TSTP Solution File: GEO642+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO642+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 : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:29:40 EDT 2023
% Result : Theorem 14.06s 2.15s
% Output : Proof 14.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO642+1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 30 00:34:23 EDT 2023
% 0.12/0.34 % CPUTime :
% 14.06/2.15 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 14.06/2.15
% 14.06/2.15 % SZS status Theorem
% 14.06/2.15
% 14.18/2.18 % SZS output start Proof
% 14.18/2.18 Take the following subset of the input axioms:
% 14.18/2.18 fof(exemplo6GDDFULL81109108, conjecture, ![A, B, C, D, E, F, O, P, G, NWPNT1, NWPNT2, NWPNT3, NWPNT4, NWPNT5, NWPNT6, NWPNT7, NWPNT8]: ((midp(O, B, A) & (circle(O, A, NWPNT1, NWPNT2) & (circle(O, A, C, NWPNT3) & (circle(O, A, P, NWPNT4) & (circle(C, B, NWPNT5, NWPNT6) & (circle(O, A, D, NWPNT7) & (circle(C, B, D, NWPNT8) & (coll(G, B, P) & (coll(G, A, D) & (coll(E, A, C) & (coll(E, B, P) & (coll(F, A, D) & coll(F, C, P))))))))))))) => perp(E, F, A, D))).
% 14.18/2.18 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 14.18/2.18 fof(ruleD10, axiom, ![B2, C2, E2, F2, A2_2, D2]: ((para(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => perp(A2_2, B2, E2, F2))).
% 14.18/2.18 fof(ruleD12, axiom, ![B2, C2, A2_2, O2]: ((cong(O2, A2_2, O2, B2) & cong(O2, A2_2, O2, C2)) => circle(O2, A2_2, B2, C2))).
% 14.18/2.18 fof(ruleD14, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, B2, D2, C2))).
% 14.18/2.18 fof(ruleD15, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 14.18/2.18 fof(ruleD16, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 14.18/2.18 fof(ruleD17, axiom, ![B2, C2, E2, A2_2, D2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 14.18/2.18 fof(ruleD19, axiom, ![Q, U, V, P2, B2, C2, A2_2, D2]: (eqangle(A2_2, B2, C2, D2, P2, Q, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P2, Q))).
% 14.18/2.18 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 14.18/2.18 fof(ruleD3, axiom, ![B2, C2, A2_2, D2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 14.18/2.18 fof(ruleD39, axiom, ![P2, B2, C2, A2_2, D2, Q2]: (eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2) => para(A2_2, B2, C2, D2))).
% 14.18/2.18 fof(ruleD40, axiom, ![P2, B2, C2, A2_2, D2, Q2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 14.18/2.18 fof(ruleD42b, axiom, ![P2, B2, A2_2, Q2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 14.18/2.18 fof(ruleD43, axiom, ![R, P2, B2, C2, A2_2, Q2]: ((cyclic(A2_2, B2, C2, P2) & (cyclic(A2_2, B2, C2, Q2) & (cyclic(A2_2, B2, C2, R) & eqangle(C2, A2_2, C2, B2, R, P2, R, Q2)))) => cong(A2_2, B2, P2, Q2))).
% 14.18/2.18 fof(ruleD53, axiom, ![B2, C2, A2_2, O2]: ((circle(O2, A2_2, B2, C2) & coll(O2, A2_2, C2)) => perp(A2_2, B2, B2, C2))).
% 14.18/2.18 fof(ruleD56, axiom, ![P2, B2, A2_2, Q2]: ((cong(A2_2, P2, B2, P2) & cong(A2_2, Q2, B2, Q2)) => perp(A2_2, B2, P2, Q2))).
% 14.18/2.18 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 14.18/2.18 fof(ruleD68, axiom, ![B2, C2, A2_2]: (midp(A2_2, B2, C2) => cong(A2_2, B2, A2_2, C2))).
% 14.18/2.18 fof(ruleD69, axiom, ![B2, C2, A2_2]: (midp(A2_2, B2, C2) => coll(A2_2, B2, C2))).
% 14.18/2.18 fof(ruleD7, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(A2_2, B2, D2, C2))).
