TSTP Solution File: GEO575+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO575+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 : n009.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 23:29:23 EDT 2023
% Result : Theorem 12.26s 1.95s
% Output : Proof 12.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO575+1 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.35 % Computer : n009.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Tue Aug 29 19:22:20 EDT 2023
% 0.12/0.35 % CPUTime :
% 12.26/1.95 Command-line arguments: --flatten
% 12.26/1.95
% 12.26/1.95 % SZS status Theorem
% 12.26/1.95
% 12.50/2.00 % SZS output start Proof
% 12.50/2.00 Take the following subset of the input axioms:
% 12.50/2.01 fof(exemplo6GDDFULL214037, conjecture, ![A, B, C, O, H, C1, A1, NWPNT1, NWPNT2]: ((circle(O, A, B, C) & (perp(A, B, C, H) & (perp(A, C, B, H) & (perp(B, C, A, H) & (circle(O, C, C1, NWPNT1) & (coll(C1, C, H) & (circle(O, A, A1, NWPNT2) & coll(A1, A, H)))))))) => cong(B, A1, B, C1))).
% 12.50/2.01 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 12.50/2.01 fof(ruleD11, axiom, ![M, B2, A2_2]: (midp(M, B2, A2_2) => midp(M, A2_2, B2))).
% 12.50/2.01 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))).
% 12.50/2.01 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))).
% 12.50/2.01 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 12.50/2.01 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))).
% 12.50/2.01 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 12.50/2.01 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))).
% 12.50/2.01 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))).
% 12.50/2.01 fof(ruleD41, axiom, ![B2, A2_2, P2, Q2]: (cyclic(A2_2, B2, P2, Q2) => eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2))).
% 12.50/2.01 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))).
% 12.50/2.01 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))).
% 12.50/2.01 fof(ruleD45, axiom, ![F, B2, C2, E2, A2_2]: ((midp(E2, A2_2, B2) & (para(E2, F, B2, C2) & coll(F, A2_2, C2))) => midp(F, A2_2, C2))).
% 12.50/2.01 fof(ruleD51, axiom, ![B2, C2, A2_2, M2, O2]: ((circle(O2, A2_2, B2, C2) & (coll(M2, B2, C2) & eqangle(A2_2, B2, A2_2, C2, O2, B2, O2, M2))) => midp(M2, B2, C2))).
% 12.50/2.01 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))).
% 12.50/2.01 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 12.50/2.01 fof(ruleD68, axiom, ![B2, C2, A2_2]: (midp(A2_2, B2, C2) => cong(A2_2, B2, A2_2, C2))).
% 12.50/2.01 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 12.50/2.01 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))).
% 12.50/2.01
% 12.50/2.01 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.50/2.01 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.50/2.01 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.50/2.01 fresh(y, y, x1...xn) = u
% 12.50/2.01 C => fresh(s, t, x1...xn) = v
% 12.50/2.01 where fresh is a fresh function symbol and x1..xn are the free
% 12.50/2.01 variables of u and v.
% 12.50/2.01 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.50/2.01 input problem has no model of domain size 1).
% 12.50/2.01
% 12.50/2.01 The encoding turns the above axioms into the following unit equations and goals:
% 12.50/2.01
% 12.50/2.01 Axiom 1 (exemplo6GDDFULL214037): coll(a1, a, h) = true.
% 12.50/2.01 Axiom 2 (exemplo6GDDFULL214037_5): circle(o, c, c1, nwpnt1) = true.
% 12.50/2.01 Axiom 3 (exemplo6GDDFULL214037_2): perp(b, c, a, h) = true.
% 12.50/2.01 Axiom 4 (ruleD45): fresh181(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 5 (ruleD51): fresh179(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 6 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 7 (ruleD11): fresh144(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 8 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 9 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 10 (ruleD45): fresh98(X, X, Y, Z, W) = midp(W, Y, Z).
% 12.50/2.01 Axiom 11 (ruleD51): fresh89(X, X, Y, Z, W) = midp(W, Y, Z).
% 12.50/2.01 Axiom 12 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 13 (ruleD68): fresh63(X, X, Y, Z, W) = true.
