0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.33	% Computer   : n026.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.33	% CPULimit   : 1200
0.13/0.33	% WCLimit    : 120
0.13/0.33	% DateTime   : Tue Jul 13 14:41:44 EDT 2021
0.13/0.33	% CPUTime    : 
13.01/2.03	% SZS status Theorem
13.01/2.03	
13.73/2.09	% SZS output start Proof
13.73/2.09	Take the following subset of the input axioms:
13.73/2.10	  fof(exemplo6GDDFULL81109104, conjecture, ![A, B, C, H, D, E, F, G, NWPNT1, NWPNT2, NWPNT3]: (perp(C, H, D, H) <= (circle(E, A, G, NWPNT3) & (perp(E, G, G, D) & (para(A, D, C, B) & (midp(F, C, D) & (coll(H, A, B) & (perp(H, F, A, B) & (coll(C, G, D) & (circle(E, A, NWPNT1, NWPNT2) & midp(E, A, B))))))))))).
13.73/2.10	  fof(ruleD1, axiom, ![A, B, C]: (coll(A, B, C) => coll(A, C, B))).
13.73/2.10	  fof(ruleD10, axiom, ![A, B, C, D, E, F]: ((perp(C, D, E, F) & para(A, B, C, D)) => perp(A, B, E, F))).
13.73/2.10	  fof(ruleD14, axiom, ![A, B, C, D]: (cyclic(A, B, D, C) <= cyclic(A, B, C, D))).
13.73/2.10	  fof(ruleD15, axiom, ![A, B, C, D]: (cyclic(A, B, C, D) => cyclic(A, C, B, D))).
13.73/2.10	  fof(ruleD16, axiom, ![A, B, C, D]: (cyclic(B, A, C, D) <= cyclic(A, B, C, D))).
13.73/2.10	  fof(ruleD17, axiom, ![A, B, C, D, E]: ((cyclic(A, B, C, D) & cyclic(A, B, C, E)) => cyclic(B, C, D, E))).
13.73/2.10	  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))).
13.73/2.10	  fof(ruleD2, axiom, ![A, B, C]: (coll(B, A, C) <= coll(A, B, C))).
13.73/2.10	  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))).
13.73/2.10	  fof(ruleD23, axiom, ![A, B, C, D]: (cong(A, B, D, C) <= cong(A, B, C, D))).
13.73/2.10	  fof(ruleD24, axiom, ![A, B, C, D]: (cong(A, B, C, D) => cong(C, D, A, B))).
13.73/2.10	  fof(ruleD40, axiom, ![A, B, C, P, Q, D]: (eqangle(A, B, P, Q, C, D, P, Q) <= para(A, B, C, D))).
13.73/2.10	  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))).
13.73/2.10	  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)))))).
13.73/2.10	  fof(ruleD56, axiom, ![A, B, P, Q]: (perp(A, B, P, Q) <= (cong(A, P, B, P) & cong(A, Q, B, Q)))).
13.73/2.10	  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))).
13.73/2.10	  fof(ruleD66, axiom, ![A, B, C]: (coll(A, B, C) <= para(A, B, A, C))).
13.73/2.10	  fof(ruleD68, axiom, ![A, B, C]: (cong(A, B, A, C) <= midp(A, B, C))).
13.73/2.10	  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))).
13.73/2.10	  fof(ruleD8, axiom, ![A, B, C, D]: (perp(C, D, A, B) <= perp(A, B, C, D))).
13.73/2.10	  fof(ruleD9, axiom, ![A, B, C, D, E, F]: (para(A, B, E, F) <= (perp(C, D, E, F) & perp(A, B, C, D)))).
13.73/2.10	
13.73/2.10	Now clausify the problem and encode Horn clauses using encoding 3 of
13.73/2.10	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
13.73/2.10	We repeatedly replace C & s=t => u=v by the two clauses:
13.73/2.10	  fresh(y, y, x1...xn) = u
13.73/2.10	  C => fresh(s, t, x1...xn) = v
13.73/2.10	where fresh is a fresh function symbol and x1..xn are the free
13.73/2.10	variables of u and v.
13.73/2.10	A predicate p(X) is encoded as p(X)=true (this is sound, because the
13.73/2.10	input problem has no model of domain size 1).
13.73/2.10	
13.73/2.10	The encoding turns the above axioms into the following unit equations and goals:
13.73/2.10	
13.73/2.10	Axiom 1 (exemplo6GDDFULL81109104_5): midp(e, a, b) = true.
13.73/2.10	Axiom 2 (exemplo6GDDFULL81109104_4): para(a, d, c, b) = true.
