TSTP Solution File: GEO618+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO618+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 : n003.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 23:29:34 EDT 2023
% Result : Theorem 8.57s 1.50s
% Output : Proof 9.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO618+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 : n003.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 21:56:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 8.57/1.50 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 8.57/1.50
% 8.57/1.50 % SZS status Theorem
% 8.57/1.50
% 9.34/1.57 % SZS output start Proof
% 9.34/1.57 Take the following subset of the input axioms:
% 9.34/1.58 fof(exemplo6GDDFULL618080, conjecture, ![A, B, C, O, U, T]: ((eqangle(U, A, A, C, U, A, A, B) & (coll(U, B, C) & (circle(O, A, B, C) & (perp(A, O, A, T) & coll(T, B, C))))) => cong(T, A, T, U))).
% 9.34/1.58 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 9.34/1.58 fof(ruleD10, axiom, ![D, E, F, B2, C2, A2_2]: ((para(A2_2, B2, C2, D) & perp(C2, D, E, F)) => perp(A2_2, B2, E, F))).
% 9.34/1.58 fof(ruleD14, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, B2, D2, C2))).
% 9.34/1.58 fof(ruleD15, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 9.34/1.58 fof(ruleD16, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 9.34/1.58 fof(ruleD17, axiom, ![B2, C2, D2, A2_2, E2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 9.34/1.58 fof(ruleD19, axiom, ![P, Q, V, B2, C2, D2, A2_2, U2]: (eqangle(A2_2, B2, C2, D2, P, Q, U2, V) => eqangle(C2, D2, A2_2, B2, U2, V, P, Q))).
% 9.34/1.58 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 9.34/1.58 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))).
% 9.34/1.58 fof(ruleD23, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(A2_2, B2, D2, C2))).
% 9.34/1.58 fof(ruleD24, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(C2, D2, A2_2, B2))).
% 9.34/1.58 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 9.34/1.58 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))).
% 9.34/1.58 fof(ruleD4, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(A2_2, B2, D2, C2))).
% 9.34/1.58 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))).
% 9.34/1.58 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))).
% 9.34/1.58 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))).
% 9.34/1.58 fof(ruleD45, axiom, ![B2, C2, A2_2, E2, F2]: ((midp(E2, A2_2, B2) & (para(E2, F2, B2, C2) & coll(F2, A2_2, C2))) => midp(F2, A2_2, C2))).
% 9.34/1.58 fof(ruleD5, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(C2, D2, A2_2, B2))).
% 9.34/1.58 fof(ruleD51, axiom, ![M, O2, B2, C2, A2_2]: ((circle(O2, A2_2, B2, C2) & (coll(M, B2, C2) & eqangle(A2_2, B2, A2_2, C2, O2, B2, O2, M))) => midp(M, B2, C2))).
% 9.34/1.58 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))).
% 9.34/1.58 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 9.34/1.58 fof(ruleD68, axiom, ![B2, C2, A2_2]: (midp(A2_2, B2, C2) => cong(A2_2, B2, A2_2, C2))).
% 9.34/1.58 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))).
% 9.34/1.58 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 9.34/1.58 fof(ruleD9, axiom, ![B2, C2, D2, A2_2, E2, F2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => para(A2_2, B2, E2, F2))).
% 9.34/1.58 fof(ruleX14, axiom, ![B2, C2, D2, A2_2]: ?[O2]: ((perp(A2_2, C2, C2, B2) & cyclic(A2_2, B2, C2, D2)) => circle(O2, A2_2, B2, C2))).
% 9.34/1.58
% 9.34/1.58 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.34/1.58 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.34/1.58 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.34/1.58 fresh(y, y, x1...xn) = u
% 9.34/1.58 C => fresh(s, t, x1...xn) = v
% 9.34/1.58 where fresh is a fresh function symbol and x1..xn are the free
% 9.34/1.58 variables of u and v.
