TSTP Solution File: GEO544+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO544+1 : TPTP v8.1.2. Released v7.5.0.
% 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 : n023.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 : Wed Aug 30 23:29:15 EDT 2023
% Result : Theorem 34.85s 4.87s
% Output : Proof 37.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO544+1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 22:09:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 34.85/4.87 Command-line arguments: --flatten
% 34.85/4.87
% 34.85/4.87 % SZS status Theorem
% 34.85/4.87
% 36.59/5.11 % SZS output start Proof
% 36.59/5.11 Take the following subset of the input axioms:
% 36.59/5.12 fof(exemplo6GDDFULL012004, conjecture, ![A, B, C, D, M, O, Q, S, J, I, NWPNT1]: ((circle(O, A, B, C) & (circle(O, A, D, NWPNT1) & (midp(Q, C, B) & (midp(S, A, D) & (midp(J, S, Q) & (coll(O, J, M) & (cong(O, J, O, M) & (coll(I, A, D) & coll(I, B, C))))))))) => perp(S, M, B, C))).
% 36.59/5.12 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 36.59/5.12 fof(ruleD10, axiom, ![E, F, B2, C2, D2, A2_2]: ((para(A2_2, B2, C2, D2) & perp(C2, D2, E, F)) => perp(A2_2, B2, E, F))).
% 36.59/5.12 fof(ruleD11, axiom, ![B2, A2_2, M2]: (midp(M2, B2, A2_2) => midp(M2, A2_2, B2))).
% 36.59/5.12 fof(ruleD17, axiom, ![B2, C2, D2, E2, A2_2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 36.59/5.12 fof(ruleD19, axiom, ![P, U, V, B2, C2, D2, A2_2, Q2]: (eqangle(A2_2, B2, C2, D2, P, Q2, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P, Q2))).
% 36.59/5.12 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 36.59/5.12 fof(ruleD21, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(A2_2, B2, P2, Q2, C2, D2, U2, V2))).
% 36.59/5.12 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 36.59/5.12 fof(ruleD4, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(A2_2, B2, D2, C2))).
% 36.59/5.12 fof(ruleD40, axiom, ![B2, C2, D2, A2_2, P2, Q2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 36.59/5.12 fof(ruleD41, axiom, ![B2, A2_2, P2, Q2]: (cyclic(A2_2, B2, P2, Q2) => eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2))).
% 36.59/5.12 fof(ruleD42b, axiom, ![B2, A2_2, P2, Q2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 36.59/5.12 fof(ruleD43, axiom, ![R, B2, C2, A2_2, P2, Q2]: ((cyclic(A2_2, B2, C2, P2) & (cyclic(A2_2, B2, C2, Q2) & (cyclic(A2_2, B2, C2, R) & eqangle(C2, A2_2, C2, B2, R, P2, R, Q2)))) => cong(A2_2, B2, P2, Q2))).
% 36.59/5.12 fof(ruleD44, axiom, ![B2, C2, E2, F2, A2_2]: ((midp(E2, A2_2, B2) & midp(F2, A2_2, C2)) => para(E2, F2, B2, C2))).
% 36.59/5.12 fof(ruleD45, axiom, ![B2, C2, E2, F2, A2_2]: ((midp(E2, A2_2, B2) & (para(E2, F2, B2, C2) & coll(F2, A2_2, C2))) => midp(F2, A2_2, C2))).
% 36.59/5.12 fof(ruleD51, axiom, ![B2, C2, A2_2, M2, O2]: ((circle(O2, A2_2, B2, C2) & (coll(M2, B2, C2) & eqangle(A2_2, B2, A2_2, C2, O2, B2, O2, M2))) => midp(M2, B2, C2))).
% 36.59/5.12 fof(ruleD56, axiom, ![B2, A2_2, P2, Q2]: ((cong(A2_2, P2, B2, P2) & cong(A2_2, Q2, B2, Q2)) => perp(A2_2, B2, P2, Q2))).
% 36.59/5.12 fof(ruleD63, axiom, ![B2, C2, D2, A2_2, M2]: ((midp(M2, A2_2, B2) & midp(M2, C2, D2)) => para(A2_2, C2, B2, D2))).
% 36.59/5.12 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 36.59/5.12 fof(ruleD68, axiom, ![B2, C2, A2_2]: (midp(A2_2, B2, C2) => cong(A2_2, B2, A2_2, C2))).
% 36.59/5.12 fof(ruleD73, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & para(P2, Q2, U2, V2)) => para(A2_2, B2, C2, D2))).
% 36.59/5.12 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 36.59/5.13 fof(ruleD9, axiom, ![B2, C2, D2, E2, F2, A2_2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => para(A2_2, B2, E2, F2))).
% 36.59/5.13
% 36.59/5.13 Now clausify the problem and encode Horn clauses using encoding 3 of
% 36.59/5.13 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 36.59/5.13 We repeatedly replace C & s=t => u=v by the two clauses:
% 36.59/5.13 fresh(y, y, x1...xn) = u
% 36.59/5.13 C => fresh(s, t, x1...xn) = v
% 36.59/5.13 where fresh is a fresh function symbol and x1..xn are the free
% 36.59/5.13 variables of u and v.
% 36.59/5.13 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 36.59/5.13 input problem has no model of domain size 1).
% 36.59/5.13
% 36.59/5.13 The encoding turns the above axioms into the following unit equations and goals:
% 36.59/5.13
% 36.59/5.13 Axiom 1 (exemplo6GDDFULL012004_5): midp(q, c, b) = true.
% 36.59/5.13 Axiom 2 (exemplo6GDDFULL012004_3): midp(s, a, d) = true.
% 36.59/5.13 Axiom 3 (exemplo6GDDFULL012004_1): coll(i, b, c) = true.
% 36.59/5.13 Axiom 4 (exemplo6GDDFULL012004): coll(o, j, m) = true.
% 36.59/5.13 Axiom 5 (exemplo6GDDFULL012004_8): circle(o, a, d, nwpnt1) = true.
% 36.59/5.13 Axiom 6 (ruleD45): fresh181(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 7 (ruleD51): fresh179(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 8 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 9 (ruleD11): fresh144(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 10 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 11 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 12 (ruleD45): fresh98(X, X, Y, Z, W) = midp(W, Y, Z).
% 36.59/5.13 Axiom 13 (ruleD51): fresh89(X, X, Y, Z, W) = midp(W, Y, Z).
% 36.59/5.13 Axiom 14 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 15 (ruleD68): fresh63(X, X, Y, Z, W) = true.
% 36.59/5.13 Axiom 16 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 17 (ruleD10): fresh145(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 18 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 19 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 36.59/5.13 Axiom 20 (ruleD4): fresh105(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 21 (ruleD41): fresh103(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 22 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 36.59/5.13 Axiom 23 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 24 (ruleD44): fresh99(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 25 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 36.59/5.13 Axiom 26 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 27 (ruleD63): fresh69(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 28 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 29 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 30 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 36.59/5.13 Axiom 31 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 36.59/5.13 Axiom 32 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 36.59/5.13 Axiom 33 (ruleD44): fresh100(X, X, Y, Z, W, V, U) = para(V, U, Z, W).
% 36.59/5.13 Axiom 34 (ruleD63): fresh70(X, X, Y, Z, W, V, U) = para(Y, W, Z, V).
% 36.59/5.13 Axiom 35 (ruleD45): fresh180(X, X, Y, Z, W, V, U) = fresh181(coll(U, Y, W), true, Y, W, U).
