0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.34	% Computer   : n012.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% WCLimit    : 120
0.20/0.34	% DateTime   : Tue Jul 13 14:20:16 EDT 2021
0.20/0.34	% CPUTime    : 
12.68/1.94	% SZS status Theorem
12.68/1.94	
12.68/1.97	% SZS output start Proof
12.68/1.97	Take the following subset of the input axioms:
12.68/1.98	  fof(exemplo6GDDFULL618075y, conjecture, ![A, B, C, H, D, E, F, G, NWPNT1, NWPNT2, NWPNT3, NWPNT4, NWPNT5, NWPNT6, NWPNT7, NWPNT8]: ((circle(A, B, NWPNT1, NWPNT2) & (circle(C, B, D, NWPNT6) & (circle(C, B, G, NWPNT8) & (coll(H, C, G) & (coll(H, A, F) & (coll(G, B, F) & (circle(A, B, F, NWPNT7) & (midp(E, D, B) & (circle(A, B, D, NWPNT5) & circle(C, B, NWPNT3, NWPNT4)))))))))) => eqangle(F, D, D, G, A, H, H, C))).
12.68/1.98	  fof(ruleD1, axiom, ![A, B, C]: (coll(A, B, C) => coll(A, C, B))).
12.68/1.98	  fof(ruleD14, axiom, ![A, B, C, D]: (cyclic(A, B, D, C) <= cyclic(A, B, C, D))).
12.68/1.98	  fof(ruleD15, axiom, ![A, B, C, D]: (cyclic(A, B, C, D) => cyclic(A, C, B, D))).
12.68/1.98	  fof(ruleD16, axiom, ![A, B, C, D]: (cyclic(B, A, C, D) <= cyclic(A, B, C, D))).
12.68/1.98	  fof(ruleD17, axiom, ![A, B, C, D, E]: ((cyclic(A, B, C, D) & cyclic(A, B, C, E)) => cyclic(B, C, D, E))).
12.68/1.98	  fof(ruleD19, axiom, ![A, B, C, P, Q, D, U, V]: (eqangle(C, D, A, B, U, V, P, Q) <= eqangle(A, B, C, D, P, Q, U, V))).
12.68/1.98	  fof(ruleD2, axiom, ![A, B, C]: (coll(B, A, C) <= coll(A, B, C))).
12.68/1.98	  fof(ruleD21, axiom, ![A, B, C, P, Q, D, U, V]: (eqangle(A, B, P, Q, C, D, U, V) <= eqangle(A, B, C, D, P, Q, U, V))).
12.68/1.98	  fof(ruleD22, axiom, ![A, B, C, P, Q, H, D, U, V, E, F, G]: ((eqangle(A, B, C, D, P, Q, U, V) & eqangle(P, Q, U, V, E, F, G, H)) => eqangle(A, B, C, D, E, F, G, H))).
12.68/1.98	  fof(ruleD40, axiom, ![A, B, C, P, Q, D]: (eqangle(A, B, P, Q, C, D, P, Q) <= para(A, B, C, D))).
12.68/1.98	  fof(ruleD42b, axiom, ![A, B, P, Q]: ((eqangle(P, A, P, B, Q, A, Q, B) & coll(P, Q, B)) => cyclic(A, B, P, Q))).
12.68/1.98	  fof(ruleD43, axiom, ![A, B, C, P, Q, R]: (cong(A, B, P, Q) <= (cyclic(A, B, C, P) & (eqangle(C, A, C, B, R, P, R, Q) & (cyclic(A, B, C, R) & cyclic(A, B, C, Q)))))).
12.68/1.98	  fof(ruleD44, axiom, ![A, B, C, E, F]: ((midp(E, A, B) & midp(F, A, C)) => para(E, F, B, C))).
12.68/1.98	  fof(ruleD56, axiom, ![A, B, P, Q]: (perp(A, B, P, Q) <= (cong(A, P, B, P) & cong(A, Q, B, Q)))).
12.68/1.98	  fof(ruleD66, axiom, ![A, B, C]: (coll(A, B, C) <= para(A, B, A, C))).
12.68/1.98	  fof(ruleD73, axiom, ![A, B, C, P, Q, D, U, V]: ((para(P, Q, U, V) & eqangle(A, B, C, D, P, Q, U, V)) => para(A, B, C, D))).
12.68/1.98	  fof(ruleD8, axiom, ![A, B, C, D]: (perp(C, D, A, B) <= perp(A, B, C, D))).
