0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.12/0.33	% Computer   : n011.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1200
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Tue Jul 13 14:16:25 EDT 2021
0.12/0.33	% CPUTime    : 
13.10/3.03	% SZS status Theorem
13.29/3.04	
13.76/3.14	% SZS output start Proof
13.76/3.14	Take the following subset of the input axioms:
13.76/3.14	  fof(exemplo6GDDFULL214040, conjecture, ![A, B, C, E, I]: (cong(E, I, E, A) <= (eqangle(I, A, A, B, I, A, A, C) & (eqangle(I, C, C, A, I, C, C, B) & (coll(E, A, C) & (para(A, B, E, I) & eqangle(I, B, B, C, I, B, B, A))))))).
13.76/3.14	  fof(ruleD1, axiom, ![A, B, C]: (coll(A, B, C) => coll(A, C, B))).
13.76/3.14	  fof(ruleD14, axiom, ![A, B, C, D]: (cyclic(A, B, D, C) <= cyclic(A, B, C, D))).
13.76/3.14	  fof(ruleD15, axiom, ![A, B, C, D]: (cyclic(A, B, C, D) => cyclic(A, C, B, D))).
13.76/3.14	  fof(ruleD16, axiom, ![A, B, C, D]: (cyclic(B, A, C, D) <= cyclic(A, B, C, D))).
13.76/3.14	  fof(ruleD17, axiom, ![A, B, C, D, E]: ((cyclic(A, B, C, D) & cyclic(A, B, C, E)) => cyclic(B, C, D, E))).
13.76/3.14	  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))).
13.76/3.14	  fof(ruleD2, axiom, ![A, B, C]: (coll(B, A, C) <= coll(A, B, C))).
13.76/3.14	  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))).
13.76/3.14	  fof(ruleD23, axiom, ![A, B, C, D]: (cong(A, B, D, C) <= cong(A, B, C, D))).
13.76/3.14	  fof(ruleD24, axiom, ![A, B, C, D]: (cong(A, B, C, D) => cong(C, D, A, B))).
13.76/3.14	  fof(ruleD3, axiom, ![A, B, C, D]: (coll(C, D, A) <= (coll(A, B, C) & coll(A, B, D)))).
13.76/3.14	  fof(ruleD39, axiom, ![A, B, C, P, Q, D]: (para(A, B, C, D) <= eqangle(A, B, P, Q, C, D, P, Q))).
13.76/3.14	  fof(ruleD40, axiom, ![A, B, C, P, Q, D]: (eqangle(A, B, P, Q, C, D, P, Q) <= para(A, B, C, D))).
13.76/3.14	  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))).
13.76/3.14	  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)))))).
13.76/3.14	  fof(ruleD52, axiom, ![A, B, C, M]: ((midp(M, A, C) & perp(A, B, B, C)) => cong(A, M, B, M))).
13.76/3.14	  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))).
13.76/3.14	  fof(ruleD66, axiom, ![A, B, C]: (coll(A, B, C) <= para(A, B, A, C))).
13.76/3.14	  fof(ruleD67, axiom, ![A, B, C]: ((cong(A, B, A, C) & coll(A, B, C)) => midp(A, B, C))).
13.76/3.14	  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))).
13.76/3.14	  fof(ruleD8, axiom, ![A, B, C, D]: (perp(C, D, A, B) <= perp(A, B, C, D))).
13.76/3.14	
13.76/3.14	Now clausify the problem and encode Horn clauses using encoding 3 of
13.76/3.14	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
13.76/3.14	We repeatedly replace C & s=t => u=v by the two clauses:
13.76/3.14	  fresh(y, y, x1...xn) = u
13.76/3.14	  C => fresh(s, t, x1...xn) = v
13.76/3.14	where fresh is a fresh function symbol and x1..xn are the free
13.76/3.14	variables of u and v.
13.76/3.14	A predicate p(X) is encoded as p(X)=true (this is sound, because the
13.76/3.14	input problem has no model of domain size 1).
13.76/3.14	
13.76/3.14	The encoding turns the above axioms into the following unit equations and goals:
13.76/3.14	
13.76/3.14	Axiom 1 (exemplo6GDDFULL214040_1): para(a, b, e, i) = true.
