TSTP Solution File: GEO643+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO643+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 : n020.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 23:29:40 EDT 2023
% Result : Theorem 36.96s 5.06s
% Output : Proof 37.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO643+1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.13 % 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 : n020.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 23:12:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 36.96/5.06 Command-line arguments: --no-flatten-goal
% 36.96/5.06
% 36.96/5.06 % SZS status Theorem
% 36.96/5.06
% 37.26/5.07 % SZS output start Proof
% 37.26/5.07 Take the following subset of the input axioms:
% 37.26/5.08 fof(exemplo6GDDFULL81109109F, conjecture, ![A, B, C, D, E, F, G, H, I, J]: ((coll(C, A, B) & (coll(E, A, D) & (coll(F, B, E) & (coll(F, C, D) & (circle(G, D, E, F) & (circle(H, A, C, D) & (circle(I, B, C, F) & circle(J, B, A, E)))))))) => cyclic(I, J, H, G))).
% 37.26/5.08 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 37.26/5.08 fof(ruleD14, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, B2, D2, C2))).
% 37.26/5.08 fof(ruleD15, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 37.26/5.08 fof(ruleD16, axiom, ![B2, C2, A2_2, D2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 37.26/5.08 fof(ruleD17, axiom, ![B2, C2, A2_2, D2, E2]: ((cyclic(A2_2, B2, C2, D2) & cyclic(A2_2, B2, C2, E2)) => cyclic(B2, C2, D2, E2))).
% 37.26/5.08 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))).
% 37.26/5.08 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 37.26/5.08 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))).
% 37.26/5.08 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))).
% 37.26/5.08 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))).
% 37.26/5.08 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 37.26/5.08 fof(ruleD8, axiom, ![B2, C2, A2_2, D2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 37.26/5.08 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))).
% 37.26/5.08 fof(ruleX11, axiom, ![O, B2, C2, A2_2]: ?[P2]: (circle(O, A2_2, B2, C2) => perp(P2, A2_2, A2_2, O))).
% 37.26/5.08
% 37.26/5.08 Now clausify the problem and encode Horn clauses using encoding 3 of
% 37.26/5.08 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 37.26/5.08 We repeatedly replace C & s=t => u=v by the two clauses:
% 37.26/5.08 fresh(y, y, x1...xn) = u
% 37.26/5.08 C => fresh(s, t, x1...xn) = v
% 37.26/5.08 where fresh is a fresh function symbol and x1..xn are the free
% 37.26/5.08 variables of u and v.
% 37.26/5.08 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 37.26/5.08 input problem has no model of domain size 1).
% 37.26/5.08
% 37.26/5.08 The encoding turns the above axioms into the following unit equations and goals:
% 37.26/5.08
% 37.26/5.08 Axiom 1 (ruleX11): fresh39(X, X, Y, Z) = true.
% 37.26/5.08 Axiom 2 (exemplo6GDDFULL81109109F_4): circle(h, a, c, d) = true.
% 37.26/5.08 Axiom 3 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 37.26/5.08 Axiom 4 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 37.26/5.08 Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 37.26/5.08 Axiom 6 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 7 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 8 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 9 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 10 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 11 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 37.26/5.08 Axiom 12 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 13 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 14 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 37.26/5.08 Axiom 15 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 37.26/5.08 Axiom 16 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 37.26/5.08 Axiom 17 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 37.26/5.08 Axiom 18 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 37.26/5.08 Axiom 19 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 37.26/5.08 Axiom 20 (ruleX11): fresh39(circle(X, Y, Z, W), true, Y, X) = perp(p3(Y, X), Y, Y, X).
% 37.26/5.08 Axiom 21 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 37.26/5.08 Axiom 22 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 37.26/5.08 Axiom 23 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 37.26/5.08 Axiom 24 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 37.26/5.08 Axiom 25 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 37.26/5.08 Axiom 26 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 37.26/5.08 Axiom 27 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 37.26/5.08 Axiom 28 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 37.26/5.08 Axiom 29 (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).
% 37.26/5.08 Axiom 30 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 37.26/5.08 Axiom 31 (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).
% 37.26/5.08 Axiom 32 (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).
% 37.26/5.08
% 37.26/5.08 Lemma 33: perp(p3(a, h), a, a, h) = true.
% 37.26/5.08 Proof:
% 37.26/5.08 perp(p3(a, h), a, a, h)
% 37.26/5.08 = { by axiom 20 (ruleX11) R->L }
% 37.26/5.08 fresh39(circle(h, a, c, d), true, a, h)
% 37.26/5.08 = { by axiom 2 (exemplo6GDDFULL81109109F_4) }
% 37.26/5.08 fresh39(true, true, a, h)
% 37.26/5.08 = { by axiom 1 (ruleX11) }
% 37.26/5.08 true
% 37.26/5.08
% 37.26/5.08 Lemma 34: para(X, Y, X, Y) = true.