12.68/1.98	  fof(ruleD9, axiom, ![A, B, C, D, E, F]: (para(A, B, E, F) <= (perp(C, D, E, F) & perp(A, B, C, D)))).
12.68/1.98	
12.68/1.98	Now clausify the problem and encode Horn clauses using encoding 3 of
12.68/1.98	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
12.68/1.98	We repeatedly replace C & s=t => u=v by the two clauses:
12.68/1.98	  fresh(y, y, x1...xn) = u
12.68/1.98	  C => fresh(s, t, x1...xn) = v
12.68/1.98	where fresh is a fresh function symbol and x1..xn are the free
12.68/1.98	variables of u and v.
12.68/1.98	A predicate p(X) is encoded as p(X)=true (this is sound, because the
12.68/1.98	input problem has no model of domain size 1).
12.68/1.98	
12.68/1.98	The encoding turns the above axioms into the following unit equations and goals:
12.68/1.98	
12.68/1.98	Axiom 1 (exemplo6GDDFULL618075y_3): midp(e, d, b) = true.
12.68/1.98	Axiom 2 (ruleD1): fresh147(X, X, Y, Z, W) = true.
12.68/1.98	Axiom 3 (ruleD2): fresh134(X, X, Y, Z, W) = true.
12.68/1.98	Axiom 4 (ruleD66): fresh66(X, X, Y, Z, W) = true.
12.68/1.98	Axiom 5 (ruleD14): fresh141(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 6 (ruleD15): fresh140(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 7 (ruleD16): fresh139(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 8 (ruleD17): fresh137(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 9 (ruleD42b): fresh103(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
12.68/1.98	Axiom 10 (ruleD42b): fresh102(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 11 (ruleD43): fresh101(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 12 (ruleD44): fresh99(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 13 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
12.68/1.98	Axiom 14 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 15 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 16 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 17 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
12.68/1.98	Axiom 18 (ruleD1): fresh147(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
12.68/1.98	Axiom 19 (ruleD17): fresh138(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
12.68/1.98	Axiom 20 (ruleD2): fresh134(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
12.68/1.98	Axiom 21 (ruleD44): fresh100(X, X, Y, Z, W, V, U) = para(V, U, Z, W).
12.68/1.98	Axiom 22 (ruleD43): fresh159(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
12.68/1.98	Axiom 23 (ruleD40): fresh105(X, X, Y, Z, W, V, U, T) = true.
12.68/1.98	Axiom 24 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
12.68/1.98	Axiom 25 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
12.68/1.98	Axiom 26 (ruleD14): fresh141(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
12.68/1.98	Axiom 27 (ruleD15): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
12.68/1.98	Axiom 28 (ruleD16): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
12.68/1.98	Axiom 29 (ruleD44): fresh100(midp(X, Y, Z), true, Y, W, Z, V, X) = fresh99(midp(V, Y, W), true, W, Z, V, X).
12.68/1.98	Axiom 30 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
12.68/1.98	Axiom 31 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
12.68/1.98	Axiom 32 (ruleD17): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh137(cyclic(X, Y, Z, V), true, Y, Z, V, W).
12.68/1.98	Axiom 33 (ruleD19): fresh135(X, X, Y, Z, W, V, U, T, S, X2) = true.
12.68/1.98	Axiom 34 (ruleD21): fresh132(X, X, Y, Z, W, V, U, T, S, X2) = true.
12.68/1.98	Axiom 35 (ruleD22): fresh130(X, X, Y, Z, W, V, U, T, S, X2) = true.
12.68/1.98	Axiom 36 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
12.68/1.98	Axiom 37 (ruleD43): fresh158(X, X, Y, Z, W, V, U, T) = fresh159(cyclic(Y, Z, W, V), true, Y, Z, W, V, U, T).
12.68/1.98	Axiom 38 (ruleD43): fresh157(X, X, Y, Z, W, V, U, T) = fresh158(cyclic(Y, Z, W, U), true, Y, Z, W, V, U, T).
12.68/1.98	Axiom 39 (ruleD40): fresh105(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
12.68/1.98	Axiom 40 (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).
12.68/1.98	Axiom 41 (ruleD42b): fresh103(eqangle(X, Y, X, Z, W, Y, W, Z), true, Y, Z, X, W) = fresh102(coll(X, W, Z), true, Y, Z, X, W).
12.68/1.98	Axiom 42 (ruleD43): fresh157(cyclic(X, Y, Z, W), true, X, Y, Z, V, U, W) = fresh101(eqangle(Z, X, Z, Y, W, V, W, U), true, X, Y, V, U).
