TSTP Solution File: GEO605+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO605+1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:29:30 EDT 2023
% Result : Theorem 12.44s 2.05s
% Output : Proof 12.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO605+1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.17/0.35 % Computer : n026.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Aug 29 23:40:50 EDT 2023
% 0.17/0.35 % CPUTime :
% 12.44/2.05 Command-line arguments: --no-flatten-goal
% 12.44/2.05
% 12.44/2.05 % SZS status Theorem
% 12.44/2.06
% 12.44/2.10 % SZS output start Proof
% 12.44/2.10 Take the following subset of the input axioms:
% 12.44/2.10 fof(exemplo6GDDFULL618067, conjecture, ![A, B, C, M, O, I, IC, IB, MIDPNT1, MIDPNT2, MIDPNT3]: ((eqangle(I, M, M, B, I, M, M, C) & (eqangle(I, B, B, C, I, B, B, M) & (eqangle(I, C, C, M, I, C, C, B) & (perp(B, I, B, IC) & (perp(C, I, C, IB) & (coll(IC, C, I) & (coll(IB, B, I) & (midp(A, IB, IC) & (midp(MIDPNT1, B, I) & (perp(B, I, MIDPNT1, O) & (midp(MIDPNT2, B, C) & (perp(B, C, MIDPNT2, O) & (midp(MIDPNT3, I, C) & perp(I, C, MIDPNT3, O)))))))))))))) => perp(A, B, B, O))).
% 12.44/2.10 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 12.44/2.10 fof(ruleD10, axiom, ![D, E, F, B2, C2, A2_2]: ((para(A2_2, B2, C2, D) & perp(C2, D, E, F)) => perp(A2_2, B2, E, F))).
% 12.44/2.10 fof(ruleD17, axiom, ![B2, C2, D2, E2, A2_2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 12.44/2.10 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))).
% 12.44/2.10 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 12.44/2.10 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))).
% 12.44/2.10 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 12.44/2.10 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))).
% 12.44/2.10 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))).
% 12.44/2.10 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))).
% 12.44/2.10 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))).
% 12.44/2.10 fof(ruleD44, axiom, ![B2, C2, E2, F2, A2_2]: ((midp(E2, A2_2, B2) & midp(F2, A2_2, C2)) => para(E2, F2, B2, C2))).
% 12.44/2.10 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))).
% 12.44/2.10 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 12.44/2.10 fof(ruleD67, axiom, ![B2, C2, A2_2]: ((cong(A2_2, B2, A2_2, C2) & coll(A2_2, B2, C2)) => midp(A2_2, B2, C2))).
% 12.44/2.10 fof(ruleD73, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & para(P2, Q2, U2, V2)) => para(A2_2, B2, C2, D2))).
% 12.44/2.10 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 12.44/2.10 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))).
% 12.44/2.10
% 12.44/2.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.44/2.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.44/2.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.44/2.10 fresh(y, y, x1...xn) = u
% 12.44/2.10 C => fresh(s, t, x1...xn) = v
% 12.44/2.10 where fresh is a fresh function symbol and x1..xn are the free
% 12.44/2.10 variables of u and v.
% 12.44/2.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.44/2.10 input problem has no model of domain size 1).
% 12.44/2.10
% 12.44/2.10 The encoding turns the above axioms into the following unit equations and goals:
% 12.44/2.10
% 12.44/2.10 Axiom 1 (exemplo6GDDFULL618067_9): midp(midpnt2, b, c) = true.
% 12.44/2.10 Axiom 2 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 12.44/2.10 Axiom 3 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 12.44/2.10 Axiom 4 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 12.44/2.10 Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 12.44/2.10 Axiom 6 (ruleD67): fresh65(X, X, Y, Z, W) = midp(Y, Z, W).
% 12.44/2.10 Axiom 7 (ruleD67): fresh64(X, X, Y, Z, W) = true.
% 12.44/2.10 Axiom 8 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 9 (ruleD10): fresh145(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 10 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 11 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 12.44/2.10 Axiom 12 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 13 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 12.44/2.10 Axiom 14 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 15 (ruleD44): fresh99(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 16 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 12.44/2.10 Axiom 17 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 18 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 19 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 20 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 12.44/2.10 Axiom 21 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 12.44/2.10 Axiom 22 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 12.44/2.10 Axiom 23 (ruleD44): fresh100(X, X, Y, Z, W, V, U) = para(V, U, Z, W).
