TSTP Solution File: KLE005+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n027.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 05:35:23 EDT 2023
% Result : Theorem 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE005+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n027.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 : Tue Aug 29 11:32:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.41
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 Take the following subset of the input axioms:
% 0.19/0.42 fof(additive_identity, axiom, ![A]: addition(A, zero)=A).
% 0.19/0.42 fof(goals, conjecture, c(one)=zero).
% 0.19/0.42 fof(left_annihilation, axiom, ![A2]: multiplication(zero, A2)=zero).
% 0.19/0.42 fof(multiplicative_right_identity, axiom, ![A2]: multiplication(A2, one)=A2).
% 0.19/0.42 fof(right_annihilation, axiom, ![A2]: multiplication(A2, zero)=zero).
% 0.19/0.42 fof(test_1, axiom, ![X0]: (test(X0) <=> ?[X1]: complement(X1, X0))).
% 0.19/0.42 fof(test_2, axiom, ![X0_2, X1_2]: (complement(X1_2, X0_2) <=> (multiplication(X0_2, X1_2)=zero & (multiplication(X1_2, X0_2)=zero & addition(X0_2, X1_2)=one)))).
% 0.19/0.42 fof(test_3, axiom, ![X0_2, X1_2]: (test(X0_2) => (c(X0_2)=X1_2 <=> complement(X0_2, X1_2)))).
% 0.19/0.42
% 0.19/0.42 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.42 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.42 fresh(y, y, x1...xn) = u
% 0.19/0.42 C => fresh(s, t, x1...xn) = v
% 0.19/0.42 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.42 variables of u and v.
% 0.19/0.42 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.42 input problem has no model of domain size 1).
% 0.19/0.42
% 0.19/0.42 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.42
% 0.19/0.42 Axiom 1 (additive_identity): addition(X, zero) = X.
% 0.19/0.42 Axiom 2 (multiplicative_right_identity): multiplication(X, one) = X.
% 0.19/0.42 Axiom 3 (right_annihilation): multiplication(X, zero) = zero.
% 0.19/0.42 Axiom 4 (left_annihilation): multiplication(zero, X) = zero.
% 0.19/0.42 Axiom 5 (test_1_1): fresh10(X, X, Y) = true.
% 0.19/0.42 Axiom 6 (test_2): fresh14(X, X, Y, Z) = true.
% 0.19/0.42 Axiom 7 (test_2): fresh9(X, X, Y, Z) = complement(Z, Y).
% 0.19/0.42 Axiom 8 (test_2_2): fresh7(X, X, Y, Z) = zero.
% 0.19/0.42 Axiom 9 (test_3): fresh5(X, X, Y, Z) = complement(Y, Z).
% 0.19/0.42 Axiom 10 (test_3): fresh4(X, X, Y, Z) = true.
% 0.19/0.42 Axiom 11 (test_1_1): fresh10(complement(X, Y), true, Y) = test(Y).
% 0.19/0.42 Axiom 12 (test_3): fresh5(test(X), true, X, Y) = fresh4(c(X), Y, X, Y).
% 0.19/0.42 Axiom 13 (test_2): fresh13(X, X, Y, Z) = fresh14(addition(Y, Z), one, Y, Z).
% 0.19/0.42 Axiom 14 (test_2): fresh13(multiplication(X, Y), zero, Y, X) = fresh9(multiplication(Y, X), zero, Y, X).
% 0.19/0.42 Axiom 15 (test_2_2): fresh7(complement(X, Y), true, Y, X) = multiplication(Y, X).
% 0.19/0.42
% 0.19/0.42 Goal 1 (goals): c(one) = zero.
% 0.19/0.42 Proof:
% 0.19/0.42 c(one)
% 0.19/0.42 = { by axiom 2 (multiplicative_right_identity) R->L }
% 0.19/0.42 multiplication(c(one), one)
% 0.19/0.42 = { by axiom 15 (test_2_2) R->L }
% 0.19/0.42 fresh7(complement(one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 9 (test_3) R->L }
% 0.19/0.42 fresh7(fresh5(true, true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 5 (test_1_1) R->L }
% 0.19/0.42 fresh7(fresh5(fresh10(true, true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 6 (test_2) R->L }
% 0.19/0.42 fresh7(fresh5(fresh10(fresh14(one, one, one, zero), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 1 (additive_identity) R->L }
% 0.19/0.42 fresh7(fresh5(fresh10(fresh14(addition(one, zero), one, one, zero), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 13 (test_2) R->L }
% 0.19/0.42 fresh7(fresh5(fresh10(fresh13(zero, zero, one, zero), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 4 (left_annihilation) R->L }
% 0.19/0.42 fresh7(fresh5(fresh10(fresh13(multiplication(zero, one), zero, one, zero), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 14 (test_2) }
% 0.19/0.42 fresh7(fresh5(fresh10(fresh9(multiplication(one, zero), zero, one, zero), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 3 (right_annihilation) }
% 0.19/0.42 fresh7(fresh5(fresh10(fresh9(zero, zero, one, zero), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 7 (test_2) }
% 0.19/0.42 fresh7(fresh5(fresh10(complement(zero, one), true, one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 11 (test_1_1) }
% 0.19/0.42 fresh7(fresh5(test(one), true, one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 12 (test_3) }
% 0.19/0.42 fresh7(fresh4(c(one), c(one), one, c(one)), true, c(one), one)
% 0.19/0.42 = { by axiom 10 (test_3) }
% 0.19/0.42 fresh7(true, true, c(one), one)
% 0.19/0.42 = { by axiom 8 (test_2_2) }
% 0.19/0.42 zero
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------