TSTP Solution File: GEO581+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO581+1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:29:24 EDT 2023
% Result : Theorem 11.56s 1.74s
% Output : Proof 11.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO581+1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.07 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.06/0.25 % Computer : n007.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Aug 29 18:43:13 EDT 2023
% 0.06/0.26 % CPUTime :
% 11.56/1.74 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 11.56/1.74
% 11.56/1.74 % SZS status Theorem
% 11.56/1.74
% 11.56/1.77 % SZS output start Proof
% 11.56/1.77 Take the following subset of the input axioms:
% 11.56/1.78 fof(exemplo6GDDFULL416043, conjecture, ![A, B, C, E, F, P]: ((perp(C, A, C, B) & (eqangle(B, A, A, E, A, E, E, F) & (cong(A, E, E, F) & (coll(P, B, E) & coll(P, A, F))))) => eqangle(A, C, C, P, P, C, C, B))).
% 11.56/1.78 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 11.56/1.78 fof(ruleD14, axiom, ![D, B2, C2, A2_2]: (cyclic(A2_2, B2, C2, D) => cyclic(A2_2, B2, D, C2))).
% 11.56/1.78 fof(ruleD15, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 11.56/1.78 fof(ruleD17, axiom, ![B2, C2, D2, E2, A2_2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 11.56/1.78 fof(ruleD19, axiom, ![Q, U, V, B2, C2, D2, A2_2, P2]: (eqangle(A2_2, B2, C2, D2, P2, Q, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P2, Q))).
% 11.56/1.78 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 11.56/1.78 fof(ruleD20, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(P2, Q2, U2, V2, A2_2, B2, C2, D2))).
% 11.56/1.78 fof(ruleD21, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(A2_2, B2, P2, Q2, C2, D2, U2, V2))).
% 11.56/1.78 fof(ruleD22, axiom, ![G, H, B2, C2, D2, E2, F2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & eqangle(P2, Q2, U2, V2, E2, F2, G, H)) => eqangle(A2_2, B2, C2, D2, E2, F2, G, H))).
% 11.56/1.78 fof(ruleD39, axiom, ![B2, C2, D2, A2_2, P2, Q2]: (eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2) => para(A2_2, B2, C2, D2))).
% 11.56/1.78 fof(ruleD40, axiom, ![B2, C2, D2, A2_2, P2, Q2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 11.56/1.78 fof(ruleD42b, axiom, ![B2, A2_2, P2, Q2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 11.56/1.78 fof(ruleD43, axiom, ![R, B2, C2, A2_2, P2, Q2]: ((cyclic(A2_2, B2, C2, P2) & (cyclic(A2_2, B2, C2, Q2) & (cyclic(A2_2, B2, C2, R) & eqangle(C2, A2_2, C2, B2, R, P2, R, Q2)))) => cong(A2_2, B2, P2, Q2))).
% 11.56/1.78 fof(ruleD56, axiom, ![B2, A2_2, P2, Q2]: ((cong(A2_2, P2, B2, P2) & cong(A2_2, Q2, B2, Q2)) => perp(A2_2, B2, P2, Q2))).
% 11.56/1.78 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 11.56/1.78 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 11.56/1.78 fof(ruleD9, axiom, ![B2, C2, D2, E2, F2, A2_2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => para(A2_2, B2, E2, F2))).
% 11.56/1.78
% 11.56/1.78 Now clausify the problem and encode Horn clauses using encoding 3 of
% 11.56/1.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 11.56/1.78 We repeatedly replace C & s=t => u=v by the two clauses:
% 11.56/1.78 fresh(y, y, x1...xn) = u
% 11.56/1.78 C => fresh(s, t, x1...xn) = v
% 11.56/1.78 where fresh is a fresh function symbol and x1..xn are the free
% 11.56/1.78 variables of u and v.
% 11.56/1.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 11.56/1.78 input problem has no model of domain size 1).
% 11.56/1.78
% 11.56/1.78 The encoding turns the above axioms into the following unit equations and goals:
% 11.56/1.78
% 11.56/1.78 Axiom 1 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 11.56/1.78 Axiom 2 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 11.56/1.78 Axiom 3 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 11.56/1.78 Axiom 4 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 5 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 6 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 7 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 8 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 9 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 11.56/1.78 Axiom 10 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 11 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 11.56/1.78 Axiom 12 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 13 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 14 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 11.56/1.78 Axiom 15 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 11.56/1.78 Axiom 16 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 11.56/1.78 Axiom 17 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 11.56/1.78 Axiom 18 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 11.56/1.78 Axiom 19 (exemplo6GDDFULL416043_4): eqangle(b, a, a, e, a, e, e, f) = true.