% 12.44/2.10 Axiom 24 (ruleD10): fresh147(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
% 12.44/2.10 Axiom 25 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 12.44/2.10 Axiom 26 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 12.44/2.10 Axiom 27 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 12.44/2.10 Axiom 28 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 12.44/2.10 Axiom 29 (exemplo6GDDFULL618067_13): eqangle(i, m, m, b, i, m, m, c) = true.
% 12.44/2.10 Axiom 30 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 12.44/2.10 Axiom 31 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 12.44/2.10 Axiom 32 (ruleD67): fresh65(cong(X, Y, X, Z), true, X, Y, Z) = fresh64(coll(X, Y, Z), true, X, Y, Z).
% 12.44/2.10 Axiom 33 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 12.44/2.10 Axiom 34 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 12.44/2.10 Axiom 35 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 12.44/2.10 Axiom 36 (ruleD44): fresh100(midp(X, Y, Z), true, Y, W, Z, V, X) = fresh99(midp(V, Y, W), true, W, Z, V, X).
% 12.44/2.10 Axiom 37 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 12.44/2.10 Axiom 38 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 12.44/2.10 Axiom 39 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 12.44/2.10 Axiom 40 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 12.44/2.10 Axiom 41 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 12.44/2.10 Axiom 42 (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).
% 12.44/2.10 Axiom 43 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 12.44/2.10 Axiom 44 (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).
% 12.44/2.10 Axiom 45 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 12.44/2.10 Axiom 46 (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).
% 12.44/2.10 Axiom 47 (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).
% 12.44/2.10 Axiom 48 (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).
% 12.44/2.10 Axiom 49 (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).
% 12.44/2.10 Axiom 50 (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).
% 12.44/2.10
% 12.44/2.10 Lemma 51: para(m, b, m, c) = true.
% 12.44/2.10 Proof:
% 12.44/2.10 para(m, b, m, c)
% 12.44/2.10 = { by axiom 45 (ruleD39) R->L }
% 12.44/2.10 fresh106(eqangle(m, b, i, m, m, c, i, m), true, m, b, m, c)
% 12.44/2.10 = { by axiom 48 (ruleD19) R->L }
% 12.44/2.10 fresh106(fresh134(eqangle(i, m, m, b, i, m, m, c), true, i, m, m, b, i, m, m, c), true, m, b, m, c)
% 12.44/2.10 = { by axiom 29 (exemplo6GDDFULL618067_13) }
% 12.44/2.11 fresh106(fresh134(true, true, i, m, m, b, i, m, m, c), true, m, b, m, c)
% 12.44/2.11 = { by axiom 34 (ruleD19) }
% 12.44/2.11 fresh106(true, true, m, b, m, c)
% 12.44/2.11 = { by axiom 12 (ruleD39) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 52: eqangle(i, m, X, Y, i, m, X, Y) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 eqangle(i, m, X, Y, i, m, X, Y)
% 12.44/2.11 = { by axiom 43 (ruleD40) R->L }
% 12.44/2.11 fresh104(para(i, m, i, m), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 38 (ruleD73) R->L }
% 12.44/2.11 fresh104(fresh58(true, true, i, m, i, m, m, b, m, c), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 35 (ruleD21) R->L }
% 12.44/2.11 fresh104(fresh58(fresh131(true, true, i, m, m, b, i, m, m, c), true, i, m, i, m, m, b, m, c), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 29 (exemplo6GDDFULL618067_13) R->L }
% 12.44/2.11 fresh104(fresh58(fresh131(eqangle(i, m, m, b, i, m, m, c), true, i, m, m, b, i, m, m, c), true, i, m, i, m, m, b, m, c), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 49 (ruleD21) }
