TSTP Solution File: GEO586+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO586+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 : n008.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 23:29:26 EDT 2023
% Result : Theorem 15.05s 2.38s
% Output : Proof 15.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO586+1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % 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 : n008.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 22:55:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 15.05/2.38 Command-line arguments: --no-flatten-goal
% 15.05/2.38
% 15.05/2.38 % SZS status Theorem
% 15.05/2.38
% 15.88/2.40 % SZS output start Proof
% 15.88/2.40 Take the following subset of the input axioms:
% 15.88/2.41 fof(exemplo6GDDFULL416048, conjecture, ![A, B, C, D, E, O, I, NWPNT1]: ((circle(O, A, B, C) & (circle(O, A, D, NWPNT1) & (coll(E, A, C) & (coll(E, B, D) & circle(I, A, B, E))))) => perp(I, E, C, D))).
% 15.88/2.41 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 15.88/2.41 fof(ruleD10, axiom, ![F, B2, C2, A2_2, D2, E2]: ((para(A2_2, B2, C2, D2) & perp(C2, D2, E2, F)) => perp(A2_2, B2, E2, F))).
% 15.88/2.41 fof(ruleD15, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 15.88/2.41 fof(ruleD16, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 15.88/2.41 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))).
% 15.88/2.41 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 15.88/2.41 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))).
% 15.88/2.41 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))).
% 15.88/2.41 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))).
% 15.88/2.41 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))).
% 15.88/2.41 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))).
% 15.88/2.41 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 15.88/2.41 fof(ruleD8, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 15.88/2.41 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))).
% 15.88/2.41 fof(ruleX11, axiom, ![B2, C2, O2, A2_2]: ?[P2]: (circle(O2, A2_2, B2, C2) => perp(P2, A2_2, A2_2, O2))).
% 15.88/2.41
% 15.88/2.41 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.88/2.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.88/2.41 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.88/2.41 fresh(y, y, x1...xn) = u
% 15.88/2.41 C => fresh(s, t, x1...xn) = v
% 15.88/2.41 where fresh is a fresh function symbol and x1..xn are the free
% 15.88/2.41 variables of u and v.
% 15.88/2.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.88/2.41 input problem has no model of domain size 1).
% 15.88/2.41
% 15.88/2.41 The encoding turns the above axioms into the following unit equations and goals:
% 15.88/2.41
% 15.88/2.41 Axiom 1 (ruleX11): fresh39(X, X, Y, Z) = true.
% 15.88/2.41 Axiom 2 (exemplo6GDDFULL416048_2): circle(i, a, b, e) = true.
% 15.88/2.41 Axiom 3 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 15.88/2.41 Axiom 4 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 15.88/2.41 Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 15.88/2.41 Axiom 6 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 7 (ruleD10): fresh145(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 8 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 9 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 10 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 11 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 15.88/2.41 Axiom 12 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 13 (ruleD56): fresh80(X, X, Y, Z, W, V) = perp(Y, Z, W, V).
% 15.88/2.41 Axiom 14 (ruleD56): fresh79(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 15 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 16 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 15.88/2.41 Axiom 17 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 15.88/2.41 Axiom 18 (ruleD10): fresh147(X, X, Y, Z, W, V, U, T) = perp(Y, Z, U, T).
% 15.88/2.41 Axiom 19 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 15.88/2.41 Axiom 20 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 15.88/2.41 Axiom 21 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 15.88/2.41 Axiom 22 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 15.88/2.41 Axiom 23 (ruleX11): fresh39(circle(X, Y, Z, W), true, Y, X) = perp(p3(Y, X), Y, Y, X).
% 15.88/2.41 Axiom 24 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 15.88/2.41 Axiom 25 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 15.88/2.41 Axiom 26 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 15.88/2.41 Axiom 27 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 15.88/2.41 Axiom 28 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 15.88/2.41 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).
% 15.88/2.41 Axiom 30 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 15.88/2.41 Axiom 31 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 15.88/2.41 Axiom 32 (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).
% 15.88/2.41 Axiom 33 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 15.88/2.41 Axiom 34 (ruleD9): fresh51(perp(X, Y, Z, W), true, V, U, X, Y, Z, W) = fresh50(perp(V, U, X, Y), true, V, U, Z, W).
% 15.88/2.41 Axiom 35 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 15.88/2.41 Axiom 36 (ruleD42b): fresh102(eqangle(X, Y, X, Z, W, Y, W, Z), true, Y, Z, X, W) = fresh101(coll(X, W, Z), true, Y, Z, X, W).
