TSTP Solution File: GEO563+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO563+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 23:29:20 EDT 2023
% Result : Theorem 46.31s 6.25s
% Output : Proof 47.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO563+1 : TPTP v8.1.2. Released v7.5.0.
% 0.04/0.13 % 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 : n007.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 20:17:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 46.31/6.25 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 46.31/6.25
% 46.31/6.25 % SZS status Theorem
% 46.31/6.25
% 46.85/6.29 % SZS output start Proof
% 46.85/6.29 Take the following subset of the input axioms:
% 46.85/6.29 fof(exemplo6GDDFULL214024, conjecture, ![O, P, Q, R, X, Y, O1, S, I, NWPNT1, NWPNT2]: ((circle(O1, Q, R, P) & (circle(O1, Q, S, NWPNT1) & (coll(Y, Q, S) & (circle(O, Y, P, Q) & (circle(O, Q, X, NWPNT2) & (coll(I, R, S) & coll(I, Y, X))))))) => eqangle(R, I, I, X, R, P, P, X))).
% 46.85/6.29 fof(ruleD1, axiom, ![B, C, A2]: (coll(A2, B, C) => coll(A2, C, B))).
% 46.85/6.29 fof(ruleD14, axiom, ![D, B2, C2, A2_2]: (cyclic(A2_2, B2, C2, D) => cyclic(A2_2, B2, D, C2))).
% 46.85/6.29 fof(ruleD15, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 46.85/6.29 fof(ruleD17, axiom, ![E, B2, C2, A2_2, D2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E)) => cyclic(B2, C2, D2, E))).
% 46.85/6.29 fof(ruleD18, axiom, ![U, V, P2, B2, C2, A2_2, D2, Q2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U, V) => eqangle(B2, A2_2, C2, D2, P2, Q2, U, V))).
% 46.85/6.29 fof(ruleD19, axiom, ![P2, B2, C2, A2_2, D2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(C2, D2, A2_2, B2, U2, V2, P2, Q2))).
% 46.85/6.29 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 46.85/6.29 fof(ruleD20, axiom, ![P2, B2, C2, A2_2, D2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(P2, Q2, U2, V2, A2_2, B2, C2, D2))).
% 46.85/6.29 fof(ruleD21, axiom, ![P2, B2, C2, A2_2, D2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(A2_2, B2, P2, Q2, C2, D2, U2, V2))).
% 46.85/6.29 fof(ruleD22, axiom, ![F, G, H, P2, B2, C2, A2_2, D2, Q2, E2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & eqangle(P2, Q2, U2, V2, E2, F, G, H)) => eqangle(A2_2, B2, C2, D2, E2, F, G, H))).
% 46.85/6.29 fof(ruleD39, axiom, ![P2, B2, C2, A2_2, D2, Q2]: (eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2) => para(A2_2, B2, C2, D2))).
% 46.85/6.29 fof(ruleD40, axiom, ![P2, B2, C2, A2_2, D2, Q2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 46.85/6.29 fof(ruleD41, axiom, ![P2, B2, A2_2, Q2]: (cyclic(A2_2, B2, P2, Q2) => eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2))).
% 46.85/6.29 fof(ruleD42b, axiom, ![P2, B2, A2_2, Q2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 46.85/6.29 fof(ruleD48, axiom, ![B2, C2, O2, A2_2, X2]: ((circle(O2, A2_2, B2, C2) & perp(O2, A2_2, A2_2, X2)) => eqangle(A2_2, X2, A2_2, B2, C2, A2_2, C2, B2))).
% 46.85/6.29 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 46.85/6.29 fof(ruleD7, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(A2_2, B2, D2, C2))).
% 46.85/6.29 fof(ruleD8, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 46.85/6.29 fof(ruleX11, axiom, ![B2, C2, O2, A2_2]: ?[P2]: (circle(O2, A2_2, B2, C2) => perp(P2, A2_2, A2_2, O2))).
% 46.85/6.29
% 46.85/6.29 Now clausify the problem and encode Horn clauses using encoding 3 of
% 46.85/6.29 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 46.85/6.29 We repeatedly replace C & s=t => u=v by the two clauses:
% 46.85/6.29 fresh(y, y, x1...xn) = u
% 46.85/6.29 C => fresh(s, t, x1...xn) = v
% 46.85/6.29 where fresh is a fresh function symbol and x1..xn are the free
% 46.85/6.29 variables of u and v.
% 46.85/6.29 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 46.85/6.29 input problem has no model of domain size 1).