% 12.44/2.11 fresh104(fresh58(eqangle(i, m, i, m, m, b, m, c), true, i, m, i, m, m, b, m, c), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 50 (ruleD73) }
% 12.44/2.11 fresh104(fresh57(para(m, b, m, c), true, i, m, i, m), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by lemma 51 }
% 12.44/2.11 fresh104(fresh57(true, true, i, m, i, m), true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 18 (ruleD73) }
% 12.44/2.11 fresh104(true, true, i, m, i, m, X, Y)
% 12.44/2.11 = { by axiom 27 (ruleD40) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 53: coll(X, X, Y) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 coll(X, X, Y)
% 12.44/2.11 = { by axiom 25 (ruleD1) R->L }
% 12.44/2.11 fresh146(coll(X, Y, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 26 (ruleD2) R->L }
% 12.44/2.11 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 31 (ruleD66) R->L }
% 12.44/2.11 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 45 (ruleD39) R->L }
% 12.44/2.11 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, i, m, Y, X, i, m), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 48 (ruleD19) R->L }
% 12.44/2.11 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(i, m, Y, X, i, m, Y, X), true, i, m, Y, X, i, m, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by lemma 52 }
% 12.44/2.11 fresh146(fresh133(fresh66(fresh106(fresh134(true, true, i, m, Y, X, i, m, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 34 (ruleD19) }
% 12.44/2.11 fresh146(fresh133(fresh66(fresh106(true, true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 12 (ruleD39) }
% 12.44/2.11 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 5 (ruleD66) }
% 12.44/2.11 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 12.44/2.11 = { by axiom 3 (ruleD2) }
% 12.44/2.11 fresh146(true, true, X, Y, X)
% 12.44/2.11 = { by axiom 2 (ruleD1) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 54: coll(X, Y, Z) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 coll(X, Y, Z)
% 12.44/2.11 = { by axiom 11 (ruleD3) R->L }
% 12.44/2.11 fresh120(true, true, Z, Z, X, Y)
% 12.44/2.11 = { by lemma 53 R->L }
% 12.44/2.11 fresh120(coll(Z, Z, Y), true, Z, Z, X, Y)
% 12.44/2.11 = { by axiom 30 (ruleD3) }
% 12.44/2.11 fresh119(coll(Z, Z, X), true, Z, X, Y)
% 12.44/2.11 = { by lemma 53 }
% 12.44/2.11 fresh119(true, true, Z, X, Y)
% 12.44/2.11 = { by axiom 4 (ruleD3) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 55: cyclic(m, m, i, X) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 cyclic(m, m, i, X)
% 12.44/2.11 = { by axiom 13 (ruleD42b) R->L }
% 12.44/2.11 fresh102(true, true, m, m, i, X)
% 12.44/2.11 = { by axiom 35 (ruleD21) R->L }
% 12.44/2.11 fresh102(fresh131(true, true, i, m, X, m, i, m, X, m), true, m, m, i, X)
% 12.44/2.11 = { by lemma 52 R->L }
% 12.44/2.11 fresh102(fresh131(eqangle(i, m, X, m, i, m, X, m), true, i, m, X, m, i, m, X, m), true, m, m, i, X)
% 12.44/2.11 = { by axiom 49 (ruleD21) }
% 12.44/2.11 fresh102(eqangle(i, m, i, m, X, m, X, m), true, m, m, i, X)
% 12.44/2.11 = { by axiom 46 (ruleD42b) }
% 12.44/2.11 fresh101(coll(i, X, m), true, m, m, i, X)
% 12.44/2.11 = { by lemma 54 }
% 12.44/2.11 fresh101(true, true, m, m, i, X)
% 12.44/2.11 = { by axiom 14 (ruleD42b) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 56: cyclic(m, i, X, Y) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 cyclic(m, i, X, Y)
% 12.44/2.11 = { by axiom 22 (ruleD17) R->L }
% 12.44/2.11 fresh137(true, true, m, m, i, X, Y)
% 12.44/2.11 = { by lemma 55 R->L }
