TSTP Solution File: GEO635+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO635+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 : n027.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 23:29:38 EDT 2023
% Result : Theorem 20.18s 2.99s
% Output : Proof 20.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO635+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
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 20:13:08 EDT 2023
% 0.13/0.35 % CPUTime :
% 20.18/2.99 Command-line arguments: --flatten
% 20.18/2.99
% 20.18/2.99 % SZS status Theorem
% 20.18/2.99
% 20.53/3.03 % SZS output start Proof
% 20.53/3.03 Take the following subset of the input axioms:
% 20.53/3.04 fof(exemplo6GDDFULL8110998, conjecture, ![A, B, C, D, E, F, G, NWPNT1, NWPNT2]: ((circle(D, A, B, C) & (coll(E, A, B) & (circle(D, A, F, NWPNT1) & (eqangle(A, C, C, E, F, C, C, B) & (circle(D, C, G, NWPNT2) & coll(G, C, E)))))) => para(A, B, G, F))).
% 20.53/3.04 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 20.53/3.04 fof(ruleD15, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 20.53/3.04 fof(ruleD16, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 20.53/3.04 fof(ruleD19, axiom, ![P, Q, U, V, B2, C2, A2_2, D2]: (eqangle(A2_2, B2, C2, D2, P, Q, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P, Q))).
% 20.53/3.04 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 20.53/3.04 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))).
% 20.53/3.04 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))).
% 20.53/3.04 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))).
% 20.53/3.04 fof(ruleD43, axiom, ![R, P2, B2, C2, A2_2, 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))).
% 20.53/3.04 fof(ruleD56, axiom, ![P2, B2, A2_2, Q2]: ((cong(A2_2, P2, B2, P2) & cong(A2_2, Q2, B2, Q2)) => perp(A2_2, B2, P2, Q2))).
% 20.53/3.04 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 20.53/3.04 fof(ruleD8, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 20.53/3.04 fof(ruleD9, axiom, ![B2, C2, A2_2, D2, E2, F2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => para(A2_2, B2, E2, F2))).
% 20.53/3.04 fof(ruleX11, axiom, ![O, B2, C2, A2_2]: ?[P2]: (circle(O, A2_2, B2, C2) => perp(P2, A2_2, A2_2, O))).
% 20.53/3.04
% 20.53/3.04 Now clausify the problem and encode Horn clauses using encoding 3 of
% 20.53/3.04 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 20.53/3.04 We repeatedly replace C & s=t => u=v by the two clauses:
% 20.53/3.04 fresh(y, y, x1...xn) = u
% 20.53/3.04 C => fresh(s, t, x1...xn) = v
% 20.53/3.04 where fresh is a fresh function symbol and x1..xn are the free
% 20.53/3.04 variables of u and v.
% 20.53/3.04 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 20.53/3.04 input problem has no model of domain size 1).
% 20.53/3.04
% 20.53/3.04 The encoding turns the above axioms into the following unit equations and goals:
% 20.53/3.04
% 20.53/3.04 Axiom 1 (exemplo6GDDFULL8110998): coll(e, a, b) = true.
% 20.53/3.04 Axiom 2 (ruleX11): fresh39(X, X, Y, Z) = true.
% 20.53/3.04 Axiom 3 (exemplo6GDDFULL8110998_3): circle(d, a, f, nwpnt1) = true.
% 20.53/3.04 Axiom 4 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 20.53/3.04 Axiom 5 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 20.53/3.04 Axiom 6 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 20.53/3.04 Axiom 7 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 8 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 9 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 10 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 11 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 20.53/3.04 Axiom 12 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 13 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 20.53/3.04 Axiom 14 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 15 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 16 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 20.53/3.04 Axiom 17 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 20.53/3.04 Axiom 18 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 20.53/3.04 Axiom 19 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 20.53/3.04 Axiom 20 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 20.53/3.04 Axiom 21 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 20.53/3.04 Axiom 22 (ruleX11): fresh39(circle(X, Y, Z, W), true, Y, X) = perp(p3(Y, X), Y, Y, X).
