TSTP Solution File: SEU363+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU363+1 : 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 17:52:24 EDT 2023
% Result : Theorem 8.82s 1.85s
% Output : Proof 9.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU363+1 : 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 19:34:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 8.82/1.85 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 8.82/1.85
% 8.82/1.85 % SZS status Theorem
% 8.82/1.85
% 8.82/1.87 % SZS output start Proof
% 8.82/1.87 Take the following subset of the input axioms:
% 9.49/1.89 fof(cc1_relset_1, axiom, ![A, B, C]: (element(C, powerset(cartesian_product2(A, B))) => relation(C))).
% 9.49/1.89 fof(d14_yellow_0, axiom, ![A2]: (rel_str(A2) => ![B2]: (subrelstr(B2, A2) => (full_subrelstr(B2, A2) <=> the_InternalRel(B2)=relation_restriction_as_relation_of(the_InternalRel(A2), the_carrier(B2)))))).
% 9.49/1.89 fof(d9_orders_2, axiom, ![A2_2]: (rel_str(A2_2) => ![B2]: (element(B2, the_carrier(A2_2)) => ![C2]: (element(C2, the_carrier(A2_2)) => (related(A2_2, B2, C2) <=> in(ordered_pair(B2, C2), the_InternalRel(A2_2))))))).
% 9.49/1.89 fof(dt_m1_yellow_0, axiom, ![A2_2]: (rel_str(A2_2) => ![B2]: (subrelstr(B2, A2_2) => rel_str(B2)))).
% 9.49/1.89 fof(dt_m2_relset_1, axiom, ![C2, B2, A2_2]: (relation_of2_as_subset(C2, A2_2, B2) => element(C2, powerset(cartesian_product2(A2_2, B2))))).
% 9.49/1.89 fof(dt_u1_orders_2, axiom, ![A2_2]: (rel_str(A2_2) => relation_of2_as_subset(the_InternalRel(A2_2), the_carrier(A2_2), the_carrier(A2_2)))).
% 9.49/1.89 fof(redefinition_k1_toler_1, axiom, ![B2, A2_2]: (relation(A2_2) => relation_restriction_as_relation_of(A2_2, B2)=relation_restriction(A2_2, B2))).
% 9.49/1.89 fof(t106_zfmisc_1, axiom, ![D, C2, B2, A2_2]: (in(ordered_pair(A2_2, B2), cartesian_product2(C2, D)) <=> (in(A2_2, C2) & in(B2, D)))).
% 9.49/1.89 fof(t16_wellord1, axiom, ![C2, B2, A2_2]: (relation(C2) => (in(A2_2, relation_restriction(C2, B2)) <=> (in(A2_2, C2) & in(A2_2, cartesian_product2(B2, B2)))))).
% 9.49/1.89 fof(t61_yellow_0, conjecture, ![A3]: (rel_str(A3) => ![B2]: ((full_subrelstr(B2, A3) & subrelstr(B2, A3)) => ![C2]: (element(C2, the_carrier(A3)) => ![D2]: (element(D2, the_carrier(A3)) => ![E]: (element(E, the_carrier(B2)) => ![F]: (element(F, the_carrier(B2)) => ((E=C2 & (F=D2 & (related(A3, C2, D2) & (in(E, the_carrier(B2)) & in(F, the_carrier(B2)))))) => related(B2, E, F))))))))).
% 9.49/1.89
% 9.49/1.89 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.49/1.89 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.49/1.89 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.49/1.89 fresh(y, y, x1...xn) = u
% 9.49/1.89 C => fresh(s, t, x1...xn) = v
% 9.49/1.89 where fresh is a fresh function symbol and x1..xn are the free
% 9.49/1.89 variables of u and v.
% 9.49/1.89 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.49/1.89 input problem has no model of domain size 1).
% 9.49/1.89
% 9.49/1.89 The encoding turns the above axioms into the following unit equations and goals:
% 9.49/1.89
% 9.49/1.89 Axiom 1 (t61_yellow_0): e = c.
% 9.49/1.89 Axiom 2 (t61_yellow_0_1): f = d.
