TSTP Solution File: GEO577+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO577+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 : n021.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 23:29:23 EDT 2023
% Result : Theorem 12.08s 1.95s
% Output : Proof 12.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO577+1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 00:09:15 EDT 2023
% 0.14/0.36 % CPUTime :
% 12.08/1.95 Command-line arguments: --no-flatten-goal
% 12.08/1.95
% 12.08/1.95 % SZS status Theorem
% 12.08/1.95
% 12.46/1.97 % SZS output start Proof
% 12.46/1.97 Take the following subset of the input axioms:
% 12.46/1.97 fof(exemplo6GDDFULL214039, conjecture, ![A, B, C, M, O, I, L1, NWPNT1, NWPNT2]: ((eqangle(I, A, A, B, I, A, A, C) & (eqangle(I, B, B, C, I, B, B, A) & (eqangle(I, C, C, A, I, C, C, B) & (circle(O, A, B, C) & (circle(O, C, M, NWPNT1) & (coll(M, C, I) & (perp(B, I, B, L1) & circle(O, A, L1, NWPNT2)))))))) => para(M, L1, A, I))).
% 12.46/1.97 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 12.46/1.97 fof(ruleD17, axiom, ![D, E, B2, C2, A2_2]: ((cyclic(A2_2, B2, C2, D) & cyclic(A2_2, B2, C2, E)) => cyclic(B2, C2, D, E))).
% 12.46/1.97 fof(ruleD19, axiom, ![P, Q, U, V, B2, C2, D2, A2_2]: (eqangle(A2_2, B2, C2, D2, P, Q, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P, Q))).
% 12.46/1.97 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 12.46/1.97 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))).
% 12.46/1.97 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 12.46/1.97 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))).
% 12.46/1.97 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))).
% 12.46/1.97 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))).
% 12.46/1.97 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))).
% 12.46/1.97 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))).
% 12.46/1.97 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 12.46/1.97 fof(ruleD73, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & para(P2, Q2, U2, V2)) => para(A2_2, B2, C2, D2))).
% 12.46/1.97 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 12.46/1.97 fof(ruleD9, axiom, ![F, B2, C2, D2, E2, A2_2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F)) => para(A2_2, B2, E2, F))).
% 12.46/1.97
% 12.46/1.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.46/1.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.46/1.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.46/1.97 fresh(y, y, x1...xn) = u
% 12.46/1.97 C => fresh(s, t, x1...xn) = v
% 12.46/1.97 where fresh is a fresh function symbol and x1..xn are the free
% 12.46/1.97 variables of u and v.
% 12.46/1.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.46/1.97 input problem has no model of domain size 1).
% 12.46/1.97
% 12.46/1.97 The encoding turns the above axioms into the following unit equations and goals:
% 12.46/1.97
% 12.46/1.97 Axiom 1 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 12.46/1.97 Axiom 2 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 12.46/1.97 Axiom 3 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 12.46/1.97 Axiom 4 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 12.46/1.97 Axiom 5 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 6 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 7 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 12.46/1.97 Axiom 8 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 9 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 12.46/1.97 Axiom 10 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 11 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 12.46/1.97 Axiom 12 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 13 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 14 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 15 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 12.46/1.97 Axiom 16 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 12.46/1.97 Axiom 17 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 12.46/1.97 Axiom 18 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 12.46/1.97 Axiom 19 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 12.46/1.97 Axiom 20 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 12.46/1.97 Axiom 21 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 12.46/1.97 Axiom 22 (exemplo6GDDFULL214039_5): eqangle(i, b, b, c, i, b, b, a) = true.
% 12.46/1.97 Axiom 23 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 12.46/1.97 Axiom 24 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 12.46/1.97 Axiom 25 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 12.46/1.97 Axiom 26 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 12.46/1.97 Axiom 27 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 12.46/1.97 Axiom 28 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 12.46/1.97 Axiom 29 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 12.46/1.97 Axiom 30 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 12.46/1.97 Axiom 31 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 12.46/1.97 Axiom 32 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 12.46/1.97 Axiom 33 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 12.46/1.97 Axiom 34 (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).
% 12.46/1.97 Axiom 35 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 12.46/1.97 Axiom 36 (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).
% 12.46/1.97 Axiom 37 (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).
% 12.46/1.97 Axiom 38 (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).