% 20.53/3.04 Axiom 23 (ruleD50): fresh91(X, X, Y, Z, W, V, U) = eqangle(Y, Z, Y, W, V, Z, V, U).
% 20.53/3.04 Axiom 24 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 20.53/3.04 Axiom 25 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 20.53/3.04 Axiom 26 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 20.53/3.04 Axiom 27 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 20.53/3.04 Axiom 28 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 20.53/3.04 Axiom 29 (ruleD56): fresh80(cong(X, Y, Z, Y), true, X, Z, W, Y) = fresh79(cong(X, W, Z, W), true, X, Z, W, Y).
% 20.53/3.04 Axiom 30 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 20.53/3.04 Axiom 31 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 20.53/3.04 Axiom 32 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 20.53/3.04 Axiom 33 (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).
% 20.53/3.04 Axiom 34 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 20.53/3.04 Axiom 35 (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).
% 20.53/3.04 Axiom 36 (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).
% 20.53/3.04 Axiom 37 (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).
% 20.53/3.04
% 20.53/3.04 Lemma 38: fresh104(X, X, Y, Z, W, V, U, T) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 fresh104(X, X, Y, Z, W, V, U, T)
% 20.53/3.04 = { by axiom 20 (ruleD40) }
% 20.53/3.04 true
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 coll(e, a, b)
% 20.53/3.04
% 20.53/3.04 Lemma 39: fresh104(para(X, Y, Z, W), coll(e, a, b), X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 20.53/3.04 Proof:
% 20.53/3.04 fresh104(para(X, Y, Z, W), coll(e, a, b), X, Y, Z, W, V, U)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.04 fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U)
% 20.53/3.04 = { by axiom 32 (ruleD40) }
% 20.53/3.04 eqangle(X, Y, V, U, Z, W, V, U)
% 20.53/3.04
% 20.53/3.04 Lemma 40: perp(p3(a, d), a, a, d) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 perp(p3(a, d), a, a, d)
% 20.53/3.04 = { by axiom 22 (ruleX11) R->L }
% 20.53/3.04 fresh39(circle(d, a, f, nwpnt1), true, a, d)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh39(circle(d, a, f, nwpnt1), coll(e, a, b), a, d)
% 20.53/3.04 = { by axiom 3 (exemplo6GDDFULL8110998_3) }
% 20.53/3.04 fresh39(true, coll(e, a, b), a, d)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh39(coll(e, a, b), coll(e, a, b), a, d)
% 20.53/3.04 = { by axiom 2 (ruleX11) }
% 20.53/3.04 true
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 coll(e, a, b)
% 20.53/3.04
% 20.53/3.04 Lemma 41: fresh51(perp(X, Y, Z, W), coll(e, a, b), V, U, X, Y, Z, W) = fresh50(perp(V, U, X, Y), coll(e, a, b), V, U, Z, W).
% 20.53/3.04 Proof:
% 20.53/3.04 fresh51(perp(X, Y, Z, W), coll(e, a, b), V, U, X, Y, Z, W)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.04 fresh51(perp(X, Y, Z, W), true, V, U, X, Y, Z, W)
% 20.53/3.04 = { by axiom 33 (ruleD9) }
% 20.53/3.04 fresh50(perp(V, U, X, Y), true, V, U, Z, W)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh50(perp(V, U, X, Y), coll(e, a, b), V, U, Z, W)
% 20.53/3.04
% 20.53/3.04 Lemma 42: fresh52(perp(X, Y, Z, W), coll(e, a, b), X, Y, Z, W) = perp(Z, W, X, Y).
