TSTP Solution File: GEO644+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO644+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 : n011.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 23:29:40 EDT 2023
% Result : Theorem 12.29s 2.04s
% Output : Proof 14.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : GEO644+1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 22:49:12 EDT 2023
% 0.14/0.36 % CPUTime :
% 12.29/2.04 Command-line arguments: --flatten
% 12.29/2.04
% 12.29/2.04 % SZS status Theorem
% 12.29/2.04
% 14.20/2.23 % SZS output start Proof
% 14.20/2.23 Take the following subset of the input axioms:
% 14.20/2.24 fof(exemplo6GDDFULLmoreE0061, conjecture, ![A, B, C, D, E, F, G, H]: ((para(B, C, A, D) & (para(A, B, C, D) & (midp(E, C, D) & (midp(F, B, A) & (coll(G, A, C) & (coll(G, D, F) & (coll(H, B, E) & coll(H, A, C)))))))) => cong(A, G, G, H))).
% 14.20/2.24 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 14.20/2.24 fof(ruleD10, axiom, ![B2, C2, D2, E2, F2, A2_2]: ((para(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => perp(A2_2, B2, E2, F2))).
% 14.20/2.24 fof(ruleD11, axiom, ![M, B2, A2_2]: (midp(M, B2, A2_2) => midp(M, A2_2, B2))).
% 14.20/2.24 fof(ruleD14, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, B2, D2, C2))).
% 14.20/2.24 fof(ruleD15, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 14.20/2.24 fof(ruleD16, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 14.20/2.24 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))).
% 14.20/2.24 fof(ruleD19, axiom, ![P, Q, U, V, B2, C2, D2, A2_2]: (eqangle(A2_2, B2, C2, D2, P, Q, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P, Q))).
% 14.20/2.24 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 14.20/2.24 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))).
% 14.20/2.24 fof(ruleD23, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(A2_2, B2, D2, C2))).
% 14.20/2.24 fof(ruleD24, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(C2, D2, A2_2, B2))).
% 14.20/2.24 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 14.20/2.24 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))).
% 14.20/2.24 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))).
% 14.20/2.24 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))).
% 14.20/2.24 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))).
% 14.20/2.24 fof(ruleD52, axiom, ![B2, C2, A2_2, M2]: ((perp(A2_2, B2, B2, C2) & midp(M2, A2_2, C2)) => cong(A2_2, M2, B2, M2))).
% 14.20/2.24 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))).
% 14.20/2.24 fof(ruleD57, axiom, ![B2, A2_2, P2, Q2]: ((cong(A2_2, P2, B2, P2) & (cong(A2_2, Q2, B2, Q2) & cyclic(A2_2, B2, P2, Q2))) => perp(P2, A2_2, A2_2, Q2))).
% 14.20/2.24 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 14.20/2.24 fof(ruleD68, axiom, ![B2, C2, A2_2]: (midp(A2_2, B2, C2) => cong(A2_2, B2, A2_2, C2))).
% 14.20/2.24 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))).
% 14.20/2.24 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 14.20/2.24 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))).
% 14.20/2.24
% 14.20/2.24 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.20/2.24 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.20/2.24 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.20/2.24 fresh(y, y, x1...xn) = u
% 14.20/2.24 C => fresh(s, t, x1...xn) = v
% 14.20/2.24 where fresh is a fresh function symbol and x1..xn are the free
% 14.20/2.24 variables of u and v.
% 14.20/2.24 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.20/2.24 input problem has no model of domain size 1).
% 14.20/2.24
% 14.20/2.24 The encoding turns the above axioms into the following unit equations and goals:
% 14.20/2.24
% 14.20/2.24 Axiom 1 (exemplo6GDDFULLmoreE0061_6): midp(f, b, a) = true.
% 14.20/2.24 Axiom 2 (exemplo6GDDFULLmoreE0061_2): coll(h, b, e) = true.
% 14.20/2.24 Axiom 3 (exemplo6GDDFULLmoreE0061): coll(g, d, f) = true.
% 14.20/2.24 Axiom 4 (exemplo6GDDFULLmoreE0061_4): para(b, c, a, d) = true.
% 14.20/2.24 Axiom 5 (ruleD45): fresh181(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 6 (ruleD57): fresh177(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 7 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 8 (ruleD11): fresh144(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 9 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 10 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 11 (ruleD45): fresh98(X, X, Y, Z, W) = midp(W, Y, Z).
% 14.20/2.24 Axiom 12 (ruleD52): fresh87(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 13 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 14 (ruleD68): fresh63(X, X, Y, Z, W) = true.
% 14.20/2.24 Axiom 15 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 16 (ruleD10): fresh145(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 17 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 18 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 19 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 20 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 21 (ruleD23): fresh128(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 22 (ruleD24): fresh127(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 23 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 14.20/2.24 Axiom 24 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 14.20/2.24 Axiom 25 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 26 (ruleD52): fresh88(X, X, Y, Z, W, V) = cong(Y, V, Z, V).
