TSTP Solution File: GEO579+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO579+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 : n014.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 4.48s 0.97s
% Output : Proof 4.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO579+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 : n014.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
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 29 21:37:30 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.48/0.97 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 4.48/0.97
% 4.48/0.97 % SZS status Theorem
% 4.48/0.97
% 4.48/0.99 % SZS output start Proof
% 4.48/0.99 Take the following subset of the input axioms:
% 4.48/0.99 fof(exemplo6GDDFULL416041, conjecture, ![A, B, C, X, Y, I, L]: ((eqangle(I, A, A, B, I, A, A, C) & (eqangle(I, B, B, C, I, B, B, A) & (eqangle(I, C, C, A, I, C, C, B) & (perp(Y, I, A, C) & (coll(Y, A, C) & (perp(L, I, B, C) & (coll(L, B, C) & (perp(X, B, A, I) & coll(X, A, I))))))))) => coll(X, Y, L))).
% 4.48/0.99 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 4.48/0.99 fof(ruleD19, axiom, ![D, P, Q, U, V, B2, C2, A2_2]: (eqangle(A2_2, B2, C2, D, P, Q, U, V) => eqangle(C2, D, A2_2, B2, U, V, P, Q))).
% 4.48/0.99 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 4.48/0.99 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))).
% 4.48/0.99 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 4.48/0.99 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))).
% 4.48/0.99 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))).
% 4.48/0.99 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 4.48/0.99 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))).
% 4.48/0.99
% 4.48/0.99 Now clausify the problem and encode Horn clauses using encoding 3 of
% 4.48/0.99 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 4.48/0.99 We repeatedly replace C & s=t => u=v by the two clauses:
% 4.48/0.99 fresh(y, y, x1...xn) = u
% 4.48/0.99 C => fresh(s, t, x1...xn) = v
% 4.48/0.99 where fresh is a fresh function symbol and x1..xn are the free
% 4.48/0.99 variables of u and v.
% 4.48/0.99 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 4.48/0.99 input problem has no model of domain size 1).
% 4.48/0.99
% 4.48/0.99 The encoding turns the above axioms into the following unit equations and goals:
% 4.48/0.99
% 4.48/0.99 Axiom 1 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 4.48/0.99 Axiom 2 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 4.48/0.99 Axiom 3 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 4.48/0.99 Axiom 4 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 4.48/0.99 Axiom 5 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 4.48/0.99 Axiom 6 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 4.48/0.99 Axiom 7 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 4.48/0.99 Axiom 8 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 4.48/0.99 Axiom 9 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 4.48/0.99 Axiom 10 (exemplo6GDDFULL416041_7): eqangle(i, c, c, a, i, c, c, b) = true.
% 4.48/0.99 Axiom 11 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 4.48/0.99 Axiom 12 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 4.48/0.99 Axiom 13 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 4.48/0.99 Axiom 14 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 4.48/0.99 Axiom 15 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 4.48/0.99 Axiom 16 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 4.48/0.99 Axiom 17 (ruleD40): fresh104(para(X, Y, Z, W), true, X, Y, Z, W, V, U) = eqangle(X, Y, V, U, Z, W, V, U).
% 4.48/0.99 Axiom 18 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 4.48/0.99 Axiom 19 (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).
% 4.48/0.99 Axiom 20 (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).
% 4.48/1.00 Axiom 21 (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).
% 4.48/1.00
% 4.48/1.00 Lemma 22: coll(X, X, Y) = true.
% 4.48/1.00 Proof:
% 4.48/1.00 coll(X, X, Y)
% 4.48/1.00 = { by axiom 8 (ruleD1) R->L }
% 4.48/1.00 fresh146(coll(X, Y, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 9 (ruleD2) R->L }
% 4.48/1.00 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 13 (ruleD66) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 18 (ruleD39) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, i, c, Y, X, i, c), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 19 (ruleD19) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(i, c, Y, X, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 17 (ruleD40) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(para(i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 16 (ruleD73) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(true, true, i, c, i, c, c, a, c, b), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 15 (ruleD21) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(fresh131(true, true, i, c, c, a, i, c, c, b), true, i, c, i, c, c, a, c, b), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 10 (exemplo6GDDFULL416041_7) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(fresh131(eqangle(i, c, c, a, i, c, c, b), true, i, c, c, a, i, c, c, b), true, i, c, i, c, c, a, c, b), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 20 (ruleD21) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(eqangle(i, c, i, c, c, a, c, b), true, i, c, i, c, c, a, c, b), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 21 (ruleD73) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(para(c, a, c, b), true, i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 18 (ruleD39) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(eqangle(c, a, i, c, c, b, i, c), true, c, a, c, b), true, i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 19 (ruleD19) R->L }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(fresh134(eqangle(i, c, c, a, i, c, c, b), true, i, c, c, a, i, c, c, b), true, c, a, c, b), true, i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 10 (exemplo6GDDFULL416041_7) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(fresh134(true, true, i, c, c, a, i, c, c, b), true, c, a, c, b), true, i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 14 (ruleD19) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(true, true, c, a, c, b), true, i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 6 (ruleD39) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(true, true, i, c, i, c), true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 7 (ruleD73) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(true, true, i, c, i, c, Y, X), true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 12 (ruleD40) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(fresh134(true, true, i, c, Y, X, i, c, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 14 (ruleD19) }
% 4.48/1.00 fresh146(fresh133(fresh66(fresh106(true, true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 6 (ruleD39) }
% 4.48/1.00 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 4 (ruleD66) }
% 4.48/1.00 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 4.48/1.00 = { by axiom 2 (ruleD2) }
% 4.48/1.00 fresh146(true, true, X, Y, X)
% 4.48/1.00 = { by axiom 1 (ruleD1) }
% 4.48/1.00 true
% 4.48/1.00
% 4.48/1.00 Goal 1 (exemplo6GDDFULL416041_9): coll(x, y, l) = true.
% 4.48/1.00 Proof:
% 4.48/1.00 coll(x, y, l)
% 4.48/1.00 = { by axiom 5 (ruleD3) R->L }
% 4.48/1.00 fresh120(true, true, l, l, x, y)
% 4.48/1.00 = { by lemma 22 R->L }
% 4.48/1.00 fresh120(coll(l, l, y), true, l, l, x, y)
% 4.48/1.00 = { by axiom 11 (ruleD3) }
% 4.48/1.00 fresh119(coll(l, l, x), true, l, x, y)
% 4.48/1.00 = { by lemma 22 }
% 4.48/1.00 fresh119(true, true, l, x, y)
% 4.48/1.00 = { by axiom 3 (ruleD3) }
% 4.48/1.00 true
% 4.48/1.00 % SZS output end Proof
% 4.48/1.00
% 4.48/1.00 RESULT: Theorem (the conjecture is true).
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