% 14.18/2.18 fof(ruleD8, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 14.18/2.18 fof(ruleD9, axiom, ![B2, C2, E2, F2, A2_2, D2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => para(A2_2, B2, E2, F2))).
% 14.18/2.19 fof(ruleX15, axiom, ![B2, C2, E2, F2, A2_2]: ?[P2]: ((perp(A2_2, C2, C2, B2) & coll(B2, E2, F2)) => (coll(P2, E2, F2) & perp(P2, A2_2, E2, F2)))).
% 14.18/2.19
% 14.18/2.19 Now clausify the problem and encode Horn clauses using encoding 3 of
% 14.18/2.19 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 14.18/2.19 We repeatedly replace C & s=t => u=v by the two clauses:
% 14.18/2.19 fresh(y, y, x1...xn) = u
% 14.18/2.19 C => fresh(s, t, x1...xn) = v
% 14.18/2.19 where fresh is a fresh function symbol and x1..xn are the free
% 14.18/2.19 variables of u and v.
% 14.18/2.19 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 14.18/2.19 input problem has no model of domain size 1).
% 14.18/2.19
% 14.18/2.19 The encoding turns the above axioms into the following unit equations and goals:
% 14.18/2.19
% 14.18/2.19 Axiom 1 (exemplo6GDDFULL81109108_6): midp(o, b, a) = true.
% 14.18/2.19 Axiom 2 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 3 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 4 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 5 (ruleD53): fresh85(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 6 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 7 (ruleD68): fresh63(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 8 (ruleD69): fresh62(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 9 (ruleX15_1): fresh32(X, X, Y, Z, W) = true.
% 14.18/2.19 Axiom 10 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 11 (ruleD10): fresh145(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 12 (ruleD12): fresh143(X, X, Y, Z, W, V) = circle(V, Y, Z, W).
% 14.18/2.19 Axiom 13 (ruleD12): fresh142(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 14 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 15 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 16 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 17 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 18 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 14.18/2.19 Axiom 19 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 20 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 14.18/2.19 Axiom 21 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 22 (ruleD53): fresh86(X, X, Y, Z, W, V) = perp(Y, Z, Z, W).
% 14.18/2.19 Axiom 23 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 14.18/2.19 Axiom 24 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 25 (ruleD7): fresh61(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 26 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 27 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 14.18/2.19 Axiom 28 (ruleX15_1): fresh33(X, X, Y, Z, W, V) = perp(p3(Y, W, V), Y, W, V).
% 14.18/2.19 Axiom 29 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 14.18/2.19 Axiom 30 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 14.18/2.19 Axiom 31 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 14.18/2.19 Axiom 32 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 14.18/2.19 Axiom 33 (ruleD68): fresh63(midp(X, Y, Z), true, X, Y, Z) = cong(X, Y, X, Z).
% 14.18/2.19 Axiom 34 (ruleD69): fresh62(midp(X, Y, Z), true, X, Y, Z) = coll(X, Y, Z).
% 14.18/2.19 Axiom 35 (ruleD10): fresh147(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
% 14.18/2.19 Axiom 36 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 14.18/2.19 Axiom 37 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 14.18/2.19 Axiom 38 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 14.18/2.19 Axiom 39 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 14.18/2.19 Axiom 40 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 14.18/2.19 Axiom 41 (ruleD12): fresh143(cong(X, Y, X, Z), true, Y, W, Z, X) = fresh142(cong(X, Y, X, W), true, Y, W, Z, X).
% 14.18/2.19 Axiom 42 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 14.18/2.19 Axiom 43 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 14.18/2.19 Axiom 44 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 14.18/2.19 Axiom 45 (ruleD53): fresh86(circle(X, Y, Z, W), true, Y, Z, W, X) = fresh85(coll(X, Y, W), true, Y, Z, W).
% 14.18/2.19 Axiom 46 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 14.18/2.19 Axiom 47 (ruleD7): fresh61(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(X, Y, W, Z).
% 14.18/2.19 Axiom 48 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 14.18/2.19 Axiom 49 (ruleX15_1): fresh33(perp(X, Y, Y, Z), true, X, Z, W, V) = fresh32(coll(Z, W, V), true, X, W, V).
