TSTP Solution File: SEU247+2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU247+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 : n013.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 17:51:48 EDT 2023
% Result : Theorem 44.90s 6.13s
% Output : Proof 44.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU247+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
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 19:01:32 EDT 2023
% 0.19/0.34 % CPUTime :
% 44.90/6.13 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 44.90/6.13
% 44.90/6.13 % SZS status Theorem
% 44.90/6.13
% 44.90/6.13 % SZS output start Proof
% 44.90/6.13 Take the following subset of the input axioms:
% 44.90/6.13 fof(t140_relat_1, lemma, ![B, C, A2]: (relation(C) => relation_dom_restriction(relation_rng_restriction(A2, C), B)=relation_rng_restriction(A2, relation_dom_restriction(C, B)))).
% 44.90/6.13 fof(t17_wellord1, lemma, ![B2, A2_2]: (relation(B2) => relation_restriction(B2, A2_2)=relation_dom_restriction(relation_rng_restriction(A2_2, B2), A2_2))).
% 44.90/6.13 fof(t18_wellord1, conjecture, ![A, B2]: (relation(B2) => relation_restriction(B2, A)=relation_rng_restriction(A, relation_dom_restriction(B2, A)))).
% 44.90/6.14
% 44.90/6.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 44.90/6.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 44.90/6.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 44.90/6.14 fresh(y, y, x1...xn) = u
% 44.90/6.14 C => fresh(s, t, x1...xn) = v
% 44.90/6.14 where fresh is a fresh function symbol and x1..xn are the free
% 44.90/6.14 variables of u and v.
% 44.90/6.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 44.90/6.14 input problem has no model of domain size 1).
% 44.90/6.14
% 44.90/6.14 The encoding turns the above axioms into the following unit equations and goals:
% 44.90/6.14
% 44.90/6.14 Axiom 1 (t18_wellord1): relation(b5) = true2.
% 44.90/6.14 Axiom 2 (t17_wellord1): fresh173(X, X, Y, Z) = relation_restriction(Z, Y).
% 44.90/6.14 Axiom 3 (t140_relat_1): fresh200(X, X, Y, Z, W) = relation_rng_restriction(Y, relation_dom_restriction(W, Z)).
% 44.90/6.14 Axiom 4 (t17_wellord1): fresh173(relation(X), true2, Y, X) = relation_dom_restriction(relation_rng_restriction(Y, X), Y).
% 44.90/6.14 Axiom 5 (t140_relat_1): fresh200(relation(X), true2, Y, Z, X) = relation_dom_restriction(relation_rng_restriction(Y, X), Z).
% 44.90/6.14
% 44.90/6.14 Goal 1 (t18_wellord1_1): relation_restriction(b5, a) = relation_rng_restriction(a, relation_dom_restriction(b5, a)).
% 44.90/6.14 Proof:
% 44.90/6.14 relation_restriction(b5, a)
% 44.90/6.14 = { by axiom 2 (t17_wellord1) R->L }
% 44.90/6.14 fresh173(true2, true2, a, b5)
% 44.90/6.14 = { by axiom 1 (t18_wellord1) R->L }
% 44.90/6.14 fresh173(relation(b5), true2, a, b5)
% 44.90/6.14 = { by axiom 4 (t17_wellord1) }
% 44.90/6.14 relation_dom_restriction(relation_rng_restriction(a, b5), a)
% 44.90/6.14 = { by axiom 5 (t140_relat_1) R->L }
% 44.90/6.14 fresh200(relation(b5), true2, a, a, b5)
% 44.90/6.14 = { by axiom 1 (t18_wellord1) }
% 44.90/6.14 fresh200(true2, true2, a, a, b5)
% 44.90/6.14 = { by axiom 3 (t140_relat_1) }
% 44.90/6.14 relation_rng_restriction(a, relation_dom_restriction(b5, a))
% 44.90/6.14 % SZS output end Proof
% 44.90/6.14
% 44.90/6.14 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------