TSTP Solution File: GEO578+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO578+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 : n016.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 13.35s 2.03s
% Output : Proof 13.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO578+1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 19:43:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 13.35/2.03 Command-line arguments: --no-flatten-goal
% 13.35/2.03
% 13.35/2.03 % SZS status Theorem
% 13.35/2.03
% 13.50/2.08 % SZS output start Proof
% 13.50/2.08 Take the following subset of the input axioms:
% 13.50/2.08 fof(exemplo6GDDFULL214040, conjecture, ![A, B, C, E, I]: ((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) & (para(A, B, E, I) & coll(E, A, C))))) => cong(E, I, E, A))).
% 13.50/2.08 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 13.50/2.08 fof(ruleD17, axiom, ![D, B2, C2, A2_2, E2]: ((cyclic(A2_2, B2, C2, D) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D, E2))).
% 13.50/2.09 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))).
% 13.50/2.09 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 13.50/2.09 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))).
% 13.50/2.09 fof(ruleD23, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(A2_2, B2, D2, C2))).
% 13.50/2.09 fof(ruleD24, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(C2, D2, A2_2, B2))).
% 13.50/2.09 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 13.50/2.09 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))).
% 13.50/2.09 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))).
% 13.50/2.09 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))).
% 13.50/2.09 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))).
% 13.50/2.09 fof(ruleD52, axiom, ![M, B2, C2, A2_2]: ((perp(A2_2, B2, B2, C2) & midp(M, A2_2, C2)) => cong(A2_2, M, B2, M))).
% 13.50/2.09 fof(ruleD57, axiom, ![B2, A2_2, P2, Q2]: ((cong(A2_2, P2, B2, P2) & (cong(A2_2, Q2, B2, Q2) & cyclic(A2_2, B2, P2, Q2))) => perp(P2, A2_2, A2_2, Q2))).
% 13.50/2.09 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 13.50/2.09 fof(ruleD67, axiom, ![B2, C2, A2_2]: ((cong(A2_2, B2, A2_2, C2) & coll(A2_2, B2, C2)) => midp(A2_2, B2, C2))).
% 13.50/2.09 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))).
% 13.50/2.09 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 13.50/2.09
% 13.50/2.09 Now clausify the problem and encode Horn clauses using encoding 3 of
% 13.50/2.09 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 13.50/2.09 We repeatedly replace C & s=t => u=v by the two clauses:
% 13.50/2.09 fresh(y, y, x1...xn) = u
% 13.50/2.09 C => fresh(s, t, x1...xn) = v
% 13.50/2.09 where fresh is a fresh function symbol and x1..xn are the free
% 13.50/2.09 variables of u and v.
% 13.50/2.09 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 13.50/2.09 input problem has no model of domain size 1).
% 13.50/2.09
% 13.50/2.09 The encoding turns the above axioms into the following unit equations and goals:
% 13.50/2.09
% 13.50/2.09 Axiom 1 (exemplo6GDDFULL214040_1): para(a, b, e, i) = true.
% 13.50/2.09 Axiom 2 (ruleD57): fresh177(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 3 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 4 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 5 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 6 (ruleD52): fresh87(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 7 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 8 (ruleD67): fresh65(X, X, Y, Z, W) = midp(Y, Z, W).
% 13.50/2.09 Axiom 9 (ruleD67): fresh64(X, X, Y, Z, W) = true.
% 13.50/2.09 Axiom 10 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 11 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 12 (ruleD23): fresh128(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 13 (ruleD24): fresh127(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 14 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 13.50/2.09 Axiom 15 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 16 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 13.50/2.09 Axiom 17 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 18 (ruleD52): fresh88(X, X, Y, Z, W, V) = cong(Y, V, Z, V).
% 13.50/2.09 Axiom 19 (ruleD57): fresh78(X, X, Y, Z, W, V) = perp(W, Y, Y, V).
% 13.50/2.09 Axiom 20 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 21 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 13.50/2.09 Axiom 22 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 13.50/2.09 Axiom 23 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 13.50/2.09 Axiom 24 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 13.50/2.09 Axiom 25 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 13.50/2.09 Axiom 26 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 13.50/2.09 Axiom 27 (exemplo6GDDFULL214040_3): eqangle(i, c, c, a, i, c, c, b) = true.