% 36.59/5.13 Axiom 36 (ruleD51): fresh178(X, X, Y, Z, W, V, U) = fresh179(coll(V, Z, W), true, Z, W, V).
% 36.59/5.13 Axiom 37 (ruleD10): fresh147(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
% 36.59/5.13 Axiom 38 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 36.59/5.13 Axiom 39 (ruleD11): fresh144(midp(X, Y, Z), true, Z, Y, X) = midp(X, Z, Y).
% 36.59/5.13 Axiom 40 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 36.59/5.13 Axiom 41 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 36.59/5.13 Axiom 42 (ruleD68): fresh63(midp(X, Y, Z), true, X, Y, Z) = cong(X, Y, X, Z).
% 36.59/5.13 Axiom 43 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 36.59/5.13 Axiom 44 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 36.59/5.13 Axiom 45 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 36.59/5.13 Axiom 46 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 36.59/5.13 Axiom 47 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 36.59/5.13 Axiom 48 (ruleD45): fresh180(midp(X, Y, Z), true, Y, Z, W, X, V) = fresh98(para(X, V, Z, W), true, Y, W, V).
% 36.59/5.13 Axiom 49 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 36.59/5.13 Axiom 50 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 36.59/5.13 Axiom 51 (ruleD4): fresh105(para(X, Y, Z, W), true, X, Y, Z, W) = para(X, Y, W, Z).
% 36.59/5.13 Axiom 52 (ruleD41): fresh103(cyclic(X, Y, Z, W), true, X, Y, Z, W) = eqangle(Z, X, Z, Y, W, X, W, Y).
% 36.59/5.13 Axiom 53 (ruleD44): fresh100(midp(X, Y, Z), true, Y, W, Z, V, X) = fresh99(midp(V, Y, W), true, W, Z, V, X).
% 36.59/5.13 Axiom 54 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 36.59/5.13 Axiom 55 (ruleD63): fresh70(midp(X, Y, Z), true, W, V, Y, Z, X) = fresh69(midp(X, W, V), true, W, V, Y, Z).
% 36.59/5.13 Axiom 56 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 36.59/5.13 Axiom 57 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 36.59/5.13 Axiom 58 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 36.59/5.13 Axiom 59 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 36.59/5.13 Axiom 60 (ruleD10): fresh147(perp(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh145(para(V, U, X, Y), true, V, U, Z, W).
% 36.59/5.13 Axiom 61 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 36.59/5.13 Axiom 62 (ruleD9): fresh51(perp(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh50(perp(V, U, X, Y), true, V, U, Z, W).
% 36.59/5.13 Axiom 63 (ruleD42b): fresh102(eqangle(X, Y, X, Z, W, Y, W, Z), true, Y, Z, X, W) = fresh101(coll(X, W, Z), true, Y, Z, X, W).
% 36.59/5.13 Axiom 64 (ruleD51): fresh178(eqangle(X, Y, X, Z, W, Y, W, V), true, X, Y, Z, V, W) = fresh89(circle(W, X, Y, Z), true, Y, Z, V).
% 36.59/5.13 Axiom 65 (ruleD43): fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W) = fresh184(cyclic(Y, Z, X, W), true, Y, Z, X, V, U).
% 36.59/5.13 Axiom 66 (ruleD19): fresh134(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = eqangle(Z, W, X, Y, T, S, V, U).
% 36.59/5.13 Axiom 67 (ruleD21): fresh131(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = eqangle(X, Y, V, U, Z, W, T, S).
% 36.59/5.13 Axiom 68 (ruleD73): fresh58(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = fresh57(para(V, U, T, S), true, X, Y, Z, W).
% 36.59/5.13
% 36.59/5.13 Lemma 69: midp(s, a, d) = midp(q, c, b).
% 36.59/5.13 Proof:
% 36.59/5.13 midp(s, a, d)
% 36.59/5.13 = { by axiom 2 (exemplo6GDDFULL012004_3) }
% 36.59/5.13 true
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.13 midp(q, c, b)
% 36.59/5.13
% 36.59/5.13 Lemma 70: coll(i, b, c) = midp(s, a, d).
% 36.59/5.13 Proof:
% 36.59/5.13 coll(i, b, c)
% 36.59/5.13 = { by axiom 3 (exemplo6GDDFULL012004_1) }
% 36.59/5.13 true
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.13 midp(q, c, b)
% 36.59/5.13 = { by lemma 69 R->L }
% 36.59/5.13 midp(s, a, d)
% 36.59/5.13
% 36.59/5.13 Lemma 71: coll(o, j, m) = coll(i, b, c).
% 36.59/5.13 Proof:
% 36.59/5.13 coll(o, j, m)
% 36.59/5.13 = { by axiom 4 (exemplo6GDDFULL012004) }
% 36.59/5.13 true
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.13 midp(q, c, b)
% 36.59/5.13 = { by lemma 69 R->L }
% 36.59/5.13 midp(s, a, d)
% 36.59/5.13 = { by lemma 70 R->L }
% 36.59/5.13 coll(i, b, c)
% 36.59/5.13
% 36.59/5.13 Lemma 72: para(q, q, b, b) = coll(o, j, m).
% 36.59/5.13 Proof:
% 36.59/5.13 para(q, q, b, b)
% 36.59/5.13 = { by axiom 33 (ruleD44) R->L }
% 36.59/5.13 fresh100(coll(o, j, m), coll(o, j, m), c, b, b, q, q)
% 36.59/5.13 = { by lemma 71 }
% 36.59/5.13 fresh100(coll(i, b, c), coll(o, j, m), c, b, b, q, q)
% 36.59/5.13 = { by lemma 70 }
% 36.59/5.13 fresh100(midp(s, a, d), coll(o, j, m), c, b, b, q, q)
% 36.59/5.13 = { by lemma 69 }
% 36.59/5.13 fresh100(midp(q, c, b), coll(o, j, m), c, b, b, q, q)
% 36.59/5.13 = { by lemma 71 }
% 36.59/5.13 fresh100(midp(q, c, b), coll(i, b, c), c, b, b, q, q)
% 36.59/5.13 = { by lemma 70 }
% 36.59/5.13 fresh100(midp(q, c, b), midp(s, a, d), c, b, b, q, q)
% 36.59/5.13 = { by lemma 69 }
% 36.59/5.13 fresh100(midp(q, c, b), midp(q, c, b), c, b, b, q, q)
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.13 fresh100(midp(q, c, b), true, c, b, b, q, q)
% 36.59/5.13 = { by axiom 53 (ruleD44) }
% 36.59/5.13 fresh99(midp(q, c, b), true, b, b, q, q)
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.13 fresh99(midp(q, c, b), midp(q, c, b), b, b, q, q)
% 36.59/5.13 = { by lemma 69 R->L }
% 36.59/5.13 fresh99(midp(q, c, b), midp(s, a, d), b, b, q, q)
% 36.59/5.13 = { by lemma 70 R->L }
% 36.59/5.13 fresh99(midp(q, c, b), coll(i, b, c), b, b, q, q)
% 36.59/5.13 = { by lemma 71 R->L }
% 36.59/5.13 fresh99(midp(q, c, b), coll(o, j, m), b, b, q, q)
% 36.59/5.13 = { by lemma 69 R->L }
% 36.59/5.13 fresh99(midp(s, a, d), coll(o, j, m), b, b, q, q)
% 36.59/5.13 = { by lemma 70 R->L }
% 36.59/5.13 fresh99(coll(i, b, c), coll(o, j, m), b, b, q, q)
% 36.59/5.13 = { by lemma 71 R->L }
% 36.59/5.13 fresh99(coll(o, j, m), coll(o, j, m), b, b, q, q)
% 36.59/5.13 = { by axiom 24 (ruleD44) }
% 36.59/5.13 true
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.13 midp(q, c, b)
% 36.59/5.13 = { by lemma 69 R->L }
% 36.59/5.13 midp(s, a, d)
% 36.59/5.13 = { by lemma 70 R->L }
% 36.59/5.13 coll(i, b, c)
% 36.59/5.13 = { by lemma 71 R->L }
% 36.59/5.13 coll(o, j, m)
% 36.59/5.13
% 36.59/5.13 Lemma 73: fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(o, j, m), X, Y, Z, W, V, U, T, S) = eqangle(X, Y, V, U, Z, W, T, S).
