TSTP Solution File: GRP031-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP031-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n023.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 01:16:41 EDT 2023
% Result : Unsatisfiable 0.17s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP031-1 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31 % Computer : n023.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 29 01:07:10 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.36 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.17/0.36
% 0.17/0.36 % SZS status Unsatisfiable
% 0.17/0.36
% 0.17/0.36 % SZS output start Proof
% 0.17/0.36 Take the following subset of the input axioms:
% 0.17/0.36 fof(associativity1, axiom, ![X, Y, Z, W, U, V]: (~product(X, Y, U) | (~product(Y, Z, V) | (~product(U, Z, W) | product(X, V, W))))).
% 0.17/0.36 fof(associativity2, axiom, ![X2, Y2, Z2, W2, U2, V2]: (~product(X2, Y2, U2) | (~product(Y2, Z2, V2) | (~product(X2, V2, W2) | product(U2, Z2, W2))))).
% 0.17/0.36 fof(left_identity, hypothesis, ![A]: product(identity, A, A)).
% 0.17/0.36 fof(left_inverse, hypothesis, ![A2]: product(inverse(A2), A2, identity)).
% 0.17/0.36 fof(prove_a_has_an_inverse, negated_conjecture, ![A2]: ~product(a, A2, identity)).
% 0.17/0.36 fof(total_function1, axiom, ![X2, Y2]: product(X2, Y2, multiply(X2, Y2))).
% 0.17/0.36 fof(total_function2, axiom, ![X2, Y2, Z2, W2]: (~product(X2, Y2, Z2) | (~product(X2, Y2, W2) | Z2=W2))).
% 0.17/0.36
% 0.17/0.36 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.36 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.36 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.36 fresh(y, y, x1...xn) = u
% 0.17/0.36 C => fresh(s, t, x1...xn) = v
% 0.17/0.36 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.36 variables of u and v.
% 0.17/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.37 input problem has no model of domain size 1).
% 0.17/0.37
% 0.17/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.37
% 0.17/0.37 Axiom 1 (left_identity): product(identity, X, X) = true2.
% 0.17/0.37 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true2.
% 0.17/0.37 Axiom 3 (total_function2): fresh(X, X, Y, Z) = Z.
% 0.17/0.37 Axiom 4 (total_function1): product(X, Y, multiply(X, Y)) = true2.
% 0.17/0.37 Axiom 5 (associativity1): fresh8(X, X, Y, Z, W) = true2.
% 0.17/0.37 Axiom 6 (associativity2): fresh6(X, X, Y, Z, W) = true2.
% 0.17/0.37 Axiom 7 (total_function2): fresh2(X, X, Y, Z, W, V) = W.
% 0.17/0.37 Axiom 8 (associativity1): fresh4(X, X, Y, Z, W, V, U) = product(Y, V, U).
% 0.17/0.37 Axiom 9 (associativity2): fresh3(X, X, Y, Z, W, V, U) = product(W, V, U).
% 0.17/0.37 Axiom 10 (associativity1): fresh7(X, X, Y, Z, W, V, U, T) = fresh8(product(Y, Z, W), true2, Y, U, T).
% 0.17/0.37 Axiom 11 (associativity2): fresh5(X, X, Y, Z, W, V, U, T) = fresh6(product(Y, Z, W), true2, W, V, T).
% 0.17/0.37 Axiom 12 (total_function2): fresh2(product(X, Y, Z), true2, X, Y, W, Z) = fresh(product(X, Y, W), true2, W, Z).
% 0.17/0.37 Axiom 13 (associativity1): fresh7(product(X, Y, Z), true2, W, V, X, Y, U, Z) = fresh4(product(V, Y, U), true2, W, V, X, U, Z).
% 0.17/0.37 Axiom 14 (associativity2): fresh5(product(X, Y, Z), true2, W, X, V, Y, Z, U) = fresh3(product(W, Z, U), true2, W, X, V, Y, U).
