TSTP Solution File: GEO008-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO008-1 : 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 : n005.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 23:26:46 EDT 2023
% Result : Timeout 294.14s 38.04s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO008-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.12/0.13 % 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 : n005.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 19:52:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 294.14/38.04 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 294.14/38.04
% 294.14/38.04 % SZS status Unsatisfiable
% 294.14/38.04
% 294.78/38.05 % SZS output start Proof
% 294.78/38.05 Take the following subset of the input axioms:
% 294.78/38.05 fof(b_between_c_and_d, hypothesis, between(c, b, d)).
% 294.78/38.05 fof(c_between_a_and_e, hypothesis, between(a, c, e)).
% 294.78/38.05 fof(d_between_a_and_e, hypothesis, between(a, d, e)).
% 294.78/38.05 fof(identity_for_betweeness, axiom, ![X, Y]: (~between(X, Y, X) | X=Y)).
% 294.78/38.05 fof(identity_for_equidistance, axiom, ![Z, X2, Y2]: (~equidistant(X2, Y2, Z, Z) | X2=Y2)).
% 294.78/38.05 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)))).
% 294.78/38.05 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))))).
% 294.78/38.05 fof(prove_betweenness, negated_conjecture, ~between(a, b, e)).
% 294.78/38.05 fof(segment_construction1, axiom, ![V2, X2, Y2, W2]: between(X2, Y2, extension(X2, Y2, W2, V2))).
% 294.78/38.05 fof(segment_construction2, axiom, ![V2, X2, Y2, W2]: equidistant(Y2, extension(X2, Y2, W2, V2), W2, V2)).
% 294.78/38.05
% 294.78/38.05 Now clausify the problem and encode Horn clauses using encoding 3 of
% 294.78/38.05 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 294.78/38.05 We repeatedly replace C & s=t => u=v by the two clauses:
% 294.78/38.05 fresh(y, y, x1...xn) = u
% 294.78/38.05 C => fresh(s, t, x1...xn) = v
% 294.78/38.05 where fresh is a fresh function symbol and x1..xn are the free
% 294.78/38.05 variables of u and v.
% 294.78/38.05 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 294.78/38.05 input problem has no model of domain size 1).
% 294.78/38.05
% 294.78/38.05 The encoding turns the above axioms into the following unit equations and goals:
% 294.78/38.05
% 294.78/38.05 Axiom 1 (c_between_a_and_e): between(a, c, e) = true.
% 294.78/38.05 Axiom 2 (d_between_a_and_e): between(a, d, e) = true.
% 294.78/38.05 Axiom 3 (b_between_c_and_d): between(c, b, d) = true.
% 294.78/38.05 Axiom 4 (identity_for_equidistance): fresh(X, X, Y, Z) = Z.
% 294.78/38.05 Axiom 5 (identity_for_betweeness): fresh2(X, X, Y, Z) = Z.
% 294.78/38.05 Axiom 6 (segment_construction1): between(X, Y, extension(X, Y, Z, W)) = true.
% 294.78/38.05 Axiom 7 (identity_for_betweeness): fresh2(between(X, Y, X), true, X, Y) = X.
% 294.78/38.05 Axiom 8 (segment_construction2): equidistant(X, extension(Y, X, Z, W), Z, W) = true.
% 294.78/38.05 Axiom 9 (identity_for_equidistance): fresh(equidistant(X, Y, Z, Z), true, X, Y) = X.
% 294.78/38.05 Axiom 10 (outer_pasch1): fresh10(X, X, Y, Z, W, V, U) = between(Y, outer_pasch(Z, Y, V, U, W), V).
% 294.78/38.05 Axiom 11 (outer_pasch1): fresh9(X, X, Y, Z, W, V, U) = true.
% 294.78/38.05 Axiom 12 (outer_pasch2): fresh8(X, X, Y, Z, W, V, U) = between(U, Z, outer_pasch(Z, Y, V, U, W)).
% 294.78/38.05 Axiom 13 (outer_pasch2): fresh7(X, X, Y, Z, W, V, U) = true.
% 294.78/38.05 Axiom 14 (outer_pasch1): fresh10(between(X, Y, Z), true, W, V, Y, X, Z) = fresh9(between(W, V, Y), true, W, V, Y, X, Z).
% 294.78/38.05 Axiom 15 (outer_pasch2): fresh8(between(X, Y, Z), true, W, V, Y, X, Z) = fresh7(between(W, V, Y), true, W, V, Y, X, Z).
% 294.78/38.05
% 294.78/38.05 Lemma 16: between(X, Y, Y) = true.