12.68/1.98	Axiom 43 (ruleD22): fresh131(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = eqangle(Y, Z, W, V, Y2, Z2, W2, V2).
12.68/1.98	Axiom 44 (ruleD19): fresh135(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).
12.68/1.98	Axiom 45 (ruleD21): fresh132(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).
12.68/1.98	Axiom 46 (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).
12.68/1.98	Axiom 47 (ruleD22): fresh131(eqangle(X, Y, Z, W, V, U, T, S), true, X2, Y2, Z2, W2, X, Y, Z, W, V, U, T, S) = fresh130(eqangle(X2, Y2, Z2, W2, X, Y, Z, W), true, X2, Y2, Z2, W2, V, U, T, S).
12.68/1.98	
12.68/1.98	Lemma 48: para(e, e, b, b) = true.
12.68/1.98	Proof:
12.68/1.98	  para(e, e, b, b)
12.68/1.98	= { by axiom 21 (ruleD44) R->L }
12.68/1.98	  fresh100(true, true, d, b, b, e, e)
12.68/1.98	= { by axiom 1 (exemplo6GDDFULL618075y_3) R->L }
12.68/1.98	  fresh100(midp(e, d, b), true, d, b, b, e, e)
12.68/1.98	= { by axiom 29 (ruleD44) }
12.68/1.98	  fresh99(midp(e, d, b), true, b, b, e, e)
12.68/1.98	= { by axiom 1 (exemplo6GDDFULL618075y_3) }
12.68/1.98	  fresh99(true, true, b, b, e, e)
12.68/1.98	= { by axiom 12 (ruleD44) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 49: para(X, Y, X, Y) = true.
12.68/1.98	Proof:
12.68/1.98	  para(X, Y, X, Y)
12.68/1.98	= { by axiom 36 (ruleD73) R->L }
12.68/1.98	  fresh58(true, true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 34 (ruleD21) R->L }
12.68/1.98	  fresh58(fresh132(true, true, X, Y, e, e, X, Y, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 33 (ruleD19) R->L }
12.68/1.98	  fresh58(fresh132(fresh135(true, true, e, e, X, Y, b, b, X, Y), true, X, Y, e, e, X, Y, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 23 (ruleD40) R->L }
12.68/1.98	  fresh58(fresh132(fresh135(fresh105(true, true, e, e, b, b, X, Y), true, e, e, X, Y, b, b, X, Y), true, X, Y, e, e, X, Y, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by lemma 48 R->L }
12.68/1.98	  fresh58(fresh132(fresh135(fresh105(para(e, e, b, b), true, e, e, b, b, X, Y), true, e, e, X, Y, b, b, X, Y), true, X, Y, e, e, X, Y, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 39 (ruleD40) }
12.68/1.98	  fresh58(fresh132(fresh135(eqangle(e, e, X, Y, b, b, X, Y), true, e, e, X, Y, b, b, X, Y), true, X, Y, e, e, X, Y, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 44 (ruleD19) }
12.68/1.98	  fresh58(fresh132(eqangle(X, Y, e, e, X, Y, b, b), true, X, Y, e, e, X, Y, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 45 (ruleD21) }
12.68/1.98	  fresh58(eqangle(X, Y, X, Y, e, e, b, b), true, X, Y, X, Y, e, e, b, b)
12.68/1.98	= { by axiom 46 (ruleD73) }
12.68/1.98	  fresh57(para(e, e, b, b), true, X, Y, X, Y)
12.68/1.98	= { by lemma 48 }
12.68/1.98	  fresh57(true, true, X, Y, X, Y)
12.68/1.98	= { by axiom 15 (ruleD73) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 50: eqangle(X, Y, Z, W, X, Y, Z, W) = true.
12.68/1.98	Proof:
12.68/1.98	  eqangle(X, Y, Z, W, X, Y, Z, W)
12.68/1.98	= { by axiom 39 (ruleD40) R->L }
12.68/1.98	  fresh105(para(X, Y, X, Y), true, X, Y, X, Y, Z, W)
12.68/1.98	= { by lemma 49 }
12.68/1.98	  fresh105(true, true, X, Y, X, Y, Z, W)
12.68/1.98	= { by axiom 23 (ruleD40) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 51: cyclic(X, Y, X, Z) = true.
