TSTP Solution File: GEO570+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO570+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 : n028.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 23:29:21 EDT 2023
% Result : Theorem 15.41s 2.33s
% Output : Proof 16.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO570+1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 22:39:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 15.41/2.33 Command-line arguments: --flatten
% 15.41/2.33
% 15.41/2.33 % SZS status Theorem
% 15.41/2.33
% 15.41/2.39 % SZS output start Proof
% 15.41/2.39 Take the following subset of the input axioms:
% 15.41/2.40 fof(exemplo6GDDFULL214032, conjecture, ![A, B, C, M, O, R, N, S, NWPNT1]: ((circle(O, B, C, R) & (circle(O, B, S, NWPNT1) & (coll(A, B, R) & (coll(A, C, S) & (perp(M, A, R, S) & (coll(M, R, S) & (perp(N, A, B, C) & coll(N, B, C)))))))) => eqangle(B, A, A, M, N, A, A, C))).
% 15.41/2.40 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 15.41/2.40 fof(ruleD17, axiom, ![D, E, B2, C2, A2_2]: ((cyclic(A2_2, B2, C2, D) & cyclic(A2_2, B2, C2, E)) => cyclic(B2, C2, D, E))).
% 15.41/2.40 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))).
% 15.41/2.40 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 15.41/2.40 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))).
% 15.41/2.40 fof(ruleD22, axiom, ![F, G, H, B2, C2, D2, E2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & eqangle(P2, Q2, U2, V2, E2, F, G, H)) => eqangle(A2_2, B2, C2, D2, E2, F, G, H))).
% 15.41/2.40 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 15.41/2.40 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))).
% 15.41/2.40 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))).
% 15.41/2.40 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))).
% 15.41/2.40 fof(ruleD43, axiom, ![B2, C2, A2_2, P2, Q2, R2]: ((cyclic(A2_2, B2, C2, P2) & (cyclic(A2_2, B2, C2, Q2) & (cyclic(A2_2, B2, C2, R2) & eqangle(C2, A2_2, C2, B2, R2, P2, R2, Q2)))) => cong(A2_2, B2, P2, Q2))).
% 15.41/2.40 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))).
% 15.41/2.40 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 15.41/2.40 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 15.41/2.40 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))).
% 15.41/2.40
% 15.41/2.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.41/2.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.41/2.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.41/2.40 fresh(y, y, x1...xn) = u
% 15.41/2.40 C => fresh(s, t, x1...xn) = v
% 15.41/2.40 where fresh is a fresh function symbol and x1..xn are the free
% 15.41/2.40 variables of u and v.
% 15.41/2.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.41/2.40 input problem has no model of domain size 1).
% 15.41/2.40
% 15.41/2.40 The encoding turns the above axioms into the following unit equations and goals:
% 15.41/2.40
% 15.41/2.40 Axiom 1 (exemplo6GDDFULL214032_2): coll(m, r, s) = true.
% 15.41/2.40 Axiom 2 (exemplo6GDDFULL214032): coll(a, c, s) = true.
% 15.41/2.40 Axiom 3 (exemplo6GDDFULL214032_4): perp(m, a, r, s) = true.
% 15.41/2.40 Axiom 4 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 15.41/2.40 Axiom 5 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 15.41/2.40 Axiom 6 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 15.41/2.40 Axiom 7 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 15.41/2.40 Axiom 8 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 9 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 10 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 15.41/2.40 Axiom 11 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 12 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 15.41/2.40 Axiom 13 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 14 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 15.41/2.40 Axiom 15 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 16 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 17 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 15.41/2.40 Axiom 18 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 15.41/2.40 Axiom 19 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 15.41/2.40 Axiom 20 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 15.41/2.40 Axiom 21 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 15.41/2.40 Axiom 22 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 15.41/2.40 Axiom 23 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 15.41/2.40 Axiom 24 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 15.41/2.40 Axiom 25 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 15.41/2.40 Axiom 26 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 15.41/2.40 Axiom 27 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 15.41/2.40 Axiom 28 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 15.41/2.40 Axiom 29 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 15.41/2.40 Axiom 30 (ruleD22): fresh129(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 15.41/2.40 Axiom 31 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 15.41/2.40 Axiom 32 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 15.41/2.40 Axiom 33 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 15.41/2.40 Axiom 34 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 15.41/2.40 Axiom 35 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 15.41/2.40 Axiom 36 (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).
