TSTP Solution File: GEO620+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO620+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 : n022.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 23:29:34 EDT 2023
% Result : Theorem 4.59s 0.98s
% Output : Proof 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO620+1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 18:57:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.59/0.98 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 4.59/0.98
% 4.59/0.98 % SZS status Theorem
% 4.59/0.98
% 5.16/1.00 % SZS output start Proof
% 5.16/1.00 Take the following subset of the input axioms:
% 5.16/1.00 fof(exemplo6GDDFULL8110982, conjecture, ![A, B, C, E, O, I, J, L]: ((eqangle(O, A, A, B, O, A, A, C) & (eqangle(O, B, B, C, O, B, B, A) & (eqangle(O, C, C, A, O, C, C, B) & (perp(I, C, A, O) & (coll(I, A, O) & (perp(A, O, A, E) & (perp(J, C, A, E) & (coll(J, A, E) & (perp(L, C, B, O) & coll(L, B, O)))))))))) => coll(I, L, J))).
% 5.16/1.00 fof(ruleD1, axiom, ![A2, B2, C2]: (coll(A2, B2, C2) => coll(A2, C2, B2))).
% 5.16/1.00 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))).
% 5.16/1.00 fof(ruleD2, axiom, ![B2, C2, A2_2]: (coll(A2_2, B2, C2) => coll(B2, A2_2, C2))).
% 5.16/1.00 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))).
% 5.16/1.00 fof(ruleD3, axiom, ![B2, C2, D2, A2_2]: ((coll(A2_2, B2, C2) & coll(A2_2, B2, D2)) => coll(C2, D2, A2_2))).
% 5.16/1.00 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))).
% 5.16/1.00 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))).
% 5.16/1.00 fof(ruleD66, axiom, ![B2, C2, A2_2]: (para(A2_2, B2, A2_2, C2) => coll(A2_2, B2, C2))).
% 5.16/1.00 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))).
% 5.16/1.00
% 5.16/1.00 Now clausify the problem and encode Horn clauses using encoding 3 of
% 5.16/1.00 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 5.16/1.00 We repeatedly replace C & s=t => u=v by the two clauses:
% 5.16/1.00 fresh(y, y, x1...xn) = u
% 5.16/1.00 C => fresh(s, t, x1...xn) = v
% 5.16/1.00 where fresh is a fresh function symbol and x1..xn are the free
% 5.16/1.00 variables of u and v.
% 5.16/1.00 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 5.16/1.00 input problem has no model of domain size 1).
% 5.16/1.00
% 5.16/1.00 The encoding turns the above axioms into the following unit equations and goals:
% 5.16/1.00
% 5.16/1.00 Axiom 1 (ruleD1): fresh146(X, X, Y, Z, W) = true.
% 5.16/1.00 Axiom 2 (ruleD2): fresh133(X, X, Y, Z, W) = true.
% 5.16/1.00 Axiom 3 (ruleD3): fresh119(X, X, Y, Z, W) = true.
% 5.16/1.00 Axiom 4 (ruleD66): fresh66(X, X, Y, Z, W) = true.
% 5.16/1.00 Axiom 5 (ruleD3): fresh120(X, X, Y, Z, W, V) = coll(W, V, Y).
% 5.16/1.00 Axiom 6 (ruleD39): fresh106(X, X, Y, Z, W, V) = true.
% 5.16/1.00 Axiom 7 (ruleD73): fresh57(X, X, Y, Z, W, V) = true.
% 5.16/1.00 Axiom 8 (ruleD1): fresh146(coll(X, Y, Z), true, X, Y, Z) = coll(X, Z, Y).
% 5.16/1.00 Axiom 9 (ruleD2): fresh133(coll(X, Y, Z), true, X, Y, Z) = coll(Y, X, Z).
% 5.16/1.00 Axiom 10 (exemplo6GDDFULL8110982_9): eqangle(o, a, a, b, o, a, a, c) = true.
% 5.16/1.00 Axiom 11 (ruleD3): fresh120(coll(X, Y, Z), true, X, Y, W, Z) = fresh119(coll(X, Y, W), true, X, W, Z).
% 5.16/1.00 Axiom 12 (ruleD40): fresh104(X, X, Y, Z, W, V, U, T) = true.
% 5.16/1.00 Axiom 13 (ruleD66): fresh66(para(X, Y, X, Z), true, X, Y, Z) = coll(X, Y, Z).