% 9.34/1.58 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.34/1.58 input problem has no model of domain size 1).
% 9.34/1.58
% 9.34/1.58 The encoding turns the above axioms into the following unit equations and goals:
% 9.34/1.58
% 9.34/1.58 Axiom 1 (exemplo6GDDFULL618080_2): perp(a, o, a, t) = true.
% 9.34/1.58 Axiom 2 (ruleD45): fresh181(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 3 (ruleD51): fresh179(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 4 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 5 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 6 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 7 (ruleD45): fresh98(X, X, Y, Z, W) = midp(W, Y, Z).
% 9.34/1.58 Axiom 8 (ruleD51): fresh89(X, X, Y, Z, W) = midp(W, Y, Z).
% 9.34/1.58 Axiom 9 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 10 (ruleD68): fresh63(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 11 (ruleX14): fresh36(X, X, Y, Z, W) = true.
% 9.34/1.58 Axiom 12 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 13 (ruleD10): fresh145(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 14 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 15 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 16 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 17 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 18 (ruleD23): fresh128(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 19 (ruleD24): fresh127(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 20 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 9.34/1.58 Axiom 21 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 22 (ruleD4): fresh105(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 23 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 9.34/1.58 Axiom 24 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 25 (ruleD5): fresh92(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 26 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 9.34/1.58 Axiom 27 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 28 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 29 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 30 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 9.34/1.58 Axiom 31 (ruleX14): fresh37(X, X, Y, Z, W) = circle(o2(Y, Z, W), Y, Z, W).
% 9.34/1.58 Axiom 32 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 9.34/1.58 Axiom 33 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 9.34/1.58 Axiom 34 (exemplo6GDDFULL618080_4): eqangle(u, a, a, c, u, a, a, b) = true.
% 9.34/1.58 Axiom 35 (ruleD45): fresh180(X, X, Y, Z, W, V, U) = fresh181(coll(U, Y, W), true, Y, W, U).
% 9.34/1.58 Axiom 36 (ruleD51): fresh178(X, X, Y, Z, W, V, U) = fresh179(coll(V, Z, W), true, Z, W, V).
% 9.34/1.58 Axiom 37 (ruleD10): fresh147(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
% 9.34/1.58 Axiom 38 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 9.34/1.58 Axiom 39 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 9.34/1.58 Axiom 40 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 9.34/1.58 Axiom 41 (ruleD68): fresh63(midp(X, Y, Z), true, X, Y, Z) = cong(X, Y, X, Z).
% 9.34/1.58 Axiom 42 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 9.34/1.58 Axiom 43 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 9.34/1.58 Axiom 44 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 9.34/1.58 Axiom 45 (ruleX14): fresh37(cyclic(X, Y, Z, W), true, X, Y, Z) = fresh36(perp(X, Z, Z, Y), true, X, Y, Z).
% 9.34/1.58 Axiom 46 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 9.34/1.58 Axiom 47 (ruleD45): fresh180(midp(X, Y, Z), true, Y, Z, W, X, V) = fresh98(para(X, V, Z, W), true, Y, W, V).
% 9.34/1.58 Axiom 48 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 9.34/1.58 Axiom 49 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 9.34/1.58 Axiom 50 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 9.34/1.58 Axiom 51 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 9.34/1.58 Axiom 52 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 9.34/1.58 Axiom 53 (ruleD23): fresh128(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(X, Y, W, Z).
% 9.34/1.58 Axiom 54 (ruleD24): fresh127(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(Z, W, X, Y).
% 9.34/1.58 Axiom 55 (ruleD4): fresh105(para(X, Y, Z, W), true, X, Y, Z, W) = para(X, Y, W, Z).
% 9.34/1.58 Axiom 56 (ruleD5): fresh92(para(X, Y, Z, W), true, X, Y, Z, W) = para(Z, W, X, Y).