12.68/1.98	Proof:
12.68/1.98	  cyclic(X, Y, X, Z)
12.68/1.98	= { by axiom 28 (ruleD16) R->L }
12.68/1.98	  fresh139(cyclic(Y, X, X, Z), true, Y, X, X, Z)
12.68/1.98	= { by axiom 26 (ruleD14) R->L }
12.68/1.98	  fresh139(fresh141(cyclic(Y, X, Z, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 27 (ruleD15) R->L }
12.68/1.98	  fresh139(fresh141(fresh140(cyclic(Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 9 (ruleD42b) R->L }
12.68/1.98	  fresh139(fresh141(fresh140(fresh103(true, true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by lemma 50 R->L }
12.68/1.98	  fresh139(fresh141(fresh140(fresh103(eqangle(X, Y, X, Z, X, Y, X, Z), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 41 (ruleD42b) }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(coll(X, X, Z), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 18 (ruleD1) R->L }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(fresh147(coll(X, Z, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 20 (ruleD2) R->L }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(fresh147(fresh134(coll(Z, X, X), true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 24 (ruleD66) R->L }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(fresh147(fresh134(fresh66(para(Z, X, Z, X), true, Z, X, X), true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by lemma 49 }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(fresh147(fresh134(fresh66(true, true, Z, X, X), true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 4 (ruleD66) }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(fresh147(fresh134(true, true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 3 (ruleD2) }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(fresh147(true, true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 2 (ruleD1) }
12.68/1.98	  fresh139(fresh141(fresh140(fresh102(true, true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 10 (ruleD42b) }
12.68/1.98	  fresh139(fresh141(fresh140(true, true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 6 (ruleD15) }
12.68/1.98	  fresh139(fresh141(true, true, Y, X, Z, X), true, Y, X, X, Z)
12.68/1.98	= { by axiom 5 (ruleD14) }
12.68/1.98	  fresh139(true, true, Y, X, X, Z)
12.68/1.98	= { by axiom 7 (ruleD16) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 52: cyclic(X, Y, Z, W) = true.
12.68/1.98	Proof:
12.68/1.98	  cyclic(X, Y, Z, W)
12.68/1.98	= { by axiom 19 (ruleD17) R->L }
12.68/1.98	  fresh138(true, true, Y, X, Y, Z, W)
12.68/1.98	= { by lemma 51 R->L }
12.68/1.98	  fresh138(cyclic(Y, X, Y, W), true, Y, X, Y, Z, W)
12.68/1.98	= { by axiom 32 (ruleD17) }
12.68/1.98	  fresh137(cyclic(Y, X, Y, Z), true, X, Y, Z, W)
12.68/1.98	= { by lemma 51 }
12.68/1.98	  fresh137(true, true, X, Y, Z, W)
12.68/1.98	= { by axiom 8 (ruleD17) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 53: cong(X, Y, X, Y) = true.
12.68/1.98	Proof:
12.68/1.98	  cong(X, Y, X, Y)
12.68/1.98	= { by axiom 22 (ruleD43) R->L }
12.68/1.98	  fresh159(true, true, X, Y, Z, X, Y, Z)
12.68/1.98	= { by lemma 52 R->L }
12.68/1.98	  fresh159(cyclic(X, Y, Z, X), true, X, Y, Z, X, Y, Z)
12.68/1.98	= { by axiom 37 (ruleD43) R->L }
12.68/1.98	  fresh158(true, true, X, Y, Z, X, Y, Z)
12.68/1.98	= { by lemma 52 R->L }
12.68/1.98	  fresh158(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y, Z)
12.68/1.98	= { by axiom 38 (ruleD43) R->L }
12.68/1.98	  fresh157(true, true, X, Y, Z, X, Y, Z)
12.68/1.98	= { by lemma 52 R->L }
12.68/1.98	  fresh157(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y, Z)
12.68/1.98	= { by axiom 42 (ruleD43) }
12.68/1.98	  fresh101(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, X, Y)
12.68/1.98	= { by lemma 50 }
12.68/1.98	  fresh101(true, true, X, Y, X, Y)
12.68/1.98	= { by axiom 11 (ruleD43) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 54: perp(X, X, Y, Z) = true.
12.68/1.98	Proof:
12.68/1.98	  perp(X, X, Y, Z)
12.68/1.98	= { by axiom 13 (ruleD56) R->L }
12.68/1.98	  fresh80(true, true, X, X, Y, Z)
12.68/1.98	= { by lemma 53 R->L }
12.68/1.98	  fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
12.68/1.98	= { by axiom 30 (ruleD56) }
12.68/1.98	  fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
12.68/1.98	= { by lemma 53 }
12.68/1.98	  fresh79(true, true, X, X, Y, Z)
12.68/1.98	= { by axiom 14 (ruleD56) }
12.68/1.98	  true
12.68/1.98	
12.68/1.98	Lemma 55: eqangle(X, Y, Z, W, V, U, Z, W) = true.
