TSTP Solution File: GEO543+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO543+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:29:15 EDT 2023
% Result : Theorem 22.48s 3.25s
% Output : Proof 23.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO543+1 : TPTP v8.1.2. Released v7.5.0.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 19:35:48 EDT 2023
% 0.14/0.36 % CPUTime :
% 22.48/3.25 Command-line arguments: --flatten
% 22.48/3.25
% 22.48/3.25 % SZS status Theorem
% 22.48/3.25
% 23.21/3.34 % SZS output start Proof
% 23.21/3.34 Take the following subset of the input axioms:
% 23.21/3.35 fof(exemplo6GDDFULL012003, conjecture, ![A, B, C, D, E, F, P, Q, H, A1]: ((perp(D, A, B, C) & (coll(D, B, C) & (perp(E, B, A, C) & (coll(E, A, C) & (perp(F, C, A, B) & (coll(F, A, B) & (coll(H, B, E) & (coll(H, C, F) & (midp(A1, C, B) & (midp(P, E, B) & midp(Q, F, C))))))))))) => cyclic(P, Q, H, D))).
% 23.21/3.35 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 23.21/3.35 fof(ruleD11, axiom, ![M, B2, A2_2]: (midp(M, B2, A2_2) => midp(M, A2_2, B2))).
% 23.21/3.35 fof(ruleD17, axiom, ![B2, C2, D2, A2_2, E2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 23.21/3.35 fof(ruleD19, axiom, ![U, V, B2, C2, D2, P2, Q2, A2_2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P2, Q2))).
% 23.21/3.35 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 23.21/3.35 fof(ruleD21, axiom, ![B2, C2, D2, P2, Q2, U2, V2, A2_2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(A2_2, B2, P2, Q2, C2, D2, U2, V2))).
% 23.21/3.35 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 23.21/3.35 fof(ruleD4, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(A2_2, B2, D2, C2))).
% 23.21/3.35 fof(ruleD40, axiom, ![B2, C2, D2, P2, Q2, A2_2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 23.21/3.35 fof(ruleD42b, axiom, ![B2, P2, Q2, A2_2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 23.21/3.35 fof(ruleD44, axiom, ![B2, C2, A2_2, E2, F2]: ((midp(E2, A2_2, B2) & midp(F2, A2_2, C2)) => para(E2, F2, B2, C2))).
% 23.21/3.35 fof(ruleD63, axiom, ![B2, C2, D2, A2_2, M2]: ((midp(M2, A2_2, B2) & midp(M2, C2, D2)) => para(A2_2, C2, B2, D2))).
% 23.21/3.35 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 23.21/3.35 fof(ruleD73, axiom, ![B2, C2, D2, P2, Q2, U2, V2, A2_2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & para(P2, Q2, U2, V2)) => para(A2_2, B2, C2, D2))).
% 23.21/3.35
% 23.21/3.35 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.21/3.35 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.21/3.35 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.21/3.35 fresh(y, y, x1...xn) = u
% 23.21/3.35 C => fresh(s, t, x1...xn) = v
% 23.21/3.35 where fresh is a fresh function symbol and x1..xn are the free
% 23.21/3.35 variables of u and v.
% 23.21/3.35 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.21/3.35 input problem has no model of domain size 1).
% 23.21/3.35
% 23.21/3.35 The encoding turns the above axioms into the following unit equations and goals:
% 23.21/3.35
% 23.21/3.35 Axiom 1 (exemplo6GDDFULL012003_10): midp(a1, c, b) = true.
% 23.21/3.35 Axiom 2 (exemplo6GDDFULL012003_8): midp(p, e, b) = true.
% 23.21/3.35 Axiom 3 (exemplo6GDDFULL012003): coll(d, b, c) = true.
% 23.21/3.35 Axiom 4 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 23.21/3.35 Axiom 5 (ruleD11): fresh144(X, X, Y, Z, W) = true.