% 15.41/2.40 Axiom 37 (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).
% 15.41/2.40 Axiom 38 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 15.41/2.40 Axiom 39 (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).
% 15.41/2.40 Axiom 40 (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).
% 15.41/2.40 Axiom 41 (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).
% 15.41/2.40 Axiom 42 (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).
% 15.41/2.40 Axiom 43 (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).
% 15.41/2.40
% 15.41/2.40 Lemma 44: coll(a, c, s) = coll(m, r, s).
% 15.41/2.40 Proof:
% 15.41/2.40 coll(a, c, s)
% 15.41/2.40 = { by axiom 2 (exemplo6GDDFULL214032) }
% 15.41/2.40 true
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 15.41/2.40 coll(m, r, s)
% 15.41/2.40
% 15.41/2.40 Lemma 45: fresh134(X, X, Y, Z, W, V, U, T, S, X2) = coll(a, c, s).
% 15.41/2.40 Proof:
% 15.41/2.40 fresh134(X, X, Y, Z, W, V, U, T, S, X2)
% 15.41/2.40 = { by axiom 28 (ruleD19) }
% 15.41/2.40 true
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 15.41/2.40 coll(m, r, s)
% 15.41/2.40 = { by lemma 44 R->L }
% 15.41/2.40 coll(a, c, s)
% 15.41/2.40
% 15.41/2.40 Lemma 46: fresh104(para(X, Y, Z, W), coll(a, c, s), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 15.41/2.40 Proof:
% 15.41/2.40 fresh104(para(X, Y, Z, W), coll(a, c, s), X, Y, Z, W, V, U)
% 15.41/2.40 = { by lemma 44 }
% 15.41/2.40 fresh104(para(X, Y, Z, W), coll(m, r, s), X, Y, Z, W, V, U)
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 15.41/2.40 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 15.41/2.40 = { by axiom 35 (ruleD40) }
% 15.41/2.40 eqangle(X, Y, V, U, Z, W, V, U)
% 15.41/2.40
% 15.41/2.40 Lemma 47: perp(m, a, r, s) = coll(a, c, s).
% 15.41/2.40 Proof:
% 15.41/2.40 perp(m, a, r, s)
% 15.41/2.40 = { by axiom 3 (exemplo6GDDFULL214032_4) }
% 15.41/2.40 true
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 15.41/2.40 coll(m, r, s)
% 15.41/2.40 = { by lemma 44 R->L }
% 15.41/2.40 coll(a, c, s)
% 15.41/2.40
% 15.41/2.40 Lemma 48: fresh51(perp(X, Y, Z, W), coll(a, c, s), V, U, X, Y, Z, W) = fresh50(perp(V, U, X, Y), coll(a, c, s), V, U, Z, W).
% 15.41/2.40 Proof:
% 15.41/2.40 fresh51(perp(X, Y, Z, W), coll(a, c, s), V, U, X, Y, Z, W)
% 15.41/2.40 = { by lemma 44 }
% 15.41/2.40 fresh51(perp(X, Y, Z, W), coll(m, r, s), V, U, X, Y, Z, W)
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 15.41/2.40 fresh51(perp(X, Y, Z, W), true, V, U, X, Y, Z, W)
% 15.41/2.40 = { by axiom 36 (ruleD9) }
% 15.41/2.40 fresh50(perp(V, U, X, Y), true, V, U, Z, W)
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 15.41/2.40 fresh50(perp(V, U, X, Y), coll(m, r, s), V, U, Z, W)
% 15.41/2.40 = { by lemma 44 R->L }
% 15.41/2.40 fresh50(perp(V, U, X, Y), coll(a, c, s), V, U, Z, W)
% 15.41/2.40
% 15.41/2.40 Lemma 49: fresh52(perp(X, Y, Z, W), coll(a, c, s), X, Y, Z, W) = perp(Z, W, X, Y).
