TSTP Solution File: GEO617+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO617+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 : n026.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 23:29:33 EDT 2023
% Result : Theorem 15.68s 2.39s
% Output : Proof 16.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO617+1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 20:06:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 15.68/2.39 Command-line arguments: --flatten
% 15.68/2.39
% 15.68/2.39 % SZS status Theorem
% 15.68/2.39
% 15.68/2.47 % SZS output start Proof
% 15.68/2.47 Take the following subset of the input axioms:
% 16.42/2.48 fof(exemplo6GDDFULL618079, conjecture, ![A, B, C, D, E, F]: ((circle(D, A, B, C) & (eqangle(E, C, C, B, E, C, C, A) & (coll(E, A, B) & (perp(F, C, A, B) & coll(F, A, B))))) => eqangle(F, C, C, E, E, C, C, D))).
% 16.42/2.48 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 16.42/2.48 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))).
% 16.42/2.48 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))).
% 16.42/2.48 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 16.42/2.48 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))).
% 16.42/2.48 fof(ruleD22, axiom, ![G, H, B2, C2, D2, E2, F2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & eqangle(P2, Q2, U2, V2, E2, F2, G, H)) => eqangle(A2_2, B2, C2, D2, E2, F2, G, H))).
% 16.42/2.48 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 16.42/2.48 fof(ruleD39, axiom, ![B2, C2, D2, A2_2, P2, Q2]: (eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2) => para(A2_2, B2, C2, D2))).
% 16.42/2.48 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))).
% 16.42/2.48 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))).
% 16.42/2.48 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))).
% 16.42/2.48 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))).
% 16.42/2.48 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 16.42/2.48 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))).
% 16.42/2.48 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 16.42/2.48 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))).
% 16.42/2.48
% 16.42/2.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 16.42/2.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 16.42/2.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 16.42/2.49 fresh(y, y, x1...xn) = u
% 16.42/2.49 C => fresh(s, t, x1...xn) = v
% 16.42/2.49 where fresh is a fresh function symbol and x1..xn are the free
% 16.42/2.49 variables of u and v.
% 16.42/2.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 16.42/2.49 input problem has no model of domain size 1).
% 16.42/2.49
% 16.42/2.49 The encoding turns the above axioms into the following unit equations and goals:
% 16.42/2.49
% 16.42/2.49 Axiom 1 (exemplo6GDDFULL618079_1): coll(f, a, b) = true.
% 16.42/2.49 Axiom 2 (exemplo6GDDFULL618079): coll(e, a, b) = true.
% 16.42/2.49 Axiom 3 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 16.42/2.49 Axiom 4 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 16.42/2.49 Axiom 5 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 16.42/2.49 Axiom 6 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 16.42/2.49 Axiom 7 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 8 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 9 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 16.42/2.49 Axiom 10 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 11 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 16.42/2.49 Axiom 12 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 13 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 16.42/2.49 Axiom 14 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 15 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 16 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 17 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 16.42/2.49 Axiom 18 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 16.42/2.49 Axiom 19 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 16.42/2.49 Axiom 20 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 16.42/2.49 Axiom 21 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 16.42/2.49 Axiom 22 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 16.42/2.49 Axiom 23 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 16.42/2.49 Axiom 24 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 16.42/2.49 Axiom 25 (exemplo6GDDFULL618079_4): eqangle(e, c, c, b, e, c, c, a) = true.
% 16.42/2.49 Axiom 26 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 16.42/2.49 Axiom 27 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 16.42/2.49 Axiom 28 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 16.42/2.49 Axiom 29 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 16.42/2.49 Axiom 30 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 16.42/2.49 Axiom 31 (ruleD22): fresh129(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 16.42/2.49 Axiom 32 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 16.42/2.49 Axiom 33 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 16.42/2.49 Axiom 34 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 16.42/2.49 Axiom 35 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 16.42/2.49 Axiom 36 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 16.42/2.49 Axiom 37 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 16.42/2.49 Axiom 38 (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).
% 16.42/2.49 Axiom 39 (ruleD22): fresh130(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = eqangle(Y, Z, W, V, Y2, Z2, W2, V2).
% 16.42/2.49 Axiom 40 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 16.42/2.49 Axiom 41 (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).
% 16.42/2.49 Axiom 42 (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).
