TSTP Solution File: SEU257+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU257+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 : n029.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 17:51:52 EDT 2023
% Result : Theorem 103.25s 15.26s
% Output : Proof 103.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU257+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
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:21:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 103.25/15.26 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 103.25/15.26
% 103.25/15.26 % SZS status Theorem
% 103.25/15.26
% 103.25/15.27 % SZS output start Proof
% 103.25/15.27 Take the following subset of the input axioms:
% 103.25/15.28 fof(d4_wellord1, axiom, ![A2]: (relation(A2) => (well_ordering(A2) <=> (reflexive(A2) & (transitive(A2) & (antisymmetric(A2) & (connected(A2) & well_founded_relation(A2)))))))).
% 103.25/15.28 fof(dt_k2_wellord1, axiom, ![B, A2_2]: (relation(A2_2) => relation(relation_restriction(A2_2, B)))).
% 103.25/15.28 fof(t22_wellord1, lemma, ![B2, A2_2]: (relation(B2) => (reflexive(B2) => reflexive(relation_restriction(B2, A2_2))))).
% 103.25/15.28 fof(t23_wellord1, lemma, ![B2, A2_2]: (relation(B2) => (connected(B2) => connected(relation_restriction(B2, A2_2))))).
% 103.25/15.28 fof(t24_wellord1, lemma, ![B2, A2_2]: (relation(B2) => (transitive(B2) => transitive(relation_restriction(B2, A2_2))))).
% 103.25/15.28 fof(t25_wellord1, lemma, ![B2, A2_2]: (relation(B2) => (antisymmetric(B2) => antisymmetric(relation_restriction(B2, A2_2))))).
% 103.25/15.28 fof(t31_wellord1, lemma, ![B2, A2_2]: (relation(B2) => (well_founded_relation(B2) => well_founded_relation(relation_restriction(B2, A2_2))))).
% 103.25/15.28 fof(t32_wellord1, conjecture, ![A, B2]: (relation(B2) => (well_ordering(B2) => well_ordering(relation_restriction(B2, A))))).
% 103.25/15.28
% 103.25/15.28 Now clausify the problem and encode Horn clauses using encoding 3 of
% 103.25/15.28 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 103.25/15.29 We repeatedly replace C & s=t => u=v by the two clauses:
% 103.25/15.29 fresh(y, y, x1...xn) = u
% 103.25/15.29 C => fresh(s, t, x1...xn) = v
% 103.25/15.29 where fresh is a fresh function symbol and x1..xn are the free
% 103.25/15.29 variables of u and v.
% 103.25/15.29 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 103.25/15.29 input problem has no model of domain size 1).
% 103.25/15.29
% 103.25/15.29 The encoding turns the above axioms into the following unit equations and goals:
% 103.25/15.29
% 103.25/15.29 Axiom 1 (t32_wellord1): relation(b4) = true2.
% 103.25/15.29 Axiom 2 (t32_wellord1_1): well_ordering(b4) = true2.
% 103.25/15.29 Axiom 3 (d4_wellord1): fresh819(X, X, Y) = true2.
% 103.25/15.29 Axiom 4 (d4_wellord1): fresh817(X, X, Y) = well_ordering(Y).
% 103.25/15.29 Axiom 5 (d4_wellord1_1): fresh404(X, X, Y) = antisymmetric(Y).
% 103.25/15.29 Axiom 6 (d4_wellord1_1): fresh403(X, X, Y) = true2.
% 103.25/15.29 Axiom 7 (d4_wellord1_2): fresh402(X, X, Y) = connected(Y).
% 103.25/15.29 Axiom 8 (d4_wellord1_2): fresh401(X, X, Y) = true2.
% 103.25/15.29 Axiom 9 (d4_wellord1_3): fresh400(X, X, Y) = transitive(Y).
% 103.25/15.29 Axiom 10 (d4_wellord1_3): fresh399(X, X, Y) = true2.
% 103.25/15.29 Axiom 11 (d4_wellord1_4): fresh398(X, X, Y) = well_founded_relation(Y).
% 103.25/15.29 Axiom 12 (d4_wellord1_4): fresh397(X, X, Y) = true2.
% 103.25/15.29 Axiom 13 (d4_wellord1_5): fresh396(X, X, Y) = reflexive(Y).
% 103.25/15.29 Axiom 14 (d4_wellord1_5): fresh395(X, X, Y) = true2.
% 103.25/15.29 Axiom 15 (d4_wellord1): fresh818(X, X, Y) = fresh819(relation(Y), true2, Y).
% 103.25/15.29 Axiom 16 (d4_wellord1): fresh815(X, X, Y) = fresh818(connected(Y), true2, Y).
% 103.25/15.29 Axiom 17 (d4_wellord1): fresh816(X, X, Y) = fresh817(antisymmetric(Y), true2, Y).
% 103.25/15.29 Axiom 18 (d4_wellord1): fresh814(X, X, Y) = fresh816(transitive(Y), true2, Y).
