TSTP Solution File: GRP028-2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP028-2 : TPTP v8.1.2. Released v1.1.0.
% 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 : n013.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 : Thu Aug 31 01:16:40 EDT 2023
% Result : Unsatisfiable 0.16s 0.40s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : GRP028-2 : TPTP v8.1.2. Released v1.1.0.
% 0.06/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 21:47:16 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.16/0.40 Command-line arguments: --ground-connectedness --complete-subsets
% 0.16/0.40
% 0.16/0.40 % SZS status Unsatisfiable
% 0.16/0.40
% 0.16/0.41 % SZS output start Proof
% 0.16/0.41 Take the following subset of the input axioms:
% 0.16/0.41 fof(associativity2, axiom, ![X, Y, Z, W, U, V]: (~product(X, Y, U) | (~product(Y, Z, V) | (~product(X, V, W) | product(U, Z, W))))).
% 0.16/0.41 fof(left_soln, hypothesis, ![X2, Y2]: product(left_solution(X2, Y2), X2, Y2)).
% 0.16/0.41 fof(prove_there_is_a_right_identity, negated_conjecture, ![X2]: ~product(not_identity(X2), X2, not_identity(X2))).
% 0.16/0.41 fof(right_soln, hypothesis, ![X2, Y2]: product(X2, right_solution(X2, Y2), Y2)).
% 0.16/0.41 fof(total_function1, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 0.16/0.41 fof(total_function2, axiom, ![X2, Y2, Z2, W2]: (~product(X2, Y2, Z2) | (~product(X2, Y2, W2) | Z2=W2))).
% 0.16/0.41
% 0.16/0.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.41 fresh(y, y, x1...xn) = u
% 0.16/0.41 C => fresh(s, t, x1...xn) = v
% 0.16/0.41 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.41 variables of u and v.
% 0.16/0.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.41 input problem has no model of domain size 1).
% 0.16/0.41
% 0.16/0.41 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.41
% 0.16/0.41 Axiom 1 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.16/0.41 Axiom 2 (associativity2): fresh6(X, X, Y, Z, W) = true2.
% 0.16/0.41 Axiom 3 (total_function1): product(X, Y, multiply(X, Y)) = true2.
% 0.16/0.41 Axiom 4 (right_soln): product(X, right_solution(X, Y), Y) = true2.
% 0.16/0.41 Axiom 5 (left_soln): product(left_solution(X, Y), X, Y) = true2.
% 0.16/0.41 Axiom 6 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.16/0.41 Axiom 7 (associativity2): fresh3(X, X, Y, Z, W, V, U) = product(W, V, U).
% 0.16/0.41 Axiom 8 (associativity2): fresh5(X, X, Y, Z, W, V, U, T) = fresh6(product(Y, Z, W), true2, W, V, T).
% 0.16/0.41 Axiom 9 (total_function2): fresh2(product(X, Y, Z), true2, X, Y, W, Z) = fresh(product(X, Y, W), true2, W, Z).
% 0.16/0.41 Axiom 10 (associativity2): fresh5(product(X, Y, Z), true2, W, X, V, Y, Z, U) = fresh3(product(W, Z, U), true2, W, X, V, Y, U).
% 0.16/0.41
% 0.16/0.41 Lemma 11: fresh(product(X, Y, Z), true2, Z, multiply(X, Y)) = Z.
% 0.16/0.41 Proof:
% 0.16/0.41 fresh(product(X, Y, Z), true2, Z, multiply(X, Y))
% 0.16/0.41 = { by axiom 9 (total_function2) R->L }
% 0.16/0.41 fresh2(product(X, Y, multiply(X, Y)), true2, X, Y, Z, multiply(X, Y))
% 0.16/0.41 = { by axiom 3 (total_function1) }
% 0.16/0.41 fresh2(true2, true2, X, Y, Z, multiply(X, Y))
% 0.16/0.41 = { by axiom 6 (total_function2) }
% 0.16/0.41 Z
% 0.16/0.41
% 0.16/0.41 Goal 1 (prove_there_is_a_right_identity): product(not_identity(X), X, not_identity(X)) = true2.
% 0.16/0.41 The goal is true when:
% 0.16/0.41 X = right_solution(X, X)
% 0.16/0.41
% 0.16/0.41 Proof:
% 0.16/0.41 product(not_identity(right_solution(X, X)), right_solution(X, X), not_identity(right_solution(X, X)))
% 0.16/0.41 = { by lemma 11 R->L }
% 0.16/0.41 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(product(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.41 = { by axiom 7 (associativity2) R->L }
% 0.16/0.41 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(fresh3(true2, true2, left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 5 (left_soln) R->L }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(fresh3(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true2, left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 10 (associativity2) R->L }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(fresh5(product(X, right_solution(X, X), multiply(X, right_solution(X, X))), true2, left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 3 (total_function1) }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(fresh5(true2, true2, left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 8 (associativity2) }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(fresh6(product(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X)), true2, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 3 (total_function1) }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(fresh6(true2, true2, multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X), not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 2 (associativity2) }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), fresh(true2, true2, not_identity(right_solution(X, X)), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X))))
% 0.16/0.42 = { by axiom 1 (total_function2) }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(multiply(left_solution(multiply(X, right_solution(X, X)), not_identity(right_solution(X, X))), X), right_solution(X, X)))
% 0.16/0.42 = { by axiom 1 (total_function2) R->L }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(multiply(left_solution(fresh(true2, true2, X, multiply(X, right_solution(X, X))), not_identity(right_solution(X, X))), X), right_solution(X, X)))
% 0.16/0.42 = { by axiom 4 (right_soln) R->L }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(multiply(left_solution(fresh(product(X, right_solution(X, X), X), true2, X, multiply(X, right_solution(X, X))), not_identity(right_solution(X, X))), X), right_solution(X, X)))
% 0.16/0.42 = { by lemma 11 }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(multiply(left_solution(X, not_identity(right_solution(X, X))), X), right_solution(X, X)))
% 0.16/0.42 = { by axiom 1 (total_function2) R->L }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(fresh(true2, true2, not_identity(right_solution(X, X)), multiply(left_solution(X, not_identity(right_solution(X, X))), X)), right_solution(X, X)))
% 0.16/0.42 = { by axiom 5 (left_soln) R->L }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(fresh(product(left_solution(X, not_identity(right_solution(X, X))), X, not_identity(right_solution(X, X))), true2, not_identity(right_solution(X, X)), multiply(left_solution(X, not_identity(right_solution(X, X))), X)), right_solution(X, X)))
% 0.16/0.42 = { by lemma 11 }
% 0.16/0.42 product(not_identity(right_solution(X, X)), right_solution(X, X), multiply(not_identity(right_solution(X, X)), right_solution(X, X)))
% 0.16/0.42 = { by axiom 3 (total_function1) }
% 0.16/0.42 true2
% 0.16/0.42 % SZS output end Proof
% 0.16/0.42
% 0.16/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------