TSTP Solution File: GEO062-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO062-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n004.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 23:27:09 EDT 2023
% Result : Unsatisfiable 0.21s 0.69s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO062-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.08/0.14 % 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 : n004.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
% 0.14/0.35 % DateTime : Tue Aug 29 20:22:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.69 Command-line arguments: --flatten
% 0.21/0.69
% 0.21/0.69 % SZS status Unsatisfiable
% 0.21/0.69
% 2.19/0.70 % SZS output start Proof
% 2.19/0.70 Take the following subset of the input axioms:
% 2.19/0.70 fof(d1, axiom, ![V, U]: equidistant(U, V, U, V)).
% 2.19/0.70 fof(d15, axiom, ![X, V2, W, U2]: (~between(U2, V2, W) | (~equidistant(U2, V2, U2, X) | (~equidistant(W, V2, W, X) | V2=X)))).
% 2.19/0.70 fof(d4_2, axiom, ![V2, W2, U2, X2]: (~equidistant(U2, V2, W2, X2) | equidistant(V2, U2, X2, W2))).
% 2.19/0.70 fof(i2_1, axiom, ![V2, U1, W1, U2]: equidistant(U2, V2, U1, insertion(U1, W1, U2, V2))).
% 2.19/0.70 fof(i2_3, axiom, ![V2, W2, U2, U1_2, W1_2]: (~between(U2, V2, W2) | (~equidistant(U2, W2, U1_2, W1_2) | equidistant(V2, W2, insertion(U1_2, W1_2, U2, V2), W1_2)))).
% 2.19/0.70 fof(prove_v_equals_insertion, negated_conjecture, v!=insertion(u, w, u, v)).
% 2.19/0.70 fof(t1, axiom, ![V2, W2, U2]: (~between(U2, V2, W2) | between(W2, V2, U2))).
% 2.19/0.70 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 2.19/0.70
% 2.19/0.70 Now clausify the problem and encode Horn clauses using encoding 3 of
% 2.19/0.70 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 2.19/0.70 We repeatedly replace C & s=t => u=v by the two clauses:
% 2.19/0.70 fresh(y, y, x1...xn) = u
% 2.19/0.70 C => fresh(s, t, x1...xn) = v
% 2.19/0.70 where fresh is a fresh function symbol and x1..xn are the free
% 2.19/0.70 variables of u and v.
% 2.19/0.70 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 2.19/0.70 input problem has no model of domain size 1).
% 2.19/0.70
% 2.19/0.70 The encoding turns the above axioms into the following unit equations and goals:
% 2.19/0.70
% 2.19/0.70 Axiom 1 (v_between_u_and_w): between(u, v, w) = true2.
% 2.19/0.70 Axiom 2 (d15): fresh42(X, X, Y, Z) = Z.
% 2.19/0.70 Axiom 3 (d1): equidistant(X, Y, X, Y) = true2.
% 2.19/0.70 Axiom 4 (t1): fresh11(X, X, Y, Z, W) = true2.
% 2.19/0.70 Axiom 5 (d15): fresh4(X, X, Y, Z, W) = Z.
% 2.19/0.70 Axiom 6 (d4_2): fresh26(X, X, Y, Z, W, V) = true2.
% 2.19/0.70 Axiom 7 (i2_3): fresh16(X, X, Y, Z, W, V, U) = true2.
% 2.19/0.70 Axiom 8 (d15): fresh41(X, X, Y, Z, W, V) = fresh42(equidistant(Y, Z, Y, V), true2, Z, V).
% 2.19/0.70 Axiom 9 (t1): fresh11(between(X, Y, Z), true2, X, Y, Z) = between(Z, Y, X).
% 2.19/0.70 Axiom 10 (i2_1): equidistant(X, Y, Z, insertion(Z, W, X, Y)) = true2.
% 2.19/0.70 Axiom 11 (i2_3): fresh17(X, X, Y, Z, W, V, U) = equidistant(Z, W, insertion(V, U, Y, Z), U).
