%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM024-1 : 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 08:51:39 AM UTC 2026
% Result : Unsatisfiable 4.05s 4.30s
% Output : Proof 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 31 ( 20 unt; 0 nHn; 29 RR)
% Number of literals : 46 ( 0 equ; 17 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 : 14 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(adding_zero,axiom,
equalish(add(A,n0),A),
file('NUM001-0.ax',adding_zero) ).
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(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(plus_substitution,axiom,
( equalish(A,C)
| ~ equalish(add(A,B),add(C,B)) ),
file('theBenchmark.p',plus_substitution) ).
cnf(commutativity_of_plus,axiom,
equalish(add(A,B),add(B,A)),
file('theBenchmark.p',commutativity_of_plus) ).
cnf(impossible_a_is_less_than_itself,hypothesis,
less(a,a),
file('theBenchmark.p',impossible_a_is_less_than_itself) ).
cnf(prove_a_contradiction,negated_conjecture,
~ equalish(successor(A),n0),
file('theBenchmark.p',prove_a_contradiction) ).
cnf(t1,plain,
~ equalish(successor(predecessor_of_1st_minus_2nd(a,a)),n0),
inference(start,[status(thm),parent(0:0)],[prove_a_contradiction]) ).
cnf(t2,plain,
( ~ equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),add(n0,a))
| equalish(successor(predecessor_of_1st_minus_2nd(a,a)),n0) ),
inference(extension,[status(thm),parent(t1:1)],[plus_substitution]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ equalish(a,add(n0,a))
| ~ equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a)
| equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),add(n0,a)) ),
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(a,a)
| ~ equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a)
| equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a) ),
inference(extension,[status(thm),parent(t4:2)],[transitivity]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ less(a,a)
| equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a) ),
inference(extension,[status(thm),parent(t6:2)],[less_lemma]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
less(a,a),
inference(extension,[status(thm),parent(t8:2)],[impossible_a_is_less_than_itself]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ equalish(add(a,a),add(a,a))
| equalish(a,a) ),
inference(extension,[status(thm),parent(t6:3)],[plus_substitution]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t6:3]) ).
cnf(t14,plain,
equalish(add(a,a),add(a,a)),
inference(extension,[status(thm),parent(t12:2)],[commutativity_of_plus]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ equalish(add(a,n0),add(n0,a))
| ~ equalish(a,add(a,n0))
| equalish(a,add(n0,a)) ),
inference(extension,[status(thm),parent(t4:3)],[transitivity]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
( ~ equalish(add(a,n0),a)
| equalish(a,add(a,n0)) ),
inference(extension,[status(thm),parent(t16:2)],[symmetry]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
equalish(add(a,n0),a),
inference(extension,[status(thm),parent(t18:2)],[adding_zero]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
equalish(add(a,n0),add(n0,a)),
inference(extension,[status(thm),parent(t16:3)],[commutativity_of_plus]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM024-1 : 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
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 17:35:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 4.05/4.30 % SZS status Unsatisfiable for theBenchmark
% 4.05/4.30 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------