% 9.34/1.58 Axiom 57 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 9.34/1.58 Axiom 58 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 9.34/1.58 Axiom 59 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 9.34/1.58 Axiom 60 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 9.34/1.58 Axiom 61 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 9.34/1.58 Axiom 62 (ruleD10): fresh147(perp(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh145(para(V, U, X, Y), true, V, U, Z, W).
% 9.34/1.58 Axiom 63 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 9.34/1.58 Axiom 64 (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).
% 9.34/1.58 Axiom 65 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 9.34/1.58 Axiom 66 (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).
% 9.34/1.58 Axiom 67 (ruleD51): fresh178(eqangle(X, Y, X, Z, W, Y, W, V), true, X, Y, Z, V, W) = fresh89(circle(W, X, Y, Z), true, Y, Z, V).
% 9.34/1.58 Axiom 68 (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).
% 9.34/1.58 Axiom 69 (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).
% 9.34/1.58 Axiom 70 (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).
% 9.34/1.58 Axiom 71 (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).
% 9.34/1.58
% 9.34/1.58 Lemma 72: para(u, a, u, a) = true.
% 9.34/1.58 Proof:
% 9.34/1.58 para(u, a, u, a)
% 9.34/1.58 = { by axiom 58 (ruleD73) R->L }
% 9.34/1.58 fresh58(true, true, u, a, u, a, a, c, a, b)
% 9.34/1.58 = { by axiom 52 (ruleD21) R->L }
% 9.34/1.58 fresh58(fresh131(true, true, u, a, a, c, u, a, a, b), true, u, a, u, a, a, c, a, b)
% 9.34/1.58 = { by axiom 34 (exemplo6GDDFULL618080_4) R->L }
% 9.34/1.58 fresh58(fresh131(eqangle(u, a, a, c, u, a, a, b), true, u, a, a, c, u, a, a, b), true, u, a, u, a, a, c, a, b)
% 9.34/1.58 = { by axiom 70 (ruleD21) }
% 9.34/1.58 fresh58(eqangle(u, a, u, a, a, c, a, b), true, u, a, u, a, a, c, a, b)
% 9.34/1.58 = { by axiom 71 (ruleD73) }
% 9.34/1.58 fresh57(para(a, c, a, b), true, u, a, u, a)
% 9.34/1.58 = { by axiom 65 (ruleD39) R->L }
% 9.34/1.58 fresh57(fresh106(eqangle(a, c, u, a, a, b, u, a), true, a, c, a, b), true, u, a, u, a)
% 9.34/1.58 = { by axiom 69 (ruleD19) R->L }
% 9.34/1.58 fresh57(fresh106(fresh134(eqangle(u, a, a, c, u, a, a, b), true, u, a, a, c, u, a, a, b), true, a, c, a, b), true, u, a, u, a)
% 9.34/1.58 = { by axiom 34 (exemplo6GDDFULL618080_4) }
% 9.34/1.58 fresh57(fresh106(fresh134(true, true, u, a, a, c, u, a, a, b), true, a, c, a, b), true, u, a, u, a)
% 9.34/1.58 = { by axiom 51 (ruleD19) }
% 9.34/1.58 fresh57(fresh106(true, true, a, c, a, b), true, u, a, u, a)
% 9.34/1.58 = { by axiom 21 (ruleD39) }
% 9.34/1.58 fresh57(true, true, u, a, u, a)
% 9.34/1.58 = { by axiom 28 (ruleD73) }
% 9.34/1.58 true
% 9.34/1.58
% 9.34/1.58 Lemma 73: eqangle(X, Y, u, a, X, Y, u, a) = true.
