TSTP Solution File: GEO554+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO554+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 : n003.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 23:29:18 EDT 2023
% Result : Theorem 5.76s 1.10s
% Output : Proof 5.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO554+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
% 0.13/0.34 % Computer : n003.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 21:05:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.76/1.10 Command-line arguments: --no-flatten-goal
% 5.76/1.10
% 5.76/1.10 % SZS status Theorem
% 5.76/1.10
% 5.76/1.11 % SZS output start Proof
% 5.76/1.11 Take the following subset of the input axioms:
% 5.76/1.11 fof(exemplo6GDDFULL012014, conjecture, ![A, B, C, D, E, F, G, NWPNT1, NWPNT2, NWPNT3, NWPNT4, NWPNT5, NWPNT6, NWPNT7, NWPNT8, NWPNT9]: ((perp(C, A, C, B) & (circle(A, C, NWPNT1, NWPNT2) & (circle(B, C, NWPNT3, NWPNT4) & (circle(A, C, D, NWPNT5) & (coll(C, D, E) & (circle(B, C, E, NWPNT6) & (coll(B, E, F) & (circle(B, C, F, NWPNT7) & (circle(A, C, G, NWPNT8) & circle(B, C, G, NWPNT9)))))))))) => coll(D, F, G))).
% 5.76/1.11 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 5.76/1.11 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))).
% 5.76/1.11 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 5.76/1.11 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 5.76/1.11 fof(ruleD39, axiom, ![B2, C2, D2, A2_2, P2, Q2]: (eqangle(A2_2, B2, P2, Q2, C2, D2, P2, Q2) => para(A2_2, B2, C2, D2))).
% 5.76/1.11 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))).
% 5.76/1.11 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 5.76/1.11 fof(ruleD8, axiom, ![B2, C2, D2, A2_2]: (perp(A2_2, B2, C2, D2) => perp(C2, D2, A2_2, B2))).
% 5.76/1.11 fof(ruleD9, axiom, ![B2, C2, D2, E2, F2, A2_2]: ((perp(A2_2, B2, C2, D2) & perp(C2, D2, E2, F2)) => para(A2_2, B2, E2, F2))).
% 5.76/1.11
% 5.76/1.11 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.76/1.11 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.76/1.11 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.76/1.11 fresh(y, y, x1...xn) = u
% 5.76/1.11 C => fresh(s, t, x1...xn) = v
% 5.76/1.11 where fresh is a fresh function symbol and x1..xn are the free
% 5.76/1.11 variables of u and v.
% 5.76/1.11 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.76/1.11 input problem has no model of domain size 1).
% 5.76/1.11
% 5.76/1.11 The encoding turns the above axioms into the following unit equations and goals:
% 5.76/1.11
% 5.76/1.11 Axiom 1 (exemplo6GDDFULL012014_2): perp(c, a, c, b) = true.
% 5.76/1.11 Axiom 2 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 5.76/1.11 Axiom 3 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 5.76/1.11 Axiom 4 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 5.76/1.11 Axiom 5 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 5.76/1.11 Axiom 6 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 5.76/1.11 Axiom 7 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 5.76/1.11 Axiom 8 (ruleD8): fresh52(X, X, Y, Z, W, V) = true.
% 5.76/1.11 Axiom 9 (ruleD9): fresh50(X, X, Y, Z, W, V) = true.
% 5.76/1.11 Axiom 10 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 5.76/1.11 Axiom 11 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 5.76/1.11 Axiom 12 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 5.76/1.11 Axiom 13 (ruleD9): fresh51(X, X, Y, Z, W, V, U, T) = para(Y, Z, U, T).
% 5.76/1.11 Axiom 14 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 5.76/1.11 Axiom 15 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 5.76/1.11 Axiom 16 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 5.76/1.11 Axiom 17 (ruleD8): fresh52(perp(X, Y, Z, W), true, X, Y, Z, W) = perp(Z, W, X, Y).
% 5.76/1.11 Axiom 18 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 5.76/1.11 Axiom 19 (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).
% 5.76/1.11 Axiom 20 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 5.76/1.12 Axiom 21 (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).
% 5.76/1.12
% 5.76/1.12 Lemma 22: coll(X, X, Y) = true.
% 5.76/1.12 Proof:
% 5.76/1.12 coll(X, X, Y)
% 5.76/1.12 = { by axiom 10 (ruleD1) R->L }
% 5.76/1.12 fresh146(coll(X, Y, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 11 (ruleD2) R->L }
% 5.76/1.12 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 15 (ruleD66) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 20 (ruleD39) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, c, b, Y, X, c, b), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 21 (ruleD19) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(c, b, Y, X, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 18 (ruleD40) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(para(c, b, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 13 (ruleD9) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh51(true, true, c, b, c, a, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 1 (exemplo6GDDFULL012014_2) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh51(perp(c, a, c, b), true, c, b, c, a, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 19 (ruleD9) }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh50(perp(c, b, c, a), true, c, b, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 17 (ruleD8) R->L }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh50(fresh52(perp(c, a, c, b), true, c, a, c, b), true, c, b, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 1 (exemplo6GDDFULL012014_2) }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh50(fresh52(true, true, c, a, c, b), true, c, b, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 8 (ruleD8) }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh50(true, true, c, b, c, b), true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 9 (ruleD9) }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(true, true, c, b, c, b, Y, X), true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 12 (ruleD40) }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(fresh134(true, true, c, b, Y, X, c, b, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 16 (ruleD19) }
% 5.76/1.12 fresh146(fresh133(fresh66(fresh106(true, true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 7 (ruleD39) }
% 5.76/1.12 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 5 (ruleD66) }
% 5.76/1.12 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 5.76/1.12 = { by axiom 3 (ruleD2) }
% 5.76/1.12 fresh146(true, true, X, Y, X)
% 5.76/1.12 = { by axiom 2 (ruleD1) }
% 5.76/1.12 true
% 5.76/1.12
% 5.76/1.12 Goal 1 (exemplo6GDDFULL012014_10): coll(d, f, g) = true.
% 5.76/1.12 Proof:
% 5.76/1.12 coll(d, f, g)
% 5.76/1.12 = { by axiom 6 (ruleD3) R->L }
% 5.76/1.12 fresh120(true, true, g, g, d, f)
% 5.76/1.12 = { by lemma 22 R->L }
% 5.76/1.12 fresh120(coll(g, g, f), true, g, g, d, f)
% 5.76/1.12 = { by axiom 14 (ruleD3) }
% 5.76/1.12 fresh119(coll(g, g, d), true, g, d, f)
% 5.76/1.12 = { by lemma 22 }
% 5.76/1.12 fresh119(true, true, g, d, f)
% 5.76/1.12 = { by axiom 4 (ruleD3) }
% 5.76/1.12 true
% 5.76/1.12 % SZS output end Proof
% 5.76/1.12
% 5.76/1.12 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------