% 16.42/2.49 Axiom 43 (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).
% 16.42/2.49 Axiom 44 (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).
% 16.42/2.49 Axiom 45 (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).
% 16.42/2.49 Axiom 46 (ruleD22): fresh130(eqangle(X, Y, Z, W, V, U, T, S), true, X2, Y2, Z2, W2, X, Y, Z, W, V, U, T, S) = fresh129(eqangle(X2, Y2, Z2, W2, X, Y, Z, W), true, X2, Y2, Z2, W2, V, U, T, S).
% 16.42/2.49
% 16.42/2.49 Lemma 47: coll(e, a, b) = coll(f, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49 = { by axiom 2 (exemplo6GDDFULL618079) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 48: fresh106(X, X, Y, Z, W, V) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh106(X, X, Y, Z, W, V)
% 16.42/2.49 = { by axiom 10 (ruleD39) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 49: fresh134(X, X, Y, Z, W, V, U, T, S, X2) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh134(X, X, Y, Z, W, V, U, T, S, X2)
% 16.42/2.49 = { by axiom 29 (ruleD19) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 50: fresh104(para(X, Y, Z, W), coll(e, a, b), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh104(para(X, Y, Z, W), coll(e, a, b), X, Y, Z, W, V, U)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh104(para(X, Y, Z, W), coll(f, a, b), X, Y, Z, W, V, U)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 16.42/2.49 = { by axiom 37 (ruleD40) }
% 16.42/2.49 eqangle(X, Y, V, U, Z, W, V, U)
% 16.42/2.49
% 16.42/2.49 Lemma 51: fresh131(X, X, Y, Z, W, V, U, T, S, X2) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh131(X, X, Y, Z, W, V, U, T, S, X2)
% 16.42/2.49 = { by axiom 30 (ruleD21) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 52: eqangle(e, c, c, b, e, c, c, a) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 eqangle(e, c, c, b, e, c, c, a)
% 16.42/2.49 = { by axiom 25 (exemplo6GDDFULL618079_4) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 53: fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(e, a, b), X, Y, Z, W, V, U, T, S) = eqangle(X, Y, V, U, Z, W, T, S).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(e, a, b), X, Y, Z, W, V, U, T, S)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(f, a, b), X, Y, Z, W, V, U, T, S)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh131(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S)
% 16.42/2.49 = { by axiom 44 (ruleD21) }
% 16.42/2.49 eqangle(X, Y, V, U, Z, W, T, S)
% 16.42/2.49
% 16.42/2.49 Lemma 54: fresh106(eqangle(X, Y, Z, W, V, U, Z, W), coll(e, a, b), X, Y, V, U) = para(X, Y, V, U).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh106(eqangle(X, Y, Z, W, V, U, Z, W), coll(e, a, b), X, Y, V, U)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh106(eqangle(X, Y, Z, W, V, U, Z, W), coll(f, a, b), X, Y, V, U)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U)
% 16.42/2.49 = { by axiom 40 (ruleD39) }
% 16.42/2.49 para(X, Y, V, U)
% 16.42/2.49
% 16.42/2.49 Lemma 55: fresh134(eqangle(X, Y, Z, W, V, U, T, S), coll(e, a, b), X, Y, Z, W, V, U, T, S) = eqangle(Z, W, X, Y, T, S, V, U).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh134(eqangle(X, Y, Z, W, V, U, T, S), coll(e, a, b), X, Y, Z, W, V, U, T, S)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh134(eqangle(X, Y, Z, W, V, U, T, S), coll(f, a, b), X, Y, Z, W, V, U, T, S)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh134(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S)
% 16.42/2.49 = { by axiom 43 (ruleD19) }
% 16.42/2.49 eqangle(Z, W, X, Y, T, S, V, U)
% 16.42/2.49
% 16.42/2.49 Lemma 56: para(c, b, c, a) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 para(c, b, c, a)
% 16.42/2.49 = { by lemma 54 R->L }
% 16.42/2.49 fresh106(eqangle(c, b, e, c, c, a, e, c), coll(e, a, b), c, b, c, a)
% 16.42/2.49 = { by lemma 55 R->L }
% 16.42/2.49 fresh106(fresh134(eqangle(e, c, c, b, e, c, c, a), coll(e, a, b), e, c, c, b, e, c, c, a), coll(e, a, b), c, b, c, a)
% 16.42/2.49 = { by lemma 52 }
% 16.42/2.49 fresh106(fresh134(coll(e, a, b), coll(e, a, b), e, c, c, b, e, c, c, a), coll(e, a, b), c, b, c, a)
% 16.42/2.49 = { by lemma 49 }
% 16.42/2.49 fresh106(coll(e, a, b), coll(e, a, b), c, b, c, a)
% 16.42/2.49 = { by lemma 48 }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 57: fresh104(X, X, Y, Z, W, V, U, T) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 fresh104(X, X, Y, Z, W, V, U, T)
% 16.42/2.49 = { by axiom 22 (ruleD40) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 58: eqangle(e, c, X, Y, e, c, X, Y) = coll(e, a, b).