% 11.56/1.78 Axiom 20 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 11.56/1.78 Axiom 21 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 11.56/1.78 Axiom 22 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 11.56/1.78 Axiom 23 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 11.56/1.78 Axiom 24 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 11.56/1.78 Axiom 25 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 11.56/1.78 Axiom 26 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 11.56/1.78 Axiom 27 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 11.56/1.78 Axiom 28 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 11.56/1.78 Axiom 29 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 11.56/1.78 Axiom 30 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 11.56/1.78 Axiom 31 (ruleD20): fresh132(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 11.56/1.78 Axiom 32 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 11.56/1.78 Axiom 33 (ruleD22): fresh129(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 11.56/1.78 Axiom 34 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 11.56/1.78 Axiom 35 (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).
% 11.56/1.78 Axiom 36 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 11.56/1.78 Axiom 37 (ruleD42b): fresh102(eqangle(X, Y, X, Z, W, Y, W, Z), true, Y, Z, X, W) = fresh101(coll(X, W, Z), true, Y, Z, X, W).
% 11.56/1.78 Axiom 38 (ruleD22): fresh130(X, X, Y, Z, W, V, U, T, S, X2, Y2, Z2, W2, V2) = eqangle(Y, Z, W, V, Y2, Z2, W2, V2).
% 11.56/1.78 Axiom 39 (ruleD43): fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W) = fresh184(cyclic(Y, Z, X, W), true, Y, Z, X, V, U).
% 11.56/1.78 Axiom 40 (ruleD19): fresh134(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).
% 11.56/1.78 Axiom 41 (ruleD20): fresh132(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = eqangle(V, U, T, S, X, Y, Z, W).
% 11.56/1.78 Axiom 42 (ruleD21): fresh131(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).
% 11.56/1.78 Axiom 43 (ruleD22): fresh130(eqangle(X, Y, Z, W, V, U, T, S), true, X2, Y2, Z2, W2, X, Y, Z, W, V, U, T, S) = fresh129(eqangle(X2, Y2, Z2, W2, X, Y, Z, W), true, X2, Y2, Z2, W2, V, U, T, S).
% 11.56/1.78
% 11.56/1.78 Lemma 44: eqangle(a, e, X, Y, a, e, X, Y) = true.
% 11.56/1.78 Proof:
% 11.56/1.78 eqangle(a, e, X, Y, a, e, X, Y)
% 11.56/1.78 = { by axiom 34 (ruleD40) R->L }
% 11.56/1.78 fresh104(para(a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 36 (ruleD39) R->L }
% 11.56/1.78 fresh104(fresh106(eqangle(a, e, e, f, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 38 (ruleD22) R->L }
% 11.56/1.78 fresh104(fresh106(fresh130(true, true, a, e, e, f, b, a, a, e, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 19 (exemplo6GDDFULL416043_4) R->L }
% 11.56/1.78 fresh104(fresh106(fresh130(eqangle(b, a, a, e, a, e, e, f), true, a, e, e, f, b, a, a, e, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 43 (ruleD22) }
% 11.56/1.78 fresh104(fresh106(fresh129(eqangle(a, e, e, f, b, a, a, e), true, a, e, e, f, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 41 (ruleD20) R->L }
% 11.56/1.78 fresh104(fresh106(fresh129(fresh132(eqangle(b, a, a, e, a, e, e, f), true, b, a, a, e, a, e, e, f), true, a, e, e, f, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 19 (exemplo6GDDFULL416043_4) }
% 11.56/1.78 fresh104(fresh106(fresh129(fresh132(true, true, b, a, a, e, a, e, e, f), true, a, e, e, f, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 31 (ruleD20) }
% 11.56/1.78 fresh104(fresh106(fresh129(true, true, a, e, e, f, a, e, e, f), true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 33 (ruleD22) }
% 11.56/1.78 fresh104(fresh106(true, true, a, e, a, e), true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 8 (ruleD39) }
% 11.56/1.78 fresh104(true, true, a, e, a, e, X, Y)
% 11.56/1.78 = { by axiom 20 (ruleD40) }
% 11.56/1.78 true
% 11.56/1.78
% 11.56/1.78 Lemma 45: para(X, Y, X, Y) = true.
