0.12/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.14	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.14/0.36	% Computer   : n012.cluster.edu
0.14/0.36	% Model      : x86_64 x86_64
0.14/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory     : 8042.1875MB
0.14/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit   : 1200
0.14/0.36	% WCLimit    : 120
0.14/0.36	% DateTime   : Tue Jul 13 14:27:01 EDT 2021
0.14/0.36	% CPUTime    : 
22.05/3.18	% SZS status Theorem
22.05/3.18	
22.40/3.20	% SZS output start Proof
22.40/3.20	Take the following subset of the input axioms:
22.40/3.21	  fof(exemplo6GDDFULLmoreE02211, conjecture, ![A, B, C, D, E, F, G, MIDPNT1, MIDPNT2, MIDPNT3]: (para(G, E, A, B) <= (midp(MIDPNT2, A, C) & (perp(A, C, MIDPNT2, D) & (midp(MIDPNT3, B, C) & (perp(B, D, B, E) & (perp(F, D, A, B) & (coll(F, A, B) & (coll(G, D, F) & (coll(G, A, C) & (perp(C, D, C, E) & (perp(B, C, MIDPNT3, D) & (perp(A, B, MIDPNT1, D) & midp(MIDPNT1, A, B)))))))))))))).
22.40/3.21	  fof(ruleD1, axiom, ![A, B, C]: (coll(A, B, C) => coll(A, C, B))).
22.40/3.21	  fof(ruleD14, axiom, ![A, B, C, D]: (cyclic(A, B, D, C) <= cyclic(A, B, C, D))).
22.40/3.21	  fof(ruleD15, axiom, ![A, B, C, D]: (cyclic(A, B, C, D) => cyclic(A, C, B, D))).
22.40/3.21	  fof(ruleD16, axiom, ![A, B, C, D]: (cyclic(B, A, C, D) <= cyclic(A, B, C, D))).
22.40/3.21	  fof(ruleD17, axiom, ![A, B, C, D, E]: ((cyclic(A, B, C, D) & cyclic(A, B, C, E)) => cyclic(B, C, D, E))).
22.40/3.21	  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))).
22.40/3.21	  fof(ruleD2, axiom, ![A, B, C]: (coll(B, A, C) <= coll(A, B, C))).
22.40/3.21	  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))).
22.40/3.21	  fof(ruleD40, axiom, ![A, B, C, P, Q, D]: (eqangle(A, B, P, Q, C, D, P, Q) <= para(A, B, C, D))).
22.40/3.21	  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))).
22.40/3.21	  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)))))).
22.40/3.21	  fof(ruleD44, axiom, ![A, B, C, E, F]: ((midp(E, A, B) & midp(F, A, C)) => para(E, F, B, C))).
22.40/3.21	  fof(ruleD56, axiom, ![A, B, P, Q]: (perp(A, B, P, Q) <= (cong(A, P, B, P) & cong(A, Q, B, Q)))).
22.40/3.21	  fof(ruleD66, axiom, ![A, B, C]: (coll(A, B, C) <= para(A, B, A, C))).
22.40/3.21	  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))).
22.40/3.21	  fof(ruleD8, axiom, ![A, B, C, D]: (perp(C, D, A, B) <= perp(A, B, C, D))).
22.40/3.21	  fof(ruleD9, axiom, ![A, B, C, D, E, F]: (para(A, B, E, F) <= (perp(C, D, E, F) & perp(A, B, C, D)))).
22.40/3.21	
22.40/3.21	Now clausify the problem and encode Horn clauses using encoding 3 of
22.40/3.21	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
22.40/3.21	We repeatedly replace C & s=t => u=v by the two clauses:
22.40/3.21	  fresh(y, y, x1...xn) = u
22.40/3.21	  C => fresh(s, t, x1...xn) = v
22.40/3.21	where fresh is a fresh function symbol and x1..xn are the free
22.40/3.21	variables of u and v.
22.40/3.21	A predicate p(X) is encoded as p(X)=true (this is sound, because the
22.40/3.21	input problem has no model of domain size 1).
22.40/3.21	
22.40/3.21	The encoding turns the above axioms into the following unit equations and goals:
22.40/3.21	
22.40/3.21	Axiom 1 (exemplo6GDDFULLmoreE02211_9): midp(midpnt1, a, b) = true.
22.40/3.21	Axiom 2 (ruleD1): fresh147(X, X, Y, Z, W) = true.
22.40/3.21	Axiom 3 (ruleD2): fresh134(X, X, Y, Z, W) = true.