% 12.50/2.01 Axiom 14 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 15 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 16 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 12.50/2.01 Axiom 17 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 18 (ruleD41): fresh103(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 19 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 12.50/2.01 Axiom 20 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 21 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 12.50/2.01 Axiom 22 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 23 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 24 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 12.50/2.01 Axiom 25 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 12.50/2.01 Axiom 26 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 12.50/2.01 Axiom 27 (ruleD45): fresh180(X, X, Y, Z, W, V, U) = fresh181(coll(U, Y, W), true, Y, W, U).
% 12.50/2.01 Axiom 28 (ruleD51): fresh178(X, X, Y, Z, W, V, U) = fresh179(coll(V, Z, W), true, Z, W, V).
% 12.50/2.01 Axiom 29 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 12.50/2.01 Axiom 30 (ruleD11): fresh144(midp(X, Y, Z), true, Z, Y, X) = midp(X, Z, Y).
% 12.50/2.01 Axiom 31 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 12.50/2.01 Axiom 32 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 12.50/2.01 Axiom 33 (ruleD68): fresh63(midp(X, Y, Z), true, X, Y, Z) = cong(X, Y, X, Z).
% 12.50/2.01 Axiom 34 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 12.50/2.01 Axiom 35 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 12.50/2.01 Axiom 36 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 12.50/2.01 Axiom 37 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 12.50/2.01 Axiom 38 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 12.50/2.01 Axiom 39 (ruleD45): fresh180(midp(X, Y, Z), true, Y, Z, W, X, V) = fresh98(para(X, V, Z, W), true, Y, W, V).
% 12.50/2.01 Axiom 40 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 12.50/2.01 Axiom 41 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 12.50/2.01 Axiom 42 (ruleD41): fresh103(cyclic(X, Y, Z, W), true, X, Y, Z, W) = eqangle(Z, X, Z, Y, W, X, W, Y).
% 12.50/2.01 Axiom 43 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 12.50/2.01 Axiom 44 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 12.50/2.01 Axiom 45 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 12.50/2.01 Axiom 46 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 12.50/2.01 Axiom 47 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 12.50/2.01 Axiom 48 (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).
% 12.50/2.01 Axiom 49 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 12.50/2.01 Axiom 50 (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).
% 12.50/2.01 Axiom 51 (ruleD51): fresh178(eqangle(X, Y, X, Z, W, Y, W, V), true, X, Y, Z, V, W) = fresh89(circle(W, X, Y, Z), true, Y, Z, V).
% 12.50/2.01 Axiom 52 (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).
% 12.50/2.01 Axiom 53 (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).
% 12.50/2.01 Axiom 54 (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).
% 12.50/2.01
% 12.50/2.01 Lemma 55: fresh104(para(X, Y, Z, W), coll(a1, a, h), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 12.50/2.01 Proof:
% 12.50/2.01 fresh104(para(X, Y, Z, W), coll(a1, a, h), X, Y, Z, W, V, U)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 12.50/2.01 = { by axiom 47 (ruleD40) }
% 12.50/2.01 eqangle(X, Y, V, U, Z, W, V, U)
% 12.50/2.01
% 12.50/2.01 Lemma 56: perp(b, c, a, h) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 perp(b, c, a, h)
% 12.50/2.01 = { by axiom 3 (exemplo6GDDFULL214037_2) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01
% 12.50/2.01 Lemma 57: fresh51(perp(X, Y, Z, W), coll(a1, a, h), V, U, X, Y, Z, W) = fresh50(perp(V, U, X, Y), coll(a1, a, h), V, U, Z, W).
% 12.50/2.01 Proof:
% 12.50/2.01 fresh51(perp(X, Y, Z, W), coll(a1, a, h), V, U, X, Y, Z, W)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh51(perp(X, Y, Z, W), true, V, U, X, Y, Z, W)
% 12.50/2.01 = { by axiom 48 (ruleD9) }
% 12.50/2.01 fresh50(perp(V, U, X, Y), true, V, U, Z, W)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 fresh50(perp(V, U, X, Y), coll(a1, a, h), V, U, Z, W)
% 12.50/2.01
% 12.50/2.01 Lemma 58: fresh52(perp(X, Y, Z, W), coll(a1, a, h), X, Y, Z, W) = perp(Z, W, X, Y).
