TSTP Solution File: GEO147-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO147-1 : 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 : n012.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 23:27:38 EDT 2023
% Result : Unsatisfiable 0.19s 0.55s
% 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
% 0.07/0.12 % Problem : GEO147-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % 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 : n012.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 19:49:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.55
% 0.19/0.55 % SZS status Unsatisfiable
% 0.19/0.55
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 Take the following subset of the input axioms:
% 0.19/0.55 fof(at_on_trajectory_10, axiom, ![B, A2]: (~once(at(A2, B)) | incident_o(B, trajectory_of(A2)))).
% 0.19/0.55 fof(conjunction_at_the_same_time_8, axiom, ![B2, A2_2]: (~once(at_the_same_time(A2_2, B2)) | once(A2_2))).
% 0.19/0.55 fof(conjunction_at_the_same_time_9, axiom, ![A, B2]: (~once(at_the_same_time(A, B2)) | once(B2))).
% 0.19/0.55 fof(connect_defn_1, axiom, ![C, B2, A2_2]: (~connect(A2_2, B2, C) | once(at_the_same_time(at(A2_2, C), at(B2, C))))).
% 0.19/0.55 fof(t13_156, negated_conjecture, connect(sk28, sk29, sk27)).
% 0.19/0.55 fof(t13_157, negated_conjecture, ~incident_o(sk27, trajectory_of(sk28)) | ~incident_o(sk27, trajectory_of(sk29))).
% 0.19/0.55 fof(trajectories_are_oriented_curves_12, axiom, ![A3]: trajectory_of(A3)=ax3_sk1(A3)).
% 0.19/0.55
% 0.19/0.55 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.55 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.55 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.55 fresh(y, y, x1...xn) = u
% 0.19/0.55 C => fresh(s, t, x1...xn) = v
% 0.19/0.55 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.55 variables of u and v.
% 0.19/0.55 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.55 input problem has no model of domain size 1).
% 0.19/0.55
% 0.19/0.55 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.55
% 0.19/0.55 Axiom 1 (trajectories_are_oriented_curves_12): trajectory_of(X) = ax3_sk1(X).
% 0.19/0.55 Axiom 2 (conjunction_at_the_same_time_8): fresh62(X, X, Y) = true2.
% 0.19/0.55 Axiom 3 (conjunction_at_the_same_time_9): fresh61(X, X, Y) = true2.
% 0.19/0.55 Axiom 4 (t13_156): connect(sk28, sk29, sk27) = true2.
% 0.19/0.55 Axiom 5 (at_on_trajectory_10): fresh75(X, X, Y, Z) = true2.
% 0.19/0.55 Axiom 6 (connect_defn_1): fresh60(X, X, Y, Z, W) = true2.
% 0.19/0.55 Axiom 7 (conjunction_at_the_same_time_8): fresh62(once(at_the_same_time(X, Y)), true2, X) = once(X).
% 0.19/0.55 Axiom 8 (conjunction_at_the_same_time_9): fresh61(once(at_the_same_time(X, Y)), true2, Y) = once(Y).
% 0.19/0.55 Axiom 9 (at_on_trajectory_10): fresh75(once(at(X, Y)), true2, X, Y) = incident_o(Y, trajectory_of(X)).
% 0.19/0.56 Axiom 10 (connect_defn_1): fresh60(connect(X, Y, Z), true2, X, Y, Z) = once(at_the_same_time(at(X, Z), at(Y, Z))).
% 0.19/0.56
% 0.19/0.56 Lemma 11: fresh75(once(at(X, Y)), true2, X, Y) = incident_o(Y, ax3_sk1(X)).
% 0.19/0.56 Proof:
% 0.19/0.56 fresh75(once(at(X, Y)), true2, X, Y)
% 0.19/0.56 = { by axiom 9 (at_on_trajectory_10) }
% 0.19/0.56 incident_o(Y, trajectory_of(X))
% 0.19/0.56 = { by axiom 1 (trajectories_are_oriented_curves_12) }
% 0.19/0.56 incident_o(Y, ax3_sk1(X))
% 0.19/0.56
% 0.19/0.56 Lemma 12: once(at_the_same_time(at(sk28, sk27), at(sk29, sk27))) = true2.