22.40/3.21	Axiom 4 (ruleD66): fresh66(X, X, Y, Z, W) = true.
22.40/3.21	Axiom 5 (ruleD14): fresh141(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 6 (ruleD15): fresh140(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 7 (ruleD16): fresh139(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 8 (ruleD17): fresh137(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 9 (ruleD42b): fresh103(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
22.40/3.21	Axiom 10 (ruleD42b): fresh102(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 11 (ruleD43): fresh101(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 12 (ruleD44): fresh99(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 13 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
22.40/3.21	Axiom 14 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 15 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 16 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 17 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
22.40/3.21	Axiom 18 (ruleD1): fresh147(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
22.40/3.21	Axiom 19 (ruleD17): fresh138(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
22.40/3.21	Axiom 20 (ruleD2): fresh134(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
22.40/3.21	Axiom 21 (ruleD44): fresh100(X, X, Y, Z, W, V, U) = para(V, U, Z, W).
22.40/3.21	Axiom 22 (ruleD43): fresh159(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
22.40/3.21	Axiom 23 (ruleD40): fresh105(X, X, Y, Z, W, V, U, T) = true.
22.40/3.21	Axiom 24 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
22.40/3.21	Axiom 25 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
22.40/3.21	Axiom 26 (ruleD14): fresh141(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
22.40/3.21	Axiom 27 (ruleD15): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
22.40/3.21	Axiom 28 (ruleD16): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
22.40/3.21	Axiom 29 (ruleD44): fresh100(midp(X, Y, Z), true, Y, W, Z, V, X) = fresh99(midp(V, Y, W), true, W, Z, V, X).
22.40/3.21	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).
22.40/3.21	Axiom 31 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
22.40/3.21	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).
22.40/3.21	Axiom 33 (ruleD19): fresh135(X, X, Y, Z, W, V, U, T, S, X2) = true.
22.40/3.21	Axiom 34 (ruleD21): fresh132(X, X, Y, Z, W, V, U, T, S, X2) = true.
22.40/3.21	Axiom 35 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
22.40/3.21	Axiom 36 (ruleD43): fresh158(X, X, Y, Z, W, V, U, T) = fresh159(cyclic(Y, Z, W, V), true, Y, Z, W, V, U, T).
22.40/3.21	Axiom 37 (ruleD43): fresh157(X, X, Y, Z, W, V, U, T) = fresh158(cyclic(Y, Z, W, U), true, Y, Z, W, V, U, T).
22.40/3.21	Axiom 38 (ruleD40): fresh105(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
22.40/3.21	Axiom 39 (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).
22.40/3.21	Axiom 40 (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).
22.40/3.21	Axiom 41 (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).
22.40/3.21	Axiom 42 (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).
22.40/3.21	Axiom 43 (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).
22.40/3.21	Axiom 44 (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).
22.40/3.21	
22.40/3.21	Lemma 45: para(midpnt1, midpnt1, b, b) = true.
22.40/3.21	Proof:
22.40/3.21	  para(midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 21 (ruleD44) R->L }
22.40/3.21	  fresh100(true, true, a, b, b, midpnt1, midpnt1)
22.40/3.21	= { by axiom 1 (exemplo6GDDFULLmoreE02211_9) R->L }
22.40/3.21	  fresh100(midp(midpnt1, a, b), true, a, b, b, midpnt1, midpnt1)
22.40/3.21	= { by axiom 29 (ruleD44) }
22.40/3.21	  fresh99(midp(midpnt1, a, b), true, b, b, midpnt1, midpnt1)
22.40/3.21	= { by axiom 1 (exemplo6GDDFULLmoreE02211_9) }
22.40/3.21	  fresh99(true, true, b, b, midpnt1, midpnt1)
22.40/3.21	= { by axiom 12 (ruleD44) }
22.40/3.21	  true
22.40/3.21	
22.40/3.21	Lemma 46: para(X, Y, X, Y) = true.
