TSTP Solution File: SET203-6 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET203-6 : 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 : n026.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 15:31:40 EDT 2023
% Result : Unsatisfiable 0.21s 0.61s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET203-6 : 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
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:16:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.61
% 0.21/0.61 % SZS status Unsatisfiable
% 0.21/0.61
% 0.21/0.61 % SZS output start Proof
% 0.21/0.61 Take the following subset of the input axioms:
% 0.21/0.61 fof(cartesian_product3, axiom, ![X, Y, U, V]: (~member(U, X) | (~member(V, Y) | member(ordered_pair(U, V), cross_product(X, Y))))).
% 0.21/0.61 fof(class_elements_are_sets, axiom, ![X2]: subclass(X2, universal_class)).
% 0.21/0.61 fof(prove_corollary_to_X_product_property1_1, negated_conjecture, member(u, x)).
% 0.21/0.61 fof(prove_corollary_to_X_product_property1_2, negated_conjecture, member(v, y)).
% 0.21/0.61 fof(prove_corollary_to_X_product_property1_3, negated_conjecture, ~member(ordered_pair(u, v), cross_product(universal_class, universal_class))).
% 0.21/0.61 fof(subclass_members, axiom, ![X2, Y2, U2]: (~subclass(X2, Y2) | (~member(U2, X2) | member(U2, Y2)))).
% 0.21/0.61
% 0.21/0.61 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.61 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.61 fresh(y, y, x1...xn) = u
% 0.21/0.61 C => fresh(s, t, x1...xn) = v
% 0.21/0.61 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.61 variables of u and v.
% 0.21/0.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.61 input problem has no model of domain size 1).
% 0.21/0.61
% 0.21/0.61 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.61
% 0.21/0.61 Axiom 1 (class_elements_are_sets): subclass(X, universal_class) = true2.
% 0.21/0.61 Axiom 2 (prove_corollary_to_X_product_property1_1): member(u, x) = true2.
% 0.21/0.61 Axiom 3 (prove_corollary_to_X_product_property1_2): member(v, y) = true2.
% 0.21/0.61 Axiom 4 (subclass_members): fresh15(X, X, Y, Z) = true2.
% 0.21/0.61 Axiom 5 (subclass_members): fresh16(X, X, Y, Z, W) = member(W, Z).
% 0.21/0.61 Axiom 6 (cartesian_product3): fresh74(X, X, Y, Z, W, V) = true2.
% 0.21/0.61 Axiom 7 (cartesian_product3): fresh75(X, X, Y, Z, W, V) = member(ordered_pair(Y, W), cross_product(Z, V)).
% 0.21/0.61 Axiom 8 (subclass_members): fresh16(member(X, Y), true2, Y, Z, X) = fresh15(subclass(Y, Z), true2, Z, X).
% 0.21/0.61 Axiom 9 (cartesian_product3): fresh75(member(X, Y), true2, Z, W, X, Y) = fresh74(member(Z, W), true2, Z, W, X, Y).
% 0.21/0.61
% 0.21/0.61 Goal 1 (prove_corollary_to_X_product_property1_3): member(ordered_pair(u, v), cross_product(universal_class, universal_class)) = true2.
% 0.21/0.61 Proof:
% 0.21/0.61 member(ordered_pair(u, v), cross_product(universal_class, universal_class))
% 0.21/0.61 = { by axiom 7 (cartesian_product3) R->L }
% 0.21/0.61 fresh75(true2, true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 4 (subclass_members) R->L }
% 0.21/0.61 fresh75(fresh15(true2, true2, universal_class, v), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 1 (class_elements_are_sets) R->L }
% 0.21/0.61 fresh75(fresh15(subclass(y, universal_class), true2, universal_class, v), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 8 (subclass_members) R->L }
% 0.21/0.61 fresh75(fresh16(member(v, y), true2, y, universal_class, v), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 3 (prove_corollary_to_X_product_property1_2) }
% 0.21/0.61 fresh75(fresh16(true2, true2, y, universal_class, v), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 5 (subclass_members) }
% 0.21/0.61 fresh75(member(v, universal_class), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 9 (cartesian_product3) }
% 0.21/0.61 fresh74(member(u, universal_class), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 5 (subclass_members) R->L }
% 0.21/0.61 fresh74(fresh16(true2, true2, x, universal_class, u), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 2 (prove_corollary_to_X_product_property1_1) R->L }
% 0.21/0.61 fresh74(fresh16(member(u, x), true2, x, universal_class, u), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 8 (subclass_members) }
% 0.21/0.61 fresh74(fresh15(subclass(x, universal_class), true2, universal_class, u), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 1 (class_elements_are_sets) }
% 0.21/0.61 fresh74(fresh15(true2, true2, universal_class, u), true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 4 (subclass_members) }
% 0.21/0.61 fresh74(true2, true2, u, universal_class, v, universal_class)
% 0.21/0.61 = { by axiom 6 (cartesian_product3) }
% 0.21/0.61 true2
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61
% 0.21/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------