% 12.50/2.01 Proof:
% 12.50/2.01 fresh52(perp(X, Y, Z, W), coll(a1, a, h), X, Y, Z, W)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh52(perp(X, Y, Z, W), true, X, Y, Z, W)
% 12.50/2.01 = { by axiom 44 (ruleD8) }
% 12.50/2.01 perp(Z, W, X, Y)
% 12.50/2.01
% 12.50/2.01 Lemma 59: fresh52(X, X, Y, Z, W, V) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 fresh52(X, X, Y, Z, W, V)
% 12.50/2.01 = { by axiom 23 (ruleD8) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01
% 12.50/2.01 Lemma 60: fresh50(X, X, Y, Z, W, V) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 fresh50(X, X, Y, Z, W, V)
% 12.50/2.01 = { by axiom 24 (ruleD9) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01
% 12.50/2.01 Lemma 61: fresh104(X, X, Y, Z, W, V, U, T) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 fresh104(X, X, Y, Z, W, V, U, T)
% 12.50/2.01 = { by axiom 32 (ruleD40) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01
% 12.50/2.01 Lemma 62: eqangle(a, h, X, Y, a, h, X, Y) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 eqangle(a, h, X, Y, a, h, X, Y)
% 12.50/2.01 = { by lemma 55 R->L }
% 12.50/2.01 fresh104(para(a, h, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by axiom 34 (ruleD9) R->L }
% 12.50/2.01 fresh104(fresh51(coll(a1, a, h), coll(a1, a, h), a, h, b, c, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 56 R->L }
% 12.50/2.01 fresh104(fresh51(perp(b, c, a, h), coll(a1, a, h), a, h, b, c, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 57 }
% 12.50/2.01 fresh104(fresh50(perp(a, h, b, c), coll(a1, a, h), a, h, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 58 R->L }
% 12.50/2.01 fresh104(fresh50(fresh52(perp(b, c, a, h), coll(a1, a, h), b, c, a, h), coll(a1, a, h), a, h, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 56 }
% 12.50/2.01 fresh104(fresh50(fresh52(coll(a1, a, h), coll(a1, a, h), b, c, a, h), coll(a1, a, h), a, h, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 59 }
% 12.50/2.01 fresh104(fresh50(coll(a1, a, h), coll(a1, a, h), a, h, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 60 }
% 12.50/2.01 fresh104(coll(a1, a, h), coll(a1, a, h), a, h, a, h, X, Y)
% 12.50/2.01 = { by lemma 61 }
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01
% 12.50/2.01 Lemma 63: para(X, Y, X, Y) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 para(X, Y, X, Y)
% 12.50/2.01 = { by axiom 49 (ruleD39) R->L }
% 12.50/2.01 fresh106(eqangle(X, Y, a, h, X, Y, a, h), true, X, Y, X, Y)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 fresh106(eqangle(X, Y, a, h, X, Y, a, h), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.01 = { by axiom 53 (ruleD19) R->L }
% 12.50/2.01 fresh106(fresh134(eqangle(a, h, X, Y, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 fresh106(fresh134(eqangle(a, h, X, Y, a, h, X, Y), coll(a1, a, h), a, h, X, Y, a, h, X, Y), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.01 = { by lemma 62 }
% 12.50/2.01 fresh106(fresh134(coll(a1, a, h), coll(a1, a, h), a, h, X, Y, a, h, X, Y), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.01 = { by axiom 40 (ruleD19) }
% 12.50/2.01 fresh106(true, coll(a1, a, h), X, Y, X, Y)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 fresh106(coll(a1, a, h), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.01 = { by axiom 17 (ruleD39) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01
% 12.50/2.01 Lemma 64: coll(a1, a, h) = coll(X, X, Y).