% 294.78/38.05 Proof:
% 294.78/38.05 between(X, Y, Y)
% 294.78/38.05 = { by axiom 9 (identity_for_equidistance) R->L }
% 294.78/38.05 between(X, Y, fresh(equidistant(Y, extension(X, Y, Z, Z), Z, Z), true, Y, extension(X, Y, Z, Z)))
% 294.78/38.05 = { by axiom 8 (segment_construction2) }
% 294.78/38.05 between(X, Y, fresh(true, true, Y, extension(X, Y, Z, Z)))
% 294.78/38.05 = { by axiom 4 (identity_for_equidistance) }
% 294.78/38.05 between(X, Y, extension(X, Y, Z, Z))
% 294.78/38.05 = { by axiom 6 (segment_construction1) }
% 294.78/38.05 true
% 294.78/38.05
% 294.78/38.05 Lemma 17: between(c, outer_pasch(b, c, a, e, d), a) = true.
% 294.78/38.05 Proof:
% 294.78/38.05 between(c, outer_pasch(b, c, a, e, d), a)
% 294.78/38.05 = { by axiom 10 (outer_pasch1) R->L }
% 294.78/38.05 fresh10(true, true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 2 (d_between_a_and_e) R->L }
% 294.78/38.05 fresh10(between(a, d, e), true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 14 (outer_pasch1) }
% 294.78/38.05 fresh9(between(c, b, d), true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 3 (b_between_c_and_d) }
% 294.78/38.05 fresh9(true, true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 11 (outer_pasch1) }
% 294.78/38.05 true
% 294.78/38.05
% 294.78/38.05 Lemma 18: between(a, outer_pasch(b, c, a, e, d), c) = true.
% 294.78/38.05 Proof:
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), c)
% 294.78/38.05 = { by axiom 7 (identity_for_betweeness) R->L }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), fresh2(between(c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a), c), true, c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a)))
% 294.78/38.05 = { by axiom 10 (outer_pasch1) R->L }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), fresh2(fresh10(true, true, c, outer_pasch(b, c, a, e, d), a, c, a), true, c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a)))
% 294.78/38.05 = { by lemma 16 R->L }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), fresh2(fresh10(between(c, a, a), true, c, outer_pasch(b, c, a, e, d), a, c, a), true, c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a)))
% 294.78/38.05 = { by axiom 14 (outer_pasch1) }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), fresh2(fresh9(between(c, outer_pasch(b, c, a, e, d), a), true, c, outer_pasch(b, c, a, e, d), a, c, a), true, c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a)))
% 294.78/38.05 = { by lemma 17 }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), fresh2(fresh9(true, true, c, outer_pasch(b, c, a, e, d), a, c, a), true, c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a)))
% 294.78/38.05 = { by axiom 11 (outer_pasch1) }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), fresh2(true, true, c, outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a)))
% 294.78/38.05 = { by axiom 5 (identity_for_betweeness) }
% 294.78/38.05 between(a, outer_pasch(b, c, a, e, d), outer_pasch(outer_pasch(b, c, a, e, d), c, c, a, a))
% 294.78/38.05 = { by axiom 12 (outer_pasch2) R->L }
% 294.78/38.05 fresh8(true, true, c, outer_pasch(b, c, a, e, d), a, c, a)
% 294.78/38.05 = { by lemma 16 R->L }
% 294.78/38.05 fresh8(between(c, a, a), true, c, outer_pasch(b, c, a, e, d), a, c, a)
% 294.78/38.05 = { by axiom 15 (outer_pasch2) }
% 294.78/38.05 fresh7(between(c, outer_pasch(b, c, a, e, d), a), true, c, outer_pasch(b, c, a, e, d), a, c, a)
% 294.78/38.05 = { by lemma 17 }
% 294.78/38.05 fresh7(true, true, c, outer_pasch(b, c, a, e, d), a, c, a)
% 294.78/38.05 = { by axiom 13 (outer_pasch2) }
% 294.78/38.05 true
% 294.78/38.05
% 294.78/38.05 Lemma 19: between(e, b, outer_pasch(b, c, a, e, d)) = true.
% 294.78/38.05 Proof:
% 294.78/38.05 between(e, b, outer_pasch(b, c, a, e, d))
% 294.78/38.05 = { by axiom 12 (outer_pasch2) R->L }
% 294.78/38.05 fresh8(true, true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 2 (d_between_a_and_e) R->L }
% 294.78/38.05 fresh8(between(a, d, e), true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 15 (outer_pasch2) }
% 294.78/38.05 fresh7(between(c, b, d), true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 3 (b_between_c_and_d) }
% 294.78/38.05 fresh7(true, true, c, b, d, a, e)
% 294.78/38.05 = { by axiom 13 (outer_pasch2) }
% 294.78/38.05 true
% 294.78/38.05
% 294.78/38.05 Lemma 20: between(e, outer_pasch(b, c, a, e, d), a) = true.