% 12.44/2.11 fresh137(cyclic(m, m, i, Y), true, m, m, i, X, Y)
% 12.44/2.11 = { by axiom 41 (ruleD17) }
% 12.44/2.11 fresh136(cyclic(m, m, i, X), true, m, i, X, Y)
% 12.44/2.11 = { by lemma 55 }
% 12.44/2.11 fresh136(true, true, m, i, X, Y)
% 12.44/2.11 = { by axiom 10 (ruleD17) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 57: cyclic(i, X, Y, Z) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 cyclic(i, X, Y, Z)
% 12.44/2.11 = { by axiom 22 (ruleD17) R->L }
% 12.44/2.11 fresh137(true, true, m, i, X, Y, Z)
% 12.44/2.11 = { by lemma 56 R->L }
% 12.44/2.11 fresh137(cyclic(m, i, X, Z), true, m, i, X, Y, Z)
% 12.44/2.11 = { by axiom 41 (ruleD17) }
% 12.44/2.11 fresh136(cyclic(m, i, X, Y), true, i, X, Y, Z)
% 12.44/2.11 = { by lemma 56 }
% 12.44/2.11 fresh136(true, true, i, X, Y, Z)
% 12.44/2.11 = { by axiom 10 (ruleD17) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 58: cyclic(X, Y, Z, W) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 cyclic(X, Y, Z, W)
% 12.44/2.11 = { by axiom 22 (ruleD17) R->L }
% 12.44/2.11 fresh137(true, true, i, X, Y, Z, W)
% 12.44/2.11 = { by lemma 57 R->L }
% 12.44/2.11 fresh137(cyclic(i, X, Y, W), true, i, X, Y, Z, W)
% 12.44/2.11 = { by axiom 41 (ruleD17) }
% 12.44/2.11 fresh136(cyclic(i, X, Y, Z), true, X, Y, Z, W)
% 12.44/2.11 = { by lemma 57 }
% 12.44/2.11 fresh136(true, true, X, Y, Z, W)
% 12.44/2.11 = { by axiom 10 (ruleD17) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 59: fresh182(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
% 12.44/2.11 Proof:
% 12.44/2.11 fresh182(X, X, Y, Z, W, V, U, T)
% 12.44/2.11 = { by axiom 40 (ruleD43) }
% 12.44/2.11 fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U)
% 12.44/2.11 = { by lemma 58 }
% 12.44/2.11 fresh183(true, true, Y, Z, W, V, U)
% 12.44/2.11 = { by axiom 21 (ruleD43) }
% 12.44/2.11 cong(Y, Z, V, U)
% 12.44/2.11
% 12.44/2.11 Lemma 60: fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W)
% 12.44/2.11 = { by axiom 47 (ruleD43) }
% 12.44/2.11 fresh184(cyclic(Y, Z, X, W), true, Y, Z, X, V, U)
% 12.44/2.11 = { by lemma 58 }
% 12.44/2.11 fresh184(true, true, Y, Z, X, V, U)
% 12.44/2.11 = { by axiom 33 (ruleD43) }
% 12.44/2.11 fresh185(cyclic(Y, Z, X, V), true, Y, Z, V, U)
% 12.44/2.11 = { by lemma 58 }
% 12.44/2.11 fresh185(true, true, Y, Z, V, U)
% 12.44/2.11 = { by axiom 8 (ruleD43) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 61: cong(b, X, c, X) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 cong(b, X, c, X)
% 12.44/2.11 = { by lemma 59 R->L }
% 12.44/2.11 fresh182(true, true, b, X, m, c, X, m)
% 12.44/2.11 = { by axiom 27 (ruleD40) R->L }
% 12.44/2.11 fresh182(fresh104(true, true, m, b, m, c, m, X), true, b, X, m, c, X, m)
% 12.44/2.11 = { by lemma 51 R->L }
% 12.44/2.11 fresh182(fresh104(para(m, b, m, c), true, m, b, m, c, m, X), true, b, X, m, c, X, m)
% 12.44/2.11 = { by axiom 43 (ruleD40) }
% 12.44/2.11 fresh182(eqangle(m, b, m, X, m, c, m, X), true, b, X, m, c, X, m)
% 12.44/2.11 = { by lemma 60 }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Lemma 62: perp(b, c, X, Y) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 perp(b, c, X, Y)
% 12.44/2.11 = { by axiom 16 (ruleD56) R->L }
% 12.44/2.11 fresh80(true, true, b, c, X, Y)
% 12.44/2.11 = { by lemma 61 R->L }
% 12.44/2.11 fresh80(cong(b, Y, c, Y), true, b, c, X, Y)
% 12.44/2.11 = { by axiom 37 (ruleD56) }
% 12.44/2.11 fresh79(cong(b, X, c, X), true, b, c, X, Y)
% 12.44/2.11 = { by lemma 61 }
% 12.44/2.11 fresh79(true, true, b, c, X, Y)
% 12.44/2.11 = { by axiom 17 (ruleD56) }
% 12.44/2.11 true
% 12.44/2.11
% 12.44/2.11 Goal 1 (exemplo6GDDFULL618067_14): perp(a, b, b, o) = true.