13.76/3.14	Axiom 2 (ruleD57): fresh179(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 3 (ruleD1): fresh147(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 4 (ruleD2): fresh134(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 5 (ruleD3): fresh120(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 6 (ruleD52): fresh87(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 7 (ruleD66): fresh66(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 8 (ruleD67): fresh65(X, X, Y, Z, W) = midp(Y, Z, W).
13.76/3.14	Axiom 9 (ruleD67): fresh64(X, X, Y, Z, W) = true.
13.76/3.14	Axiom 10 (ruleD14): fresh141(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 11 (ruleD15): fresh140(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 12 (ruleD16): fresh139(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 13 (ruleD17): fresh137(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 14 (ruleD23): fresh129(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 15 (ruleD24): fresh128(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 16 (ruleD3): fresh121(X, X, Y, Z, W, V) = coll(W, V, Y).
13.76/3.14	Axiom 17 (ruleD39): fresh107(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 18 (ruleD42b): fresh103(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
13.76/3.14	Axiom 19 (ruleD42b): fresh102(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 20 (ruleD43): fresh101(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 21 (ruleD52): fresh88(X, X, Y, Z, W, V) = cong(Y, V, Z, V).
13.76/3.14	Axiom 22 (ruleD57): fresh78(X, X, Y, Z, W, V) = perp(W, Y, Y, V).
13.76/3.14	Axiom 23 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 24 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
13.76/3.14	Axiom 25 (ruleD1): fresh147(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
13.76/3.14	Axiom 26 (ruleD17): fresh138(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
13.76/3.14	Axiom 27 (ruleD2): fresh134(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
13.76/3.14	Axiom 28 (ruleD57): fresh178(X, X, Y, Z, W, V) = fresh179(cong(Y, W, Z, W), true, Y, W, V).
13.76/3.14	Axiom 29 (ruleD43): fresh159(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
13.76/3.14	Axiom 30 (ruleD3): fresh121(coll(X, Y, Z), true, X, Y, W, Z) = fresh120(coll(X, Y, W), true, X, W, Z).
13.76/3.14	Axiom 31 (ruleD40): fresh105(X, X, Y, Z, W, V, U, T) = true.
13.76/3.14	Axiom 32 (ruleD52): fresh88(midp(X, Y, Z), true, Y, W, Z, X) = fresh87(perp(Y, W, W, Z), true, Y, W, X).
13.76/3.14	Axiom 33 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
13.76/3.14	Axiom 34 (ruleD67): fresh65(cong(X, Y, X, Z), true, X, Y, Z) = fresh64(coll(X, Y, Z), true, X, Y, Z).
13.76/3.14	Axiom 35 (exemplo6GDDFULL214040_3): eqangle(i, c, c, a, i, c, c, b) = true.
13.76/3.14	Axiom 36 (ruleD14): fresh141(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
13.76/3.14	Axiom 37 (ruleD15): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
13.76/3.14	Axiom 38 (ruleD16): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
13.76/3.14	Axiom 39 (ruleD23): fresh129(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(X, Y, W, Z).
13.76/3.14	Axiom 40 (ruleD24): fresh128(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(Z, W, X, Y).
13.76/3.14	Axiom 41 (ruleD57): fresh178(cyclic(X, Y, Z, W), true, X, Y, Z, W) = fresh78(cong(X, W, Y, W), true, X, Y, Z, W).
13.76/3.15	Axiom 42 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
13.76/3.15	Axiom 43 (ruleD17): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh137(cyclic(X, Y, Z, V), true, Y, Z, V, W).
13.76/3.15	Axiom 44 (ruleD19): fresh135(X, X, Y, Z, W, V, U, T, S, X2) = true.
13.76/3.15	Axiom 45 (ruleD21): fresh132(X, X, Y, Z, W, V, U, T, S, X2) = true.
13.76/3.15	Axiom 46 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
13.76/3.15	Axiom 47 (ruleD43): fresh158(X, X, Y, Z, W, V, U, T) = fresh159(cyclic(Y, Z, W, V), true, Y, Z, W, V, U, T).
13.76/3.15	Axiom 48 (ruleD43): fresh157(X, X, Y, Z, W, V, U, T) = fresh158(cyclic(Y, Z, W, U), true, Y, Z, W, V, U, T).
13.76/3.15	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).
