TSTP Solution File: GEO594+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO594+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 : n032.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 23:29:28 EDT 2023
% Result : Theorem 6.22s 1.12s
% Output : Proof 6.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GEO594+1 : TPTP v8.1.2. Released v7.5.0.
% 0.05/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Aug 29 20:37:16 EDT 2023
% 0.10/0.29 % CPUTime :
% 6.22/1.12 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 6.22/1.12
% 6.22/1.12 % SZS status Theorem
% 6.22/1.12
% 6.43/1.16 % SZS output start Proof
% 6.43/1.16 Take the following subset of the input axioms:
% 6.43/1.16 fof(exemplo6GDDFULL416056, conjecture, ![A, B, D, E, M, O]: (((cong(M, A, A, B) | cong(M, A, M, B)) & (circle(O, A, B, M) & (coll(D, M, O) & (coll(D, A, B) & (perp(A, O, A, E) & para(A, O, E, M)))))) => cong(M, E, M, D))).
% 6.43/1.16 fof(ruleD1, axiom, ![C, A2, B2]: (coll(A2, B2, C) => coll(A2, C, B2))).
% 6.43/1.16 fof(ruleD14, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, B2, D2, C2))).
% 6.43/1.16 fof(ruleD15, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(A2_2, C2, B2, D2))).
% 6.43/1.16 fof(ruleD16, axiom, ![B2, C2, D2, A2_2]: (cyclic(A2_2, B2, C2, D2) => cyclic(B2, A2_2, C2, D2))).
% 6.43/1.16 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))).
% 6.43/1.16 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))).
% 6.43/1.16 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 6.43/1.16 fof(ruleD21, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: (eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) => eqangle(A2_2, B2, P2, Q2, C2, D2, U2, V2))).
% 6.43/1.16 fof(ruleD23, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(A2_2, B2, D2, C2))).
% 6.43/1.16 fof(ruleD24, axiom, ![B2, C2, D2, A2_2]: (cong(A2_2, B2, C2, D2) => cong(C2, D2, A2_2, B2))).
% 6.43/1.16 fof(ruleD4, axiom, ![B2, C2, D2, A2_2]: (para(A2_2, B2, C2, D2) => para(A2_2, B2, D2, C2))).
% 6.43/1.16 fof(ruleD40, axiom, ![B2, C2, D2, A2_2, P2, Q2]: (para(A2_2, B2, C2, D2) => eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2))).
% 6.43/1.16 fof(ruleD42b, axiom, ![B2, A2_2, P2, Q2]: ((eqangle(P2, A2_2, P2, B2, Q2, A2_2, Q2, B2) & coll(P2, Q2, B2)) => cyclic(A2_2, B2, P2, Q2))).
% 6.43/1.16 fof(ruleD43, axiom, ![R, B2, C2, A2_2, P2, 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))).
% 6.43/1.16 fof(ruleD52, axiom, ![B2, C2, A2_2, M2]: ((perp(A2_2, B2, B2, C2) & midp(M2, A2_2, C2)) => cong(A2_2, M2, B2, M2))).
% 6.43/1.16 fof(ruleD57, axiom, ![B2, A2_2, P2, Q2]: ((cong(A2_2, P2, B2, P2) & (cong(A2_2, Q2, B2, Q2) & cyclic(A2_2, B2, P2, Q2))) => perp(P2, A2_2, A2_2, Q2))).
% 6.43/1.16 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 6.43/1.16 fof(ruleD67, axiom, ![B2, C2, A2_2]: ((cong(A2_2, B2, A2_2, C2) & coll(A2_2, B2, C2)) => midp(A2_2, B2, C2))).
% 6.43/1.16 fof(ruleD73, axiom, ![B2, C2, D2, A2_2, P2, Q2, U2, V2]: ((eqangle(A2_2, B2, C2, D2, P2, Q2, U2, V2) & para(P2, Q2, U2, V2)) => para(A2_2, B2, C2, D2))).
% 6.43/1.17 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 6.43/1.17
% 6.43/1.17 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.43/1.17 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.43/1.17 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.43/1.17 fresh(y, y, x1...xn) = u
% 6.43/1.17 C => fresh(s, t, x1...xn) = v
% 6.43/1.17 where fresh is a fresh function symbol and x1..xn are the free
% 6.43/1.17 variables of u and v.