% 23.21/3.35 Axiom 6 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 23.21/3.35 Axiom 7 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 23.21/3.35 Axiom 8 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 23.21/3.35 Axiom 9 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 23.21/3.35 Axiom 10 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 23.21/3.35 Axiom 11 (ruleD4): fresh105(X, X, Y, Z, W, V) = true.
% 23.21/3.35 Axiom 12 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 23.21/3.35 Axiom 13 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 23.21/3.35 Axiom 14 (ruleD44): fresh99(X, X, Y, Z, W, V) = true.
% 23.21/3.35 Axiom 15 (ruleD63): fresh69(X, X, Y, Z, W, V) = true.
% 23.21/3.35 Axiom 16 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 23.21/3.35 Axiom 17 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 23.21/3.35 Axiom 18 (ruleD44): fresh100(X, X, Y, Z, W, V, U) = para(V, U, Z, W).
% 23.21/3.35 Axiom 19 (ruleD63): fresh70(X, X, Y, Z, W, V, U) = para(Y, W, Z, V).
% 23.21/3.35 Axiom 20 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 23.21/3.35 Axiom 21 (ruleD11): fresh144(midp(X, Y, Z), true, Z, Y, X) = midp(X, Z, Y).
% 23.21/3.35 Axiom 22 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 23.21/3.35 Axiom 23 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 23.21/3.35 Axiom 24 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 23.21/3.35 Axiom 25 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 23.21/3.35 Axiom 26 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 23.21/3.35 Axiom 27 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 23.21/3.35 Axiom 28 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 23.21/3.35 Axiom 29 (ruleD4): fresh105(para(X, Y, Z, W), true, X, Y, Z, W) = para(X, Y, W, Z).
% 23.21/3.35 Axiom 30 (ruleD44): fresh100(midp(X, Y, Z), true, Y, W, Z, V, X) = fresh99(midp(V, Y, W), true, W, Z, V, X).
% 23.21/3.35 Axiom 31 (ruleD63): fresh70(midp(X, Y, Z), true, W, V, Y, Z, X) = fresh69(midp(X, W, V), true, W, V, Y, Z).
% 23.21/3.35 Axiom 32 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 23.21/3.35 Axiom 33 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 23.21/3.35 Axiom 34 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 23.21/3.35 Axiom 35 (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).
% 23.21/3.35 Axiom 36 (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).
% 23.21/3.35 Axiom 37 (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).
% 23.21/3.35 Axiom 38 (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).
% 23.21/3.35
% 23.21/3.35 Lemma 39: midp(p, e, b) = midp(a1, c, b).
% 23.21/3.35 Proof:
% 23.21/3.35 midp(p, e, b)
% 23.21/3.35 = { by axiom 2 (exemplo6GDDFULL012003_8) }
% 23.21/3.35 true
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.35 midp(a1, c, b)
% 23.21/3.35
% 23.21/3.35 Lemma 40: coll(d, b, c) = midp(p, e, b).
% 23.21/3.35 Proof:
% 23.21/3.35 coll(d, b, c)
% 23.21/3.35 = { by axiom 3 (exemplo6GDDFULL012003) }
% 23.21/3.35 true
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.35 midp(a1, c, b)
% 23.21/3.35 = { by lemma 39 R->L }
% 23.21/3.35 midp(p, e, b)
% 23.21/3.35
% 23.21/3.35 Lemma 41: para(a1, a1, b, b) = coll(d, b, c).