13.73/2.10	Axiom 3 (ruleD57): fresh179(X, X, Y, Z, W) = true.
13.73/2.10	Axiom 4 (ruleD1): fresh147(X, X, Y, Z, W) = true.
13.73/2.10	Axiom 5 (ruleD2): fresh134(X, X, Y, Z, W) = true.
13.73/2.10	Axiom 6 (ruleD66): fresh66(X, X, Y, Z, W) = true.
13.73/2.10	Axiom 7 (ruleD68): fresh63(X, X, Y, Z, W) = true.
13.73/2.10	Axiom 8 (ruleD10): fresh146(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 9 (ruleD14): fresh141(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 10 (ruleD15): fresh140(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 11 (ruleD16): fresh139(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 12 (ruleD17): fresh137(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 13 (ruleD23): fresh129(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 14 (ruleD24): fresh128(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 15 (ruleD42b): fresh103(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
13.73/2.10	Axiom 16 (ruleD42b): fresh102(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 17 (ruleD43): fresh101(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 18 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
13.73/2.10	Axiom 19 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 20 (ruleD57): fresh78(X, X, Y, Z, W, V) = perp(W, Y, Y, V).
13.73/2.10	Axiom 21 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 22 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 23 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
13.73/2.10	Axiom 24 (ruleD17): fresh138(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
13.73/2.10	Axiom 25 (ruleD43): fresh159(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
13.73/2.10	Axiom 26 (ruleD10): fresh148(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
13.73/2.10	Axiom 27 (ruleD1): fresh147(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
13.73/2.10	Axiom 28 (ruleD2): fresh134(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
13.73/2.10	Axiom 29 (ruleD40): fresh105(X, X, Y, Z, W, V, U, T) = true.
13.73/2.10	Axiom 30 (ruleD68): fresh63(midp(X, Y, Z), true, X, Y, Z) = cong(X, Y, X, Z).
13.73/2.10	Axiom 31 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
13.73/2.10	Axiom 32 (ruleD57): fresh178(X, X, Y, Z, W, V) = fresh179(cong(Y, W, Z, W), true, Y, W, V).
13.73/2.10	Axiom 33 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
13.73/2.10	Axiom 34 (ruleD14): fresh141(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
13.73/2.10	Axiom 35 (ruleD15): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
13.73/2.10	Axiom 36 (ruleD16): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
13.73/2.10	Axiom 37 (ruleD19): fresh135(X, X, Y, Z, W, V, U, T, S, X2) = true.
13.73/2.10	Axiom 38 (ruleD21): fresh132(X, X, Y, Z, W, V, U, T, S, X2) = true.
13.73/2.10	Axiom 39 (ruleD23): fresh129(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(X, Y, W, Z).
13.73/2.10	Axiom 40 (ruleD24): fresh128(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(Z, W, X, Y).
13.73/2.10	Axiom 41 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
13.73/2.10	Axiom 42 (ruleD57): fresh178(cyclic(X, Y, Z, W), true, X, Y, Z, W) = fresh78(cong(X, W, Y, W), true, X, Y, Z, W).
13.73/2.10	Axiom 43 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
13.73/2.10	Axiom 44 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
13.73/2.10	Axiom 45 (ruleD17): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh137(cyclic(X, Y, Z, V), true, Y, Z, V, W).
13.73/2.10	Axiom 46 (ruleD43): fresh158(X, X, Y, Z, W, V, U, T) = fresh159(cyclic(Y, Z, W, V), true, Y, Z, W, V, U, T).
13.73/2.10	Axiom 47 (ruleD43): fresh157(X, X, Y, Z, W, V, U, T) = fresh158(cyclic(Y, Z, W, U), true, Y, Z, W, V, U, T).
13.73/2.10	Axiom 48 (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).
13.73/2.10	Axiom 49 (ruleD40): fresh105(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
13.73/2.10	Axiom 50 (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).
13.73/2.10	Axiom 51 (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).
13.73/2.10	Axiom 52 (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).
13.73/2.10	Axiom 53 (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).
13.73/2.10	Axiom 54 (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).
13.73/2.11	Axiom 55 (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).
13.73/2.11	
13.73/2.11	Lemma 56: para(X, Y, X, Y) = true.
