%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG003-1 : 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 : 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 08:54:53 AM UTC 2026
% Result : Unsatisfiable 1.06s 1.39s
% Output : Proof 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 26 unt; 0 nHn; 37 RR)
% Number of literals : 62 ( 8 equ; 25 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity2,axiom,
sum(X,additive_identity,X),
file('RNG001-0.ax',additive_identity2) ).
cnf(right_inverse,axiom,
sum(X,additive_inverse(X),additive_identity),
file('RNG001-0.ax',right_inverse) ).
cnf(associativity_of_addition1,axiom,
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('RNG001-0.ax',associativity_of_addition1) ).
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(addition_is_well_defined,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('RNG001-0.ax',addition_is_well_defined) ).
cnf(a_plus_c_is_d,hypothesis,
sum(a,c,d),
file('theBenchmark.p',a_plus_c_is_d) ).
cnf(b_plus_c_is_d,hypothesis,
sum(b,c,d),
file('theBenchmark.p',b_plus_c_is_d) ).
cnf(prove_a_equals_b,negated_conjecture,
a != b,
file('theBenchmark.p',prove_a_equals_b) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(t1,plain,
a != b,
inference(start,[status(thm),parent(0:0)],[prove_a_equals_b]) ).
cnf(t2,plain,
( b != a
| a = b ),
inference(extension,[status(thm),parent(t1:1)],[equality_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ sum(additive_inverse(c),d,a)
| ~ sum(additive_inverse(c),d,b)
| b = a ),
inference(extension,[status(thm),parent(t2:2)],[addition_is_well_defined]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ sum(d,additive_inverse(c),b)
| sum(additive_inverse(c),d,b) ),
inference(extension,[status(thm),parent(t4:2)],[commutativity_of_addition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ sum(c,additive_inverse(c),additive_identity)
| ~ sum(b,additive_identity,b)
| ~ sum(b,c,d)
| sum(d,additive_inverse(c),b) ),
inference(extension,[status(thm),parent(t6:2)],[associativity_of_addition2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
sum(b,c,d),
inference(extension,[status(thm),parent(t8:2)],[b_plus_c_is_d]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
sum(b,additive_identity,b),
inference(extension,[status(thm),parent(t8:3)],[additive_identity2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
sum(c,additive_inverse(c),additive_identity),
inference(extension,[status(thm),parent(t8:4)],[right_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
cnf(t16,plain,
( ~ sum(c,a,d)
| ~ sum(additive_identity,a,a)
| ~ sum(additive_inverse(c),c,additive_identity)
| sum(additive_inverse(c),d,a) ),
inference(extension,[status(thm),parent(t4:3)],[associativity_of_addition1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
( ~ sum(c,additive_inverse(c),additive_identity)
| sum(additive_inverse(c),c,additive_identity) ),
inference(extension,[status(thm),parent(t16:2)],[commutativity_of_addition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
sum(c,additive_inverse(c),additive_identity),
inference(extension,[status(thm),parent(t18:2)],[right_inverse]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ sum(a,additive_identity,a)
| sum(additive_identity,a,a) ),
inference(extension,[status(thm),parent(t16:3)],[commutativity_of_addition]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t16:3]) ).
cnf(t24,plain,
sum(a,additive_identity,a),
inference(extension,[status(thm),parent(t22:2)],[additive_identity2]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
( ~ sum(a,c,d)
| sum(c,a,d) ),
inference(extension,[status(thm),parent(t16:4)],[commutativity_of_addition]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t16:4]) ).
cnf(t28,plain,
sum(a,c,d),
inference(extension,[status(thm),parent(t26:2)],[a_plus_c_is_d]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % 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 20:34:50 UTC 2026
% 0.13/0.36 % CPUTime :
% 1.06/1.39 % SZS status Unsatisfiable for theBenchmark
% 1.06/1.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------