% 15.88/2.41 Axiom 37 (ruleD43): fresh182(eqangle(X, Y, X, Z, W, V, W, U), true, Y, Z, X, V, U, W) = fresh184(cyclic(Y, Z, X, W), true, Y, Z, X, V, U).
% 15.88/2.41 Axiom 38 (ruleD19): fresh134(eqangle(X, Y, Z, W, V, U, T, S), true, X, Y, Z, W, V, U, T, S) = eqangle(Z, W, X, Y, T, S, V, U).
% 15.88/2.41
% 15.88/2.41 Lemma 39: perp(p3(a, i), a, a, i) = true.
% 15.88/2.41 Proof:
% 15.88/2.41 perp(p3(a, i), a, a, i)
% 15.88/2.41 = { by axiom 23 (ruleX11) R->L }
% 15.88/2.41 fresh39(circle(i, a, b, e), true, a, i)
% 15.88/2.41 = { by axiom 2 (exemplo6GDDFULL416048_2) }
% 15.88/2.41 fresh39(true, true, a, i)
% 15.88/2.41 = { by axiom 1 (ruleX11) }
% 15.88/2.41 true
% 15.88/2.41
% 15.88/2.41 Lemma 40: para(X, Y, X, Y) = true.
% 15.88/2.41 Proof:
% 15.88/2.41 para(X, Y, X, Y)
% 15.88/2.41 = { by axiom 35 (ruleD39) R->L }
% 15.88/2.41 fresh106(eqangle(X, Y, a, i, X, Y, a, i), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 38 (ruleD19) R->L }
% 15.88/2.41 fresh106(fresh134(eqangle(a, i, X, Y, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 33 (ruleD40) R->L }
% 15.88/2.41 fresh106(fresh134(fresh104(para(a, i, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 22 (ruleD9) R->L }
% 15.88/2.41 fresh106(fresh134(fresh104(fresh51(true, true, a, i, p3(a, i), a, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by lemma 39 R->L }
% 15.88/2.41 fresh106(fresh134(fresh104(fresh51(perp(p3(a, i), a, a, i), true, a, i, p3(a, i), a, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 34 (ruleD9) }
% 15.88/2.41 fresh106(fresh134(fresh104(fresh50(perp(a, i, p3(a, i), a), true, a, i, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 30 (ruleD8) R->L }
% 15.88/2.41 fresh106(fresh134(fresh104(fresh50(fresh52(perp(p3(a, i), a, a, i), true, p3(a, i), a, a, i), true, a, i, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by lemma 39 }
% 15.88/2.41 fresh106(fresh134(fresh104(fresh50(fresh52(true, true, p3(a, i), a, a, i), true, a, i, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 15 (ruleD8) }
% 15.88/2.41 fresh106(fresh134(fresh104(fresh50(true, true, a, i, a, i), true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 16 (ruleD9) }
% 15.88/2.41 fresh106(fresh134(fresh104(true, true, a, i, a, i, X, Y), true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 21 (ruleD40) }
% 15.88/2.41 fresh106(fresh134(true, true, a, i, X, Y, a, i, X, Y), true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 28 (ruleD19) }
% 15.88/2.41 fresh106(true, true, X, Y, X, Y)
% 15.88/2.41 = { by axiom 10 (ruleD39) }
% 15.88/2.41 true
% 15.88/2.41
% 15.88/2.41 Lemma 41: cyclic(X, Y, Z, Z) = true.