% 36.59/5.13 Proof:
% 36.59/5.13 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(o, j, m), X, Y, Z, W, V, U, T, S)
% 36.59/5.13 = { by lemma 71 }
% 36.59/5.13 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(i, b, c), X, Y, Z, W, V, U, T, S)
% 36.59/5.13 = { by lemma 70 }
% 36.59/5.13 fresh131(eqangle(X, Y, Z, W, V, U, T, S), midp(s, a, d), X, Y, Z, W, V, U, T, S)
% 36.59/5.13 = { by lemma 69 }
% 36.59/5.13 fresh131(eqangle(X, Y, Z, W, V, U, T, S), midp(q, c, b), X, Y, Z, W, V, U, T, S)
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.13 fresh131(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S)
% 36.59/5.13 = { by axiom 67 (ruleD21) }
% 36.59/5.13 eqangle(X, Y, V, U, Z, W, T, S)
% 36.59/5.13
% 36.59/5.13 Lemma 74: fresh104(para(X, Y, Z, W), coll(o, j, m), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 36.59/5.13 Proof:
% 36.59/5.13 fresh104(para(X, Y, Z, W), coll(o, j, m), X, Y, Z, W, V, U)
% 36.59/5.13 = { by lemma 71 }
% 36.59/5.13 fresh104(para(X, Y, Z, W), coll(i, b, c), X, Y, Z, W, V, U)
% 36.59/5.13 = { by lemma 70 }
% 36.59/5.13 fresh104(para(X, Y, Z, W), midp(s, a, d), X, Y, Z, W, V, U)
% 36.59/5.13 = { by lemma 69 }
% 36.59/5.13 fresh104(para(X, Y, Z, W), midp(q, c, b), X, Y, Z, W, V, U)
% 36.59/5.13 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.13 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 36.59/5.13 = { by axiom 61 (ruleD40) }
% 36.59/5.14 eqangle(X, Y, V, U, Z, W, V, U)
% 36.59/5.14
% 36.59/5.14 Lemma 75: fresh104(X, X, Y, Z, W, V, U, T) = coll(o, j, m).
% 36.59/5.14 Proof:
% 36.59/5.14 fresh104(X, X, Y, Z, W, V, U, T)
% 36.59/5.14 = { by axiom 41 (ruleD40) }
% 36.59/5.14 true
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.14 midp(q, c, b)
% 36.59/5.14 = { by lemma 69 R->L }
% 36.59/5.14 midp(s, a, d)
% 36.59/5.14 = { by lemma 70 R->L }
% 36.59/5.14 coll(i, b, c)
% 36.59/5.14 = { by lemma 71 R->L }
% 36.59/5.14 coll(o, j, m)
% 36.59/5.14
% 36.59/5.14 Lemma 76: fresh131(X, X, Y, Z, W, V, U, T, S, X2) = coll(o, j, m).
% 36.59/5.14 Proof:
% 36.59/5.14 fresh131(X, X, Y, Z, W, V, U, T, S, X2)
% 36.59/5.14 = { by axiom 50 (ruleD21) }
% 36.59/5.14 true
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.14 midp(q, c, b)
% 36.59/5.14 = { by lemma 69 R->L }
% 36.59/5.14 midp(s, a, d)
% 36.59/5.14 = { by lemma 70 R->L }
% 36.59/5.14 coll(i, b, c)
% 36.59/5.14 = { by lemma 71 R->L }
% 36.59/5.14 coll(o, j, m)
% 36.59/5.14
% 36.59/5.14 Lemma 77: coll(o, j, m) = coll(X, X, Y).
% 36.59/5.14 Proof:
% 36.59/5.14 coll(o, j, m)
% 36.59/5.14 = { by lemma 71 }
% 36.59/5.14 coll(i, b, c)
% 36.59/5.14 = { by lemma 70 }
% 36.59/5.14 midp(s, a, d)
% 36.59/5.14 = { by lemma 69 }
% 36.59/5.14 midp(q, c, b)
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.14 true
% 36.59/5.14 = { by axiom 8 (ruleD1) R->L }
% 36.59/5.14 fresh146(coll(o, j, m), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 71 }
% 36.59/5.14 fresh146(coll(i, b, c), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 70 }
% 36.59/5.14 fresh146(midp(s, a, d), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 69 }
% 36.59/5.14 fresh146(midp(q, c, b), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.14 fresh146(true, coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 10 (ruleD2) R->L }
% 36.59/5.14 fresh146(fresh133(coll(o, j, m), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 71 }
% 36.59/5.14 fresh146(fresh133(coll(i, b, c), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 70 }
% 36.59/5.14 fresh146(fresh133(midp(s, a, d), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 69 }
% 36.59/5.14 fresh146(fresh133(midp(q, c, b), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.14 fresh146(fresh133(true, coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 14 (ruleD66) R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(coll(o, j, m), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 71 }
% 36.59/5.14 fresh146(fresh133(fresh66(coll(i, b, c), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 70 }
% 36.59/5.14 fresh146(fresh133(fresh66(midp(s, a, d), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 69 }
% 36.59/5.14 fresh146(fresh133(fresh66(midp(q, c, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.14 fresh146(fresh133(fresh66(true, coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 28 (ruleD73) R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh57(coll(o, j, m), coll(o, j, m), Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 72 R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh57(para(q, q, b, b), coll(o, j, m), Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 71 }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh57(para(q, q, b, b), coll(i, b, c), Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 70 }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh57(para(q, q, b, b), midp(s, a, d), Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 69 }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh57(para(q, q, b, b), midp(q, c, b), Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh57(para(q, q, b, b), true, Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 68 (ruleD73) R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, q, q, b, b), true, Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, q, q, b, b), midp(q, c, b), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 69 R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, q, q, b, b), midp(s, a, d), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 70 R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, q, q, b, b), coll(i, b, c), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 71 R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by lemma 73 R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(fresh131(eqangle(Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.14 = { by axiom 66 (ruleD19) R->L }
% 36.59/5.14 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(q, q, Y, X, b, b, Y, X), true, q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(q, q, Y, X, b, b, Y, X), midp(q, c, b), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 69 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(q, q, Y, X, b, b, Y, X), midp(s, a, d), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 70 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(q, q, Y, X, b, b, Y, X), coll(i, b, c), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 71 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(q, q, Y, X, b, b, Y, X), coll(o, j, m), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 74 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(fresh104(para(q, q, b, b), coll(o, j, m), q, q, b, b, Y, X), coll(o, j, m), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 72 }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(fresh104(coll(o, j, m), coll(o, j, m), q, q, b, b, Y, X), coll(o, j, m), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 75 }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(coll(o, j, m), coll(o, j, m), q, q, Y, X, b, b, Y, X), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 49 (ruleD19) }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(true, coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(midp(q, c, b), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 69 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(midp(s, a, d), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 70 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(coll(i, b, c), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 71 R->L }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(fresh131(coll(o, j, m), coll(o, j, m), Y, X, q, q, Y, X, b, b), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 76 }
% 36.59/5.15 fresh146(fresh133(fresh66(fresh58(coll(o, j, m), coll(o, j, m), Y, X, Y, X, q, q, b, b), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 56 (ruleD73) }
% 36.59/5.15 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(o, j, m), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(i, b, c), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 fresh146(fresh133(fresh66(para(Y, X, Y, X), midp(s, a, d), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 fresh146(fresh133(fresh66(para(Y, X, Y, X), midp(q, c, b), Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.15 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 46 (ruleD66) }
% 36.59/5.15 fresh146(fresh133(coll(Y, X, X), coll(o, j, m), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 fresh146(fresh133(coll(Y, X, X), coll(i, b, c), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 fresh146(fresh133(coll(Y, X, X), midp(s, a, d), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 fresh146(fresh133(coll(Y, X, X), midp(q, c, b), Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.15 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by axiom 40 (ruleD2) }
% 36.59/5.15 fresh146(coll(X, Y, X), coll(o, j, m), X, Y, X)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 fresh146(coll(X, Y, X), coll(i, b, c), X, Y, X)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 fresh146(coll(X, Y, X), midp(s, a, d), X, Y, X)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 fresh146(coll(X, Y, X), midp(q, c, b), X, Y, X)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.15 fresh146(coll(X, Y, X), true, X, Y, X)
% 36.59/5.15 = { by axiom 38 (ruleD1) }
% 36.59/5.15 coll(X, X, Y)
% 36.59/5.15
% 36.59/5.15 Lemma 78: coll(o, j, m) = coll(X, Y, Z).