% 13.50/2.09 Axiom 28 (ruleD57): fresh176(X, X, Y, Z, W, V) = fresh177(cong(Y, W, Z, W), true, Y, W, V).
% 13.50/2.09 Axiom 29 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 13.50/2.09 Axiom 30 (ruleD52): fresh88(midp(X, Y, Z), true, Y, W, Z, X) = fresh87(perp(Y, W, W, Z), true, Y, W, X).
% 13.50/2.09 Axiom 31 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 13.50/2.09 Axiom 32 (ruleD67): fresh65(cong(X, Y, X, Z), true, X, Y, Z) = fresh64(coll(X, Y, Z), true, X, Y, Z).
% 13.50/2.09 Axiom 33 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 13.50/2.09 Axiom 34 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 13.50/2.09 Axiom 35 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 13.50/2.09 Axiom 36 (ruleD23): fresh128(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(X, Y, W, Z).
% 13.50/2.09 Axiom 37 (ruleD24): fresh127(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(Z, W, X, Y).
% 13.50/2.09 Axiom 38 (ruleD57): fresh176(cyclic(X, Y, Z, W), true, X, Y, Z, W) = fresh78(cong(X, W, Y, W), true, X, Y, Z, W).
% 13.50/2.09 Axiom 39 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 13.50/2.09 Axiom 40 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 13.50/2.09 Axiom 41 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 13.50/2.09 Axiom 42 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 13.50/2.09 Axiom 43 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 13.50/2.09 Axiom 44 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 13.50/2.09 Axiom 45 (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).
% 13.50/2.09 Axiom 46 (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).
% 13.50/2.09 Axiom 47 (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).
% 13.50/2.09 Axiom 48 (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).
% 13.50/2.09 Axiom 49 (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).
% 13.50/2.09
% 13.50/2.09 Lemma 50: para(X, Y, X, Y) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 para(X, Y, X, Y)
% 13.50/2.09 = { by axiom 39 (ruleD73) R->L }
% 13.50/2.09 fresh58(true, true, X, Y, X, Y, a, b, e, i)
% 13.50/2.09 = { by axiom 35 (ruleD21) R->L }
% 13.50/2.09 fresh58(fresh131(true, true, X, Y, a, b, X, Y, e, i), true, X, Y, X, Y, a, b, e, i)
% 13.50/2.09 = { by axiom 34 (ruleD19) R->L }
% 13.50/2.09 fresh58(fresh131(fresh134(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)
% 13.50/2.09 = { by axiom 26 (ruleD40) R->L }
% 13.50/2.09 fresh58(fresh131(fresh134(fresh104(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)
% 13.50/2.09 = { by axiom 1 (exemplo6GDDFULL214040_1) R->L }
% 13.50/2.09 fresh58(fresh131(fresh134(fresh104(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)
% 13.50/2.09 = { by axiom 43 (ruleD40) }
% 13.50/2.09 fresh58(fresh131(fresh134(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)
% 13.50/2.09 = { by axiom 47 (ruleD19) }
% 13.50/2.09 fresh58(fresh131(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)
% 13.50/2.09 = { by axiom 48 (ruleD21) }
% 13.50/2.09 fresh58(eqangle(X, Y, X, Y, a, b, e, i), true, X, Y, X, Y, a, b, e, i)
% 13.50/2.09 = { by axiom 49 (ruleD73) }
% 13.50/2.09 fresh57(para(a, b, e, i), true, X, Y, X, Y)
% 13.50/2.09 = { by axiom 1 (exemplo6GDDFULL214040_1) }
% 13.50/2.09 fresh57(true, true, X, Y, X, Y)
% 13.50/2.09 = { by axiom 20 (ruleD73) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 51: coll(X, X, Y) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 coll(X, X, Y)
