TSTP Solution File: SET053-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SET053-6 : 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 : n032.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 15:30:53 EDT 2023
% Result : Unsatisfiable 0.16s 0.49s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET053-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 08:58:43 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.49 Command-line arguments: --no-flatten-goal
% 0.16/0.49
% 0.16/0.49 % SZS status Unsatisfiable
% 0.16/0.49
% 0.16/0.49 % SZS output start Proof
% 0.16/0.49 Take the following subset of the input axioms:
% 0.16/0.49 fof(cartesian_product2, axiom, ![X, Y, U, V]: (~member(ordered_pair(U, V), cross_product(X, Y)) | member(V, Y))).
% 0.16/0.49 fof(class_elements_are_sets, axiom, ![X2]: subclass(X2, universal_class)).
% 0.16/0.49 fof(prove_corollary_2_to_cartesian_product_1, negated_conjecture, member(ordered_pair(u, v), cross_product(x, y))).
% 0.16/0.49 fof(prove_corollary_2_to_cartesian_product_2, negated_conjecture, ~member(v, universal_class)).
% 0.16/0.49 fof(subclass_members, axiom, ![X2, Y2, U2]: (~subclass(X2, Y2) | (~member(U2, X2) | member(U2, Y2)))).
% 0.16/0.49
% 0.16/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.49 fresh(y, y, x1...xn) = u
% 0.16/0.49 C => fresh(s, t, x1...xn) = v
% 0.16/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.49 variables of u and v.
% 0.16/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.49 input problem has no model of domain size 1).
% 0.16/0.49
% 0.16/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.49
% 0.16/0.49 Axiom 1 (class_elements_are_sets): subclass(X, universal_class) = true2.
% 0.16/0.49 Axiom 2 (cartesian_product2): fresh64(X, X, Y, Z) = true2.
% 0.16/0.49 Axiom 3 (subclass_members): fresh10(X, X, Y, Z) = true2.
% 0.16/0.49 Axiom 4 (subclass_members): fresh11(X, X, Y, Z, W) = member(W, Z).
% 0.16/0.49 Axiom 5 (prove_corollary_2_to_cartesian_product_1): member(ordered_pair(u, v), cross_product(x, y)) = true2.
% 0.16/0.49 Axiom 6 (subclass_members): fresh11(member(X, Y), true2, Y, Z, X) = fresh10(subclass(Y, Z), true2, Z, X).
% 0.16/0.49 Axiom 7 (cartesian_product2): fresh64(member(ordered_pair(X, Y), cross_product(Z, W)), true2, Y, W) = member(Y, W).
% 0.16/0.49
% 0.16/0.49 Goal 1 (prove_corollary_2_to_cartesian_product_2): member(v, universal_class) = true2.
% 0.16/0.49 Proof:
% 0.16/0.49 member(v, universal_class)
% 0.16/0.49 = { by axiom 4 (subclass_members) R->L }
% 0.16/0.49 fresh11(true2, true2, y, universal_class, v)
% 0.16/0.49 = { by axiom 2 (cartesian_product2) R->L }
% 0.16/0.49 fresh11(fresh64(true2, true2, v, y), true2, y, universal_class, v)
% 0.16/0.49 = { by axiom 5 (prove_corollary_2_to_cartesian_product_1) R->L }
% 0.16/0.49 fresh11(fresh64(member(ordered_pair(u, v), cross_product(x, y)), true2, v, y), true2, y, universal_class, v)
% 0.16/0.49 = { by axiom 7 (cartesian_product2) }
% 0.16/0.49 fresh11(member(v, y), true2, y, universal_class, v)
% 0.16/0.49 = { by axiom 6 (subclass_members) }
% 0.16/0.49 fresh10(subclass(y, universal_class), true2, universal_class, v)
% 0.16/0.49 = { by axiom 1 (class_elements_are_sets) }
% 0.16/0.49 fresh10(true2, true2, universal_class, v)
% 0.16/0.49 = { by axiom 3 (subclass_members) }
% 0.16/0.49 true2
% 0.16/0.49 % SZS output end Proof
% 0.16/0.49
% 0.16/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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