% 36.59/5.15 Proof:
% 36.59/5.15 coll(o, j, m)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 coll(i, b, c)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 midp(s, a, d)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 midp(q, c, b)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.15 true
% 36.59/5.15 = { by axiom 11 (ruleD3) R->L }
% 36.59/5.15 fresh119(coll(o, j, m), coll(o, j, m), Z, X, Y)
% 36.59/5.15 = { by lemma 77 }
% 36.59/5.15 fresh119(coll(Z, Z, X), coll(o, j, m), Z, X, Y)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 fresh119(coll(Z, Z, X), coll(i, b, c), Z, X, Y)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 fresh119(coll(Z, Z, X), midp(s, a, d), Z, X, Y)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 fresh119(coll(Z, Z, X), midp(q, c, b), Z, X, Y)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.15 fresh119(coll(Z, Z, X), true, Z, X, Y)
% 36.59/5.15 = { by axiom 45 (ruleD3) R->L }
% 36.59/5.15 fresh120(coll(Z, Z, Y), true, Z, Z, X, Y)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.15 fresh120(coll(Z, Z, Y), midp(q, c, b), Z, Z, X, Y)
% 36.59/5.15 = { by lemma 69 R->L }
% 36.59/5.15 fresh120(coll(Z, Z, Y), midp(s, a, d), Z, Z, X, Y)
% 36.59/5.15 = { by lemma 70 R->L }
% 36.59/5.15 fresh120(coll(Z, Z, Y), coll(i, b, c), Z, Z, X, Y)
% 36.59/5.15 = { by lemma 71 R->L }
% 36.59/5.15 fresh120(coll(Z, Z, Y), coll(o, j, m), Z, Z, X, Y)
% 36.59/5.15 = { by lemma 77 R->L }
% 36.59/5.15 fresh120(coll(o, j, m), coll(o, j, m), Z, Z, X, Y)
% 36.59/5.15 = { by axiom 19 (ruleD3) }
% 36.59/5.15 coll(X, Y, Z)
% 36.59/5.15
% 36.59/5.15 Lemma 79: fresh144(midp(X, Y, Z), coll(o, j, m), Z, Y, X) = midp(X, Z, Y).
% 36.59/5.15 Proof:
% 36.59/5.15 fresh144(midp(X, Y, Z), coll(o, j, m), Z, Y, X)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 fresh144(midp(X, Y, Z), coll(i, b, c), Z, Y, X)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 fresh144(midp(X, Y, Z), midp(s, a, d), Z, Y, X)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 fresh144(midp(X, Y, Z), midp(q, c, b), Z, Y, X)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.15 fresh144(midp(X, Y, Z), true, Z, Y, X)
% 36.59/5.15 = { by axiom 39 (ruleD11) }
% 36.59/5.15 midp(X, Z, Y)
% 36.59/5.15
% 36.59/5.15 Lemma 80: fresh144(X, X, Y, Z, W) = coll(o, j, m).
% 36.59/5.15 Proof:
% 36.59/5.15 fresh144(X, X, Y, Z, W)
% 36.59/5.15 = { by axiom 9 (ruleD11) }
% 36.59/5.15 true
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.15 midp(q, c, b)
% 36.59/5.15 = { by lemma 69 R->L }
% 36.59/5.15 midp(s, a, d)
% 36.59/5.15 = { by lemma 70 R->L }
% 36.59/5.15 coll(i, b, c)
% 36.59/5.15 = { by lemma 71 R->L }
% 36.59/5.15 coll(o, j, m)
% 36.59/5.15
% 36.59/5.15 Lemma 81: eqangle(b, c, X, Y, b, c, X, Y) = coll(o, j, m).
% 36.59/5.15 Proof:
% 36.59/5.15 eqangle(b, c, X, Y, b, c, X, Y)
% 36.59/5.15 = { by lemma 74 R->L }
% 36.59/5.15 fresh104(para(b, c, b, c), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by axiom 51 (ruleD4) R->L }
% 36.59/5.15 fresh104(fresh105(para(b, c, c, b), true, b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.15 fresh104(fresh105(para(b, c, c, b), midp(q, c, b), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by lemma 69 R->L }
% 36.59/5.15 fresh104(fresh105(para(b, c, c, b), midp(s, a, d), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by lemma 70 R->L }
% 36.59/5.15 fresh104(fresh105(para(b, c, c, b), coll(i, b, c), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by lemma 71 R->L }
% 36.59/5.15 fresh104(fresh105(para(b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by axiom 34 (ruleD63) R->L }
% 36.59/5.15 fresh104(fresh105(fresh70(coll(o, j, m), coll(o, j, m), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by lemma 71 }
% 36.59/5.15 fresh104(fresh105(fresh70(coll(i, b, c), coll(o, j, m), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by lemma 70 }
% 36.59/5.15 fresh104(fresh105(fresh70(midp(s, a, d), coll(o, j, m), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.15 = { by lemma 69 }
% 36.59/5.15 fresh104(fresh105(fresh70(midp(q, c, b), coll(o, j, m), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 71 }
% 36.59/5.16 fresh104(fresh105(fresh70(midp(q, c, b), coll(i, b, c), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 70 }
% 36.59/5.16 fresh104(fresh105(fresh70(midp(q, c, b), midp(s, a, d), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 69 }
% 36.59/5.16 fresh104(fresh105(fresh70(midp(q, c, b), midp(q, c, b), b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.16 fresh104(fresh105(fresh70(midp(q, c, b), true, b, c, c, b, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 55 (ruleD63) }
% 36.59/5.16 fresh104(fresh105(fresh69(midp(q, b, c), true, b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(midp(q, b, c), midp(q, c, b), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(midp(q, b, c), midp(s, a, d), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(midp(q, b, c), coll(i, b, c), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(midp(q, b, c), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 79 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(fresh144(midp(q, c, b), coll(o, j, m), b, c, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(fresh144(midp(s, a, d), coll(o, j, m), b, c, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(fresh144(coll(i, b, c), coll(o, j, m), b, c, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh104(fresh105(fresh69(fresh144(coll(o, j, m), coll(o, j, m), b, c, q), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 80 }
% 36.59/5.16 fresh104(fresh105(fresh69(coll(o, j, m), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 27 (ruleD63) }
% 36.59/5.16 fresh104(fresh105(true, coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh104(fresh105(midp(q, c, b), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh104(fresh105(midp(s, a, d), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh104(fresh105(coll(i, b, c), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh104(fresh105(coll(o, j, m), coll(o, j, m), b, c, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 20 (ruleD4) }
% 36.59/5.16 fresh104(true, coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh104(midp(q, c, b), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh104(midp(s, a, d), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh104(coll(i, b, c), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh104(coll(o, j, m), coll(o, j, m), b, c, b, c, X, Y)
% 36.59/5.16 = { by lemma 75 }
% 36.59/5.16 coll(o, j, m)
% 36.59/5.16
% 36.59/5.16 Lemma 82: cyclic(c, c, b, X) = coll(o, j, m).