% 13.50/2.09 = { by axiom 24 (ruleD1) R->L }
% 13.50/2.09 fresh146(coll(X, Y, X), true, X, Y, X)
% 13.50/2.09 = { by axiom 25 (ruleD2) R->L }
% 13.50/2.09 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 13.50/2.09 = { by axiom 31 (ruleD66) R->L }
% 13.50/2.09 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 13.50/2.09 = { by lemma 50 }
% 13.50/2.09 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 13.50/2.09 = { by axiom 7 (ruleD66) }
% 13.50/2.09 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 13.50/2.09 = { by axiom 4 (ruleD2) }
% 13.50/2.09 fresh146(true, true, X, Y, X)
% 13.50/2.09 = { by axiom 3 (ruleD1) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 52: coll(X, Y, Z) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 coll(X, Y, Z)
% 13.50/2.09 = { by axiom 14 (ruleD3) R->L }
% 13.50/2.09 fresh120(true, true, Z, Z, X, Y)
% 13.50/2.09 = { by lemma 51 R->L }
% 13.50/2.09 fresh120(coll(Z, Z, Y), true, Z, Z, X, Y)
% 13.50/2.09 = { by axiom 29 (ruleD3) }
% 13.50/2.09 fresh119(coll(Z, Z, X), true, Z, X, Y)
% 13.50/2.09 = { by lemma 51 }
% 13.50/2.09 fresh119(true, true, Z, X, Y)
% 13.50/2.09 = { by axiom 5 (ruleD3) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 53: para(c, a, c, b) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 para(c, a, c, b)
% 13.50/2.09 = { by axiom 44 (ruleD39) R->L }
% 13.50/2.09 fresh106(eqangle(c, a, i, c, c, b, i, c), true, c, a, c, b)
% 13.50/2.09 = { by axiom 47 (ruleD19) R->L }
% 13.50/2.09 fresh106(fresh134(eqangle(i, c, c, a, i, c, c, b), true, i, c, c, a, i, c, c, b), true, c, a, c, b)
% 13.50/2.09 = { by axiom 27 (exemplo6GDDFULL214040_3) }
% 13.50/2.09 fresh106(fresh134(true, true, i, c, c, a, i, c, c, b), true, c, a, c, b)
% 13.50/2.09 = { by axiom 34 (ruleD19) }
% 13.50/2.09 fresh106(true, true, c, a, c, b)
% 13.50/2.09 = { by axiom 15 (ruleD39) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 54: cyclic(c, c, i, X) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 cyclic(c, c, i, X)
% 13.50/2.09 = { by axiom 16 (ruleD42b) R->L }
% 13.50/2.09 fresh102(true, true, c, c, i, X)
% 13.50/2.09 = { by axiom 35 (ruleD21) R->L }
% 13.50/2.09 fresh102(fresh131(true, true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 26 (ruleD40) R->L }
% 13.50/2.09 fresh102(fresh131(fresh104(true, true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 20 (ruleD73) R->L }
% 13.50/2.09 fresh102(fresh131(fresh104(fresh57(true, true, i, c, i, c), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by lemma 53 R->L }
% 13.50/2.09 fresh102(fresh131(fresh104(fresh57(para(c, a, c, b), true, i, c, i, c), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 49 (ruleD73) R->L }
% 13.50/2.09 fresh102(fresh131(fresh104(fresh58(eqangle(i, c, i, c, c, a, c, b), true, i, c, i, c, c, a, c, b), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 48 (ruleD21) R->L }
% 13.50/2.09 fresh102(fresh131(fresh104(fresh58(fresh131(eqangle(i, c, c, a, i, c, c, b), true, i, c, c, a, i, c, c, b), true, i, c, i, c, c, a, c, b), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 27 (exemplo6GDDFULL214040_3) }
% 13.50/2.09 fresh102(fresh131(fresh104(fresh58(fresh131(true, true, i, c, c, a, i, c, c, b), true, i, c, i, c, c, a, c, b), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 35 (ruleD21) }