% 15.41/2.40 Proof:
% 15.41/2.40 fresh52(perp(X, Y, Z, W), coll(a, c, s), X, Y, Z, W)
% 15.41/2.40 = { by lemma 44 }
% 15.41/2.40 fresh52(perp(X, Y, Z, W), coll(m, r, s), X, Y, Z, W)
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 15.41/2.40 fresh52(perp(X, Y, Z, W), true, X, Y, Z, W)
% 15.41/2.40 = { by axiom 32 (ruleD8) }
% 15.41/2.40 perp(Z, W, X, Y)
% 15.41/2.40
% 15.41/2.40 Lemma 50: fresh52(X, X, Y, Z, W, V) = coll(a, c, s).
% 15.41/2.40 Proof:
% 15.41/2.40 fresh52(X, X, Y, Z, W, V)
% 15.41/2.40 = { by axiom 16 (ruleD8) }
% 15.41/2.40 true
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 15.41/2.40 coll(m, r, s)
% 15.41/2.40 = { by lemma 44 R->L }
% 15.41/2.40 coll(a, c, s)
% 15.41/2.40
% 15.41/2.40 Lemma 51: fresh50(X, X, Y, Z, W, V) = coll(a, c, s).
% 15.41/2.40 Proof:
% 15.41/2.40 fresh50(X, X, Y, Z, W, V)
% 15.41/2.40 = { by axiom 17 (ruleD9) }
% 15.41/2.40 true
% 15.41/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 15.41/2.40 coll(m, r, s)
% 15.41/2.40 = { by lemma 44 R->L }
% 15.41/2.40 coll(a, c, s)
% 15.41/2.40
% 15.41/2.40 Lemma 52: fresh104(X, X, Y, Z, W, V, U, T) = coll(a, c, s).
% 15.41/2.40 Proof:
% 16.16/2.40 fresh104(X, X, Y, Z, W, V, U, T)
% 16.16/2.40 = { by axiom 22 (ruleD40) }
% 16.16/2.40 true
% 16.16/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.40 coll(m, r, s)
% 16.16/2.40 = { by lemma 44 R->L }
% 16.16/2.40 coll(a, c, s)
% 16.16/2.40
% 16.16/2.40 Lemma 53: eqangle(r, s, X, Y, r, s, X, Y) = coll(a, c, s).
% 16.16/2.40 Proof:
% 16.16/2.40 eqangle(r, s, X, Y, r, s, X, Y)
% 16.16/2.40 = { by lemma 46 R->L }
% 16.16/2.40 fresh104(para(r, s, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by axiom 23 (ruleD9) R->L }
% 16.16/2.40 fresh104(fresh51(coll(a, c, s), coll(a, c, s), r, s, m, a, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 47 R->L }
% 16.16/2.40 fresh104(fresh51(perp(m, a, r, s), coll(a, c, s), r, s, m, a, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 48 }
% 16.16/2.40 fresh104(fresh50(perp(r, s, m, a), coll(a, c, s), r, s, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 49 R->L }
% 16.16/2.40 fresh104(fresh50(fresh52(perp(m, a, r, s), coll(a, c, s), m, a, r, s), coll(a, c, s), r, s, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 47 }
% 16.16/2.40 fresh104(fresh50(fresh52(coll(a, c, s), coll(a, c, s), m, a, r, s), coll(a, c, s), r, s, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 50 }
% 16.16/2.40 fresh104(fresh50(coll(a, c, s), coll(a, c, s), r, s, r, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 51 }
% 16.16/2.40 fresh104(coll(a, c, s), coll(a, c, s), r, s, r, s, X, Y)
% 16.16/2.40 = { by lemma 52 }
% 16.16/2.40 coll(a, c, s)
% 16.16/2.40
% 16.16/2.40 Lemma 54: fresh134(eqangle(X, Y, Z, W, V, U, T, S), coll(a, c, s), X, Y, Z, W, V, U, T, S) = eqangle(Z, W, X, Y, T, S, V, U).