% 9.34/1.58 Proof:
% 9.34/1.58 eqangle(X, Y, u, a, X, Y, u, a)
% 9.34/1.58 = { by axiom 69 (ruleD19) R->L }
% 9.34/1.58 fresh134(eqangle(u, a, X, Y, u, a, X, Y), true, u, a, X, Y, u, a, X, Y)
% 9.34/1.58 = { by axiom 63 (ruleD40) R->L }
% 9.34/1.58 fresh134(fresh104(para(u, a, u, a), true, u, a, u, a, X, Y), true, u, a, X, Y, u, a, X, Y)
% 9.34/1.58 = { by lemma 72 }
% 9.34/1.58 fresh134(fresh104(true, true, u, a, u, a, X, Y), true, u, a, X, Y, u, a, X, Y)
% 9.34/1.58 = { by axiom 40 (ruleD40) }
% 9.34/1.58 fresh134(true, true, u, a, X, Y, u, a, X, Y)
% 9.34/1.58 = { by axiom 51 (ruleD19) }
% 9.34/1.58 true
% 9.34/1.58
% 9.34/1.58 Lemma 74: para(X, Y, X, Y) = true.
% 9.34/1.58 Proof:
% 9.34/1.58 para(X, Y, X, Y)
% 9.34/1.58 = { by axiom 65 (ruleD39) R->L }
% 9.34/1.58 fresh106(eqangle(X, Y, u, a, X, Y, u, a), true, X, Y, X, Y)
% 9.34/1.58 = { by lemma 73 }
% 9.34/1.58 fresh106(true, true, X, Y, X, Y)
% 9.34/1.58 = { by axiom 21 (ruleD39) }
% 9.34/1.58 true
% 9.34/1.58
% 9.34/1.58 Lemma 75: coll(X, Y, Y) = true.
% 9.34/1.58 Proof:
% 9.34/1.58 coll(X, Y, Y)
% 9.34/1.58 = { by axiom 44 (ruleD66) R->L }
% 9.34/1.58 fresh66(para(X, Y, X, Y), true, X, Y, Y)
% 9.34/1.58 = { by lemma 74 }
% 9.34/1.58 fresh66(true, true, X, Y, Y)
% 9.34/1.58 = { by axiom 9 (ruleD66) }
% 9.34/1.58 true
% 9.34/1.58
% 9.34/1.58 Lemma 76: coll(X, X, Y) = true.
% 9.34/1.58 Proof:
% 9.34/1.58 coll(X, X, Y)
% 9.34/1.58 = { by axiom 38 (ruleD1) R->L }
% 9.34/1.58 fresh146(coll(X, Y, X), true, X, Y, X)
% 9.34/1.58 = { by axiom 39 (ruleD2) R->L }
% 9.34/1.58 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 9.34/1.58 = { by lemma 75 }
% 9.34/1.58 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 9.34/1.58 = { by axiom 5 (ruleD2) }
% 9.34/1.58 fresh146(true, true, X, Y, X)
% 9.34/1.58 = { by axiom 4 (ruleD1) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 77: cyclic(X, a, u, u) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 cyclic(X, a, u, u)
% 9.34/1.59 = { by axiom 23 (ruleD42b) R->L }
% 9.34/1.59 fresh102(true, true, X, a, u, u)
% 9.34/1.59 = { by lemma 73 R->L }
% 9.34/1.59 fresh102(eqangle(u, X, u, a, u, X, u, a), true, X, a, u, u)
% 9.34/1.59 = { by axiom 66 (ruleD42b) }
% 9.34/1.59 fresh101(coll(u, u, a), true, X, a, u, u)
% 9.34/1.59 = { by axiom 38 (ruleD1) R->L }
% 9.34/1.59 fresh101(fresh146(coll(u, a, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 39 (ruleD2) R->L }
% 9.34/1.59 fresh101(fresh146(fresh133(coll(a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 44 (ruleD66) R->L }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(para(a, u, a, u), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 55 (ruleD4) R->L }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(fresh105(para(a, u, u, a), true, a, u, u, a), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 56 (ruleD5) R->L }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(para(u, a, a, u), true, u, a, a, u), true, a, u, u, a), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 55 (ruleD4) R->L }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(fresh105(para(u, a, u, a), true, u, a, u, a), true, u, a, a, u), true, a, u, u, a), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by lemma 72 }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(fresh105(true, true, u, a, u, a), true, u, a, a, u), true, a, u, u, a), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 22 (ruleD4) }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(true, true, u, a, a, u), true, a, u, u, a), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 25 (ruleD5) }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(fresh105(true, true, a, u, u, a), true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 22 (ruleD4) }