% 9.49/1.89 Axiom 3 (t61_yellow_0_8): rel_str(a) = true2.
% 9.49/1.89 Axiom 4 (t61_yellow_0_9): subrelstr(b, a) = true2.
% 9.49/1.89 Axiom 5 (t61_yellow_0_10): full_subrelstr(b, a) = true2.
% 9.49/1.89 Axiom 6 (t61_yellow_0_2): in(e, the_carrier(b)) = true2.
% 9.49/1.89 Axiom 7 (t61_yellow_0_3): in(f, the_carrier(b)) = true2.
% 9.49/1.89 Axiom 8 (t61_yellow_0_6): element(e, the_carrier(b)) = true2.
% 9.49/1.89 Axiom 9 (t61_yellow_0_7): element(f, the_carrier(b)) = true2.
% 9.49/1.89 Axiom 10 (t61_yellow_0_4): element(c, the_carrier(a)) = true2.
% 9.49/1.89 Axiom 11 (t61_yellow_0_5): element(d, the_carrier(a)) = true2.
% 9.49/1.89 Axiom 12 (t61_yellow_0_11): related(a, c, d) = true2.
% 9.49/1.89 Axiom 13 (cc1_relset_1): fresh40(X, X, Y) = true2.
% 9.49/1.89 Axiom 14 (dt_m1_yellow_0): fresh28(X, X, Y) = true2.
% 9.49/1.89 Axiom 15 (dt_u1_orders_2): fresh26(X, X, Y) = true2.
% 9.49/1.89 Axiom 16 (d14_yellow_0_1): fresh52(X, X, Y, Z) = the_InternalRel(Z).
% 9.49/1.89 Axiom 17 (d14_yellow_0_1): fresh35(X, X, Y, Z) = relation_restriction_as_relation_of(the_InternalRel(Y), the_carrier(Z)).
% 9.49/1.89 Axiom 18 (dt_m1_yellow_0): fresh29(X, X, Y, Z) = rel_str(Z).
% 9.49/1.89 Axiom 19 (redefinition_k1_toler_1): fresh20(X, X, Y, Z) = relation_restriction(Y, Z).
% 9.49/1.89 Axiom 20 (d14_yellow_0_1): fresh51(X, X, Y, Z) = fresh52(rel_str(Y), true2, Y, Z).
% 9.49/1.89 Axiom 21 (d9_orders_2_1): fresh48(X, X, Y, Z, W) = true2.
% 9.49/1.89 Axiom 22 (d9_orders_2): fresh45(X, X, Y, Z, W) = related(Y, Z, W).
% 9.49/1.89 Axiom 23 (t16_wellord1): fresh42(X, X, Y, Z, W) = true2.
% 9.49/1.89 Axiom 24 (d9_orders_2): fresh34(X, X, Y, Z, W) = true2.
% 9.49/1.89 Axiom 25 (d9_orders_2_1): fresh33(X, X, Y, Z, W) = in(ordered_pair(Z, W), the_InternalRel(Y)).
% 9.49/1.89 Axiom 26 (dt_m2_relset_1): fresh27(X, X, Y, Z, W) = true2.
% 9.49/1.89 Axiom 27 (redefinition_k1_toler_1): fresh20(relation(X), true2, X, Y) = relation_restriction_as_relation_of(X, Y).
% 9.49/1.89 Axiom 28 (t16_wellord1): fresh13(X, X, Y, Z, W) = in(Y, relation_restriction(W, Z)).
% 9.49/1.89 Axiom 29 (dt_u1_orders_2): fresh26(rel_str(X), true2, X) = relation_of2_as_subset(the_InternalRel(X), the_carrier(X), the_carrier(X)).
% 9.49/1.89 Axiom 30 (d9_orders_2_1): fresh46(X, X, Y, Z, W) = fresh47(rel_str(Y), true2, Y, Z, W).
% 9.49/1.89 Axiom 31 (d14_yellow_0_1): fresh51(full_subrelstr(X, Y), true2, Y, X) = fresh35(subrelstr(X, Y), true2, Y, X).
