)
| ~ equalish(X,Y) ),
file('theBenchmark.p',transitivity) ).
cnf(deny_addition_lemma,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)),
file('theBenchmark.p',deny_addition_lemma) ).
cnf(t1,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(start,[status(thm),parent(0:0)],[deny_addition_lemma]) ).
cnf(t2,plain,
( ~ equalish(successor(add(a,n0)),successor(a))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| equalish(add(a,successor(n0)),successor(a)) ),
inference(extension,[status(thm),parent(t1:1)],[transitivity]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equalish(successor(add(a,n0)),successor(add(a,n0)))
| ~ equalish(add(a,successor(n0)),successor(add(a,n0)))
| equalish(add(a,successor(n0)),successor(add(a,n0))) ),
inference(extension,[status(thm),parent(t2:2)],[transitivity]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
equalish(add(a,successor(n0)),successor(add(a,n0))),
inference(extension,[status(thm),parent(t4:2)],[addition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
equalish(successor(add(a,n0)),successor(add(a,n0))),
inference(extension,[status(thm),parent(t4:3)],[reflexivity]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ equalish(add(a,n0),a)
| equalish(successor(add(a,n0)),successor(a)) ),
inference(extension,[status(thm),parent(t2:3)],[successor_substitution]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
equalish(add(a,n0),a),
inference(extension,[status(thm),parent(t10:2)],[adding_zero]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020-1 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.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 : Sat Sep 19 17:36:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------