13.76/3.15	Axiom 50 (ruleD39): fresh107(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
13.76/3.15	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).
13.76/3.15	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).
13.76/3.15	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).
13.76/3.15	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).
13.76/3.15	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).
13.76/3.15	
13.76/3.15	Lemma 56: para(X, Y, X, Y) = true.
13.76/3.15	Proof:
13.76/3.15	  para(X, Y, X, Y)
13.76/3.15	= { by axiom 46 (ruleD73) R->L }
13.76/3.15	  fresh58(true, true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 45 (ruleD21) R->L }
13.76/3.15	  fresh58(fresh132(true, true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 44 (ruleD19) R->L }
13.76/3.15	  fresh58(fresh132(fresh135(true, true, a, b, X, Y, e, i, X, Y), true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 31 (ruleD40) R->L }
13.76/3.15	  fresh58(fresh132(fresh135(fresh105(true, true, a, b, e, i, X, Y), true, a, b, X, Y, e, i, X, Y), true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 1 (exemplo6GDDFULL214040_1) R->L }
13.76/3.15	  fresh58(fresh132(fresh135(fresh105(para(a, b, e, i), true, a, b, e, i, X, Y), true, a, b, X, Y, e, i, X, Y), true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 49 (ruleD40) }
13.76/3.15	  fresh58(fresh132(fresh135(eqangle(a, b, X, Y, e, i, X, Y), true, a, b, X, Y, e, i, X, Y), true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 53 (ruleD19) }
13.76/3.15	  fresh58(fresh132(eqangle(X, Y, a, b, X, Y, e, i), true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 54 (ruleD21) }
13.76/3.15	  fresh58(eqangle(X, Y, X, Y, a, b, e, i), true, X, Y, X, Y, a, b, e, i)
13.76/3.15	= { by axiom 55 (ruleD73) }
13.76/3.15	  fresh57(para(a, b, e, i), true, X, Y, X, Y)
13.76/3.15	= { by axiom 1 (exemplo6GDDFULL214040_1) }
13.76/3.15	  fresh57(true, true, X, Y, X, Y)
13.76/3.15	= { by axiom 23 (ruleD73) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Lemma 57: coll(X, X, Y) = true.
13.76/3.15	Proof:
13.76/3.15	  coll(X, X, Y)
13.76/3.15	= { by axiom 25 (ruleD1) R->L }
13.76/3.15	  fresh147(coll(X, Y, X), true, X, Y, X)
13.76/3.15	= { by axiom 27 (ruleD2) R->L }
13.76/3.15	  fresh147(fresh134(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
13.76/3.15	= { by axiom 33 (ruleD66) R->L }
13.76/3.15	  fresh147(fresh134(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
13.76/3.15	= { by lemma 56 }
13.76/3.15	  fresh147(fresh134(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
13.76/3.15	= { by axiom 7 (ruleD66) }
13.76/3.15	  fresh147(fresh134(true, true, Y, X, X), true, X, Y, X)
13.76/3.15	= { by axiom 4 (ruleD2) }
13.76/3.15	  fresh147(true, true, X, Y, X)
13.76/3.15	= { by axiom 3 (ruleD1) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Lemma 58: eqangle(X, Y, Z, W, X, Y, Z, W) = true.
13.76/3.15	Proof:
13.76/3.15	  eqangle(X, Y, Z, W, X, Y, Z, W)
13.76/3.15	= { by axiom 49 (ruleD40) R->L }
13.76/3.15	  fresh105(para(X, Y, X, Y), true, X, Y, X, Y, Z, W)
13.76/3.15	= { by lemma 56 }
13.76/3.15	  fresh105(true, true, X, Y, X, Y, Z, W)
13.76/3.15	= { by axiom 31 (ruleD40) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Lemma 59: cyclic(X, Y, Z, Z) = true.
13.76/3.15	Proof:
13.76/3.15	  cyclic(X, Y, Z, Z)
13.76/3.15	= { by axiom 18 (ruleD42b) R->L }
13.76/3.15	  fresh103(true, true, X, Y, Z, Z)
13.76/3.15	= { by lemma 58 R->L }
13.76/3.15	  fresh103(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, Z)
13.76/3.15	= { by axiom 51 (ruleD42b) }
13.76/3.15	  fresh102(coll(Z, Z, Y), true, X, Y, Z, Z)
13.76/3.15	= { by lemma 57 }
13.76/3.15	  fresh102(true, true, X, Y, Z, Z)
13.76/3.15	= { by axiom 19 (ruleD42b) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Lemma 60: cyclic(X, Y, X, Z) = true.