% 14.18/2.19 Axiom 50 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 14.18/2.19 Axiom 51 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 14.18/2.19 Axiom 52 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 14.18/2.19 Axiom 53 (ruleD10): fresh147(perp(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh145(para(V, U, X, Y), true, V, U, Z, W).
% 14.18/2.19 Axiom 54 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 14.18/2.19 Axiom 55 (ruleD9): fresh51(perp(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh50(perp(V, U, X, Y), true, V, U, Z, W).
% 14.18/2.19 Axiom 56 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 14.18/2.19 Axiom 57 (ruleD42b): fresh102(eqangle(X, Y, X, Z, W, Y, W, Z), true, Y, Z, X, W) = fresh101(coll(X, W, Z), true, Y, Z, X, W).
% 14.18/2.19 Axiom 58 (ruleD43): fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W) = fresh184(cyclic(Y, Z, X, W), true, Y, Z, X, V, U).
% 14.18/2.19 Axiom 59 (ruleD19): fresh134(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = eqangle(Z, W, X, Y, T, S, V, U).
% 14.18/2.19
% 14.18/2.19 Lemma 60: cong(o, b, o, a) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 cong(o, b, o, a)
% 14.18/2.19 = { by axiom 33 (ruleD68) R->L }
% 14.18/2.19 fresh63(midp(o, b, a), true, o, b, a)
% 14.18/2.19 = { by axiom 1 (exemplo6GDDFULL81109108_6) }
% 14.18/2.19 fresh63(true, true, o, b, a)
% 14.18/2.19 = { by axiom 7 (ruleD68) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 61: perp(b, a, a, a) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 perp(b, a, a, a)
% 14.18/2.19 = { by axiom 22 (ruleD53) R->L }
% 14.18/2.19 fresh86(true, true, b, a, a, o)
% 14.18/2.19 = { by axiom 13 (ruleD12) R->L }
% 14.18/2.19 fresh86(fresh142(true, true, b, a, a, o), true, b, a, a, o)
% 14.18/2.19 = { by lemma 60 R->L }
% 14.18/2.19 fresh86(fresh142(cong(o, b, o, a), true, b, a, a, o), true, b, a, a, o)
% 14.18/2.19 = { by axiom 41 (ruleD12) R->L }
% 14.18/2.19 fresh86(fresh143(cong(o, b, o, a), true, b, a, a, o), true, b, a, a, o)
% 14.18/2.19 = { by lemma 60 }
% 14.18/2.19 fresh86(fresh143(true, true, b, a, a, o), true, b, a, a, o)
% 14.18/2.19 = { by axiom 12 (ruleD12) }
% 14.18/2.19 fresh86(circle(o, b, a, a), true, b, a, a, o)
% 14.18/2.19 = { by axiom 45 (ruleD53) }
% 14.18/2.19 fresh85(coll(o, b, a), true, b, a, a)
% 14.18/2.19 = { by axiom 34 (ruleD69) R->L }
% 14.18/2.19 fresh85(fresh62(midp(o, b, a), true, o, b, a), true, b, a, a)
% 14.18/2.19 = { by axiom 1 (exemplo6GDDFULL81109108_6) }
% 14.18/2.19 fresh85(fresh62(true, true, o, b, a), true, b, a, a)
% 14.18/2.19 = { by axiom 8 (ruleD69) }
% 14.18/2.19 fresh85(true, true, b, a, a)
% 14.18/2.19 = { by axiom 5 (ruleD53) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 62: perp(a, a, b, a) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 perp(a, a, b, a)
% 14.18/2.19 = { by axiom 48 (ruleD8) R->L }
% 14.18/2.19 fresh52(perp(b, a, a, a), true, b, a, a, a)
% 14.18/2.19 = { by lemma 61 }
% 14.18/2.19 fresh52(true, true, b, a, a, a)
% 14.18/2.19 = { by axiom 26 (ruleD8) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 63: eqangle(X, Y, a, a, X, Y, a, a) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 eqangle(X, Y, a, a, X, Y, a, a)
% 14.18/2.19 = { by axiom 59 (ruleD19) R->L }
% 14.18/2.19 fresh134(eqangle(a, a, X, Y, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by axiom 54 (ruleD40) R->L }
% 14.18/2.19 fresh134(fresh104(para(a, a, a, a), true, a, a, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by axiom 39 (ruleD9) R->L }