% 5.16/1.00 Axiom 14 (ruleD19): fresh134(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 5.16/1.00 Axiom 15 (ruleD21): fresh131(X, X, Y, Z, W, V, U, T, S, X2) = true.
% 5.16/1.00 Axiom 16 (ruleD73): fresh58(X, X, Y, Z, W, V, U, T, S, X2) = para(Y, Z, W, V).
% 5.16/1.00 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).
% 5.16/1.00 Axiom 18 (ruleD39): fresh106(eqangle(X, Y, Z, W, V, U, Z, W), true, X, Y, V, U) = para(X, Y, V, U).
% 5.16/1.00 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).
% 5.16/1.00 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).
% 5.16/1.01 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).
% 5.16/1.01
% 5.16/1.01 Lemma 22: coll(X, X, Y) = true.
% 5.16/1.01 Proof:
% 5.16/1.01 coll(X, X, Y)
% 5.16/1.01 = { by axiom 8 (ruleD1) R->L }
% 5.16/1.01 fresh146(coll(X, Y, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 9 (ruleD2) R->L }
% 5.16/1.01 fresh146(fresh133(coll(Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 13 (ruleD66) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(para(Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 18 (ruleD39) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(eqangle(Y, X, o, a, Y, X, o, a), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 19 (ruleD19) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(eqangle(o, a, Y, X, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 17 (ruleD40) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(para(o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 16 (ruleD73) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(true, true, o, a, o, a, a, b, a, c), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 15 (ruleD21) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(fresh131(true, true, o, a, a, b, o, a, a, c), true, o, a, o, a, a, b, a, c), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 10 (exemplo6GDDFULL8110982_9) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(fresh131(eqangle(o, a, a, b, o, a, a, c), true, o, a, a, b, o, a, a, c), true, o, a, o, a, a, b, a, c), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 20 (ruleD21) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh58(eqangle(o, a, o, a, a, b, a, c), true, o, a, o, a, a, b, a, c), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 21 (ruleD73) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(para(a, b, a, c), true, o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 18 (ruleD39) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(eqangle(a, b, o, a, a, c, o, a), true, a, b, a, c), true, o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 19 (ruleD19) R->L }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(fresh134(eqangle(o, a, a, b, o, a, a, c), true, o, a, a, b, o, a, a, c), true, a, b, a, c), true, o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 10 (exemplo6GDDFULL8110982_9) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(fresh134(true, true, o, a, a, b, o, a, a, c), true, a, b, a, c), true, o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 14 (ruleD19) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(fresh106(true, true, a, b, a, c), true, o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 6 (ruleD39) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(fresh57(true, true, o, a, o, a), true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 7 (ruleD73) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(fresh104(true, true, o, a, o, a, Y, X), true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 12 (ruleD40) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(fresh134(true, true, o, a, Y, X, o, a, Y, X), true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 14 (ruleD19) }
% 5.16/1.01 fresh146(fresh133(fresh66(fresh106(true, true, Y, X, Y, X), true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 6 (ruleD39) }
% 5.16/1.01 fresh146(fresh133(fresh66(true, true, Y, X, X), true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 4 (ruleD66) }
% 5.16/1.01 fresh146(fresh133(true, true, Y, X, X), true, X, Y, X)
% 5.16/1.01 = { by axiom 2 (ruleD2) }
% 5.16/1.01 fresh146(true, true, X, Y, X)
% 5.16/1.01 = { by axiom 1 (ruleD1) }
% 5.16/1.01 true
% 5.16/1.01
% 5.16/1.01 Goal 1 (exemplo6GDDFULL8110982_10): coll(i, l, j) = true.
% 5.16/1.01 Proof:
% 5.16/1.01 coll(i, l, j)
% 5.16/1.01 = { by axiom 5 (ruleD3) R->L }
% 5.16/1.01 fresh120(true, true, j, j, i, l)
% 5.16/1.01 = { by lemma 22 R->L }
% 5.16/1.01 fresh120(coll(j, j, l), true, j, j, i, l)
% 5.16/1.01 = { by axiom 11 (ruleD3) }
% 5.16/1.01 fresh119(coll(j, j, i), true, j, i, l)
% 5.16/1.01 = { by lemma 22 }
% 5.16/1.01 fresh119(true, true, j, i, l)
% 5.16/1.01 = { by axiom 3 (ruleD3) }
% 5.16/1.01 true
% 5.16/1.01 % SZS output end Proof
% 5.16/1.01
% 5.16/1.01 RESULT: Theorem (the conjecture is true).
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