% 9.34/1.59 fresh101(fresh146(fresh133(fresh66(true, true, a, u, u), true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 9 (ruleD66) }
% 9.34/1.59 fresh101(fresh146(fresh133(true, true, a, u, u), true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 5 (ruleD2) }
% 9.34/1.59 fresh101(fresh146(true, true, u, a, u), true, X, a, u, u)
% 9.34/1.59 = { by axiom 4 (ruleD1) }
% 9.34/1.59 fresh101(true, true, X, a, u, u)
% 9.34/1.59 = { by axiom 24 (ruleD42b) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 78: eqangle(X, Y, Z, W, X, Y, Z, W) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 eqangle(X, Y, Z, W, X, Y, Z, W)
% 9.34/1.59 = { by axiom 63 (ruleD40) R->L }
% 9.34/1.59 fresh104(para(X, Y, X, Y), true, X, Y, X, Y, Z, W)
% 9.34/1.59 = { by lemma 74 }
% 9.34/1.59 fresh104(true, true, X, Y, X, Y, Z, W)
% 9.34/1.59 = { by axiom 40 (ruleD40) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 79: cyclic(a, u, u, X) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 cyclic(a, u, u, X)
% 9.34/1.59 = { by axiom 48 (ruleD14) R->L }
% 9.34/1.59 fresh140(cyclic(a, u, X, u), true, a, u, X, u)
% 9.34/1.59 = { by axiom 49 (ruleD15) R->L }
% 9.34/1.59 fresh140(fresh139(cyclic(a, X, u, u), true, a, X, u, u), true, a, u, X, u)
% 9.34/1.59 = { by axiom 50 (ruleD16) R->L }
% 9.34/1.59 fresh140(fresh139(fresh138(cyclic(X, a, u, u), true, X, a, u, u), true, a, X, u, u), true, a, u, X, u)
% 9.34/1.59 = { by lemma 77 }
% 9.34/1.59 fresh140(fresh139(fresh138(true, true, X, a, u, u), true, a, X, u, u), true, a, u, X, u)
% 9.34/1.59 = { by axiom 16 (ruleD16) }
% 9.34/1.59 fresh140(fresh139(true, true, a, X, u, u), true, a, u, X, u)
% 9.34/1.59 = { by axiom 15 (ruleD15) }
% 9.34/1.59 fresh140(true, true, a, u, X, u)
% 9.34/1.59 = { by axiom 14 (ruleD14) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 80: cyclic(u, u, X, Y) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 cyclic(u, u, X, Y)
% 9.34/1.59 = { by axiom 33 (ruleD17) R->L }
% 9.34/1.59 fresh137(true, true, a, u, u, X, Y)
% 9.34/1.59 = { by lemma 79 R->L }
% 9.34/1.59 fresh137(cyclic(a, u, u, Y), true, a, u, u, X, Y)
% 9.34/1.59 = { by axiom 61 (ruleD17) }
% 9.34/1.59 fresh136(cyclic(a, u, u, X), true, u, u, X, Y)
% 9.34/1.59 = { by lemma 79 }
% 9.34/1.59 fresh136(true, true, u, u, X, Y)
% 9.34/1.59 = { by axiom 17 (ruleD17) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 81: cyclic(u, X, Y, Z) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 cyclic(u, X, Y, Z)
% 9.34/1.59 = { by axiom 33 (ruleD17) R->L }
% 9.34/1.59 fresh137(true, true, u, u, X, Y, Z)
% 9.34/1.59 = { by lemma 80 R->L }
% 9.34/1.59 fresh137(cyclic(u, u, X, Z), true, u, u, X, Y, Z)
% 9.34/1.59 = { by axiom 61 (ruleD17) }
% 9.34/1.59 fresh136(cyclic(u, u, X, Y), true, u, X, Y, Z)