% 16.42/2.49 Proof:
% 16.42/2.49 eqangle(e, c, X, Y, e, c, X, Y)
% 16.42/2.49 = { by lemma 50 R->L }
% 16.42/2.49 fresh104(para(e, c, e, c), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by axiom 33 (ruleD73) R->L }
% 16.42/2.49 fresh104(fresh58(coll(e, a, b), coll(e, a, b), e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 51 R->L }
% 16.42/2.49 fresh104(fresh58(fresh131(coll(e, a, b), coll(e, a, b), e, c, c, b, e, c, c, a), coll(e, a, b), e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 52 R->L }
% 16.42/2.49 fresh104(fresh58(fresh131(eqangle(e, c, c, b, e, c, c, a), coll(e, a, b), e, c, c, b, e, c, c, a), coll(e, a, b), e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 53 }
% 16.42/2.49 fresh104(fresh58(eqangle(e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh104(fresh58(eqangle(e, c, e, c, c, b, c, a), coll(f, a, b), e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh104(fresh58(eqangle(e, c, e, c, c, b, c, a), true, e, c, e, c, c, b, c, a), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by axiom 45 (ruleD73) }
% 16.42/2.49 fresh104(fresh57(para(c, b, c, a), true, e, c, e, c), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 fresh104(fresh57(para(c, b, c, a), coll(f, a, b), e, c, e, c), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 fresh104(fresh57(para(c, b, c, a), coll(e, a, b), e, c, e, c), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 56 }
% 16.42/2.49 fresh104(fresh57(coll(e, a, b), coll(e, a, b), e, c, e, c), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by axiom 15 (ruleD73) }
% 16.42/2.49 fresh104(true, coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.42/2.49 fresh104(coll(f, a, b), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 47 R->L }
% 16.42/2.49 fresh104(coll(e, a, b), coll(e, a, b), e, c, e, c, X, Y)
% 16.42/2.49 = { by lemma 57 }
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49
% 16.42/2.49 Lemma 59: coll(e, a, b) = coll(X, X, Y).
% 16.42/2.49 Proof:
% 16.42/2.49 coll(e, a, b)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 coll(f, a, b)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 true
% 16.42/2.49 = { by axiom 3 (ruleD1) R->L }
% 16.42/2.49 fresh146(coll(e, a, b), coll(e, a, b), X, Y, X)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh146(coll(f, a, b), coll(e, a, b), X, Y, X)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh146(true, coll(e, a, b), X, Y, X)
% 16.42/2.49 = { by axiom 4 (ruleD2) R->L }
% 16.42/2.49 fresh146(fresh133(coll(e, a, b), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.42/2.49 = { by lemma 47 }
% 16.42/2.49 fresh146(fresh133(coll(f, a, b), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.42/2.49 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.42/2.49 fresh146(fresh133(true, coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.42/2.50 = { by axiom 6 (ruleD66) R->L }
% 16.42/2.50 fresh146(fresh133(fresh66(coll(e, a, b), coll(e, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.42/2.50 = { by lemma 48 R->L }
% 16.42/2.50 fresh146(fresh133(fresh66(fresh106(coll(e, a, b), coll(e, a, b), Y, X, Y, X), coll(e, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.42/2.50 = { by lemma 49 R->L }
% 16.56/2.50 fresh146(fresh133(fresh66(fresh106(fresh134(coll(e, a, b), coll(e, a, b), e, c, Y, X, e, c, Y, X), coll(e, a, b), Y, X, Y, X), coll(e, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by lemma 58 R->L }
% 16.56/2.50 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(e, c, Y, X, e, c, Y, X), coll(e, a, b), e, c, Y, X, e, c, Y, X), coll(e, a, b), Y, X, Y, X), coll(e, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by lemma 55 }