% 6.43/1.17 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.43/1.17 input problem has no model of domain size 1).
% 6.43/1.17
% 6.43/1.17 The encoding turns the above axioms into the following unit equations and goals:
% 6.43/1.17
% 6.43/1.17 Axiom 1 (exemplo6GDDFULL416056_2): para(a, o, e, m) = true.
% 6.43/1.17 Axiom 2 (ruleD57): fresh177(X, X, Y, Z, W) = true.
% 6.43/1.17 Axiom 3 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 6.43/1.17 Axiom 4 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 6.43/1.17 Axiom 5 (ruleD52): fresh87(X, X, Y, Z, W) = true.
% 6.43/1.17 Axiom 6 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 6.43/1.17 Axiom 7 (ruleD67): fresh65(X, X, Y, Z, W) = midp(Y, Z, W).
% 6.43/1.17 Axiom 8 (ruleD67): fresh64(X, X, Y, Z, W) = true.
% 6.43/1.17 Axiom 9 (ruleD43): fresh185(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 10 (ruleD14): fresh140(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 11 (ruleD15): fresh139(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 12 (ruleD16): fresh138(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 13 (ruleD17): fresh136(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 14 (ruleD23): fresh128(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 15 (ruleD24): fresh127(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 16 (ruleD4): fresh105(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 17 (ruleD42b): fresh102(X, X, Y, Z, W, V) = cyclic(Y, Z, W, V).
% 6.43/1.17 Axiom 18 (ruleD42b): fresh101(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 19 (ruleD52): fresh88(X, X, Y, Z, W, V) = cong(Y, V, Z, V).
% 6.43/1.17 Axiom 20 (ruleD57): fresh78(X, X, Y, Z, W, V) = perp(W, Y, Y, V).
% 6.43/1.17 Axiom 21 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 22 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 6.43/1.17 Axiom 23 (ruleD43): fresh183(X, X, Y, Z, W, V, U) = cong(Y, Z, V, U).
% 6.43/1.17 Axiom 24 (ruleD17): fresh137(X, X, Y, Z, W, V, U) = cyclic(Z, W, V, U).
% 6.43/1.17 Axiom 25 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 6.43/1.17 Axiom 26 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 6.43/1.17 Axiom 27 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 6.43/1.17 Axiom 28 (ruleD57): fresh176(X, X, Y, Z, W, V) = fresh177(cong(Y, W, Z, W), true, Y, W, V).
% 6.43/1.17 Axiom 29 (ruleD52): fresh88(midp(X, Y, Z), true, Y, W, Z, X) = fresh87(perp(Y, W, W, Z), true, Y, W, X).
% 6.43/1.17 Axiom 30 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 6.43/1.17 Axiom 31 (ruleD67): fresh65(cong(X, Y, X, Z), true, X, Y, Z) = fresh64(coll(X, Y, Z), true, X, Y, Z).
% 6.43/1.17 Axiom 32 (ruleD43): fresh184(X, X, Y, Z, W, V, U) = fresh185(cyclic(Y, Z, W, V), true, Y, Z, V, U).
% 6.43/1.17 Axiom 33 (ruleD14): fresh140(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Y, W, Z).
% 6.43/1.17 Axiom 34 (ruleD15): fresh139(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(X, Z, Y, W).
% 6.43/1.17 Axiom 35 (ruleD16): fresh138(cyclic(X, Y, Z, W), true, X, Y, Z, W) = cyclic(Y, X, Z, W).
% 6.43/1.17 Axiom 36 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 6.43/1.17 Axiom 37 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 6.43/1.17 Axiom 38 (ruleD23): fresh128(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(X, Y, W, Z).
% 6.43/1.17 Axiom 39 (ruleD24): fresh127(cong(X, Y, Z, W), true, X, Y, Z, W) = cong(Z, W, X, Y).
% 6.43/1.17 Axiom 40 (ruleD4): fresh105(para(X, Y, Z, W), true, X, Y, Z, W) = para(X, Y, W, Z).
% 6.43/1.17 Axiom 41 (ruleD57): fresh176(cyclic(X, Y, Z, W), true, X, Y, Z, W) = fresh78(cong(X, W, Y, W), true, X, Y, Z, W).
