TSTP Solution File: GEO117+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 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 23:27:29 EDT 2023
% Result : Theorem 0.20s 0.52s
% 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
% 0.10/0.12 % Problem : GEO117+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.13 % 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 23:22:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.52 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.52
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 Take the following subset of the input axioms:
% 0.20/0.53 fof(between_c_defn, axiom, ![C, P, Q, R]: (between_c(C, P, Q, R) <=> (P!=R & ?[Cpp]: (part_of(Cpp, C) & (end_point(P, Cpp) & (end_point(R, Cpp) & inner_point(Q, Cpp))))))).
% 0.20/0.53 fof(between_o_defn, axiom, ![O, P3, Q2, R2]: (between_o(O, P3, Q2, R2) <=> ((ordered_by(O, P3, Q2) & ordered_by(O, Q2, R2)) | (ordered_by(O, R2, Q2) & ordered_by(O, Q2, P3))))).
% 0.20/0.53 fof(c6, axiom, ![C2, P3]: (end_point(P3, C2) => ?[Q2]: (end_point(Q2, C2) & P3!=Q2))).
% 0.20/0.53 fof(closed_defn, axiom, ![C2]: (closed(C2) <=> ~?[P3]: end_point(P3, C2))).
% 0.20/0.53 fof(inner_point_defn, axiom, ![C2, P3]: (inner_point(P3, C2) <=> (incident_c(P3, C2) & ~end_point(P3, C2)))).
% 0.20/0.53 fof(o3, axiom, ![O2, P2, Q2, R2]: (between_o(O2, P2, Q2, R2) <=> ?[C2]: (![P3]: (incident_o(P3, O2) <=> incident_c(P3, C2)) & between_c(C2, P2, Q2, R2)))).
% 0.20/0.53 fof(theorem_4_4, conjecture, ![O2, P3]: ~ordered_by(O2, P3, P3)).
% 0.20/0.53
% 0.20/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.53 fresh(y, y, x1...xn) = u
% 0.20/0.53 C => fresh(s, t, x1...xn) = v
% 0.20/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.53 variables of u and v.
% 0.20/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.53 input problem has no model of domain size 1).
% 0.20/0.53
% 0.20/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.53
% 0.20/0.53 Axiom 1 (theorem_4_4): ordered_by(o, p, p) = true2.
% 0.20/0.53 Axiom 2 (between_o_defn_4): fresh61(X, X, Y, Z, W, V) = between_o(Y, Z, W, V).
% 0.20/0.53 Axiom 3 (between_o_defn_4): fresh60(X, X, Y, Z, W, V) = true2.
% 0.20/0.53 Axiom 4 (o3_3): fresh32(X, X, Y, Z, W, V) = true2.
% 0.20/0.53 Axiom 5 (between_o_defn_4): fresh61(ordered_by(X, Y, Z), true2, X, W, Y, Z) = fresh60(ordered_by(X, W, Y), true2, X, W, Y, Z).
% 0.20/0.53 Axiom 6 (o3_3): fresh32(between_o(X, Y, Z, W), true2, Y, Z, W, X) = between_c(c(Y, Z, W, X), Y, Z, W).
% 0.20/0.53
% 0.20/0.53 Goal 1 (between_c_defn_5): between_c(X, Y, Z, Y) = true2.
% 0.20/0.53 The goal is true when:
% 0.20/0.53 X = c(p, p, p, o)
% 0.20/0.53 Y = p
% 0.20/0.53 Z = p
% 0.20/0.53
% 0.20/0.53 Proof:
% 0.20/0.53 between_c(c(p, p, p, o), p, p, p)
% 0.20/0.53 = { by axiom 6 (o3_3) R->L }
% 0.20/0.53 fresh32(between_o(o, p, p, p), true2, p, p, p, o)
% 0.20/0.53 = { by axiom 2 (between_o_defn_4) R->L }
% 0.20/0.53 fresh32(fresh61(true2, true2, o, p, p, p), true2, p, p, p, o)
% 0.20/0.53 = { by axiom 1 (theorem_4_4) R->L }
% 0.20/0.53 fresh32(fresh61(ordered_by(o, p, p), true2, o, p, p, p), true2, p, p, p, o)
% 0.20/0.53 = { by axiom 5 (between_o_defn_4) }
% 0.20/0.53 fresh32(fresh60(ordered_by(o, p, p), true2, o, p, p, p), true2, p, p, p, o)
% 0.20/0.53 = { by axiom 1 (theorem_4_4) }
% 0.20/0.53 fresh32(fresh60(true2, true2, o, p, p, p), true2, p, p, p, o)
% 0.20/0.53 = { by axiom 3 (between_o_defn_4) }
% 0.20/0.53 fresh32(true2, true2, p, p, p, o)
% 0.20/0.53 = { by axiom 4 (o3_3) }
% 0.20/0.53 true2
% 0.20/0.53 % SZS output end Proof
% 0.20/0.53
% 0.20/0.53 RESULT: Theorem (the conjecture is true).
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