% 12.46/1.97 Axiom 39 (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).
% 12.46/1.97 Axiom 40 (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).
% 12.46/1.97
% 12.46/1.97 Lemma 41: para(b, c, b, a) = true.
% 12.46/1.97 Proof:
% 12.46/1.97 para(b, c, b, a)
% 12.46/1.97 = { by axiom 35 (ruleD39) R->L }
% 12.46/1.97 fresh106(eqangle(b, c, i, b, b, a, i, b), true, b, c, b, a)
% 12.46/1.97 = { by axiom 38 (ruleD19) R->L }
% 12.46/1.97 fresh106(fresh134(eqangle(i, b, b, c, i, b, b, a), true, i, b, b, c, i, b, b, a), true, b, c, b, a)
% 12.46/1.97 = { by axiom 22 (exemplo6GDDFULL214039_5) }
% 12.46/1.97 fresh106(fresh134(true, true, i, b, b, c, i, b, b, a), true, b, c, b, a)
% 12.46/1.97 = { by axiom 26 (ruleD19) }
% 12.46/1.97 fresh106(true, true, b, c, b, a)
% 12.46/1.97 = { by axiom 8 (ruleD39) }
% 12.46/1.97 true
% 12.46/1.97
% 12.46/1.97 Lemma 42: eqangle(i, b, X, Y, i, b, X, Y) = true.
% 12.46/1.97 Proof:
% 12.46/1.97 eqangle(i, b, X, Y, i, b, X, Y)
% 12.46/1.97 = { by axiom 33 (ruleD40) R->L }
% 12.46/1.97 fresh104(para(i, b, i, b), true, i, b, i, b, X, Y)
% 12.46/1.97 = { by axiom 29 (ruleD73) R->L }
% 12.46/1.97 fresh104(fresh58(true, true, i, b, i, b, b, c, b, a), true, i, b, i, b, X, Y)
% 12.46/1.97 = { by axiom 27 (ruleD21) R->L }
% 12.46/1.97 fresh104(fresh58(fresh131(true, true, i, b, b, c, i, b, b, a), true, i, b, i, b, b, c, b, a), true, i, b, i, b, X, Y)
% 12.46/1.97 = { by axiom 22 (exemplo6GDDFULL214039_5) R->L }
% 12.46/1.97 fresh104(fresh58(fresh131(eqangle(i, b, b, c, i, b, b, a), true, i, b, b, c, i, b, b, a), true, i, b, i, b, b, c, b, a), true, i, b, i, b, X, Y)
% 12.46/1.98 = { by axiom 39 (ruleD21) }
% 12.46/1.98 fresh104(fresh58(eqangle(i, b, i, b, b, c, b, a), true, i, b, i, b, b, c, b, a), true, i, b, i, b, X, Y)
% 12.46/1.98 = { by axiom 40 (ruleD73) }
% 12.46/1.98 fresh104(fresh57(para(b, c, b, a), true, i, b, i, b), true, i, b, i, b, X, Y)
% 12.46/1.98 = { by lemma 41 }
% 12.46/1.98 fresh104(fresh57(true, true, i, b, i, b), true, i, b, i, b, X, Y)
% 12.46/1.98 = { by axiom 13 (ruleD73) }
% 12.46/1.98 fresh104(true, true, i, b, i, b, X, Y)
% 12.46/1.98 = { by axiom 20 (ruleD40) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 43: coll(X, X, Y) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 coll(X, X, Y)
% 12.46/1.98 = { by axiom 18 (ruleD1) R->L }
% 12.46/1.98 fresh146(coll(X, Y, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 19 (ruleD2) R->L }
% 12.46/1.98 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 24 (ruleD66) R->L }
% 12.46/1.98 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 35 (ruleD39) R->L }
% 12.46/1.98 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, i, b, Y, X, i, b), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 38 (ruleD19) R->L }
% 12.46/1.98 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(i, b, Y, X, i, b, Y, X), true, i, b, Y, X, i, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by lemma 42 }
% 12.46/1.98 fresh146(fresh133(fresh66(fresh106(fresh134(true, true, i, b, Y, X, i, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 26 (ruleD19) }