% 46.85/6.29
% 46.85/6.29 The encoding turns the above axioms into the following unit equations and goals:
% 46.85/6.29
% 46.85/6.29 Axiom 1 (exemplo6GDDFULL214024_3): circle(o1, q, r, p) = true.
% 46.85/6.29 Axiom 2 (ruleX11): fresh39(X, X, Y, Z) = true.
% 46.85/6.29 Axiom 3 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 46.85/6.29 Axiom 4 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 46.85/6.29 Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 46.85/6.29 Axiom 6 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 7 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 8 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 9 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 10 (ruleD41): fresh103(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 11 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 46.85/6.29 Axiom 12 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 13 (ruleD48): fresh95(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 14 (ruleD7): fresh61(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 15 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 46.85/6.29 Axiom 16 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 46.85/6.30 Axiom 17 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 46.85/6.30 Axiom 18 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 46.85/6.30 Axiom 19 (ruleX11): fresh39(circle(X, Y, Z, W), true, Y, X) = perp(p4(Y, X), Y, Y, X).
% 46.85/6.30 Axiom 20 (ruleD48): fresh96(X, X, Y, Z, W, V, U) = eqangle(Y, U, Y, Z, W, Y, W, Z).
% 46.85/6.30 Axiom 21 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 46.85/6.30 Axiom 22 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 46.85/6.30 Axiom 23 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 46.85/6.30 Axiom 24 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 46.85/6.30 Axiom 25 (ruleD41): fresh103(cyclic(X, Y, Z, W), true, X, Y, Z, W) = eqangle(Z, X, Z, Y, W, X, W, Y).
% 46.85/6.30 Axiom 26 (ruleD7): fresh61(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(X, Y, W, Z).
% 46.85/6.30 Axiom 27 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 46.85/6.30 Axiom 28 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 46.85/6.30 Axiom 29 (ruleD18): fresh135(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 46.85/6.30 Axiom 30 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 46.85/6.30 Axiom 31 (ruleD20): fresh132(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 46.85/6.30 Axiom 32 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 46.85/6.30 Axiom 33 (ruleD22): fresh129(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 46.85/6.30 Axiom 34 (ruleD48): fresh96(circle(X, Y, Z, W), true, Y, Z, W, X, V) = fresh95(perp(X, Y, Y, V), true, Y, Z, W, V).
% 46.85/6.30 Axiom 35 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 46.85/6.30 Axiom 36 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 46.85/6.30 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).
% 46.85/6.30 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).
% 46.85/6.30 Axiom 39 (ruleD18): fresh135(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = eqangle(Y, X, Z, W, V, U, T, S).
% 46.85/6.30 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).
% 46.85/6.30 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).
% 46.85/6.30 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).
% 46.85/6.30 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).
% 46.85/6.30
% 46.85/6.30 Lemma 44: eqangle(p4(q, o1), q, q, r, p, q, p, r) = true.
% 46.85/6.30 Proof:
% 46.85/6.30 eqangle(p4(q, o1), q, q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 39 (ruleD18) R->L }
% 46.85/6.30 fresh135(eqangle(q, p4(q, o1), q, r, p, q, p, r), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 20 (ruleD48) R->L }
% 46.85/6.30 fresh135(fresh96(true, true, q, r, p, o1, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 1 (exemplo6GDDFULL214024_3) R->L }
% 46.85/6.30 fresh135(fresh96(circle(o1, q, r, p), true, q, r, p, o1, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 34 (ruleD48) }
% 46.85/6.30 fresh135(fresh95(perp(o1, q, q, p4(q, o1)), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 26 (ruleD7) R->L }
% 46.85/6.30 fresh135(fresh95(fresh61(perp(o1, q, p4(q, o1), q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 27 (ruleD8) R->L }
% 46.85/6.30 fresh135(fresh95(fresh61(fresh52(perp(p4(q, o1), q, o1, q), true, p4(q, o1), q, o1, q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 26 (ruleD7) R->L }
% 46.85/6.30 fresh135(fresh95(fresh61(fresh52(fresh61(perp(p4(q, o1), q, q, o1), true, p4(q, o1), q, q, o1), true, p4(q, o1), q, o1, q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 19 (ruleX11) R->L }
% 46.85/6.30 fresh135(fresh95(fresh61(fresh52(fresh61(fresh39(circle(o1, q, r, p), true, q, o1), true, p4(q, o1), q, q, o1), true, p4(q, o1), q, o1, q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 1 (exemplo6GDDFULL214024_3) }
% 46.85/6.30 fresh135(fresh95(fresh61(fresh52(fresh61(fresh39(true, true, q, o1), true, p4(q, o1), q, q, o1), true, p4(q, o1), q, o1, q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 2 (ruleX11) }
% 46.85/6.30 fresh135(fresh95(fresh61(fresh52(fresh61(true, true, p4(q, o1), q, q, o1), true, p4(q, o1), q, o1, q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 14 (ruleD7) }
% 46.85/6.30 fresh135(fresh95(fresh61(fresh52(true, true, p4(q, o1), q, o1, q), true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 15 (ruleD8) }
% 46.85/6.30 fresh135(fresh95(fresh61(true, true, o1, q, p4(q, o1), q), true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 14 (ruleD7) }
% 46.85/6.30 fresh135(fresh95(true, true, q, r, p, p4(q, o1)), true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 13 (ruleD48) }
% 46.85/6.30 fresh135(true, true, q, p4(q, o1), q, r, p, q, p, r)
% 46.85/6.30 = { by axiom 29 (ruleD18) }
% 46.85/6.30 true
% 46.85/6.30
% 46.85/6.30 Lemma 45: eqangle(p, q, X, Y, p, q, X, Y) = true.