% 20.53/3.04 Proof:
% 20.53/3.04 fresh52(perp(X, Y, Z, W), coll(e, a, b), X, Y, Z, W)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.04 fresh52(perp(X, Y, Z, W), true, X, Y, Z, W)
% 20.53/3.04 = { by axiom 30 (ruleD8) }
% 20.53/3.04 perp(Z, W, X, Y)
% 20.53/3.04
% 20.53/3.04 Lemma 43: fresh52(X, X, Y, Z, W, V) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 fresh52(X, X, Y, Z, W, V)
% 20.53/3.04 = { by axiom 15 (ruleD8) }
% 20.53/3.04 true
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 coll(e, a, b)
% 20.53/3.04
% 20.53/3.04 Lemma 44: fresh50(X, X, Y, Z, W, V) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 fresh50(X, X, Y, Z, W, V)
% 20.53/3.04 = { by axiom 16 (ruleD9) }
% 20.53/3.04 true
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 coll(e, a, b)
% 20.53/3.04
% 20.53/3.04 Lemma 45: para(X, Y, X, Y) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 para(X, Y, X, Y)
% 20.53/3.04 = { by axiom 34 (ruleD39) R->L }
% 20.53/3.04 fresh106(eqangle(X, Y, a, d, X, Y, a, d), true, X, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh106(eqangle(X, Y, a, d, X, Y, a, d), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 37 (ruleD19) R->L }
% 20.53/3.04 fresh106(fresh134(eqangle(a, d, X, Y, a, d, X, Y), true, a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh106(fresh134(eqangle(a, d, X, Y, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 39 R->L }
% 20.53/3.04 fresh106(fresh134(fresh104(para(a, d, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 21 (ruleD9) R->L }
% 20.53/3.04 fresh106(fresh134(fresh104(fresh51(coll(e, a, b), coll(e, a, b), a, d, p3(a, d), a, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 40 R->L }
% 20.53/3.04 fresh106(fresh134(fresh104(fresh51(perp(p3(a, d), a, a, d), coll(e, a, b), a, d, p3(a, d), a, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 41 }
% 20.53/3.04 fresh106(fresh134(fresh104(fresh50(perp(a, d, p3(a, d), a), coll(e, a, b), a, d, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 42 R->L }
% 20.53/3.04 fresh106(fresh134(fresh104(fresh50(fresh52(perp(p3(a, d), a, a, d), coll(e, a, b), p3(a, d), a, a, d), coll(e, a, b), a, d, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 40 }
% 20.53/3.04 fresh106(fresh134(fresh104(fresh50(fresh52(coll(e, a, b), coll(e, a, b), p3(a, d), a, a, d), coll(e, a, b), a, d, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 43 }
% 20.53/3.04 fresh106(fresh134(fresh104(fresh50(coll(e, a, b), coll(e, a, b), a, d, a, d), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 44 }
% 20.53/3.04 fresh106(fresh134(fresh104(coll(e, a, b), coll(e, a, b), a, d, a, d, X, Y), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by lemma 38 }
% 20.53/3.04 fresh106(fresh134(coll(e, a, b), coll(e, a, b), a, d, X, Y, a, d, X, Y), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 28 (ruleD19) }
% 20.53/3.04 fresh106(true, coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh106(coll(e, a, b), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 10 (ruleD39) }
% 20.53/3.04 true
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 coll(e, a, b)
% 20.53/3.04
% 20.53/3.04 Lemma 46: cyclic(X, Y, Z, Z) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 cyclic(X, Y, Z, Z)
% 20.53/3.04 = { by axiom 11 (ruleD42b) R->L }
% 20.53/3.04 fresh102(coll(e, a, b), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by lemma 38 R->L }
% 20.53/3.04 fresh102(fresh104(coll(e, a, b), coll(e, a, b), Z, X, Z, X, Z, Y), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by lemma 45 R->L }