% 11.56/1.78 Proof:
% 11.56/1.78 para(X, Y, X, Y)
% 11.56/1.78 = { by axiom 36 (ruleD39) R->L }
% 11.56/1.78 fresh106(eqangle(X, Y, a, e, X, Y, a, e), true, X, Y, X, Y)
% 11.56/1.78 = { by axiom 40 (ruleD19) R->L }
% 11.56/1.78 fresh106(fresh134(eqangle(a, e, X, Y, a, e, X, Y), true, a, e, X, Y, a, e, X, Y), true, X, Y, X, Y)
% 11.56/1.78 = { by lemma 44 }
% 11.56/1.78 fresh106(fresh134(true, true, a, e, X, Y, a, e, X, Y), true, X, Y, X, Y)
% 11.56/1.78 = { by axiom 30 (ruleD19) }
% 11.56/1.78 fresh106(true, true, X, Y, X, Y)
% 11.56/1.78 = { by axiom 8 (ruleD39) }
% 11.56/1.78 true
% 11.56/1.78
% 11.56/1.78 Lemma 46: cyclic(e, a, a, X) = true.
% 11.56/1.78 Proof:
% 11.56/1.78 cyclic(e, a, a, X)
% 11.56/1.78 = { by axiom 24 (ruleD14) R->L }
% 11.56/1.78 fresh140(cyclic(e, a, X, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 25 (ruleD15) R->L }
% 11.56/1.78 fresh140(fresh139(cyclic(e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 9 (ruleD42b) R->L }
% 11.56/1.78 fresh140(fresh139(fresh102(true, true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by lemma 44 R->L }
% 11.56/1.78 fresh140(fresh139(fresh102(eqangle(a, e, a, X, a, e, a, X), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 37 (ruleD42b) }
% 11.56/1.78 fresh140(fresh139(fresh101(coll(a, a, X), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 16 (ruleD1) R->L }
% 11.56/1.78 fresh140(fresh139(fresh101(fresh146(coll(a, X, a), true, a, X, a), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 18 (ruleD2) R->L }
% 11.56/1.78 fresh140(fresh139(fresh101(fresh146(fresh133(coll(X, a, a), true, X, a, a), true, a, X, a), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 21 (ruleD66) R->L }
% 11.56/1.78 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(para(X, a, X, a), true, X, a, a), true, X, a, a), true, a, X, a), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by lemma 45 }
% 11.56/1.78 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(true, true, X, a, a), true, X, a, a), true, a, X, a), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 3 (ruleD66) }
% 11.56/1.78 fresh140(fresh139(fresh101(fresh146(fresh133(true, true, X, a, a), true, a, X, a), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 2 (ruleD2) }
% 11.56/1.78 fresh140(fresh139(fresh101(fresh146(true, true, a, X, a), true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 1 (ruleD1) }
% 11.56/1.78 fresh140(fresh139(fresh101(true, true, e, X, a, a), true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 10 (ruleD42b) }
% 11.56/1.78 fresh140(fresh139(true, true, e, X, a, a), true, e, a, X, a)
% 11.56/1.78 = { by axiom 6 (ruleD15) }
% 11.56/1.78 fresh140(true, true, e, a, X, a)
% 11.56/1.78 = { by axiom 5 (ruleD14) }
% 11.56/1.78 true
% 11.56/1.78
% 11.56/1.78 Lemma 47: cyclic(a, a, X, Y) = true.
% 11.56/1.78 Proof:
% 11.56/1.78 cyclic(a, a, X, Y)
% 11.56/1.78 = { by axiom 17 (ruleD17) R->L }
% 11.56/1.78 fresh137(true, true, e, a, a, X, Y)
% 11.56/1.78 = { by lemma 46 R->L }
% 11.56/1.78 fresh137(cyclic(e, a, a, Y), true, e, a, a, X, Y)
% 11.56/1.78 = { by axiom 29 (ruleD17) }
% 11.56/1.78 fresh136(cyclic(e, a, a, X), true, a, a, X, Y)
% 11.56/1.78 = { by lemma 46 }
% 11.56/1.78 fresh136(true, true, a, a, X, Y)
% 11.56/1.78 = { by axiom 7 (ruleD17) }
% 11.56/1.78 true
% 11.56/1.78
% 11.56/1.78 Lemma 48: cyclic(a, X, Y, Z) = true.