% 12.44/2.11 Proof:
% 12.44/2.11 perp(a, b, b, o)
% 12.44/2.11 = { by axiom 24 (ruleD10) R->L }
% 12.44/2.11 fresh147(true, true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 9 (ruleD10) R->L }
% 12.44/2.11 fresh147(fresh145(true, true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 15 (ruleD44) R->L }
% 12.44/2.11 fresh147(fresh145(fresh99(true, true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 7 (ruleD67) R->L }
% 12.44/2.11 fresh147(fresh145(fresh99(fresh64(true, true, m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by lemma 54 R->L }
% 12.44/2.11 fresh147(fresh145(fresh99(fresh64(coll(m, b, b), true, m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 32 (ruleD67) R->L }
% 12.44/2.11 fresh147(fresh145(fresh99(fresh65(cong(m, b, m, b), true, m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by lemma 59 R->L }
% 12.44/2.11 fresh147(fresh145(fresh99(fresh65(fresh182(true, true, m, b, i, m, b, i), true, m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by lemma 52 R->L }
% 12.44/2.11 fresh147(fresh145(fresh99(fresh65(fresh182(eqangle(i, m, i, b, i, m, i, b), true, m, b, i, m, b, i), true, m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by lemma 60 }
% 12.44/2.11 fresh147(fresh145(fresh99(fresh65(true, true, m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 6 (ruleD67) }
% 12.44/2.11 fresh147(fresh145(fresh99(midp(m, b, b), true, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 36 (ruleD44) R->L }
% 12.44/2.11 fresh147(fresh145(fresh100(midp(midpnt2, b, c), true, b, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 1 (exemplo6GDDFULL618067_9) }
% 12.44/2.11 fresh147(fresh145(fresh100(true, true, b, b, c, m, midpnt2), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 23 (ruleD44) }
% 12.44/2.11 fresh147(fresh145(para(m, midpnt2, b, c), true, m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 42 (ruleD10) R->L }
% 12.44/2.11 fresh147(fresh147(perp(b, c, b, o), true, m, midpnt2, b, c, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by lemma 62 }
% 12.44/2.11 fresh147(fresh147(true, true, m, midpnt2, b, c, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 24 (ruleD10) }
% 12.44/2.11 fresh147(perp(m, midpnt2, b, o), true, a, b, m, midpnt2, b, o)
% 12.44/2.11 = { by axiom 42 (ruleD10) }
% 12.44/2.11 fresh145(para(a, b, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by axiom 28 (ruleD9) R->L }
% 12.44/2.11 fresh145(fresh51(true, true, a, b, b, c, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by lemma 62 R->L }
% 12.44/2.11 fresh145(fresh51(perp(b, c, m, midpnt2), true, a, b, b, c, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by axiom 44 (ruleD9) }
% 12.44/2.11 fresh145(fresh50(perp(a, b, b, c), true, a, b, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by axiom 39 (ruleD8) R->L }
% 12.44/2.11 fresh145(fresh50(fresh52(perp(b, c, a, b), true, b, c, a, b), true, a, b, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by lemma 62 }
% 12.44/2.11 fresh145(fresh50(fresh52(true, true, b, c, a, b), true, a, b, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by axiom 19 (ruleD8) }
% 12.44/2.11 fresh145(fresh50(true, true, a, b, m, midpnt2), true, a, b, b, o)
% 12.44/2.11 = { by axiom 20 (ruleD9) }
% 12.44/2.11 fresh145(true, true, a, b, b, o)
% 12.44/2.11 = { by axiom 9 (ruleD10) }
% 12.44/2.11 true
% 12.44/2.11 % SZS output end Proof
% 12.44/2.11
% 12.44/2.11 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------