% 16.16/2.40 Proof:
% 16.16/2.40 fresh134(eqangle(X, Y, Z, W, V, U, T, S), coll(a, c, s), X, Y, Z, W, V, U, T, S)
% 16.16/2.40 = { by lemma 44 }
% 16.16/2.40 fresh134(eqangle(X, Y, Z, W, V, U, T, S), coll(m, r, s), X, Y, Z, W, V, U, T, S)
% 16.16/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.40 fresh134(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S)
% 16.16/2.40 = { by axiom 41 (ruleD19) }
% 16.16/2.40 eqangle(Z, W, X, Y, T, S, V, U)
% 16.16/2.40
% 16.16/2.40 Lemma 55: coll(a, c, s) = coll(X, X, Y).
% 16.16/2.40 Proof:
% 16.16/2.40 coll(a, c, s)
% 16.16/2.40 = { by lemma 44 }
% 16.16/2.40 coll(m, r, s)
% 16.16/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.40 true
% 16.16/2.40 = { by axiom 4 (ruleD1) R->L }
% 16.16/2.40 fresh146(coll(a, c, s), coll(a, c, s), X, Y, X)
% 16.16/2.40 = { by lemma 44 }
% 16.16/2.40 fresh146(coll(m, r, s), coll(a, c, s), X, Y, X)
% 16.16/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.40 fresh146(true, coll(a, c, s), X, Y, X)
% 16.16/2.40 = { by axiom 5 (ruleD2) R->L }
% 16.16/2.40 fresh146(fresh133(coll(a, c, s), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.40 = { by lemma 44 }
% 16.16/2.40 fresh146(fresh133(coll(m, r, s), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.40 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh146(fresh133(true, coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 7 (ruleD66) R->L }
% 16.16/2.41 fresh146(fresh133(fresh66(coll(a, c, s), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh146(fresh133(fresh66(coll(m, r, s), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh146(fresh133(fresh66(true, coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 11 (ruleD39) R->L }
% 16.16/2.41 fresh146(fresh133(fresh66(fresh106(coll(a, c, s), coll(a, c, s), Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 45 R->L }
% 16.16/2.41 fresh146(fresh133(fresh66(fresh106(fresh134(coll(a, c, s), coll(a, c, s), r, s, Y, X, r, s, Y, X), coll(a, c, s), Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 53 R->L }
% 16.16/2.41 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(r, s, Y, X, r, s, Y, X), coll(a, c, s), r, s, Y, X, r, s, Y, X), coll(a, c, s), Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 54 }
% 16.16/2.41 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, r, s, Y, X, r, s), coll(a, c, s), Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, r, s, Y, X, r, s), coll(m, r, s), Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, r, s, Y, X, r, s), true, Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 38 (ruleD39) }
% 16.16/2.41 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(a, c, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(m, r, s), Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 26 (ruleD66) }
% 16.16/2.41 fresh146(fresh133(coll(Y, X, X), coll(a, c, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh146(fresh133(coll(Y, X, X), coll(m, r, s), Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by axiom 21 (ruleD2) }
% 16.16/2.41 fresh146(coll(X, Y, X), coll(a, c, s), X, Y, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh146(coll(X, Y, X), coll(m, r, s), X, Y, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh146(coll(X, Y, X), true, X, Y, X)
% 16.16/2.41 = { by axiom 20 (ruleD1) }
% 16.16/2.41 coll(X, X, Y)
% 16.16/2.41
% 16.16/2.41 Lemma 56: fresh131(X, X, Y, Z, W, V, U, T, S, X2) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 fresh131(X, X, Y, Z, W, V, U, T, S, X2)
% 16.16/2.41 = { by axiom 29 (ruleD21) }
% 16.16/2.41 true
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 coll(m, r, s)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 57: fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(a, c, s), X, Y, Z, W, V, U, T, S) = eqangle(X, Y, V, U, Z, W, T, S).