% 12.50/2.01 Proof:
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 6 (ruleD1) R->L }
% 12.50/2.01 fresh146(coll(a1, a, h), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh146(true, coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 8 (ruleD2) R->L }
% 12.50/2.01 fresh146(fresh133(coll(a1, a, h), coll(a1, a, h), Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh146(fresh133(true, coll(a1, a, h), Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 12 (ruleD66) R->L }
% 12.50/2.01 fresh146(fresh133(fresh66(coll(a1, a, h), coll(a1, a, h), Y, X, X), coll(a1, a, h), Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by lemma 63 R->L }
% 12.50/2.01 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(a1, a, h), Y, X, X), coll(a1, a, h), Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), coll(a1, a, h), Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 37 (ruleD66) }
% 12.50/2.01 fresh146(fresh133(coll(Y, X, X), coll(a1, a, h), Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 31 (ruleD2) }
% 12.50/2.01 fresh146(coll(X, Y, X), coll(a1, a, h), X, Y, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh146(coll(X, Y, X), true, X, Y, X)
% 12.50/2.01 = { by axiom 29 (ruleD1) }
% 12.50/2.01 coll(X, X, Y)
% 12.50/2.01
% 12.50/2.01 Lemma 65: coll(a1, a, h) = coll(X, Y, Z).
% 12.50/2.01 Proof:
% 12.50/2.01 coll(a1, a, h)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 true
% 12.50/2.01 = { by axiom 9 (ruleD3) R->L }
% 12.50/2.01 fresh119(coll(a1, a, h), coll(a1, a, h), Z, X, Y)
% 12.50/2.01 = { by lemma 64 }
% 12.50/2.01 fresh119(coll(Z, Z, X), coll(a1, a, h), Z, X, Y)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh119(coll(Z, Z, X), true, Z, X, Y)
% 12.50/2.01 = { by axiom 36 (ruleD3) R->L }
% 12.50/2.01 fresh120(coll(Z, Z, Y), true, Z, Z, X, Y)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.01 fresh120(coll(Z, Z, Y), coll(a1, a, h), Z, Z, X, Y)
% 12.50/2.01 = { by lemma 64 R->L }
% 12.50/2.01 fresh120(coll(a1, a, h), coll(a1, a, h), Z, Z, X, Y)
% 12.50/2.01 = { by axiom 16 (ruleD3) }
% 12.50/2.01 coll(X, Y, Z)
% 12.50/2.01
% 12.50/2.01 Lemma 66: cyclic(h, h, a, X) = coll(a1, a, h).
% 12.50/2.01 Proof:
% 12.50/2.01 cyclic(h, h, a, X)
% 12.50/2.01 = { by axiom 19 (ruleD42b) R->L }
% 12.50/2.01 fresh102(coll(a1, a, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh102(true, coll(a1, a, h), h, h, a, X)
% 12.50/2.01 = { by axiom 41 (ruleD21) R->L }
% 12.50/2.01 fresh102(fresh131(coll(a1, a, h), coll(a1, a, h), a, h, X, h, a, h, X, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.01 = { by lemma 62 R->L }
% 12.50/2.01 fresh102(fresh131(eqangle(a, h, X, h, a, h, X, h), coll(a1, a, h), a, h, X, h, a, h, X, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.01 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.01 fresh102(fresh131(eqangle(a, h, X, h, a, h, X, h), true, a, h, X, h, a, h, X, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.01 = { by axiom 54 (ruleD21) }
% 12.50/2.01 fresh102(eqangle(a, h, a, h, X, h, X, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.02 = { by axiom 35 (ruleD50) R->L }
% 12.50/2.02 fresh102(fresh91(Y, Y, a, h, h, X, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh102(fresh91(Y, Y, a, h, h, X, h), true, h, h, a, X)
% 12.50/2.02 = { by axiom 35 (ruleD50) }
% 12.50/2.02 fresh102(eqangle(a, h, a, h, X, h, X, h), true, h, h, a, X)
% 12.50/2.02 = { by axiom 50 (ruleD42b) }
% 12.50/2.02 fresh101(coll(a, X, h), true, h, h, a, X)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh101(coll(a, X, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.02 = { by lemma 65 R->L }
% 12.50/2.02 fresh101(coll(a1, a, h), coll(a1, a, h), h, h, a, X)
% 12.50/2.02 = { by axiom 20 (ruleD42b) }
% 12.50/2.02 true
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Lemma 67: fresh137(cyclic(X, Y, Z, W), coll(a1, a, h), X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), coll(a1, a, h), Y, Z, V, W).
