TSTP Solution File: GEO001-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO001-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 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 : n018.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 23:26:41 EDT 2023
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO001-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.13/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 23:15:03 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Take the following subset of the input axioms:
% 0.20/0.45 fof(b_between_a_and_c, hypothesis, between(a, b, c)).
% 0.20/0.45 fof(identity_for_betweeness, axiom, ![X, Y]: (~between(X, Y, X) | X=Y)).
% 0.20/0.45 fof(identity_for_equidistance, axiom, ![Z, X2, Y2]: (~equidistant(X2, Y2, Z, Z) | X2=Y2)).
% 0.20/0.45 fof(outer_pasch1, axiom, ![V, W, X2, Y2, Z2]: (~between(X2, W, V) | (~between(Y2, V, Z2) | between(X2, outer_pasch(W, X2, Y2, Z2, V), Y2)))).
% 0.20/0.45 fof(outer_pasch2, axiom, ![V2, X2, Y2, W2, Z2]: (~between(X2, W2, V2) | (~between(Y2, V2, Z2) | between(Z2, W2, outer_pasch(W2, X2, Y2, Z2, V2))))).
% 0.20/0.45 fof(prove_b_between_c_and_a, negated_conjecture, ~between(c, b, a)).
% 0.20/0.45 fof(segment_construction1, axiom, ![V2, X2, Y2, W2]: between(X2, Y2, extension(X2, Y2, W2, V2))).
% 0.20/0.45 fof(segment_construction2, axiom, ![V2, X2, Y2, W2]: equidistant(Y2, extension(X2, Y2, W2, V2), W2, V2)).
% 0.20/0.45
% 0.20/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.45 fresh(y, y, x1...xn) = u
% 0.20/0.45 C => fresh(s, t, x1...xn) = v
% 0.20/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.45 variables of u and v.
% 0.20/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.45 input problem has no model of domain size 1).
% 0.20/0.45
% 0.20/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.45
% 0.20/0.46 Axiom 1 (b_between_a_and_c): between(a, b, c) = true.
% 0.20/0.46 Axiom 2 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.20/0.46 Axiom 3 (identity_for_betweeness): fresh2(X, X, Y, Z) = Z.
% 0.20/0.46 Axiom 4 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 0.20/0.46 Axiom 5 (outer_pasch1): fresh9(X, X, Y, Z, W, V, U) = true.
% 0.20/0.46 Axiom 6 (outer_pasch2): fresh7(X, X, Y, Z, W, V, U) = true.
% 0.20/0.46 Axiom 7 (identity_for_betweeness): fresh2(between(X, Y, X), true, X, Y) = X.
% 0.20/0.46 Axiom 8 (outer_pasch1): fresh10(X, X, Y, Z, W, V, U) = between(Y, outer_pasch(Z, Y, V, U, W), V).
% 0.20/0.46 Axiom 9 (outer_pasch2): fresh8(X, X, Y, Z, W, V, U) = between(U, Z, outer_pasch(Z, Y, V, U, W)).
% 0.20/0.46 Axiom 10 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.20/0.46 Axiom 11 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.20/0.46 Axiom 12 (outer_pasch1): fresh10(between(X, Y, Z), true, W, V, Y, X, Z) = fresh9(between(W, V, Y), true, W, V, Y, X, Z).
% 0.20/0.46 Axiom 13 (outer_pasch2): fresh8(between(X, Y, Z), true, W, V, Y, X, Z) = fresh7(between(W, V, Y), true, W, V, Y, X, Z).
% 0.20/0.46
% 0.20/0.46 Lemma 14: between(X, Y, Y) = true.
% 0.20/0.46 Proof:
% 0.20/0.46 between(X, Y, Y)
% 0.20/0.46 = { by axiom 11 (identity_for_equidistance) R->L }
% 0.20/0.46 between(X, Y, fresh(equidistant(Y, extension(X, Y, Z, Z), Z, Z), true, Y, extension(X, Y, Z, Z)))
% 0.20/0.46 = { by axiom 10 (segment_construction2) }
% 0.20/0.46 between(X, Y, fresh(true, true, Y, extension(X, Y, Z, Z)))
% 0.20/0.46 = { by axiom 2 (identity_for_equidistance) }
% 0.20/0.46 between(X, Y, extension(X, Y, Z, Z))
% 0.20/0.46 = { by axiom 4 (segment_construction1) }
% 0.20/0.46 true
% 0.20/0.46
% 0.20/0.46 Goal 1 (prove_b_between_c_and_a): between(c, b, a) = true.
% 0.20/0.46 Proof:
% 0.20/0.46 between(c, b, a)
% 0.20/0.46 = { by axiom 7 (identity_for_betweeness) R->L }
% 0.20/0.46 between(c, b, fresh2(between(a, outer_pasch(b, a, a, c, c), a), true, a, outer_pasch(b, a, a, c, c)))
% 0.20/0.46 = { by axiom 8 (outer_pasch1) R->L }
% 0.20/0.46 between(c, b, fresh2(fresh10(true, true, a, b, c, a, c), true, a, outer_pasch(b, a, a, c, c)))
% 0.20/0.46 = { by lemma 14 R->L }
% 0.20/0.46 between(c, b, fresh2(fresh10(between(a, c, c), true, a, b, c, a, c), true, a, outer_pasch(b, a, a, c, c)))
% 0.20/0.46 = { by axiom 12 (outer_pasch1) }
% 0.20/0.46 between(c, b, fresh2(fresh9(between(a, b, c), true, a, b, c, a, c), true, a, outer_pasch(b, a, a, c, c)))
% 0.20/0.46 = { by axiom 1 (b_between_a_and_c) }
% 0.20/0.46 between(c, b, fresh2(fresh9(true, true, a, b, c, a, c), true, a, outer_pasch(b, a, a, c, c)))
% 0.20/0.46 = { by axiom 5 (outer_pasch1) }
% 0.20/0.46 between(c, b, fresh2(true, true, a, outer_pasch(b, a, a, c, c)))
% 0.20/0.46 = { by axiom 3 (identity_for_betweeness) }
% 0.20/0.46 between(c, b, outer_pasch(b, a, a, c, c))
% 0.20/0.46 = { by axiom 9 (outer_pasch2) R->L }
% 0.20/0.46 fresh8(true, true, a, b, c, a, c)
% 0.20/0.46 = { by lemma 14 R->L }
% 0.20/0.46 fresh8(between(a, c, c), true, a, b, c, a, c)
% 0.20/0.46 = { by axiom 13 (outer_pasch2) }
% 0.20/0.46 fresh7(between(a, b, c), true, a, b, c, a, c)
% 0.20/0.46 = { by axiom 1 (b_between_a_and_c) }
% 0.20/0.46 fresh7(true, true, a, b, c, a, c)
% 0.20/0.46 = { by axiom 6 (outer_pasch2) }
% 0.20/0.46 true
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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