% 14.20/2.24 Axiom 27 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 14.20/2.24 Axiom 28 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 29 (ruleD57): fresh78(X, X, Y, Z, W, V) = perp(W, Y, Y, V).
% 14.20/2.24 Axiom 30 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 31 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 32 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 14.20/2.24 Axiom 33 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 14.20/2.24 Axiom 34 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 14.20/2.24 Axiom 35 (ruleD45): fresh180(X, X, Y, Z, W, V, U) = fresh181(coll(U, Y, W), true, Y, W, U).
% 14.20/2.24 Axiom 36 (ruleD10): fresh147(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
% 14.20/2.24 Axiom 37 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 14.20/2.24 Axiom 38 (ruleD11): fresh144(midp(X, Y, Z), true, Z, Y, X) = midp(X, Z, Y).
% 14.20/2.24 Axiom 39 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 14.20/2.24 Axiom 40 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 14.20/2.24 Axiom 41 (ruleD68): fresh63(midp(X, Y, Z), true, X, Y, Z) = cong(X, Y, X, Z).
% 14.20/2.24 Axiom 42 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 14.20/2.24 Axiom 43 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 14.20/2.24 Axiom 44 (ruleD57): fresh176(X, X, Y, Z, W, V) = fresh177(cong(Y, W, Z, W), true, Y, W, V).
% 14.20/2.24 Axiom 45 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 14.20/2.24 Axiom 46 (ruleD52): fresh88(midp(X, Y, Z), true, Y, W, Z, X) = fresh87(perp(Y, W, W, Z), true, Y, W, X).
% 14.20/2.24 Axiom 47 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 14.20/2.24 Axiom 48 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 14.20/2.24 Axiom 49 (ruleD45): fresh180(midp(X, Y, Z), true, Y, Z, W, X, V) = fresh98(para(X, V, Z, W), true, Y, W, V).
% 14.20/2.24 Axiom 50 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 14.20/2.24 Axiom 51 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 14.20/2.24 Axiom 52 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 14.20/2.24 Axiom 53 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 14.20/2.24 Axiom 54 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 14.20/2.24 Axiom 55 (ruleD23): fresh128(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(X, Y, W, Z).
% 14.20/2.24 Axiom 56 (ruleD24): fresh127(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(Z, W, X, Y).
% 14.20/2.24 Axiom 57 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 14.20/2.24 Axiom 58 (ruleD57): fresh176(cyclic(X, Y, Z, W), true, X, Y, Z, W) = fresh78(cong(X, W, Y, W), true, X, Y, Z, W).
% 14.20/2.24 Axiom 59 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 14.20/2.24 Axiom 60 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 14.20/2.24 Axiom 61 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 14.20/2.24 Axiom 62 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 14.20/2.24 Axiom 63 (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).
% 14.20/2.24 Axiom 64 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 14.20/2.24 Axiom 65 (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).
% 14.20/2.24 Axiom 66 (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).
% 14.20/2.24 Axiom 67 (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).
% 14.20/2.24 Axiom 68 (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).
% 14.20/2.24 Axiom 69 (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).
% 14.20/2.24 Axiom 70 (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).
% 14.20/2.24
% 14.20/2.24 Lemma 71: coll(h, b, e) = midp(f, b, a).
% 14.20/2.24 Proof:
% 14.20/2.24 coll(h, b, e)
% 14.20/2.24 = { by axiom 2 (exemplo6GDDFULLmoreE0061_2) }
% 14.20/2.24 true
% 14.20/2.24 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.24 midp(f, b, a)
% 14.20/2.24
% 14.20/2.24 Lemma 72: coll(g, d, f) = coll(h, b, e).
% 14.20/2.24 Proof:
% 14.20/2.24 coll(g, d, f)
% 14.20/2.24 = { by axiom 3 (exemplo6GDDFULLmoreE0061) }
% 14.20/2.24 true
% 14.20/2.24 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.24 midp(f, b, a)
% 14.20/2.24 = { by lemma 71 R->L }
% 14.20/2.24 coll(h, b, e)
% 14.20/2.24
% 14.20/2.24 Lemma 73: fresh104(X, X, Y, Z, W, V, U, T) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 fresh104(X, X, Y, Z, W, V, U, T)
% 14.20/2.25 = { by axiom 40 (ruleD40) }
% 14.20/2.25 true
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 midp(f, b, a)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 coll(h, b, e)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25
% 14.20/2.25 Lemma 74: para(b, c, a, d) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 para(b, c, a, d)
% 14.20/2.25 = { by axiom 4 (exemplo6GDDFULLmoreE0061_4) }
% 14.20/2.25 true
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 midp(f, b, a)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 coll(h, b, e)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25
% 14.20/2.25 Lemma 75: fresh104(para(X, Y, Z, W), coll(g, d, f), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 14.20/2.25 Proof:
% 14.20/2.25 fresh104(para(X, Y, Z, W), coll(g, d, f), X, Y, Z, W, V, U)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh104(para(X, Y, Z, W), coll(h, b, e), X, Y, Z, W, V, U)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh104(para(X, Y, Z, W), midp(f, b, a), X, Y, Z, W, V, U)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 14.20/2.25 = { by axiom 64 (ruleD40) }
% 14.20/2.25 eqangle(X, Y, V, U, Z, W, V, U)
% 14.20/2.25
% 14.20/2.25 Lemma 76: para(X, Y, X, Y) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 para(X, Y, X, Y)
% 14.20/2.25 = { by axiom 59 (ruleD73) R->L }