% 9.49/1.89 Axiom 32 (dt_m1_yellow_0): fresh29(subrelstr(X, Y), true2, Y, X) = fresh28(rel_str(Y), true2, X).
% 9.49/1.89 Axiom 33 (t106_zfmisc_1): fresh17(X, X, Y, Z, W, V) = in(ordered_pair(Y, Z), cartesian_product2(W, V)).
% 9.49/1.89 Axiom 34 (t106_zfmisc_1): fresh16(X, X, Y, Z, W, V) = true2.
% 9.49/1.89 Axiom 35 (t16_wellord1): fresh41(X, X, Y, Z, W) = fresh42(in(Y, W), true2, Y, Z, W).
% 9.49/1.89 Axiom 36 (d9_orders_2_1): fresh47(X, X, Y, Z, W) = fresh48(element(Z, the_carrier(Y)), true2, Y, Z, W).
% 9.49/1.89 Axiom 37 (d9_orders_2): fresh44(X, X, Y, Z, W) = fresh45(element(Z, the_carrier(Y)), true2, Y, Z, W).
% 9.49/1.89 Axiom 38 (d9_orders_2): fresh43(X, X, Y, Z, W) = fresh44(element(W, the_carrier(Y)), true2, Y, Z, W).
% 9.49/1.89 Axiom 39 (cc1_relset_1): fresh40(element(X, powerset(cartesian_product2(Y, Z))), true2, X) = relation(X).
% 9.49/1.89 Axiom 40 (d9_orders_2_1): fresh46(related(X, Y, Z), true2, X, Y, Z) = fresh33(element(Z, the_carrier(X)), true2, X, Y, Z).
% 9.49/1.89 Axiom 41 (dt_m2_relset_1): fresh27(relation_of2_as_subset(X, Y, Z), true2, Y, Z, X) = element(X, powerset(cartesian_product2(Y, Z))).
% 9.49/1.89 Axiom 42 (t106_zfmisc_1): fresh17(in(X, Y), true2, Z, X, W, Y) = fresh16(in(Z, W), true2, Z, X, W, Y).
% 9.49/1.89 Axiom 43 (t16_wellord1): fresh41(relation(X), true2, Y, Z, X) = fresh13(in(Y, cartesian_product2(Z, Z)), true2, Y, Z, X).
% 9.49/1.89 Axiom 44 (d9_orders_2): fresh43(rel_str(X), true2, X, Y, Z) = fresh34(in(ordered_pair(Y, Z), the_InternalRel(X)), true2, X, Y, Z).
% 9.49/1.89
% 9.49/1.89 Lemma 45: relation(the_InternalRel(a)) = true2.
% 9.49/1.89 Proof:
% 9.49/1.89 relation(the_InternalRel(a))
% 9.49/1.89 = { by axiom 39 (cc1_relset_1) R->L }
% 9.49/1.89 fresh40(element(the_InternalRel(a), powerset(cartesian_product2(the_carrier(a), the_carrier(a)))), true2, the_InternalRel(a))
% 9.49/1.89 = { by axiom 41 (dt_m2_relset_1) R->L }
% 9.49/1.89 fresh40(fresh27(relation_of2_as_subset(the_InternalRel(a), the_carrier(a), the_carrier(a)), true2, the_carrier(a), the_carrier(a), the_InternalRel(a)), true2, the_InternalRel(a))
% 9.49/1.89 = { by axiom 29 (dt_u1_orders_2) R->L }
% 9.49/1.89 fresh40(fresh27(fresh26(rel_str(a), true2, a), true2, the_carrier(a), the_carrier(a), the_InternalRel(a)), true2, the_InternalRel(a))
% 9.49/1.89 = { by axiom 3 (t61_yellow_0_8) }
% 9.49/1.89 fresh40(fresh27(fresh26(true2, true2, a), true2, the_carrier(a), the_carrier(a), the_InternalRel(a)), true2, the_InternalRel(a))
% 9.49/1.89 = { by axiom 15 (dt_u1_orders_2) }
% 9.49/1.89 fresh40(fresh27(true2, true2, the_carrier(a), the_carrier(a), the_InternalRel(a)), true2, the_InternalRel(a))
% 9.49/1.89 = { by axiom 26 (dt_m2_relset_1) }
% 9.49/1.89 fresh40(true2, true2, the_InternalRel(a))
% 9.49/1.89 = { by axiom 13 (cc1_relset_1) }
% 9.49/1.89 true2
% 9.49/1.89
% 9.49/1.89 Goal 1 (t61_yellow_0_12): related(b, e, f) = true2.
