0.06/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.11	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.10/0.32	% Computer   : n031.cluster.edu
0.10/0.32	% Model      : x86_64 x86_64
0.10/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.32	% Memory     : 8042.1875MB
0.10/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.32	% CPULimit   : 1200
0.10/0.32	% WCLimit    : 120
0.10/0.32	% DateTime   : Tue Jul 13 14:40:44 EDT 2021
0.10/0.32	% CPUTime    : 
26.51/3.71	% SZS status Theorem
26.51/3.71	
27.21/3.78	% SZS output start Proof
27.21/3.78	Take the following subset of the input axioms:
27.21/3.78	  fof(exemplo6GDDFULL618068, conjecture, ![A, B, P, D, E, F, G, I, NWPNT1, NWPNT2, NWPNT3, NWPNT4, NWPNT5, NWPNT6, NWPNT7, NWPNT8, NWPNT9, NWPNT01]: ((perp(P, A, P, B) & (circle(A, P, D, NWPNT5) & (circle(A, D, E, NWPNT6) & (circle(B, P, I, NWPNT8) & (coll(F, D, I) & (circle(B, F, G, NWPNT01) & (coll(G, F, B) & (circle(B, P, F, NWPNT9) & (circle(A, P, I, NWPNT7) & (coll(E, D, A) & (circle(B, P, NWPNT3, NWPNT4) & circle(A, P, NWPNT1, NWPNT2)))))))))))) => perp(G, F, D, E))).
27.21/3.78	  fof(ruleD1, axiom, ![A, B, C]: (coll(A, B, C) => coll(A, C, B))).
27.21/3.78	  fof(ruleD10, axiom, ![A, B, C, D, E, F]: ((perp(C, D, E, F) & para(A, B, C, D)) => perp(A, B, E, F))).
27.21/3.78	  fof(ruleD14, axiom, ![A, B, C, D]: (cyclic(A, B, D, C) <= cyclic(A, B, C, D))).
27.21/3.78	  fof(ruleD15, axiom, ![A, B, C, D]: (cyclic(A, B, C, D) => cyclic(A, C, B, D))).
27.21/3.78	  fof(ruleD16, axiom, ![A, B, C, D]: (cyclic(B, A, C, D) <= cyclic(A, B, C, D))).
27.21/3.78	  fof(ruleD17, axiom, ![A, B, C, D, E]: ((cyclic(A, B, C, D) & cyclic(A, B, C, E)) => cyclic(B, C, D, E))).
27.21/3.78	  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))).
27.21/3.78	  fof(ruleD2, axiom, ![A, B, C]: (coll(B, A, C) <= coll(A, B, C))).
27.21/3.78	  fof(ruleD39, axiom, ![A, B, C, P, Q, D]: (para(A, B, C, D) <= eqangle(A, B, P, Q, C, D, P, Q))).
27.21/3.78	  fof(ruleD4, axiom, ![A, B, C, D]: (para(A, B, C, D) => para(A, B, D, C))).
27.21/3.78	  fof(ruleD40, axiom, ![A, B, C, P, Q, D]: (eqangle(A, B, P, Q, C, D, P, Q) <= para(A, B, C, D))).
27.21/3.78	  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))).
27.21/3.78	  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)))))).
27.21/3.78	  fof(ruleD56, axiom, ![A, B, P, Q]: (perp(A, B, P, Q) <= (cong(A, P, B, P) & cong(A, Q, B, Q)))).
27.21/3.78	  fof(ruleD57, axiom, ![A, B, P, Q]: ((cyclic(A, B, P, Q) & (cong(A, Q, B, Q) & cong(A, P, B, P))) => perp(P, A, A, Q))).
27.21/3.78	  fof(ruleD66, axiom, ![A, B, C]: (coll(A, B, C) <= para(A, B, A, C))).
27.21/3.78	  fof(ruleD7, axiom, ![A, B, C, D]: (perp(A, B, D, C) <= perp(A, B, C, D))).
27.21/3.78	  fof(ruleD8, axiom, ![A, B, C, D]: (perp(C, D, A, B) <= perp(A, B, C, D))).
27.21/3.78	  fof(ruleD9, axiom, ![A, B, C, D, E, F]: (para(A, B, E, F) <= (perp(C, D, E, F) & perp(A, B, C, D)))).
27.21/3.78	
27.21/3.78	Now clausify the problem and encode Horn clauses using encoding 3 of
27.21/3.78	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
27.21/3.78	We repeatedly replace C & s=t => u=v by the two clauses:
27.21/3.78	  fresh(y, y, x1...xn) = u
27.21/3.78	  C => fresh(s, t, x1...xn) = v
27.21/3.78	where fresh is a fresh function symbol and x1..xn are the free
27.21/3.78	variables of u and v.