% 16.16/2.41 Proof:
% 16.16/2.41 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(a, c, s), X, Y, Z, W, V, U, T, S)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(m, r, s), X, Y, Z, W, V, U, T, S)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh131(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S)
% 16.16/2.41 = { by axiom 42 (ruleD21) }
% 16.16/2.41 eqangle(X, Y, V, U, Z, W, T, S)
% 16.16/2.41
% 16.16/2.41 Lemma 58: cyclic(s, s, r, X) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 cyclic(s, s, r, X)
% 16.16/2.41 = { by axiom 12 (ruleD42b) R->L }
% 16.16/2.41 fresh102(coll(a, c, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 56 R->L }
% 16.16/2.41 fresh102(fresh131(coll(a, c, s), coll(a, c, s), r, s, X, s, r, s, X, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 53 R->L }
% 16.16/2.41 fresh102(fresh131(eqangle(r, s, X, s, r, s, X, s), coll(a, c, s), r, s, X, s, r, s, X, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 57 }
% 16.16/2.41 fresh102(eqangle(r, s, r, s, X, s, X, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 24 (ruleD50) R->L }
% 16.16/2.41 fresh102(fresh91(Y, Y, r, s, s, X, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh102(fresh91(Y, Y, r, s, s, X, s), coll(m, r, s), s, s, r, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh102(fresh91(Y, Y, r, s, s, X, s), true, s, s, r, X)
% 16.16/2.41 = { by axiom 24 (ruleD50) }
% 16.16/2.41 fresh102(eqangle(r, s, r, s, X, s, X, s), true, s, s, r, X)
% 16.16/2.41 = { by axiom 39 (ruleD42b) }
% 16.16/2.41 fresh101(coll(r, X, s), true, s, s, r, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh101(coll(r, X, s), coll(m, r, s), s, s, r, X)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh101(coll(r, X, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 10 (ruleD3) R->L }
% 16.16/2.41 fresh101(fresh120(coll(a, c, s), coll(a, c, s), s, s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 55 }
% 16.16/2.41 fresh101(fresh120(coll(s, s, X), coll(a, c, s), s, s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh101(fresh120(coll(s, s, X), coll(m, r, s), s, s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh101(fresh120(coll(s, s, X), true, s, s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 25 (ruleD3) }
% 16.16/2.41 fresh101(fresh119(coll(s, s, r), true, s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh101(fresh119(coll(s, s, r), coll(m, r, s), s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh101(fresh119(coll(s, s, r), coll(a, c, s), s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 55 R->L }
% 16.16/2.41 fresh101(fresh119(coll(a, c, s), coll(a, c, s), s, r, X), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 6 (ruleD3) }
% 16.16/2.41 fresh101(true, coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh101(coll(m, r, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh101(coll(a, c, s), coll(a, c, s), s, s, r, X)
% 16.16/2.41 = { by axiom 13 (ruleD42b) }
% 16.16/2.41 true
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 coll(m, r, s)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 59: fresh137(cyclic(X, Y, Z, W), coll(a, c, s), X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), coll(a, c, s), Y, Z, V, W).