% 9.49/1.89 Proof:
% 9.49/1.89 related(b, e, f)
% 9.49/1.89 = { by axiom 22 (d9_orders_2) R->L }
% 9.49/1.89 fresh45(true2, true2, b, e, f)
% 9.49/1.89 = { by axiom 8 (t61_yellow_0_6) R->L }
% 9.49/1.89 fresh45(element(e, the_carrier(b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 37 (d9_orders_2) R->L }
% 9.49/1.89 fresh44(true2, true2, b, e, f)
% 9.49/1.89 = { by axiom 9 (t61_yellow_0_7) R->L }
% 9.49/1.89 fresh44(element(f, the_carrier(b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 38 (d9_orders_2) R->L }
% 9.49/1.89 fresh43(true2, true2, b, e, f)
% 9.49/1.89 = { by axiom 14 (dt_m1_yellow_0) R->L }
% 9.49/1.89 fresh43(fresh28(true2, true2, b), true2, b, e, f)
% 9.49/1.89 = { by axiom 3 (t61_yellow_0_8) R->L }
% 9.49/1.89 fresh43(fresh28(rel_str(a), true2, b), true2, b, e, f)
% 9.49/1.89 = { by axiom 32 (dt_m1_yellow_0) R->L }
% 9.49/1.89 fresh43(fresh29(subrelstr(b, a), true2, a, b), true2, b, e, f)
% 9.49/1.89 = { by axiom 4 (t61_yellow_0_9) }
% 9.49/1.89 fresh43(fresh29(true2, true2, a, b), true2, b, e, f)
% 9.49/1.89 = { by axiom 18 (dt_m1_yellow_0) }
% 9.49/1.89 fresh43(rel_str(b), true2, b, e, f)
% 9.49/1.89 = { by axiom 44 (d9_orders_2) }
% 9.49/1.89 fresh34(in(ordered_pair(e, f), the_InternalRel(b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 16 (d14_yellow_0_1) R->L }
% 9.49/1.89 fresh34(in(ordered_pair(e, f), fresh52(true2, true2, a, b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 3 (t61_yellow_0_8) R->L }
% 9.49/1.89 fresh34(in(ordered_pair(e, f), fresh52(rel_str(a), true2, a, b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 20 (d14_yellow_0_1) R->L }
% 9.49/1.89 fresh34(in(ordered_pair(e, f), fresh51(true2, true2, a, b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 5 (t61_yellow_0_10) R->L }
% 9.49/1.89 fresh34(in(ordered_pair(e, f), fresh51(full_subrelstr(b, a), true2, a, b)), true2, b, e, f)
% 9.49/1.89 = { by axiom 31 (d14_yellow_0_1) }
% 9.49/1.89 fresh34(in(ordered_pair(e, f), fresh35(subrelstr(b, a), true2, a, b)), true2, b, e, f)
% 9.49/1.90 = { by axiom 4 (t61_yellow_0_9) }
% 9.49/1.90 fresh34(in(ordered_pair(e, f), fresh35(true2, true2, a, b)), true2, b, e, f)
% 9.49/1.90 = { by axiom 17 (d14_yellow_0_1) }
% 9.49/1.90 fresh34(in(ordered_pair(e, f), relation_restriction_as_relation_of(the_InternalRel(a), the_carrier(b))), true2, b, e, f)
% 9.49/1.90 = { by axiom 27 (redefinition_k1_toler_1) R->L }
% 9.49/1.90 fresh34(in(ordered_pair(e, f), fresh20(relation(the_InternalRel(a)), true2, the_InternalRel(a), the_carrier(b))), true2, b, e, f)
% 9.49/1.90 = { by lemma 45 }
% 9.49/1.90 fresh34(in(ordered_pair(e, f), fresh20(true2, true2, the_InternalRel(a), the_carrier(b))), true2, b, e, f)
% 9.49/1.90 = { by axiom 19 (redefinition_k1_toler_1) }
% 9.49/1.90 fresh34(in(ordered_pair(e, f), relation_restriction(the_InternalRel(a), the_carrier(b))), true2, b, e, f)
% 9.49/1.90 = { by axiom 28 (t16_wellord1) R->L }
% 9.49/1.90 fresh34(fresh13(true2, true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 34 (t106_zfmisc_1) R->L }
% 9.49/1.90 fresh34(fresh13(fresh16(true2, true2, e, f, the_carrier(b), the_carrier(b)), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 6 (t61_yellow_0_2) R->L }