22.40/3.21	Proof:
22.40/3.21	  para(X, Y, X, Y)
22.40/3.21	= { by axiom 35 (ruleD73) R->L }
22.40/3.21	  fresh58(true, true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 34 (ruleD21) R->L }
22.40/3.21	  fresh58(fresh132(true, true, X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 33 (ruleD19) R->L }
22.40/3.21	  fresh58(fresh132(fresh135(true, true, midpnt1, midpnt1, X, Y, b, b, X, Y), true, X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 23 (ruleD40) R->L }
22.40/3.21	  fresh58(fresh132(fresh135(fresh105(true, true, midpnt1, midpnt1, b, b, X, Y), true, midpnt1, midpnt1, X, Y, b, b, X, Y), true, X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by lemma 45 R->L }
22.40/3.21	  fresh58(fresh132(fresh135(fresh105(para(midpnt1, midpnt1, b, b), true, midpnt1, midpnt1, b, b, X, Y), true, midpnt1, midpnt1, X, Y, b, b, X, Y), true, X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 38 (ruleD40) }
22.40/3.21	  fresh58(fresh132(fresh135(eqangle(midpnt1, midpnt1, X, Y, b, b, X, Y), true, midpnt1, midpnt1, X, Y, b, b, X, Y), true, X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 42 (ruleD19) }
22.40/3.21	  fresh58(fresh132(eqangle(X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, midpnt1, midpnt1, X, Y, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 43 (ruleD21) }
22.40/3.21	  fresh58(eqangle(X, Y, X, Y, midpnt1, midpnt1, b, b), true, X, Y, X, Y, midpnt1, midpnt1, b, b)
22.40/3.21	= { by axiom 44 (ruleD73) }
22.40/3.21	  fresh57(para(midpnt1, midpnt1, b, b), true, X, Y, X, Y)
22.40/3.21	= { by lemma 45 }
22.40/3.21	  fresh57(true, true, X, Y, X, Y)
22.40/3.21	= { by axiom 15 (ruleD73) }
22.40/3.21	  true
22.40/3.21	
22.40/3.21	Lemma 47: eqangle(X, Y, Z, W, X, Y, Z, W) = true.
22.40/3.21	Proof:
22.40/3.21	  eqangle(X, Y, Z, W, X, Y, Z, W)
22.40/3.21	= { by axiom 38 (ruleD40) R->L }
22.40/3.21	  fresh105(para(X, Y, X, Y), true, X, Y, X, Y, Z, W)
22.40/3.21	= { by lemma 46 }
22.40/3.21	  fresh105(true, true, X, Y, X, Y, Z, W)
22.40/3.21	= { by axiom 23 (ruleD40) }
22.40/3.21	  true
22.40/3.21	
22.40/3.21	Lemma 48: cyclic(X, Y, X, Z) = true.
22.40/3.21	Proof:
22.40/3.21	  cyclic(X, Y, X, Z)
22.40/3.21	= { by axiom 28 (ruleD16) R->L }
22.40/3.21	  fresh139(cyclic(Y, X, X, Z), true, Y, X, X, Z)
22.40/3.21	= { by axiom 26 (ruleD14) R->L }
22.40/3.21	  fresh139(fresh141(cyclic(Y, X, Z, X), true, Y, X, Z, X), true, Y, X, X, Z)
22.40/3.21	= { by axiom 27 (ruleD15) R->L }
22.40/3.21	  fresh139(fresh141(fresh140(cyclic(Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
22.40/3.21	= { by axiom 9 (ruleD42b) R->L }
22.40/3.21	  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)
22.40/3.21	= { by lemma 47 R->L }
22.40/3.21	  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)
22.40/3.21	= { by axiom 40 (ruleD42b) }
22.40/3.21	  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)
22.40/3.21	= { by axiom 18 (ruleD1) R->L }
22.40/3.21	  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)
22.40/3.21	= { by axiom 20 (ruleD2) R->L }
22.40/3.21	  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)
22.40/3.21	= { by axiom 24 (ruleD66) R->L }
22.40/3.21	  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)
22.40/3.21	= { by lemma 46 }
22.40/3.21	  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)
22.40/3.21	= { by axiom 4 (ruleD66) }
22.40/3.21	  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)
22.40/3.21	= { by axiom 3 (ruleD2) }
22.40/3.21	  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)
22.40/3.21	= { by axiom 2 (ruleD1) }
22.40/3.21	  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)
22.40/3.21	= { by axiom 10 (ruleD42b) }
22.40/3.21	  fresh139(fresh141(fresh140(true, true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
22.40/3.21	= { by axiom 6 (ruleD15) }
22.40/3.21	  fresh139(fresh141(true, true, Y, X, Z, X), true, Y, X, X, Z)
22.40/3.21	= { by axiom 5 (ruleD14) }
22.40/3.21	  fresh139(true, true, Y, X, X, Z)
22.40/3.21	= { by axiom 7 (ruleD16) }
22.40/3.21	  true
22.40/3.21	
22.40/3.21	Lemma 49: cyclic(X, Y, Z, W) = true.