% 103.25/15.29 Axiom 19 (d4_wellord1): fresh814(reflexive(X), true2, X) = fresh815(well_founded_relation(X), true2, X).
% 103.25/15.29 Axiom 20 (d4_wellord1_1): fresh404(well_ordering(X), true2, X) = fresh403(relation(X), true2, X).
% 103.25/15.29 Axiom 21 (d4_wellord1_2): fresh402(well_ordering(X), true2, X) = fresh401(relation(X), true2, X).
% 103.25/15.29 Axiom 22 (d4_wellord1_3): fresh400(well_ordering(X), true2, X) = fresh399(relation(X), true2, X).
% 103.25/15.29 Axiom 23 (d4_wellord1_4): fresh398(well_ordering(X), true2, X) = fresh397(relation(X), true2, X).
% 103.25/15.29 Axiom 24 (d4_wellord1_5): fresh396(well_ordering(X), true2, X) = fresh395(relation(X), true2, X).
% 103.25/15.29 Axiom 25 (dt_k2_wellord1): fresh339(X, X, Y, Z) = true2.
% 103.25/15.29 Axiom 26 (t22_wellord1): fresh168(X, X, Y, Z) = reflexive(relation_restriction(Z, Y)).
% 103.25/15.29 Axiom 27 (t22_wellord1): fresh167(X, X, Y, Z) = true2.
% 103.25/15.29 Axiom 28 (t23_wellord1): fresh163(X, X, Y, Z) = connected(relation_restriction(Z, Y)).
% 103.25/15.29 Axiom 29 (t23_wellord1): fresh162(X, X, Y, Z) = true2.
% 103.25/15.29 Axiom 30 (t24_wellord1): fresh161(X, X, Y, Z) = transitive(relation_restriction(Z, Y)).
% 103.25/15.29 Axiom 31 (t24_wellord1): fresh160(X, X, Y, Z) = true2.
% 103.25/15.29 Axiom 32 (t25_wellord1): fresh157(X, X, Y, Z) = antisymmetric(relation_restriction(Z, Y)).
% 103.25/15.29 Axiom 33 (t25_wellord1): fresh156(X, X, Y, Z) = true2.
% 103.25/15.29 Axiom 34 (t31_wellord1): fresh148(X, X, Y, Z) = well_founded_relation(relation_restriction(Z, Y)).
% 103.25/15.29 Axiom 35 (t31_wellord1): fresh147(X, X, Y, Z) = true2.
% 103.25/15.29 Axiom 36 (dt_k2_wellord1): fresh339(relation(X), true2, X, Y) = relation(relation_restriction(X, Y)).
% 103.25/15.29 Axiom 37 (t22_wellord1): fresh168(reflexive(X), true2, Y, X) = fresh167(relation(X), true2, Y, X).
% 103.25/15.29 Axiom 38 (t23_wellord1): fresh163(connected(X), true2, Y, X) = fresh162(relation(X), true2, Y, X).
% 103.25/15.29 Axiom 39 (t24_wellord1): fresh161(transitive(X), true2, Y, X) = fresh160(relation(X), true2, Y, X).
% 103.25/15.29 Axiom 40 (t25_wellord1): fresh157(antisymmetric(X), true2, Y, X) = fresh156(relation(X), true2, Y, X).
% 103.25/15.29 Axiom 41 (t31_wellord1): fresh148(well_founded_relation(X), true2, Y, X) = fresh147(relation(X), true2, Y, X).
% 103.25/15.29
% 103.25/15.29 Goal 1 (t32_wellord1_2): well_ordering(relation_restriction(b4, a)) = true2.
