TSTP Solution File: GEO178+2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GEO178+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n008.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 23:27:48 EDT 2023
% Result : Theorem 0.19s 0.39s
% 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 : GEO178+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 22:36:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --ground-connectedness --complete-subsets
% 0.19/0.39
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Take the following subset of the input axioms:
% 0.19/0.39 fof(con, conjecture, ![X, Y, Z]: ((distinct_points(X, Y) & apart_point_and_line(Z, line_connecting(X, Y))) => (distinct_points(Z, X) & distinct_points(Z, Y)))).
% 0.19/0.39 fof(con1, axiom, ![X2, Y2, Z2]: (distinct_points(X2, Y2) => (apart_point_and_line(Z2, line_connecting(X2, Y2)) => (distinct_points(Z2, X2) & distinct_points(Z2, Y2))))).
% 0.19/0.39
% 0.19/0.39 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.39 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.39 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.39 fresh(y, y, x1...xn) = u
% 0.19/0.39 C => fresh(s, t, x1...xn) = v
% 0.19/0.39 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.39 variables of u and v.
% 0.19/0.39 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.39 input problem has no model of domain size 1).
% 0.19/0.39
% 0.19/0.39 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.39
% 0.19/0.39 Axiom 1 (con): distinct_points(x, y) = true2.
% 0.19/0.39 Axiom 2 (con1): fresh7(X, X, Y, Z) = true2.
% 0.19/0.39 Axiom 3 (con1_1): fresh5(X, X, Y, Z) = true2.
% 0.19/0.39 Axiom 4 (con_1): apart_point_and_line(z, line_connecting(x, y)) = true2.
% 0.19/0.39 Axiom 5 (con1): fresh9(X, X, Y, Z, W) = distinct_points(W, Y).
% 0.19/0.39 Axiom 6 (con1_1): fresh6(X, X, Y, Z, W) = distinct_points(W, Z).
% 0.19/0.39 Axiom 7 (con1): fresh9(apart_point_and_line(X, line_connecting(Y, Z)), true2, Y, Z, X) = fresh7(distinct_points(Y, Z), true2, Y, X).
% 0.19/0.39 Axiom 8 (con1_1): fresh6(apart_point_and_line(X, line_connecting(Y, Z)), true2, Y, Z, X) = fresh5(distinct_points(Y, Z), true2, Z, X).
% 0.19/0.39
% 0.19/0.39 Goal 1 (con_2): tuple(distinct_points(z, x), distinct_points(z, y)) = tuple(true2, true2).
% 0.19/0.39 Proof:
% 0.19/0.39 tuple(distinct_points(z, x), distinct_points(z, y))
% 0.19/0.39 = { by axiom 6 (con1_1) R->L }
% 0.19/0.39 tuple(distinct_points(z, x), fresh6(true2, true2, x, y, z))
% 0.19/0.39 = { by axiom 4 (con_1) R->L }
% 0.19/0.39 tuple(distinct_points(z, x), fresh6(apart_point_and_line(z, line_connecting(x, y)), true2, x, y, z))
% 0.19/0.39 = { by axiom 8 (con1_1) }
% 0.19/0.39 tuple(distinct_points(z, x), fresh5(distinct_points(x, y), true2, y, z))
% 0.19/0.39 = { by axiom 1 (con) }
% 0.19/0.39 tuple(distinct_points(z, x), fresh5(true2, true2, y, z))
% 0.19/0.39 = { by axiom 3 (con1_1) }
% 0.19/0.39 tuple(distinct_points(z, x), true2)
% 0.19/0.39 = { by axiom 5 (con1) R->L }
% 0.19/0.39 tuple(fresh9(true2, true2, x, y, z), true2)
% 0.19/0.39 = { by axiom 4 (con_1) R->L }
% 0.19/0.39 tuple(fresh9(apart_point_and_line(z, line_connecting(x, y)), true2, x, y, z), true2)
% 0.19/0.39 = { by axiom 7 (con1) }
% 0.19/0.39 tuple(fresh7(distinct_points(x, y), true2, x, z), true2)
% 0.19/0.39 = { by axiom 1 (con) }
% 0.19/0.39 tuple(fresh7(true2, true2, x, z), true2)
% 0.19/0.39 = { by axiom 2 (con1) }
% 0.19/0.39 tuple(true2, true2)
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Theorem (the conjecture is true).
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