27.21/3.78	A predicate p(X) is encoded as p(X)=true (this is sound, because the
27.21/3.78	input problem has no model of domain size 1).
27.21/3.78	
27.21/3.78	The encoding turns the above axioms into the following unit equations and goals:
27.21/3.78	
27.21/3.78	Axiom 1 (exemplo6GDDFULL618068): perp(p, a, p, b) = true.
27.21/3.78	Axiom 2 (ruleD57): fresh179(X, X, Y, Z, W) = true.
27.21/3.78	Axiom 3 (ruleD1): fresh147(X, X, Y, Z, W) = true.
27.21/3.78	Axiom 4 (ruleD2): fresh134(X, X, Y, Z, W) = true.
27.21/3.78	Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
27.21/3.78	Axiom 6 (ruleD10): fresh146(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 7 (ruleD14): fresh141(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 8 (ruleD15): fresh140(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 9 (ruleD16): fresh139(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 10 (ruleD17): fresh137(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 11 (ruleD39): fresh107(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 12 (ruleD4): fresh106(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 13 (ruleD42b): fresh103(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
27.21/3.78	Axiom 14 (ruleD42b): fresh102(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 15 (ruleD43): fresh101(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 16 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
27.21/3.78	Axiom 17 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 18 (ruleD57): fresh78(X, X, Y, Z, W, V) = perp(W, Y, Y, V).
27.21/3.78	Axiom 19 (ruleD7): fresh61(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 20 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 21 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
27.21/3.78	Axiom 22 (ruleD1): fresh147(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
27.21/3.78	Axiom 23 (ruleD17): fresh138(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
27.21/3.78	Axiom 24 (ruleD2): fresh134(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
27.21/3.78	Axiom 25 (ruleD57): fresh178(X, X, Y, Z, W, V) = fresh179(cong(Y, W, Z, W), true, Y, W, V).
27.21/3.78	Axiom 26 (ruleD43): fresh159(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
27.21/3.78	Axiom 27 (ruleD10): fresh148(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
27.21/3.78	Axiom 28 (ruleD40): fresh105(X, X, Y, Z, W, V, U, T) = true.
27.21/3.78	Axiom 29 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
27.21/3.78	Axiom 30 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
27.21/3.78	Axiom 31 (ruleD14): fresh141(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
27.21/3.78	Axiom 32 (ruleD15): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
27.21/3.78	Axiom 33 (ruleD16): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
27.21/3.78	Axiom 34 (ruleD4): fresh106(para(X, Y, Z, W), true, X, Y, Z, W) = para(X, Y, W, Z).
27.21/3.78	Axiom 35 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
27.21/3.78	Axiom 36 (ruleD57): fresh178(cyclic(X, Y, Z, W), true, X, Y, Z, W) = fresh78(cong(X, W, Y, W), true, X, Y, Z, W).
27.21/3.78	Axiom 37 (ruleD7): fresh61(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(X, Y, W, Z).
27.21/3.78	Axiom 38 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
27.21/3.78	Axiom 39 (ruleD17): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh137(cyclic(X, Y, Z, V), true, Y, Z, V, W).
27.21/3.78	Axiom 40 (ruleD19): fresh135(X, X, Y, Z, W, V, U, T, S, X2) = true.
27.21/3.78	Axiom 41 (ruleD43): fresh158(X, X, Y, Z, W, V, U, T) = fresh159(cyclic(Y, Z, W, V), true, Y, Z, W, V, U, T).
27.21/3.78	Axiom 42 (ruleD43): fresh157(X, X, Y, Z, W, V, U, T) = fresh158(cyclic(Y, Z, W, U), true, Y, Z, W, V, U, T).
27.21/3.79	Axiom 43 (ruleD10): fresh148(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = fresh146(perp(Z, W, V, U), true, X, Y, V, U).
27.21/3.79	Axiom 44 (ruleD40): fresh105(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
27.21/3.79	Axiom 45 (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).
27.21/3.79	Axiom 46 (ruleD39): fresh107(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
27.21/3.79	Axiom 47 (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).
27.21/3.79	Axiom 48 (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).
27.21/3.79	Axiom 49 (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).
27.21/3.79	
27.21/3.79	Lemma 50: fresh50(perp(X, Y, p, a), true, X, Y, p, b) = para(X, Y, p, b).