13.73/2.11	Proof:
13.73/2.11	  para(X, Y, X, Y)
13.73/2.11	= { by axiom 43 (ruleD73) R->L }
13.73/2.11	  fresh58(true, true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 38 (ruleD21) R->L }
13.73/2.11	  fresh58(fresh132(true, true, X, Y, a, d, X, Y, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 37 (ruleD19) R->L }
13.73/2.11	  fresh58(fresh132(fresh135(true, true, a, d, X, Y, c, b, X, Y), true, X, Y, a, d, X, Y, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 29 (ruleD40) R->L }
13.73/2.11	  fresh58(fresh132(fresh135(fresh105(true, true, a, d, c, b, X, Y), true, a, d, X, Y, c, b, X, Y), true, X, Y, a, d, X, Y, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 2 (exemplo6GDDFULL81109104_4) R->L }
13.73/2.11	  fresh58(fresh132(fresh135(fresh105(para(a, d, c, b), true, a, d, c, b, X, Y), true, a, d, X, Y, c, b, X, Y), true, X, Y, a, d, X, Y, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 49 (ruleD40) }
13.73/2.11	  fresh58(fresh132(fresh135(eqangle(a, d, X, Y, c, b, X, Y), true, a, d, X, Y, c, b, X, Y), true, X, Y, a, d, X, Y, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 53 (ruleD19) }
13.73/2.11	  fresh58(fresh132(eqangle(X, Y, a, d, X, Y, c, b), true, X, Y, a, d, X, Y, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 54 (ruleD21) }
13.73/2.11	  fresh58(eqangle(X, Y, X, Y, a, d, c, b), true, X, Y, X, Y, a, d, c, b)
13.73/2.11	= { by axiom 55 (ruleD73) }
13.73/2.11	  fresh57(para(a, d, c, b), true, X, Y, X, Y)
13.73/2.11	= { by axiom 2 (exemplo6GDDFULL81109104_4) }
13.73/2.11	  fresh57(true, true, X, Y, X, Y)
13.73/2.11	= { by axiom 21 (ruleD73) }
13.73/2.11	  true
13.73/2.11	
13.73/2.11	Lemma 57: eqangle(X, Y, Z, W, X, Y, Z, W) = true.
13.73/2.11	Proof:
13.73/2.11	  eqangle(X, Y, Z, W, X, Y, Z, W)
13.73/2.11	= { by axiom 49 (ruleD40) R->L }
13.73/2.11	  fresh105(para(X, Y, X, Y), true, X, Y, X, Y, Z, W)
13.73/2.11	= { by lemma 56 }
13.73/2.11	  fresh105(true, true, X, Y, X, Y, Z, W)
13.73/2.11	= { by axiom 29 (ruleD40) }
13.73/2.11	  true
13.73/2.11	
13.73/2.11	Lemma 58: cyclic(X, Y, X, Z) = true.
13.73/2.11	Proof:
13.73/2.11	  cyclic(X, Y, X, Z)
13.73/2.11	= { by axiom 36 (ruleD16) R->L }
13.73/2.11	  fresh139(cyclic(Y, X, X, Z), true, Y, X, X, Z)
13.73/2.11	= { by axiom 34 (ruleD14) R->L }
13.73/2.11	  fresh139(fresh141(cyclic(Y, X, Z, X), true, Y, X, Z, X), true, Y, X, X, Z)
13.73/2.11	= { by axiom 35 (ruleD15) R->L }
13.73/2.11	  fresh139(fresh141(fresh140(cyclic(Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
13.73/2.11	= { by axiom 15 (ruleD42b) R->L }
13.73/2.11	  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)
13.73/2.11	= { by lemma 57 R->L }
13.73/2.11	  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)
13.73/2.11	= { by axiom 51 (ruleD42b) }
13.73/2.11	  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)
13.73/2.11	= { by axiom 27 (ruleD1) R->L }
13.73/2.11	  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)
13.73/2.11	= { by axiom 28 (ruleD2) R->L }
13.73/2.11	  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)
13.73/2.11	= { by axiom 33 (ruleD66) R->L }
13.73/2.11	  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)
13.73/2.11	= { by lemma 56 }
13.73/2.11	  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)
13.73/2.11	= { by axiom 6 (ruleD66) }
13.73/2.11	  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)
13.73/2.11	= { by axiom 5 (ruleD2) }
13.73/2.11	  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)
13.73/2.11	= { by axiom 4 (ruleD1) }
13.73/2.11	  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)
13.73/2.11	= { by axiom 16 (ruleD42b) }
13.73/2.11	  fresh139(fresh141(fresh140(true, true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
13.73/2.11	= { by axiom 10 (ruleD15) }
13.73/2.11	  fresh139(fresh141(true, true, Y, X, Z, X), true, Y, X, X, Z)
13.73/2.11	= { by axiom 9 (ruleD14) }
13.73/2.11	  fresh139(true, true, Y, X, X, Z)
13.73/2.11	= { by axiom 11 (ruleD16) }
13.73/2.11	  true
13.73/2.11	
13.73/2.11	Lemma 59: cyclic(X, Y, Z, W) = true.