13.76/3.15	Proof:
13.76/3.15	  cyclic(X, Y, X, Z)
13.76/3.15	= { by axiom 38 (ruleD16) R->L }
13.76/3.15	  fresh139(cyclic(Y, X, X, Z), true, Y, X, X, Z)
13.76/3.15	= { by axiom 36 (ruleD14) R->L }
13.76/3.15	  fresh139(fresh141(cyclic(Y, X, Z, X), true, Y, X, Z, X), true, Y, X, X, Z)
13.76/3.15	= { by axiom 37 (ruleD15) R->L }
13.76/3.15	  fresh139(fresh141(fresh140(cyclic(Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
13.76/3.15	= { by lemma 59 }
13.76/3.15	  fresh139(fresh141(fresh140(true, true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
13.76/3.15	= { by axiom 11 (ruleD15) }
13.76/3.15	  fresh139(fresh141(true, true, Y, X, Z, X), true, Y, X, X, Z)
13.76/3.15	= { by axiom 10 (ruleD14) }
13.76/3.15	  fresh139(true, true, Y, X, X, Z)
13.76/3.15	= { by axiom 12 (ruleD16) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Lemma 61: cyclic(X, Y, Z, W) = true.
13.76/3.15	Proof:
13.76/3.15	  cyclic(X, Y, Z, W)
13.76/3.15	= { by axiom 26 (ruleD17) R->L }
13.76/3.15	  fresh138(true, true, Y, X, Y, Z, W)
13.76/3.15	= { by lemma 60 R->L }
13.76/3.15	  fresh138(cyclic(Y, X, Y, W), true, Y, X, Y, Z, W)
13.76/3.15	= { by axiom 43 (ruleD17) }
13.76/3.15	  fresh137(cyclic(Y, X, Y, Z), true, X, Y, Z, W)
13.76/3.15	= { by lemma 60 }
13.76/3.15	  fresh137(true, true, X, Y, Z, W)
13.76/3.15	= { by axiom 13 (ruleD17) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Lemma 62: fresh157(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
13.76/3.15	Proof:
13.76/3.15	  fresh157(X, X, Y, Z, W, V, U, T)
13.76/3.15	= { by axiom 48 (ruleD43) }
13.76/3.15	  fresh158(cyclic(Y, Z, W, U), true, Y, Z, W, V, U, T)
13.76/3.15	= { by lemma 61 }
13.76/3.15	  fresh158(true, true, Y, Z, W, V, U, T)
13.76/3.15	= { by axiom 47 (ruleD43) }
13.76/3.15	  fresh159(cyclic(Y, Z, W, V), true, Y, Z, W, V, U, T)
13.76/3.15	= { by lemma 61 }
13.76/3.15	  fresh159(true, true, Y, Z, W, V, U, T)
13.76/3.15	= { by axiom 29 (ruleD43) }
13.76/3.15	  cong(Y, Z, V, U)
13.76/3.15	
13.76/3.15	Lemma 63: cong(a, X, b, X) = true.
