%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG005-1 : 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 : n015.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 1.89s 2.14s
% Output : Proof 1.89s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('RNG001-0.ax',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X),
file('RNG001-0.ax',additive_identity2) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('RNG001-0.ax',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('RNG001-0.ax',closure_of_addition) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X),X,additive_identity),
file('RNG001-0.ax',left_inverse) ).
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(associativity_of_multiplication1,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('RNG001-0.ax',associativity_of_multiplication1) ).
cnf(associativity_of_multiplication2,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('RNG001-0.ax',associativity_of_multiplication2) ).
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(distributivity2,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('RNG001-0.ax',distributivity2) ).
cnf(distributivity3,axiom,
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('RNG001-0.ax',distributivity3) ).
cnf(distributivity4,axiom,
( product(V3,X,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('RNG001-0.ax',distributivity4) ).
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(multiplication_is_well_defined,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('RNG001-0.ax',multiplication_is_well_defined) ).
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_id,negated_conjecture,
~ sum(c,d,additive_identity),
file('theBenchmark.p',prove_sum_is_additive_id) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( multiply(Eq_x_0,Eq_x_1) = multiply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( add(Eq_x_0,Eq_x_1) = add(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( additive_inverse(Eq_x_0) = additive_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sum(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sum(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(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-1 : 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
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 20:37:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 1.89/2.14 % SZS status Unsatisfiable for theBenchmark
% 1.89/2.14 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------