% 12.50/2.02 Proof:
% 12.50/2.02 fresh137(cyclic(X, Y, Z, W), coll(a1, a, h), X, Y, Z, V, W)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W)
% 12.50/2.02 = { by axiom 46 (ruleD17) }
% 12.50/2.02 fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh136(cyclic(X, Y, Z, V), coll(a1, a, h), Y, Z, V, W)
% 12.50/2.02
% 12.50/2.02 Lemma 68: fresh136(X, X, Y, Z, W, V) = coll(a1, a, h).
% 12.50/2.02 Proof:
% 12.50/2.02 fresh136(X, X, Y, Z, W, V)
% 12.50/2.02 = { by axiom 15 (ruleD17) }
% 12.50/2.02 true
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Lemma 69: cyclic(h, a, X, Y) = coll(a1, a, h).
% 12.50/2.02 Proof:
% 12.50/2.02 cyclic(h, a, X, Y)
% 12.50/2.02 = { by axiom 26 (ruleD17) R->L }
% 12.50/2.02 fresh137(coll(a1, a, h), coll(a1, a, h), h, h, a, X, Y)
% 12.50/2.02 = { by lemma 66 R->L }
% 12.50/2.02 fresh137(cyclic(h, h, a, Y), coll(a1, a, h), h, h, a, X, Y)
% 12.50/2.02 = { by lemma 67 }
% 12.50/2.02 fresh136(cyclic(h, h, a, X), coll(a1, a, h), h, a, X, Y)
% 12.50/2.02 = { by lemma 66 }
% 12.50/2.02 fresh136(coll(a1, a, h), coll(a1, a, h), h, a, X, Y)
% 12.50/2.02 = { by lemma 68 }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Lemma 70: cyclic(a, X, Y, Z) = coll(a1, a, h).
% 12.50/2.02 Proof:
% 12.50/2.02 cyclic(a, X, Y, Z)
% 12.50/2.02 = { by axiom 26 (ruleD17) R->L }
% 12.50/2.02 fresh137(coll(a1, a, h), coll(a1, a, h), h, a, X, Y, Z)
% 12.50/2.02 = { by lemma 69 R->L }
% 12.50/2.02 fresh137(cyclic(h, a, X, Z), coll(a1, a, h), h, a, X, Y, Z)
% 12.50/2.02 = { by lemma 67 }
% 12.50/2.02 fresh136(cyclic(h, a, X, Y), coll(a1, a, h), a, X, Y, Z)
% 12.50/2.02 = { by lemma 69 }
% 12.50/2.02 fresh136(coll(a1, a, h), coll(a1, a, h), a, X, Y, Z)
% 12.50/2.02 = { by lemma 68 }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Lemma 71: cyclic(X, Y, Z, W) = coll(a1, a, h).
% 12.50/2.02 Proof:
% 12.50/2.02 cyclic(X, Y, Z, W)
% 12.50/2.02 = { by axiom 26 (ruleD17) R->L }
% 12.50/2.02 fresh137(coll(a1, a, h), coll(a1, a, h), a, X, Y, Z, W)
% 12.50/2.02 = { by lemma 70 R->L }
% 12.50/2.02 fresh137(cyclic(a, X, Y, W), coll(a1, a, h), a, X, Y, Z, W)
% 12.50/2.02 = { by lemma 67 }
% 12.50/2.02 fresh136(cyclic(a, X, Y, Z), coll(a1, a, h), X, Y, Z, W)
% 12.50/2.02 = { by lemma 70 }
% 12.50/2.02 fresh136(coll(a1, a, h), coll(a1, a, h), X, Y, Z, W)
% 12.50/2.02 = { by lemma 68 }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Lemma 72: cong(X, Y, X, Y) = coll(a1, a, h).