% 9.34/1.59 = { by lemma 80 }
% 9.34/1.59 fresh136(true, true, u, X, Y, Z)
% 9.34/1.59 = { by axiom 17 (ruleD17) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 82: cyclic(X, Y, Z, W) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 cyclic(X, Y, Z, W)
% 9.34/1.59 = { by axiom 33 (ruleD17) R->L }
% 9.34/1.59 fresh137(true, true, u, X, Y, Z, W)
% 9.34/1.59 = { by lemma 81 R->L }
% 9.34/1.59 fresh137(cyclic(u, X, Y, W), true, u, X, Y, Z, W)
% 9.34/1.59 = { by axiom 61 (ruleD17) }
% 9.34/1.59 fresh136(cyclic(u, X, Y, Z), true, X, Y, Z, W)
% 9.34/1.59 = { by lemma 81 }
% 9.34/1.59 fresh136(true, true, X, Y, Z, W)
% 9.34/1.59 = { by axiom 17 (ruleD17) }
% 9.34/1.59 true
% 9.34/1.59
% 9.34/1.59 Lemma 83: cong(u, X, u, X) = true.
% 9.34/1.59 Proof:
% 9.34/1.59 cong(u, X, u, X)
% 9.34/1.59 = { by axiom 53 (ruleD23) R->L }
% 9.34/1.59 fresh128(cong(u, X, X, u), true, u, X, X, u)
% 9.34/1.59 = { by axiom 54 (ruleD24) R->L }
% 9.34/1.59 fresh128(fresh127(cong(X, u, u, X), true, X, u, u, X), true, u, X, X, u)
% 9.34/1.59 = { by axiom 53 (ruleD23) R->L }
% 9.34/1.59 fresh128(fresh127(fresh128(cong(X, u, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.34/1.59 = { by axiom 32 (ruleD43) R->L }
% 9.34/1.59 fresh128(fresh127(fresh128(fresh183(true, true, X, u, a, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.34/1.59 = { by axiom 15 (ruleD15) R->L }
% 9.34/1.59 fresh128(fresh127(fresh128(fresh183(fresh139(true, true, X, a, u, u), true, X, u, a, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.34/1.59 = { by lemma 77 R->L }
% 9.34/1.59 fresh128(fresh127(fresh128(fresh183(fresh139(cyclic(X, a, u, u), true, X, a, u, u), true, X, u, a, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 49 (ruleD15) }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh183(cyclic(X, u, a, u), true, X, u, a, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 60 (ruleD43) R->L }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh182(true, true, X, u, a, X, u, a), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by lemma 78 R->L }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh182(eqangle(a, X, a, u, a, X, a, u), true, X, u, a, X, u, a), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 68 (ruleD43) }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh184(cyclic(X, u, a, a), true, X, u, a, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by lemma 82 }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh184(true, true, X, u, a, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 46 (ruleD43) }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh185(cyclic(X, u, a, X), true, X, u, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by lemma 82 }
% 9.61/1.59 fresh128(fresh127(fresh128(fresh185(true, true, X, u, X, u), true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 12 (ruleD43) }
% 9.61/1.59 fresh128(fresh127(fresh128(true, true, X, u, X, u), true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 18 (ruleD23) }
% 9.61/1.59 fresh128(fresh127(true, true, X, u, u, X), true, u, X, X, u)
% 9.61/1.59 = { by axiom 19 (ruleD24) }
% 9.61/1.59 fresh128(true, true, u, X, X, u)
% 9.61/1.59 = { by axiom 18 (ruleD23) }
% 9.61/1.59 true
% 9.61/1.59
% 9.61/1.59 Lemma 84: perp(u, u, X, Y) = true.
