TSTP Solution File: SEU010+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n028.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 17:50:47 EDT 2023
% Result : Theorem 0.21s 0.52s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n028.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 19:49:04 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.52 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.52
% 0.21/0.52 % SZS status Theorem
% 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(reflexivity_r1_tarski, axiom, ![A, B]: subset(A, A)).
% 0.21/0.52 fof(t42_funct_1, conjecture, ![A3]: ((relation(A3) & function(A3)) => (relation_composition(identity_relation(relation_dom(A3)), A3)=A3 & relation_composition(A3, identity_relation(relation_rng(A3)))=A3))).
% 0.21/0.52 fof(t77_relat_1, axiom, ![A2, B2]: (relation(B2) => (subset(relation_dom(B2), A2) => relation_composition(identity_relation(A2), B2)=B2))).
% 0.21/0.52 fof(t79_relat_1, axiom, ![B2, A2_2]: (relation(B2) => (subset(relation_rng(B2), A2_2) => relation_composition(B2, identity_relation(A2_2))=B2))).
% 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 (t42_funct_1): relation(a) = true2.
% 0.21/0.52 Axiom 2 (reflexivity_r1_tarski): subset(X, X) = true2.
% 0.21/0.52 Axiom 3 (t79_relat_1): fresh(X, X, Y, Z) = Z.
% 0.21/0.52 Axiom 4 (t77_relat_1): fresh6(X, X, Y, Z) = relation_composition(identity_relation(Y), Z).
% 0.21/0.52 Axiom 5 (t79_relat_1): fresh5(X, X, Y, Z) = relation_composition(Z, identity_relation(Y)).
% 0.21/0.52 Axiom 6 (t77_relat_1): fresh2(X, X, Y, Z) = Z.
% 0.21/0.52 Axiom 7 (t77_relat_1): fresh6(subset(relation_dom(X), Y), true2, Y, X) = fresh2(relation(X), true2, Y, X).
% 0.21/0.52 Axiom 8 (t79_relat_1): fresh5(subset(relation_rng(X), Y), true2, Y, X) = fresh(relation(X), true2, Y, X).
% 0.21/0.52
% 0.21/0.52 Goal 1 (t42_funct_1_2): tuple3(relation_composition(identity_relation(relation_dom(a)), a), relation_composition(a, identity_relation(relation_rng(a)))) = tuple3(a, a).
% 0.21/0.52 Proof:
% 0.21/0.52 tuple3(relation_composition(identity_relation(relation_dom(a)), a), relation_composition(a, identity_relation(relation_rng(a))))
% 0.21/0.52 = { by axiom 5 (t79_relat_1) R->L }
% 0.21/0.52 tuple3(relation_composition(identity_relation(relation_dom(a)), a), fresh5(true2, true2, relation_rng(a), a))
% 0.21/0.52 = { by axiom 2 (reflexivity_r1_tarski) R->L }
% 0.21/0.52 tuple3(relation_composition(identity_relation(relation_dom(a)), a), fresh5(subset(relation_rng(a), relation_rng(a)), true2, relation_rng(a), a))
% 0.21/0.52 = { by axiom 8 (t79_relat_1) }
% 0.21/0.52 tuple3(relation_composition(identity_relation(relation_dom(a)), a), fresh(relation(a), true2, relation_rng(a), a))
% 0.21/0.52 = { by axiom 1 (t42_funct_1) }
% 0.21/0.52 tuple3(relation_composition(identity_relation(relation_dom(a)), a), fresh(true2, true2, relation_rng(a), a))
% 0.21/0.52 = { by axiom 3 (t79_relat_1) }
% 0.21/0.52 tuple3(relation_composition(identity_relation(relation_dom(a)), a), a)
% 0.21/0.52 = { by axiom 4 (t77_relat_1) R->L }
% 0.21/0.52 tuple3(fresh6(true2, true2, relation_dom(a), a), a)
% 0.21/0.52 = { by axiom 2 (reflexivity_r1_tarski) R->L }
% 0.21/0.52 tuple3(fresh6(subset(relation_dom(a), relation_dom(a)), true2, relation_dom(a), a), a)
% 0.21/0.52 = { by axiom 7 (t77_relat_1) }
% 0.21/0.52 tuple3(fresh2(relation(a), true2, relation_dom(a), a), a)
% 0.21/0.52 = { by axiom 1 (t42_funct_1) }
% 0.21/0.52 tuple3(fresh2(true2, true2, relation_dom(a), a), a)
% 0.21/0.52 = { by axiom 6 (t77_relat_1) }
% 0.21/0.52 tuple3(a, a)
% 0.21/0.52 % SZS output end Proof
% 0.21/0.52
% 0.21/0.52 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------