% 14.18/2.19 fresh134(fresh104(fresh51(true, true, a, a, b, a, a, a), true, a, a, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by lemma 61 R->L }
% 14.18/2.19 fresh134(fresh104(fresh51(perp(b, a, a, a), true, a, a, b, a, a, a), true, a, a, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by axiom 55 (ruleD9) }
% 14.18/2.19 fresh134(fresh104(fresh50(perp(a, a, b, a), true, a, a, a, a), true, a, a, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by lemma 62 }
% 14.18/2.19 fresh134(fresh104(fresh50(true, true, a, a, a, a), true, a, a, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by axiom 27 (ruleD9) }
% 14.18/2.19 fresh134(fresh104(true, true, a, a, a, a, X, Y), true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by axiom 37 (ruleD40) }
% 14.18/2.19 fresh134(true, true, a, a, X, Y, a, a, X, Y)
% 14.18/2.19 = { by axiom 52 (ruleD19) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 64: para(X, Y, X, Y) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 para(X, Y, X, Y)
% 14.18/2.19 = { by axiom 56 (ruleD39) R->L }
% 14.18/2.19 fresh106(eqangle(X, Y, a, a, X, Y, a, a), true, X, Y, X, Y)
% 14.18/2.19 = { by lemma 63 }
% 14.18/2.19 fresh106(true, true, X, Y, X, Y)
% 14.18/2.19 = { by axiom 19 (ruleD39) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 65: coll(X, X, Y) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 coll(X, X, Y)
% 14.18/2.19 = { by axiom 30 (ruleD1) R->L }
% 14.18/2.19 fresh146(coll(X, Y, X), true, X, Y, X)
% 14.18/2.19 = { by axiom 32 (ruleD2) R->L }
% 14.18/2.19 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 14.18/2.19 = { by axiom 38 (ruleD66) R->L }
% 14.18/2.19 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 14.18/2.19 = { by lemma 64 }
% 14.18/2.19 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 14.18/2.19 = { by axiom 6 (ruleD66) }
% 14.18/2.19 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 14.18/2.19 = { by axiom 3 (ruleD2) }
% 14.18/2.19 fresh146(true, true, X, Y, X)
% 14.18/2.19 = { by axiom 2 (ruleD1) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 66: cyclic(a, a, a, X) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 cyclic(a, a, a, X)
% 14.18/2.19 = { by axiom 42 (ruleD14) R->L }
% 14.18/2.19 fresh140(cyclic(a, a, X, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 43 (ruleD15) R->L }
% 14.18/2.19 fresh140(fresh139(cyclic(a, X, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 44 (ruleD16) R->L }
% 14.18/2.19 fresh140(fresh139(fresh138(cyclic(X, a, a, a), true, X, a, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 20 (ruleD42b) R->L }
% 14.18/2.19 fresh140(fresh139(fresh138(fresh102(true, true, X, a, a, a), true, X, a, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by lemma 63 R->L }
% 14.18/2.19 fresh140(fresh139(fresh138(fresh102(eqangle(a, X, a, a, a, X, a, a), true, X, a, a, a), true, X, a, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 57 (ruleD42b) }
% 14.18/2.19 fresh140(fresh139(fresh138(fresh101(coll(a, a, a), true, X, a, a, a), true, X, a, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by lemma 65 }
% 14.18/2.19 fresh140(fresh139(fresh138(fresh101(true, true, X, a, a, a), true, X, a, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 21 (ruleD42b) }
% 14.18/2.19 fresh140(fresh139(fresh138(true, true, X, a, a, a), true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 16 (ruleD16) }
% 14.18/2.19 fresh140(fresh139(true, true, a, X, a, a), true, a, a, X, a)
% 14.18/2.19 = { by axiom 15 (ruleD15) }
% 14.18/2.19 fresh140(true, true, a, a, X, a)