% 36.59/5.16 Proof:
% 36.59/5.16 cyclic(c, c, b, X)
% 36.59/5.16 = { by axiom 22 (ruleD42b) R->L }
% 36.59/5.16 fresh102(coll(o, j, m), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by lemma 76 R->L }
% 36.59/5.16 fresh102(fresh131(coll(o, j, m), coll(o, j, m), b, c, X, c, b, c, X, c), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by lemma 81 R->L }
% 36.59/5.16 fresh102(fresh131(eqangle(b, c, X, c, b, c, X, c), coll(o, j, m), b, c, X, c, b, c, X, c), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by lemma 73 }
% 36.59/5.16 fresh102(eqangle(b, c, b, c, X, c, X, c), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by axiom 44 (ruleD50) R->L }
% 36.59/5.16 fresh102(fresh91(Y, Y, b, c, c, X, c), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by lemma 71 }
% 36.59/5.16 fresh102(fresh91(Y, Y, b, c, c, X, c), coll(i, b, c), c, c, b, X)
% 36.59/5.16 = { by lemma 70 }
% 36.59/5.16 fresh102(fresh91(Y, Y, b, c, c, X, c), midp(s, a, d), c, c, b, X)
% 36.59/5.16 = { by lemma 69 }
% 36.59/5.16 fresh102(fresh91(Y, Y, b, c, c, X, c), midp(q, c, b), c, c, b, X)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.16 fresh102(fresh91(Y, Y, b, c, c, X, c), true, c, c, b, X)
% 36.59/5.16 = { by axiom 44 (ruleD50) }
% 36.59/5.16 fresh102(eqangle(b, c, b, c, X, c, X, c), true, c, c, b, X)
% 36.59/5.16 = { by axiom 63 (ruleD42b) }
% 36.59/5.16 fresh101(coll(b, X, c), true, c, c, b, X)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh101(coll(b, X, c), midp(q, c, b), c, c, b, X)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh101(coll(b, X, c), midp(s, a, d), c, c, b, X)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh101(coll(b, X, c), coll(i, b, c), c, c, b, X)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh101(coll(b, X, c), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by lemma 78 R->L }
% 36.59/5.16 fresh101(coll(o, j, m), coll(o, j, m), c, c, b, X)
% 36.59/5.16 = { by axiom 23 (ruleD42b) }
% 36.59/5.16 true
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 midp(q, c, b)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 midp(s, a, d)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 coll(i, b, c)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 coll(o, j, m)
% 36.59/5.16
% 36.59/5.16 Lemma 83: fresh137(cyclic(X, Y, Z, W), coll(o, j, m), X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), coll(o, j, m), Y, Z, V, W).
% 36.59/5.16 Proof:
% 36.59/5.16 fresh137(cyclic(X, Y, Z, W), coll(o, j, m), X, Y, Z, V, W)
% 36.59/5.16 = { by lemma 71 }
% 36.59/5.16 fresh137(cyclic(X, Y, Z, W), coll(i, b, c), X, Y, Z, V, W)
% 36.59/5.16 = { by lemma 70 }
% 36.59/5.16 fresh137(cyclic(X, Y, Z, W), midp(s, a, d), X, Y, Z, V, W)
% 36.59/5.16 = { by lemma 69 }
% 36.59/5.16 fresh137(cyclic(X, Y, Z, W), midp(q, c, b), X, Y, Z, V, W)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.16 fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W)
% 36.59/5.16 = { by axiom 59 (ruleD17) }
% 36.59/5.16 fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh136(cyclic(X, Y, Z, V), midp(q, c, b), Y, Z, V, W)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh136(cyclic(X, Y, Z, V), midp(s, a, d), Y, Z, V, W)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh136(cyclic(X, Y, Z, V), coll(i, b, c), Y, Z, V, W)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh136(cyclic(X, Y, Z, V), coll(o, j, m), Y, Z, V, W)
% 36.59/5.16
% 36.59/5.16 Lemma 84: fresh136(X, X, Y, Z, W, V) = coll(o, j, m).
% 36.59/5.16 Proof:
% 36.59/5.16 fresh136(X, X, Y, Z, W, V)
% 36.59/5.16 = { by axiom 18 (ruleD17) }
% 36.59/5.16 true
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 midp(q, c, b)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 midp(s, a, d)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 coll(i, b, c)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 coll(o, j, m)
% 36.59/5.16
% 36.59/5.16 Lemma 85: cyclic(c, b, X, Y) = coll(o, j, m).
% 36.59/5.16 Proof:
% 36.59/5.16 cyclic(c, b, X, Y)
% 36.59/5.16 = { by axiom 32 (ruleD17) R->L }
% 36.59/5.16 fresh137(coll(o, j, m), coll(o, j, m), c, c, b, X, Y)
% 36.59/5.16 = { by lemma 82 R->L }
% 36.59/5.16 fresh137(cyclic(c, c, b, Y), coll(o, j, m), c, c, b, X, Y)
% 36.59/5.16 = { by lemma 83 }
% 36.59/5.16 fresh136(cyclic(c, c, b, X), coll(o, j, m), c, b, X, Y)
% 36.59/5.16 = { by lemma 82 }
% 36.59/5.16 fresh136(coll(o, j, m), coll(o, j, m), c, b, X, Y)
% 36.59/5.16 = { by lemma 84 }
% 36.59/5.16 coll(o, j, m)
% 36.59/5.16
% 36.59/5.16 Lemma 86: cyclic(b, X, Y, Z) = coll(o, j, m).
% 36.59/5.16 Proof:
% 36.59/5.16 cyclic(b, X, Y, Z)
% 36.59/5.16 = { by axiom 32 (ruleD17) R->L }
% 36.59/5.16 fresh137(coll(o, j, m), coll(o, j, m), c, b, X, Y, Z)
% 36.59/5.16 = { by lemma 85 R->L }
% 36.59/5.16 fresh137(cyclic(c, b, X, Z), coll(o, j, m), c, b, X, Y, Z)
% 36.59/5.16 = { by lemma 83 }
% 36.59/5.16 fresh136(cyclic(c, b, X, Y), coll(o, j, m), b, X, Y, Z)
% 36.59/5.16 = { by lemma 85 }
% 36.59/5.16 fresh136(coll(o, j, m), coll(o, j, m), b, X, Y, Z)
% 36.59/5.16 = { by lemma 84 }
% 36.59/5.16 coll(o, j, m)
% 36.59/5.16
% 36.59/5.16 Lemma 87: cyclic(X, Y, Z, W) = coll(o, j, m).
