TSTP Solution File: CSR023+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CSR023+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 : n002.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 0.20s 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
% 0.11/0.12 % Problem : CSR023+1 : TPTP v8.1.2. Bugfixed v3.1.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n002.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 : Mon Aug 28 07:37:04 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.52 Command-line arguments: --no-flatten-goal
% 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:
% 0.20/0.52 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)))))).
% 0.20/0.52 fof(happens_holds, axiom, ![Fluent, Time2, Event2]: ((happens(Event2, Time2) & initiates(Event2, Fluent, Time2)) => holdsAt(Fluent, plus(Time2, n1)))).
% 0.20/0.52 fof(initiates_all_defn, axiom, ![Time2, Fluent2, Event2]: (initiates(Event2, Fluent2, Time2) <=> ((Event2=push & (Fluent2=forwards & ~happens(pull, Time2))) | ((Event2=pull & (Fluent2=backwards & ~happens(push, Time2))) | (Event2=pull & (Fluent2=spinning & happens(push, Time2))))))).
% 0.20/0.52 fof(plus1_2, axiom, plus(n1, n2)=n3).
% 0.20/0.52 fof(spinning_3, conjecture, holdsAt(spinning, n3)).
% 0.20/0.52 fof(symmetry_of_plus, axiom, ![X, Y]: plus(X, Y)=plus(Y, X)).
% 0.20/0.52
% 0.20/0.52 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.52 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.52 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.52 fresh(y, y, x1...xn) = u
% 0.20/0.52 C => fresh(s, t, x1...xn) = v
% 0.20/0.52 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.52 variables of u and v.
% 0.20/0.52 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.52 input problem has no model of domain size 1).
% 0.20/0.52
% 0.20/0.52 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.52
% 0.20/0.52 Axiom 1 (symmetry_of_plus): plus(X, Y) = plus(Y, X).
% 0.20/0.52 Axiom 2 (plus1_2): plus(n1, n2) = n3.
% 0.20/0.52 Axiom 3 (happens_all_defn_1): fresh56(X, X, Y, Z) = happens(Y, Z).
% 0.20/0.52 Axiom 4 (happens_all_defn_1): fresh55(X, X, Y, Z) = true2.
% 0.20/0.52 Axiom 5 (happens_all_defn_1): fresh56(X, n2, Y, X) = fresh55(Y, push, Y, X).
% 0.20/0.52 Axiom 6 (happens_all_defn_3): fresh51(X, X, Y, Z) = happens(Y, Z).
% 0.20/0.52 Axiom 7 (happens_all_defn_3): fresh50(X, X, Y, Z) = true2.
% 0.20/0.52 Axiom 8 (happens_all_defn_3): fresh51(X, n2, Y, X) = fresh50(Y, pull, Y, X).
% 0.20/0.52 Axiom 9 (happens_holds): fresh48(X, X, Y, Z) = true2.
% 0.20/0.52 Axiom 10 (initiates_all_defn_2): fresh64(X, X, Y, Z, W) = true2.
% 0.20/0.52 Axiom 11 (initiates_all_defn_2): fresh63(X, X, Y, Z, W) = fresh64(Y, pull, Y, Z, W).
% 0.20/0.52 Axiom 12 (happens_holds): fresh49(X, X, Y, Z, W) = holdsAt(W, plus(Z, n1)).
% 0.20/0.52 Axiom 13 (initiates_all_defn_2): fresh43(X, X, Y, Z, W) = initiates(Y, Z, W).
% 0.20/0.52 Axiom 14 (initiates_all_defn_2): fresh63(happens(push, X), true2, Y, Z, X) = fresh43(Z, spinning, Y, Z, X).
% 0.20/0.52 Axiom 15 (happens_holds): fresh49(initiates(X, Y, Z), true2, X, Z, Y) = fresh48(happens(X, Z), true2, Z, Y).
% 0.20/0.52
% 0.20/0.52 Goal 1 (spinning_3): holdsAt(spinning, n3) = true2.
% 0.20/0.52 Proof:
% 0.20/0.52 holdsAt(spinning, n3)
% 0.20/0.52 = { by axiom 2 (plus1_2) R->L }
% 0.20/0.52 holdsAt(spinning, plus(n1, n2))
% 0.20/0.52 = { by axiom 1 (symmetry_of_plus) }
% 0.20/0.52 holdsAt(spinning, plus(n2, n1))
% 0.20/0.52 = { by axiom 12 (happens_holds) R->L }
% 0.20/0.52 fresh49(true2, true2, pull, n2, spinning)
% 0.20/0.52 = { by axiom 10 (initiates_all_defn_2) R->L }
% 0.20/0.52 fresh49(fresh64(pull, pull, pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.52 = { by axiom 11 (initiates_all_defn_2) R->L }
% 0.20/0.52 fresh49(fresh63(true2, true2, pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.53 = { by axiom 4 (happens_all_defn_1) R->L }
% 0.20/0.53 fresh49(fresh63(fresh55(push, push, push, n2), true2, pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.53 = { by axiom 5 (happens_all_defn_1) R->L }
% 0.20/0.53 fresh49(fresh63(fresh56(n2, n2, push, n2), true2, pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.53 = { by axiom 3 (happens_all_defn_1) }
% 0.20/0.53 fresh49(fresh63(happens(push, n2), true2, pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.53 = { by axiom 14 (initiates_all_defn_2) }
% 0.20/0.53 fresh49(fresh43(spinning, spinning, pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.53 = { by axiom 13 (initiates_all_defn_2) }
% 0.20/0.53 fresh49(initiates(pull, spinning, n2), true2, pull, n2, spinning)
% 0.20/0.53 = { by axiom 15 (happens_holds) }
% 0.20/0.53 fresh48(happens(pull, n2), true2, n2, spinning)
% 0.20/0.53 = { by axiom 6 (happens_all_defn_3) R->L }
% 0.20/0.53 fresh48(fresh51(n2, n2, pull, n2), true2, n2, spinning)
% 0.20/0.53 = { by axiom 8 (happens_all_defn_3) }
% 0.20/0.53 fresh48(fresh50(pull, pull, pull, n2), true2, n2, spinning)
% 0.20/0.53 = { by axiom 7 (happens_all_defn_3) }
% 0.20/0.53 fresh48(true2, true2, n2, spinning)
% 0.20/0.53 = { by axiom 9 (happens_holds) }
% 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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