% 14.18/2.19 = { by axiom 14 (ruleD14) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 67: cyclic(a, a, X, Y) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 cyclic(a, a, X, Y)
% 14.18/2.19 = { by axiom 31 (ruleD17) R->L }
% 14.18/2.19 fresh137(true, true, a, a, a, X, Y)
% 14.18/2.19 = { by lemma 66 R->L }
% 14.18/2.19 fresh137(cyclic(a, a, a, Y), true, a, a, a, X, Y)
% 14.18/2.19 = { by axiom 51 (ruleD17) }
% 14.18/2.19 fresh136(cyclic(a, a, a, X), true, a, a, X, Y)
% 14.18/2.19 = { by lemma 66 }
% 14.18/2.19 fresh136(true, true, a, a, X, Y)
% 14.18/2.19 = { by axiom 17 (ruleD17) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 68: cyclic(a, X, Y, Z) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 cyclic(a, X, Y, Z)
% 14.18/2.19 = { by axiom 31 (ruleD17) R->L }
% 14.18/2.19 fresh137(true, true, a, a, X, Y, Z)
% 14.18/2.19 = { by lemma 67 R->L }
% 14.18/2.19 fresh137(cyclic(a, a, X, Z), true, a, a, X, Y, Z)
% 14.18/2.19 = { by axiom 51 (ruleD17) }
% 14.18/2.19 fresh136(cyclic(a, a, X, Y), true, a, X, Y, Z)
% 14.18/2.19 = { by lemma 67 }
% 14.18/2.19 fresh136(true, true, a, X, Y, Z)
% 14.18/2.19 = { by axiom 17 (ruleD17) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 69: cyclic(X, Y, Z, W) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 cyclic(X, Y, Z, W)
% 14.18/2.19 = { by axiom 31 (ruleD17) R->L }
% 14.18/2.19 fresh137(true, true, a, X, Y, Z, W)
% 14.18/2.19 = { by lemma 68 R->L }
% 14.18/2.19 fresh137(cyclic(a, X, Y, W), true, a, X, Y, Z, W)
% 14.18/2.19 = { by axiom 51 (ruleD17) }
% 14.18/2.19 fresh136(cyclic(a, X, Y, Z), true, X, Y, Z, W)
% 14.18/2.19 = { by lemma 68 }
% 14.18/2.19 fresh136(true, true, X, Y, Z, W)
% 14.18/2.19 = { by axiom 17 (ruleD17) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 70: cong(X, Y, X, Y) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 cong(X, Y, X, Y)
% 14.18/2.19 = { by axiom 29 (ruleD43) R->L }
% 14.18/2.19 fresh183(true, true, X, Y, Z, X, Y)
% 14.18/2.19 = { by lemma 69 R->L }
% 14.18/2.19 fresh183(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y)
% 14.18/2.19 = { by axiom 50 (ruleD43) R->L }
% 14.18/2.19 fresh182(true, true, X, Y, Z, X, Y, Z)
% 14.18/2.19 = { by axiom 37 (ruleD40) R->L }
% 14.18/2.19 fresh182(fresh104(true, true, Z, X, Z, X, Z, Y), true, X, Y, Z, X, Y, Z)
% 14.18/2.19 = { by lemma 64 R->L }
% 14.18/2.19 fresh182(fresh104(para(Z, X, Z, X), true, Z, X, Z, X, Z, Y), true, X, Y, Z, X, Y, Z)
% 14.18/2.19 = { by axiom 54 (ruleD40) }
% 14.18/2.19 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, X, Y, Z)
% 14.18/2.19 = { by axiom 58 (ruleD43) }
% 14.18/2.19 fresh184(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y)
% 14.18/2.19 = { by lemma 69 }
% 14.18/2.19 fresh184(true, true, X, Y, Z, X, Y)
% 14.18/2.19 = { by axiom 40 (ruleD43) }
% 14.18/2.19 fresh185(cyclic(X, Y, Z, X), true, X, Y, X, Y)
% 14.18/2.19 = { by lemma 69 }
% 14.18/2.19 fresh185(true, true, X, Y, X, Y)
% 14.18/2.19 = { by axiom 10 (ruleD43) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Lemma 71: perp(X, X, Y, Z) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 perp(X, X, Y, Z)
% 14.18/2.19 = { by axiom 23 (ruleD56) R->L }
% 14.18/2.19 fresh80(true, true, X, X, Y, Z)
% 14.18/2.19 = { by lemma 70 R->L }
% 14.18/2.19 fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
% 14.18/2.19 = { by axiom 46 (ruleD56) }
% 14.18/2.19 fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
% 14.18/2.19 = { by lemma 70 }
% 14.18/2.19 fresh79(true, true, X, X, Y, Z)
% 14.18/2.19 = { by axiom 24 (ruleD56) }
% 14.18/2.19 true
% 14.18/2.19
% 14.18/2.19 Goal 1 (exemplo6GDDFULL81109108_13): perp(e, f, a, d) = true.