27.21/3.79	Proof:
27.21/3.79	  fresh50(perp(X, Y, p, a), true, X, Y, p, b)
27.21/3.79	= { by axiom 45 (ruleD9) R->L }
27.21/3.79	  fresh51(perp(p, a, p, b), true, X, Y, p, a, p, b)
27.21/3.79	= { by axiom 1 (exemplo6GDDFULL618068) }
27.21/3.79	  fresh51(true, true, X, Y, p, a, p, b)
27.21/3.79	= { by axiom 30 (ruleD9) }
27.21/3.79	  para(X, Y, p, b)
27.21/3.79	
27.21/3.79	Lemma 51: eqangle(X, Y, p, b, X, Y, p, b) = true.
27.21/3.79	Proof:
27.21/3.79	  eqangle(X, Y, p, b, X, Y, p, b)
27.21/3.79	= { by axiom 49 (ruleD19) R->L }
27.21/3.79	  fresh135(eqangle(p, b, X, Y, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 44 (ruleD40) R->L }
27.21/3.79	  fresh135(fresh105(para(p, b, p, b), true, p, b, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by lemma 50 R->L }
27.21/3.79	  fresh135(fresh105(fresh50(perp(p, b, p, a), true, p, b, p, b), true, p, b, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 38 (ruleD8) R->L }
27.21/3.79	  fresh135(fresh105(fresh50(fresh52(perp(p, a, p, b), true, p, a, p, b), true, p, b, p, b), true, p, b, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 1 (exemplo6GDDFULL618068) }
27.21/3.79	  fresh135(fresh105(fresh50(fresh52(true, true, p, a, p, b), true, p, b, p, b), true, p, b, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 20 (ruleD8) }
27.21/3.79	  fresh135(fresh105(fresh50(true, true, p, b, p, b), true, p, b, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 21 (ruleD9) }
27.21/3.79	  fresh135(fresh105(true, true, p, b, p, b, X, Y), true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 28 (ruleD40) }
27.21/3.79	  fresh135(true, true, p, b, X, Y, p, b, X, Y)
27.21/3.79	= { by axiom 40 (ruleD19) }
27.21/3.79	  true
27.21/3.79	
27.21/3.79	Lemma 52: cyclic(b, p, p, X) = true.
27.21/3.79	Proof:
27.21/3.79	  cyclic(b, p, p, X)
27.21/3.79	= { by axiom 31 (ruleD14) R->L }
27.21/3.79	  fresh141(cyclic(b, p, X, p), true, b, p, X, p)
27.21/3.79	= { by axiom 32 (ruleD15) R->L }
27.21/3.79	  fresh141(fresh140(cyclic(b, X, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 33 (ruleD16) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(cyclic(X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 13 (ruleD42b) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh103(true, true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by lemma 51 R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh103(eqangle(p, X, p, b, p, X, p, b), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 47 (ruleD42b) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(coll(p, p, b), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 22 (ruleD1) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(coll(p, b, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 24 (ruleD2) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(coll(b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 29 (ruleD66) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(para(b, p, b, p), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 34 (ruleD4) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(para(b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by lemma 50 R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(fresh50(perp(b, p, p, a), true, b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 38 (ruleD8) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(fresh50(fresh52(perp(p, a, b, p), true, p, a, b, p), true, b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 37 (ruleD7) R->L }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(fresh50(fresh52(fresh61(perp(p, a, p, b), true, p, a, p, b), true, p, a, b, p), true, b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 1 (exemplo6GDDFULL618068) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(fresh50(fresh52(fresh61(true, true, p, a, p, b), true, p, a, b, p), true, b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 19 (ruleD7) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(fresh50(fresh52(true, true, p, a, b, p), true, b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 20 (ruleD8) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(fresh50(true, true, b, p, p, b), true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 21 (ruleD9) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(fresh106(true, true, b, p, p, b), true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 12 (ruleD4) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(fresh66(true, true, b, p, p), true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 5 (ruleD66) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(fresh134(true, true, b, p, p), true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 4 (ruleD2) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(fresh147(true, true, p, b, p), true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 3 (ruleD1) }
27.21/3.79	  fresh141(fresh140(fresh139(fresh102(true, true, X, b, p, p), true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.79	= { by axiom 14 (ruleD42b) }
27.21/3.80	  fresh141(fresh140(fresh139(true, true, X, b, p, p), true, b, X, p, p), true, b, p, X, p)
27.21/3.80	= { by axiom 9 (ruleD16) }
27.21/3.80	  fresh141(fresh140(true, true, b, X, p, p), true, b, p, X, p)
27.21/3.80	= { by axiom 8 (ruleD15) }
27.21/3.80	  fresh141(true, true, b, p, X, p)
27.21/3.80	= { by axiom 7 (ruleD14) }
27.21/3.80	  true
27.21/3.80	
27.21/3.80	Lemma 53: cyclic(p, p, X, Y) = true.