% 9.61/1.59 Proof:
% 9.61/1.59 perp(u, u, X, Y)
% 9.61/1.59 = { by axiom 26 (ruleD56) R->L }
% 9.61/1.59 fresh80(true, true, u, u, X, Y)
% 9.61/1.59 = { by lemma 83 R->L }
% 9.61/1.59 fresh80(cong(u, Y, u, Y), true, u, u, X, Y)
% 9.61/1.59 = { by axiom 57 (ruleD56) }
% 9.61/1.59 fresh79(cong(u, X, u, X), true, u, u, X, Y)
% 9.61/1.59 = { by lemma 83 }
% 9.61/1.59 fresh79(true, true, u, u, X, Y)
% 9.61/1.59 = { by axiom 27 (ruleD56) }
% 9.61/1.59 true
% 9.61/1.59
% 9.61/1.59 Lemma 85: para(X, Y, Z, W) = true.
% 9.61/1.59 Proof:
% 9.61/1.59 para(X, Y, Z, W)
% 9.61/1.59 = { by axiom 42 (ruleD9) R->L }
% 9.61/1.59 fresh51(true, true, X, Y, u, u, Z, W)
% 9.61/1.59 = { by lemma 84 R->L }
% 9.61/1.59 fresh51(perp(u, u, Z, W), true, X, Y, u, u, Z, W)
% 9.61/1.59 = { by axiom 64 (ruleD9) }
% 9.61/1.59 fresh50(perp(X, Y, u, u), true, X, Y, Z, W)
% 9.61/1.59 = { by axiom 59 (ruleD8) R->L }
% 9.61/1.59 fresh50(fresh52(perp(u, u, X, Y), true, u, u, X, Y), true, X, Y, Z, W)
% 9.61/1.59 = { by lemma 84 }
% 9.61/1.59 fresh50(fresh52(true, true, u, u, X, Y), true, X, Y, Z, W)
% 9.61/1.59 = { by axiom 29 (ruleD8) }
% 9.61/1.59 fresh50(true, true, X, Y, Z, W)
% 9.61/1.59 = { by axiom 30 (ruleD9) }
% 9.61/1.59 true
% 9.61/1.59
% 9.61/1.59 Goal 1 (exemplo6GDDFULL618080_5): cong(t, a, t, u) = true.
% 9.61/1.59 Proof:
% 9.61/1.59 cong(t, a, t, u)
% 9.61/1.59 = { by axiom 41 (ruleD68) R->L }
% 9.61/1.59 fresh63(midp(t, a, u), true, t, a, u)
% 9.61/1.59 = { by axiom 7 (ruleD45) R->L }
% 9.61/1.59 fresh63(fresh98(true, true, a, u, t), true, t, a, u)
% 9.61/1.59 = { by lemma 85 R->L }
% 9.61/1.59 fresh63(fresh98(para(a, t, a, u), true, a, u, t), true, t, a, u)
% 9.61/1.59 = { by axiom 47 (ruleD45) R->L }
% 9.61/1.59 fresh63(fresh180(midp(a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.59 = { by axiom 8 (ruleD51) R->L }
% 9.61/1.59 fresh63(fresh180(fresh89(true, true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.59 = { by axiom 11 (ruleX14) R->L }
% 9.61/1.59 fresh63(fresh180(fresh89(fresh36(true, true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.59 = { by axiom 13 (ruleD10) R->L }
% 9.61/1.59 fresh63(fresh180(fresh89(fresh36(fresh145(true, true, X, a, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.59 = { by lemma 85 R->L }
% 9.61/1.59 fresh63(fresh180(fresh89(fresh36(fresh145(para(X, a, a, t), true, X, a, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.59 = { by axiom 62 (ruleD10) R->L }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(perp(a, t, a, a), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 59 (ruleD8) R->L }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(fresh52(perp(a, a, a, t), true, a, a, a, t), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 37 (ruleD10) R->L }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(fresh52(fresh147(true, true, a, a, a, o, a, t), true, a, a, a, t), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 1 (exemplo6GDDFULL618080_2) R->L }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(fresh52(fresh147(perp(a, o, a, t), true, a, a, a, o, a, t), true, a, a, a, t), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 62 (ruleD10) }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(fresh52(fresh145(para(a, a, a, o), true, a, a, a, t), true, a, a, a, t), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by