% 14.18/2.19 Proof:
% 14.18/2.19 perp(e, f, a, d)
% 14.18/2.19 = { by axiom 35 (ruleD10) R->L }
% 14.18/2.19 fresh147(true, true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.19 = { by axiom 9 (ruleX15_1) R->L }
% 14.18/2.19 fresh147(fresh32(true, true, a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.19 = { by axiom 4 (ruleD3) R->L }
% 14.18/2.19 fresh147(fresh32(fresh119(true, true, d, b, a), true, a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.19 = { by lemma 65 R->L }
% 14.18/2.19 fresh147(fresh32(fresh119(coll(d, d, b), true, d, b, a), true, a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.19 = { by axiom 36 (ruleD3) R->L }
% 14.18/2.19 fresh147(fresh32(fresh120(coll(d, d, a), true, d, d, b, a), true, a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.19 = { by lemma 65 }
% 14.18/2.20 fresh147(fresh32(fresh120(true, true, d, d, b, a), true, a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by axiom 18 (ruleD3) }
% 14.18/2.20 fresh147(fresh32(coll(b, a, d), true, a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by axiom 49 (ruleX15_1) R->L }
% 14.18/2.20 fresh147(fresh33(perp(a, a, a, b), true, a, b, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by axiom 47 (ruleD7) R->L }
% 14.18/2.20 fresh147(fresh33(fresh61(perp(a, a, b, a), true, a, a, b, a), true, a, b, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by lemma 62 }
% 14.18/2.20 fresh147(fresh33(fresh61(true, true, a, a, b, a), true, a, b, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by axiom 25 (ruleD7) }
% 14.18/2.20 fresh147(fresh33(true, true, a, b, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by axiom 28 (ruleX15_1) }
% 14.18/2.20 fresh147(perp(p3(a, a, d), a, a, d), true, e, f, p3(a, a, d), a, a, d)
% 14.18/2.20 = { by axiom 53 (ruleD10) }
% 14.18/2.20 fresh145(para(e, f, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by axiom 39 (ruleD9) R->L }
% 14.18/2.20 fresh145(fresh51(true, true, e, f, X, X, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by lemma 71 R->L }
% 14.18/2.20 fresh145(fresh51(perp(X, X, p3(a, a, d), a), true, e, f, X, X, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by axiom 55 (ruleD9) }
% 14.18/2.20 fresh145(fresh50(perp(e, f, X, X), true, e, f, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by axiom 48 (ruleD8) R->L }
% 14.18/2.20 fresh145(fresh50(fresh52(perp(X, X, e, f), true, X, X, e, f), true, e, f, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by lemma 71 }
% 14.18/2.20 fresh145(fresh50(fresh52(true, true, X, X, e, f), true, e, f, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by axiom 26 (ruleD8) }
% 14.18/2.20 fresh145(fresh50(true, true, e, f, p3(a, a, d), a), true, e, f, a, d)
% 14.18/2.20 = { by axiom 27 (ruleD9) }
% 14.18/2.20 fresh145(true, true, e, f, a, d)
% 14.18/2.20 = { by axiom 11 (ruleD10) }
% 14.18/2.20 true
% 14.18/2.20 % SZS output end Proof
% 14.18/2.20
% 14.18/2.20 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------