27.21/3.80	Proof:
27.21/3.80	  cyclic(p, p, X, Y)
27.21/3.80	= { by axiom 23 (ruleD17) R->L }
27.21/3.80	  fresh138(true, true, b, p, p, X, Y)
27.21/3.80	= { by lemma 52 R->L }
27.21/3.80	  fresh138(cyclic(b, p, p, Y), true, b, p, p, X, Y)
27.21/3.80	= { by axiom 39 (ruleD17) }
27.21/3.80	  fresh137(cyclic(b, p, p, X), true, p, p, X, Y)
27.21/3.80	= { by lemma 52 }
27.21/3.80	  fresh137(true, true, p, p, X, Y)
27.21/3.80	= { by axiom 10 (ruleD17) }
27.21/3.80	  true
27.21/3.80	
27.21/3.80	Lemma 54: cyclic(p, X, Y, Z) = true.
27.21/3.80	Proof:
27.21/3.80	  cyclic(p, X, Y, Z)
27.21/3.80	= { by axiom 23 (ruleD17) R->L }
27.21/3.80	  fresh138(true, true, p, p, X, Y, Z)
27.21/3.80	= { by lemma 53 R->L }
27.21/3.80	  fresh138(cyclic(p, p, X, Z), true, p, p, X, Y, Z)
27.21/3.80	= { by axiom 39 (ruleD17) }
27.21/3.80	  fresh137(cyclic(p, p, X, Y), true, p, X, Y, Z)
27.21/3.80	= { by lemma 53 }
27.21/3.80	  fresh137(true, true, p, X, Y, Z)
27.21/3.80	= { by axiom 10 (ruleD17) }
27.21/3.80	  true
27.21/3.80	
27.21/3.80	Lemma 55: cyclic(X, Y, Z, W) = true.
27.21/3.80	Proof:
27.21/3.80	  cyclic(X, Y, Z, W)
27.21/3.80	= { by axiom 23 (ruleD17) R->L }
27.21/3.80	  fresh138(true, true, p, X, Y, Z, W)
27.21/3.80	= { by lemma 54 R->L }
27.21/3.80	  fresh138(cyclic(p, X, Y, W), true, p, X, Y, Z, W)
27.21/3.80	= { by axiom 39 (ruleD17) }
27.21/3.80	  fresh137(cyclic(p, X, Y, Z), true, X, Y, Z, W)
27.21/3.80	= { by lemma 54 }
27.21/3.80	  fresh137(true, true, X, Y, Z, W)
27.21/3.80	= { by axiom 10 (ruleD17) }
27.21/3.80	  true
27.21/3.80	
27.21/3.80	Lemma 56: cong(X, Y, X, Y) = true.
27.21/3.80	Proof:
27.21/3.80	  cong(X, Y, X, Y)
27.21/3.80	= { by axiom 26 (ruleD43) R->L }
27.21/3.80	  fresh159(true, true, X, Y, Z, X, Y, Z)
27.21/3.80	= { by lemma 55 R->L }
27.21/3.80	  fresh159(cyclic(X, Y, Z, X), true, X, Y, Z, X, Y, Z)
27.21/3.80	= { by axiom 41 (ruleD43) R->L }
27.21/3.80	  fresh158(true, true, X, Y, Z, X, Y, Z)
27.21/3.80	= { by lemma 55 R->L }
27.21/3.80	  fresh158(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y, Z)
27.21/3.80	= { by axiom 42 (ruleD43) R->L }
27.21/3.80	  fresh157(true, true, X, Y, Z, X, Y, Z)
27.21/3.80	= { by lemma 55 R->L }
27.21/3.80	  fresh157(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y, Z)
27.21/3.80	= { by axiom 48 (ruleD43) }
27.21/3.80	  fresh101(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, X, Y)
27.21/3.80	= { by axiom 44 (ruleD40) R->L }
27.21/3.80	  fresh101(fresh105(para(Z, X, Z, X), true, Z, X, Z, X, Z, Y), true, X, Y, X, Y)
27.21/3.80	= { by axiom 46 (ruleD39) R->L }
27.21/3.80	  fresh101(fresh105(fresh107(eqangle(Z, X, p, b, Z, X, p, b), true, Z, X, Z, X), true, Z, X, Z, X, Z, Y), true, X, Y, X, Y)
27.21/3.80	= { by lemma 51 }
27.21/3.80	  fresh101(fresh105(fresh107(true, true, Z, X, Z, X), true, Z, X, Z, X, Z, Y), true, X, Y, X, Y)
27.21/3.80	= { by axiom 11 (ruleD39) }
27.21/3.80	  fresh101(fresh105(true, true, Z, X, Z, X, Z, Y), true, X, Y, X, Y)
27.21/3.80	= { by axiom 28 (ruleD40) }
27.21/3.80	  fresh101(true, true, X, Y, X, Y)
27.21/3.80	= { by axiom 15 (ruleD43) }
27.21/3.80	  true
27.21/3.80	
27.21/3.80	Lemma 57: perp(X, X, Y, Z) = true.