% 16.56/2.50 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, e, c, Y, X, e, c), coll(e, a, b), Y, X, Y, X), coll(e, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by lemma 54 }
% 16.56/2.50 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(e, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(f, a, b), Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by axiom 27 (ruleD66) }
% 16.56/2.50 fresh146(fresh133(coll(Y, X, X), coll(e, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh146(fresh133(coll(Y, X, X), coll(f, a, b), Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by axiom 21 (ruleD2) }
% 16.56/2.50 fresh146(coll(X, Y, X), coll(e, a, b), X, Y, X)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh146(coll(X, Y, X), coll(f, a, b), X, Y, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh146(coll(X, Y, X), true, X, Y, X)
% 16.56/2.50 = { by axiom 20 (ruleD1) }
% 16.56/2.50 coll(X, X, Y)
% 16.56/2.50
% 16.56/2.50 Lemma 60: cyclic(c, c, e, X) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 cyclic(c, c, e, X)
% 16.56/2.50 = { by axiom 11 (ruleD42b) R->L }
% 16.56/2.50 fresh102(coll(e, a, b), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 51 R->L }
% 16.56/2.50 fresh102(fresh131(coll(e, a, b), coll(e, a, b), e, c, X, c, e, c, X, c), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 58 R->L }
% 16.56/2.50 fresh102(fresh131(eqangle(e, c, X, c, e, c, X, c), coll(e, a, b), e, c, X, c, e, c, X, c), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 53 }
% 16.56/2.50 fresh102(eqangle(e, c, e, c, X, c, X, c), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 24 (ruleD50) R->L }
% 16.56/2.50 fresh102(fresh91(Y, Y, e, c, c, X, c), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh102(fresh91(Y, Y, e, c, c, X, c), coll(f, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh102(fresh91(Y, Y, e, c, c, X, c), true, c, c, e, X)
% 16.56/2.50 = { by axiom 24 (ruleD50) }
% 16.56/2.50 fresh102(eqangle(e, c, e, c, X, c, X, c), true, c, c, e, X)
% 16.56/2.50 = { by axiom 41 (ruleD42b) }
% 16.56/2.50 fresh101(coll(e, X, c), true, c, c, e, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh101(coll(e, X, c), coll(f, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh101(coll(e, X, c), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 9 (ruleD3) R->L }
% 16.56/2.50 fresh101(fresh120(coll(e, a, b), coll(e, a, b), c, c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 59 }
% 16.56/2.50 fresh101(fresh120(coll(c, c, X), coll(e, a, b), c, c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh101(fresh120(coll(c, c, X), coll(f, a, b), c, c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh101(fresh120(coll(c, c, X), true, c, c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 26 (ruleD3) }
% 16.56/2.50 fresh101(fresh119(coll(c, c, e), true, c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh101(fresh119(coll(c, c, e), coll(f, a, b), c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh101(fresh119(coll(c, c, e), coll(e, a, b), c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 59 R->L }
% 16.56/2.50 fresh101(fresh119(coll(e, a, b), coll(e, a, b), c, e, X), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 5 (ruleD3) }
% 16.56/2.50 fresh101(true, coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh101(coll(f, a, b), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh101(coll(e, a, b), coll(e, a, b), c, c, e, X)
% 16.56/2.50 = { by axiom 12 (ruleD42b) }
% 16.56/2.50 true
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 coll(f, a, b)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 61: fresh137(cyclic(X, Y, Z, W), coll(e, a, b), X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), coll(e, a, b), Y, Z, V, W).