% 11.56/1.78 Proof:
% 11.56/1.78 cyclic(a, X, Y, Z)
% 11.56/1.78 = { by axiom 17 (ruleD17) R->L }
% 11.56/1.78 fresh137(true, true, a, a, X, Y, Z)
% 11.56/1.78 = { by lemma 47 R->L }
% 11.56/1.78 fresh137(cyclic(a, a, X, Z), true, a, a, X, Y, Z)
% 11.56/1.78 = { by axiom 29 (ruleD17) }
% 11.56/1.78 fresh136(cyclic(a, a, X, Y), true, a, X, Y, Z)
% 11.56/1.78 = { by lemma 47 }
% 11.56/1.78 fresh136(true, true, a, X, Y, Z)
% 11.56/1.78 = { by axiom 7 (ruleD17) }
% 11.56/1.78 true
% 11.56/1.78
% 11.56/1.78 Lemma 49: cyclic(X, Y, Z, W) = true.
% 11.56/1.78 Proof:
% 11.56/1.78 cyclic(X, Y, Z, W)
% 11.56/1.78 = { by axiom 17 (ruleD17) R->L }
% 11.56/1.78 fresh137(true, true, a, X, Y, Z, W)
% 11.56/1.78 = { by lemma 48 R->L }
% 11.56/1.78 fresh137(cyclic(a, X, Y, W), true, a, X, Y, Z, W)
% 11.56/1.78 = { by axiom 29 (ruleD17) }
% 11.56/1.79 fresh136(cyclic(a, X, Y, Z), true, X, Y, Z, W)
% 11.56/1.79 = { by lemma 48 }
% 11.56/1.79 fresh136(true, true, X, Y, Z, W)
% 11.56/1.79 = { by axiom 7 (ruleD17) }
% 11.56/1.79 true
% 11.56/1.79
% 11.56/1.79 Lemma 50: eqangle(X, Y, Z, W, X, Y, Z, W) = true.
% 11.56/1.79 Proof:
% 11.56/1.79 eqangle(X, Y, Z, W, X, Y, Z, W)
% 11.56/1.79 = { by axiom 34 (ruleD40) R->L }
% 11.56/1.79 fresh104(para(X, Y, X, Y), true, X, Y, X, Y, Z, W)
% 11.56/1.79 = { by lemma 45 }
% 11.56/1.79 fresh104(true, true, X, Y, X, Y, Z, W)
% 11.56/1.79 = { by axiom 20 (ruleD40) }
% 11.56/1.79 true
% 11.56/1.79
% 11.56/1.79 Lemma 51: cong(X, Y, X, Y) = true.
% 11.56/1.79 Proof:
% 11.56/1.79 cong(X, Y, X, Y)
% 11.56/1.79 = { by axiom 15 (ruleD43) R->L }
% 11.56/1.79 fresh183(true, true, X, Y, Z, X, Y)
% 11.56/1.79 = { by lemma 49 R->L }
% 11.56/1.79 fresh183(cyclic(X, Y, Z, Y), true, X, Y, Z, X, Y)
% 11.56/1.79 = { by axiom 28 (ruleD43) R->L }
% 11.56/1.79 fresh182(true, true, X, Y, Z, X, Y, Z)
% 11.56/1.79 = { by lemma 50 R->L }
% 11.56/1.79 fresh182(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, X, Y, Z)
% 11.56/1.79 = { by axiom 39 (ruleD43) }
% 11.56/1.79 fresh184(cyclic(X, Y, Z, Z), true, X, Y, Z, X, Y)
% 11.56/1.79 = { by lemma 49 }
% 11.56/1.79 fresh184(true, true, X, Y, Z, X, Y)
% 11.56/1.79 = { by axiom 23 (ruleD43) }
% 11.56/1.79 fresh185(cyclic(X, Y, Z, X), true, X, Y, X, Y)
% 11.56/1.79 = { by lemma 49 }
% 11.56/1.79 fresh185(true, true, X, Y, X, Y)
% 11.56/1.79 = { by axiom 4 (ruleD43) }
% 11.56/1.79 true
% 11.56/1.79
% 11.56/1.79 Lemma 52: perp(X, X, Y, Z) = true.
% 11.56/1.79 Proof:
% 11.56/1.79 perp(X, X, Y, Z)
% 11.56/1.79 = { by axiom 11 (ruleD56) R->L }
% 11.56/1.79 fresh80(true, true, X, X, Y, Z)
% 11.56/1.79 = { by lemma 51 R->L }
% 11.56/1.79 fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
% 11.56/1.79 = { by axiom 26 (ruleD56) }
% 11.56/1.79 fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
% 11.56/1.79 = { by lemma 51 }
% 11.56/1.79 fresh79(true, true, X, X, Y, Z)
% 11.56/1.79 = { by axiom 12 (ruleD56) }
% 11.56/1.79 true
% 11.56/1.79
% 11.56/1.79 Lemma 53: eqangle(X, Y, Z, W, V, U, Z, W) = true.