% 36.59/5.16 Proof:
% 36.59/5.16 cyclic(X, Y, Z, W)
% 36.59/5.16 = { by axiom 32 (ruleD17) R->L }
% 36.59/5.16 fresh137(coll(o, j, m), coll(o, j, m), b, X, Y, Z, W)
% 36.59/5.16 = { by lemma 86 R->L }
% 36.59/5.16 fresh137(cyclic(b, X, Y, W), coll(o, j, m), b, X, Y, Z, W)
% 36.59/5.16 = { by lemma 83 }
% 36.59/5.16 fresh136(cyclic(b, X, Y, Z), coll(o, j, m), X, Y, Z, W)
% 36.59/5.16 = { by lemma 86 }
% 36.59/5.16 fresh136(coll(o, j, m), coll(o, j, m), X, Y, Z, W)
% 36.59/5.16 = { by lemma 84 }
% 36.59/5.16 coll(o, j, m)
% 36.59/5.16
% 36.59/5.16 Lemma 88: cong(c, X, c, X) = coll(o, j, m).
% 36.59/5.16 Proof:
% 36.59/5.16 cong(c, X, c, X)
% 36.59/5.16 = { by axiom 31 (ruleD43) R->L }
% 36.59/5.16 fresh183(coll(o, j, m), coll(o, j, m), c, X, b, c, X)
% 36.59/5.16 = { by lemma 87 R->L }
% 36.59/5.16 fresh183(cyclic(c, X, b, X), coll(o, j, m), c, X, b, c, X)
% 36.59/5.16 = { by lemma 71 }
% 36.59/5.16 fresh183(cyclic(c, X, b, X), coll(i, b, c), c, X, b, c, X)
% 36.59/5.16 = { by lemma 70 }
% 36.59/5.16 fresh183(cyclic(c, X, b, X), midp(s, a, d), c, X, b, c, X)
% 36.59/5.16 = { by lemma 69 }
% 36.59/5.16 fresh183(cyclic(c, X, b, X), midp(q, c, b), c, X, b, c, X)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.16 fresh183(cyclic(c, X, b, X), true, c, X, b, c, X)
% 36.59/5.16 = { by axiom 58 (ruleD43) R->L }
% 36.59/5.16 fresh182(coll(o, j, m), coll(o, j, m), c, X, b, c, X, b)
% 36.59/5.16 = { by lemma 81 R->L }
% 36.59/5.16 fresh182(eqangle(b, c, b, X, b, c, b, X), coll(o, j, m), c, X, b, c, X, b)
% 36.59/5.16 = { by lemma 71 }
% 36.59/5.16 fresh182(eqangle(b, c, b, X, b, c, b, X), coll(i, b, c), c, X, b, c, X, b)
% 36.59/5.16 = { by lemma 70 }
% 36.59/5.16 fresh182(eqangle(b, c, b, X, b, c, b, X), midp(s, a, d), c, X, b, c, X, b)
% 36.59/5.16 = { by lemma 69 }
% 36.59/5.16 fresh182(eqangle(b, c, b, X, b, c, b, X), midp(q, c, b), c, X, b, c, X, b)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.16 fresh182(eqangle(b, c, b, X, b, c, b, X), true, c, X, b, c, X, b)
% 36.59/5.16 = { by axiom 65 (ruleD43) }
% 36.59/5.16 fresh184(cyclic(c, X, b, b), true, c, X, b, c, X)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh184(cyclic(c, X, b, b), midp(q, c, b), c, X, b, c, X)
% 36.59/5.16 = { by lemma 69 R->L }
% 36.59/5.16 fresh184(cyclic(c, X, b, b), midp(s, a, d), c, X, b, c, X)
% 36.59/5.16 = { by lemma 70 R->L }
% 36.59/5.16 fresh184(cyclic(c, X, b, b), coll(i, b, c), c, X, b, c, X)
% 36.59/5.16 = { by lemma 71 R->L }
% 36.59/5.16 fresh184(cyclic(c, X, b, b), coll(o, j, m), c, X, b, c, X)
% 36.59/5.16 = { by lemma 87 }
% 36.59/5.16 fresh184(coll(o, j, m), coll(o, j, m), c, X, b, c, X)
% 36.59/5.16 = { by axiom 47 (ruleD43) }
% 36.59/5.16 fresh185(cyclic(c, X, b, c), true, c, X, c, X)
% 36.59/5.16 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.16 fresh185(cyclic(c, X, b, c), midp(q, c, b), c, X, c, X)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh185(cyclic(c, X, b, c), midp(s, a, d), c, X, c, X)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh185(cyclic(c, X, b, c), coll(i, b, c), c, X, c, X)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh185(cyclic(c, X, b, c), coll(o, j, m), c, X, c, X)
% 36.59/5.17 = { by lemma 87 }
% 36.59/5.17 fresh185(coll(o, j, m), coll(o, j, m), c, X, c, X)
% 36.59/5.17 = { by axiom 16 (ruleD43) }
% 36.59/5.17 true
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 midp(q, c, b)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 midp(s, a, d)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 coll(i, b, c)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 coll(o, j, m)
% 36.59/5.17
% 36.59/5.17 Lemma 89: fresh79(cong(X, W, Z, W), coll(o, j, m), X, Z, W, Y) = fresh80(cong(X, Y, Z, Y), coll(o, j, m), X, Z, W, Y).
% 36.59/5.17 Proof:
% 36.59/5.17 fresh79(cong(X, W, Z, W), coll(o, j, m), X, Z, W, Y)
% 36.59/5.17 = { by lemma 71 }
% 36.59/5.17 fresh79(cong(X, W, Z, W), coll(i, b, c), X, Z, W, Y)
% 36.59/5.17 = { by lemma 70 }
% 36.59/5.17 fresh79(cong(X, W, Z, W), midp(s, a, d), X, Z, W, Y)
% 36.59/5.17 = { by lemma 69 }
% 36.59/5.17 fresh79(cong(X, W, Z, W), midp(q, c, b), X, Z, W, Y)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.17 fresh79(cong(X, W, Z, W), true, X, Z, W, Y)
% 36.59/5.17 = { by axiom 54 (ruleD56) R->L }
% 36.59/5.17 fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh80(cong(X, Y, Z, Y), midp(q, c, b), X, Z, W, Y)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh80(cong(X, Y, Z, Y), midp(s, a, d), X, Z, W, Y)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh80(cong(X, Y, Z, Y), coll(i, b, c), X, Z, W, Y)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh80(cong(X, Y, Z, Y), coll(o, j, m), X, Z, W, Y)
% 36.59/5.17
% 36.59/5.17 Lemma 90: fresh79(X, X, Y, Z, W, V) = coll(o, j, m).
% 36.59/5.17 Proof:
% 36.59/5.17 fresh79(X, X, Y, Z, W, V)
% 36.59/5.17 = { by axiom 26 (ruleD56) }
% 36.59/5.17 true
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 midp(q, c, b)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 midp(s, a, d)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 coll(i, b, c)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 coll(o, j, m)
% 36.59/5.17
% 36.59/5.17 Lemma 91: perp(c, c, X, Y) = coll(o, j, m).
