TSTP Solution File: GEO040-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO040-3 : 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 : n011.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 23:27:00 EDT 2023
% Result : Unsatisfiable 0.21s 0.62s
% 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
% 0.08/0.14 % Problem : GEO040-3 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.15 % 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 : n011.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
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Aug 29 23:51:12 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.62 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.62
% 0.21/0.62 % SZS status Unsatisfiable
% 0.21/0.62
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 Take the following subset of the input axioms:
% 0.21/0.62 fof(identity_for_betweeness, axiom, ![X, Y]: (~between(X, Y, X) | X=Y)).
% 0.21/0.62 fof(inner_pasch1, axiom, ![V, W, U, X2, Y2]: (~between(U, V, W) | (~between(Y2, X2, W) | between(V, inner_pasch(U, V, W, X2, Y2), Y2)))).
% 0.21/0.62 fof(inner_pasch2, axiom, ![V2, X2, Y2, W2, U2]: (~between(U2, V2, W2) | (~between(Y2, X2, W2) | between(X2, inner_pasch(U2, V2, W2, X2, Y2), U2)))).
% 0.21/0.62 fof(prove_u_is_v, negated_conjecture, u!=v).
% 0.21/0.62 fof(u_between_v_and_w, hypothesis, between(v, u, w)).
% 0.21/0.62 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 0.21/0.62
% 0.21/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.62 fresh(y, y, x1...xn) = u
% 0.21/0.62 C => fresh(s, t, x1...xn) = v
% 0.21/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.62 variables of u and v.
% 0.21/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.62 input problem has no model of domain size 1).
% 0.21/0.62
% 0.21/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.62
% 0.21/0.62 Axiom 1 (v_between_u_and_w): between(u, v, w) = true.
% 0.21/0.62 Axiom 2 (u_between_v_and_w): between(v, u, w) = true.
% 0.21/0.62 Axiom 3 (identity_for_betweeness): fresh3(X, X, Y, Z) = Z.
% 0.21/0.62 Axiom 4 (identity_for_betweeness): fresh3(between(X, Y, X), true, X, Y) = X.
% 0.21/0.62 Axiom 5 (inner_pasch1): fresh10(X, X, Y, Z, W, V, U) = between(Z, inner_pasch(Y, Z, W, U, V), V).
% 0.21/0.62 Axiom 6 (inner_pasch1): fresh9(X, X, Y, Z, W, V, U) = true.
% 0.21/0.62 Axiom 7 (inner_pasch2): fresh8(X, X, Y, Z, W, V, U) = between(U, inner_pasch(Y, Z, W, U, V), Y).
% 0.21/0.62 Axiom 8 (inner_pasch2): fresh7(X, X, Y, Z, W, V, U) = true.
% 0.21/0.62 Axiom 9 (inner_pasch1): fresh10(between(X, Y, Z), true, W, V, Z, X, Y) = fresh9(between(W, V, Z), true, W, V, Z, X, Y).
% 0.21/0.62 Axiom 10 (inner_pasch2): fresh8(between(X, Y, Z), true, W, V, Z, X, Y) = fresh7(between(W, V, Z), true, W, V, Z, X, Y).
% 0.21/0.62
% 0.21/0.62 Goal 1 (prove_u_is_v): u = v.
% 0.21/0.62 Proof:
% 0.21/0.62 u
% 0.21/0.62 = { by axiom 4 (identity_for_betweeness) R->L }
% 0.21/0.63 fresh3(between(u, v, u), true, u, v)
% 0.21/0.63 = { by axiom 4 (identity_for_betweeness) R->L }
% 0.21/0.63 fresh3(between(u, fresh3(between(v, inner_pasch(u, v, w, u, v), v), true, v, inner_pasch(u, v, w, u, v)), u), true, u, v)
% 0.21/0.63 = { by axiom 5 (inner_pasch1) R->L }
% 0.21/0.63 fresh3(between(u, fresh3(fresh10(true, true, u, v, w, v, u), true, v, inner_pasch(u, v, w, u, v)), u), true, u, v)
% 0.21/0.63 = { by axiom 2 (u_between_v_and_w) R->L }
% 0.21/0.63 fresh3(between(u, fresh3(fresh10(between(v, u, w), true, u, v, w, v, u), true, v, inner_pasch(u, v, w, u, v)), u), true, u, v)
% 0.21/0.63 = { by axiom 9 (inner_pasch1) }
% 0.21/0.63 fresh3(between(u, fresh3(fresh9(between(u, v, w), true, u, v, w, v, u), true, v, inner_pasch(u, v, w, u, v)), u), true, u, v)
% 0.21/0.63 = { by axiom 1 (v_between_u_and_w) }
% 0.21/0.63 fresh3(between(u, fresh3(fresh9(true, true, u, v, w, v, u), true, v, inner_pasch(u, v, w, u, v)), u), true, u, v)
% 0.21/0.63 = { by axiom 6 (inner_pasch1) }
% 0.21/0.63 fresh3(between(u, fresh3(true, true, v, inner_pasch(u, v, w, u, v)), u), true, u, v)
% 0.21/0.63 = { by axiom 3 (identity_for_betweeness) }
% 0.21/0.63 fresh3(between(u, inner_pasch(u, v, w, u, v), u), true, u, v)
% 0.21/0.63 = { by axiom 7 (inner_pasch2) R->L }
% 0.21/0.63 fresh3(fresh8(true, true, u, v, w, v, u), true, u, v)
% 0.21/0.63 = { by axiom 2 (u_between_v_and_w) R->L }
% 0.21/0.63 fresh3(fresh8(between(v, u, w), true, u, v, w, v, u), true, u, v)
% 0.21/0.63 = { by axiom 10 (inner_pasch2) }
% 0.21/0.63 fresh3(fresh7(between(u, v, w), true, u, v, w, v, u), true, u, v)
% 0.21/0.63 = { by axiom 1 (v_between_u_and_w) }
% 0.21/0.63 fresh3(fresh7(true, true, u, v, w, v, u), true, u, v)
% 0.21/0.63 = { by axiom 8 (inner_pasch2) }
% 0.21/0.63 fresh3(true, true, u, v)
% 0.21/0.63 = { by axiom 3 (identity_for_betweeness) }
% 0.21/0.63 v
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63
% 0.21/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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