TSTP Solution File: SET059-6 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET059-6 : 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 : 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 15:30:56 EDT 2023
% Result : Unsatisfiable 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET059-6 : 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
% 0.13/0.35 % Computer : n027.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 15:23:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.52 Command-line arguments: --no-flatten-goal
% 0.21/0.52
% 0.21/0.52 % SZS status Unsatisfiable
% 0.21/0.52
% 0.21/0.52 % SZS output start Proof
% 0.21/0.52 Take the following subset of the input axioms:
% 0.21/0.52 fof(not_subclass_members2, axiom, ![X, Y]: (~member(not_subclass_element(X, Y), Y) | subclass(X, Y))).
% 0.21/0.52 fof(prove_equality4_1, negated_conjecture, member(not_subclass_element(x, y), y)).
% 0.21/0.52 fof(prove_equality4_2, negated_conjecture, member(not_subclass_element(y, x), x)).
% 0.21/0.52 fof(prove_equality4_3, negated_conjecture, x!=y).
% 0.21/0.52 fof(subclass_implies_equal, axiom, ![X2, Y2]: (~subclass(X2, Y2) | (~subclass(Y2, X2) | X2=Y2))).
% 0.21/0.52
% 0.21/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.52 fresh(y, y, x1...xn) = u
% 0.21/0.52 C => fresh(s, t, x1...xn) = v
% 0.21/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.52 variables of u and v.
% 0.21/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.52 input problem has no model of domain size 1).
% 0.21/0.52
% 0.21/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.52
% 0.21/0.52 Axiom 1 (not_subclass_members2): fresh29(X, X, Y, Z) = true2.
% 0.21/0.52 Axiom 2 (subclass_implies_equal): fresh4(X, X, Y, Z) = Y.
% 0.21/0.52 Axiom 3 (subclass_implies_equal): fresh3(X, X, Y, Z) = Z.
% 0.21/0.52 Axiom 4 (prove_equality4_1): member(not_subclass_element(x, y), y) = true2.
% 0.21/0.52 Axiom 5 (prove_equality4_2): member(not_subclass_element(y, x), x) = true2.
% 0.21/0.52 Axiom 6 (subclass_implies_equal): fresh4(subclass(X, Y), true2, Y, X) = fresh3(subclass(Y, X), true2, Y, X).
% 0.21/0.53 Axiom 7 (not_subclass_members2): fresh29(member(not_subclass_element(X, Y), Y), true2, X, Y) = subclass(X, Y).
% 0.21/0.53
% 0.21/0.53 Goal 1 (prove_equality4_3): x = y.
% 0.21/0.53 Proof:
% 0.21/0.53 x
% 0.21/0.53 = { by axiom 3 (subclass_implies_equal) R->L }
% 0.21/0.53 fresh3(true2, true2, y, x)
% 0.21/0.53 = { by axiom 1 (not_subclass_members2) R->L }
% 0.21/0.53 fresh3(fresh29(true2, true2, y, x), true2, y, x)
% 0.21/0.53 = { by axiom 5 (prove_equality4_2) R->L }
% 0.21/0.53 fresh3(fresh29(member(not_subclass_element(y, x), x), true2, y, x), true2, y, x)
% 0.21/0.53 = { by axiom 7 (not_subclass_members2) }
% 0.21/0.53 fresh3(subclass(y, x), true2, y, x)
% 0.21/0.53 = { by axiom 6 (subclass_implies_equal) R->L }
% 0.21/0.53 fresh4(subclass(x, y), true2, y, x)
% 0.21/0.53 = { by axiom 7 (not_subclass_members2) R->L }
% 0.21/0.53 fresh4(fresh29(member(not_subclass_element(x, y), y), true2, x, y), true2, y, x)
% 0.21/0.53 = { by axiom 4 (prove_equality4_1) }
% 0.21/0.53 fresh4(fresh29(true2, true2, x, y), true2, y, x)
% 0.21/0.53 = { by axiom 1 (not_subclass_members2) }
% 0.21/0.53 fresh4(true2, true2, y, x)
% 0.21/0.53 = { by axiom 2 (subclass_implies_equal) }
% 0.21/0.53 y
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53
% 0.21/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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