% 16.56/2.50 Proof:
% 16.56/2.50 fresh137(cyclic(X, Y, Z, W), coll(e, a, b), X, Y, Z, V, W)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh137(cyclic(X, Y, Z, W), coll(f, a, b), X, Y, Z, V, W)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W)
% 16.56/2.50 = { by axiom 36 (ruleD17) }
% 16.56/2.50 fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh136(cyclic(X, Y, Z, V), coll(f, a, b), Y, Z, V, W)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh136(cyclic(X, Y, Z, V), coll(e, a, b), Y, Z, V, W)
% 16.56/2.50
% 16.56/2.50 Lemma 62: fresh136(X, X, Y, Z, W, V) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 fresh136(X, X, Y, Z, W, V)
% 16.56/2.50 = { by axiom 8 (ruleD17) }
% 16.56/2.50 true
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 coll(f, a, b)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 63: cyclic(c, e, X, Y) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 cyclic(c, e, X, Y)
% 16.56/2.50 = { by axiom 19 (ruleD17) R->L }
% 16.56/2.50 fresh137(coll(e, a, b), coll(e, a, b), c, c, e, X, Y)
% 16.56/2.50 = { by lemma 60 R->L }
% 16.56/2.50 fresh137(cyclic(c, c, e, Y), coll(e, a, b), c, c, e, X, Y)
% 16.56/2.50 = { by lemma 61 }
% 16.56/2.50 fresh136(cyclic(c, c, e, X), coll(e, a, b), c, e, X, Y)
% 16.56/2.50 = { by lemma 60 }
% 16.56/2.50 fresh136(coll(e, a, b), coll(e, a, b), c, e, X, Y)
% 16.56/2.50 = { by lemma 62 }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 64: cyclic(e, X, Y, Z) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 cyclic(e, X, Y, Z)
% 16.56/2.50 = { by axiom 19 (ruleD17) R->L }
% 16.56/2.50 fresh137(coll(e, a, b), coll(e, a, b), c, e, X, Y, Z)
% 16.56/2.50 = { by lemma 63 R->L }
% 16.56/2.50 fresh137(cyclic(c, e, X, Z), coll(e, a, b), c, e, X, Y, Z)
% 16.56/2.50 = { by lemma 61 }
% 16.56/2.50 fresh136(cyclic(c, e, X, Y), coll(e, a, b), e, X, Y, Z)
% 16.56/2.50 = { by lemma 63 }
% 16.56/2.50 fresh136(coll(e, a, b), coll(e, a, b), e, X, Y, Z)
% 16.56/2.50 = { by lemma 62 }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 65: cyclic(X, Y, Z, W) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 cyclic(X, Y, Z, W)
% 16.56/2.50 = { by axiom 19 (ruleD17) R->L }
% 16.56/2.50 fresh137(coll(e, a, b), coll(e, a, b), e, X, Y, Z, W)
% 16.56/2.50 = { by lemma 64 R->L }
% 16.56/2.50 fresh137(cyclic(e, X, Y, W), coll(e, a, b), e, X, Y, Z, W)
% 16.56/2.50 = { by lemma 61 }
% 16.56/2.50 fresh136(cyclic(e, X, Y, Z), coll(e, a, b), X, Y, Z, W)
% 16.56/2.50 = { by lemma 64 }
% 16.56/2.50 fresh136(coll(e, a, b), coll(e, a, b), X, Y, Z, W)
% 16.56/2.50 = { by lemma 62 }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 66: cong(b, X, a, X) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 cong(b, X, a, X)
% 16.56/2.50 = { by axiom 18 (ruleD43) R->L }
% 16.56/2.50 fresh183(coll(e, a, b), coll(e, a, b), b, X, c, a, X)
% 16.56/2.50 = { by lemma 65 R->L }
% 16.56/2.50 fresh183(cyclic(b, X, c, X), coll(e, a, b), b, X, c, a, X)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh183(cyclic(b, X, c, X), coll(f, a, b), b, X, c, a, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh183(cyclic(b, X, c, X), true, b, X, c, a, X)
% 16.56/2.50 = { by axiom 35 (ruleD43) R->L }
% 16.56/2.50 fresh182(coll(e, a, b), coll(e, a, b), b, X, c, a, X, c)
% 16.56/2.50 = { by lemma 57 R->L }
% 16.56/2.50 fresh182(fresh104(coll(e, a, b), coll(e, a, b), c, b, c, a, c, X), coll(e, a, b), b, X, c, a, X, c)
% 16.56/2.50 = { by lemma 56 R->L }
% 16.56/2.50 fresh182(fresh104(para(c, b, c, a), coll(e, a, b), c, b, c, a, c, X), coll(e, a, b), b, X, c, a, X, c)
% 16.56/2.50 = { by lemma 50 }
% 16.56/2.50 fresh182(eqangle(c, b, c, X, c, a, c, X), coll(e, a, b), b, X, c, a, X, c)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh182(eqangle(c, b, c, X, c, a, c, X), coll(f, a, b), b, X, c, a, X, c)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh182(eqangle(c, b, c, X, c, a, c, X), true, b, X, c, a, X, c)
% 16.56/2.50 = { by axiom 42 (ruleD43) }
% 16.56/2.50 fresh184(cyclic(b, X, c, c), true, b, X, c, a, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh184(cyclic(b, X, c, c), coll(f, a, b), b, X, c, a, X)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh184(cyclic(b, X, c, c), coll(e, a, b), b, X, c, a, X)
% 16.56/2.50 = { by lemma 65 }
