TSTP Solution File: GEO034-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO034-3 : 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 : n019.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 23:26:57 EDT 2023
% Result : Unsatisfiable 7.16s 1.34s
% Output : Proof 7.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO034-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n019.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 21:09:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 7.16/1.34 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 7.16/1.34
% 7.16/1.34 % SZS status Unsatisfiable
% 7.16/1.34
% 7.16/1.34 % SZS output start Proof
% 7.16/1.34 Take the following subset of the input axioms:
% 7.16/1.34 fof(d1, axiom, ![V, U]: equidistant(U, V, U, V)).
% 7.16/1.34 fof(d12, axiom, ![X, W, X1, V1, U1, W1, V3, U2]: (~equidistant(U2, V3, U1, V1) | (~equidistant(U2, W, U1, W1) | (~equidistant(U2, X, U1, X1) | (~equidistant(W, X, W1, X1) | (~between(U2, V3, W) | (~between(U1, V1, W1) | equidistant(V3, X, V1, X1)))))))).
% 7.16/1.34 fof(d7, axiom, ![V3, U2]: equidistant(U2, U2, V3, V3)).
% 7.16/1.34 fof(identity_for_equidistance, axiom, ![Y, Z, X2]: (~equidistant(X2, Y, Z, Z) | X2=Y)).
% 7.16/1.34 fof(prove_v_is_x, negated_conjecture, v!=x).
% 7.16/1.35 fof(t1, axiom, ![V3, W2, U2]: (~between(U2, V3, W2) | between(W2, V3, U2))).
% 7.16/1.35 fof(transitivity_for_equidistance, axiom, ![V2, X2, Y2, Z2, V3, W2]: (~equidistant(X2, Y2, Z2, V3) | (~equidistant(X2, Y2, V2, W2) | equidistant(Z2, V3, V2, W2)))).
% 7.16/1.35 fof(u_to_v_equals_u_to_x, hypothesis, equidistant(u, v, u, x)).
% 7.16/1.35 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 7.16/1.35 fof(w_to_v_equals_w_to_x, hypothesis, equidistant(w, v, w, x)).
% 7.16/1.35
% 7.16/1.35 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.16/1.35 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.16/1.35 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.16/1.35 fresh(y, y, x1...xn) = u
% 7.16/1.35 C => fresh(s, t, x1...xn) = v
% 7.16/1.35 where fresh is a fresh function symbol and x1..xn are the free
% 7.16/1.35 variables of u and v.
% 7.16/1.35 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.16/1.35 input problem has no model of domain size 1).
% 7.16/1.35
% 7.16/1.35 The encoding turns the above axioms into the following unit equations and goals:
% 7.16/1.35
% 7.16/1.35 Axiom 1 (v_between_u_and_w): between(u, v, w) = true2.
% 7.16/1.35 Axiom 2 (identity_for_equidistance): fresh2(X, X, Y, Z) = Z.
% 7.16/1.35 Axiom 3 (d7): equidistant(X, X, Y, Y) = true2.
% 7.16/1.35 Axiom 4 (d1): equidistant(X, Y, X, Y) = true2.
% 7.16/1.35 Axiom 5 (u_to_v_equals_u_to_x): equidistant(u, v, u, x) = true2.
% 7.16/1.35 Axiom 6 (w_to_v_equals_w_to_x): equidistant(w, v, w, x) = true2.
% 7.16/1.35 Axiom 7 (t1): fresh10(X, X, Y, Z, W) = true2.
% 7.16/1.35 Axiom 8 (d12): fresh50(X, X, Y, Z, W, V) = true2.
% 7.16/1.35 Axiom 9 (transitivity_for_equidistance): fresh8(X, X, Y, Z, W, V) = true2.
% 7.16/1.35 Axiom 10 (d12): fresh48(X, X, Y, Z, W, V, U, T) = equidistant(Z, U, V, T).
% 7.16/1.35 Axiom 11 (t1): fresh10(between(X, Y, Z), true2, X, Y, Z) = between(Z, Y, X).
% 7.16/1.35 Axiom 12 (transitivity_for_equidistance): fresh9(X, X, Y, Z, W, V, U, T) = equidistant(W, V, U, T).
% 7.16/1.35 Axiom 13 (identity_for_equidistance): fresh2(equidistant(X, Y, Z, Z), true2, X, Y) = X.
% 7.16/1.35 Axiom 14 (d12): fresh49(X, X, Y, Z, W, V, U, T, S, X2) = fresh50(equidistant(Y, Z, W, V), true2, Z, V, S, X2).