% 103.25/15.29 Proof:
% 103.25/15.29 well_ordering(relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 4 (d4_wellord1) R->L }
% 103.25/15.29 fresh817(true2, true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 33 (t25_wellord1) R->L }
% 103.25/15.29 fresh817(fresh156(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 1 (t32_wellord1) R->L }
% 103.25/15.29 fresh817(fresh156(relation(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 40 (t25_wellord1) R->L }
% 103.25/15.29 fresh817(fresh157(antisymmetric(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 5 (d4_wellord1_1) R->L }
% 103.25/15.29 fresh817(fresh157(fresh404(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 2 (t32_wellord1_1) R->L }
% 103.25/15.29 fresh817(fresh157(fresh404(well_ordering(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 20 (d4_wellord1_1) }
% 103.25/15.29 fresh817(fresh157(fresh403(relation(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 1 (t32_wellord1) }
% 103.25/15.29 fresh817(fresh157(fresh403(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 6 (d4_wellord1_1) }
% 103.25/15.29 fresh817(fresh157(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 32 (t25_wellord1) }
% 103.25/15.29 fresh817(antisymmetric(relation_restriction(b4, a)), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 17 (d4_wellord1) R->L }
% 103.25/15.29 fresh816(true2, true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 31 (t24_wellord1) R->L }
% 103.25/15.29 fresh816(fresh160(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 1 (t32_wellord1) R->L }
% 103.25/15.29 fresh816(fresh160(relation(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 39 (t24_wellord1) R->L }
% 103.25/15.29 fresh816(fresh161(transitive(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 9 (d4_wellord1_3) R->L }
% 103.25/15.29 fresh816(fresh161(fresh400(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 2 (t32_wellord1_1) R->L }
% 103.25/15.29 fresh816(fresh161(fresh400(well_ordering(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 22 (d4_wellord1_3) }
% 103.25/15.29 fresh816(fresh161(fresh399(relation(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 1 (t32_wellord1) }
% 103.25/15.29 fresh816(fresh161(fresh399(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 10 (d4_wellord1_3) }
% 103.25/15.29 fresh816(fresh161(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 30 (t24_wellord1) }
% 103.25/15.29 fresh816(transitive(relation_restriction(b4, a)), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 18 (d4_wellord1) R->L }
% 103.25/15.29 fresh814(true2, true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 27 (t22_wellord1) R->L }
% 103.25/15.29 fresh814(fresh167(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 1 (t32_wellord1) R->L }
% 103.25/15.29 fresh814(fresh167(relation(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 37 (t22_wellord1) R->L }
% 103.25/15.29 fresh814(fresh168(reflexive(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 13 (d4_wellord1_5) R->L }
% 103.25/15.29 fresh814(fresh168(fresh396(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 2 (t32_wellord1_1) R->L }
% 103.25/15.29 fresh814(fresh168(fresh396(well_ordering(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 24 (d4_wellord1_5) }
% 103.25/15.29 fresh814(fresh168(fresh395(relation(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 1 (t32_wellord1) }
% 103.25/15.29 fresh814(fresh168(fresh395(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 14 (d4_wellord1_5) }
% 103.25/15.29 fresh814(fresh168(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 26 (t22_wellord1) }
% 103.25/15.29 fresh814(reflexive(relation_restriction(b4, a)), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 19 (d4_wellord1) }
% 103.25/15.29 fresh815(well_founded_relation(relation_restriction(b4, a)), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 34 (t31_wellord1) R->L }
% 103.25/15.29 fresh815(fresh148(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.29 = { by axiom 12 (d4_wellord1_4) R->L }
% 103.25/15.29 fresh815(fresh148(fresh397(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 1 (t32_wellord1) R->L }
% 103.25/15.30 fresh815(fresh148(fresh397(relation(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 23 (d4_wellord1_4) R->L }
% 103.25/15.30 fresh815(fresh148(fresh398(well_ordering(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 2 (t32_wellord1_1) }
% 103.25/15.30 fresh815(fresh148(fresh398(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 11 (d4_wellord1_4) }
% 103.25/15.30 fresh815(fresh148(well_founded_relation(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 41 (t31_wellord1) }
% 103.25/15.30 fresh815(fresh147(relation(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 1 (t32_wellord1) }
% 103.25/15.30 fresh815(fresh147(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 35 (t31_wellord1) }
% 103.25/15.30 fresh815(true2, true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 16 (d4_wellord1) }
% 103.25/15.30 fresh818(connected(relation_restriction(b4, a)), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 28 (t23_wellord1) R->L }
% 103.25/15.30 fresh818(fresh163(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 8 (d4_wellord1_2) R->L }
% 103.25/15.30 fresh818(fresh163(fresh401(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 1 (t32_wellord1) R->L }
% 103.25/15.30 fresh818(fresh163(fresh401(relation(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 21 (d4_wellord1_2) R->L }
% 103.25/15.30 fresh818(fresh163(fresh402(well_ordering(b4), true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 2 (t32_wellord1_1) }
% 103.25/15.30 fresh818(fresh163(fresh402(true2, true2, b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 7 (d4_wellord1_2) }
% 103.25/15.30 fresh818(fresh163(connected(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 38 (t23_wellord1) }
% 103.25/15.30 fresh818(fresh162(relation(b4), true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 1 (t32_wellord1) }
% 103.25/15.30 fresh818(fresh162(true2, true2, a, b4), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 29 (t23_wellord1) }
% 103.25/15.30 fresh818(true2, true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 15 (d4_wellord1) }
% 103.25/15.30 fresh819(relation(relation_restriction(b4, a)), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 36 (dt_k2_wellord1) R->L }
% 103.25/15.30 fresh819(fresh339(relation(b4), true2, b4, a), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 1 (t32_wellord1) }
% 103.25/15.30 fresh819(fresh339(true2, true2, b4, a), true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 25 (dt_k2_wellord1) }
% 103.25/15.30 fresh819(true2, true2, relation_restriction(b4, a))
% 103.25/15.30 = { by axiom 3 (d4_wellord1) }
% 103.25/15.30 true2
% 103.25/15.30 % SZS output end Proof
% 103.25/15.30
% 103.25/15.30 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------