% 14.20/2.25 fresh58(coll(g, d, f), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh58(coll(h, b, e), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh58(midp(f, b, a), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh58(true, coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 54 (ruleD21) R->L }
% 14.20/2.25 fresh58(fresh131(coll(g, d, f), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh58(fresh131(coll(h, b, e), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh58(fresh131(midp(f, b, a), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh58(fresh131(true, coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 53 (ruleD19) R->L }
% 14.20/2.25 fresh58(fresh131(fresh134(coll(g, d, f), coll(g, d, f), b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 73 R->L }
% 14.20/2.25 fresh58(fresh131(fresh134(fresh104(coll(g, d, f), coll(g, d, f), b, c, a, d, X, Y), coll(g, d, f), b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 74 R->L }
% 14.20/2.25 fresh58(fresh131(fresh134(fresh104(para(b, c, a, d), coll(g, d, f), b, c, a, d, X, Y), coll(g, d, f), b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 75 }
% 14.20/2.25 fresh58(fresh131(fresh134(eqangle(b, c, X, Y, a, d, X, Y), coll(g, d, f), b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh58(fresh131(fresh134(eqangle(b, c, X, Y, a, d, X, Y), coll(h, b, e), b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh58(fresh131(fresh134(eqangle(b, c, X, Y, a, d, X, Y), midp(f, b, a), b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh58(fresh131(fresh134(eqangle(b, c, X, Y, a, d, X, Y), true, b, c, X, Y, a, d, X, Y), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 68 (ruleD19) }
% 14.20/2.25 fresh58(fresh131(eqangle(X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh58(fresh131(eqangle(X, Y, b, c, X, Y, a, d), coll(h, b, e), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh58(fresh131(eqangle(X, Y, b, c, X, Y, a, d), midp(f, b, a), X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh58(fresh131(eqangle(X, Y, b, c, X, Y, a, d), true, X, Y, b, c, X, Y, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 69 (ruleD21) }
% 14.20/2.25 fresh58(eqangle(X, Y, X, Y, b, c, a, d), coll(g, d, f), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh58(eqangle(X, Y, X, Y, b, c, a, d), coll(h, b, e), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh58(eqangle(X, Y, X, Y, b, c, a, d), midp(f, b, a), X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh58(eqangle(X, Y, X, Y, b, c, a, d), true, X, Y, X, Y, b, c, a, d)
% 14.20/2.25 = { by axiom 70 (ruleD73) }
% 14.20/2.25 fresh57(para(b, c, a, d), true, X, Y, X, Y)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh57(para(b, c, a, d), midp(f, b, a), X, Y, X, Y)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh57(para(b, c, a, d), coll(h, b, e), X, Y, X, Y)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh57(para(b, c, a, d), coll(g, d, f), X, Y, X, Y)
% 14.20/2.25 = { by lemma 74 }
% 14.20/2.25 fresh57(coll(g, d, f), coll(g, d, f), X, Y, X, Y)
% 14.20/2.25 = { by axiom 30 (ruleD73) }
% 14.20/2.25 true
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 midp(f, b, a)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 coll(h, b, e)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25
% 14.20/2.25 Lemma 77: coll(g, d, f) = coll(X, X, Y).
% 14.20/2.25 Proof:
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 coll(h, b, e)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 midp(f, b, a)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 true
% 14.20/2.25 = { by axiom 7 (ruleD1) R->L }
% 14.20/2.25 fresh146(coll(g, d, f), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh146(coll(h, b, e), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh146(midp(f, b, a), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh146(true, coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 9 (ruleD2) R->L }
% 14.20/2.25 fresh146(fresh133(coll(g, d, f), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh146(fresh133(coll(h, b, e), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh146(fresh133(midp(f, b, a), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh146(fresh133(true, coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 13 (ruleD66) R->L }
% 14.20/2.25 fresh146(fresh133(fresh66(coll(g, d, f), coll(g, d, f), Y, X, X), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 76 R->L }
% 14.20/2.25 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(g, d, f), Y, X, X), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(h, b, e), Y, X, X), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh146(fresh133(fresh66(para(Y, X, Y, X), midp(f, b, a), Y, X, X), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 47 (ruleD66) }
% 14.20/2.25 fresh146(fresh133(coll(Y, X, X), coll(g, d, f), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh146(fresh133(coll(Y, X, X), coll(h, b, e), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh146(fresh133(coll(Y, X, X), midp(f, b, a), Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by axiom 39 (ruleD2) }
% 14.20/2.25 fresh146(coll(X, Y, X), coll(g, d, f), X, Y, X)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh146(coll(X, Y, X), coll(h, b, e), X, Y, X)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh146(coll(X, Y, X), midp(f, b, a), X, Y, X)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh146(coll(X, Y, X), true, X, Y, X)
% 14.20/2.25 = { by axiom 37 (ruleD1) }
% 14.20/2.25 coll(X, X, Y)
% 14.20/2.25
% 14.20/2.25 Lemma 78: eqangle(X, Y, Z, W, X, Y, Z, W) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 eqangle(X, Y, Z, W, X, Y, Z, W)
% 14.20/2.25 = { by lemma 75 R->L }