% 23.21/3.35 Proof:
% 23.21/3.35 para(a1, a1, b, b)
% 23.21/3.35 = { by axiom 18 (ruleD44) R->L }
% 23.21/3.35 fresh100(coll(d, b, c), coll(d, b, c), c, b, b, a1, a1)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh100(midp(p, e, b), coll(d, b, c), c, b, b, a1, a1)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh100(midp(a1, c, b), coll(d, b, c), c, b, b, a1, a1)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh100(midp(a1, c, b), midp(p, e, b), c, b, b, a1, a1)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh100(midp(a1, c, b), midp(a1, c, b), c, b, b, a1, a1)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 fresh100(midp(a1, c, b), true, c, b, b, a1, a1)
% 23.21/3.35 = { by axiom 30 (ruleD44) }
% 23.21/3.35 fresh99(midp(a1, c, b), true, b, b, a1, a1)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.35 fresh99(midp(a1, c, b), midp(a1, c, b), b, b, a1, a1)
% 23.21/3.35 = { by lemma 39 R->L }
% 23.21/3.35 fresh99(midp(a1, c, b), midp(p, e, b), b, b, a1, a1)
% 23.21/3.35 = { by lemma 40 R->L }
% 23.21/3.35 fresh99(midp(a1, c, b), coll(d, b, c), b, b, a1, a1)
% 23.21/3.35 = { by lemma 39 R->L }
% 23.21/3.35 fresh99(midp(p, e, b), coll(d, b, c), b, b, a1, a1)
% 23.21/3.35 = { by lemma 40 R->L }
% 23.21/3.35 fresh99(coll(d, b, c), coll(d, b, c), b, b, a1, a1)
% 23.21/3.35 = { by axiom 14 (ruleD44) }
% 23.21/3.35 true
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.35 midp(a1, c, b)
% 23.21/3.35 = { by lemma 39 R->L }
% 23.21/3.35 midp(p, e, b)
% 23.21/3.35 = { by lemma 40 R->L }
% 23.21/3.35 coll(d, b, c)
% 23.21/3.35
% 23.21/3.35 Lemma 42: fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(d, b, c), X, Y, Z, W, V, U, T, S) = eqangle(X, Y, V, U, Z, W, T, S).
% 23.21/3.35 Proof:
% 23.21/3.35 fresh131(eqangle(X, Y, Z, W, V, U, T, S), coll(d, b, c), X, Y, Z, W, V, U, T, S)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh131(eqangle(X, Y, Z, W, V, U, T, S), midp(p, e, b), X, Y, Z, W, V, U, T, S)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh131(eqangle(X, Y, Z, W, V, U, T, S), midp(a1, c, b), X, Y, Z, W, V, U, T, S)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 fresh131(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S)
% 23.21/3.35 = { by axiom 37 (ruleD21) }
% 23.21/3.35 eqangle(X, Y, V, U, Z, W, T, S)
% 23.21/3.35
% 23.21/3.35 Lemma 43: fresh104(para(X, Y, Z, W), coll(d, b, c), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 23.21/3.35 Proof:
% 23.21/3.35 fresh104(para(X, Y, Z, W), coll(d, b, c), X, Y, Z, W, V, U)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh104(para(X, Y, Z, W), midp(p, e, b), X, Y, Z, W, V, U)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh104(para(X, Y, Z, W), midp(a1, c, b), X, Y, Z, W, V, U)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 23.21/3.35 = { by axiom 34 (ruleD40) }
% 23.21/3.35 eqangle(X, Y, V, U, Z, W, V, U)
% 23.21/3.35
% 23.21/3.35 Lemma 44: fresh104(X, X, Y, Z, W, V, U, T) = coll(d, b, c).
% 23.21/3.35 Proof:
% 23.21/3.35 fresh104(X, X, Y, Z, W, V, U, T)
% 23.21/3.35 = { by axiom 23 (ruleD40) }
% 23.21/3.35 true
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.35 midp(a1, c, b)
% 23.21/3.35 = { by lemma 39 R->L }
% 23.21/3.35 midp(p, e, b)
% 23.21/3.35 = { by lemma 40 R->L }
% 23.21/3.35 coll(d, b, c)
% 23.21/3.35
% 23.21/3.35 Lemma 45: fresh131(X, X, Y, Z, W, V, U, T, S, X2) = coll(d, b, c).
% 23.21/3.35 Proof:
% 23.21/3.35 fresh131(X, X, Y, Z, W, V, U, T, S, X2)
% 23.21/3.35 = { by axiom 28 (ruleD21) }
% 23.21/3.35 true
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.35 midp(a1, c, b)
% 23.21/3.35 = { by lemma 39 R->L }
% 23.21/3.35 midp(p, e, b)
% 23.21/3.35 = { by lemma 40 R->L }
% 23.21/3.35 coll(d, b, c)
% 23.21/3.35
% 23.21/3.35 Lemma 46: coll(d, b, c) = coll(X, X, Y).
