TSTP Solution File: SEU148+2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU148+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : Thu Aug 31 17:51:12 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU148+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n006.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 : Wed Aug 23 23:52:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.56
% 0.20/0.56 % SZS status Theorem
% 0.20/0.56
% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Take the following subset of the input axioms:
% 0.20/0.56 fof(d1_tarski, axiom, ![B, A2]: (B=singleton(A2) <=> ![C]: (in(C, B) <=> C=A2))).
% 0.20/0.56 fof(l2_zfmisc_1, lemma, ![B2, A2_2]: (subset(singleton(A2_2), B2) <=> in(A2_2, B2))).
% 0.20/0.56 fof(t6_zfmisc_1, conjecture, ![A, B2]: (subset(singleton(A), singleton(B2)) => A=B2)).
% 0.20/0.56
% 0.20/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.56 fresh(y, y, x1...xn) = u
% 0.20/0.56 C => fresh(s, t, x1...xn) = v
% 0.20/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.56 variables of u and v.
% 0.20/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.56 input problem has no model of domain size 1).
% 0.20/0.56
% 0.20/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.56
% 0.20/0.56 Axiom 1 (l2_zfmisc_1_1): fresh39(X, X, Y, Z) = true2.
% 0.20/0.56 Axiom 2 (d1_tarski_3): fresh15(X, X, Y, Z) = Y.
% 0.20/0.56 Axiom 3 (t6_zfmisc_1): subset(singleton(a), singleton(b)) = true2.
% 0.20/0.56 Axiom 4 (d1_tarski_3): fresh16(X, X, Y, Z, W) = W.
% 0.20/0.56 Axiom 5 (l2_zfmisc_1_1): fresh39(subset(singleton(X), Y), true2, X, Y) = in(X, Y).
% 0.20/0.56 Axiom 6 (d1_tarski_3): fresh16(in(X, Y), true2, Z, Y, X) = fresh15(Y, singleton(Z), Z, X).
% 0.20/0.56
% 0.20/0.56 Goal 1 (t6_zfmisc_1_1): a = b.
% 0.20/0.56 Proof:
% 0.20/0.56 a
% 0.20/0.56 = { by axiom 4 (d1_tarski_3) R->L }
% 0.20/0.56 fresh16(true2, true2, b, singleton(b), a)
% 0.20/0.56 = { by axiom 1 (l2_zfmisc_1_1) R->L }
% 0.20/0.56 fresh16(fresh39(true2, true2, a, singleton(b)), true2, b, singleton(b), a)
% 0.20/0.56 = { by axiom 3 (t6_zfmisc_1) R->L }
% 0.20/0.56 fresh16(fresh39(subset(singleton(a), singleton(b)), true2, a, singleton(b)), true2, b, singleton(b), a)
% 0.20/0.56 = { by axiom 5 (l2_zfmisc_1_1) }
% 0.20/0.56 fresh16(in(a, singleton(b)), true2, b, singleton(b), a)
% 0.20/0.56 = { by axiom 6 (d1_tarski_3) }
% 0.20/0.56 fresh15(singleton(b), singleton(b), b, a)
% 0.20/0.56 = { by axiom 2 (d1_tarski_3) }
% 0.20/0.56 b
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------