% 12.50/2.02 Proof:
% 12.50/2.02 cong(X, Y, X, Y)
% 12.50/2.02 = { by axiom 25 (ruleD43) R->L }
% 12.50/2.02 fresh183(coll(a1, a, h), coll(a1, a, h), X, Y, Z, X, Y)
% 12.50/2.02 = { by lemma 71 R->L }
% 12.50/2.02 fresh183(cyclic(X, Y, Z, Y), coll(a1, a, h), X, Y, Z, X, Y)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh183(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y)
% 12.50/2.02 = { by axiom 45 (ruleD43) R->L }
% 12.50/2.02 fresh182(coll(a1, a, h), coll(a1, a, h), X, Y, Z, X, Y, Z)
% 12.50/2.02 = { by lemma 61 R->L }
% 12.50/2.02 fresh182(fresh104(coll(a1, a, h), coll(a1, a, h), Z, X, Z, X, Z, Y), coll(a1, a, h), X, Y, Z, X, Y, Z)
% 12.50/2.02 = { by lemma 63 R->L }
% 12.50/2.02 fresh182(fresh104(para(Z, X, Z, X), coll(a1, a, h), Z, X, Z, X, Z, Y), coll(a1, a, h), X, Y, Z, X, Y, Z)
% 12.50/2.02 = { by lemma 55 }
% 12.50/2.02 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), coll(a1, a, h), X, Y, Z, X, Y, Z)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, X, Y, Z)
% 12.50/2.02 = { by axiom 52 (ruleD43) }
% 12.50/2.02 fresh184(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh184(cyclic(X, Y, Z, Z), coll(a1, a, h), X, Y, Z, X, Y)
% 12.50/2.02 = { by lemma 71 }
% 12.50/2.02 fresh184(coll(a1, a, h), coll(a1, a, h), X, Y, Z, X, Y)
% 12.50/2.02 = { by axiom 38 (ruleD43) }
% 12.50/2.02 fresh185(cyclic(X, Y, Z, X), true, X, Y, X, Y)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh185(cyclic(X, Y, Z, X), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.02 = { by lemma 71 }
% 12.50/2.02 fresh185(coll(a1, a, h), coll(a1, a, h), X, Y, X, Y)
% 12.50/2.02 = { by axiom 14 (ruleD43) }
% 12.50/2.02 true
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Lemma 73: perp(X, X, Y, Z) = coll(a1, a, h).
% 12.50/2.02 Proof:
% 12.50/2.02 perp(X, X, Y, Z)
% 12.50/2.02 = { by axiom 21 (ruleD56) R->L }
% 12.50/2.02 fresh80(coll(a1, a, h), coll(a1, a, h), X, X, Y, Z)
% 12.50/2.02 = { by lemma 72 R->L }
% 12.50/2.02 fresh80(cong(X, Z, X, Z), coll(a1, a, h), X, X, Y, Z)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
% 12.50/2.02 = { by axiom 43 (ruleD56) }
% 12.50/2.02 fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh79(cong(X, Y, X, Y), coll(a1, a, h), X, X, Y, Z)
% 12.50/2.02 = { by lemma 72 }
% 12.50/2.02 fresh79(coll(a1, a, h), coll(a1, a, h), X, X, Y, Z)
% 12.50/2.02 = { by axiom 22 (ruleD56) }
% 12.50/2.02 true
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 coll(a1, a, h)
% 12.50/2.02
% 12.50/2.02 Goal 1 (exemplo6GDDFULL214037_8): cong(b, a1, b, c1) = true.
