TSTP Solution File: FLD001-3 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : FLD001-3 : 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 22:36:45 EDT 2023
% Result : Unsatisfiable 6.42s 1.26s
% Output : Proof 7.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : FLD001-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 23:27:07 EDT 2023
% 0.15/0.35 % CPUTime :
% 6.42/1.26 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 6.42/1.26
% 6.42/1.26 % SZS status Unsatisfiable
% 6.42/1.26
% 6.42/1.27 % SZS output start Proof
% 6.42/1.27 Take the following subset of the input axioms:
% 6.42/1.27 fof(a_is_defined, hypothesis, defined(a)).
% 6.42/1.27 fof(commutativity_multiplication, axiom, ![X, Y, Z]: (product(Y, X, Z) | ~product(X, Y, Z))).
% 6.42/1.27 fof(distributivity_2, axiom, ![C, D, B, A2, X2, Y2, Z2]: (product(A2, Z2, B) | (~sum(X2, Y2, A2) | (~product(X2, Z2, C) | (~product(Y2, Z2, D) | ~sum(C, D, B)))))).
% 6.42/1.27 fof(existence_of_identity_addition, axiom, ![X2]: (sum(additive_identity, X2, X2) | ~defined(X2))).
% 6.42/1.27 fof(existence_of_identity_multiplication, axiom, ![X2]: (product(multiplicative_identity, X2, X2) | ~defined(X2))).
% 6.42/1.27 fof(not_product_4, negated_conjecture, ~product(multiplicative_identity, a, b)).
% 6.42/1.27 fof(sum_3, hypothesis, sum(additive_identity, a, b)).
% 6.42/1.27 fof(well_definedness_of_additive_identity, axiom, defined(additive_identity)).
% 6.42/1.27
% 6.42/1.27 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.42/1.27 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.42/1.27 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.42/1.27 fresh(y, y, x1...xn) = u
% 6.42/1.27 C => fresh(s, t, x1...xn) = v
% 6.42/1.27 where fresh is a fresh function symbol and x1..xn are the free
% 6.42/1.27 variables of u and v.
% 6.42/1.27 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.42/1.27 input problem has no model of domain size 1).
% 6.42/1.27
% 6.42/1.27 The encoding turns the above axioms into the following unit equations and goals:
% 6.42/1.27
% 6.42/1.27 Axiom 1 (a_is_defined): defined(a) = true.
% 6.42/1.27 Axiom 2 (well_definedness_of_additive_identity): defined(additive_identity) = true.
% 6.42/1.27 Axiom 3 (existence_of_identity_addition): fresh14(X, X, Y) = true.
% 6.42/1.27 Axiom 4 (existence_of_identity_multiplication): fresh13(X, X, Y) = true.
% 6.42/1.27 Axiom 5 (sum_3): sum(additive_identity, a, b) = true.
% 6.42/1.27 Axiom 6 (existence_of_identity_addition): fresh14(defined(X), true, X) = sum(additive_identity, X, X).
% 6.42/1.27 Axiom 7 (existence_of_identity_multiplication): fresh13(defined(X), true, X) = product(multiplicative_identity, X, X).
% 6.42/1.27 Axiom 8 (distributivity_2): fresh32(X, X, Y, Z, W) = true.
% 6.42/1.27 Axiom 9 (commutativity_multiplication): fresh17(X, X, Y, Z, W) = true.
% 6.42/1.27 Axiom 10 (distributivity_2): fresh30(X, X, Y, Z, W, V, U) = product(Y, Z, W).
% 6.42/1.27 Axiom 11 (commutativity_multiplication): fresh17(product(X, Y, Z), true, Y, X, Z) = product(Y, X, Z).
% 6.42/1.27 Axiom 12 (distributivity_2): fresh31(X, X, Y, Z, W, V, U, T, S) = fresh32(sum(V, U, Y), true, Y, Z, W).
% 6.42/1.27 Axiom 13 (distributivity_2): fresh29(X, X, Y, Z, W, V, U, T, S) = fresh30(sum(T, S, W), true, Y, Z, W, V, U).
% 6.42/1.27 Axiom 14 (distributivity_2): fresh29(product(X, Y, Z), true, W, Y, V, U, X, T, Z) = fresh31(product(U, Y, T), true, W, Y, V, U, X, T, Z).
