%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : BOO013-3 : 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 : n018.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 08:13:58 AM UTC 2026
% Result : Unsatisfiable 21.65s 21.90s
% Output : Proof 21.71s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)),
file('BOO002-0.ax',closure_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)),
file('BOO002-0.ax',closure_of_multiplication) ).
cnf(commutativity_of_addition,axiom,
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('BOO002-0.ax',commutativity_of_addition) ).
cnf(commutativity_of_multiplication,axiom,
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('BOO002-0.ax',commutativity_of_multiplication) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X),
file('BOO002-0.ax',additive_identity1) ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X),
file('BOO002-0.ax',additive_identity2) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X),
file('BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_identity2,axiom,
product(X,multiplicative_identity,X),
file('BOO002-0.ax',multiplicative_identity2) ).
cnf(distributivity1,axiom,
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('BOO002-0.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('BOO002-0.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('BOO002-0.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('BOO002-0.ax',distributivity4) ).
cnf(distributivity5,axiom,
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('BOO002-0.ax',distributivity5) ).
cnf(distributivity6,axiom,
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('BOO002-0.ax',distributivity6) ).
cnf(distributivity7,axiom,
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('BOO002-0.ax',distributivity7) ).
cnf(distributivity8,axiom,
( sum(V3,X,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('BOO002-0.ax',distributivity8) ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity),
file('BOO002-0.ax',additive_inverse1) ).
cnf(additive_inverse2,axiom,
sum(X,inverse(X),multiplicative_identity),
file('BOO002-0.ax',additive_inverse2) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity),
file('BOO002-0.ax',multiplicative_inverse1) ).
cnf(multiplicative_inverse2,axiom,
product(X,inverse(X),additive_identity),
file('BOO002-0.ax',multiplicative_inverse2) ).
cnf(addition_is_well_defined,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('BOO002-0.ax',addition_is_well_defined) ).
cnf(multiplication_is_well_defined,axiom,
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('BOO002-0.ax',multiplication_is_well_defined) ).
cnf(inverse_is_an_involution,axiom,
inverse(inverse(X)) = X,
file('theBenchmark.p',inverse_is_an_involution) ).
cnf(sum_to_multiplicative_identity1,negated_conjecture,
sum(x,y,multiplicative_identity),
file('theBenchmark.p',sum_to_multiplicative_identity1) ).
cnf(sum_to_multiplicative_identity2,negated_conjecture,
sum(x,z,multiplicative_identity),
file('theBenchmark.p',sum_to_multiplicative_identity2) ).
cnf(product_to_additive_identity1,negated_conjecture,
product(x,y,additive_identity),
file('theBenchmark.p',product_to_additive_identity1) ).
cnf(product_to_additive_identity2,negated_conjecture,
product(x,z,additive_identity),
file('theBenchmark.p',product_to_additive_identity2) ).
cnf(prove_both_inverse_are_equal,negated_conjecture,
y != z,
file('theBenchmark.p',prove_both_inverse_are_equal) ).
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,
( 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_5,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_6,axiom,
( inverse(Eq_x_0) = 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 : BOO013-3 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 13:37:57 UTC 2026
% 0.12/0.36 % CPUTime :
% 21.65/21.90 % SZS status Unsatisfiable for theBenchmark
% 21.65/21.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------