% 6.43/1.17 Axiom 42 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 6.43/1.17 Axiom 43 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 6.43/1.17 Axiom 44 (ruleD43): fresh182(X, X, Y, Z, W, V, U, T) = fresh183(cyclic(Y, Z, W, U), true, Y, Z, W, V, U).
% 6.43/1.17 Axiom 45 (ruleD17): fresh137(cyclic(X, Y, Z, W), true, X, Y, Z, V, W) = fresh136(cyclic(X, Y, Z, V), true, Y, Z, V, W).
% 6.43/1.17 Axiom 46 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 6.43/1.17 Axiom 47 (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).
% 6.43/1.17 Axiom 48 (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).
% 6.43/1.17 Axiom 49 (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).
% 6.43/1.17 Axiom 50 (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).
% 6.43/1.17 Axiom 51 (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).
% 6.43/1.17
% 6.43/1.17 Lemma 52: para(X, Y, X, Y) = true.
% 6.43/1.17 Proof:
% 6.43/1.17 para(X, Y, X, Y)
% 6.43/1.17 = { by axiom 42 (ruleD73) R->L }
% 6.43/1.17 fresh58(true, true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 37 (ruleD21) R->L }
% 6.43/1.17 fresh58(fresh131(true, true, X, Y, a, o, X, Y, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 36 (ruleD19) R->L }
% 6.43/1.17 fresh58(fresh131(fresh134(true, true, a, o, X, Y, e, m, X, Y), true, X, Y, a, o, X, Y, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 27 (ruleD40) R->L }
% 6.43/1.17 fresh58(fresh131(fresh134(fresh104(true, true, a, o, e, m, X, Y), true, a, o, X, Y, e, m, X, Y), true, X, Y, a, o, X, Y, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 1 (exemplo6GDDFULL416056_2) R->L }
% 6.43/1.17 fresh58(fresh131(fresh134(fresh104(para(a, o, e, m), true, a, o, e, m, X, Y), true, a, o, X, Y, e, m, X, Y), true, X, Y, a, o, X, Y, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 46 (ruleD40) }
% 6.43/1.17 fresh58(fresh131(fresh134(eqangle(a, o, X, Y, e, m, X, Y), true, a, o, X, Y, e, m, X, Y), true, X, Y, a, o, X, Y, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 49 (ruleD19) }
% 6.43/1.17 fresh58(fresh131(eqangle(X, Y, a, o, X, Y, e, m), true, X, Y, a, o, X, Y, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 50 (ruleD21) }
% 6.43/1.17 fresh58(eqangle(X, Y, X, Y, a, o, e, m), true, X, Y, X, Y, a, o, e, m)
% 6.43/1.17 = { by axiom 51 (ruleD73) }
% 6.43/1.17 fresh57(para(a, o, e, m), true, X, Y, X, Y)
% 6.43/1.17 = { by axiom 1 (exemplo6GDDFULL416056_2) }
% 6.43/1.17 fresh57(true, true, X, Y, X, Y)
% 6.43/1.17 = { by axiom 21 (ruleD73) }
% 6.43/1.17 true
% 6.43/1.17
% 6.43/1.17 Lemma 53: coll(X, Y, Y) = true.
% 6.43/1.17 Proof:
% 6.43/1.17 coll(X, Y, Y)
% 6.43/1.17 = { by axiom 30 (ruleD66) R->L }
% 6.43/1.17 fresh66(para(X, Y, X, Y), true, X, Y, Y)
% 6.43/1.17 = { by lemma 52 }
% 6.43/1.17 fresh66(true, true, X, Y, Y)
% 6.43/1.17 = { by axiom 6 (ruleD66) }
% 6.43/1.17 true
% 6.43/1.17
% 6.43/1.17 Lemma 54: cyclic(X, Y, Z, Y) = true.