% 14.20/2.25 fresh104(para(X, Y, X, Y), coll(g, d, f), X, Y, X, Y, Z, W)
% 14.20/2.25 = { by lemma 76 }
% 14.20/2.25 fresh104(coll(g, d, f), coll(g, d, f), X, Y, X, Y, Z, W)
% 14.20/2.25 = { by lemma 73 }
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25
% 14.20/2.25 Lemma 79: cyclic(X, Y, X, Z) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 cyclic(X, Y, X, Z)
% 14.20/2.25 = { by axiom 52 (ruleD16) R->L }
% 14.20/2.25 fresh138(cyclic(Y, X, X, Z), true, Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(cyclic(Y, X, X, Z), midp(f, b, a), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(cyclic(Y, X, X, Z), coll(h, b, e), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(cyclic(Y, X, X, Z), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 50 (ruleD14) R->L }
% 14.20/2.25 fresh138(fresh140(cyclic(Y, X, Z, X), true, Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(fresh140(cyclic(Y, X, Z, X), midp(f, b, a), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(fresh140(cyclic(Y, X, Z, X), coll(h, b, e), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(fresh140(cyclic(Y, X, Z, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 51 (ruleD15) R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(cyclic(Y, Z, X, X), true, Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(cyclic(Y, Z, X, X), midp(f, b, a), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(cyclic(Y, Z, X, X), coll(h, b, e), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(cyclic(Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 24 (ruleD42b) R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(coll(g, d, f), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 78 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(eqangle(X, Y, X, Z, X, Y, X, Z), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 43 (ruleD50) R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(fresh91(W, W, X, Y, Z, X, Z), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(fresh91(W, W, X, Y, Z, X, Z), coll(h, b, e), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(fresh91(W, W, X, Y, Z, X, Z), midp(f, b, a), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(fresh91(W, W, X, Y, Z, X, Z), true, Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 43 (ruleD50) }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh102(eqangle(X, Y, X, Z, X, Y, X, Z), true, Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 66 (ruleD42b) }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh101(coll(X, X, Z), true, Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh101(coll(X, X, Z), midp(f, b, a), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh101(coll(X, X, Z), coll(h, b, e), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh101(coll(X, X, Z), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 77 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(fresh101(coll(g, d, f), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 25 (ruleD42b) }
% 14.20/2.25 fresh138(fresh140(fresh139(true, coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(midp(f, b, a), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(coll(h, b, e), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(fresh140(fresh139(coll(g, d, f), coll(g, d, f), Y, Z, X, X), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 18 (ruleD15) }
% 14.20/2.25 fresh138(fresh140(true, coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(fresh140(midp(f, b, a), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(fresh140(coll(h, b, e), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(fresh140(coll(g, d, f), coll(g, d, f), Y, X, Z, X), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 17 (ruleD14) }
% 14.20/2.25 fresh138(true, coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh138(midp(f, b, a), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh138(coll(h, b, e), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh138(coll(g, d, f), coll(g, d, f), Y, X, X, Z)
% 14.20/2.25 = { by axiom 19 (ruleD16) }
% 14.20/2.25 true
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 midp(f, b, a)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 coll(h, b, e)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25
% 14.20/2.25 Lemma 80: cyclic(X, Y, Z, W) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 cyclic(X, Y, Z, W)
% 14.20/2.25 = { by axiom 34 (ruleD17) R->L }
% 14.20/2.25 fresh137(coll(g, d, f), coll(g, d, f), Y, X, Y, Z, W)
% 14.20/2.25 = { by lemma 79 R->L }
% 14.20/2.25 fresh137(cyclic(Y, X, Y, W), coll(g, d, f), Y, X, Y, Z, W)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh137(cyclic(Y, X, Y, W), coll(h, b, e), Y, X, Y, Z, W)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh137(cyclic(Y, X, Y, W), midp(f, b, a), Y, X, Y, Z, W)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh137(cyclic(Y, X, Y, W), true, Y, X, Y, Z, W)
% 14.20/2.25 = { by axiom 62 (ruleD17) }
% 14.20/2.25 fresh136(cyclic(Y, X, Y, Z), true, X, Y, Z, W)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh136(cyclic(Y, X, Y, Z), midp(f, b, a), X, Y, Z, W)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh136(cyclic(Y, X, Y, Z), coll(h, b, e), X, Y, Z, W)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh136(cyclic(Y, X, Y, Z), coll(g, d, f), X, Y, Z, W)
% 14.20/2.25 = { by lemma 79 }
% 14.20/2.25 fresh136(coll(g, d, f), coll(g, d, f), X, Y, Z, W)
% 14.20/2.25 = { by axiom 20 (ruleD17) }
% 14.20/2.25 true
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 midp(f, b, a)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 coll(h, b, e)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 coll(g, d, f)
% 14.20/2.25
% 14.20/2.25 Lemma 81: cong(X, Y, X, Y) = coll(g, d, f).
