TSTP Solution File: GEO603+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO603+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 : n025.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 23:29:30 EDT 2023
% Result : Theorem 0.21s 0.81s
% Output : Proof 2.60s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO603+1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 21:46:41 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.81 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.81
% 0.21/0.81 % SZS status Theorem
% 0.21/0.81
% 2.60/0.82 % SZS output start Proof
% 2.60/0.82 Take the following subset of the input axioms:
% 2.60/0.82 fof(exemplo6GDDFULL618065, conjecture, ![A, B, C, D, E, F, G]: ((circle(D, A, B, C) & (coll(E, A, B) & (para(B, C, F, E) & (coll(F, A, C) & circle(G, A, E, F))))) => coll(A, G, D))).
% 2.60/0.82 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 2.60/0.82 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))).
% 2.60/0.82 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 2.60/0.82 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))).
% 2.60/0.82 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 2.60/0.82 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))).
% 2.60/0.82 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 2.60/0.82 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))).
% 2.60/0.82
% 2.60/0.82 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.60/0.82 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.60/0.82 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.60/0.82 fresh(y, y, x1...xn) = u
% 2.60/0.82 C => fresh(s, t, x1...xn) = v
% 2.60/0.82 where fresh is a fresh function symbol and x1..xn are the free
% 2.60/0.82 variables of u and v.
% 2.60/0.82 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.60/0.82 input problem has no model of domain size 1).
% 2.60/0.82
% 2.60/0.82 The encoding turns the above axioms into the following unit equations and goals:
% 2.60/0.82
% 2.60/0.82 Axiom 1 (exemplo6GDDFULL618065_2): para(b, c, f, e) = true.
% 2.60/0.82 Axiom 2 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 2.60/0.82 Axiom 3 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 2.60/0.82 Axiom 4 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 2.60/0.82 Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 2.60/0.82 Axiom 6 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 2.60/0.82 Axiom 7 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 2.60/0.82 Axiom 8 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 2.60/0.82 Axiom 9 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 2.60/0.82 Axiom 10 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 2.60/0.82 Axiom 11 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 2.60/0.82 Axiom 12 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 2.60/0.82 Axiom 13 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 2.60/0.82 Axiom 14 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 2.60/0.82 Axiom 15 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 2.60/0.82 Axiom 16 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 2.60/0.82 Axiom 17 (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).
% 2.60/0.83 Axiom 18 (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).
% 2.60/0.83 Axiom 19 (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).
% 2.60/0.83
% 2.60/0.83 Lemma 20: coll(X, X, Y) = true.
% 2.60/0.83 Proof:
% 2.60/0.83 coll(X, X, Y)
% 2.60/0.83 = { by axiom 8 (ruleD1) R->L }
% 2.60/0.83 fresh146(coll(X, Y, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 9 (ruleD2) R->L }
% 2.60/0.83 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 12 (ruleD66) R->L }
% 2.60/0.83 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 15 (ruleD73) R->L }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(true, true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 14 (ruleD21) R->L }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(fresh131(true, true, Y, X, b, c, Y, X, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 13 (ruleD19) R->L }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(true, true, b, c, Y, X, f, e, Y, X), true, Y, X, b, c, Y, X, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 10 (ruleD40) R->L }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(fresh104(true, true, b, c, f, e, Y, X), true, b, c, Y, X, f, e, Y, X), true, Y, X, b, c, Y, X, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 1 (exemplo6GDDFULL618065_2) R->L }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(fresh104(para(b, c, f, e), true, b, c, f, e, Y, X), true, b, c, Y, X, f, e, Y, X), true, Y, X, b, c, Y, X, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 16 (ruleD40) }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(fresh131(fresh134(eqangle(b, c, Y, X, f, e, Y, X), true, b, c, Y, X, f, e, Y, X), true, Y, X, b, c, Y, X, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 17 (ruleD19) }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(fresh131(eqangle(Y, X, b, c, Y, X, f, e), true, Y, X, b, c, Y, X, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 18 (ruleD21) }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh58(eqangle(Y, X, Y, X, b, c, f, e), true, Y, X, Y, X, b, c, f, e), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 19 (ruleD73) }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh57(para(b, c, f, e), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 1 (exemplo6GDDFULL618065_2) }
% 2.60/0.83 fresh146(fresh133(fresh66(fresh57(true, true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 7 (ruleD73) }
% 2.60/0.83 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 5 (ruleD66) }
% 2.60/0.83 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 2.60/0.83 = { by axiom 3 (ruleD2) }
% 2.60/0.83 fresh146(true, true, X, Y, X)
% 2.60/0.83 = { by axiom 2 (ruleD1) }
% 2.60/0.83 true
% 2.60/0.83
% 2.60/0.83 Goal 1 (exemplo6GDDFULL618065_5): coll(a, g, d) = true.
% 2.60/0.83 Proof:
% 2.60/0.83 coll(a, g, d)
% 2.60/0.83 = { by axiom 6 (ruleD3) R->L }
% 2.60/0.83 fresh120(true, true, d, d, a, g)
% 2.60/0.83 = { by lemma 20 R->L }
% 2.60/0.83 fresh120(coll(d, d, g), true, d, d, a, g)
% 2.60/0.83 = { by axiom 11 (ruleD3) }
% 2.60/0.83 fresh119(coll(d, d, a), true, d, a, g)
% 2.60/0.83 = { by lemma 20 }
% 2.60/0.83 fresh119(true, true, d, a, g)
% 2.60/0.83 = { by axiom 4 (ruleD3) }
% 2.60/0.83 true
% 2.60/0.83 % SZS output end Proof
% 2.60/0.83
% 2.60/0.83 RESULT: Theorem (the conjecture is true).
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