lemma 85 }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(fresh52(fresh145(true, true, a, a, a, t), true, a, a, a, t), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 13 (ruleD10) }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(fresh52(true, true, a, a, a, t), true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 29 (ruleD8) }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(fresh147(true, true, X, a, a, t, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 37 (ruleD10) }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh36(perp(X, a, a, a), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 45 (ruleX14) R->L }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh37(cyclic(X, a, a, Y), true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by lemma 82 }
% 9.61/1.60 fresh63(fresh180(fresh89(fresh37(true, true, X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 31 (ruleX14) }
% 9.61/1.60 fresh63(fresh180(fresh89(circle(o2(X, a, a), X, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 67 (ruleD51) R->L }
% 9.61/1.60 fresh63(fresh180(fresh178(eqangle(X, a, X, a, o2(X, a, a), a, o2(X, a, a), a), true, X, a, a, a, o2(X, a, a)), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 70 (ruleD21) R->L }
% 9.61/1.60 fresh63(fresh180(fresh178(fresh131(eqangle(X, a, o2(X, a, a), a, X, a, o2(X, a, a), a), true, X, a, o2(X, a, a), a, X, a, o2(X, a, a), a), true, X, a, a, a, o2(X, a, a)), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by lemma 78 }
% 9.61/1.60 fresh63(fresh180(fresh178(fresh131(true, true, X, a, o2(X, a, a), a, X, a, o2(X, a, a), a), true, X, a, a, a, o2(X, a, a)), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 52 (ruleD21) }
% 9.61/1.60 fresh63(fresh180(fresh178(true, true, X, a, a, a, o2(X, a, a)), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 36 (ruleD51) }
% 9.61/1.60 fresh63(fresh180(fresh179(coll(a, a, a), true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by lemma 75 }
% 9.61/1.60 fresh63(fresh180(fresh179(true, true, a, a, a), true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 3 (ruleD51) }
% 9.61/1.60 fresh63(fresh180(true, true, a, a, u, a, t), true, t, a, u)
% 9.61/1.60 = { by axiom 35 (ruleD45) }
% 9.61/1.60 fresh63(fresh181(coll(t, a, u), true, a, u, t), true, t, a, u)
% 9.61/1.60 = { by axiom 20 (ruleD3) R->L }
% 9.61/1.60 fresh63(fresh181(fresh120(true, true, u, u, t, a), true, a, u, t), true, t, a, u)
% 9.61/1.60 = { by lemma 76 R->L }
% 9.61/1.60 fresh63(fresh181(fresh120(coll(u, u, a), true, u, u, t, a), true, a, u, t), true, t, a, u)
% 9.61/1.60 = { by axiom 43 (ruleD3) }
% 9.61/1.60 fresh63(fresh181(fresh119(coll(u, u, t), true, u, t, a), true, a, u, t), true, t, a, u)
% 9.61/1.60 = { by lemma 76 }
% 9.61/1.60 fresh63(fresh181(fresh119(true, true, u, t, a), true, a, u, t), true, t, a, u)
% 9.61/1.60 = { by axiom 6 (ruleD3) }
% 9.61/1.60 fresh63(fresh181(true, true, a, u, t), true, t, a, u)
% 9.61/1.60 = { by axiom 2 (ruleD45) }
% 9.61/1.60 fresh63(true, true, t, a, u)
% 9.61/1.60 = { by axiom 10 (ruleD68) }
% 9.61/1.60 true
% 9.61/1.60 % SZS output end Proof
% 9.61/1.60
% 9.61/1.60 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------