% 6.43/1.17 Proof:
% 6.43/1.17 cyclic(X, Y, Z, Y)
% 6.43/1.17 = { by axiom 34 (ruleD15) R->L }
% 6.43/1.17 fresh139(cyclic(X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 17 (ruleD42b) R->L }
% 6.43/1.17 fresh139(fresh102(true, true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 27 (ruleD40) R->L }
% 6.43/1.17 fresh139(fresh102(fresh104(true, true, Y, X, Y, X, Y, Z), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by lemma 52 R->L }
% 6.43/1.17 fresh139(fresh102(fresh104(para(Y, X, Y, X), true, Y, X, Y, X, Y, Z), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 46 (ruleD40) }
% 6.43/1.17 fresh139(fresh102(eqangle(Y, X, Y, Z, Y, X, Y, Z), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 47 (ruleD42b) }
% 6.43/1.17 fresh139(fresh101(coll(Y, Y, Z), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 25 (ruleD1) R->L }
% 6.43/1.17 fresh139(fresh101(fresh146(coll(Y, Z, Y), true, Y, Z, Y), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 26 (ruleD2) R->L }
% 6.43/1.17 fresh139(fresh101(fresh146(fresh133(coll(Z, Y, Y), true, Z, Y, Y), true, Y, Z, Y), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by lemma 53 }
% 6.43/1.17 fresh139(fresh101(fresh146(fresh133(true, true, Z, Y, Y), true, Y, Z, Y), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 4 (ruleD2) }
% 6.43/1.17 fresh139(fresh101(fresh146(true, true, Y, Z, Y), true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 3 (ruleD1) }
% 6.43/1.17 fresh139(fresh101(true, true, X, Z, Y, Y), true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 18 (ruleD42b) }
% 6.43/1.17 fresh139(true, true, X, Z, Y, Y)
% 6.43/1.17 = { by axiom 11 (ruleD15) }
% 6.43/1.17 true
% 6.43/1.17
% 6.43/1.17 Lemma 55: cyclic(X, Y, Y, Z) = true.
% 6.43/1.17 Proof:
% 6.43/1.17 cyclic(X, Y, Y, Z)
% 6.43/1.17 = { by axiom 33 (ruleD14) R->L }
% 6.43/1.17 fresh140(cyclic(X, Y, Z, Y), true, X, Y, Z, Y)
% 6.43/1.17 = { by lemma 54 }
% 6.43/1.17 fresh140(true, true, X, Y, Z, Y)
% 6.43/1.17 = { by axiom 10 (ruleD14) }
% 6.43/1.17 true
% 6.43/1.17
% 6.43/1.17 Lemma 56: cong(X, Y, X, Y) = true.
% 6.43/1.17 Proof:
% 6.43/1.17 cong(X, Y, X, Y)
% 6.43/1.17 = { by axiom 23 (ruleD43) R->L }
% 6.43/1.17 fresh183(true, true, X, Y, X, X, Y)
% 6.43/1.17 = { by lemma 54 R->L }
% 6.43/1.17 fresh183(cyclic(X, Y, X, Y), true, X, Y, X, X, Y)
% 6.43/1.17 = { by axiom 44 (ruleD43) R->L }
% 6.43/1.17 fresh182(true, true, X, Y, X, X, Y, X)
% 6.43/1.17 = { by axiom 27 (ruleD40) R->L }
% 6.43/1.17 fresh182(fresh104(true, true, X, X, X, X, X, Y), true, X, Y, X, X, Y, X)
% 6.43/1.17 = { by axiom 16 (ruleD4) R->L }
% 6.43/1.17 fresh182(fresh104(fresh105(true, true, X, X, X, X), true, X, X, X, X, X, Y), true, X, Y, X, X, Y, X)
% 6.43/1.17 = { by lemma 52 R->L }
% 6.43/1.17 fresh182(fresh104(fresh105(para(X, X, X, X), true, X, X, X, X), true, X, X, X, X, X, Y), true, X, Y, X, X, Y, X)
% 6.43/1.17 = { by axiom 40 (ruleD4) }
% 6.43/1.17 fresh182(fresh104(para(X, X, X, X), true, X, X, X, X, X, Y), true, X, Y, X, X, Y, X)
% 6.43/1.17 = { by axiom 46 (ruleD40) }
% 6.43/1.17 fresh182(eqangle(X, X, X, Y, X, X, X, Y), true, X, Y, X, X, Y, X)
% 6.43/1.17 = { by axiom 48 (ruleD43) }
% 6.43/1.17 fresh184(cyclic(X, Y, X, X), true, X, Y, X, X, Y)
% 6.43/1.17 = { by axiom 35 (ruleD16) R->L }
% 6.43/1.17 fresh184(fresh138(cyclic(Y, X, X, X), true, Y, X, X, X), true, X, Y, X, X, Y)
% 6.43/1.17 = { by lemma 55 }
% 6.43/1.17 fresh184(fresh138(true, true, Y, X, X, X), true, X, Y, X, X, Y)
% 6.43/1.17 = { by axiom 12 (ruleD16) }
% 6.43/1.17 fresh184(true, true, X, Y, X, X, Y)
% 6.43/1.17 = { by axiom 32 (ruleD43) }
% 6.43/1.17 fresh185(cyclic(X, Y, X, X), true, X, Y, X, Y)
% 6.43/1.17 = { by axiom 35 (ruleD16) R->L }
% 6.43/1.17 fresh185(fresh138(cyclic(Y, X, X, X), true, Y, X, X, X), true, X, Y, X, Y)
% 6.43/1.17 = { by lemma 54 }
% 6.43/1.17 fresh185(fresh138(true, true, Y, X, X, X), true, X, Y, X, Y)
% 6.43/1.17 = { by axiom 12 (ruleD16) }
% 6.43/1.17 fresh185(true, true, X, Y, X, Y)
% 6.43/1.17 = { by axiom 9 (ruleD43) }
% 6.43/1.17 true
% 6.43/1.17
% 6.43/1.17 Goal 1 (exemplo6GDDFULL416056_6): cong(m, e, m, d) = true.