% 23.21/3.35 Proof:
% 23.21/3.35 coll(d, b, c)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 midp(p, e, b)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 midp(a1, c, b)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 true
% 23.21/3.35 = { by axiom 4 (ruleD1) R->L }
% 23.21/3.35 fresh146(coll(d, b, c), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh146(midp(p, e, b), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh146(midp(a1, c, b), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 fresh146(true, coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by axiom 6 (ruleD2) R->L }
% 23.21/3.35 fresh146(fresh133(coll(d, b, c), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh146(fresh133(midp(p, e, b), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh146(fresh133(midp(a1, c, b), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 fresh146(fresh133(true, coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by axiom 8 (ruleD66) R->L }
% 23.21/3.35 fresh146(fresh133(fresh66(coll(d, b, c), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by lemma 40 }
% 23.21/3.35 fresh146(fresh133(fresh66(midp(p, e, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by lemma 39 }
% 23.21/3.35 fresh146(fresh133(fresh66(midp(a1, c, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.35 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.35 fresh146(fresh133(fresh66(true, coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.36 = { by axiom 16 (ruleD73) R->L }
% 23.21/3.36 fresh146(fresh133(fresh66(fresh57(coll(d, b, c), coll(d, b, c), Y, X, Y, X), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 41 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh57(para(a1, a1, b, b), coll(d, b, c), Y, X, Y, X), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh57(para(a1, a1, b, b), midp(p, e, b), Y, X, Y, X), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 39 }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh57(para(a1, a1, b, b), midp(a1, c, b), Y, X, Y, X), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh57(para(a1, a1, b, b), true, Y, X, Y, X), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 38 (ruleD73) R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, a1, a1, b, b), true, Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, a1, a1, b, b), midp(a1, c, b), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 39 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, a1, a1, b, b), midp(p, e, b), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 42 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(eqangle(Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 36 (ruleD19) R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(a1, a1, Y, X, b, b, Y, X), true, a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(a1, a1, Y, X, b, b, Y, X), midp(a1, c, b), a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 39 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(a1, a1, Y, X, b, b, Y, X), midp(p, e, b), a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(a1, a1, Y, X, b, b, Y, X), coll(d, b, c), a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 43 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(fresh104(para(a1, a1, b, b), coll(d, b, c), a1, a1, b, b, Y, X), coll(d, b, c), a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 41 }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(fresh104(coll(d, b, c), coll(d, b, c), a1, a1, b, b, Y, X), coll(d, b, c), a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 44 }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(coll(d, b, c), coll(d, b, c), a1, a1, Y, X, b, b, Y, X), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 27 (ruleD19) }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(true, coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(midp(a1, c, b), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 39 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(midp(p, e, b), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 R->L }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(fresh131(coll(d, b, c), coll(d, b, c), Y, X, a1, a1, Y, X, b, b), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 45 }
% 23.21/3.37 fresh146(fresh133(fresh66(fresh58(coll(d, b, c), coll(d, b, c), Y, X, Y, X, a1, a1, b, b), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 32 (ruleD73) }
% 23.21/3.37 fresh146(fresh133(fresh66(para(Y, X, Y, X), coll(d, b, c), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 }
% 23.21/3.37 fresh146(fresh133(fresh66(para(Y, X, Y, X), midp(p, e, b), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 39 }
% 23.21/3.37 fresh146(fresh133(fresh66(para(Y, X, Y, X), midp(a1, c, b), Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.37 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 26 (ruleD66) }
% 23.21/3.37 fresh146(fresh133(coll(Y, X, X), coll(d, b, c), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 }
% 23.21/3.37 fresh146(fresh133(coll(Y, X, X), midp(p, e, b), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 39 }
% 23.21/3.37 fresh146(fresh133(coll(Y, X, X), midp(a1, c, b), Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.37 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by axiom 22 (ruleD2) }
% 23.21/3.37 fresh146(coll(X, Y, X), coll(d, b, c), X, Y, X)
% 23.21/3.37 = { by lemma 40 }
% 23.21/3.37 fresh146(coll(X, Y, X), midp(p, e, b), X, Y, X)
% 23.21/3.37 = { by lemma 39 }
% 23.21/3.37 fresh146(coll(X, Y, X), midp(a1, c, b), X, Y, X)
% 23.21/3.37 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.37 fresh146(coll(X, Y, X), true, X, Y, X)
% 23.21/3.37 = { by axiom 20 (ruleD1) }
% 23.21/3.37 coll(X, X, Y)
% 23.21/3.37
% 23.21/3.37 Lemma 47: cyclic(c, c, b, X) = coll(d, b, c).