13.73/2.11	Proof:
13.73/2.11	  cyclic(X, Y, Z, W)
13.73/2.11	= { by axiom 24 (ruleD17) R->L }
13.73/2.11	  fresh138(true, true, Y, X, Y, Z, W)
13.73/2.11	= { by lemma 58 R->L }
13.73/2.11	  fresh138(cyclic(Y, X, Y, W), true, Y, X, Y, Z, W)
13.73/2.11	= { by axiom 45 (ruleD17) }
13.73/2.11	  fresh137(cyclic(Y, X, Y, Z), true, X, Y, Z, W)
13.73/2.11	= { by lemma 58 }
13.73/2.11	  fresh137(true, true, X, Y, Z, W)
13.73/2.11	= { by axiom 12 (ruleD17) }
13.73/2.11	  true
13.73/2.11	
13.73/2.11	Lemma 60: cong(X, Y, X, Y) = true.
13.73/2.11	Proof:
13.73/2.11	  cong(X, Y, X, Y)
13.73/2.11	= { by axiom 25 (ruleD43) R->L }
13.73/2.11	  fresh159(true, true, X, Y, Z, X, Y, Z)
13.73/2.11	= { by lemma 59 R->L }
13.73/2.11	  fresh159(cyclic(X, Y, Z, X), true, X, Y, Z, X, Y, Z)
13.73/2.11	= { by axiom 46 (ruleD43) R->L }
13.73/2.11	  fresh158(true, true, X, Y, Z, X, Y, Z)
13.73/2.11	= { by lemma 59 R->L }
13.73/2.11	  fresh158(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y, Z)
13.73/2.11	= { by axiom 47 (ruleD43) R->L }
13.73/2.11	  fresh157(true, true, X, Y, Z, X, Y, Z)
13.73/2.11	= { by lemma 59 R->L }
14.11/2.11	  fresh157(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y, Z)
14.11/2.11	= { by axiom 52 (ruleD43) }
14.11/2.11	  fresh101(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, X, Y)
14.11/2.11	= { by lemma 57 }
14.11/2.11	  fresh101(true, true, X, Y, X, Y)
14.11/2.11	= { by axiom 17 (ruleD43) }
14.11/2.11	  true
14.11/2.11	
14.11/2.11	Lemma 61: perp(X, X, Y, Z) = true.
14.11/2.11	Proof:
14.11/2.12	  perp(X, X, Y, Z)
14.11/2.12	= { by axiom 18 (ruleD56) R->L }
14.11/2.12	  fresh80(true, true, X, X, Y, Z)
14.11/2.12	= { by lemma 60 R->L }
14.11/2.12	  fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
14.11/2.12	= { by axiom 41 (ruleD56) }
14.11/2.12	  fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
14.11/2.12	= { by lemma 60 }
14.11/2.12	  fresh79(true, true, X, X, Y, Z)
14.11/2.12	= { by axiom 19 (ruleD56) }
14.11/2.12	  true
14.11/2.12	
14.11/2.12	Lemma 62: cong(b, e, a, e) = true.
14.11/2.12	Proof:
14.11/2.12	  cong(b, e, a, e)
14.11/2.12	= { by axiom 39 (ruleD23) R->L }
14.11/2.12	  fresh129(cong(b, e, e, a), true, b, e, e, a)
14.11/2.12	= { by axiom 40 (ruleD24) R->L }
14.11/2.12	  fresh129(fresh128(cong(e, a, b, e), true, e, a, b, e), true, b, e, e, a)
14.11/2.12	= { by axiom 39 (ruleD23) R->L }
14.11/2.12	  fresh129(fresh128(fresh129(cong(e, a, e, b), true, e, a, e, b), true, e, a, b, e), true, b, e, e, a)
14.11/2.12	= { by axiom 30 (ruleD68) R->L }
14.11/2.12	  fresh129(fresh128(fresh129(fresh63(midp(e, a, b), true, e, a, b), true, e, a, e, b), true, e, a, b, e), true, b, e, e, a)
14.11/2.12	= { by axiom 1 (exemplo6GDDFULL81109104_5) }
14.11/2.12	  fresh129(fresh128(fresh129(fresh63(true, true, e, a, b), true, e, a, e, b), true, e, a, b, e), true, b, e, e, a)
14.11/2.12	= { by axiom 7 (ruleD68) }
14.11/2.12	  fresh129(fresh128(fresh129(true, true, e, a, e, b), true, e, a, b, e), true, b, e, e, a)
14.11/2.12	= { by axiom 13 (ruleD23) }
14.11/2.12	  fresh129(fresh128(true, true, e, a, b, e), true, b, e, e, a)
14.11/2.12	= { by axiom 14 (ruleD24) }
14.11/2.12	  fresh129(true, true, b, e, e, a)
14.11/2.12	= { by axiom 13 (ruleD23) }
14.11/2.12	  true
14.11/2.12	
14.11/2.12	Lemma 63: para(X, Y, Z, W) = true.
