%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 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 : n001.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 08:54:53 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 16 unt; 0 nHn; 18 RR)
% Number of literals : 30 ( 0 equ; 12 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 12 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_inverse,axiom,
sum(X,additive_inverse(X),additive_identity),
file('theBenchmark.p',right_inverse) ).
cnf(commutativity_of_addition,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('theBenchmark.p',commutativity_of_addition) ).
cnf(distributivity3,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('theBenchmark.p',distributivity3) ).
cnf(multiplicative_identity1,axiom,
product(additive_identity,X,additive_identity),
file('theBenchmark.p',multiplicative_identity1) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('theBenchmark.p',a_times_b) ).
cnf(a_inverse_times_b,hypothesis,
product(additive_inverse(a),b,c),
file('theBenchmark.p',a_inverse_times_b) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(t1,plain,
~ sum(c,d,additive_identity),
inference(start,[status(thm),parent(0:0)],[prove_sum_is_additive_identity]) ).
cnf(t2,plain,
( ~ product(a,b,d)
| ~ sum(additive_inverse(a),a,additive_identity)
| ~ product(additive_identity,b,additive_identity)
| ~ product(additive_inverse(a),b,c)
| sum(c,d,additive_identity) ),
inference(extension,[status(thm),parent(t1:1)],[distributivity3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
product(additive_inverse(a),b,c),
inference(extension,[status(thm),parent(t2:2)],[a_inverse_times_b]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
product(additive_identity,b,additive_identity),
inference(extension,[status(thm),parent(t2:3)],[multiplicative_identity1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( ~ sum(a,additive_inverse(a),additive_identity)
| sum(additive_inverse(a),a,additive_identity) ),
inference(extension,[status(thm),parent(t2:4)],[commutativity_of_addition]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
sum(a,additive_inverse(a),additive_identity),
inference(extension,[status(thm),parent(t8:2)],[right_inverse]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
product(a,b,d),
inference(extension,[status(thm),parent(t2:5)],[a_times_b]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-2 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 20:40:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------