% 37.26/5.08 Proof:
% 37.26/5.08 para(X, Y, X, Y)
% 37.26/5.08 = { by axiom 30 (ruleD39) R->L }
% 37.26/5.08 fresh106(eqangle(X, Y, a, h, X, Y, a, h), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 32 (ruleD19) R->L }
% 37.26/5.08 fresh106(fresh134(eqangle(a, h, X, Y, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 28 (ruleD40) R->L }
% 37.26/5.08 fresh106(fresh134(fresh104(para(a, h, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 19 (ruleD9) R->L }
% 37.26/5.08 fresh106(fresh134(fresh104(fresh51(true, true, a, h, p3(a, h), a, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by lemma 33 R->L }
% 37.26/5.08 fresh106(fresh134(fresh104(fresh51(perp(p3(a, h), a, a, h), true, a, h, p3(a, h), a, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 29 (ruleD9) }
% 37.26/5.08 fresh106(fresh134(fresh104(fresh50(perp(a, h, p3(a, h), a), true, a, h, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 26 (ruleD8) R->L }
% 37.26/5.08 fresh106(fresh134(fresh104(fresh50(fresh52(perp(p3(a, h), a, a, h), true, p3(a, h), a, a, h), true, a, h, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by lemma 33 }
% 37.26/5.08 fresh106(fresh134(fresh104(fresh50(fresh52(true, true, p3(a, h), a, a, h), true, a, h, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 13 (ruleD8) }
% 37.26/5.08 fresh106(fresh134(fresh104(fresh50(true, true, a, h, a, h), true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 14 (ruleD9) }
% 37.26/5.08 fresh106(fresh134(fresh104(true, true, a, h, a, h, X, Y), true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 18 (ruleD40) }
% 37.26/5.08 fresh106(fresh134(true, true, a, h, X, Y, a, h, X, Y), true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 25 (ruleD19) }
% 37.26/5.08 fresh106(true, true, X, Y, X, Y)
% 37.26/5.08 = { by axiom 10 (ruleD39) }
% 37.26/5.08 true
% 37.26/5.08
% 37.26/5.08 Lemma 35: cyclic(X, Y, X, Z) = true.
% 37.26/5.08 Proof:
% 37.26/5.08 cyclic(X, Y, X, Z)
% 37.26/5.08 = { by axiom 24 (ruleD16) R->L }
% 37.26/5.08 fresh138(cyclic(Y, X, X, Z), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 22 (ruleD14) R->L }
% 37.26/5.08 fresh138(fresh140(cyclic(Y, X, Z, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 23 (ruleD15) R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(cyclic(Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 11 (ruleD42b) R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh102(true, true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 18 (ruleD40) R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh102(fresh104(true, true, X, Y, X, Y, X, Z), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by lemma 34 R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh102(fresh104(para(X, Y, X, Y), true, X, Y, X, Y, X, Z), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 28 (ruleD40) }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh102(eqangle(X, Y, X, Z, X, Y, X, Z), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 31 (ruleD42b) }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(coll(X, X, Z), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 16 (ruleD1) R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(fresh146(coll(X, Z, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 17 (ruleD2) R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(fresh146(fresh133(coll(Z, X, X), true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 21 (ruleD66) R->L }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(para(Z, X, Z, X), true, Z, X, X), true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by lemma 34 }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(fresh146(fresh133(fresh66(true, true, Z, X, X), true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 5 (ruleD66) }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(fresh146(fresh133(true, true, Z, X, X), true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 4 (ruleD2) }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(fresh146(true, true, X, Z, X), true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 3 (ruleD1) }
% 37.26/5.08 fresh138(fresh140(fresh139(fresh101(true, true, Y, Z, X, X), true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 12 (ruleD42b) }
% 37.26/5.08 fresh138(fresh140(fresh139(true, true, Y, Z, X, X), true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 7 (ruleD15) }
% 37.26/5.08 fresh138(fresh140(true, true, Y, X, Z, X), true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 6 (ruleD14) }
% 37.26/5.08 fresh138(true, true, Y, X, X, Z)
% 37.26/5.08 = { by axiom 8 (ruleD16) }
% 37.26/5.08 true
% 37.26/5.08
% 37.26/5.08 Goal 1 (exemplo6GDDFULL81109109F_8): cyclic(i, j, h, g) = true.
% 37.26/5.08 Proof:
% 37.26/5.08 cyclic(i, j, h, g)
% 37.26/5.08 = { by axiom 15 (ruleD17) R->L }
% 37.26/5.08 fresh137(true, true, j, i, j, h, g)
% 37.26/5.08 = { by lemma 35 R->L }
% 37.26/5.08 fresh137(cyclic(j, i, j, g), true, j, i, j, h, g)
% 37.26/5.08 = { by axiom 27 (ruleD17) }
% 37.26/5.08 fresh136(cyclic(j, i, j, h), true, i, j, h, g)
% 37.26/5.08 = { by lemma 35 }
% 37.26/5.08 fresh136(true, true, i, j, h, g)
% 37.26/5.08 = { by axiom 9 (ruleD17) }
% 37.26/5.08 true
% 37.26/5.08 % SZS output end Proof
% 37.26/5.08
% 37.26/5.08 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------