14.11/2.12	Proof:
14.11/2.12	  para(X, Y, Z, W)
14.11/2.12	= { by axiom 31 (ruleD9) R->L }
14.11/2.12	  fresh51(true, true, X, Y, V, V, Z, W)
14.11/2.12	= { by lemma 61 R->L }
14.11/2.12	  fresh51(perp(V, V, Z, W), true, X, Y, V, V, Z, W)
14.11/2.12	= { by axiom 50 (ruleD9) }
14.11/2.12	  fresh50(perp(X, Y, V, V), true, X, Y, Z, W)
14.11/2.12	= { by axiom 44 (ruleD8) R->L }
14.11/2.12	  fresh50(fresh52(perp(V, V, X, Y), true, V, V, X, Y), true, X, Y, Z, W)
14.11/2.12	= { by lemma 61 }
14.11/2.12	  fresh50(fresh52(true, true, V, V, X, Y), true, X, Y, Z, W)
14.11/2.12	= { by axiom 22 (ruleD8) }
14.11/2.12	  fresh50(true, true, X, Y, Z, W)
14.11/2.12	= { by axiom 23 (ruleD9) }
14.11/2.12	  true
14.11/2.12	
14.11/2.12	Goal 1 (exemplo6GDDFULL81109104_9): perp(c, h, d, h) = true.
14.11/2.12	Proof:
14.11/2.12	  perp(c, h, d, h)
14.11/2.12	= { by axiom 26 (ruleD10) R->L }
14.11/2.12	  fresh148(true, true, c, h, b, e, d, h)
14.11/2.12	= { by lemma 63 R->L }
14.11/2.12	  fresh148(para(c, h, b, e), true, c, h, b, e, d, h)
14.11/2.12	= { by axiom 48 (ruleD10) }
14.11/2.12	  fresh146(perp(b, e, d, h), true, c, h, d, h)
14.11/2.12	= { by axiom 44 (ruleD8) R->L }
14.11/2.12	  fresh146(fresh52(perp(d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 26 (ruleD10) R->L }
14.11/2.12	  fresh146(fresh52(fresh148(true, true, d, h, e, b, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by lemma 63 R->L }
14.11/2.12	  fresh146(fresh52(fresh148(para(d, h, e, b), true, d, h, e, b, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 48 (ruleD10) }
14.11/2.12	  fresh146(fresh52(fresh146(perp(e, b, b, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 20 (ruleD57) R->L }
14.11/2.12	  fresh146(fresh52(fresh146(fresh78(true, true, b, a, e, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by lemma 62 R->L }
14.11/2.12	  fresh146(fresh52(fresh146(fresh78(cong(b, e, a, e), true, b, a, e, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 42 (ruleD57) R->L }
14.11/2.12	  fresh146(fresh52(fresh146(fresh178(cyclic(b, a, e, e), true, b, a, e, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by lemma 59 }
14.11/2.12	  fresh146(fresh52(fresh146(fresh178(true, true, b, a, e, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 32 (ruleD57) }
14.11/2.12	  fresh146(fresh52(fresh146(fresh179(cong(b, e, a, e), true, b, e, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by lemma 62 }
14.11/2.12	  fresh146(fresh52(fresh146(fresh179(true, true, b, e, e), true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 3 (ruleD57) }
14.11/2.12	  fresh146(fresh52(fresh146(true, true, d, h, b, e), true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 8 (ruleD10) }
14.11/2.12	  fresh146(fresh52(true, true, d, h, b, e), true, c, h, d, h)
14.11/2.12	= { by axiom 22 (ruleD8) }
14.11/2.12	  fresh146(true, true, c, h, d, h)
14.11/2.12	= { by axiom 8 (ruleD10) }
14.11/2.12	  true
14.11/2.12	% SZS output end Proof
14.11/2.12	
14.11/2.12	RESULT: Theorem (the conjecture is true).
14.11/2.13	EOF