% 2.19/0.70 Axiom 12 (d15): fresh41(between(X, Y, Z), true2, X, Y, Z, W) = fresh4(equidistant(Z, Y, Z, W), true2, X, Y, W).
% 2.19/0.70 Axiom 13 (d4_2): fresh26(equidistant(X, Y, Z, W), true2, X, Y, Z, W) = equidistant(Y, X, W, Z).
% 2.19/0.70 Axiom 14 (i2_3): fresh17(between(X, Y, Z), true2, X, Y, Z, W, V) = fresh16(equidistant(X, Z, W, V), true2, X, Y, Z, W, V).
% 2.19/0.70
% 2.19/0.70 Goal 1 (prove_v_equals_insertion): v = insertion(u, w, u, v).
% 2.19/0.70 Proof:
% 2.19/0.70 v
% 2.19/0.70 = { by axiom 5 (d15) R->L }
% 2.19/0.70 fresh4(between(u, v, w), between(u, v, w), w, v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) }
% 2.19/0.70 fresh4(true2, between(u, v, w), w, v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 10 (i2_1) R->L }
% 2.19/0.70 fresh4(equidistant(u, v, u, insertion(u, w, u, v)), between(u, v, w), w, v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) }
% 2.19/0.70 fresh4(equidistant(u, v, u, insertion(u, w, u, v)), true2, w, v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 12 (d15) R->L }
% 2.19/0.70 fresh41(between(w, v, u), true2, w, v, u, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.70 fresh41(between(w, v, u), between(u, v, w), w, v, u, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 9 (t1) R->L }
% 2.19/0.70 fresh41(fresh11(between(u, v, w), true2, u, v, w), between(u, v, w), w, v, u, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.70 fresh41(fresh11(between(u, v, w), between(u, v, w), u, v, w), between(u, v, w), w, v, u, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 4 (t1) }
% 2.19/0.70 fresh41(true2, between(u, v, w), w, v, u, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.70 fresh41(between(u, v, w), between(u, v, w), w, v, u, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 8 (d15) }
% 2.19/0.70 fresh42(equidistant(w, v, w, insertion(u, w, u, v)), true2, v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.70 fresh42(equidistant(w, v, w, insertion(u, w, u, v)), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 13 (d4_2) R->L }
% 2.19/0.70 fresh42(fresh26(equidistant(v, w, insertion(u, w, u, v), w), true2, v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.70 fresh42(fresh26(equidistant(v, w, insertion(u, w, u, v), w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 11 (i2_3) R->L }
% 2.19/0.70 fresh42(fresh26(fresh17(between(u, v, w), between(u, v, w), u, v, w, u, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) }
% 2.19/0.70 fresh42(fresh26(fresh17(between(u, v, w), true2, u, v, w, u, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 14 (i2_3) }
% 2.19/0.70 fresh42(fresh26(fresh16(equidistant(u, w, u, w), true2, u, v, w, u, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.70 fresh42(fresh26(fresh16(equidistant(u, w, u, w), between(u, v, w), u, v, w, u, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.70 = { by axiom 3 (d1) }
% 2.19/0.71 fresh42(fresh26(fresh16(true2, between(u, v, w), u, v, w, u, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.71 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.71 fresh42(fresh26(fresh16(between(u, v, w), between(u, v, w), u, v, w, u, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.71 = { by axiom 7 (i2_3) }
% 2.19/0.71 fresh42(fresh26(true2, between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.71 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.71 fresh42(fresh26(between(u, v, w), between(u, v, w), v, w, insertion(u, w, u, v), w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.71 = { by axiom 6 (d4_2) }
% 2.19/0.71 fresh42(true2, between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.71 = { by axiom 1 (v_between_u_and_w) R->L }
% 2.19/0.71 fresh42(between(u, v, w), between(u, v, w), v, insertion(u, w, u, v))
% 2.19/0.71 = { by axiom 2 (d15) }
% 2.19/0.71 insertion(u, w, u, v)
% 2.19/0.71 % SZS output end Proof
% 2.19/0.71
% 2.19/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
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