% 14.20/2.25 Proof:
% 14.20/2.25 cong(X, Y, X, Y)
% 14.20/2.25 = { by axiom 33 (ruleD43) R->L }
% 14.20/2.25 fresh183(coll(g, d, f), coll(g, d, f), X, Y, Z, X, Y)
% 14.20/2.25 = { by lemma 80 R->L }
% 14.20/2.25 fresh183(cyclic(X, Y, Z, Y), coll(g, d, f), X, Y, Z, X, Y)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh183(cyclic(X, Y, Z, Y), coll(h, b, e), X, Y, Z, X, Y)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh183(cyclic(X, Y, Z, Y), midp(f, b, a), X, Y, Z, X, Y)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh183(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y)
% 14.20/2.25 = { by axiom 61 (ruleD43) R->L }
% 14.20/2.25 fresh182(coll(g, d, f), coll(g, d, f), X, Y, Z, X, Y, Z)
% 14.20/2.25 = { by lemma 78 R->L }
% 14.20/2.25 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), coll(g, d, f), X, Y, Z, X, Y, Z)
% 14.20/2.25 = { by lemma 72 }
% 14.20/2.25 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), coll(h, b, e), X, Y, Z, X, Y, Z)
% 14.20/2.25 = { by lemma 71 }
% 14.20/2.25 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), midp(f, b, a), X, Y, Z, X, Y, Z)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.25 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, X, Y, Z)
% 14.20/2.25 = { by axiom 67 (ruleD43) }
% 14.20/2.25 fresh184(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y)
% 14.20/2.25 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.25 fresh184(cyclic(X, Y, Z, Z), midp(f, b, a), X, Y, Z, X, Y)
% 14.20/2.25 = { by lemma 71 R->L }
% 14.20/2.25 fresh184(cyclic(X, Y, Z, Z), coll(h, b, e), X, Y, Z, X, Y)
% 14.20/2.25 = { by lemma 72 R->L }
% 14.20/2.25 fresh184(cyclic(X, Y, Z, Z), coll(g, d, f), X, Y, Z, X, Y)
% 14.20/2.25 = { by lemma 80 }
% 14.20/2.25 fresh184(coll(g, d, f), coll(g, d, f), X, Y, Z, X, Y)
% 14.20/2.26 = { by axiom 48 (ruleD43) }
% 14.20/2.26 fresh185(cyclic(X, Y, Z, X), true, X, Y, X, Y)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh185(cyclic(X, Y, Z, X), midp(f, b, a), X, Y, X, Y)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh185(cyclic(X, Y, Z, X), coll(h, b, e), X, Y, X, Y)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh185(cyclic(X, Y, Z, X), coll(g, d, f), X, Y, X, Y)
% 14.20/2.26 = { by lemma 80 }
% 14.20/2.26 fresh185(coll(g, d, f), coll(g, d, f), X, Y, X, Y)
% 14.20/2.26 = { by axiom 15 (ruleD43) }
% 14.20/2.26 true
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 midp(f, b, a)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 coll(h, b, e)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 82: perp(X, X, Y, Z) = coll(g, d, f).
% 14.20/2.26 Proof:
% 14.20/2.26 perp(X, X, Y, Z)
% 14.20/2.26 = { by axiom 27 (ruleD56) R->L }
% 14.20/2.26 fresh80(coll(g, d, f), coll(g, d, f), X, X, Y, Z)
% 14.20/2.26 = { by lemma 81 R->L }
% 14.20/2.26 fresh80(cong(X, Z, X, Z), coll(g, d, f), X, X, Y, Z)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh80(cong(X, Z, X, Z), coll(h, b, e), X, X, Y, Z)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh80(cong(X, Z, X, Z), midp(f, b, a), X, X, Y, Z)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
% 14.20/2.26 = { by axiom 57 (ruleD56) }
% 14.20/2.26 fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh79(cong(X, Y, X, Y), midp(f, b, a), X, X, Y, Z)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh79(cong(X, Y, X, Y), coll(h, b, e), X, X, Y, Z)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh79(cong(X, Y, X, Y), coll(g, d, f), X, X, Y, Z)
% 14.20/2.26 = { by lemma 81 }
% 14.20/2.26 fresh79(coll(g, d, f), coll(g, d, f), X, X, Y, Z)
% 14.20/2.26 = { by axiom 28 (ruleD56) }
% 14.20/2.26 true
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 midp(f, b, a)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 coll(h, b, e)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 83: fresh128(cong(X, Y, Z, W), coll(g, d, f), X, Y, Z, W) = cong(X, Y, W, Z).
