TSTP Solution File: GEO580+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO580+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 23:29:24 EDT 2023
% Result : Theorem 5.00s 1.07s
% Output : Proof 5.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO580+1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.13 % 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 : n007.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 19:28:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.00/1.07 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 5.00/1.07
% 5.00/1.07 % SZS status Theorem
% 5.00/1.07
% 5.50/1.09 % SZS output start Proof
% 5.50/1.09 Take the following subset of the input axioms:
% 5.50/1.10 fof(exemplo6GDDFULL416042, conjecture, ![A, B, C, D, E, F, G, H]: ((eqangle(D, A, A, B, D, A, A, C) & (eqangle(D, B, B, C, D, B, B, A) & (eqangle(D, C, C, A, D, C, C, B) & (perp(E, A, B, C) & (coll(E, B, C) & (perp(F, B, A, D) & (coll(F, A, D) & (perp(G, C, A, D) & (coll(G, A, D) & midp(H, C, B)))))))))) => cyclic(E, F, G, H))).
% 5.50/1.10 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 5.50/1.10 fof(ruleD14, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, B2, D2, C2))).
% 5.50/1.10 fof(ruleD15, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 5.50/1.10 fof(ruleD16, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 5.50/1.10 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))).
% 5.50/1.10 fof(ruleD19, axiom, ![P, Q, U, V, B2, C2, D2, A2_2]: (eqangle(A2_2, B2, C2, D2, P, Q, U, V) => eqangle(C2, D2, A2_2, B2, U, V, P, Q))).
% 5.50/1.10 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 5.50/1.10 fof(ruleD21, axiom, ![B2, C2, D2, P2, Q2, U2, V2, A2_2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(A2_2, B2, P2, Q2, C2, D2, U2, V2))).
% 5.50/1.10 fof(ruleD39, axiom, ![B2, C2, D2, P2, Q2, A2_2]: (eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2) => para(A2_2, B2, C2, D2))).
% 5.50/1.10 fof(ruleD4, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(A2_2, B2, D2, C2))).
% 5.50/1.10 fof(ruleD40, axiom, ![B2, C2, D2, P2, Q2, A2_2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 5.50/1.10 fof(ruleD42b, axiom, ![B2, P2, Q2, A2_2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 5.50/1.10 fof(ruleD5, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(C2, D2, A2_2, B2))).
% 5.50/1.10 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 5.50/1.10 fof(ruleD73, axiom, ![B2, C2, D2, P2, Q2, U2, V2, A2_2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & para(P2, Q2, U2, V2)) => para(A2_2, B2, C2, D2))).
% 5.50/1.10
% 5.50/1.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.50/1.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.50/1.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.50/1.10 fresh(y, y, x1...xn) = u
% 5.50/1.10 C => fresh(s, t, x1...xn) = v
% 5.50/1.10 where fresh is a fresh function symbol and x1..xn are the free
% 5.50/1.10 variables of u and v.
% 5.50/1.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.50/1.10 input problem has no model of domain size 1).
% 5.50/1.10
% 5.50/1.10 The encoding turns the above axioms into the following unit equations and goals:
% 5.50/1.10
% 5.50/1.10 Axiom 1 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 5.50/1.10 Axiom 2 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 5.50/1.10 Axiom 3 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 5.50/1.10 Axiom 4 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 5 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 6 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 7 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 8 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 9 (ruleD4): fresh105(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 10 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 5.50/1.10 Axiom 11 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 12 (ruleD5): fresh92(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 13 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 5.50/1.10 Axiom 14 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 5.50/1.10 Axiom 15 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 5.50/1.10 Axiom 16 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 5.50/1.10 Axiom 17 (exemplo6GDDFULL416042_9): eqangle(d, a, a, b, d, a, a, c) = true.
% 5.50/1.10 Axiom 18 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 5.50/1.10 Axiom 19 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 5.50/1.10 Axiom 20 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 5.50/1.10 Axiom 21 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 5.50/1.10 Axiom 22 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 5.50/1.10 Axiom 23 (ruleD4): fresh105(para(X, Y, Z, W), true, X, Y, Z, W) = para(X, Y, W, Z).
% 5.50/1.10 Axiom 24 (ruleD5): fresh92(para(X, Y, Z, W), true, X, Y, Z, W) = para(Z, W, X, Y).