% 16.16/2.41 Proof:
% 16.16/2.41 fresh137(cyclic(X, Y, Z, W), coll(a, c, s), X, Y, Z, V, W)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh137(cyclic(X, Y, Z, W), coll(m, r, s), X, Y, Z, V, W)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W)
% 16.16/2.41 = { by axiom 34 (ruleD17) }
% 16.16/2.41 fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh136(cyclic(X, Y, Z, V), coll(m, r, s), Y, Z, V, W)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh136(cyclic(X, Y, Z, V), coll(a, c, s), Y, Z, V, W)
% 16.16/2.41
% 16.16/2.41 Lemma 60: fresh136(X, X, Y, Z, W, V) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 fresh136(X, X, Y, Z, W, V)
% 16.16/2.41 = { by axiom 9 (ruleD17) }
% 16.16/2.41 true
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 coll(m, r, s)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 61: cyclic(s, r, X, Y) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 cyclic(s, r, X, Y)
% 16.16/2.41 = { by axiom 19 (ruleD17) R->L }
% 16.16/2.41 fresh137(coll(a, c, s), coll(a, c, s), s, s, r, X, Y)
% 16.16/2.41 = { by lemma 58 R->L }
% 16.16/2.41 fresh137(cyclic(s, s, r, Y), coll(a, c, s), s, s, r, X, Y)
% 16.16/2.41 = { by lemma 59 }
% 16.16/2.41 fresh136(cyclic(s, s, r, X), coll(a, c, s), s, r, X, Y)
% 16.16/2.41 = { by lemma 58 }
% 16.16/2.41 fresh136(coll(a, c, s), coll(a, c, s), s, r, X, Y)
% 16.16/2.41 = { by lemma 60 }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 62: cyclic(r, X, Y, Z) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 cyclic(r, X, Y, Z)
% 16.16/2.41 = { by axiom 19 (ruleD17) R->L }
% 16.16/2.41 fresh137(coll(a, c, s), coll(a, c, s), s, r, X, Y, Z)
% 16.16/2.41 = { by lemma 61 R->L }
% 16.16/2.41 fresh137(cyclic(s, r, X, Z), coll(a, c, s), s, r, X, Y, Z)
% 16.16/2.41 = { by lemma 59 }
% 16.16/2.41 fresh136(cyclic(s, r, X, Y), coll(a, c, s), r, X, Y, Z)
% 16.16/2.41 = { by lemma 61 }
% 16.16/2.41 fresh136(coll(a, c, s), coll(a, c, s), r, X, Y, Z)
% 16.16/2.41 = { by lemma 60 }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 63: cyclic(X, Y, Z, W) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 cyclic(X, Y, Z, W)
% 16.16/2.41 = { by axiom 19 (ruleD17) R->L }
% 16.16/2.41 fresh137(coll(a, c, s), coll(a, c, s), r, X, Y, Z, W)
% 16.16/2.41 = { by lemma 62 R->L }
% 16.16/2.41 fresh137(cyclic(r, X, Y, W), coll(a, c, s), r, X, Y, Z, W)
% 16.16/2.41 = { by lemma 59 }
% 16.16/2.41 fresh136(cyclic(r, X, Y, Z), coll(a, c, s), X, Y, Z, W)
% 16.16/2.41 = { by lemma 62 }
% 16.16/2.41 fresh136(coll(a, c, s), coll(a, c, s), X, Y, Z, W)
% 16.16/2.41 = { by lemma 60 }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 64: cong(s, X, s, X) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 cong(s, X, s, X)
% 16.16/2.41 = { by axiom 18 (ruleD43) R->L }
% 16.16/2.41 fresh183(coll(a, c, s), coll(a, c, s), s, X, r, s, X)
% 16.16/2.41 = { by lemma 63 R->L }
% 16.16/2.41 fresh183(cyclic(s, X, r, X), coll(a, c, s), s, X, r, s, X)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh183(cyclic(s, X, r, X), coll(m, r, s), s, X, r, s, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh183(cyclic(s, X, r, X), true, s, X, r, s, X)
% 16.16/2.41 = { by axiom 33 (ruleD43) R->L }
% 16.16/2.41 fresh182(coll(a, c, s), coll(a, c, s), s, X, r, s, X, r)
% 16.16/2.41 = { by lemma 53 R->L }
% 16.16/2.41 fresh182(eqangle(r, s, r, X, r, s, r, X), coll(a, c, s), s, X, r, s, X, r)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh182(eqangle(r, s, r, X, r, s, r, X), coll(m, r, s), s, X, r, s, X, r)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh182(eqangle(r, s, r, X, r, s, r, X), true, s, X, r, s, X, r)