% 23.21/3.37 Proof:
% 23.21/3.37 cyclic(c, c, b, X)
% 23.21/3.37 = { by axiom 12 (ruleD42b) R->L }
% 23.21/3.37 fresh102(coll(d, b, c), coll(d, b, c), c, c, b, X)
% 23.21/3.37 = { by lemma 45 R->L }
% 23.21/3.37 fresh102(fresh131(coll(d, b, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.37 = { by lemma 44 R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(coll(d, b, c), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(midp(p, e, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(midp(a1, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh131(fresh104(true, coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 11 (ruleD4) R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(coll(d, b, c), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(midp(p, e, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(midp(a1, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(true, coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 15 (ruleD63) R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(coll(d, b, c), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(midp(p, e, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(midp(a1, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(true, coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 5 (ruleD11) R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(fresh144(coll(d, b, c), coll(d, b, c), b, c, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(fresh144(midp(p, e, b), coll(d, b, c), b, c, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(fresh144(midp(a1, c, b), coll(d, b, c), b, c, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(fresh144(midp(a1, c, b), midp(p, e, b), b, c, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(fresh144(midp(a1, c, b), midp(a1, c, b), b, c, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(fresh144(midp(a1, c, b), true, b, c, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 21 (ruleD11) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(midp(a1, b, c), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(midp(a1, b, c), midp(p, e, b), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(midp(a1, b, c), midp(a1, c, b), b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh69(midp(a1, b, c), true, b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 31 (ruleD63) R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh70(midp(a1, c, b), true, b, c, c, b, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh70(midp(a1, c, b), midp(a1, c, b), b, c, c, b, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh70(midp(a1, c, b), midp(p, e, b), b, c, c, b, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh70(midp(a1, c, b), coll(d, b, c), b, c, c, b, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh70(midp(p, e, b), coll(d, b, c), b, c, c, b, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 R->L }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(fresh70(coll(d, b, c), coll(d, b, c), b, c, c, b, a1), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 19 (ruleD63) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(para(b, c, c, b), coll(d, b, c), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(para(b, c, c, b), midp(p, e, b), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(para(b, c, c, b), midp(a1, c, b), b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh131(fresh104(fresh105(para(b, c, c, b), true, b, c, c, b), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 29 (ruleD4) }
% 23.21/3.38 fresh102(fresh131(fresh104(para(b, c, b, c), coll(d, b, c), b, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 43 }
% 23.21/3.38 fresh102(fresh131(eqangle(b, c, X, c, b, c, X, c), coll(d, b, c), b, c, X, c, b, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 42 }
% 23.21/3.38 fresh102(eqangle(b, c, b, c, X, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by axiom 24 (ruleD50) R->L }
