TSTP Solution File: GEO048-3 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO048-3 : 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 : n025.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 23:27:04 EDT 2023
% Result : Unsatisfiable 0.19s 0.65s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO048-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.34 % Computer : n025.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Aug 29 21:04:40 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.65 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.65
% 0.19/0.65 % SZS status Unsatisfiable
% 0.19/0.65
% 0.19/0.65 % SZS output start Proof
% 0.19/0.65 Take the following subset of the input axioms:
% 0.19/0.65 fof(inner_pasch2, axiom, ![X, Y, V, W, U]: (~between(U, V, W) | (~between(Y, X, W) | between(X, inner_pasch(U, V, W, X, Y), U)))).
% 0.19/0.65 fof(prove_conclusion2, negated_conjecture, ~between(v, inner_pasch(v1, inner_pasch(u, x, u1, v1, w), u, v, w), v1)).
% 0.19/0.65 fof(t1, axiom, ![V2, W2, U2]: (~between(U2, V2, W2) | between(W2, V2, U2))).
% 0.19/0.65 fof(v1_between_u1_and_w, hypothesis, between(u1, v1, w)).
% 0.19/0.65 fof(v_between_u_and_w, hypothesis, between(u, v, w)).
% 0.19/0.65 fof(x_between_u_and_u1, hypothesis, between(u, x, u1)).
% 0.19/0.65
% 0.19/0.65 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.65 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.65 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.65 fresh(y, y, x1...xn) = u
% 0.19/0.65 C => fresh(s, t, x1...xn) = v
% 0.19/0.65 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.65 variables of u and v.
% 0.19/0.65 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.65 input problem has no model of domain size 1).
% 0.19/0.65
% 0.19/0.65 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.65
% 0.19/0.65 Axiom 1 (x_between_u_and_u1): between(u, x, u1) = true2.
% 0.19/0.65 Axiom 2 (v_between_u_and_w): between(u, v, w) = true2.
% 0.19/0.65 Axiom 3 (v1_between_u1_and_w): between(u1, v1, w) = true2.
% 0.19/0.65 Axiom 4 (t1): fresh10(X, X, Y, Z, W) = true2.
% 0.19/0.65 Axiom 5 (inner_pasch2): fresh11(X, X, Y, Z, W, V, U) = true2.
% 0.19/0.65 Axiom 6 (inner_pasch2): fresh12(X, X, Y, Z, W, V, U) = between(U, inner_pasch(Y, Z, W, U, V), Y).
% 0.19/0.65 Axiom 7 (t1): fresh10(between(X, Y, Z), true2, X, Y, Z) = between(Z, Y, X).
% 0.19/0.65 Axiom 8 (inner_pasch2): fresh12(between(X, Y, Z), true2, W, V, Z, X, Y) = fresh11(between(W, V, Z), true2, W, V, Z, X, Y).
% 0.19/0.65
% 0.19/0.65 Goal 1 (prove_conclusion2): between(v, inner_pasch(v1, inner_pasch(u, x, u1, v1, w), u, v, w), v1) = true2.
% 0.19/0.65 Proof:
% 0.19/0.65 between(v, inner_pasch(v1, inner_pasch(u, x, u1, v1, w), u, v, w), v1)
% 0.19/0.65 = { by axiom 6 (inner_pasch2) R->L }
% 0.19/0.65 fresh12(true2, true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 4 (t1) R->L }
% 0.19/0.65 fresh12(fresh10(true2, true2, u, v, w), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 2 (v_between_u_and_w) R->L }
% 0.19/0.65 fresh12(fresh10(between(u, v, w), true2, u, v, w), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 7 (t1) }
% 0.19/0.65 fresh12(between(w, v, u), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 8 (inner_pasch2) }
% 0.19/0.65 fresh11(between(v1, inner_pasch(u, x, u1, v1, w), u), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 6 (inner_pasch2) R->L }
% 0.19/0.65 fresh11(fresh12(true2, true2, u, x, u1, w, v1), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 4 (t1) R->L }
% 0.19/0.65 fresh11(fresh12(fresh10(true2, true2, u1, v1, w), true2, u, x, u1, w, v1), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 3 (v1_between_u1_and_w) R->L }
% 0.19/0.65 fresh11(fresh12(fresh10(between(u1, v1, w), true2, u1, v1, w), true2, u, x, u1, w, v1), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 7 (t1) }
% 0.19/0.65 fresh11(fresh12(between(w, v1, u1), true2, u, x, u1, w, v1), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 8 (inner_pasch2) }
% 0.19/0.65 fresh11(fresh11(between(u, x, u1), true2, u, x, u1, w, v1), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 1 (x_between_u_and_u1) }
% 0.19/0.65 fresh11(fresh11(true2, true2, u, x, u1, w, v1), true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 5 (inner_pasch2) }
% 0.19/0.65 fresh11(true2, true2, v1, inner_pasch(u, x, u1, v1, w), u, w, v)
% 0.19/0.65 = { by axiom 5 (inner_pasch2) }
% 0.19/0.65 true2
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65
% 0.19/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
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