TSTP Solution File: GEO047-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO047-3 : 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 : 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 23:27:03 EDT 2023
% Result : Unsatisfiable 0.21s 0.51s
% 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
% 0.00/0.13 % Problem : GEO047-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % 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 : n026.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 23:03:21 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.51 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.51
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 Take the following subset of the input axioms:
% 0.21/0.51 fof(b8, axiom, ![X, V, W, U]: (~between(U, V, X) | (~between(V, W, X) | between(U, W, X)))).
% 0.21/0.51 fof(prove_v_between_u_and_x, negated_conjecture, ~between(u, v, x)).
% 0.21/0.51 fof(t1, axiom, ![V2, W2, U2]: (~between(U2, V2, W2) | between(W2, V2, U2))).
% 0.21/0.51 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 0.21/0.51 fof(w_between_u_and_x, hypothesis, between(u, w, x)).
% 0.21/0.51
% 0.21/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.51 fresh(y, y, x1...xn) = u
% 0.21/0.51 C => fresh(s, t, x1...xn) = v
% 0.21/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.51 variables of u and v.
% 0.21/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.51 input problem has no model of domain size 1).
% 0.21/0.51
% 0.21/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.51
% 0.21/0.51 Axiom 1 (v_between_u_and_w): between(u, v, w) = true.
% 0.21/0.51 Axiom 2 (w_between_u_and_x): between(u, w, x) = true.
% 0.21/0.51 Axiom 3 (b8): fresh27(X, X, Y, Z, W) = true.
% 0.21/0.51 Axiom 4 (t1): fresh10(X, X, Y, Z, W) = true.
% 0.21/0.51 Axiom 5 (b8): fresh28(X, X, Y, Z, W, V) = between(Y, V, W).
% 0.21/0.51 Axiom 6 (t1): fresh10(between(X, Y, Z), true, X, Y, Z) = between(Z, Y, X).
% 0.21/0.52 Axiom 7 (b8): fresh28(between(X, Y, Z), true, W, X, Z, Y) = fresh27(between(W, X, Z), true, W, Z, Y).
% 0.21/0.52
% 0.21/0.52 Goal 1 (prove_v_between_u_and_x): between(u, v, x) = true.
% 0.21/0.52 Proof:
% 0.21/0.52 between(u, v, x)
% 0.21/0.52 = { by axiom 6 (t1) R->L }
% 0.21/0.52 fresh10(between(x, v, u), true, x, v, u)
% 0.21/0.52 = { by axiom 5 (b8) R->L }
% 0.21/0.52 fresh10(fresh28(true, true, x, w, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 4 (t1) R->L }
% 0.21/0.52 fresh10(fresh28(fresh10(true, true, u, v, w), true, x, w, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 1 (v_between_u_and_w) R->L }
% 0.21/0.52 fresh10(fresh28(fresh10(between(u, v, w), true, u, v, w), true, x, w, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 6 (t1) }
% 0.21/0.52 fresh10(fresh28(between(w, v, u), true, x, w, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 7 (b8) }
% 0.21/0.52 fresh10(fresh27(between(x, w, u), true, x, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 6 (t1) R->L }
% 0.21/0.52 fresh10(fresh27(fresh10(between(u, w, x), true, u, w, x), true, x, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 2 (w_between_u_and_x) }
% 0.21/0.52 fresh10(fresh27(fresh10(true, true, u, w, x), true, x, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 4 (t1) }
% 0.21/0.52 fresh10(fresh27(true, true, x, u, v), true, x, v, u)
% 0.21/0.52 = { by axiom 3 (b8) }
% 0.21/0.52 fresh10(true, true, x, v, u)
% 0.21/0.52 = { by axiom 4 (t1) }
% 0.21/0.52 true
% 0.21/0.52 % SZS output end Proof
% 0.21/0.52
% 0.21/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
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