% 12.46/1.98 fresh146(fresh133(fresh66(fresh106(true, true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 8 (ruleD39) }
% 12.46/1.98 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 4 (ruleD66) }
% 12.46/1.98 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 12.46/1.98 = { by axiom 2 (ruleD2) }
% 12.46/1.98 fresh146(true, true, X, Y, X)
% 12.46/1.98 = { by axiom 1 (ruleD1) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 44: cyclic(b, b, i, X) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 cyclic(b, b, i, X)
% 12.46/1.98 = { by axiom 9 (ruleD42b) R->L }
% 12.46/1.98 fresh102(true, true, b, b, i, X)
% 12.46/1.98 = { by axiom 27 (ruleD21) R->L }
% 12.46/1.98 fresh102(fresh131(true, true, i, b, X, b, i, b, X, b), true, b, b, i, X)
% 12.46/1.98 = { by lemma 42 R->L }
% 12.46/1.98 fresh102(fresh131(eqangle(i, b, X, b, i, b, X, b), true, i, b, X, b, i, b, X, b), true, b, b, i, X)
% 12.46/1.98 = { by axiom 39 (ruleD21) }
% 12.46/1.98 fresh102(eqangle(i, b, i, b, X, b, X, b), true, b, b, i, X)
% 12.46/1.98 = { by axiom 36 (ruleD42b) }
% 12.46/1.98 fresh101(coll(i, X, b), true, b, b, i, X)
% 12.46/1.98 = { by axiom 7 (ruleD3) R->L }
% 12.46/1.98 fresh101(fresh120(true, true, b, b, i, X), true, b, b, i, X)
% 12.46/1.98 = { by lemma 43 R->L }
% 12.46/1.98 fresh101(fresh120(coll(b, b, X), true, b, b, i, X), true, b, b, i, X)
% 12.46/1.98 = { by axiom 23 (ruleD3) }
% 12.46/1.98 fresh101(fresh119(coll(b, b, i), true, b, i, X), true, b, b, i, X)
% 12.46/1.98 = { by lemma 43 }
% 12.46/1.98 fresh101(fresh119(true, true, b, i, X), true, b, b, i, X)
% 12.46/1.98 = { by axiom 3 (ruleD3) }
% 12.46/1.98 fresh101(true, true, b, b, i, X)
% 12.46/1.98 = { by axiom 10 (ruleD42b) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 45: cyclic(b, i, X, Y) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 cyclic(b, i, X, Y)
% 12.46/1.98 = { by axiom 17 (ruleD17) R->L }
% 12.46/1.98 fresh137(true, true, b, b, i, X, Y)
% 12.46/1.98 = { by lemma 44 R->L }
% 12.46/1.98 fresh137(cyclic(b, b, i, Y), true, b, b, i, X, Y)
% 12.46/1.98 = { by axiom 32 (ruleD17) }
% 12.46/1.98 fresh136(cyclic(b, b, i, X), true, b, i, X, Y)
% 12.46/1.98 = { by lemma 44 }
% 12.46/1.98 fresh136(true, true, b, i, X, Y)
% 12.46/1.98 = { by axiom 6 (ruleD17) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 46: cyclic(i, X, Y, Z) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 cyclic(i, X, Y, Z)
% 12.46/1.98 = { by axiom 17 (ruleD17) R->L }
% 12.46/1.98 fresh137(true, true, b, i, X, Y, Z)
% 12.46/1.98 = { by lemma 45 R->L }
% 12.46/1.98 fresh137(cyclic(b, i, X, Z), true, b, i, X, Y, Z)
% 12.46/1.98 = { by axiom 32 (ruleD17) }
% 12.46/1.98 fresh136(cyclic(b, i, X, Y), true, i, X, Y, Z)
% 12.46/1.98 = { by lemma 45 }
% 12.46/1.98 fresh136(true, true, i, X, Y, Z)
% 12.46/1.98 = { by axiom 6 (ruleD17) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 47: cyclic(X, Y, Z, W) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 cyclic(X, Y, Z, W)
% 12.46/1.98 = { by axiom 17 (ruleD17) R->L }