% 20.53/3.04 fresh102(fresh104(para(Z, X, Z, X), coll(e, a, b), Z, X, Z, X, Z, Y), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by lemma 39 }
% 20.53/3.04 fresh102(eqangle(Z, X, Z, Y, Z, X, Z, Y), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 23 (ruleD50) R->L }
% 20.53/3.04 fresh102(fresh91(W, W, Z, X, Y, Z, Y), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.04 fresh102(fresh91(W, W, Z, X, Y, Z, Y), true, X, Y, Z, Z)
% 20.53/3.04 = { by axiom 23 (ruleD50) }
% 20.53/3.04 fresh102(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, Z)
% 20.53/3.04 = { by axiom 35 (ruleD42b) }
% 20.53/3.04 fresh101(coll(Z, Z, Y), true, X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(coll(Z, Z, Y), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 18 (ruleD1) R->L }
% 20.53/3.04 fresh101(fresh146(coll(Z, Y, Z), true, Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(fresh146(coll(Z, Y, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 19 (ruleD2) R->L }
% 20.53/3.04 fresh101(fresh146(fresh133(coll(Y, Z, Z), true, Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(fresh146(fresh133(coll(Y, Z, Z), coll(e, a, b), Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 24 (ruleD66) R->L }
% 20.53/3.04 fresh101(fresh146(fresh133(fresh66(para(Y, Z, Y, Z), true, Y, Z, Z), coll(e, a, b), Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(fresh146(fresh133(fresh66(para(Y, Z, Y, Z), coll(e, a, b), Y, Z, Z), coll(e, a, b), Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by lemma 45 }
% 20.53/3.04 fresh101(fresh146(fresh133(fresh66(coll(e, a, b), coll(e, a, b), Y, Z, Z), coll(e, a, b), Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 6 (ruleD66) }
% 20.53/3.04 fresh101(fresh146(fresh133(true, coll(e, a, b), Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(fresh146(fresh133(coll(e, a, b), coll(e, a, b), Y, Z, Z), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 5 (ruleD2) }
% 20.53/3.04 fresh101(fresh146(true, coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(fresh146(coll(e, a, b), coll(e, a, b), Z, Y, Z), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 4 (ruleD1) }
% 20.53/3.04 fresh101(true, coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh101(coll(e, a, b), coll(e, a, b), X, Y, Z, Z)
% 20.53/3.04 = { by axiom 12 (ruleD42b) }
% 20.53/3.04 true
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 coll(e, a, b)
% 20.53/3.04
% 20.53/3.04 Lemma 47: cong(X, Y, X, Y) = coll(e, a, b).
% 20.53/3.04 Proof:
% 20.53/3.04 cong(X, Y, X, Y)
% 20.53/3.04 = { by axiom 17 (ruleD43) R->L }
% 20.53/3.04 fresh183(coll(e, a, b), coll(e, a, b), X, Y, Y, X, Y)
% 20.53/3.04 = { by lemma 46 R->L }
% 20.53/3.04 fresh183(cyclic(X, Y, Y, Y), coll(e, a, b), X, Y, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.04 fresh183(cyclic(X, Y, Y, Y), true, X, Y, Y, X, Y)
% 20.53/3.04 = { by axiom 31 (ruleD43) R->L }
% 20.53/3.04 fresh182(coll(e, a, b), coll(e, a, b), X, Y, Y, X, Y, Y)
% 20.53/3.04 = { by lemma 38 R->L }
% 20.53/3.04 fresh182(fresh104(coll(e, a, b), coll(e, a, b), Y, X, Y, X, Y, Y), coll(e, a, b), X, Y, Y, X, Y, Y)
% 20.53/3.04 = { by lemma 45 R->L }
% 20.53/3.04 fresh182(fresh104(para(Y, X, Y, X), coll(e, a, b), Y, X, Y, X, Y, Y), coll(e, a, b), X, Y, Y, X, Y, Y)
% 20.53/3.04 = { by lemma 39 }
% 20.53/3.04 fresh182(eqangle(Y, X, Y, Y, Y, X, Y, Y), coll(e, a, b), X, Y, Y, X, Y, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.04 fresh182(eqangle(Y, X, Y, Y, Y, X, Y, Y), true, X, Y, Y, X, Y, Y)
% 20.53/3.04 = { by axiom 36 (ruleD43) }
% 20.53/3.04 fresh184(cyclic(X, Y, Y, Y), true, X, Y, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh184(cyclic(X, Y, Y, Y), coll(e, a, b), X, Y, Y, X, Y)