22.40/3.21	Proof:
22.40/3.21	  cyclic(X, Y, Z, W)
22.40/3.21	= { by axiom 19 (ruleD17) R->L }
22.40/3.21	  fresh138(true, true, Y, X, Y, Z, W)
22.40/3.21	= { by lemma 48 R->L }
22.40/3.21	  fresh138(cyclic(Y, X, Y, W), true, Y, X, Y, Z, W)
22.40/3.21	= { by axiom 32 (ruleD17) }
22.40/3.21	  fresh137(cyclic(Y, X, Y, Z), true, X, Y, Z, W)
22.40/3.21	= { by lemma 48 }
22.40/3.21	  fresh137(true, true, X, Y, Z, W)
22.40/3.21	= { by axiom 8 (ruleD17) }
22.40/3.21	  true
22.40/3.21	
22.40/3.21	Lemma 50: cong(X, Y, X, Y) = true.
22.40/3.21	Proof:
22.40/3.21	  cong(X, Y, X, Y)
22.40/3.21	= { by axiom 22 (ruleD43) R->L }
22.40/3.21	  fresh159(true, true, X, Y, Z, X, Y, Z)
22.40/3.21	= { by lemma 49 R->L }
22.40/3.21	  fresh159(cyclic(X, Y, Z, X), true, X, Y, Z, X, Y, Z)
22.40/3.21	= { by axiom 36 (ruleD43) R->L }
22.40/3.21	  fresh158(true, true, X, Y, Z, X, Y, Z)
22.40/3.21	= { by lemma 49 R->L }
22.40/3.21	  fresh158(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y, Z)
22.40/3.21	= { by axiom 37 (ruleD43) R->L }
22.40/3.21	  fresh157(true, true, X, Y, Z, X, Y, Z)
22.40/3.21	= { by lemma 49 R->L }
22.40/3.21	  fresh157(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y, Z)
22.40/3.21	= { by axiom 41 (ruleD43) }
22.40/3.21	  fresh101(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, X, Y)
22.40/3.21	= { by lemma 47 }
22.40/3.21	  fresh101(true, true, X, Y, X, Y)
22.40/3.21	= { by axiom 11 (ruleD43) }
22.40/3.22	  true
22.40/3.22	
22.40/3.22	Lemma 51: perp(X, X, Y, Z) = true.
22.40/3.22	Proof:
22.40/3.22	  perp(X, X, Y, Z)
22.40/3.22	= { by axiom 13 (ruleD56) R->L }
22.40/3.22	  fresh80(true, true, X, X, Y, Z)
22.40/3.22	= { by lemma 50 R->L }
22.40/3.22	  fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
22.40/3.22	= { by axiom 30 (ruleD56) }
22.40/3.22	  fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
22.40/3.22	= { by lemma 50 }
22.40/3.22	  fresh79(true, true, X, X, Y, Z)
22.40/3.22	= { by axiom 14 (ruleD56) }
22.40/3.22	  true
22.40/3.22	
22.40/3.22	Goal 1 (exemplo6GDDFULLmoreE02211_12): para(g, e, a, b) = true.
22.40/3.22	Proof:
22.40/3.22	  para(g, e, a, b)
22.40/3.22	= { by axiom 25 (ruleD9) R->L }
22.40/3.22	  fresh51(true, true, g, e, X, X, a, b)
22.40/3.22	= { by lemma 51 R->L }
22.40/3.22	  fresh51(perp(X, X, a, b), true, g, e, X, X, a, b)
22.40/3.22	= { by axiom 39 (ruleD9) }
22.40/3.22	  fresh50(perp(g, e, X, X), true, g, e, a, b)
22.40/3.22	= { by axiom 31 (ruleD8) R->L }
22.40/3.22	  fresh50(fresh52(perp(X, X, g, e), true, X, X, g, e), true, g, e, a, b)
22.40/3.22	= { by lemma 51 }
22.40/3.22	  fresh50(fresh52(true, true, X, X, g, e), true, g, e, a, b)
22.40/3.22	= { by axiom 16 (ruleD8) }
22.40/3.22	  fresh50(true, true, g, e, a, b)
22.40/3.22	= { by axiom 17 (ruleD9) }
22.40/3.22	  true
22.40/3.22	% SZS output end Proof
22.40/3.22	
22.40/3.22	RESULT: Theorem (the conjecture is true).
22.40/3.23	EOF