% 23.21/3.38 fresh102(fresh91(Y, Y, b, c, c, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.38 = { by lemma 40 }
% 23.21/3.38 fresh102(fresh91(Y, Y, b, c, c, X, c), midp(p, e, b), c, c, b, X)
% 23.21/3.38 = { by lemma 39 }
% 23.21/3.38 fresh102(fresh91(Y, Y, b, c, c, X, c), midp(a1, c, b), c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.38 fresh102(fresh91(Y, Y, b, c, c, X, c), true, c, c, b, X)
% 23.21/3.38 = { by axiom 24 (ruleD50) }
% 23.21/3.38 fresh102(eqangle(b, c, b, c, X, c, X, c), true, c, c, b, X)
% 23.21/3.38 = { by axiom 35 (ruleD42b) }
% 23.21/3.38 fresh101(coll(b, X, c), true, c, c, b, X)
% 23.21/3.38 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.38 fresh101(coll(b, X, c), midp(a1, c, b), c, c, b, X)
% 23.21/3.38 = { by lemma 39 R->L }
% 23.21/3.38 fresh101(coll(b, X, c), midp(p, e, b), c, c, b, X)
% 23.21/3.38 = { by lemma 40 R->L }
% 23.21/3.39 fresh101(coll(b, X, c), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 10 (ruleD3) R->L }
% 23.21/3.39 fresh101(fresh120(coll(d, b, c), coll(d, b, c), c, c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 46 }
% 23.21/3.39 fresh101(fresh120(coll(c, c, X), coll(d, b, c), c, c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 40 }
% 23.21/3.39 fresh101(fresh120(coll(c, c, X), midp(p, e, b), c, c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 39 }
% 23.21/3.39 fresh101(fresh120(coll(c, c, X), midp(a1, c, b), c, c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.39 fresh101(fresh120(coll(c, c, X), true, c, c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 25 (ruleD3) }
% 23.21/3.39 fresh101(fresh119(coll(c, c, b), true, c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.39 fresh101(fresh119(coll(c, c, b), midp(a1, c, b), c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 39 R->L }
% 23.21/3.39 fresh101(fresh119(coll(c, c, b), midp(p, e, b), c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 40 R->L }
% 23.21/3.39 fresh101(fresh119(coll(c, c, b), coll(d, b, c), c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 46 R->L }
% 23.21/3.39 fresh101(fresh119(coll(d, b, c), coll(d, b, c), c, b, X), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 7 (ruleD3) }
% 23.21/3.39 fresh101(true, coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.39 fresh101(midp(a1, c, b), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 39 R->L }
% 23.21/3.39 fresh101(midp(p, e, b), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by lemma 40 R->L }
% 23.21/3.39 fresh101(coll(d, b, c), coll(d, b, c), c, c, b, X)
% 23.21/3.39 = { by axiom 13 (ruleD42b) }
% 23.21/3.39 true
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.39 midp(a1, c, b)
% 23.21/3.39 = { by lemma 39 R->L }
% 23.21/3.39 midp(p, e, b)
% 23.21/3.39 = { by lemma 40 R->L }
% 23.21/3.39 coll(d, b, c)
% 23.21/3.39
% 23.21/3.39 Lemma 48: fresh137(cyclic(X, Y, Z, W), coll(d, b, c), X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), coll(d, b, c), Y, Z, V, W).
% 23.21/3.39 Proof:
% 23.21/3.39 fresh137(cyclic(X, Y, Z, W), coll(d, b, c), X, Y, Z, V, W)
% 23.21/3.39 = { by lemma 40 }
% 23.21/3.39 fresh137(cyclic(X, Y, Z, W), midp(p, e, b), X, Y, Z, V, W)
% 23.21/3.39 = { by lemma 39 }
% 23.21/3.39 fresh137(cyclic(X, Y, Z, W), midp(a1, c, b), X, Y, Z, V, W)
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.39 fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W)
% 23.21/3.39 = { by axiom 33 (ruleD17) }
% 23.21/3.39 fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W)
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.39 fresh136(cyclic(X, Y, Z, V), midp(a1, c, b), Y, Z, V, W)
% 23.21/3.39 = { by lemma 39 R->L }
% 23.21/3.39 fresh136(cyclic(X, Y, Z, V), midp(p, e, b), Y, Z, V, W)
% 23.21/3.39 = { by lemma 40 R->L }
% 23.21/3.39 fresh136(cyclic(X, Y, Z, V), coll(d, b, c), Y, Z, V, W)
% 23.21/3.39
% 23.21/3.39 Lemma 49: fresh136(X, X, Y, Z, W, V) = coll(d, b, c).