% 6.43/1.17 Proof:
% 6.43/1.17 cong(m, e, m, d)
% 6.43/1.17 = { by axiom 38 (ruleD23) R->L }
% 6.43/1.17 fresh128(cong(m, e, d, m), true, m, e, d, m)
% 6.43/1.17 = { by axiom 39 (ruleD24) R->L }
% 6.43/1.17 fresh128(fresh127(cong(d, m, m, e), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 38 (ruleD23) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(cong(d, m, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 19 (ruleD52) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh88(true, true, d, e, d, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 8 (ruleD67) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh88(fresh64(true, true, m, d, d), true, d, e, d, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by lemma 53 R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh88(fresh64(coll(m, d, d), true, m, d, d), true, d, e, d, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 31 (ruleD67) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh88(fresh65(cong(m, d, m, d), true, m, d, d), true, d, e, d, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by lemma 56 }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh88(fresh65(true, true, m, d, d), true, d, e, d, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 7 (ruleD67) }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh88(midp(m, d, d), true, d, e, d, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 29 (ruleD52) }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(perp(d, e, e, d), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 43 (ruleD8) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(fresh52(perp(e, d, d, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 20 (ruleD57) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(fresh52(fresh78(true, true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by lemma 56 R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(fresh52(fresh78(cong(d, e, d, e), true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 41 (ruleD57) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(cyclic(d, d, e, e), true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by axiom 24 (ruleD17) R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(fresh137(true, true, X, d, d, e, e), true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.17 = { by lemma 55 R->L }
% 6.43/1.17 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(fresh137(cyclic(X, d, d, e), true, X, d, d, e, e), true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 45 (ruleD17) }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(fresh136(cyclic(X, d, d, e), true, d, d, e, e), true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by lemma 55 }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(fresh136(true, true, d, d, e, e), true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 13 (ruleD17) }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(fresh52(fresh176(true, true, d, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 28 (ruleD57) }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(fresh52(fresh177(cong(d, e, d, e), true, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by lemma 56 }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(fresh52(fresh177(true, true, d, e, e), true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 2 (ruleD57) }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(fresh52(true, true, e, d, d, e), true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 22 (ruleD8) }
% 6.43/1.18 fresh128(fresh127(fresh128(fresh87(true, true, d, e, m), true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 5 (ruleD52) }
% 6.43/1.18 fresh128(fresh127(fresh128(true, true, d, m, e, m), true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 14 (ruleD23) }
% 6.43/1.18 fresh128(fresh127(true, true, d, m, m, e), true, m, e, d, m)
% 6.43/1.18 = { by axiom 15 (ruleD24) }
% 6.43/1.18 fresh128(true, true, m, e, d, m)
% 6.43/1.18 = { by axiom 14 (ruleD23) }
% 6.43/1.18 true
% 6.43/1.18 % SZS output end Proof
% 6.43/1.18
% 6.43/1.18 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------