% 15.88/2.41 Proof:
% 15.88/2.41 cyclic(X, Y, Z, Z)
% 15.88/2.41 = { by axiom 11 (ruleD42b) R->L }
% 15.88/2.41 fresh102(true, true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 21 (ruleD40) R->L }
% 15.88/2.41 fresh102(fresh104(true, true, Z, X, Z, X, Z, Y), true, X, Y, Z, Z)
% 15.88/2.41 = { by lemma 40 R->L }
% 15.88/2.41 fresh102(fresh104(para(Z, X, Z, X), true, Z, X, Z, X, Z, Y), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 33 (ruleD40) }
% 15.88/2.41 fresh102(eqangle(Z, X, Z, Y, Z, X, Z, Y), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 36 (ruleD42b) }
% 15.88/2.41 fresh101(coll(Z, Z, Y), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 19 (ruleD1) R->L }
% 15.88/2.41 fresh101(fresh146(coll(Z, Y, Z), true, Z, Y, Z), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 20 (ruleD2) R->L }
% 15.88/2.41 fresh101(fresh146(fresh133(coll(Y, Z, Z), true, Y, Z, Z), true, Z, Y, Z), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 24 (ruleD66) R->L }
% 15.88/2.41 fresh101(fresh146(fresh133(fresh66(para(Y, Z, Y, Z), true, Y, Z, Z), true, Y, Z, Z), true, Z, Y, Z), true, X, Y, Z, Z)
% 15.88/2.41 = { by lemma 40 }
% 15.88/2.41 fresh101(fresh146(fresh133(fresh66(true, true, Y, Z, Z), true, Y, Z, Z), true, Z, Y, Z), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 5 (ruleD66) }
% 15.88/2.41 fresh101(fresh146(fresh133(true, true, Y, Z, Z), true, Z, Y, Z), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 4 (ruleD2) }
% 15.88/2.41 fresh101(fresh146(true, true, Z, Y, Z), true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 3 (ruleD1) }
% 15.88/2.41 fresh101(true, true, X, Y, Z, Z)
% 15.88/2.41 = { by axiom 12 (ruleD42b) }
% 15.88/2.42 true
% 15.88/2.42
% 15.88/2.42 Lemma 42: cong(X, Y, X, Y) = true.
% 15.88/2.42 Proof:
% 15.88/2.42 cong(X, Y, X, Y)
% 15.88/2.42 = { by axiom 17 (ruleD43) R->L }
% 15.88/2.42 fresh183(true, true, X, Y, Y, X, Y)
% 15.88/2.42 = { by lemma 41 R->L }
% 15.88/2.42 fresh183(cyclic(X, Y, Y, Y), true, X, Y, Y, X, Y)
% 15.88/2.42 = { by axiom 31 (ruleD43) R->L }
% 15.88/2.42 fresh182(true, true, X, Y, Y, X, Y, Y)
% 15.88/2.42 = { by axiom 21 (ruleD40) R->L }
% 15.88/2.42 fresh182(fresh104(true, true, Y, X, Y, X, Y, Y), true, X, Y, Y, X, Y, Y)
% 15.88/2.42 = { by lemma 40 R->L }
% 15.88/2.42 fresh182(fresh104(para(Y, X, Y, X), true, Y, X, Y, X, Y, Y), true, X, Y, Y, X, Y, Y)
% 15.88/2.42 = { by axiom 33 (ruleD40) }
% 15.88/2.42 fresh182(eqangle(Y, X, Y, Y, Y, X, Y, Y), true, X, Y, Y, X, Y, Y)
% 15.88/2.42 = { by axiom 37 (ruleD43) }
% 15.88/2.42 fresh184(cyclic(X, Y, Y, Y), true, X, Y, Y, X, Y)
% 15.88/2.42 = { by lemma 41 }
% 15.88/2.42 fresh184(true, true, X, Y, Y, X, Y)
% 15.88/2.42 = { by axiom 25 (ruleD43) }
% 15.88/2.42 fresh185(cyclic(X, Y, Y, X), true, X, Y, X, Y)
% 15.88/2.42 = { by axiom 27 (ruleD16) R->L }
% 15.88/2.42 fresh185(fresh138(cyclic(Y, X, Y, X), true, Y, X, Y, X), true, X, Y, X, Y)
% 15.88/2.42 = { by axiom 26 (ruleD15) R->L }
% 15.88/2.42 fresh185(fresh138(fresh139(cyclic(Y, Y, X, X), true, Y, Y, X, X), true, Y, X, Y, X), true, X, Y, X, Y)
% 15.88/2.42 = { by lemma 41 }
% 15.88/2.42 fresh185(fresh138(fresh139(true, true, Y, Y, X, X), true, Y, X, Y, X), true, X, Y, X, Y)
% 15.88/2.42 = { by axiom 8 (ruleD15) }
% 15.88/2.42 fresh185(fresh138(true, true, Y, X, Y, X), true, X, Y, X, Y)
% 15.88/2.42 = { by axiom 9 (ruleD16) }
% 15.88/2.42 fresh185(true, true, X, Y, X, Y)
% 15.88/2.42 = { by axiom 6 (ruleD43) }
% 15.88/2.42 true
% 15.88/2.42
% 15.88/2.42 Lemma 43: perp(X, X, Y, Z) = true.