% 14.20/2.26 Proof:
% 14.20/2.26 fresh128(cong(X, Y, Z, W), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh128(cong(X, Y, Z, W), coll(h, b, e), X, Y, Z, W)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh128(cong(X, Y, Z, W), midp(f, b, a), X, Y, Z, W)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh128(cong(X, Y, Z, W), true, X, Y, Z, W)
% 14.20/2.26 = { by axiom 55 (ruleD23) }
% 14.20/2.26 cong(X, Y, W, Z)
% 14.20/2.26
% 14.20/2.26 Lemma 84: fresh127(cong(X, Y, Z, W), coll(g, d, f), X, Y, Z, W) = cong(Z, W, X, Y).
% 14.20/2.26 Proof:
% 14.20/2.26 fresh127(cong(X, Y, Z, W), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh127(cong(X, Y, Z, W), coll(h, b, e), X, Y, Z, W)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh127(cong(X, Y, Z, W), midp(f, b, a), X, Y, Z, W)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh127(cong(X, Y, Z, W), true, X, Y, Z, W)
% 14.20/2.26 = { by axiom 56 (ruleD24) }
% 14.20/2.26 cong(Z, W, X, Y)
% 14.20/2.26
% 14.20/2.26 Lemma 85: fresh128(X, X, Y, Z, W, V) = coll(g, d, f).
% 14.20/2.26 Proof:
% 14.20/2.26 fresh128(X, X, Y, Z, W, V)
% 14.20/2.26 = { by axiom 21 (ruleD23) }
% 14.20/2.26 true
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 midp(f, b, a)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 coll(h, b, e)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 86: fresh127(X, X, Y, Z, W, V) = coll(g, d, f).
% 14.20/2.26 Proof:
% 14.20/2.26 fresh127(X, X, Y, Z, W, V)
% 14.20/2.26 = { by axiom 22 (ruleD24) }
% 14.20/2.26 true
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 midp(f, b, a)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 coll(h, b, e)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 87: cong(a, f, b, f) = coll(g, d, f).
% 14.20/2.26 Proof:
% 14.20/2.26 cong(a, f, b, f)
% 14.20/2.26 = { by lemma 83 R->L }
% 14.20/2.26 fresh128(cong(a, f, f, b), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 84 R->L }
% 14.20/2.26 fresh128(fresh127(cong(f, b, a, f), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 83 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(cong(f, b, f, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by axiom 41 (ruleD68) R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(fresh63(midp(f, b, a), true, f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(fresh63(midp(f, b, a), midp(f, b, a), f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(fresh63(midp(f, b, a), coll(h, b, e), f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(fresh63(midp(f, b, a), coll(g, d, f), f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(fresh63(coll(h, b, e), coll(g, d, f), f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(fresh63(coll(g, d, f), coll(g, d, f), f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by axiom 14 (ruleD68) }
% 14.20/2.26 fresh128(fresh127(fresh128(true, coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(midp(f, b, a), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(coll(h, b, e), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh128(fresh127(fresh128(coll(g, d, f), coll(g, d, f), f, b, f, a), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 85 }
% 14.20/2.26 fresh128(fresh127(coll(g, d, f), coll(g, d, f), f, b, a, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 86 }
% 14.20/2.26 fresh128(coll(g, d, f), coll(g, d, f), a, f, f, b)
% 14.20/2.26 = { by lemma 85 }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 88: para(X, Y, Z, W) = coll(g, d, f).
% 14.20/2.26 Proof:
% 14.20/2.26 para(X, Y, Z, W)
% 14.20/2.26 = { by axiom 42 (ruleD9) R->L }
% 14.20/2.26 fresh51(coll(g, d, f), coll(g, d, f), X, Y, V, V, Z, W)
% 14.20/2.26 = { by lemma 82 R->L }
% 14.20/2.26 fresh51(perp(V, V, Z, W), coll(g, d, f), X, Y, V, V, Z, W)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh51(perp(V, V, Z, W), coll(h, b, e), X, Y, V, V, Z, W)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh51(perp(V, V, Z, W), midp(f, b, a), X, Y, V, V, Z, W)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh51(perp(V, V, Z, W), true, X, Y, V, V, Z, W)
% 14.20/2.26 = { by axiom 65 (ruleD9) }
% 14.20/2.26 fresh50(perp(X, Y, V, V), true, X, Y, Z, W)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh50(perp(X, Y, V, V), midp(f, b, a), X, Y, Z, W)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh50(perp(X, Y, V, V), coll(h, b, e), X, Y, Z, W)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh50(perp(X, Y, V, V), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by axiom 60 (ruleD8) R->L }
% 14.20/2.26 fresh50(fresh52(perp(V, V, X, Y), true, V, V, X, Y), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh50(fresh52(perp(V, V, X, Y), midp(f, b, a), V, V, X, Y), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh50(fresh52(perp(V, V, X, Y), coll(h, b, e), V, V, X, Y), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh50(fresh52(perp(V, V, X, Y), coll(g, d, f), V, V, X, Y), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 82 }
% 14.20/2.26 fresh50(fresh52(coll(g, d, f), coll(g, d, f), V, V, X, Y), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by axiom 31 (ruleD8) }
% 14.20/2.26 fresh50(true, coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh50(midp(f, b, a), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh50(coll(h, b, e), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh50(coll(g, d, f), coll(g, d, f), X, Y, Z, W)
% 14.20/2.26 = { by axiom 32 (ruleD9) }
% 14.20/2.26 true
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 midp(f, b, a)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 coll(h, b, e)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 89: fresh180(X, X, Y, Z, W, V, U) = coll(g, d, f).
