TSTP Solution File: GEO053-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO053-3 : 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 : n026.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 23:27:05 EDT 2023
% Result : Unsatisfiable 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GEO053-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 19:21:05 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.54 Command-line arguments: --no-flatten-goal
% 0.21/0.54
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54
% 0.21/0.54 % SZS output start Proof
% 0.21/0.54 Take the following subset of the input axioms:
% 0.21/0.54 fof(i3, axiom, ![V, W, U]: (~between(U, V, W) | V=insertion(U, W, U, V))).
% 0.21/0.54 fof(i4, axiom, ![X, Y, Z, V2, U2, W2]: (~equidistant(W2, X, Y, Z) | insertion(U2, V2, W2, X)=insertion(U2, V2, Y, Z))).
% 0.21/0.54 fof(prove_v_equals_w, negated_conjecture, v!=w).
% 0.21/0.54 fof(t3, axiom, ![V2, U2]: between(U2, V2, V2)).
% 0.21/0.54 fof(u_to_v_equals_u_to_w, hypothesis, equidistant(u, v, u, w)).
% 0.21/0.54 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 0.21/0.54
% 0.21/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.54 fresh(y, y, x1...xn) = u
% 0.21/0.54 C => fresh(s, t, x1...xn) = v
% 0.21/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.54 variables of u and v.
% 0.21/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.54 input problem has no model of domain size 1).
% 0.21/0.54
% 0.21/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.54
% 0.21/0.54 Axiom 1 (t3): between(X, Y, Y) = true2.
% 0.21/0.55 Axiom 2 (v_between_u_and_w): between(u, v, w) = true2.
% 0.21/0.55 Axiom 3 (u_to_v_equals_u_to_w): equidistant(u, v, u, w) = true2.
% 0.21/0.55 Axiom 4 (i3): fresh4(X, X, Y, Z, W) = Z.
% 0.21/0.55 Axiom 5 (i4): fresh18(X, X, Y, Z, W, V, U, T) = insertion(U, T, W, V).
% 0.21/0.55 Axiom 6 (i3): fresh4(between(X, Y, Z), true2, X, Y, Z) = insertion(X, Z, X, Y).
% 0.21/0.55 Axiom 7 (i4): fresh18(equidistant(X, Y, Z, W), true2, X, Y, Z, W, V, U) = insertion(V, U, X, Y).
% 0.21/0.55
% 0.21/0.55 Goal 1 (prove_v_equals_w): v = w.
% 0.21/0.55 Proof:
% 0.21/0.55 v
% 0.21/0.55 = { by axiom 4 (i3) R->L }
% 0.21/0.55 fresh4(true2, true2, u, v, w)
% 0.21/0.55 = { by axiom 2 (v_between_u_and_w) R->L }
% 0.21/0.55 fresh4(between(u, v, w), true2, u, v, w)
% 0.21/0.55 = { by axiom 6 (i3) }
% 0.21/0.55 insertion(u, w, u, v)
% 0.21/0.55 = { by axiom 7 (i4) R->L }
% 0.21/0.55 fresh18(equidistant(u, v, u, w), true2, u, v, u, w, u, w)
% 0.21/0.55 = { by axiom 3 (u_to_v_equals_u_to_w) }
% 0.21/0.55 fresh18(true2, true2, u, v, u, w, u, w)
% 0.21/0.55 = { by axiom 5 (i4) }
% 0.21/0.55 insertion(u, w, u, w)
% 0.21/0.55 = { by axiom 6 (i3) R->L }
% 0.21/0.55 fresh4(between(u, w, w), true2, u, w, w)
% 0.21/0.55 = { by axiom 1 (t3) }
% 0.21/0.55 fresh4(true2, true2, u, w, w)
% 0.21/0.55 = { by axiom 4 (i3) }
% 0.21/0.55 w
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55
% 0.21/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
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