% 9.49/1.90 fresh34(fresh13(fresh16(in(e, the_carrier(b)), true2, e, f, the_carrier(b), the_carrier(b)), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 42 (t106_zfmisc_1) R->L }
% 9.49/1.90 fresh34(fresh13(fresh17(in(f, the_carrier(b)), true2, e, f, the_carrier(b), the_carrier(b)), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 7 (t61_yellow_0_3) }
% 9.49/1.90 fresh34(fresh13(fresh17(true2, true2, e, f, the_carrier(b), the_carrier(b)), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 33 (t106_zfmisc_1) }
% 9.49/1.90 fresh34(fresh13(in(ordered_pair(e, f), cartesian_product2(the_carrier(b), the_carrier(b))), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 43 (t16_wellord1) R->L }
% 9.49/1.90 fresh34(fresh41(relation(the_InternalRel(a)), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by lemma 45 }
% 9.49/1.90 fresh34(fresh41(true2, true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 35 (t16_wellord1) }
% 9.49/1.90 fresh34(fresh42(in(ordered_pair(e, f), the_InternalRel(a)), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 25 (d9_orders_2_1) R->L }
% 9.49/1.90 fresh34(fresh42(fresh33(true2, true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 11 (t61_yellow_0_5) R->L }
% 9.49/1.90 fresh34(fresh42(fresh33(element(d, the_carrier(a)), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 2 (t61_yellow_0_1) R->L }
% 9.49/1.90 fresh34(fresh42(fresh33(element(f, the_carrier(a)), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 40 (d9_orders_2_1) R->L }
% 9.49/1.90 fresh34(fresh42(fresh46(related(a, e, f), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 2 (t61_yellow_0_1) }
% 9.49/1.90 fresh34(fresh42(fresh46(related(a, e, d), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 1 (t61_yellow_0) }
% 9.49/1.90 fresh34(fresh42(fresh46(related(a, c, d), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 12 (t61_yellow_0_11) }
% 9.49/1.90 fresh34(fresh42(fresh46(true2, true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 30 (d9_orders_2_1) }
% 9.49/1.90 fresh34(fresh42(fresh47(rel_str(a), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 3 (t61_yellow_0_8) }
% 9.49/1.90 fresh34(fresh42(fresh47(true2, true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 36 (d9_orders_2_1) }
% 9.49/1.90 fresh34(fresh42(fresh48(element(e, the_carrier(a)), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 1 (t61_yellow_0) }
% 9.49/1.90 fresh34(fresh42(fresh48(element(c, the_carrier(a)), true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 10 (t61_yellow_0_4) }
% 9.49/1.90 fresh34(fresh42(fresh48(true2, true2, a, e, f), true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 21 (d9_orders_2_1) }
% 9.49/1.90 fresh34(fresh42(true2, true2, ordered_pair(e, f), the_carrier(b), the_InternalRel(a)), true2, b, e, f)
% 9.49/1.90 = { by axiom 23 (t16_wellord1) }
% 9.49/1.90 fresh34(true2, true2, b, e, f)
% 9.49/1.90 = { by axiom 24 (d9_orders_2) }
% 9.49/1.90 true2
% 9.49/1.90 % SZS output end Proof
% 9.49/1.90
% 9.49/1.90 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------