% 14.20/2.26 Proof:
% 14.20/2.26 fresh180(X, X, Y, Z, W, V, U)
% 14.20/2.26 = { by axiom 35 (ruleD45) }
% 14.20/2.26 fresh181(coll(U, Y, W), true, Y, W, U)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh181(coll(U, Y, W), midp(f, b, a), Y, W, U)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh181(coll(U, Y, W), coll(h, b, e), Y, W, U)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh181(coll(U, Y, W), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 23 (ruleD3) R->L }
% 14.20/2.26 fresh181(fresh120(coll(g, d, f), coll(g, d, f), W, W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 77 }
% 14.20/2.26 fresh181(fresh120(coll(W, W, Y), coll(g, d, f), W, W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh181(fresh120(coll(W, W, Y), coll(h, b, e), W, W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh181(fresh120(coll(W, W, Y), midp(f, b, a), W, W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh181(fresh120(coll(W, W, Y), true, W, W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 45 (ruleD3) }
% 14.20/2.26 fresh181(fresh119(coll(W, W, U), true, W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh181(fresh119(coll(W, W, U), midp(f, b, a), W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh181(fresh119(coll(W, W, U), coll(h, b, e), W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh181(fresh119(coll(W, W, U), coll(g, d, f), W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 77 R->L }
% 14.20/2.26 fresh181(fresh119(coll(g, d, f), coll(g, d, f), W, U, Y), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 10 (ruleD3) }
% 14.20/2.26 fresh181(true, coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh181(midp(f, b, a), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh181(coll(h, b, e), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh181(coll(g, d, f), coll(g, d, f), Y, W, U)
% 14.20/2.26 = { by axiom 5 (ruleD45) }
% 14.20/2.26 true
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 midp(f, b, a)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 coll(h, b, e)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 coll(g, d, f)
% 14.20/2.26
% 14.20/2.26 Lemma 90: fresh180(midp(X, Y, Z), coll(g, d, f), Y, Z, W, X, V) = fresh98(para(X, V, Z, W), coll(g, d, f), Y, W, V).
% 14.20/2.26 Proof:
% 14.20/2.26 fresh180(midp(X, Y, Z), coll(g, d, f), Y, Z, W, X, V)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh180(midp(X, Y, Z), coll(h, b, e), Y, Z, W, X, V)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh180(midp(X, Y, Z), midp(f, b, a), Y, Z, W, X, V)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh180(midp(X, Y, Z), true, Y, Z, W, X, V)
% 14.20/2.26 = { by axiom 49 (ruleD45) }
% 14.20/2.26 fresh98(para(X, V, Z, W), true, Y, W, V)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.20/2.26 fresh98(para(X, V, Z, W), midp(f, b, a), Y, W, V)
% 14.20/2.26 = { by lemma 71 R->L }
% 14.20/2.26 fresh98(para(X, V, Z, W), coll(h, b, e), Y, W, V)
% 14.20/2.26 = { by lemma 72 R->L }
% 14.20/2.26 fresh98(para(X, V, Z, W), coll(g, d, f), Y, W, V)
% 14.20/2.26
% 14.20/2.26 Goal 1 (exemplo6GDDFULLmoreE0061_8): cong(a, g, g, h) = true.
% 14.20/2.26 Proof:
% 14.20/2.26 cong(a, g, g, h)
% 14.20/2.26 = { by lemma 83 R->L }
% 14.20/2.26 fresh128(cong(a, g, h, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 84 R->L }
% 14.20/2.26 fresh128(fresh127(cong(h, g, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by axiom 26 (ruleD52) R->L }
% 14.20/2.26 fresh128(fresh127(fresh88(coll(g, d, f), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 89 R->L }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(coll(g, d, f), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(coll(h, b, e), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(midp(f, b, a), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(true, coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by axiom 8 (ruleD11) R->L }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(coll(g, d, f), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 89 R->L }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(fresh180(coll(g, d, f), coll(g, d, f), b, a, h, f, X), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(fresh180(coll(h, b, e), coll(g, d, f), b, a, h, f, X), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(fresh180(midp(f, b, a), coll(g, d, f), b, a, h, f, X), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 90 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(fresh98(para(f, X, a, h), coll(g, d, f), b, h, X), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 88 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(fresh98(coll(g, d, f), coll(g, d, f), b, h, X), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by axiom 11 (ruleD45) }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(midp(X, b, h), coll(g, d, f), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 72 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(midp(X, b, h), coll(h, b, e), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.26 = { by lemma 71 }
% 14.20/2.26 fresh128(fresh127(fresh88(fresh180(fresh144(midp(X, b, h), midp(f, b, a), h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.20/2.27 fresh128(fresh127(fresh88(fresh180(fresh144(midp(X, b, h), true, h, b, X), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.20/2.27 = { by axiom 38 (ruleD11) }
% 14.20/2.27 fresh128(fresh127(fresh88(fresh180(midp(X, h, b), coll(g, d, f), h, b, f, X, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 90 }
% 14.62/2.27 fresh128(fresh127(fresh88(fresh98(para(X, g, b, f), coll(g, d, f), h, f, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 88 }
