TPTP Problem File: KLE122-10.p

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% File     : KLE122-10 : TPTP v7.5.0. Released v7.3.0.
% Domain   : Puzzles
% Problem  : Validity of conditional rule
% 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   : 1.00 v7.3.0
% Syntax   : Number of clauses     :   33 (   0 non-Horn;  33 unit;   3 RR)
%            Number of atoms       :   33 (  33 equality)
%            Maximal clause size   :    1 (   1 average)
%            Number of predicates  :    1 (   0 propositional; 2-2 arity)
%            Number of functors    :   24 (   8 constant; 0-4 arity)
%            Number of variables   :   54 (   4 singleton)
%            Maximal term depth    :    6 (   3 average)
% SPC      : CNF_UNS_RFO_PEQ_UEQ

% Comments : Converted from KLE122+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(additive_commutativity,axiom,
    ( addition(A,B) = addition(B,A) )).

cnf(additive_associativity,axiom,
    ( addition(A,addition(B,C)) = addition(addition(A,B),C) )).

cnf(additive_identity,axiom,
    ( addition(A,zero) = A )).

cnf(additive_idempotence,axiom,
    ( addition(A,A) = A )).

cnf(multiplicative_associativity,axiom,
    ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )).

cnf(multiplicative_right_identity,axiom,
    ( multiplication(A,one) = A )).

cnf(multiplicative_left_identity,axiom,
    ( multiplication(one,A) = A )).

cnf(right_distributivity,axiom,
    ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )).

cnf(left_distributivity,axiom,
    ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )).

cnf(right_annihilation,axiom,
    ( multiplication(A,zero) = zero )).

cnf(left_annihilation,axiom,
    ( multiplication(zero,A) = zero )).

cnf(order_1,axiom,
    ( ifeq(leq(A,B),true,addition(A,B),B) = B )).

cnf(order,axiom,
    ( ifeq2(addition(A,B),B,leq(A,B),true) = true )).

cnf(domain1,axiom,
    ( multiplication(antidomain(X0),X0) = zero )).

cnf(domain2,axiom,
    ( addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1))))) = antidomain(multiplication(X0,antidomain(antidomain(X1)))) )).

cnf(domain3,axiom,
    ( addition(antidomain(antidomain(X0)),antidomain(X0)) = one )).

cnf(domain4,axiom,
    ( domain(X0) = antidomain(antidomain(X0)) )).

cnf(codomain1,axiom,
    ( multiplication(X0,coantidomain(X0)) = zero )).

cnf(codomain2,axiom,
    ( addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)) )).

cnf(codomain3,axiom,
    ( addition(coantidomain(coantidomain(X0)),coantidomain(X0)) = one )).

cnf(codomain4,axiom,
    ( codomain(X0) = coantidomain(coantidomain(X0)) )).

cnf(complement,axiom,
    ( c(X0) = antidomain(domain(X0)) )).

cnf(domain_difference,axiom,
    ( domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)) )).

cnf(forward_diamond,axiom,
    ( forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))) )).

cnf(backward_diamond,axiom,
    ( backward_diamond(X0,X1) = codomain(multiplication(codomain(X1),X0)) )).

cnf(forward_box,axiom,
    ( forward_box(X0,X1) = c(forward_diamond(X0,c(X1))) )).

cnf(backward_box,axiom,
    ( backward_box(X0,X1) = c(backward_diamond(X0,c(X1))) )).

cnf(if_then_else_definition,axiom,
    ( if_then_else(X0,X1,X2) = addition(multiplication(domain(X0),X1),multiplication(antidomain(X0),X2)) )).

cnf(goals,negated_conjecture,
    ( addition(backward_diamond(sK5_goals_X1,multiplication(antidomain(sK4_goals_X2),domain(sK3_goals_X3))),domain(sK2_goals_X4)) = domain(sK2_goals_X4) )).

cnf(goals_1,negated_conjecture,
    ( addition(backward_diamond(sK1_goals_X0,multiplication(domain(sK4_goals_X2),domain(sK3_goals_X3))),domain(sK2_goals_X4)) = domain(sK2_goals_X4) )).

cnf(goals_2,negated_conjecture,
    ( addition(backward_diamond(if_then_else(sK4_goals_X2,sK1_goals_X0,sK5_goals_X1),domain(sK3_goals_X3)),domain(sK2_goals_X4)) != domain(sK2_goals_X4) )).

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