% 16.16/2.41 = { by axiom 40 (ruleD43) }
% 16.16/2.41 fresh184(cyclic(s, X, r, r), true, s, X, r, s, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh184(cyclic(s, X, r, r), coll(m, r, s), s, X, r, s, X)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh184(cyclic(s, X, r, r), coll(a, c, s), s, X, r, s, X)
% 16.16/2.41 = { by lemma 63 }
% 16.16/2.41 fresh184(coll(a, c, s), coll(a, c, s), s, X, r, s, X)
% 16.16/2.41 = { by axiom 27 (ruleD43) }
% 16.16/2.41 fresh185(cyclic(s, X, r, s), true, s, X, s, X)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh185(cyclic(s, X, r, s), coll(m, r, s), s, X, s, X)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh185(cyclic(s, X, r, s), coll(a, c, s), s, X, s, X)
% 16.16/2.41 = { by lemma 63 }
% 16.16/2.41 fresh185(coll(a, c, s), coll(a, c, s), s, X, s, X)
% 16.16/2.41 = { by axiom 8 (ruleD43) }
% 16.16/2.41 true
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 coll(m, r, s)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 65: perp(s, s, X, Y) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 perp(s, s, X, Y)
% 16.16/2.41 = { by axiom 14 (ruleD56) R->L }
% 16.16/2.41 fresh80(coll(a, c, s), coll(a, c, s), s, s, X, Y)
% 16.16/2.41 = { by lemma 64 R->L }
% 16.16/2.41 fresh80(cong(s, Y, s, Y), coll(a, c, s), s, s, X, Y)
% 16.16/2.41 = { by lemma 44 }
% 16.16/2.41 fresh80(cong(s, Y, s, Y), coll(m, r, s), s, s, X, Y)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.41 fresh80(cong(s, Y, s, Y), true, s, s, X, Y)
% 16.16/2.41 = { by axiom 31 (ruleD56) }
% 16.16/2.41 fresh79(cong(s, X, s, X), true, s, s, X, Y)
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 fresh79(cong(s, X, s, X), coll(m, r, s), s, s, X, Y)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 fresh79(cong(s, X, s, X), coll(a, c, s), s, s, X, Y)
% 16.16/2.41 = { by lemma 64 }
% 16.16/2.41 fresh79(coll(a, c, s), coll(a, c, s), s, s, X, Y)
% 16.16/2.41 = { by axiom 15 (ruleD56) }
% 16.16/2.41 true
% 16.16/2.41 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.41 coll(m, r, s)
% 16.16/2.41 = { by lemma 44 R->L }
% 16.16/2.41 coll(a, c, s)
% 16.16/2.41
% 16.16/2.41 Lemma 66: eqangle(X, Y, Z, W, V, U, Z, W) = coll(a, c, s).
% 16.16/2.41 Proof:
% 16.16/2.41 eqangle(X, Y, Z, W, V, U, Z, W)
% 16.16/2.41 = { by lemma 46 R->L }
% 16.16/2.41 fresh104(para(X, Y, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.41 = { by axiom 23 (ruleD9) R->L }
% 16.16/2.41 fresh104(fresh51(coll(a, c, s), coll(a, c, s), X, Y, s, s, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.41 = { by lemma 65 R->L }
% 16.16/2.41 fresh104(fresh51(perp(s, s, V, U), coll(a, c, s), X, Y, s, s, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.41 = { by lemma 48 }
% 16.16/2.41 fresh104(fresh50(perp(X, Y, s, s), coll(a, c, s), X, Y, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.42 = { by lemma 49 R->L }
% 16.16/2.42 fresh104(fresh50(fresh52(perp(s, s, X, Y), coll(a, c, s), s, s, X, Y), coll(a, c, s), X, Y, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.42 = { by lemma 65 }
% 16.16/2.42 fresh104(fresh50(fresh52(coll(a, c, s), coll(a, c, s), s, s, X, Y), coll(a, c, s), X, Y, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.42 = { by lemma 50 }
% 16.16/2.42 fresh104(fresh50(coll(a, c, s), coll(a, c, s), X, Y, V, U), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.42 = { by lemma 51 }
% 16.16/2.42 fresh104(coll(a, c, s), coll(a, c, s), X, Y, V, U, Z, W)
% 16.16/2.42 = { by lemma 52 }
% 16.16/2.42 coll(a, c, s)
% 16.16/2.42
% 16.16/2.42 Goal 1 (exemplo6GDDFULL214032_8): eqangle(b, a, a, m, n, a, a, c) = true.