% 294.78/38.05 Proof:
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), a)
% 294.78/38.05 = { by axiom 7 (identity_for_betweeness) R->L }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), fresh2(between(a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c), a), true, a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c)))
% 294.78/38.05 = { by axiom 10 (outer_pasch1) R->L }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), fresh2(fresh10(true, true, a, outer_pasch(b, c, a, e, d), c, a, e), true, a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c)))
% 294.78/38.05 = { by axiom 1 (c_between_a_and_e) R->L }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), fresh2(fresh10(between(a, c, e), true, a, outer_pasch(b, c, a, e, d), c, a, e), true, a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c)))
% 294.78/38.05 = { by axiom 14 (outer_pasch1) }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), fresh2(fresh9(between(a, outer_pasch(b, c, a, e, d), c), true, a, outer_pasch(b, c, a, e, d), c, a, e), true, a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c)))
% 294.78/38.05 = { by lemma 18 }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), fresh2(fresh9(true, true, a, outer_pasch(b, c, a, e, d), c, a, e), true, a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c)))
% 294.78/38.05 = { by axiom 11 (outer_pasch1) }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), fresh2(true, true, a, outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c)))
% 294.78/38.05 = { by axiom 5 (identity_for_betweeness) }
% 294.78/38.05 between(e, outer_pasch(b, c, a, e, d), outer_pasch(outer_pasch(b, c, a, e, d), a, a, e, c))
% 294.78/38.05 = { by axiom 12 (outer_pasch2) R->L }
% 294.78/38.06 fresh8(true, true, a, outer_pasch(b, c, a, e, d), c, a, e)
% 294.78/38.06 = { by axiom 1 (c_between_a_and_e) R->L }
% 294.78/38.06 fresh8(between(a, c, e), true, a, outer_pasch(b, c, a, e, d), c, a, e)
% 294.78/38.06 = { by axiom 15 (outer_pasch2) }
% 294.78/38.06 fresh7(between(a, outer_pasch(b, c, a, e, d), c), true, a, outer_pasch(b, c, a, e, d), c, a, e)
% 294.78/38.06 = { by lemma 18 }
% 294.78/38.06 fresh7(true, true, a, outer_pasch(b, c, a, e, d), c, a, e)
% 294.78/38.06 = { by axiom 13 (outer_pasch2) }
% 294.78/38.06 true
% 294.78/38.06
% 294.78/38.06 Goal 1 (prove_betweenness): between(a, b, e) = true.
% 294.78/38.06 Proof:
% 294.78/38.06 between(a, b, e)
% 294.78/38.06 = { by axiom 7 (identity_for_betweeness) R->L }
% 294.78/38.06 between(a, b, fresh2(between(e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d)), e), true, e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d))))
% 294.78/38.06 = { by axiom 10 (outer_pasch1) R->L }
% 294.78/38.06 between(a, b, fresh2(fresh10(true, true, e, b, outer_pasch(b, c, a, e, d), e, a), true, e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d))))
% 294.78/38.06 = { by lemma 20 R->L }
% 294.78/38.06 between(a, b, fresh2(fresh10(between(e, outer_pasch(b, c, a, e, d), a), true, e, b, outer_pasch(b, c, a, e, d), e, a), true, e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d))))
% 294.78/38.06 = { by axiom 14 (outer_pasch1) }
% 294.78/38.06 between(a, b, fresh2(fresh9(between(e, b, outer_pasch(b, c, a, e, d)), true, e, b, outer_pasch(b, c, a, e, d), e, a), true, e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d))))
% 294.78/38.06 = { by lemma 19 }
% 294.78/38.06 between(a, b, fresh2(fresh9(true, true, e, b, outer_pasch(b, c, a, e, d), e, a), true, e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d))))
% 294.78/38.06 = { by axiom 11 (outer_pasch1) }
% 294.78/38.06 between(a, b, fresh2(true, true, e, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d))))
% 294.78/38.06 = { by axiom 5 (identity_for_betweeness) }
% 294.78/38.06 between(a, b, outer_pasch(b, e, e, a, outer_pasch(b, c, a, e, d)))
% 294.78/38.06 = { by axiom 12 (outer_pasch2) R->L }
% 294.78/38.06 fresh8(true, true, e, b, outer_pasch(b, c, a, e, d), e, a)
% 294.78/38.06 = { by lemma 20 R->L }
% 294.78/38.06 fresh8(between(e, outer_pasch(b, c, a, e, d), a), true, e, b, outer_pasch(b, c, a, e, d), e, a)
% 294.78/38.06 = { by axiom 15 (outer_pasch2) }
% 294.78/38.06 fresh7(between(e, b, outer_pasch(b, c, a, e, d)), true, e, b, outer_pasch(b, c, a, e, d), e, a)
% 294.78/38.06 = { by lemma 19 }
% 294.78/38.06 fresh7(true, true, e, b, outer_pasch(b, c, a, e, d), e, a)
% 294.78/38.06 = { by axiom 13 (outer_pasch2) }
% 294.78/38.06 true
% 294.78/38.06 % SZS output end Proof
% 294.78/38.06
% 294.78/38.06 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------