% 13.50/2.09 fresh102(fresh131(fresh104(fresh58(true, true, i, c, i, c, c, a, c, b), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 39 (ruleD73) }
% 13.50/2.09 fresh102(fresh131(fresh104(para(i, c, i, c), true, i, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 43 (ruleD40) }
% 13.50/2.09 fresh102(fresh131(eqangle(i, c, X, c, i, c, X, c), true, i, c, X, c, i, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 48 (ruleD21) }
% 13.50/2.09 fresh102(eqangle(i, c, i, c, X, c, X, c), true, c, c, i, X)
% 13.50/2.09 = { by axiom 45 (ruleD42b) }
% 13.50/2.09 fresh101(coll(i, X, c), true, c, c, i, X)
% 13.50/2.09 = { by lemma 52 }
% 13.50/2.09 fresh101(true, true, c, c, i, X)
% 13.50/2.09 = { by axiom 17 (ruleD42b) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 55: cyclic(c, i, X, Y) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 cyclic(c, i, X, Y)
% 13.50/2.09 = { by axiom 23 (ruleD17) R->L }
% 13.50/2.09 fresh137(true, true, c, c, i, X, Y)
% 13.50/2.09 = { by lemma 54 R->L }
% 13.50/2.09 fresh137(cyclic(c, c, i, Y), true, c, c, i, X, Y)
% 13.50/2.09 = { by axiom 42 (ruleD17) }
% 13.50/2.09 fresh136(cyclic(c, c, i, X), true, c, i, X, Y)
% 13.50/2.09 = { by lemma 54 }
% 13.50/2.09 fresh136(true, true, c, i, X, Y)
% 13.50/2.09 = { by axiom 11 (ruleD17) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 56: cyclic(i, X, Y, Z) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 cyclic(i, X, Y, Z)
% 13.50/2.09 = { by axiom 23 (ruleD17) R->L }
% 13.50/2.09 fresh137(true, true, c, i, X, Y, Z)
% 13.50/2.09 = { by lemma 55 R->L }
% 13.50/2.09 fresh137(cyclic(c, i, X, Z), true, c, i, X, Y, Z)
% 13.50/2.09 = { by axiom 42 (ruleD17) }
% 13.50/2.09 fresh136(cyclic(c, i, X, Y), true, i, X, Y, Z)
% 13.50/2.09 = { by lemma 55 }
% 13.50/2.09 fresh136(true, true, i, X, Y, Z)
% 13.50/2.09 = { by axiom 11 (ruleD17) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 57: cyclic(X, Y, Z, W) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 cyclic(X, Y, Z, W)
% 13.50/2.09 = { by axiom 23 (ruleD17) R->L }
% 13.50/2.09 fresh137(true, true, i, X, Y, Z, W)
% 13.50/2.09 = { by lemma 56 R->L }
% 13.50/2.09 fresh137(cyclic(i, X, Y, W), true, i, X, Y, Z, W)
% 13.50/2.09 = { by axiom 42 (ruleD17) }
% 13.50/2.09 fresh136(cyclic(i, X, Y, Z), true, X, Y, Z, W)
% 13.50/2.09 = { by lemma 56 }
% 13.50/2.09 fresh136(true, true, X, Y, Z, W)
% 13.50/2.09 = { by axiom 11 (ruleD17) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 58: fresh182(X, X, Y, Z, W, V, U, T) = cong(Y, Z, V, U).
% 13.50/2.09 Proof:
% 13.50/2.09 fresh182(X, X, Y, Z, W, V, U, T)
% 13.50/2.09 = { by axiom 41 (ruleD43) }
% 13.50/2.09 fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U)
% 13.50/2.09 = { by lemma 57 }
% 13.50/2.09 fresh183(true, true, Y, Z, W, V, U)
% 13.50/2.09 = { by axiom 22 (ruleD43) }
% 13.50/2.09 cong(Y, Z, V, U)
% 13.50/2.09
% 13.50/2.09 Lemma 59: fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W)
% 13.50/2.09 = { by axiom 46 (ruleD43) }
% 13.50/2.09 fresh184(cyclic(Y, Z, X, W), true, Y, Z, X, V, U)
% 13.50/2.09 = { by lemma 57 }
% 13.50/2.09 fresh184(true, true, Y, Z, X, V, U)
% 13.50/2.09 = { by axiom 33 (ruleD43) }
% 13.50/2.09 fresh185(cyclic(Y, Z, X, V), true, Y, Z, V, U)
% 13.50/2.09 = { by lemma 57 }
% 13.50/2.09 fresh185(true, true, Y, Z, V, U)
% 13.50/2.09 = { by axiom 10 (ruleD43) }
% 13.50/2.09 true
% 13.50/2.09
% 13.50/2.09 Lemma 60: cong(a, X, b, X) = true.