% 16.16/2.42 Proof:
% 16.16/2.42 eqangle(b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by axiom 37 (ruleD22) R->L }
% 16.16/2.42 fresh130(coll(a, c, s), coll(a, c, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by lemma 56 R->L }
% 16.16/2.42 fresh130(fresh131(coll(a, c, s), coll(a, c, s), X, Y, n, a, X, Y, a, c), coll(a, c, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by lemma 45 R->L }
% 16.16/2.42 fresh130(fresh131(fresh134(coll(a, c, s), coll(a, c, s), n, a, X, Y, a, c, X, Y), coll(a, c, s), X, Y, n, a, X, Y, a, c), coll(a, c, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by lemma 66 R->L }
% 16.16/2.42 fresh130(fresh131(fresh134(eqangle(n, a, X, Y, a, c, X, Y), coll(a, c, s), n, a, X, Y, a, c, X, Y), coll(a, c, s), X, Y, n, a, X, Y, a, c), coll(a, c, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by lemma 54 }
% 16.16/2.42 fresh130(fresh131(eqangle(X, Y, n, a, X, Y, a, c), coll(a, c, s), X, Y, n, a, X, Y, a, c), coll(a, c, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by lemma 57 }
% 16.16/2.42 fresh130(eqangle(X, Y, X, Y, n, a, a, c), coll(a, c, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by lemma 44 }
% 16.16/2.42 fresh130(eqangle(X, Y, X, Y, n, a, a, c), coll(m, r, s), b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by axiom 1 (exemplo6GDDFULL214032_2) }
% 16.16/2.42 fresh130(eqangle(X, Y, X, Y, n, a, a, c), true, b, a, a, m, X, Y, X, Y, n, a, a, c)
% 16.16/2.42 = { by axiom 43 (ruleD22) }
% 16.16/2.42 fresh129(eqangle(b, a, a, m, X, Y, X, Y), true, b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by axiom 1 (exemplo6GDDFULL214032_2) R->L }
% 16.16/2.42 fresh129(eqangle(b, a, a, m, X, Y, X, Y), coll(m, r, s), b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by lemma 44 R->L }
% 16.16/2.42 fresh129(eqangle(b, a, a, m, X, Y, X, Y), coll(a, c, s), b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by lemma 57 R->L }
% 16.16/2.42 fresh129(fresh131(eqangle(b, a, X, Y, a, m, X, Y), coll(a, c, s), b, a, X, Y, a, m, X, Y), coll(a, c, s), b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by lemma 66 }
% 16.16/2.42 fresh129(fresh131(coll(a, c, s), coll(a, c, s), b, a, X, Y, a, m, X, Y), coll(a, c, s), b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by lemma 56 }
% 16.16/2.42 fresh129(coll(a, c, s), coll(a, c, s), b, a, a, m, n, a, a, c)
% 16.16/2.42 = { by axiom 30 (ruleD22) }
% 16.16/2.42 true
% 16.16/2.42 % SZS output end Proof
% 16.16/2.42
% 16.16/2.42 RESULT: Theorem (the conjecture is true).
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