% 20.53/3.04 = { by lemma 46 }
% 20.53/3.04 fresh184(coll(e, a, b), coll(e, a, b), X, Y, Y, X, Y)
% 20.53/3.04 = { by axiom 25 (ruleD43) }
% 20.53/3.04 fresh185(cyclic(X, Y, Y, X), true, X, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh185(cyclic(X, Y, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 27 (ruleD16) R->L }
% 20.53/3.04 fresh185(fresh138(cyclic(Y, X, Y, X), true, Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.04 fresh185(fresh138(cyclic(Y, X, Y, X), coll(e, a, b), Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.04 = { by axiom 26 (ruleD15) R->L }
% 20.53/3.05 fresh185(fresh138(fresh139(cyclic(Y, Y, X, X), true, Y, Y, X, X), coll(e, a, b), Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.05 fresh185(fresh138(fresh139(cyclic(Y, Y, X, X), coll(e, a, b), Y, Y, X, X), coll(e, a, b), Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by lemma 46 }
% 20.53/3.05 fresh185(fresh138(fresh139(coll(e, a, b), coll(e, a, b), Y, Y, X, X), coll(e, a, b), Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by axiom 8 (ruleD15) }
% 20.53/3.05 fresh185(fresh138(true, coll(e, a, b), Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.05 fresh185(fresh138(coll(e, a, b), coll(e, a, b), Y, X, Y, X), coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by axiom 9 (ruleD16) }
% 20.53/3.05 fresh185(true, coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.05 fresh185(coll(e, a, b), coll(e, a, b), X, Y, X, Y)
% 20.53/3.05 = { by axiom 7 (ruleD43) }
% 20.53/3.05 true
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.05 coll(e, a, b)
% 20.53/3.05
% 20.53/3.05 Lemma 48: perp(X, X, Y, Z) = coll(e, a, b).
% 20.53/3.05 Proof:
% 20.53/3.05 perp(X, X, Y, Z)
% 20.53/3.05 = { by axiom 13 (ruleD56) R->L }
% 20.53/3.05 fresh80(coll(e, a, b), coll(e, a, b), X, X, Y, Z)
% 20.53/3.05 = { by lemma 47 R->L }
% 20.53/3.05 fresh80(cong(X, Z, X, Z), coll(e, a, b), X, X, Y, Z)
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.05 fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
% 20.53/3.05 = { by axiom 29 (ruleD56) }
% 20.53/3.05 fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.05 fresh79(cong(X, Y, X, Y), coll(e, a, b), X, X, Y, Z)
% 20.53/3.05 = { by lemma 47 }
% 20.53/3.05 fresh79(coll(e, a, b), coll(e, a, b), X, X, Y, Z)
% 20.53/3.05 = { by axiom 14 (ruleD56) }
% 20.53/3.05 true
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) R->L }
% 20.53/3.05 coll(e, a, b)
% 20.53/3.05
% 20.53/3.05 Goal 1 (exemplo6GDDFULL8110998_6): para(a, b, g, f) = true.
% 20.53/3.05 Proof:
% 20.53/3.05 para(a, b, g, f)
% 20.53/3.05 = { by axiom 21 (ruleD9) R->L }
% 20.53/3.05 fresh51(coll(e, a, b), coll(e, a, b), a, b, X, X, g, f)
% 20.53/3.05 = { by lemma 48 R->L }
% 20.53/3.05 fresh51(perp(X, X, g, f), coll(e, a, b), a, b, X, X, g, f)
% 20.53/3.05 = { by lemma 41 }
% 20.53/3.05 fresh50(perp(a, b, X, X), coll(e, a, b), a, b, g, f)
% 20.53/3.05 = { by lemma 42 R->L }
% 20.53/3.05 fresh50(fresh52(perp(X, X, a, b), coll(e, a, b), X, X, a, b), coll(e, a, b), a, b, g, f)
% 20.53/3.05 = { by lemma 48 }
% 20.53/3.05 fresh50(fresh52(coll(e, a, b), coll(e, a, b), X, X, a, b), coll(e, a, b), a, b, g, f)
% 20.53/3.05 = { by lemma 43 }
% 20.53/3.05 fresh50(coll(e, a, b), coll(e, a, b), a, b, g, f)
% 20.53/3.05 = { by lemma 44 }
% 20.53/3.05 coll(e, a, b)
% 20.53/3.05 = { by axiom 1 (exemplo6GDDFULL8110998) }
% 20.53/3.05 true
% 20.53/3.05 % SZS output end Proof
% 20.53/3.05
% 20.53/3.05 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------