% 23.21/3.39 Proof:
% 23.21/3.39 fresh136(X, X, Y, Z, W, V)
% 23.21/3.39 = { by axiom 9 (ruleD17) }
% 23.21/3.39 true
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) R->L }
% 23.21/3.39 midp(a1, c, b)
% 23.21/3.39 = { by lemma 39 R->L }
% 23.21/3.39 midp(p, e, b)
% 23.21/3.39 = { by lemma 40 R->L }
% 23.21/3.39 coll(d, b, c)
% 23.21/3.39
% 23.21/3.39 Lemma 50: cyclic(c, b, X, Y) = coll(d, b, c).
% 23.21/3.39 Proof:
% 23.21/3.39 cyclic(c, b, X, Y)
% 23.21/3.39 = { by axiom 17 (ruleD17) R->L }
% 23.21/3.39 fresh137(coll(d, b, c), coll(d, b, c), c, c, b, X, Y)
% 23.21/3.39 = { by lemma 47 R->L }
% 23.21/3.39 fresh137(cyclic(c, c, b, Y), coll(d, b, c), c, c, b, X, Y)
% 23.21/3.39 = { by lemma 48 }
% 23.21/3.39 fresh136(cyclic(c, c, b, X), coll(d, b, c), c, b, X, Y)
% 23.21/3.39 = { by lemma 47 }
% 23.21/3.39 fresh136(coll(d, b, c), coll(d, b, c), c, b, X, Y)
% 23.21/3.39 = { by lemma 49 }
% 23.21/3.39 coll(d, b, c)
% 23.21/3.39
% 23.21/3.39 Lemma 51: cyclic(b, X, Y, Z) = coll(d, b, c).
% 23.21/3.39 Proof:
% 23.21/3.39 cyclic(b, X, Y, Z)
% 23.21/3.39 = { by axiom 17 (ruleD17) R->L }
% 23.21/3.39 fresh137(coll(d, b, c), coll(d, b, c), c, b, X, Y, Z)
% 23.21/3.39 = { by lemma 50 R->L }
% 23.21/3.39 fresh137(cyclic(c, b, X, Z), coll(d, b, c), c, b, X, Y, Z)
% 23.21/3.39 = { by lemma 48 }
% 23.21/3.39 fresh136(cyclic(c, b, X, Y), coll(d, b, c), b, X, Y, Z)
% 23.21/3.39 = { by lemma 50 }
% 23.21/3.39 fresh136(coll(d, b, c), coll(d, b, c), b, X, Y, Z)
% 23.21/3.39 = { by lemma 49 }
% 23.21/3.39 coll(d, b, c)
% 23.21/3.39
% 23.21/3.39 Goal 1 (exemplo6GDDFULL012003_11): cyclic(p, q, h, d) = true.
% 23.21/3.39 Proof:
% 23.21/3.39 cyclic(p, q, h, d)
% 23.21/3.39 = { by axiom 17 (ruleD17) R->L }
% 23.21/3.39 fresh137(coll(d, b, c), coll(d, b, c), b, p, q, h, d)
% 23.21/3.39 = { by lemma 51 R->L }
% 23.21/3.39 fresh137(cyclic(b, p, q, d), coll(d, b, c), b, p, q, h, d)
% 23.21/3.39 = { by lemma 48 }
% 23.21/3.39 fresh136(cyclic(b, p, q, h), coll(d, b, c), p, q, h, d)
% 23.21/3.39 = { by lemma 51 }
% 23.21/3.39 fresh136(coll(d, b, c), coll(d, b, c), p, q, h, d)
% 23.21/3.39 = { by lemma 49 }
% 23.21/3.39 coll(d, b, c)
% 23.21/3.39 = { by lemma 40 }
% 23.21/3.39 midp(p, e, b)
% 23.21/3.39 = { by lemma 39 }
% 23.21/3.39 midp(a1, c, b)
% 23.21/3.39 = { by axiom 1 (exemplo6GDDFULL012003_10) }
% 23.21/3.39 true
% 23.21/3.39 % SZS output end Proof
% 23.21/3.39
% 23.21/3.39 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------