TSTP Solution File: GEO001-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO001-2 : 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 : n004.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 0.21s 0.46s
% 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
% 0.07/0.13 % Problem : GEO001-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 23:00:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.46 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.46
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46
% 0.21/0.46 % SZS output start Proof
% 0.21/0.46 Take the following subset of the input axioms:
% 0.21/0.46 fof(b_between_a_and_c, hypothesis, between(a, b, c)).
% 0.21/0.46 fof(identity_for_betweeness, axiom, ![X, Y]: (~between(X, Y, X) | X=Y)).
% 0.21/0.46 fof(identity_for_equidistance, axiom, ![Z, X2, Y2]: (~equidistant(X2, Y2, Z, Z) | X2=Y2)).
% 0.21/0.46 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)))).
% 0.21/0.46 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)))).
% 0.21/0.46 fof(prove_b_between_c_and_a, negated_conjecture, ~between(c, b, a)).
% 0.21/0.46 fof(segment_construction1, axiom, ![V2, X2, Y2, W2]: between(X2, Y2, extension(X2, Y2, W2, V2))).
% 0.21/0.46 fof(segment_construction2, axiom, ![V2, X2, Y2, W2]: equidistant(Y2, extension(X2, Y2, W2, V2), W2, V2)).
% 0.21/0.46
% 0.21/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.46 fresh(y, y, x1...xn) = u
% 0.21/0.46 C => fresh(s, t, x1...xn) = v
% 0.21/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.46 variables of u and v.
% 0.21/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.46 input problem has no model of domain size 1).
% 0.21/0.46
% 0.21/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.46
% 0.21/0.46 Axiom 1 (b_between_a_and_c): between(a, b, c) = true.
% 0.21/0.46 Axiom 2 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 0.21/0.46 Axiom 3 (identity_for_betweeness): fresh2(X, X, Y, Z) = Z.
% 0.21/0.46 Axiom 4 (inner_pasch1): fresh7(X, X, Y, Z, W, V, U) = true.
% 0.21/0.46 Axiom 5 (inner_pasch2): fresh5(X, X, Y, Z, W, V, U) = true.
% 0.21/0.46 Axiom 6 (identity_for_betweeness): fresh2(between(X, Y, X), true, X, Y) = X.
% 0.21/0.46 Axiom 7 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 0.21/0.46 Axiom 8 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 0.21/0.46 Axiom 9 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 0.21/0.46 Axiom 10 (inner_pasch1): fresh8(X, X, Y, Z, W, V, U) = between(Z, inner_pasch(Y, Z, W, U, V), V).
% 0.21/0.46 Axiom 11 (inner_pasch2): fresh6(X, X, Y, Z, W, V, U) = between(U, inner_pasch(Y, Z, W, U, V), Y).
% 0.21/0.46 Axiom 12 (inner_pasch1): fresh8(between(X, Y, Z), true, W, V, Z, X, Y) = fresh7(between(W, V, Z), true, W, V, Z, X, Y).
% 0.21/0.46 Axiom 13 (inner_pasch2): fresh6(between(X, Y, Z), true, W, V, Z, X, Y) = fresh5(between(W, V, Z), true, W, V, Z, X, Y).
% 0.21/0.46
% 0.21/0.46 Lemma 14: between(X, Y, Y) = true.
% 0.21/0.46 Proof:
% 0.21/0.46 between(X, Y, Y)
% 0.21/0.46 = { by axiom 8 (identity_for_equidistance) R->L }
% 0.21/0.46 between(X, Y, fresh(equidistant(Y, extension(X, Y, Z, Z), Z, Z), true, Y, extension(X, Y, Z, Z)))
% 0.21/0.46 = { by axiom 9 (segment_construction2) }
% 0.21/0.46 between(X, Y, fresh(true, true, Y, extension(X, Y, Z, Z)))
% 0.21/0.46 = { by axiom 2 (identity_for_equidistance) }
% 0.21/0.46 between(X, Y, extension(X, Y, Z, Z))
% 0.21/0.46 = { by axiom 7 (segment_construction1) }
% 0.21/0.46 true
% 0.21/0.46
% 0.21/0.46 Goal 1 (prove_b_between_c_and_a): between(c, b, a) = true.
% 0.21/0.46 Proof:
% 0.21/0.46 between(c, b, a)
% 0.21/0.46 = { by axiom 6 (identity_for_betweeness) R->L }
% 0.21/0.46 between(c, fresh2(between(b, inner_pasch(a, b, c, c, b), b), true, b, inner_pasch(a, b, c, c, b)), a)
% 0.21/0.46 = { by axiom 10 (inner_pasch1) R->L }
% 0.21/0.46 between(c, fresh2(fresh8(true, true, a, b, c, b, c), true, b, inner_pasch(a, b, c, c, b)), a)
% 0.21/0.46 = { by lemma 14 R->L }
% 0.21/0.46 between(c, fresh2(fresh8(between(b, c, c), true, a, b, c, b, c), true, b, inner_pasch(a, b, c, c, b)), a)
% 0.21/0.46 = { by axiom 12 (inner_pasch1) }
% 0.21/0.46 between(c, fresh2(fresh7(between(a, b, c), true, a, b, c, b, c), true, b, inner_pasch(a, b, c, c, b)), a)
% 0.21/0.47 = { by axiom 1 (b_between_a_and_c) }
% 0.21/0.47 between(c, fresh2(fresh7(true, true, a, b, c, b, c), true, b, inner_pasch(a, b, c, c, b)), a)
% 0.21/0.47 = { by axiom 4 (inner_pasch1) }
% 0.21/0.47 between(c, fresh2(true, true, b, inner_pasch(a, b, c, c, b)), a)
% 0.21/0.47 = { by axiom 3 (identity_for_betweeness) }
% 0.21/0.47 between(c, inner_pasch(a, b, c, c, b), a)
% 0.21/0.47 = { by axiom 11 (inner_pasch2) R->L }
% 0.21/0.47 fresh6(true, true, a, b, c, b, c)
% 0.21/0.47 = { by lemma 14 R->L }
% 0.21/0.47 fresh6(between(b, c, c), true, a, b, c, b, c)
% 0.21/0.47 = { by axiom 13 (inner_pasch2) }
% 0.21/0.47 fresh5(between(a, b, c), true, a, b, c, b, c)
% 0.21/0.47 = { by axiom 1 (b_between_a_and_c) }
% 0.21/0.47 fresh5(true, true, a, b, c, b, c)
% 0.21/0.47 = { by axiom 5 (inner_pasch2) }
% 0.21/0.47 true
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47
% 0.21/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
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