% 5.50/1.10 Axiom 25 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 5.50/1.10 Axiom 26 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 5.50/1.10 Axiom 27 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 5.50/1.10 Axiom 28 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 5.50/1.10 Axiom 29 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 5.50/1.10 Axiom 30 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 5.50/1.10 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).
% 5.50/1.10 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).
% 5.50/1.10 Axiom 33 (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).
% 5.50/1.10 Axiom 34 (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).
% 5.50/1.10
% 5.50/1.10 Lemma 35: para(d, a, d, a) = true.
% 5.50/1.10 Proof:
% 5.50/1.10 para(d, a, d, a)
% 5.50/1.10 = { by axiom 28 (ruleD73) R->L }
% 5.50/1.10 fresh58(true, true, d, a, d, a, a, b, a, c)
% 5.50/1.10 = { by axiom 27 (ruleD21) R->L }
% 5.50/1.10 fresh58(fresh131(true, true, d, a, a, b, d, a, a, c), true, d, a, d, a, a, b, a, c)
% 5.50/1.10 = { by axiom 17 (exemplo6GDDFULL416042_9) R->L }
% 5.50/1.10 fresh58(fresh131(eqangle(d, a, a, b, d, a, a, c), true, d, a, a, b, d, a, a, c), true, d, a, d, a, a, b, a, c)
% 5.50/1.10 = { by axiom 33 (ruleD21) }
% 5.50/1.10 fresh58(eqangle(d, a, d, a, a, b, a, c), true, d, a, d, a, a, b, a, c)
% 5.50/1.10 = { by axiom 34 (ruleD73) }
% 5.50/1.10 fresh57(para(a, b, a, c), true, d, a, d, a)
% 5.50/1.10 = { by axiom 30 (ruleD39) R->L }
% 5.50/1.10 fresh57(fresh106(eqangle(a, b, d, a, a, c, d, a), true, a, b, a, c), true, d, a, d, a)
% 5.50/1.10 = { by axiom 32 (ruleD19) R->L }
% 5.50/1.10 fresh57(fresh106(fresh134(eqangle(d, a, a, b, d, a, a, c), true, d, a, a, b, d, a, a, c), true, a, b, a, c), true, d, a, d, a)
% 5.50/1.10 = { by axiom 17 (exemplo6GDDFULL416042_9) }
% 5.50/1.10 fresh57(fresh106(fresh134(true, true, d, a, a, b, d, a, a, c), true, a, b, a, c), true, d, a, d, a)
% 5.50/1.10 = { by axiom 26 (ruleD19) }
% 5.50/1.10 fresh57(fresh106(true, true, a, b, a, c), true, d, a, d, a)
% 5.50/1.10 = { by axiom 8 (ruleD39) }
% 5.50/1.10 fresh57(true, true, d, a, d, a)
% 5.50/1.10 = { by axiom 13 (ruleD73) }
% 5.50/1.10 true
% 5.50/1.10
% 5.50/1.10 Lemma 36: cyclic(a, d, d, X) = true.
% 5.50/1.10 Proof:
% 5.50/1.10 cyclic(a, d, d, X)
% 5.50/1.10 = { by axiom 20 (ruleD14) R->L }
% 5.50/1.10 fresh140(cyclic(a, d, X, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 21 (ruleD15) R->L }
% 5.50/1.10 fresh140(fresh139(cyclic(a, X, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 22 (ruleD16) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(cyclic(X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 10 (ruleD42b) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh102(true, true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 26 (ruleD19) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh102(fresh134(true, true, d, a, d, X, d, a, d, X), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 18 (ruleD40) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh102(fresh134(fresh104(true, true, d, a, d, a, d, X), true, d, a, d, X, d, a, d, X), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by lemma 35 R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh102(fresh134(fresh104(para(d, a, d, a), true, d, a, d, a, d, X), true, d, a, d, X, d, a, d, X), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 29 (ruleD40) }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh102(fresh134(eqangle(d, a, d, X, d, a, d, X), true, d, a, d, X, d, a, d, X), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 32 (ruleD19) }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh102(eqangle(d, X, d, a, d, X, d, a), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 31 (ruleD42b) }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(coll(d, d, a), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 14 (ruleD1) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(fresh146(coll(d, a, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 16 (ruleD2) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(coll(a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 19 (ruleD66) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(para(a, d, a, d), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 23 (ruleD4) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(fresh105(para(a, d, d, a), true, a, d, d, a), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 24 (ruleD5) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(para(d, a, a, d), true, d, a, a, d), true, a, d, d, a), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.10 = { by axiom 23 (ruleD4) R->L }
% 5.50/1.10 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(fresh105(para(d, a, d, a), true, d, a, d, a), true, d, a, a, d), true, a, d, d, a), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by lemma 35 }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(fresh105(true, true, d, a, d, a), true, d, a, a, d), true, a, d, d, a), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 9 (ruleD4) }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(fresh105(fresh92(true, true, d, a, a, d), true, a, d, d, a), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 12 (ruleD5) }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(fresh105(true, true, a, d, d, a), true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 9 (ruleD4) }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(fresh66(true, true, a, d, d), true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 3 (ruleD66) }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(fresh146(fresh133(true, true, a, d, d), true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 2 (ruleD2) }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(fresh146(true, true, d, a, d), true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 1 (ruleD1) }
% 5.50/1.11 fresh140(fresh139(fresh138(fresh101(true, true, X, a, d, d), true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 11 (ruleD42b) }
% 5.50/1.11 fresh140(fresh139(fresh138(true, true, X, a, d, d), true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 6 (ruleD16) }
% 5.50/1.11 fresh140(fresh139(true, true, a, X, d, d), true, a, d, X, d)
% 5.50/1.11 = { by axiom 5 (ruleD15) }
% 5.50/1.11 fresh140(true, true, a, d, X, d)
% 5.50/1.11 = { by axiom 4 (ruleD14) }
% 5.50/1.11 true
% 5.50/1.11
% 5.50/1.11 Lemma 37: cyclic(d, d, X, Y) = true.
% 5.50/1.11 Proof:
% 5.50/1.11 cyclic(d, d, X, Y)
% 5.50/1.11 = { by axiom 15 (ruleD17) R->L }
% 5.50/1.11 fresh137(true, true, a, d, d, X, Y)
% 5.50/1.11 = { by lemma 36 R->L }
% 5.50/1.11 fresh137(cyclic(a, d, d, Y), true, a, d, d, X, Y)
% 5.50/1.11 = { by axiom 25 (ruleD17) }
% 5.50/1.11 fresh136(cyclic(a, d, d, X), true, d, d, X, Y)
% 5.50/1.11 = { by lemma 36 }
% 5.50/1.11 fresh136(true, true, d, d, X, Y)
% 5.50/1.11 = { by axiom 7 (ruleD17) }
% 5.50/1.11 true
% 5.50/1.11
% 5.50/1.11 Lemma 38: cyclic(d, X, Y, Z) = true.
% 5.50/1.11 Proof:
% 5.50/1.11 cyclic(d, X, Y, Z)
% 5.50/1.11 = { by axiom 15 (ruleD17) R->L }
% 5.50/1.11 fresh137(true, true, d, d, X, Y, Z)
% 5.50/1.11 = { by lemma 37 R->L }
% 5.50/1.11 fresh137(cyclic(d, d, X, Z), true, d, d, X, Y, Z)
% 5.50/1.11 = { by axiom 25 (ruleD17) }
% 5.50/1.11 fresh136(cyclic(d, d, X, Y), true, d, X, Y, Z)
% 5.50/1.11 = { by lemma 37 }
% 5.50/1.11 fresh136(true, true, d, X, Y, Z)
% 5.50/1.11 = { by axiom 7 (ruleD17) }
% 5.50/1.11 true
% 5.50/1.11
% 5.50/1.11 Goal 1 (exemplo6GDDFULL416042_10): cyclic(e, f, g, h) = true.
% 5.50/1.11 Proof:
% 5.50/1.11 cyclic(e, f, g, h)
% 5.50/1.11 = { by axiom 15 (ruleD17) R->L }
% 5.50/1.11 fresh137(true, true, d, e, f, g, h)
% 5.50/1.11 = { by lemma 38 R->L }
% 5.50/1.11 fresh137(cyclic(d, e, f, h), true, d, e, f, g, h)
% 5.50/1.11 = { by axiom 25 (ruleD17) }
% 5.50/1.11 fresh136(cyclic(d, e, f, g), true, e, f, g, h)
% 5.50/1.11 = { by lemma 38 }
% 5.50/1.11 fresh136(true, true, e, f, g, h)
% 5.50/1.11 = { by axiom 7 (ruleD17) }
% 5.50/1.11 true
% 5.50/1.11 % SZS output end Proof
% 5.50/1.11
% 5.50/1.11 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------