% 15.88/2.42 Proof:
% 15.88/2.42 perp(X, X, Y, Z)
% 15.88/2.42 = { by axiom 13 (ruleD56) R->L }
% 15.88/2.42 fresh80(true, true, X, X, Y, Z)
% 15.88/2.42 = { by lemma 42 R->L }
% 15.88/2.42 fresh80(cong(X, Z, X, Z), true, X, X, Y, Z)
% 15.88/2.42 = { by axiom 29 (ruleD56) }
% 15.88/2.42 fresh79(cong(X, Y, X, Y), true, X, X, Y, Z)
% 15.88/2.42 = { by lemma 42 }
% 15.88/2.42 fresh79(true, true, X, X, Y, Z)
% 15.88/2.42 = { by axiom 14 (ruleD56) }
% 15.88/2.42 true
% 15.88/2.42
% 15.88/2.42 Lemma 44: para(X, Y, Z, W) = true.
% 15.88/2.42 Proof:
% 15.88/2.42 para(X, Y, Z, W)
% 15.88/2.42 = { by axiom 22 (ruleD9) R->L }
% 15.88/2.42 fresh51(true, true, X, Y, V, V, Z, W)
% 15.88/2.42 = { by lemma 43 R->L }
% 15.88/2.42 fresh51(perp(V, V, Z, W), true, X, Y, V, V, Z, W)
% 15.88/2.42 = { by axiom 34 (ruleD9) }
% 15.88/2.42 fresh50(perp(X, Y, V, V), true, X, Y, Z, W)
% 15.88/2.42 = { by axiom 30 (ruleD8) R->L }
% 15.88/2.42 fresh50(fresh52(perp(V, V, X, Y), true, V, V, X, Y), true, X, Y, Z, W)
% 15.88/2.42 = { by lemma 43 }
% 15.88/2.42 fresh50(fresh52(true, true, V, V, X, Y), true, X, Y, Z, W)
% 15.88/2.42 = { by axiom 15 (ruleD8) }
% 15.88/2.42 fresh50(true, true, X, Y, Z, W)
% 15.88/2.42 = { by axiom 16 (ruleD9) }
% 15.88/2.42 true
% 15.88/2.42
% 15.88/2.42 Goal 1 (exemplo6GDDFULL416048_5): perp(i, e, c, d) = true.
% 15.88/2.42 Proof:
% 15.88/2.42 perp(i, e, c, d)
% 15.88/2.42 = { by axiom 18 (ruleD10) R->L }
% 15.88/2.42 fresh147(true, true, i, e, a, i, c, d)
% 15.88/2.42 = { by axiom 15 (ruleD8) R->L }
% 15.88/2.42 fresh147(fresh52(true, true, c, d, a, i), true, i, e, a, i, c, d)
% 15.88/2.42 = { by axiom 7 (ruleD10) R->L }
% 15.88/2.42 fresh147(fresh52(fresh145(true, true, c, d, a, i), true, c, d, a, i), true, i, e, a, i, c, d)
% 15.88/2.42 = { by lemma 44 R->L }
% 15.88/2.42 fresh147(fresh52(fresh145(para(c, d, p3(a, i), a), true, c, d, a, i), true, c, d, a, i), true, i, e, a, i, c, d)
% 15.88/2.42 = { by axiom 32 (ruleD10) R->L }
% 15.88/2.42 fresh147(fresh52(fresh147(perp(p3(a, i), a, a, i), true, c, d, p3(a, i), a, a, i), true, c, d, a, i), true, i, e, a, i, c, d)
% 15.88/2.42 = { by lemma 39 }
% 15.88/2.42 fresh147(fresh52(fresh147(true, true, c, d, p3(a, i), a, a, i), true, c, d, a, i), true, i, e, a, i, c, d)
% 15.88/2.42 = { by axiom 18 (ruleD10) }
% 15.88/2.42 fresh147(fresh52(perp(c, d, a, i), true, c, d, a, i), true, i, e, a, i, c, d)
% 15.88/2.42 = { by axiom 30 (ruleD8) }
% 15.88/2.42 fresh147(perp(a, i, c, d), true, i, e, a, i, c, d)
% 15.88/2.42 = { by axiom 32 (ruleD10) }
% 15.88/2.42 fresh145(para(i, e, a, i), true, i, e, c, d)
% 15.88/2.42 = { by lemma 44 }
% 15.88/2.42 fresh145(true, true, i, e, c, d)
% 15.88/2.42 = { by axiom 7 (ruleD10) }
% 15.88/2.42 true
% 15.88/2.42 % SZS output end Proof
% 15.88/2.42
% 15.88/2.42 RESULT: Theorem (the conjecture is true).
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