27.21/3.80	Proof:
27.21/3.80	  perp(X, X, Y, Z)
27.21/3.80	= { by axiom 16 (ruleD56) R->L }
27.21/3.80	  fresh80(true, true, X, X, Y, Z)
27.21/3.80	= { by lemma 56 R->L }
27.21/3.80	  fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
27.21/3.80	= { by axiom 35 (ruleD56) }
27.21/3.80	  fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
27.21/3.80	= { by lemma 56 }
27.21/3.80	  fresh79(true, true, X, X, Y, Z)
27.21/3.80	= { by axiom 17 (ruleD56) }
27.21/3.80	  true
27.21/3.80	
27.21/3.80	Goal 1 (exemplo6GDDFULL618068_12): perp(g, f, d, e) = true.
27.21/3.80	Proof:
27.21/3.80	  perp(g, f, d, e)
27.21/3.80	= { by axiom 27 (ruleD10) R->L }
27.21/3.80	  fresh148(true, true, g, f, X, d, d, e)
27.21/3.80	= { by axiom 21 (ruleD9) R->L }
27.21/3.80	  fresh148(fresh50(true, true, g, f, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by axiom 20 (ruleD8) R->L }
27.21/3.80	  fresh148(fresh50(fresh52(true, true, Y, Y, g, f), true, g, f, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by lemma 57 R->L }
27.21/3.80	  fresh148(fresh50(fresh52(perp(Y, Y, g, f), true, Y, Y, g, f), true, g, f, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by axiom 38 (ruleD8) }
27.21/3.80	  fresh148(fresh50(perp(g, f, Y, Y), true, g, f, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by axiom 45 (ruleD9) R->L }
27.21/3.80	  fresh148(fresh51(perp(Y, Y, X, d), true, g, f, Y, Y, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by lemma 57 }
27.21/3.80	  fresh148(fresh51(true, true, g, f, Y, Y, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by axiom 30 (ruleD9) }
27.21/3.80	  fresh148(para(g, f, X, d), true, g, f, X, d, d, e)
27.21/3.80	= { by axiom 43 (ruleD10) }
27.21/3.80	  fresh146(perp(X, d, d, e), true, g, f, d, e)
27.21/3.80	= { by axiom 18 (ruleD57) R->L }
27.21/3.80	  fresh146(fresh78(true, true, d, d, X, e), true, g, f, d, e)
27.21/3.80	= { by lemma 56 R->L }
27.21/3.80	  fresh146(fresh78(cong(d, e, d, e), true, d, d, X, e), true, g, f, d, e)
27.21/3.80	= { by axiom 36 (ruleD57) R->L }
27.21/3.80	  fresh146(fresh178(cyclic(d, d, X, e), true, d, d, X, e), true, g, f, d, e)
27.21/3.80	= { by lemma 55 }
27.21/3.80	  fresh146(fresh178(true, true, d, d, X, e), true, g, f, d, e)
27.21/3.80	= { by axiom 25 (ruleD57) }
27.21/3.80	  fresh146(fresh179(cong(d, X, d, X), true, d, X, e), true, g, f, d, e)
27.21/3.80	= { by lemma 56 }
27.21/3.80	  fresh146(fresh179(true, true, d, X, e), true, g, f, d, e)
27.21/3.80	= { by axiom 2 (ruleD57) }
27.21/3.80	  fresh146(true, true, g, f, d, e)
27.21/3.80	= { by axiom 6 (ruleD10) }
27.21/3.80	  true
27.21/3.80	% SZS output end Proof
27.21/3.80	
27.21/3.80	RESULT: Theorem (the conjecture is true).
27.21/3.81	EOF