% 11.56/1.79 Proof:
% 11.56/1.79 eqangle(X, Y, Z, W, V, U, Z, W)
% 11.56/1.79 = { by axiom 34 (ruleD40) R->L }
% 11.56/1.79 fresh104(para(X, Y, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by axiom 22 (ruleD9) R->L }
% 11.56/1.79 fresh104(fresh51(true, true, X, Y, T, T, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by lemma 52 R->L }
% 11.56/1.79 fresh104(fresh51(perp(T, T, V, U), true, X, Y, T, T, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by axiom 35 (ruleD9) }
% 11.56/1.79 fresh104(fresh50(perp(X, Y, T, T), true, X, Y, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by axiom 27 (ruleD8) R->L }
% 11.56/1.79 fresh104(fresh50(fresh52(perp(T, T, X, Y), true, T, T, X, Y), true, X, Y, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by lemma 52 }
% 11.56/1.79 fresh104(fresh50(fresh52(true, true, T, T, X, Y), true, X, Y, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by axiom 13 (ruleD8) }
% 11.56/1.79 fresh104(fresh50(true, true, X, Y, V, U), true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by axiom 14 (ruleD9) }
% 11.56/1.79 fresh104(true, true, X, Y, V, U, Z, W)
% 11.56/1.79 = { by axiom 20 (ruleD40) }
% 11.56/1.79 true
% 11.56/1.79
% 11.56/1.79 Goal 1 (exemplo6GDDFULL416043_5): eqangle(a, c, c, p, p, c, c, b) = true.
% 11.56/1.79 Proof:
% 11.56/1.79 eqangle(a, c, c, p, p, c, c, b)
% 11.56/1.79 = { by axiom 38 (ruleD22) R->L }
% 11.56/1.79 fresh130(true, true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by axiom 33 (ruleD22) R->L }
% 11.56/1.79 fresh130(fresh129(true, true, X, Y, X, Y, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by axiom 32 (ruleD21) R->L }
% 11.56/1.79 fresh130(fresh129(fresh131(true, true, X, Y, c, b, X, Y, c, b), true, X, Y, X, Y, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by lemma 50 R->L }
% 11.56/1.79 fresh130(fresh129(fresh131(eqangle(X, Y, c, b, X, Y, c, b), true, X, Y, c, b, X, Y, c, b), true, X, Y, X, Y, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by axiom 42 (ruleD21) }
% 11.56/1.79 fresh130(fresh129(eqangle(X, Y, X, Y, c, b, c, b), true, X, Y, X, Y, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by axiom 43 (ruleD22) R->L }
% 11.56/1.79 fresh130(fresh130(eqangle(c, b, c, b, p, c, c, b), true, X, Y, X, Y, c, b, c, b, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by lemma 53 }
% 11.56/1.79 fresh130(fresh130(true, true, X, Y, X, Y, c, b, c, b, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by axiom 38 (ruleD22) }
% 11.56/1.79 fresh130(eqangle(X, Y, X, Y, p, c, c, b), true, a, c, c, p, X, Y, X, Y, p, c, c, b)
% 11.56/1.79 = { by axiom 43 (ruleD22) }
% 11.56/1.79 fresh129(eqangle(a, c, c, p, X, Y, X, Y), true, a, c, c, p, p, c, c, b)
% 11.56/1.79 = { by axiom 42 (ruleD21) R->L }
% 11.56/1.79 fresh129(fresh131(eqangle(a, c, X, Y, c, p, X, Y), true, a, c, X, Y, c, p, X, Y), true, a, c, c, p, p, c, c, b)
% 11.56/1.79 = { by lemma 53 }
% 11.56/1.79 fresh129(fresh131(true, true, a, c, X, Y, c, p, X, Y), true, a, c, c, p, p, c, c, b)
% 11.56/1.79 = { by axiom 32 (ruleD21) }
% 11.56/1.79 fresh129(true, true, a, c, c, p, p, c, c, b)
% 11.56/1.79 = { by axiom 33 (ruleD22) }
% 11.56/1.79 true
% 11.56/1.79 % SZS output end Proof
% 11.56/1.79
% 11.56/1.79 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------