% 16.56/2.50 fresh184(coll(e, a, b), coll(e, a, b), b, X, c, a, X)
% 16.56/2.50 = { by axiom 28 (ruleD43) }
% 16.56/2.50 fresh185(cyclic(b, X, c, a), true, b, X, a, X)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh185(cyclic(b, X, c, a), coll(f, a, b), b, X, a, X)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh185(cyclic(b, X, c, a), coll(e, a, b), b, X, a, X)
% 16.56/2.50 = { by lemma 65 }
% 16.56/2.50 fresh185(coll(e, a, b), coll(e, a, b), b, X, a, X)
% 16.56/2.50 = { by axiom 7 (ruleD43) }
% 16.56/2.50 true
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 coll(f, a, b)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 67: perp(b, a, X, Y) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 perp(b, a, X, Y)
% 16.56/2.50 = { by axiom 13 (ruleD56) R->L }
% 16.56/2.50 fresh80(coll(e, a, b), coll(e, a, b), b, a, X, Y)
% 16.56/2.50 = { by lemma 66 R->L }
% 16.56/2.50 fresh80(cong(b, Y, a, Y), coll(e, a, b), b, a, X, Y)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh80(cong(b, Y, a, Y), coll(f, a, b), b, a, X, Y)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh80(cong(b, Y, a, Y), true, b, a, X, Y)
% 16.56/2.50 = { by axiom 32 (ruleD56) }
% 16.56/2.50 fresh79(cong(b, X, a, X), true, b, a, X, Y)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh79(cong(b, X, a, X), coll(f, a, b), b, a, X, Y)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh79(cong(b, X, a, X), coll(e, a, b), b, a, X, Y)
% 16.56/2.50 = { by lemma 66 }
% 16.56/2.50 fresh79(coll(e, a, b), coll(e, a, b), b, a, X, Y)
% 16.56/2.50 = { by axiom 14 (ruleD56) }
% 16.56/2.50 true
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 coll(f, a, b)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 coll(e, a, b)
% 16.56/2.50
% 16.56/2.50 Lemma 68: eqangle(X, Y, Z, W, V, U, Z, W) = coll(e, a, b).
% 16.56/2.50 Proof:
% 16.56/2.50 eqangle(X, Y, Z, W, V, U, Z, W)
% 16.56/2.50 = { by lemma 50 R->L }
% 16.56/2.50 fresh104(para(X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by axiom 23 (ruleD9) R->L }
% 16.56/2.50 fresh104(fresh51(coll(e, a, b), coll(e, a, b), X, Y, b, a, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by lemma 67 R->L }
% 16.56/2.50 fresh104(fresh51(perp(b, a, V, U), coll(e, a, b), X, Y, b, a, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by lemma 47 }
% 16.56/2.50 fresh104(fresh51(perp(b, a, V, U), coll(f, a, b), X, Y, b, a, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.50 fresh104(fresh51(perp(b, a, V, U), true, X, Y, b, a, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by axiom 38 (ruleD9) }
% 16.56/2.50 fresh104(fresh50(perp(X, Y, b, a), true, X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.50 fresh104(fresh50(perp(X, Y, b, a), coll(f, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by lemma 47 R->L }
% 16.56/2.50 fresh104(fresh50(perp(X, Y, b, a), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.50 = { by axiom 34 (ruleD8) R->L }
% 16.56/2.50 fresh104(fresh50(fresh52(perp(b, a, X, Y), true, b, a, X, Y), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.51 fresh104(fresh50(fresh52(perp(b, a, X, Y), coll(f, a, b), b, a, X, Y), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by lemma 47 R->L }
% 16.56/2.51 fresh104(fresh50(fresh52(perp(b, a, X, Y), coll(e, a, b), b, a, X, Y), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by lemma 67 }
% 16.56/2.51 fresh104(fresh50(fresh52(coll(e, a, b), coll(e, a, b), b, a, X, Y), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by axiom 16 (ruleD8) }
% 16.56/2.51 fresh104(fresh50(true, coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.51 fresh104(fresh50(coll(f, a, b), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by lemma 47 R->L }
% 16.56/2.51 fresh104(fresh50(coll(e, a, b), coll(e, a, b), X, Y, V, U), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by axiom 17 (ruleD9) }
% 16.56/2.51 fresh104(true, coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.51 fresh104(coll(f, a, b), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by lemma 47 R->L }
% 16.56/2.51 fresh104(coll(e, a, b), coll(e, a, b), X, Y, V, U, Z, W)
% 16.56/2.51 = { by lemma 57 }
% 16.56/2.51 coll(e, a, b)
% 16.56/2.51
% 16.56/2.51 Goal 1 (exemplo6GDDFULL618079_5): eqangle(f, c, c, e, e, c, c, d) = true.