% 0.17/0.37
% 0.17/0.37 Goal 1 (prove_a_has_an_inverse): product(a, X, identity) = true2.
% 0.17/0.37 The goal is true when:
% 0.17/0.37 X = inverse(a)
% 0.17/0.37
% 0.17/0.37 Proof:
% 0.17/0.37 product(a, inverse(a), identity)
% 0.17/0.37 = { by axiom 7 (total_function2) R->L }
% 0.17/0.37 product(fresh2(true2, true2, inverse(inverse(a)), identity, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 4 (total_function1) R->L }
% 0.17/0.37 product(fresh2(product(inverse(inverse(a)), identity, multiply(inverse(inverse(a)), identity)), true2, inverse(inverse(a)), identity, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 12 (total_function2) }
% 0.17/0.37 product(fresh(product(inverse(inverse(a)), identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 8 (associativity1) R->L }
% 0.17/0.37 product(fresh(fresh4(true2, true2, inverse(inverse(a)), inverse(a), identity, identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 2 (left_inverse) R->L }
% 0.17/0.37 product(fresh(fresh4(product(inverse(a), a, identity), true2, inverse(inverse(a)), inverse(a), identity, identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 13 (associativity1) R->L }
% 0.17/0.37 product(fresh(fresh7(product(identity, a, a), true2, inverse(inverse(a)), inverse(a), identity, a, identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 1 (left_identity) }
% 0.17/0.37 product(fresh(fresh7(true2, true2, inverse(inverse(a)), inverse(a), identity, a, identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 10 (associativity1) }
% 0.17/0.37 product(fresh(fresh8(product(inverse(inverse(a)), inverse(a), identity), true2, inverse(inverse(a)), identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 2 (left_inverse) }
% 0.17/0.37 product(fresh(fresh8(true2, true2, inverse(inverse(a)), identity, a), true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 5 (associativity1) }
% 0.17/0.37 product(fresh(true2, true2, a, multiply(inverse(inverse(a)), identity)), inverse(a), identity)
% 0.17/0.37 = { by axiom 3 (total_function2) }
% 0.17/0.37 product(multiply(inverse(inverse(a)), identity), inverse(a), identity)
% 0.17/0.37 = { by axiom 9 (associativity2) R->L }
% 0.17/0.37 fresh3(true2, true2, inverse(inverse(a)), identity, multiply(inverse(inverse(a)), identity), inverse(a), identity)
% 0.17/0.37 = { by axiom 2 (left_inverse) R->L }
% 0.17/0.37 fresh3(product(inverse(inverse(a)), inverse(a), identity), true2, inverse(inverse(a)), identity, multiply(inverse(inverse(a)), identity), inverse(a), identity)
% 0.17/0.37 = { by axiom 14 (associativity2) R->L }
% 0.17/0.37 fresh5(product(identity, inverse(a), inverse(a)), true2, inverse(inverse(a)), identity, multiply(inverse(inverse(a)), identity), inverse(a), inverse(a), identity)
% 0.17/0.37 = { by axiom 1 (left_identity) }
% 0.17/0.37 fresh5(true2, true2, inverse(inverse(a)), identity, multiply(inverse(inverse(a)), identity), inverse(a), inverse(a), identity)
% 0.17/0.37 = { by axiom 11 (associativity2) }
% 0.17/0.37 fresh6(product(inverse(inverse(a)), identity, multiply(inverse(inverse(a)), identity)), true2, multiply(inverse(inverse(a)), identity), inverse(a), identity)
% 0.17/0.37 = { by axiom 4 (total_function1) }
% 0.17/0.37 fresh6(true2, true2, multiply(inverse(inverse(a)), identity), inverse(a), identity)
% 0.17/0.37 = { by axiom 6 (associativity2) }
% 0.17/0.37 true2
% 0.17/0.37 % SZS output end Proof
% 0.17/0.37
% 0.17/0.37 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------