% 12.50/2.02 Proof:
% 12.50/2.02 cong(b, a1, b, c1)
% 12.50/2.02 = { by axiom 33 (ruleD68) R->L }
% 12.50/2.02 fresh63(midp(b, a1, c1), true, b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(midp(b, a1, c1), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 30 (ruleD11) R->L }
% 12.50/2.02 fresh63(fresh144(midp(b, c1, a1), true, a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(midp(b, c1, a1), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 10 (ruleD45) R->L }
% 12.50/2.02 fresh63(fresh144(fresh98(coll(a1, a, h), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 60 R->L }
% 12.50/2.02 fresh63(fresh144(fresh98(fresh50(coll(a1, a, h), coll(a1, a, h), nwpnt1, b, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 59 R->L }
% 12.50/2.02 fresh63(fresh144(fresh98(fresh50(fresh52(coll(a1, a, h), coll(a1, a, h), X, X, nwpnt1, b), coll(a1, a, h), nwpnt1, b, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 73 R->L }
% 12.50/2.02 fresh63(fresh144(fresh98(fresh50(fresh52(perp(X, X, nwpnt1, b), coll(a1, a, h), X, X, nwpnt1, b), coll(a1, a, h), nwpnt1, b, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 58 }
% 12.50/2.02 fresh63(fresh144(fresh98(fresh50(perp(nwpnt1, b, X, X), coll(a1, a, h), nwpnt1, b, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 57 R->L }
% 12.50/2.02 fresh63(fresh144(fresh98(fresh51(perp(X, X, nwpnt1, a1), coll(a1, a, h), nwpnt1, b, X, X, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 73 }
% 12.50/2.02 fresh63(fresh144(fresh98(fresh51(coll(a1, a, h), coll(a1, a, h), nwpnt1, b, X, X, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 34 (ruleD9) }
% 12.50/2.02 fresh63(fresh144(fresh98(para(nwpnt1, b, nwpnt1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh63(fresh144(fresh98(para(nwpnt1, b, nwpnt1, a1), true, c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 39 (ruleD45) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(midp(nwpnt1, c1, nwpnt1), true, c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(midp(nwpnt1, c1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 11 (ruleD51) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh89(coll(a1, a, h), coll(a1, a, h), c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh89(true, coll(a1, a, h), c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 2 (exemplo6GDDFULL214037_5) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh89(circle(o, c, c1, nwpnt1), coll(a1, a, h), c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh89(circle(o, c, c1, nwpnt1), true, c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 51 (ruleD51) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(eqangle(c, c1, c, nwpnt1, o, c1, o, nwpnt1), true, c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 35 (ruleD50) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(fresh91(Y, Y, c, c1, nwpnt1, o, nwpnt1), true, c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(fresh91(Y, Y, c, c1, nwpnt1, o, nwpnt1), coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 35 (ruleD50) }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(eqangle(c, c1, c, nwpnt1, o, c1, o, nwpnt1), coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 42 (ruleD41) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(fresh103(cyclic(c1, nwpnt1, c, o), true, c1, nwpnt1, c, o), coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(fresh103(cyclic(c1, nwpnt1, c, o), coll(a1, a, h), c1, nwpnt1, c, o), coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 71 }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(fresh103(coll(a1, a, h), coll(a1, a, h), c1, nwpnt1, c, o), coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 18 (ruleD41) }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(true, coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh178(coll(a1, a, h), coll(a1, a, h), c, c1, nwpnt1, nwpnt1, o), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 28 (ruleD51) }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh179(coll(nwpnt1, c1, nwpnt1), true, c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh179(coll(nwpnt1, c1, nwpnt1), coll(a1, a, h), c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 65 R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(fresh179(coll(a1, a, h), coll(a1, a, h), c1, nwpnt1, nwpnt1), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 5 (ruleD51) }
% 12.50/2.02 fresh63(fresh144(fresh180(true, coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh180(coll(a1, a, h), coll(a1, a, h), c1, nwpnt1, a1, nwpnt1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 27 (ruleD45) }
% 12.50/2.02 fresh63(fresh144(fresh181(coll(b, c1, a1), true, c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.50/2.02 fresh63(fresh144(fresh181(coll(b, c1, a1), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by lemma 65 R->L }
% 12.50/2.02 fresh63(fresh144(fresh181(coll(a1, a, h), coll(a1, a, h), c1, a1, b), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.02 = { by axiom 4 (ruleD45) }
% 12.50/2.03 fresh63(fresh144(true, coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.50/2.03 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.92/2.03 fresh63(fresh144(coll(a1, a, h), coll(a1, a, h), a1, c1, b), coll(a1, a, h), b, a1, c1)
% 12.92/2.03 = { by axiom 7 (ruleD11) }
% 12.92/2.03 fresh63(true, coll(a1, a, h), b, a1, c1)
% 12.92/2.03 = { by axiom 1 (exemplo6GDDFULL214037) R->L }
% 12.92/2.03 fresh63(coll(a1, a, h), coll(a1, a, h), b, a1, c1)
% 12.92/2.03 = { by axiom 13 (ruleD68) }
% 12.92/2.03 true
% 12.92/2.03 % SZS output end Proof
% 12.92/2.03
% 12.92/2.03 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------