TSTP Solution File: GEO032-3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO032-3 : 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 : n001.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 23:26:56 EDT 2023
% Result : Unsatisfiable 33.35s 4.64s
% Output : Proof 33.35s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO032-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.11/0.13 % 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 : n001.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 21:59:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 33.35/4.64 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 33.35/4.64
% 33.35/4.64 % SZS status Unsatisfiable
% 33.35/4.64
% 33.35/4.65 % SZS output start Proof
% 33.35/4.65 Take the following subset of the input axioms:
% 33.35/4.65 fof(d12, axiom, ![X, V, W, X1, V1, U, U1, W1]: (~equidistant(U, V, U1, V1) | (~equidistant(U, W, U1, W1) | (~equidistant(U, X, U1, X1) | (~equidistant(W, X, W1, X1) | (~between(U, V, W) | (~between(U1, V1, W1) | equidistant(V, X, V1, X1)))))))).
% 33.35/4.65 fof(d7, axiom, ![V2, U2]: equidistant(U2, U2, V2, V2)).
% 33.35/4.65 fof(u_to_v_equals_u1_to_v1, hypothesis, equidistant(u, v, u1, v1)).
% 33.35/4.65 fof(u_to_w_equals_u1_to_w1, hypothesis, equidistant(u, w, u1, w1)).
% 33.35/4.65 fof(v1_between_u1_and_w1, hypothesis, between(u1, v1, w1)).
% 33.35/4.65 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 33.35/4.65 fof(v_to_w_equals_v1_to_w1, negated_conjecture, ~equidistant(v, w, v1, w1)).
% 33.35/4.65
% 33.35/4.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 33.35/4.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 33.35/4.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 33.35/4.65 fresh(y, y, x1...xn) = u
% 33.35/4.65 C => fresh(s, t, x1...xn) = v
% 33.35/4.65 where fresh is a fresh function symbol and x1..xn are the free
% 33.35/4.65 variables of u and v.
% 33.35/4.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 33.35/4.65 input problem has no model of domain size 1).
% 33.35/4.65
% 33.35/4.65 The encoding turns the above axioms into the following unit equations and goals:
% 33.35/4.65
% 33.35/4.65 Axiom 1 (v_between_u_and_w): between(u, v, w) = true2.
% 33.35/4.65 Axiom 2 (v1_between_u1_and_w1): between(u1, v1, w1) = true2.
% 33.35/4.65 Axiom 3 (d7): equidistant(X, X, Y, Y) = true2.
% 33.35/4.65 Axiom 4 (u_to_v_equals_u1_to_v1): equidistant(u, v, u1, v1) = true2.
% 33.35/4.65 Axiom 5 (u_to_w_equals_u1_to_w1): equidistant(u, w, u1, w1) = true2.
% 33.35/4.65 Axiom 6 (d12): fresh40(X, X, Y, Z, W, V) = true2.
% 33.35/4.65 Axiom 7 (d12): fresh38(X, X, Y, Z, W, V, U, T) = equidistant(Z, U, V, T).
% 33.35/4.65 Axiom 8 (d12): fresh39(X, X, Y, Z, W, V, U, T, S, X2) = fresh40(equidistant(Y, Z, W, V), true2, Z, V, S, X2).
% 33.35/4.65 Axiom 9 (d12): fresh37(X, X, Y, Z, W, V, U, T, S, X2) = fresh38(equidistant(Y, U, W, T), true2, Y, Z, W, V, S, X2).
% 33.35/4.65 Axiom 10 (d12): fresh35(X, X, Y, Z, W, V, U, T, S, X2) = fresh36(between(Y, Z, U), true2, Y, Z, W, V, U, T, S, X2).
% 33.35/4.65 Axiom 11 (d12): fresh36(X, X, Y, Z, W, V, U, T, S, X2) = fresh39(equidistant(Y, S, W, X2), true2, Y, Z, W, V, U, T, S, X2).
% 33.35/4.65 Axiom 12 (d12): fresh35(between(X, Y, Z), true2, W, V, X, Y, U, Z, T, S) = fresh37(equidistant(U, T, Z, S), true2, W, V, X, Y, U, Z, T, S).
% 33.35/4.65
% 33.35/4.65 Goal 1 (v_to_w_equals_v1_to_w1): equidistant(v, w, v1, w1) = true2.
% 33.35/4.65 Proof:
% 33.35/4.65 equidistant(v, w, v1, w1)
% 33.35/4.65 = { by axiom 7 (d12) R->L }
% 33.35/4.65 fresh38(true2, true2, u, v, u1, v1, w, w1)
% 33.35/4.65 = { by axiom 5 (u_to_w_equals_u1_to_w1) R->L }
% 33.35/4.65 fresh38(equidistant(u, w, u1, w1), true2, u, v, u1, v1, w, w1)
% 33.35/4.65 = { by axiom 9 (d12) R->L }
% 33.35/4.65 fresh37(true2, true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 3 (d7) R->L }
% 33.35/4.65 fresh37(equidistant(w, w, w1, w1), true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 12 (d12) R->L }
% 33.35/4.65 fresh35(between(u1, v1, w1), true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 2 (v1_between_u1_and_w1) }
% 33.35/4.65 fresh35(true2, true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 10 (d12) }
% 33.35/4.65 fresh36(between(u, v, w), true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 1 (v_between_u_and_w) }
% 33.35/4.65 fresh36(true2, true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 11 (d12) }
% 33.35/4.65 fresh39(equidistant(u, w, u1, w1), true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 5 (u_to_w_equals_u1_to_w1) }
% 33.35/4.65 fresh39(true2, true2, u, v, u1, v1, w, w1, w, w1)
% 33.35/4.65 = { by axiom 8 (d12) }
% 33.35/4.65 fresh40(equidistant(u, v, u1, v1), true2, v, v1, w, w1)
% 33.35/4.65 = { by axiom 4 (u_to_v_equals_u1_to_v1) }
% 33.35/4.65 fresh40(true2, true2, v, v1, w, w1)
% 33.35/4.65 = { by axiom 6 (d12) }
% 33.35/4.65 true2
% 33.35/4.65 % SZS output end Proof
% 33.35/4.65
% 33.35/4.65 RESULT: Unsatisfiable (the axioms are contradictory).
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