% 6.42/1.27
% 6.42/1.27 Goal 1 (not_product_4): product(multiplicative_identity, a, b) = true.
% 6.42/1.27 Proof:
% 6.42/1.27 product(multiplicative_identity, a, b)
% 6.42/1.27 = { by axiom 11 (commutativity_multiplication) R->L }
% 6.42/1.27 fresh17(product(a, multiplicative_identity, b), true, multiplicative_identity, a, b)
% 6.42/1.27 = { by axiom 10 (distributivity_2) R->L }
% 6.42/1.27 fresh17(fresh30(true, true, a, multiplicative_identity, b, additive_identity, a), true, multiplicative_identity, a, b)
% 6.42/1.27 = { by axiom 5 (sum_3) R->L }
% 6.42/1.27 fresh17(fresh30(sum(additive_identity, a, b), true, a, multiplicative_identity, b, additive_identity, a), true, multiplicative_identity, a, b)
% 6.42/1.27 = { by axiom 13 (distributivity_2) R->L }
% 6.42/1.27 fresh17(fresh29(true, true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 6.42/1.27 = { by axiom 9 (commutativity_multiplication) R->L }
% 6.42/1.27 fresh17(fresh29(fresh17(true, true, a, multiplicative_identity, a), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 6.42/1.27 = { by axiom 4 (existence_of_identity_multiplication) R->L }
% 6.42/1.27 fresh17(fresh29(fresh17(fresh13(true, true, a), true, a, multiplicative_identity, a), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.06/1.27 = { by axiom 1 (a_is_defined) R->L }
% 7.06/1.28 fresh17(fresh29(fresh17(fresh13(defined(a), true, a), true, a, multiplicative_identity, a), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.06/1.28 = { by axiom 7 (existence_of_identity_multiplication) }
% 7.07/1.28 fresh17(fresh29(fresh17(product(multiplicative_identity, a, a), true, a, multiplicative_identity, a), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 11 (commutativity_multiplication) }
% 7.07/1.28 fresh17(fresh29(product(a, multiplicative_identity, a), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 14 (distributivity_2) }
% 7.07/1.28 fresh17(fresh31(product(additive_identity, multiplicative_identity, additive_identity), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 11 (commutativity_multiplication) R->L }
% 7.07/1.28 fresh17(fresh31(fresh17(product(multiplicative_identity, additive_identity, additive_identity), true, additive_identity, multiplicative_identity, additive_identity), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 7 (existence_of_identity_multiplication) R->L }
% 7.07/1.28 fresh17(fresh31(fresh17(fresh13(defined(additive_identity), true, additive_identity), true, additive_identity, multiplicative_identity, additive_identity), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 2 (well_definedness_of_additive_identity) }
% 7.07/1.28 fresh17(fresh31(fresh17(fresh13(true, true, additive_identity), true, additive_identity, multiplicative_identity, additive_identity), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 4 (existence_of_identity_multiplication) }
% 7.07/1.28 fresh17(fresh31(fresh17(true, true, additive_identity, multiplicative_identity, additive_identity), true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 9 (commutativity_multiplication) }
% 7.07/1.28 fresh17(fresh31(true, true, a, multiplicative_identity, b, additive_identity, a, additive_identity, a), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 12 (distributivity_2) }
% 7.07/1.28 fresh17(fresh32(sum(additive_identity, a, a), true, a, multiplicative_identity, b), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 6 (existence_of_identity_addition) R->L }
% 7.07/1.28 fresh17(fresh32(fresh14(defined(a), true, a), true, a, multiplicative_identity, b), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 1 (a_is_defined) }
% 7.07/1.28 fresh17(fresh32(fresh14(true, true, a), true, a, multiplicative_identity, b), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 3 (existence_of_identity_addition) }
% 7.07/1.28 fresh17(fresh32(true, true, a, multiplicative_identity, b), true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 8 (distributivity_2) }
% 7.07/1.28 fresh17(true, true, multiplicative_identity, a, b)
% 7.07/1.28 = { by axiom 9 (commutativity_multiplication) }
% 7.07/1.28 true
% 7.07/1.28 % SZS output end Proof
% 7.07/1.28
% 7.07/1.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------