% 36.59/5.17 Proof:
% 36.59/5.17 perp(c, c, X, Y)
% 36.59/5.17 = { by axiom 25 (ruleD56) R->L }
% 36.59/5.17 fresh80(coll(o, j, m), coll(o, j, m), c, c, X, Y)
% 36.59/5.17 = { by lemma 88 R->L }
% 36.59/5.17 fresh80(cong(c, Y, c, Y), coll(o, j, m), c, c, X, Y)
% 36.59/5.17 = { by lemma 89 R->L }
% 36.59/5.17 fresh79(cong(c, X, c, X), coll(o, j, m), c, c, X, Y)
% 36.59/5.17 = { by lemma 88 }
% 36.59/5.17 fresh79(coll(o, j, m), coll(o, j, m), c, c, X, Y)
% 36.59/5.17 = { by lemma 90 }
% 36.59/5.17 coll(o, j, m)
% 36.59/5.17
% 36.59/5.17 Lemma 92: para(X, Y, Z, W) = coll(o, j, m).
% 36.59/5.17 Proof:
% 36.59/5.17 para(X, Y, Z, W)
% 36.59/5.17 = { by axiom 43 (ruleD9) R->L }
% 36.59/5.17 fresh51(coll(o, j, m), coll(o, j, m), X, Y, c, c, Z, W)
% 36.59/5.17 = { by lemma 91 R->L }
% 36.59/5.17 fresh51(perp(c, c, Z, W), coll(o, j, m), X, Y, c, c, Z, W)
% 36.59/5.17 = { by lemma 71 }
% 36.59/5.17 fresh51(perp(c, c, Z, W), coll(i, b, c), X, Y, c, c, Z, W)
% 36.59/5.17 = { by lemma 70 }
% 36.59/5.17 fresh51(perp(c, c, Z, W), midp(s, a, d), X, Y, c, c, Z, W)
% 36.59/5.17 = { by lemma 69 }
% 36.59/5.17 fresh51(perp(c, c, Z, W), midp(q, c, b), X, Y, c, c, Z, W)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.17 fresh51(perp(c, c, Z, W), true, X, Y, c, c, Z, W)
% 36.59/5.17 = { by axiom 62 (ruleD9) }
% 36.59/5.17 fresh50(perp(X, Y, c, c), true, X, Y, Z, W)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh50(perp(X, Y, c, c), midp(q, c, b), X, Y, Z, W)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh50(perp(X, Y, c, c), midp(s, a, d), X, Y, Z, W)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh50(perp(X, Y, c, c), coll(i, b, c), X, Y, Z, W)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh50(perp(X, Y, c, c), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by axiom 57 (ruleD8) R->L }
% 36.59/5.17 fresh50(fresh52(perp(c, c, X, Y), true, c, c, X, Y), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh50(fresh52(perp(c, c, X, Y), midp(q, c, b), c, c, X, Y), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh50(fresh52(perp(c, c, X, Y), midp(s, a, d), c, c, X, Y), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh50(fresh52(perp(c, c, X, Y), coll(i, b, c), c, c, X, Y), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh50(fresh52(perp(c, c, X, Y), coll(o, j, m), c, c, X, Y), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 91 }
% 36.59/5.17 fresh50(fresh52(coll(o, j, m), coll(o, j, m), c, c, X, Y), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by axiom 29 (ruleD8) }
% 36.59/5.17 fresh50(true, coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh50(midp(q, c, b), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh50(midp(s, a, d), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh50(coll(i, b, c), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh50(coll(o, j, m), coll(o, j, m), X, Y, Z, W)
% 36.59/5.17 = { by axiom 30 (ruleD9) }
% 36.59/5.17 true
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 midp(q, c, b)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 midp(s, a, d)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 coll(i, b, c)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 coll(o, j, m)
% 36.59/5.17
% 36.59/5.17 Lemma 93: fresh180(midp(X, Y, Z), coll(o, j, m), Y, Z, W, X, V) = fresh98(para(X, V, Z, W), coll(o, j, m), Y, W, V).
% 36.59/5.17 Proof:
% 36.59/5.17 fresh180(midp(X, Y, Z), coll(o, j, m), Y, Z, W, X, V)
% 36.59/5.17 = { by lemma 71 }
% 36.59/5.17 fresh180(midp(X, Y, Z), coll(i, b, c), Y, Z, W, X, V)
% 36.59/5.17 = { by lemma 70 }
% 36.59/5.17 fresh180(midp(X, Y, Z), midp(s, a, d), Y, Z, W, X, V)
% 36.59/5.17 = { by lemma 69 }
% 36.59/5.17 fresh180(midp(X, Y, Z), midp(q, c, b), Y, Z, W, X, V)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.17 fresh180(midp(X, Y, Z), true, Y, Z, W, X, V)
% 36.59/5.17 = { by axiom 48 (ruleD45) }
% 36.59/5.17 fresh98(para(X, V, Z, W), true, Y, W, V)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh98(para(X, V, Z, W), midp(q, c, b), Y, W, V)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh98(para(X, V, Z, W), midp(s, a, d), Y, W, V)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh98(para(X, V, Z, W), coll(i, b, c), Y, W, V)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh98(para(X, V, Z, W), coll(o, j, m), Y, W, V)
% 36.59/5.17
% 36.59/5.17 Lemma 94: fresh180(X, X, Y, Z, W, V, U) = coll(o, j, m).
% 36.59/5.17 Proof:
% 36.59/5.17 fresh180(X, X, Y, Z, W, V, U)
% 36.59/5.17 = { by axiom 35 (ruleD45) }
% 36.59/5.17 fresh181(coll(U, Y, W), true, Y, W, U)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh181(coll(U, Y, W), midp(q, c, b), Y, W, U)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh181(coll(U, Y, W), midp(s, a, d), Y, W, U)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh181(coll(U, Y, W), coll(i, b, c), Y, W, U)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh181(coll(U, Y, W), coll(o, j, m), Y, W, U)
% 36.59/5.17 = { by lemma 78 R->L }
% 36.59/5.17 fresh181(coll(o, j, m), coll(o, j, m), Y, W, U)
% 36.59/5.17 = { by axiom 6 (ruleD45) }
% 36.59/5.17 true
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 midp(q, c, b)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 midp(s, a, d)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 coll(i, b, c)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 coll(o, j, m)
% 36.59/5.17
% 36.59/5.17 Lemma 95: cong(X, Y, X, Z) = coll(o, j, m).
