TSTP Solution File: CSR021+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR021+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 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 : n032.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 21:40:59 EDT 2023
% Result : Theorem 0.16s 0.46s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : CSR021+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon Aug 28 09:06:45 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.46 Command-line arguments: --no-flatten-goal
% 0.16/0.46
% 0.16/0.46 % SZS status Theorem
% 0.16/0.46
% 0.16/0.46 % SZS output start Proof
% 0.16/0.46 Take the following subset of the input axioms:
% 0.16/0.47 fof(happens_all_defn, axiom, ![Event, Time]: (happens(Event, Time) <=> ((Event=push & Time=n0) | ((Event=pull & Time=n1) | ((Event=pull & Time=n2) | (Event=push & Time=n2)))))).
% 0.16/0.47 fof(happens_not_released, axiom, ![Fluent, Time2, Event2]: ((happens(Event2, Time2) & (initiates(Event2, Fluent, Time2) | terminates(Event2, Fluent, Time2))) => ~releasedAt(Fluent, plus(Time2, n1)))).
% 0.16/0.47 fof(happens_terminates_not_holds, axiom, ![Time2, Fluent2, Event2]: ((happens(Event2, Time2) & terminates(Event2, Fluent2, Time2)) => ~holdsAt(Fluent2, plus(Time2, n1)))).
% 0.16/0.47 fof(less0, axiom, ~?[X]: less(X, n0)).
% 0.16/0.47 fof(less_property, axiom, ![Y, X2]: (less(X2, Y) <=> (~less(Y, X2) & Y!=X2))).
% 0.16/0.47 fof(not_backwards_3, conjecture, ~holdsAt(backwards, n3)).
% 0.16/0.47 fof(not_releasedAt, hypothesis, ![Time2, Fluent2]: ~releasedAt(Fluent2, Time2)).
% 0.16/0.47 fof(plus1_2, axiom, plus(n1, n2)=n3).
% 0.16/0.47 fof(releases_all_defn, axiom, ![Time2, Fluent2, Event2]: ~releases(Event2, Fluent2, Time2)).
% 0.16/0.47 fof(symmetry_of_plus, axiom, ![X2, Y2]: plus(X2, Y2)=plus(Y2, X2)).
% 0.16/0.47 fof(terminates_all_defn, axiom, ![Time2, Fluent2, Event2]: (terminates(Event2, Fluent2, Time2) <=> ((Event2=push & (Fluent2=backwards & ~happens(pull, Time2))) | ((Event2=pull & (Fluent2=forwards & ~happens(push, Time2))) | ((Event2=pull & (Fluent2=forwards & happens(push, Time2))) | ((Event2=pull & (Fluent2=backwards & happens(push, Time2))) | ((Event2=push & (Fluent2=spinning & ~happens(pull, Time2))) | (Event2=pull & (Fluent2=spinning & ~happens(push, Time2)))))))))).
% 0.16/0.47
% 0.16/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.16/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.16/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.16/0.47 fresh(y, y, x1...xn) = u
% 0.16/0.47 C => fresh(s, t, x1...xn) = v
% 0.16/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.16/0.47 variables of u and v.
% 0.16/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.16/0.47 input problem has no model of domain size 1).
% 0.16/0.47
% 0.16/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.16/0.47
% 0.16/0.47 Axiom 1 (not_backwards_3): holdsAt(backwards, n3) = true2.
% 0.16/0.47 Axiom 2 (symmetry_of_plus): plus(X, Y) = plus(Y, X).
% 0.16/0.47 Axiom 3 (plus1_2): plus(n1, n2) = n3.
% 0.16/0.47 Axiom 4 (happens_all_defn_1): fresh56(X, X, Y, Z) = happens(Y, Z).
% 0.16/0.47 Axiom 5 (happens_all_defn_1): fresh55(X, X, Y, Z) = true2.
% 0.16/0.47 Axiom 6 (happens_all_defn_1): fresh56(X, n2, Y, X) = fresh55(Y, push, Y, X).
% 0.16/0.47 Axiom 7 (happens_all_defn_3): fresh51(X, X, Y, Z) = happens(Y, Z).
% 0.16/0.47 Axiom 8 (happens_all_defn_3): fresh50(X, X, Y, Z) = true2.
% 0.16/0.47 Axiom 9 (happens_all_defn_3): fresh51(X, n2, Y, X) = fresh50(Y, pull, Y, X).
% 0.16/0.47 Axiom 10 (terminates_all_defn_4): fresh62(X, X, Y, Z, W) = true2.
% 0.16/0.47 Axiom 11 (terminates_all_defn_4): fresh61(X, X, Y, Z, W) = fresh62(Y, pull, Y, Z, W).
% 0.16/0.47 Axiom 12 (terminates_all_defn_4): fresh7(X, X, Y, Z, W) = terminates(Y, Z, W).
% 0.16/0.47 Axiom 13 (terminates_all_defn_4): fresh61(happens(push, X), true2, Y, Z, X) = fresh7(Z, backwards, Y, Z, X).
% 0.16/0.47
% 0.16/0.47 Goal 1 (happens_terminates_not_holds): tuple(happens(X, Y), terminates(X, Z, Y), holdsAt(Z, plus(Y, n1))) = tuple(true2, true2, true2).
% 0.16/0.47 The goal is true when:
% 0.16/0.47 X = pull
% 0.16/0.47 Y = n2
% 0.16/0.47 Z = backwards
% 0.16/0.47
% 0.16/0.47 Proof:
% 0.16/0.47 tuple(happens(pull, n2), terminates(pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 12 (terminates_all_defn_4) R->L }
% 0.16/0.47 tuple(happens(pull, n2), fresh7(backwards, backwards, pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 13 (terminates_all_defn_4) R->L }
% 0.16/0.47 tuple(happens(pull, n2), fresh61(happens(push, n2), true2, pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 4 (happens_all_defn_1) R->L }
% 0.16/0.47 tuple(happens(pull, n2), fresh61(fresh56(n2, n2, push, n2), true2, pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 6 (happens_all_defn_1) }
% 0.16/0.47 tuple(happens(pull, n2), fresh61(fresh55(push, push, push, n2), true2, pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 5 (happens_all_defn_1) }
% 0.16/0.47 tuple(happens(pull, n2), fresh61(true2, true2, pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 11 (terminates_all_defn_4) }
% 0.16/0.47 tuple(happens(pull, n2), fresh62(pull, pull, pull, backwards, n2), holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 10 (terminates_all_defn_4) }
% 0.16/0.47 tuple(happens(pull, n2), true2, holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 7 (happens_all_defn_3) R->L }
% 0.16/0.47 tuple(fresh51(n2, n2, pull, n2), true2, holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 9 (happens_all_defn_3) }
% 0.16/0.47 tuple(fresh50(pull, pull, pull, n2), true2, holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 8 (happens_all_defn_3) }
% 0.16/0.47 tuple(true2, true2, holdsAt(backwards, plus(n2, n1)))
% 0.16/0.47 = { by axiom 2 (symmetry_of_plus) R->L }
% 0.16/0.47 tuple(true2, true2, holdsAt(backwards, plus(n1, n2)))
% 0.16/0.47 = { by axiom 3 (plus1_2) }
% 0.16/0.47 tuple(true2, true2, holdsAt(backwards, n3))
% 0.16/0.47 = { by axiom 1 (not_backwards_3) }
% 0.16/0.47 tuple(true2, true2, true2)
% 0.16/0.47 % SZS output end Proof
% 0.16/0.47
% 0.16/0.47 RESULT: Theorem (the conjecture is true).
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