TSTP Solution File: FLD034-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD034-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 22:36:57 EDT 2023
% Result : Unsatisfiable 0.21s 0.63s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : FLD034-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 00:50:37 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.63 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.63
% 0.21/0.63 % SZS status Unsatisfiable
% 0.21/0.63
% 0.21/0.64 % SZS output start Proof
% 0.21/0.64 Take the following subset of the input axioms:
% 0.21/0.64 fof(a_is_defined, hypothesis, defined(a)).
% 0.21/0.64 fof(associativity_multiplication_2, axiom, ![X, V, W, Y, U, Z]: (product(U, Z, W) | (~product(X, Y, U) | (~product(Y, Z, V) | ~product(X, V, W))))).
% 0.21/0.64 fof(commutativity_multiplication, axiom, ![X2, Y2, Z2]: (product(Y2, X2, Z2) | ~product(X2, Y2, Z2))).
% 0.21/0.64 fof(existence_of_identity_multiplication, axiom, ![X2]: (product(multiplicative_identity, X2, X2) | ~defined(X2))).
% 0.21/0.64 fof(not_product_4, negated_conjecture, ~product(m, a, a)).
% 0.21/0.64 fof(product_3, negated_conjecture, product(multiplicative_identity, m, multiplicative_identity)).
% 0.21/0.64
% 0.21/0.64 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.64 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.64 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.64 fresh(y, y, x1...xn) = u
% 0.21/0.64 C => fresh(s, t, x1...xn) = v
% 0.21/0.64 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.64 variables of u and v.
% 0.21/0.64 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.64 input problem has no model of domain size 1).
% 0.21/0.64
% 0.21/0.64 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.64
% 0.21/0.64 Axiom 1 (a_is_defined): defined(a) = true.
% 0.21/0.64 Axiom 2 (existence_of_identity_multiplication): fresh13(X, X, Y) = true.
% 0.21/0.64 Axiom 3 (product_3): product(multiplicative_identity, m, multiplicative_identity) = true.
% 0.21/0.64 Axiom 4 (existence_of_identity_multiplication): fresh13(defined(X), true, X) = product(multiplicative_identity, X, X).
% 0.21/0.64 Axiom 5 (associativity_multiplication_2): fresh38(X, X, Y, Z, W) = true.
% 0.21/0.64 Axiom 6 (commutativity_multiplication): fresh17(X, X, Y, Z, W) = true.
% 0.21/0.64 Axiom 7 (associativity_multiplication_2): fresh19(X, X, Y, Z, W, V, U) = product(Y, Z, W).
% 0.21/0.64 Axiom 8 (associativity_multiplication_2): fresh37(X, X, Y, Z, W, V, U, T) = fresh38(product(V, U, Y), true, Y, Z, W).
% 0.21/0.64 Axiom 9 (commutativity_multiplication): fresh17(product(X, Y, Z), true, Y, X, Z) = product(Y, X, Z).
% 0.21/0.64 Axiom 10 (associativity_multiplication_2): fresh37(product(X, Y, Z), true, W, Y, V, U, X, Z) = fresh19(product(U, Z, V), true, W, Y, V, U, X).
% 0.21/0.64
% 0.21/0.64 Lemma 11: product(a, multiplicative_identity, a) = true.
% 0.21/0.64 Proof:
% 0.21/0.64 product(a, multiplicative_identity, a)
% 0.21/0.64 = { by axiom 9 (commutativity_multiplication) R->L }
% 0.21/0.64 fresh17(product(multiplicative_identity, a, a), true, a, multiplicative_identity, a)
% 0.21/0.64 = { by axiom 4 (existence_of_identity_multiplication) R->L }
% 0.21/0.64 fresh17(fresh13(defined(a), true, a), true, a, multiplicative_identity, a)
% 0.21/0.64 = { by axiom 1 (a_is_defined) }
% 0.21/0.64 fresh17(fresh13(true, true, a), true, a, multiplicative_identity, a)
% 0.21/0.64 = { by axiom 2 (existence_of_identity_multiplication) }
% 0.21/0.64 fresh17(true, true, a, multiplicative_identity, a)
% 0.21/0.64 = { by axiom 6 (commutativity_multiplication) }
% 0.21/0.64 true
% 0.21/0.64
% 0.21/0.64 Goal 1 (not_product_4): product(m, a, a) = true.
% 0.21/0.64 Proof:
% 0.21/0.64 product(m, a, a)
% 0.21/0.64 = { by axiom 9 (commutativity_multiplication) R->L }
% 0.21/0.64 fresh17(product(a, m, a), true, m, a, a)
% 0.21/0.64 = { by axiom 7 (associativity_multiplication_2) R->L }
% 0.21/0.64 fresh17(fresh19(true, true, a, m, a, a, multiplicative_identity), true, m, a, a)
% 0.21/0.64 = { by lemma 11 R->L }
% 0.21/0.64 fresh17(fresh19(product(a, multiplicative_identity, a), true, a, m, a, a, multiplicative_identity), true, m, a, a)
% 0.21/0.64 = { by axiom 10 (associativity_multiplication_2) R->L }
% 0.21/0.64 fresh17(fresh37(product(multiplicative_identity, m, multiplicative_identity), true, a, m, a, a, multiplicative_identity, multiplicative_identity), true, m, a, a)
% 0.21/0.64 = { by axiom 3 (product_3) }
% 0.21/0.64 fresh17(fresh37(true, true, a, m, a, a, multiplicative_identity, multiplicative_identity), true, m, a, a)
% 0.21/0.64 = { by axiom 8 (associativity_multiplication_2) }
% 0.21/0.64 fresh17(fresh38(product(a, multiplicative_identity, a), true, a, m, a), true, m, a, a)
% 0.21/0.64 = { by lemma 11 }
% 0.21/0.64 fresh17(fresh38(true, true, a, m, a), true, m, a, a)
% 0.21/0.64 = { by axiom 5 (associativity_multiplication_2) }
% 0.21/0.64 fresh17(true, true, m, a, a)
% 0.21/0.64 = { by axiom 6 (commutativity_multiplication) }
% 0.21/0.64 true
% 0.21/0.64 % SZS output end Proof
% 0.21/0.64
% 0.21/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------