% 36.59/5.17 Proof:
% 36.59/5.17 cong(X, Y, X, Z)
% 36.59/5.17 = { by axiom 42 (ruleD68) R->L }
% 36.59/5.17 fresh63(midp(X, Y, Z), true, X, Y, Z)
% 36.59/5.17 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.17 fresh63(midp(X, Y, Z), midp(q, c, b), X, Y, Z)
% 36.59/5.17 = { by lemma 69 R->L }
% 36.59/5.17 fresh63(midp(X, Y, Z), midp(s, a, d), X, Y, Z)
% 36.59/5.17 = { by lemma 70 R->L }
% 36.59/5.17 fresh63(midp(X, Y, Z), coll(i, b, c), X, Y, Z)
% 36.59/5.17 = { by lemma 71 R->L }
% 36.59/5.17 fresh63(midp(X, Y, Z), coll(o, j, m), X, Y, Z)
% 36.59/5.17 = { by axiom 12 (ruleD45) R->L }
% 36.59/5.18 fresh63(fresh98(coll(o, j, m), coll(o, j, m), Y, Z, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 92 R->L }
% 36.59/5.18 fresh63(fresh98(para(W, X, d, Z), coll(o, j, m), Y, Z, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 93 R->L }
% 36.59/5.18 fresh63(fresh180(midp(W, Y, d), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 79 R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(midp(W, d, Y), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 12 (ruleD45) R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh98(coll(o, j, m), coll(o, j, m), d, Y, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 92 R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh98(para(nwpnt1, W, nwpnt1, Y), coll(o, j, m), d, Y, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 93 R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(midp(nwpnt1, d, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 13 (ruleD51) R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(coll(o, j, m), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 71 }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(coll(i, b, c), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 70 }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(midp(s, a, d), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 69 }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(midp(q, c, b), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(true, coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 5 (exemplo6GDDFULL012004_8) R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(circle(o, a, d, nwpnt1), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 71 }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(circle(o, a, d, nwpnt1), coll(i, b, c), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 70 }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(circle(o, a, d, nwpnt1), midp(s, a, d), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 69 }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(circle(o, a, d, nwpnt1), midp(q, c, b), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh89(circle(o, a, d, nwpnt1), true, d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 64 (ruleD51) R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(eqangle(a, d, a, nwpnt1, o, d, o, nwpnt1), true, a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 44 (ruleD50) R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh91(V, V, a, d, nwpnt1, o, nwpnt1), true, a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh91(V, V, a, d, nwpnt1, o, nwpnt1), midp(q, c, b), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 69 R->L }
% 36.59/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh91(V, V, a, d, nwpnt1, o, nwpnt1), midp(s, a, d), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 36.59/5.18 = { by lemma 70 R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh91(V, V, a, d, nwpnt1, o, nwpnt1), coll(i, b, c), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by lemma 71 R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh91(V, V, a, d, nwpnt1, o, nwpnt1), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by axiom 44 (ruleD50) }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(eqangle(a, d, a, nwpnt1, o, d, o, nwpnt1), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by axiom 52 (ruleD41) R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh103(cyclic(d, nwpnt1, a, o), true, d, nwpnt1, a, o), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh103(cyclic(d, nwpnt1, a, o), midp(q, c, b), d, nwpnt1, a, o), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by lemma 69 R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh103(cyclic(d, nwpnt1, a, o), midp(s, a, d), d, nwpnt1, a, o), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by lemma 70 R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh103(cyclic(d, nwpnt1, a, o), coll(i, b, c), d, nwpnt1, a, o), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by lemma 71 R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh103(cyclic(d, nwpnt1, a, o), coll(o, j, m), d, nwpnt1, a, o), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by lemma 87 }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(fresh103(coll(o, j, m), coll(o, j, m), d, nwpnt1, a, o), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by axiom 21 (ruleD41) }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(true, coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(midp(q, c, b), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.18 = { by lemma 69 R->L }
% 37.05/5.18 fresh63(fresh180(fresh144(fresh180(fresh178(midp(s, a, d), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 70 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh178(coll(i, b, c), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 71 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh178(coll(o, j, m), coll(o, j, m), a, d, nwpnt1, nwpnt1, o), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by axiom 36 (ruleD51) }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh179(coll(nwpnt1, d, nwpnt1), true, d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh179(coll(nwpnt1, d, nwpnt1), midp(q, c, b), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 69 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh179(coll(nwpnt1, d, nwpnt1), midp(s, a, d), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 70 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh179(coll(nwpnt1, d, nwpnt1), coll(i, b, c), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 71 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh179(coll(nwpnt1, d, nwpnt1), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 78 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(fresh179(coll(o, j, m), coll(o, j, m), d, nwpnt1, nwpnt1), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by axiom 7 (ruleD51) }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(true, coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(midp(q, c, b), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 69 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(midp(s, a, d), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 70 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(coll(i, b, c), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 71 R->L }
% 37.05/5.19 fresh63(fresh180(fresh144(fresh180(coll(o, j, m), coll(o, j, m), d, nwpnt1, Y, nwpnt1, W), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 94 }
% 37.05/5.19 fresh63(fresh180(fresh144(coll(o, j, m), coll(o, j, m), Y, d, W), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 80 }
% 37.05/5.19 fresh63(fresh180(coll(o, j, m), coll(o, j, m), Y, d, Z, W, X), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by lemma 94 }
% 37.05/5.19 fresh63(coll(o, j, m), coll(o, j, m), X, Y, Z)
% 37.05/5.19 = { by axiom 15 (ruleD68) }
% 37.05/5.19 true
% 37.05/5.19 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 37.05/5.19 midp(q, c, b)
% 37.05/5.19 = { by lemma 69 R->L }
% 37.05/5.19 midp(s, a, d)
% 37.05/5.19 = { by lemma 70 R->L }
% 37.05/5.19 coll(i, b, c)
% 37.05/5.19 = { by lemma 71 R->L }
% 37.05/5.19 coll(o, j, m)
% 37.05/5.19
% 37.05/5.19 Goal 1 (exemplo6GDDFULL012004_9): perp(s, m, b, c) = true.
% 37.05/5.19 Proof:
% 37.05/5.19 perp(s, m, b, c)
% 37.05/5.19 = { by axiom 37 (ruleD10) R->L }
% 37.05/5.19 fresh147(coll(o, j, m), coll(o, j, m), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 90 R->L }
% 37.05/5.19 fresh147(fresh79(coll(o, j, m), coll(o, j, m), X, X, b, c), coll(o, j, m), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 95 R->L }
% 37.05/5.19 fresh147(fresh79(cong(X, b, X, b), coll(o, j, m), X, X, b, c), coll(o, j, m), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 89 }
% 37.05/5.19 fresh147(fresh80(cong(X, c, X, c), coll(o, j, m), X, X, b, c), coll(o, j, m), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 95 }
% 37.05/5.19 fresh147(fresh80(coll(o, j, m), coll(o, j, m), X, X, b, c), coll(o, j, m), s, m, X, X, b, c)
% 37.05/5.19 = { by axiom 25 (ruleD56) }
% 37.05/5.19 fresh147(perp(X, X, b, c), coll(o, j, m), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 71 }
% 37.05/5.19 fresh147(perp(X, X, b, c), coll(i, b, c), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 70 }
% 37.05/5.19 fresh147(perp(X, X, b, c), midp(s, a, d), s, m, X, X, b, c)
% 37.05/5.19 = { by lemma 69 }
% 37.05/5.19 fresh147(perp(X, X, b, c), midp(q, c, b), s, m, X, X, b, c)
% 37.05/5.19 = { by axiom 1 (exemplo6GDDFULL012004_5) }
% 37.05/5.19 fresh147(perp(X, X, b, c), true, s, m, X, X, b, c)
% 37.05/5.19 = { by axiom 60 (ruleD10) }
% 37.05/5.19 fresh145(para(s, m, X, X), true, s, m, b, c)
% 37.05/5.19 = { by axiom 1 (exemplo6GDDFULL012004_5) R->L }
% 37.05/5.19 fresh145(para(s, m, X, X), midp(q, c, b), s, m, b, c)
% 37.05/5.19 = { by lemma 69 R->L }
% 37.05/5.19 fresh145(para(s, m, X, X), midp(s, a, d), s, m, b, c)
% 37.05/5.19 = { by lemma 70 R->L }
% 37.05/5.19 fresh145(para(s, m, X, X), coll(i, b, c), s, m, b, c)
% 37.05/5.19 = { by lemma 71 R->L }
% 37.05/5.19 fresh145(para(s, m, X, X), coll(o, j, m), s, m, b, c)
% 37.05/5.19 = { by lemma 92 }
% 37.05/5.19 fresh145(coll(o, j, m), coll(o, j, m), s, m, b, c)
% 37.05/5.19 = { by axiom 17 (ruleD10) }
% 37.05/5.19 true
% 37.05/5.19 % SZS output end Proof
% 37.05/5.19
% 37.05/5.19 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------