%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n026.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 08:54:52 AM UTC 2026
% Result : Unsatisfiable 252.43s 262.77s
% Output : Proof 252.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 54 ( 39 unt; 0 nHn; 51 RR)
% Number of literals : 89 ( 16 equ; 37 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('RNG001-0.ax',additive_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('RNG001-0.ax',closure_of_multiplication) ).
cnf(right_inverse,axiom,
sum(X,additive_inverse(X),additive_identity),
file('RNG001-0.ax',right_inverse) ).
cnf(associativity_of_addition2,axiom,
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('RNG001-0.ax',associativity_of_addition2) ).
cnf(commutativity_of_addition,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('RNG001-0.ax',commutativity_of_addition) ).
cnf(distributivity1,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('RNG001-0.ax',distributivity1) ).
cnf(addition_is_well_defined,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('RNG001-0.ax',addition_is_well_defined) ).
cnf(prove_a_times_0_is_0,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('theBenchmark.p',prove_a_times_0_is_0) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_8,axiom,
( product(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ product(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ product(a,additive_identity,additive_identity),
inference(start,[status(thm),parent(0:0)],[prove_a_times_0_is_0]) ).
cnf(t2,plain,
( multiply(a,additive_identity) != additive_identity
| additive_identity != additive_identity
| ~ product(a,additive_identity,multiply(a,additive_identity))
| a != a
| product(a,additive_identity,additive_identity) ),
inference(extension,[status(thm),parent(t1:1)],[equality_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( a != a
| a = a ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sum(additive_identity,a,a)
| ~ sum(additive_identity,a,a)
| a = a ),
inference(extension,[status(thm),parent(t4:2)],[addition_is_well_defined]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
sum(additive_identity,a,a),
inference(extension,[status(thm),parent(t6:2)],[additive_identity1]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sum(additive_identity,a,a),
inference(extension,[status(thm),parent(t6:3)],[additive_identity1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(extension,[status(thm),parent(t2:3)],[closure_of_multiplication]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
cnf(t14,plain,
( additive_identity != additive_identity
| additive_identity = additive_identity ),
inference(extension,[status(thm),parent(t2:4)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:4]) ).
cnf(t16,plain,
( ~ sum(additive_identity,additive_identity,additive_identity)
| ~ sum(additive_identity,additive_identity,additive_identity)
| additive_identity = additive_identity ),
inference(extension,[status(thm),parent(t14:2)],[addition_is_well_defined]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(extension,[status(thm),parent(t16:2)],[additive_identity1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(extension,[status(thm),parent(t16:3)],[additive_identity1]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( ~ sum(additive_identity,multiply(a,additive_identity),additive_identity)
| ~ sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity))
| multiply(a,additive_identity) = additive_identity ),
inference(extension,[status(thm),parent(t2:5)],[addition_is_well_defined]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:5]) ).
cnf(t24,plain,
sum(additive_identity,multiply(a,additive_identity),multiply(a,additive_identity)),
inference(extension,[status(thm),parent(t22:2)],[additive_identity1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity)
| ~ sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity))
| sum(additive_identity,multiply(a,additive_identity),additive_identity) ),
inference(extension,[status(thm),parent(t22:3)],[associativity_of_addition2]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ sum(additive_identity,additive_identity,additive_identity)
| ~ product(a,additive_identity,multiply(a,additive_identity))
| ~ product(a,additive_identity,multiply(a,additive_identity))
| sum(multiply(a,additive_identity),multiply(a,additive_identity),multiply(a,additive_identity)) ),
inference(extension,[status(thm),parent(t26:2)],[distributivity1]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(extension,[status(thm),parent(t28:2)],[closure_of_multiplication]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(extension,[status(thm),parent(t28:3)],[closure_of_multiplication]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t28:3]) ).
cnf(t34,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(extension,[status(thm),parent(t28:4)],[additive_identity1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t28:4]) ).
cnf(t36,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(extension,[status(thm),parent(t28:5)],[closure_of_multiplication]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:5]) ).
cnf(t38,plain,
( ~ sum(multiply(a,additive_identity),additive_inverse(multiply(a,additive_identity)),additive_identity)
| sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity) ),
inference(extension,[status(thm),parent(t26:3)],[commutativity_of_addition]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t26:3]) ).
cnf(t40,plain,
sum(multiply(a,additive_identity),additive_inverse(multiply(a,additive_identity)),additive_identity),
inference(extension,[status(thm),parent(t38:2)],[right_inverse]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(l19,lemma,
sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity),
inference(lemma,[status(cth),parent(t26:3),below(t22:3)],[t26:3]) ).
cnf(t42,plain,
sum(additive_inverse(multiply(a,additive_identity)),multiply(a,additive_identity),additive_identity),
inference(lemma_extension,[status(thm),parent(t26:4)],[l19:1]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t26:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_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
% 0.09/10.39 % Computer : n026.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Sat Sep 19 20:37:02 UTC 2026
% 0.09/10.39 % CPUTime :
% 252.43/262.77 % SZS status Unsatisfiable for theBenchmark
% 252.43/262.77 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------