% 16.56/2.51 Proof:
% 16.56/2.51 eqangle(f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by axiom 39 (ruleD22) R->L }
% 16.56/2.51 fresh130(coll(e, a, b), coll(e, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by lemma 51 R->L }
% 16.56/2.51 fresh130(fresh131(coll(e, a, b), coll(e, a, b), X, Y, e, c, X, Y, c, d), coll(e, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by lemma 49 R->L }
% 16.56/2.51 fresh130(fresh131(fresh134(coll(e, a, b), coll(e, a, b), e, c, X, Y, c, d, X, Y), coll(e, a, b), X, Y, e, c, X, Y, c, d), coll(e, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by lemma 68 R->L }
% 16.56/2.51 fresh130(fresh131(fresh134(eqangle(e, c, X, Y, c, d, X, Y), coll(e, a, b), e, c, X, Y, c, d, X, Y), coll(e, a, b), X, Y, e, c, X, Y, c, d), coll(e, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by lemma 55 }
% 16.56/2.51 fresh130(fresh131(eqangle(X, Y, e, c, X, Y, c, d), coll(e, a, b), X, Y, e, c, X, Y, c, d), coll(e, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by lemma 53 }
% 16.56/2.51 fresh130(eqangle(X, Y, X, Y, e, c, c, d), coll(e, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by lemma 47 }
% 16.56/2.51 fresh130(eqangle(X, Y, X, Y, e, c, c, d), coll(f, a, b), f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by axiom 1 (exemplo6GDDFULL618079_1) }
% 16.56/2.51 fresh130(eqangle(X, Y, X, Y, e, c, c, d), true, f, c, c, e, X, Y, X, Y, e, c, c, d)
% 16.56/2.51 = { by axiom 46 (ruleD22) }
% 16.56/2.51 fresh129(eqangle(f, c, c, e, X, Y, X, Y), true, f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by axiom 1 (exemplo6GDDFULL618079_1) R->L }
% 16.56/2.51 fresh129(eqangle(f, c, c, e, X, Y, X, Y), coll(f, a, b), f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by lemma 47 R->L }
% 16.56/2.51 fresh129(eqangle(f, c, c, e, X, Y, X, Y), coll(e, a, b), f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by lemma 53 R->L }
% 16.56/2.51 fresh129(fresh131(eqangle(f, c, X, Y, c, e, X, Y), coll(e, a, b), f, c, X, Y, c, e, X, Y), coll(e, a, b), f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by lemma 68 }
% 16.56/2.51 fresh129(fresh131(coll(e, a, b), coll(e, a, b), f, c, X, Y, c, e, X, Y), coll(e, a, b), f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by lemma 51 }
% 16.56/2.51 fresh129(coll(e, a, b), coll(e, a, b), f, c, c, e, e, c, c, d)
% 16.56/2.51 = { by axiom 31 (ruleD22) }
% 16.56/2.51 true
% 16.56/2.51 % SZS output end Proof
% 16.56/2.51
% 16.56/2.51 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------