% 13.50/2.09 Proof:
% 13.50/2.09 cong(a, X, b, X)
% 13.50/2.09 = { by lemma 58 R->L }
% 13.50/2.09 fresh182(true, true, a, X, c, b, X, c)
% 13.50/2.09 = { by axiom 26 (ruleD40) R->L }
% 13.50/2.09 fresh182(fresh104(true, true, c, a, c, b, c, X), true, a, X, c, b, X, c)
% 13.50/2.10 = { by lemma 53 R->L }
% 13.50/2.10 fresh182(fresh104(para(c, a, c, b), true, c, a, c, b, c, X), true, a, X, c, b, X, c)
% 13.50/2.10 = { by axiom 43 (ruleD40) }
% 13.50/2.10 fresh182(eqangle(c, a, c, X, c, b, c, X), true, a, X, c, b, X, c)
% 13.50/2.10 = { by lemma 59 }
% 13.50/2.10 true
% 13.50/2.10
% 13.50/2.10 Goal 1 (exemplo6GDDFULL214040_5): cong(e, i, e, a) = true.
% 13.50/2.10 Proof:
% 13.50/2.10 cong(e, i, e, a)
% 13.50/2.10 = { by axiom 36 (ruleD23) R->L }
% 13.50/2.10 fresh128(cong(e, i, a, e), true, e, i, a, e)
% 13.50/2.10 = { by axiom 37 (ruleD24) R->L }
% 13.50/2.10 fresh128(fresh127(cong(a, e, e, i), true, a, e, e, i), true, e, i, a, e)
% 13.50/2.10 = { by axiom 36 (ruleD23) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(cong(a, e, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
% 13.50/2.10 = { by axiom 18 (ruleD52) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh88(true, true, a, i, a, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
% 13.50/2.10 = { by axiom 9 (ruleD67) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by lemma 52 R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 32 (ruleD67) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by lemma 58 R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh88(fresh65(fresh182(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)
% 13.50/2.10 = { by axiom 26 (ruleD40) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh88(fresh65(fresh182(fresh104(true, true, X, e, X, e, X, a), 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)
% 13.50/2.10 = { by lemma 50 R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh88(fresh65(fresh182(fresh104(para(X, e, X, e), true, X, e, X, e, X, a), 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)
% 13.50/2.10 = { by axiom 43 (ruleD40) }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh88(fresh65(fresh182(eqangle(X, e, X, a, X, e, X, a), 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)
% 13.50/2.10 = { by lemma 59 }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 8 (ruleD67) }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 30 (ruleD52) }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 40 (ruleD8) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 19 (ruleD57) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by lemma 60 R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 38 (ruleD57) R->L }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(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)
% 13.50/2.10 = { by lemma 57 }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(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)
% 13.50/2.10 = { by axiom 28 (ruleD57) }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh87(fresh52(fresh177(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)
% 13.50/2.10 = { by lemma 60 }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh87(fresh52(fresh177(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)
% 13.50/2.10 = { by axiom 2 (ruleD57) }
% 13.50/2.10 fresh128(fresh127(fresh128(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)
% 13.50/2.10 = { by axiom 21 (ruleD8) }
% 13.50/2.10 fresh128(fresh127(fresh128(fresh87(true, true, a, i, e), true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
% 13.50/2.10 = { by axiom 6 (ruleD52) }
% 13.50/2.10 fresh128(fresh127(fresh128(true, true, a, e, i, e), true, a, e, e, i), true, e, i, a, e)
% 13.50/2.10 = { by axiom 12 (ruleD23) }
% 13.50/2.10 fresh128(fresh127(true, true, a, e, e, i), true, e, i, a, e)
% 13.50/2.10 = { by axiom 13 (ruleD24) }
% 13.50/2.10 fresh128(true, true, e, i, a, e)
% 13.50/2.10 = { by axiom 12 (ruleD23) }
% 13.50/2.10 true
% 13.50/2.10 % SZS output end Proof
% 13.50/2.10
% 13.50/2.10 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------