0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.11	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.11/0.32	% Computer   : n025.cluster.edu
0.11/0.32	% Model      : x86_64 x86_64
0.11/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory     : 8042.1875MB
0.11/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 960
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Thu Jul  2 06:46:33 EDT 2020
0.11/0.32	% CPUTime    : 
0.16/0.50	% SZS status Theorem
0.16/0.50	
0.16/0.50	% SZS output start Proof
0.16/0.50	Take the following subset of the input axioms:
0.16/0.50	  fof(happens_all_defn, axiom, ![Time, Event]: (((Time=n0 & Event=push) | ((Time=n2 & push=Event) | ((pull=Event & Time=n2) | (n1=Time & pull=Event)))) <=> happens(Event, Time))).
0.16/0.50	  fof(happens_holds, axiom, ![Fluent, Time, Event]: ((initiates(Event, Fluent, Time) & happens(Event, Time)) => holdsAt(Fluent, plus(Time, n1)))).
0.16/0.50	  fof(initiates_all_defn, axiom, ![Fluent, Time, Event]: (((Event=pull & (spinning=Fluent & happens(push, Time))) | ((Fluent=forwards & (push=Event & ~happens(pull, Time))) | (Fluent=backwards & (Event=pull & ~happens(push, Time))))) <=> initiates(Event, Fluent, Time))).
0.16/0.50	  fof(plus1_2, axiom, n3=plus(n1, n2)).
0.16/0.50	  fof(spinning_3, conjecture, holdsAt(spinning, n3)).
0.16/0.50	  fof(symmetry_of_plus, axiom, ![X, Y]: plus(Y, X)=plus(X, Y)).
0.16/0.50	
0.16/0.50	Now clausify the problem and encode Horn clauses using encoding 3 of
0.16/0.50	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.16/0.50	We repeatedly replace C & s=t => u=v by the two clauses:
0.16/0.50	  fresh(y, y, x1...xn) = u
0.16/0.50	  C => fresh(s, t, x1...xn) = v
0.16/0.50	where fresh is a fresh function symbol and x1..xn are the free
0.16/0.50	variables of u and v.
0.16/0.50	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.16/0.50	input problem has no model of domain size 1).
0.16/0.50	
0.16/0.50	The encoding turns the above axioms into the following unit equations and goals:
0.16/0.50	
0.16/0.50	Axiom 1 (happens_all_defn_1): fresh53(X, X, Y, Z) = happens(Y, Z).
0.16/0.50	Axiom 2 (happens_all_defn_1): fresh52(X, X, Y, Z) = true2.
0.16/0.50	Axiom 3 (happens_all_defn_3): fresh49(X, X, Y, Z) = happens(Y, Z).
0.16/0.50	Axiom 4 (happens_all_defn_3): fresh48(X, X, Y, Z) = true2.
0.16/0.50	Axiom 5 (happens_holds): fresh47(X, X, Y, Z, W) = holdsAt(W, plus(Z, n1)).
0.16/0.50	Axiom 6 (happens_holds): fresh46(X, X, Y, Z) = true2.
0.16/0.50	Axiom 7 (initiates_all_defn_1): fresh43(X, X, Y, Z, W) = initiates(Y, Z, W).
0.16/0.50	Axiom 8 (initiates_all_defn_1): fresh57(X, X, Y, Z, W) = true2.
0.16/0.50	Axiom 9 (initiates_all_defn_1): fresh56(X, X, Y, Z, W) = fresh57(Y, pull, Y, Z, W).
0.16/0.50	Axiom 10 (happens_holds): fresh47(happens(X, Y), true2, X, Y, Z) = fresh46(initiates(X, Z, Y), true2, Y, Z).
0.16/0.50	Axiom 11 (initiates_all_defn_1): fresh56(happens(push, X), true2, Y, Z, X) = fresh43(spinning, Z, Y, Z, X).
0.16/0.50	Axiom 12 (happens_all_defn_3): fresh49(X, n2, Y, X) = fresh48(push, Y, Y, X).
0.16/0.50	Axiom 13 (happens_all_defn_1): fresh53(X, n2, Y, X) = fresh52(pull, Y, Y, X).
0.16/0.50	Axiom 14 (plus1_2): n3 = plus(n1, n2).
0.16/0.50	Axiom 15 (symmetry_of_plus): plus(X, Y) = plus(Y, X).
0.16/0.50	
0.16/0.50	Goal 1 (spinning_3): holdsAt(spinning, n3) = true2.
0.16/0.50	Proof:
0.16/0.50	  holdsAt(spinning, n3)
0.16/0.50	= { by axiom 14 (plus1_2) }
0.16/0.50	  holdsAt(spinning, plus(n1, n2))
0.16/0.50	= { by axiom 15 (symmetry_of_plus) }
0.16/0.50	  holdsAt(spinning, plus(n2, n1))
0.16/0.50	= { by axiom 5 (happens_holds) }
0.16/0.50	  fresh47(true2, true2, pull, n2, spinning)
0.16/0.50	= { by axiom 2 (happens_all_defn_1) }
0.16/0.50	  fresh47(fresh52(pull, pull, pull, n2), true2, pull, n2, spinning)
0.16/0.50	= { by axiom 13 (happens_all_defn_1) }
0.16/0.50	  fresh47(fresh53(n2, n2, pull, n2), true2, pull, n2, spinning)
0.16/0.50	= { by axiom 1 (happens_all_defn_1) }
0.16/0.50	  fresh47(happens(pull, n2), true2, pull, n2, spinning)
0.16/0.50	= { by axiom 10 (happens_holds) }
0.16/0.50	  fresh46(initiates(pull, spinning, n2), true2, n2, spinning)
0.16/0.50	= { by axiom 7 (initiates_all_defn_1) }
0.16/0.50	  fresh46(fresh43(spinning, spinning, pull, spinning, n2), true2, n2, spinning)
0.16/0.50	= { by axiom 11 (initiates_all_defn_1) }
0.16/0.50	  fresh46(fresh56(happens(push, n2), true2, pull, spinning, n2), true2, n2, spinning)
0.16/0.50	= { by axiom 3 (happens_all_defn_3) }
0.16/0.50	  fresh46(fresh56(fresh49(n2, n2, push, n2), true2, pull, spinning, n2), true2, n2, spinning)
0.16/0.50	= { by axiom 12 (happens_all_defn_3) }
0.16/0.50	  fresh46(fresh56(fresh48(push, push, push, n2), true2, pull, spinning, n2), true2, n2, spinning)
0.16/0.51	= { by axiom 4 (happens_all_defn_3) }
0.16/0.51	  fresh46(fresh56(true2, true2, pull, spinning, n2), true2, n2, spinning)
0.16/0.51	= { by axiom 9 (initiates_all_defn_1) }
0.16/0.51	  fresh46(fresh57(pull, pull, pull, spinning, n2), true2, n2, spinning)
0.16/0.51	= { by axiom 8 (initiates_all_defn_1) }
0.16/0.51	  fresh46(true2, true2, n2, spinning)
0.16/0.51	= { by axiom 6 (happens_holds) }
0.16/0.51	  true2
0.16/0.51	% SZS output end Proof
0.16/0.51	
0.16/0.51	RESULT: Theorem (the conjecture is true).
0.16/0.51	EOF