13.76/3.15	Proof:
13.76/3.15	  cong(a, X, b, X)
13.76/3.15	= { by lemma 62 R->L }
13.76/3.15	  fresh157(true, true, a, X, c, b, X, c)
13.76/3.15	= { by lemma 59 R->L }
13.76/3.15	  fresh157(cyclic(a, X, c, c), true, a, X, c, b, X, c)
13.76/3.15	= { by axiom 52 (ruleD43) }
13.76/3.15	  fresh101(eqangle(c, a, c, X, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 49 (ruleD40) R->L }
13.76/3.15	  fresh101(fresh105(para(c, a, c, b), true, c, a, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 50 (ruleD39) R->L }
13.76/3.15	  fresh101(fresh105(fresh107(eqangle(c, a, i, c, c, b, i, c), true, c, a, c, b), true, c, a, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 53 (ruleD19) R->L }
13.76/3.15	  fresh101(fresh105(fresh107(fresh135(eqangle(i, c, c, a, i, c, c, b), true, i, c, c, a, i, c, c, b), true, c, a, c, b), true, c, a, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 35 (exemplo6GDDFULL214040_3) }
13.76/3.15	  fresh101(fresh105(fresh107(fresh135(true, true, i, c, c, a, i, c, c, b), true, c, a, c, b), true, c, a, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 44 (ruleD19) }
13.76/3.15	  fresh101(fresh105(fresh107(true, true, c, a, c, b), true, c, a, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 17 (ruleD39) }
13.76/3.15	  fresh101(fresh105(true, true, c, a, c, b, c, X), true, a, X, b, X)
13.76/3.15	= { by axiom 31 (ruleD40) }
13.76/3.15	  fresh101(true, true, a, X, b, X)
13.76/3.15	= { by axiom 20 (ruleD43) }
13.76/3.15	  true
13.76/3.15	
13.76/3.15	Goal 1 (exemplo6GDDFULL214040_5): cong(e, i, e, a) = true.
13.76/3.15	Proof:
13.76/3.15	  cong(e, i, e, a)
13.76/3.15	= { by axiom 39 (ruleD23) R->L }
13.76/3.15	  fresh129(cong(e, i, a, e), true, e, i, a, e)
13.76/3.15	= { by axiom 40 (ruleD24) R->L }
13.76/3.15	  fresh129(fresh128(cong(a, e, e, i), true, a, e, e, i), true, e, i, a, e)
13.76/3.15	= { by axiom 39 (ruleD23) R->L }
13.76/3.15	  fresh129(fresh128(fresh129(cong(a, e, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.15	= { by axiom 21 (ruleD52) R->L }
13.76/3.15	  fresh129(fresh128(fresh129(fresh88(true, true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.15	= { by axiom 9 (ruleD67) R->L }
13.76/3.15	  fresh129(fresh128(fresh129(fresh88(fresh64(true, true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.15	= { by axiom 5 (ruleD3) R->L }
13.76/3.15	  fresh129(fresh128(fresh129(fresh88(fresh64(fresh120(true, true, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 57 R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh64(fresh120(coll(a, a, e), true, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 30 (ruleD3) R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh64(fresh121(coll(a, a, a), true, a, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 57 }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh64(fresh121(true, true, a, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 16 (ruleD3) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh64(coll(e, a, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 34 (ruleD67) R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh65(cong(e, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 62 R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh65(fresh157(true, true, e, a, X, e, a, X), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 61 R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh65(fresh157(cyclic(e, a, X, X), true, e, a, X, e, a, X), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 52 (ruleD43) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh65(fresh101(eqangle(X, e, X, a, X, e, X, a), true, e, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 58 }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh65(fresh101(true, true, e, a, e, a), true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 20 (ruleD43) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(fresh65(true, true, e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 8 (ruleD67) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh88(midp(e, a, a), true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 32 (ruleD52) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(perp(a, i, i, a), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 42 (ruleD8) R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(perp(i, a, a, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 22 (ruleD57) R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(fresh78(true, true, a, b, i, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 63 R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(fresh78(cong(a, i, b, i), true, a, b, i, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 41 (ruleD57) R->L }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(fresh178(cyclic(a, b, i, i), true, a, b, i, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 61 }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(fresh178(true, true, a, b, i, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 28 (ruleD57) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(fresh179(cong(a, i, b, i), true, a, i, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by lemma 63 }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(fresh179(true, true, a, i, i), true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 2 (ruleD57) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(fresh52(true, true, i, a, a, i), true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 24 (ruleD8) }
13.76/3.16	  fresh129(fresh128(fresh129(fresh87(true, true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 6 (ruleD52) }
13.76/3.16	  fresh129(fresh128(fresh129(true, true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 14 (ruleD23) }
13.76/3.16	  fresh129(fresh128(true, true, a, e, e, i), true, e, i, a, e)
13.76/3.16	= { by axiom 15 (ruleD24) }
13.76/3.16	  fresh129(true, true, e, i, a, e)
13.76/3.16	= { by axiom 14 (ruleD23) }
13.76/3.16	  true
13.76/3.16	% SZS output end Proof
13.76/3.16	
13.76/3.16	RESULT: Theorem (the conjecture is true).
13.76/3.18	EOF