% 14.62/2.27 fresh128(fresh127(fresh88(fresh98(coll(g, d, f), coll(g, d, f), h, f, g), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 11 (ruleD45) }
% 14.62/2.27 fresh128(fresh127(fresh88(midp(g, h, f), coll(g, d, f), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 72 }
% 14.62/2.27 fresh128(fresh127(fresh88(midp(g, h, f), coll(h, b, e), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 71 }
% 14.62/2.27 fresh128(fresh127(fresh88(midp(g, h, f), midp(f, b, a), h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.62/2.27 fresh128(fresh127(fresh88(midp(g, h, f), true, h, a, f, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 46 (ruleD52) }
% 14.62/2.27 fresh128(fresh127(fresh87(perp(h, a, a, f), true, h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.62/2.27 fresh128(fresh127(fresh87(perp(h, a, a, f), midp(f, b, a), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 71 R->L }
% 14.62/2.27 fresh128(fresh127(fresh87(perp(h, a, a, f), coll(h, b, e), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 72 R->L }
% 14.62/2.27 fresh128(fresh127(fresh87(perp(h, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 36 (ruleD10) R->L }
% 14.62/2.27 fresh128(fresh127(fresh87(fresh147(coll(g, d, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 72 }
% 14.62/2.27 fresh128(fresh127(fresh87(fresh147(coll(h, b, e), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 71 }
% 14.62/2.27 fresh128(fresh127(fresh87(fresh147(midp(f, b, a), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.62/2.27 fresh128(fresh127(fresh87(fresh147(true, coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by axiom 6 (ruleD57) R->L }
% 14.62/2.27 fresh128(fresh127(fresh87(fresh147(fresh177(coll(g, d, f), coll(g, d, f), a, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.62/2.27 = { by lemma 87 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh177(cong(a, f, b, f), coll(g, d, f), a, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh177(cong(a, f, b, f), coll(h, b, e), a, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh177(cong(a, f, b, f), midp(f, b, a), a, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh177(cong(a, f, b, f), true, a, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 44 (ruleD57) R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh176(coll(g, d, f), coll(g, d, f), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 80 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh176(cyclic(a, b, f, f), coll(g, d, f), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh176(cyclic(a, b, f, f), coll(h, b, e), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh176(cyclic(a, b, f, f), midp(f, b, a), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh176(cyclic(a, b, f, f), true, a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 58 (ruleD57) }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh78(cong(a, f, b, f), true, a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh78(cong(a, f, b, f), midp(f, b, a), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh78(cong(a, f, b, f), coll(h, b, e), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh78(cong(a, f, b, f), coll(g, d, f), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 87 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(fresh78(coll(g, d, f), coll(g, d, f), a, b, f, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 29 (ruleD57) }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(perp(f, a, a, f), coll(g, d, f), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(perp(f, a, a, f), coll(h, b, e), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(perp(f, a, a, f), midp(f, b, a), h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh147(perp(f, a, a, f), true, h, a, f, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 63 (ruleD10) }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh145(para(h, a, f, a), true, h, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh145(para(h, a, f, a), midp(f, b, a), h, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh145(para(h, a, f, a), coll(h, b, e), h, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh145(para(h, a, f, a), coll(g, d, f), h, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 88 }
% 14.63/2.27 fresh128(fresh127(fresh87(fresh145(coll(g, d, f), coll(g, d, f), h, a, a, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 16 (ruleD10) }
% 14.63/2.27 fresh128(fresh127(fresh87(true, coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(midp(f, b, a), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(coll(h, b, e), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 R->L }
% 14.63/2.27 fresh128(fresh127(fresh87(coll(g, d, f), coll(g, d, f), h, a, g), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 12 (ruleD52) }
% 14.63/2.27 fresh128(fresh127(true, coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) R->L }
% 14.63/2.27 fresh128(fresh127(midp(f, b, a), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 71 R->L }
% 14.63/2.27 fresh128(fresh127(coll(h, b, e), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 72 R->L }
% 14.63/2.27 fresh128(fresh127(coll(g, d, f), coll(g, d, f), h, g, a, g), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 86 }
% 14.63/2.27 fresh128(coll(g, d, f), coll(g, d, f), a, g, h, g)
% 14.63/2.27 = { by lemma 85 }
% 14.63/2.27 coll(g, d, f)
% 14.63/2.27 = { by lemma 72 }
% 14.63/2.27 coll(h, b, e)
% 14.63/2.27 = { by lemma 71 }
% 14.63/2.27 midp(f, b, a)
% 14.63/2.27 = { by axiom 1 (exemplo6GDDFULLmoreE0061_6) }
% 14.63/2.27 true
% 14.63/2.27 % SZS output end Proof
% 14.63/2.27
% 14.63/2.27 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------