% 0.19/0.56 Proof:
% 0.19/0.56 once(at_the_same_time(at(sk28, sk27), at(sk29, sk27)))
% 0.19/0.56 = { by axiom 10 (connect_defn_1) R->L }
% 0.19/0.56 fresh60(connect(sk28, sk29, sk27), true2, sk28, sk29, sk27)
% 0.19/0.56 = { by axiom 4 (t13_156) }
% 0.19/0.56 fresh60(true2, true2, sk28, sk29, sk27)
% 0.19/0.56 = { by axiom 6 (connect_defn_1) }
% 0.19/0.56 true2
% 0.19/0.56
% 0.19/0.56 Goal 1 (t13_157): tuple2(incident_o(sk27, trajectory_of(sk28)), incident_o(sk27, trajectory_of(sk29))) = tuple2(true2, true2).
% 0.19/0.56 Proof:
% 0.19/0.56 tuple2(incident_o(sk27, trajectory_of(sk28)), incident_o(sk27, trajectory_of(sk29)))
% 0.19/0.56 = { by axiom 1 (trajectories_are_oriented_curves_12) }
% 0.19/0.56 tuple2(incident_o(sk27, ax3_sk1(sk28)), incident_o(sk27, trajectory_of(sk29)))
% 0.19/0.56 = { by axiom 1 (trajectories_are_oriented_curves_12) }
% 0.19/0.56 tuple2(incident_o(sk27, ax3_sk1(sk28)), incident_o(sk27, ax3_sk1(sk29)))
% 0.19/0.56 = { by lemma 11 R->L }
% 0.19/0.56 tuple2(fresh75(once(at(sk28, sk27)), true2, sk28, sk27), incident_o(sk27, ax3_sk1(sk29)))
% 0.19/0.56 = { by axiom 7 (conjunction_at_the_same_time_8) R->L }
% 0.19/0.56 tuple2(fresh75(fresh62(once(at_the_same_time(at(sk28, sk27), at(sk29, sk27))), true2, at(sk28, sk27)), true2, sk28, sk27), incident_o(sk27, ax3_sk1(sk29)))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 tuple2(fresh75(fresh62(true2, true2, at(sk28, sk27)), true2, sk28, sk27), incident_o(sk27, ax3_sk1(sk29)))
% 0.19/0.56 = { by axiom 2 (conjunction_at_the_same_time_8) }
% 0.19/0.56 tuple2(fresh75(true2, true2, sk28, sk27), incident_o(sk27, ax3_sk1(sk29)))
% 0.19/0.56 = { by axiom 5 (at_on_trajectory_10) }
% 0.19/0.56 tuple2(true2, incident_o(sk27, ax3_sk1(sk29)))
% 0.19/0.56 = { by lemma 11 R->L }
% 0.19/0.56 tuple2(true2, fresh75(once(at(sk29, sk27)), true2, sk29, sk27))
% 0.19/0.56 = { by axiom 8 (conjunction_at_the_same_time_9) R->L }
% 0.19/0.56 tuple2(true2, fresh75(fresh61(once(at_the_same_time(at(sk28, sk27), at(sk29, sk27))), true2, at(sk29, sk27)), true2, sk29, sk27))
% 0.19/0.56 = { by lemma 12 }
% 0.19/0.56 tuple2(true2, fresh75(fresh61(true2, true2, at(sk29, sk27)), true2, sk29, sk27))
% 0.19/0.56 = { by axiom 3 (conjunction_at_the_same_time_9) }
% 0.19/0.56 tuple2(true2, fresh75(true2, true2, sk29, sk27))
% 0.19/0.56 = { by axiom 5 (at_on_trajectory_10) }
% 0.19/0.56 tuple2(true2, true2)
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56
% 0.19/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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