% 46.85/6.30 Proof:
% 46.85/6.30 eqangle(p, q, X, Y, p, q, X, Y)
% 46.85/6.30 = { by axiom 39 (ruleD18) R->L }
% 46.85/6.30 fresh135(eqangle(q, p, X, Y, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 46.85/6.30 = { by axiom 35 (ruleD40) R->L }
% 46.85/6.30 fresh135(fresh104(para(q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 46.85/6.30 = { by axiom 36 (ruleD39) R->L }
% 46.85/6.30 fresh135(fresh104(fresh106(eqangle(q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 38 (ruleD22) R->L }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh130(true, true, q, p, p, r, p4(q, o1), q, q, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by lemma 44 R->L }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh130(eqangle(p4(q, o1), q, q, r, p, q, p, r), true, q, p, p, r, p4(q, o1), q, q, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 43 (ruleD22) }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh129(eqangle(q, p, p, r, p4(q, o1), q, q, r), true, q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 39 (ruleD18) R->L }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh129(fresh135(eqangle(p, q, p, r, p4(q, o1), q, q, r), true, p, q, p, r, p4(q, o1), q, q, r), true, q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 41 (ruleD20) R->L }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh129(fresh135(fresh132(eqangle(p4(q, o1), q, q, r, p, q, p, r), true, p4(q, o1), q, q, r, p, q, p, r), true, p, q, p, r, p4(q, o1), q, q, r), true, q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by lemma 44 }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh129(fresh135(fresh132(true, true, p4(q, o1), q, q, r, p, q, p, r), true, p, q, p, r, p4(q, o1), q, q, r), true, q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 31 (ruleD20) }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh129(fresh135(true, true, p, q, p, r, p4(q, o1), q, q, r), true, q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 29 (ruleD18) }
% 47.17/6.30 fresh135(fresh104(fresh106(fresh129(true, true, q, p, p, r, p, q, p, r), true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 33 (ruleD22) }
% 47.17/6.30 fresh135(fresh104(fresh106(true, true, q, p, p, q), true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 9 (ruleD39) }
% 47.17/6.30 fresh135(fresh104(true, true, q, p, p, q, X, Y), true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 21 (ruleD40) }
% 47.17/6.30 fresh135(true, true, q, p, X, Y, p, q, X, Y)
% 47.17/6.30 = { by axiom 29 (ruleD18) }
% 47.17/6.30 true
% 47.17/6.30
% 47.17/6.30 Lemma 46: cyclic(q, p, p, X) = true.
