TSTP Solution File: GEO022-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO022-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : n032.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 23:26:53 EDT 2023
% Result : Unsatisfiable 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : GEO022-3 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Tue Aug 29 22:30:32 EDT 2023
% 0.13/0.29 % CPUTime :
% 0.13/0.37 Command-line arguments: --ground-connectedness --complete-subsets
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% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37
% 0.13/0.37 % SZS output start Proof
% 0.13/0.37 Take the following subset of the input axioms:
% 0.13/0.37 fof(d2, axiom, ![X, V, W, U]: (~equidistant(U, V, W, X) | equidistant(W, X, U, V))).
% 0.13/0.37 fof(prove_transitivity, negated_conjecture, ~equidistant(u, v, y, z)).
% 0.13/0.37 fof(transitivity_for_equidistance, axiom, ![Y, Z, V2, X2, V3, W2]: (~equidistant(X2, Y, Z, V3) | (~equidistant(X2, Y, V2, W2) | equidistant(Z, V3, V2, W2)))).
% 0.13/0.37 fof(u_to_v_equals_w_to_x, hypothesis, equidistant(u, v, w, x)).
% 0.13/0.37 fof(w_to_x_equals_y_to_z, hypothesis, equidistant(w, x, y, z)).
% 0.13/0.37
% 0.13/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.37 fresh(y, y, x1...xn) = u
% 0.13/0.37 C => fresh(s, t, x1...xn) = v
% 0.13/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.37 variables of u and v.
% 0.13/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.37 input problem has no model of domain size 1).
% 0.13/0.37
% 0.13/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.37
% 0.13/0.37 Axiom 1 (w_to_x_equals_y_to_z): equidistant(w, x, y, z) = true.
% 0.13/0.37 Axiom 2 (u_to_v_equals_w_to_x): equidistant(u, v, w, x) = true.
% 0.13/0.37 Axiom 3 (d2): fresh15(X, X, Y, Z, W, V) = true.
% 0.13/0.37 Axiom 4 (transitivity_for_equidistance): fresh3(X, X, Y, Z, W, V) = true.
% 0.13/0.37 Axiom 5 (transitivity_for_equidistance): fresh4(X, X, Y, Z, W, V, U, T) = equidistant(W, V, U, T).
% 0.13/0.37 Axiom 6 (d2): fresh15(equidistant(X, Y, Z, W), true, X, Y, Z, W) = equidistant(Z, W, X, Y).
% 0.13/0.37 Axiom 7 (transitivity_for_equidistance): fresh4(equidistant(X, Y, Z, W), true, X, Y, V, U, Z, W) = fresh3(equidistant(X, Y, V, U), true, V, U, Z, W).
% 0.13/0.37
% 0.13/0.37 Goal 1 (prove_transitivity): equidistant(u, v, y, z) = true.
% 0.13/0.37 Proof:
% 0.13/0.37 equidistant(u, v, y, z)
% 0.13/0.37 = { by axiom 5 (transitivity_for_equidistance) R->L }
% 0.13/0.37 fresh4(true, true, w, x, u, v, y, z)
% 0.13/0.37 = { by axiom 1 (w_to_x_equals_y_to_z) R->L }
% 0.13/0.37 fresh4(equidistant(w, x, y, z), true, w, x, u, v, y, z)
% 0.13/0.37 = { by axiom 7 (transitivity_for_equidistance) }
% 0.13/0.37 fresh3(equidistant(w, x, u, v), true, u, v, y, z)
% 0.13/0.37 = { by axiom 6 (d2) R->L }
% 0.13/0.37 fresh3(fresh15(equidistant(u, v, w, x), true, u, v, w, x), true, u, v, y, z)
% 0.13/0.37 = { by axiom 2 (u_to_v_equals_w_to_x) }
% 0.13/0.37 fresh3(fresh15(true, true, u, v, w, x), true, u, v, y, z)
% 0.13/0.37 = { by axiom 3 (d2) }
% 0.13/0.37 fresh3(true, true, u, v, y, z)
% 0.13/0.37 = { by axiom 4 (transitivity_for_equidistance) }
% 0.13/0.37 true
% 0.13/0.37 % SZS output end Proof
% 0.13/0.37
% 0.13/0.37 RESULT: Unsatisfiable (the axioms are contradictory).
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