% 12.46/1.98 fresh137(true, true, i, X, Y, Z, W)
% 12.46/1.98 = { by lemma 46 R->L }
% 12.46/1.98 fresh137(cyclic(i, X, Y, W), true, i, X, Y, Z, W)
% 12.46/1.98 = { by axiom 32 (ruleD17) }
% 12.46/1.98 fresh136(cyclic(i, X, Y, Z), true, X, Y, Z, W)
% 12.46/1.98 = { by lemma 46 }
% 12.46/1.98 fresh136(true, true, X, Y, Z, W)
% 12.46/1.98 = { by axiom 6 (ruleD17) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 48: cong(c, X, a, X) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 cong(c, X, a, X)
% 12.46/1.98 = { by axiom 16 (ruleD43) R->L }
% 12.46/1.98 fresh183(true, true, c, X, b, a, X)
% 12.46/1.98 = { by lemma 47 R->L }
% 12.46/1.98 fresh183(cyclic(c, X, b, X), true, c, X, b, a, X)
% 12.46/1.98 = { by axiom 31 (ruleD43) R->L }
% 12.46/1.98 fresh182(true, true, c, X, b, a, X, b)
% 12.46/1.98 = { by axiom 20 (ruleD40) R->L }
% 12.46/1.98 fresh182(fresh104(true, true, b, c, b, a, b, X), true, c, X, b, a, X, b)
% 12.46/1.98 = { by lemma 41 R->L }
% 12.46/1.98 fresh182(fresh104(para(b, c, b, a), true, b, c, b, a, b, X), true, c, X, b, a, X, b)
% 12.46/1.98 = { by axiom 33 (ruleD40) }
% 12.46/1.98 fresh182(eqangle(b, c, b, X, b, a, b, X), true, c, X, b, a, X, b)
% 12.46/1.98 = { by axiom 37 (ruleD43) }
% 12.46/1.98 fresh184(cyclic(c, X, b, b), true, c, X, b, a, X)
% 12.46/1.98 = { by lemma 47 }
% 12.46/1.98 fresh184(true, true, c, X, b, a, X)
% 12.46/1.98 = { by axiom 25 (ruleD43) }
% 12.46/1.98 fresh185(cyclic(c, X, b, a), true, c, X, a, X)
% 12.46/1.98 = { by lemma 47 }
% 12.46/1.98 fresh185(true, true, c, X, a, X)
% 12.46/1.98 = { by axiom 5 (ruleD43) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Lemma 49: perp(c, a, X, Y) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 perp(c, a, X, Y)
% 12.46/1.98 = { by axiom 11 (ruleD56) R->L }
% 12.46/1.98 fresh80(true, true, c, a, X, Y)
% 12.46/1.98 = { by lemma 48 R->L }
% 12.46/1.98 fresh80(cong(c, Y, a, Y), true, c, a, X, Y)
% 12.46/1.98 = { by axiom 28 (ruleD56) }
% 12.46/1.98 fresh79(cong(c, X, a, X), true, c, a, X, Y)
% 12.46/1.98 = { by lemma 48 }
% 12.46/1.98 fresh79(true, true, c, a, X, Y)
% 12.46/1.98 = { by axiom 12 (ruleD56) }
% 12.46/1.98 true
% 12.46/1.98
% 12.46/1.98 Goal 1 (exemplo6GDDFULL214039_8): para(m, l1, a, i) = true.
% 12.46/1.98 Proof:
% 12.46/1.98 para(m, l1, a, i)
% 12.46/1.98 = { by axiom 21 (ruleD9) R->L }
% 12.46/1.98 fresh51(true, true, m, l1, c, a, a, i)
% 12.46/1.98 = { by lemma 49 R->L }
% 12.46/1.98 fresh51(perp(c, a, a, i), true, m, l1, c, a, a, i)
% 12.46/1.98 = { by axiom 34 (ruleD9) }
% 12.46/1.98 fresh50(perp(m, l1, c, a), true, m, l1, a, i)
% 12.46/1.98 = { by axiom 30 (ruleD8) R->L }
% 12.46/1.98 fresh50(fresh52(perp(c, a, m, l1), true, c, a, m, l1), true, m, l1, a, i)
% 12.46/1.98 = { by lemma 49 }
% 12.46/1.98 fresh50(fresh52(true, true, c, a, m, l1), true, m, l1, a, i)
% 12.46/1.98 = { by axiom 14 (ruleD8) }
% 12.46/1.98 fresh50(true, true, m, l1, a, i)
% 12.46/1.98 = { by axiom 15 (ruleD9) }
% 12.46/1.98 true
% 12.46/1.98 % SZS output end Proof
% 12.46/1.98
% 12.46/1.98 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------