12.68/1.98	Proof:
12.68/1.98	  eqangle(X, Y, Z, W, V, U, Z, W)
12.68/1.98	= { by axiom 39 (ruleD40) R->L }
12.68/1.98	  fresh105(para(X, Y, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by axiom 25 (ruleD9) R->L }
12.68/1.98	  fresh105(fresh51(true, true, X, Y, T, T, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by lemma 54 R->L }
12.68/1.98	  fresh105(fresh51(perp(T, T, V, U), true, X, Y, T, T, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by axiom 40 (ruleD9) }
12.68/1.98	  fresh105(fresh50(perp(X, Y, T, T), true, X, Y, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by axiom 31 (ruleD8) R->L }
12.68/1.98	  fresh105(fresh50(fresh52(perp(T, T, X, Y), true, T, T, X, Y), true, X, Y, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by lemma 54 }
12.68/1.98	  fresh105(fresh50(fresh52(true, true, T, T, X, Y), true, X, Y, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by axiom 16 (ruleD8) }
12.68/1.98	  fresh105(fresh50(true, true, X, Y, V, U), true, X, Y, V, U, Z, W)
12.68/1.98	= { by axiom 17 (ruleD9) }
12.68/1.98	  fresh105(true, true, X, Y, V, U, Z, W)
12.68/1.98	= { by axiom 23 (ruleD40) }
12.68/1.99	  true
12.68/1.99	
12.68/1.99	Goal 1 (exemplo6GDDFULL618075y_10): eqangle(f, d, d, g, a, h, h, c) = true.
12.68/1.99	Proof:
12.68/1.99	  eqangle(f, d, d, g, a, h, h, c)
12.68/1.99	= { by axiom 43 (ruleD22) R->L }
12.68/1.99	  fresh131(true, true, f, d, d, g, X, Y, X, Y, a, h, h, c)
12.68/1.99	= { by axiom 34 (ruleD21) R->L }
12.68/1.99	  fresh131(fresh132(true, true, X, Y, a, h, X, Y, h, c), true, f, d, d, g, X, Y, X, Y, a, h, h, c)
12.68/1.99	= { by axiom 33 (ruleD19) R->L }
12.68/1.99	  fresh131(fresh132(fresh135(true, true, a, h, X, Y, h, c, X, Y), true, X, Y, a, h, X, Y, h, c), true, f, d, d, g, X, Y, X, Y, a, h, h, c)
12.68/1.99	= { by lemma 55 R->L }
12.68/1.99	  fresh131(fresh132(fresh135(eqangle(a, h, X, Y, h, c, X, Y), true, a, h, X, Y, h, c, X, Y), true, X, Y, a, h, X, Y, h, c), true, f, d, d, g, X, Y, X, Y, a, h, h, c)
12.68/1.99	= { by axiom 44 (ruleD19) }
12.68/1.99	  fresh131(fresh132(eqangle(X, Y, a, h, X, Y, h, c), true, X, Y, a, h, X, Y, h, c), true, f, d, d, g, X, Y, X, Y, a, h, h, c)
12.68/1.99	= { by axiom 45 (ruleD21) }
12.68/1.99	  fresh131(eqangle(X, Y, X, Y, a, h, h, c), true, f, d, d, g, X, Y, X, Y, a, h, h, c)
12.68/1.99	= { by axiom 47 (ruleD22) }
12.68/1.99	  fresh130(eqangle(f, d, d, g, X, Y, X, Y), true, f, d, d, g, a, h, h, c)
12.68/1.99	= { by axiom 45 (ruleD21) R->L }
12.68/1.99	  fresh130(fresh132(eqangle(f, d, X, Y, d, g, X, Y), true, f, d, X, Y, d, g, X, Y), true, f, d, d, g, a, h, h, c)
12.68/1.99	= { by lemma 55 }
12.68/1.99	  fresh130(fresh132(true, true, f, d, X, Y, d, g, X, Y), true, f, d, d, g, a, h, h, c)
12.68/1.99	= { by axiom 34 (ruleD21) }
12.68/1.99	  fresh130(true, true, f, d, d, g, a, h, h, c)
12.68/1.99	= { by axiom 35 (ruleD22) }
12.68/1.99	  true
12.68/1.99	% SZS output end Proof
12.68/1.99	
12.68/1.99	RESULT: Theorem (the conjecture is true).
12.68/1.99	EOF