% 7.16/1.35 Axiom 15 (d12): fresh47(X, X, Y, Z, W, V, U, T, S, X2) = fresh48(equidistant(Y, U, W, T), true2, Y, Z, W, V, S, X2).
% 7.16/1.35 Axiom 16 (transitivity_for_equidistance): fresh9(equidistant(X, Y, Z, W), true2, X, Y, V, U, Z, W) = fresh8(equidistant(X, Y, V, U), true2, V, U, Z, W).
% 7.16/1.35 Axiom 17 (d12): fresh45(X, X, Y, Z, W, V, U, T, S, X2) = fresh46(between(Y, Z, U), true2, Y, Z, W, V, U, T, S, X2).
% 7.16/1.35 Axiom 18 (d12): fresh46(X, X, Y, Z, W, V, U, T, S, X2) = fresh49(equidistant(Y, S, W, X2), true2, Y, Z, W, V, U, T, S, X2).
% 7.16/1.35 Axiom 19 (d12): fresh45(between(X, Y, Z), true2, W, V, X, Y, U, Z, T, S) = fresh47(equidistant(U, T, Z, S), true2, W, V, X, Y, U, Z, T, S).
% 7.16/1.35
% 7.16/1.35 Lemma 20: between(w, v, u) = true2.
% 7.16/1.35 Proof:
% 7.16/1.35 between(w, v, u)
% 7.16/1.35 = { by axiom 11 (t1) R->L }
% 7.16/1.35 fresh10(between(u, v, w), true2, u, v, w)
% 7.16/1.35 = { by axiom 1 (v_between_u_and_w) }
% 7.16/1.35 fresh10(true2, true2, u, v, w)
% 7.16/1.35 = { by axiom 7 (t1) }
% 7.16/1.35 true2
% 7.16/1.35
% 7.16/1.35 Goal 1 (prove_v_is_x): v = x.
% 7.16/1.35 Proof:
% 7.16/1.35 v
% 7.16/1.35 = { by axiom 13 (identity_for_equidistance) R->L }
% 7.16/1.35 fresh2(equidistant(v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 12 (transitivity_for_equidistance) R->L }
% 7.16/1.35 fresh2(fresh9(true2, true2, v, v, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 3 (d7) R->L }
% 7.16/1.35 fresh2(fresh9(equidistant(v, v, X, X), true2, v, v, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 16 (transitivity_for_equidistance) }
% 7.16/1.35 fresh2(fresh8(equidistant(v, v, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 10 (d12) R->L }
% 7.16/1.35 fresh2(fresh8(fresh48(true2, true2, w, v, w, v, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 4 (d1) R->L }
% 7.16/1.35 fresh2(fresh8(fresh48(equidistant(w, u, w, u), true2, w, v, w, v, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 15 (d12) R->L }
% 7.16/1.35 fresh2(fresh8(fresh47(true2, true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 5 (u_to_v_equals_u_to_x) R->L }
% 7.16/1.35 fresh2(fresh8(fresh47(equidistant(u, v, u, x), true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 19 (d12) R->L }
% 7.16/1.35 fresh2(fresh8(fresh45(between(w, v, u), true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by lemma 20 }
% 7.16/1.35 fresh2(fresh8(fresh45(true2, true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 17 (d12) }
% 7.16/1.35 fresh2(fresh8(fresh46(between(w, v, u), true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by lemma 20 }
% 7.16/1.35 fresh2(fresh8(fresh46(true2, true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 18 (d12) }
% 7.16/1.35 fresh2(fresh8(fresh49(equidistant(w, v, w, x), true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 6 (w_to_v_equals_w_to_x) }
% 7.16/1.35 fresh2(fresh8(fresh49(true2, true2, w, v, w, v, u, u, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 14 (d12) }
% 7.16/1.35 fresh2(fresh8(fresh50(equidistant(w, v, w, v), true2, v, v, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 4 (d1) }
% 7.16/1.35 fresh2(fresh8(fresh50(true2, true2, v, v, v, x), true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 8 (d12) }
% 7.16/1.35 fresh2(fresh8(true2, true2, v, x, X, X), true2, v, x)
% 7.16/1.35 = { by axiom 9 (transitivity_for_equidistance) }
% 7.16/1.35 fresh2(true2, true2, v, x)
% 7.16/1.35 = { by axiom 2 (identity_for_equidistance) }
% 7.16/1.35 x
% 7.16/1.35 % SZS output end Proof
% 7.16/1.35
% 7.16/1.35 RESULT: Unsatisfiable (the axioms are contradictory).
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