% 47.17/6.30 Proof:
% 47.17/6.30 cyclic(q, p, p, X)
% 47.17/6.30 = { by axiom 23 (ruleD14) R->L }
% 47.17/6.30 fresh140(cyclic(q, p, X, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 24 (ruleD15) R->L }
% 47.17/6.30 fresh140(fresh139(cyclic(q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 11 (ruleD42b) R->L }
% 47.17/6.30 fresh140(fresh139(fresh102(true, true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by lemma 45 R->L }
% 47.17/6.30 fresh140(fresh139(fresh102(eqangle(p, q, p, X, p, q, p, X), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 37 (ruleD42b) }
% 47.17/6.30 fresh140(fresh139(fresh101(coll(p, p, X), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 16 (ruleD1) R->L }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(coll(p, X, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 18 (ruleD2) R->L }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(coll(X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 22 (ruleD66) R->L }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(para(X, p, X, p), true, X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 36 (ruleD39) R->L }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(fresh106(eqangle(X, p, p, q, X, p, p, q), true, X, p, X, p), true, X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 40 (ruleD19) R->L }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(p, q, X, p, p, q, X, p), true, p, q, X, p, p, q, X, p), true, X, p, X, p), true, X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by lemma 45 }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(fresh106(fresh134(true, true, p, q, X, p, p, q, X, p), true, X, p, X, p), true, X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 30 (ruleD19) }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(fresh106(true, true, X, p, X, p), true, X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 9 (ruleD39) }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(true, true, X, p, p), true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 5 (ruleD66) }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(fresh133(true, true, X, p, p), true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 4 (ruleD2) }
% 47.17/6.30 fresh140(fresh139(fresh101(fresh146(true, true, p, X, p), true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 3 (ruleD1) }
% 47.17/6.30 fresh140(fresh139(fresh101(true, true, q, X, p, p), true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 12 (ruleD42b) }
% 47.17/6.30 fresh140(fresh139(true, true, q, X, p, p), true, q, p, X, p)
% 47.17/6.30 = { by axiom 7 (ruleD15) }
% 47.17/6.30 fresh140(true, true, q, p, X, p)
% 47.17/6.30 = { by axiom 6 (ruleD14) }
% 47.17/6.30 true
% 47.17/6.30
% 47.17/6.30 Lemma 47: cyclic(p, p, X, Y) = true.
% 47.17/6.30 Proof:
% 47.17/6.30 cyclic(p, p, X, Y)
% 47.17/6.30 = { by axiom 17 (ruleD17) R->L }
% 47.17/6.30 fresh137(true, true, q, p, p, X, Y)
% 47.17/6.30 = { by lemma 46 R->L }
% 47.17/6.30 fresh137(cyclic(q, p, p, Y), true, q, p, p, X, Y)
% 47.17/6.30 = { by axiom 28 (ruleD17) }
% 47.17/6.30 fresh136(cyclic(q, p, p, X), true, p, p, X, Y)
% 47.17/6.30 = { by lemma 46 }
% 47.17/6.30 fresh136(true, true, p, p, X, Y)
% 47.17/6.30 = { by axiom 8 (ruleD17) }
% 47.17/6.30 true
% 47.17/6.30
% 47.17/6.30 Goal 1 (exemplo6GDDFULL214024_7): eqangle(r, i, i, x, r, p, p, x) = true.
% 47.17/6.30 Proof:
% 47.17/6.30 eqangle(r, i, i, x, r, p, p, x)
% 47.17/6.31 = { by axiom 42 (ruleD21) R->L }
% 47.17/6.31 fresh131(eqangle(r, i, r, p, i, x, p, x), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 41 (ruleD20) R->L }
% 47.17/6.31 fresh131(fresh132(eqangle(i, x, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 39 (ruleD18) R->L }
% 47.17/6.31 fresh131(fresh132(fresh135(eqangle(x, i, p, x, r, i, r, p), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 40 (ruleD19) R->L }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(eqangle(p, x, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 39 (ruleD18) R->L }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(eqangle(x, p, x, i, r, p, r, i), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 25 (ruleD41) R->L }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(fresh103(cyclic(p, i, x, r), true, p, i, x, r), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 17 (ruleD17) R->L }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(fresh103(fresh137(true, true, p, p, i, x, r), true, p, i, x, r), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by lemma 47 R->L }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(fresh103(fresh137(cyclic(p, p, i, r), true, p, p, i, x, r), true, p, i, x, r), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 28 (ruleD17) }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(fresh103(fresh136(cyclic(p, p, i, x), true, p, i, x, r), true, p, i, x, r), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by lemma 47 }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(fresh103(fresh136(true, true, p, i, x, r), true, p, i, x, r), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 8 (ruleD17) }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(fresh103(true, true, p, i, x, r), true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 10 (ruleD41) }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(fresh135(true, true, x, p, x, i, r, p, r, i), true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 29 (ruleD18) }
% 47.17/6.31 fresh131(fresh132(fresh135(fresh134(true, true, p, x, x, i, r, p, r, i), true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 30 (ruleD19) }
% 47.17/6.31 fresh131(fresh132(fresh135(true, true, x, i, p, x, r, i, r, p), true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 29 (ruleD18) }
% 47.17/6.31 fresh131(fresh132(true, true, i, x, p, x, r, i, r, p), true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 31 (ruleD20) }
% 47.17/6.31 fresh131(true, true, r, i, r, p, i, x, p, x)
% 47.17/6.31 = { by axiom 32 (ruleD21) }
% 47.17/6.31 true
% 47.17/6.31 % SZS output end Proof
% 47.17/6.31
% 47.17/6.31 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------