TSTP Solution File: SET086+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n031.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 15:31:10 EDT 2023
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.06/0.13 % 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 : n031.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 12:22:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.53 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.53
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 Take the following subset of the input axioms:
% 0.20/0.53 fof(complement, axiom, ![X, Z]: (member(Z, complement(X)) <=> (member(Z, universal_class) & ~member(Z, X)))).
% 0.20/0.53 fof(disjoint_defn, axiom, ![Y, X2]: (disjoint(X2, Y) <=> ![U]: ~(member(U, X2) & member(U, Y)))).
% 0.20/0.53 fof(domain_of, axiom, ![X2, Z2]: (member(Z2, domain_of(X2)) <=> (member(Z2, universal_class) & restrict(X2, singleton(Z2), universal_class)!=null_class))).
% 0.20/0.53 fof(member_of_substitution, conjecture, ![X2]: ?[U2]: ((member(U2, universal_class) & X2=singleton(U2)) | (~?[Y2]: (member(Y2, universal_class) & X2=singleton(Y2)) & U2=X2))).
% 0.20/0.53 fof(null_class_defn, axiom, ![X2]: ~member(X2, null_class)).
% 0.20/0.53
% 0.20/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.53 fresh(y, y, x1...xn) = u
% 0.20/0.53 C => fresh(s, t, x1...xn) = v
% 0.20/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.53 variables of u and v.
% 0.20/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.53 input problem has no model of domain size 1).
% 0.20/0.53
% 0.20/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.53
% 0.20/0.53 Axiom 1 (member_of_substitution): fresh36(X, X) = x.
% 0.20/0.53 Axiom 2 (member_of_substitution): fresh36(X, x) = singleton(y).
% 0.20/0.53 Axiom 3 (member_of_substitution_1): fresh35(X, X) = true2.
% 0.20/0.53 Axiom 4 (member_of_substitution_1): fresh35(X, x) = member(y, universal_class).
% 0.20/0.53
% 0.20/0.53 Goal 1 (member_of_substitution_2): tuple3(x, member(X, universal_class)) = tuple3(singleton(X), true2).
% 0.20/0.53 The goal is true when:
% 0.20/0.53 X = y
% 0.20/0.53
% 0.20/0.53 Proof:
% 0.20/0.53 tuple3(x, member(y, universal_class))
% 0.20/0.53 = { by axiom 4 (member_of_substitution_1) R->L }
% 0.20/0.53 tuple3(x, fresh35(x, x))
% 0.20/0.53 = { by axiom 3 (member_of_substitution_1) }
% 0.20/0.53 tuple3(x, true2)
% 0.20/0.53 = { by axiom 1 (member_of_substitution) R->L }
% 0.20/0.53 tuple3(fresh36(x, x), true2)
% 0.20/0.53 = { by axiom 2 (member_of_substitution) }
% 0.20/0.53 tuple3(singleton(y), true2)
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53
% 0.20/0.53 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------