TPTP Problem File: BOO015-10.p
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- Solve Problem
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% File : BOO015-10 : TPTP v9.0.0. Released v7.5.0.
% Domain : Puzzles
% Problem : DeMorgan for inverse and sum (X^-1 + Y^-1) = (X * Y)^-1
% Version : Especial.
% English :
% Refs : [CS18] Claessen & Smallbone (2018), Efficient Encodings of Fi
% : [Sma18] Smallbone (2018), Email to Geoff Sutcliffe
% Source : [Sma18]
% Names :
% Status : Unsatisfiable
% Rating : 0.77 v9.0.0, 0.73 v8.2.0, 0.71 v8.1.0, 0.70 v7.5.0
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 3 RR)
% Number of literals : 27 ( 27 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 88 ( 2 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments : Converted from BOO015-1 to UEQ using [CS18].
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cnf(ifeq_axiom,axiom,
ifeq2(A,A,B,C) = B ).
cnf(ifeq_axiom_001,axiom,
ifeq(A,A,B,C) = B ).
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)) = true ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)) = true ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true ).
cnf(commutativity_of_multiplication,axiom,
ifeq(product(X,Y,Z),true,product(Y,X,Z),true) = true ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X) = true ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X) = true ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X) = true ).
cnf(multiplicative_identity2,axiom,
product(X,multiplicative_identity,X) = true ).
cnf(distributivity1,axiom,
ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true ).
cnf(distributivity2,axiom,
ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y,Z,V3),true,product(X,V3,V4),true),true),true),true) = true ).
cnf(distributivity3,axiom,
ifeq(product(V3,X,V4),true,ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true ).
cnf(distributivity4,axiom,
ifeq(product(Z,X,V2),true,ifeq(product(Y,X,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y,Z,V3),true,product(V3,X,V4),true),true),true),true) = true ).
cnf(distributivity5,axiom,
ifeq(product(Y,Z,V3),true,ifeq(sum(X,V3,V4),true,ifeq(sum(X,Z,V2),true,ifeq(sum(X,Y,V1),true,product(V1,V2,V4),true),true),true),true) = true ).
cnf(distributivity6,axiom,
ifeq(product(V1,V2,V4),true,ifeq(product(Y,Z,V3),true,ifeq(sum(X,Z,V2),true,ifeq(sum(X,Y,V1),true,sum(X,V3,V4),true),true),true),true) = true ).
cnf(distributivity7,axiom,
ifeq(product(Y,Z,V3),true,ifeq(sum(V3,X,V4),true,ifeq(sum(Z,X,V2),true,ifeq(sum(Y,X,V1),true,product(V1,V2,V4),true),true),true),true) = true ).
cnf(distributivity8,axiom,
ifeq(product(V1,V2,V4),true,ifeq(product(Y,Z,V3),true,ifeq(sum(Z,X,V2),true,ifeq(sum(Y,X,V1),true,sum(V3,X,V4),true),true),true),true) = true ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity) = true ).
cnf(additive_inverse2,axiom,
sum(X,inverse(X),multiplicative_identity) = true ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity) = true ).
cnf(multiplicative_inverse2,axiom,
product(X,inverse(X),additive_identity) = true ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V ).
cnf(x_times_y,negated_conjecture,
product(x,y,x_times_y) = true ).
cnf(x_inverse_plus_y_inverse,negated_conjecture,
sum(inverse(x),inverse(y),x_inverse_plus_y_inverse) = true ).
cnf(prove_equation,negated_conjecture,
inverse(x_times_y) != x_inverse_plus_y_inverse ).
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