TSTP Solution File: CSR006+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CSR006+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% 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 : 600s
% DateTime : Fri Jul 15 23:03:33 EDT 2022
% Result : Theorem 0.81s 1.13s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : CSR006+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.00/0.08 % Command : tptp2X_and_run_prover9 %d %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 600
% 0.11/0.27 % DateTime : Sat Jun 11 12:18:09 EDT 2022
% 0.11/0.27 % CPUTime :
% 0.46/0.77 ============================== Prover9 ===============================
% 0.46/0.77 Prover9 (32) version 2009-11A, November 2009.
% 0.46/0.77 Process 28926 was started by sandbox2 on n032.cluster.edu,
% 0.46/0.77 Sat Jun 11 12:18:10 2022
% 0.46/0.77 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28773_n032.cluster.edu".
% 0.46/0.77 ============================== end of head ===========================
% 0.46/0.77
% 0.46/0.77 ============================== INPUT =================================
% 0.46/0.77
% 0.46/0.77 % Reading from file /tmp/Prover9_28773_n032.cluster.edu
% 0.46/0.77
% 0.46/0.77 set(prolog_style_variables).
% 0.46/0.77 set(auto2).
% 0.46/0.77 % set(auto2) -> set(auto).
% 0.46/0.77 % set(auto) -> set(auto_inference).
% 0.46/0.77 % set(auto) -> set(auto_setup).
% 0.46/0.77 % set(auto_setup) -> set(predicate_elim).
% 0.46/0.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/0.77 % set(auto) -> set(auto_limits).
% 0.46/0.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/0.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/0.77 % set(auto) -> set(auto_denials).
% 0.46/0.77 % set(auto) -> set(auto_process).
% 0.46/0.77 % set(auto2) -> assign(new_constants, 1).
% 0.46/0.77 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/0.77 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/0.77 % set(auto2) -> assign(max_hours, 1).
% 0.46/0.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/0.77 % set(auto2) -> assign(max_seconds, 0).
% 0.46/0.77 % set(auto2) -> assign(max_minutes, 5).
% 0.46/0.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/0.77 % set(auto2) -> set(sort_initial_sos).
% 0.46/0.77 % set(auto2) -> assign(sos_limit, -1).
% 0.46/0.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/0.77 % set(auto2) -> assign(max_megs, 400).
% 0.46/0.77 % set(auto2) -> assign(stats, some).
% 0.46/0.77 % set(auto2) -> clear(echo_input).
% 0.46/0.77 % set(auto2) -> set(quiet).
% 0.46/0.77 % set(auto2) -> clear(print_initial_clauses).
% 0.46/0.77 % set(auto2) -> clear(print_given).
% 0.46/0.77 assign(lrs_ticks,-1).
% 0.46/0.77 assign(sos_limit,10000).
% 0.46/0.77 assign(order,kbo).
% 0.46/0.77 set(lex_order_vars).
% 0.46/0.77 clear(print_given).
% 0.46/0.77
% 0.46/0.77 % formulas(sos). % not echoed (55 formulas)
% 0.46/0.77
% 0.46/0.77 ============================== end of input ==========================
% 0.46/0.77
% 0.46/0.77 % From the command line: assign(max_seconds, 300).
% 0.46/0.77
% 0.46/0.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/0.77
% 0.46/0.77 % Formulas that are not ordinary clauses:
% 0.46/0.77 1 (all Time1 all Fluent all Time2 (stoppedIn(Time1,Fluent,Time2) <-> (exists Event exists Time (happens(Event,Time) & less(Time1,Time) & less(Time,Time2) & terminates(Event,Fluent,Time))))) # label(stoppedin_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.77 2 (all Time1 all Time2 all Fluent (startedIn(Time1,Fluent,Time2) <-> (exists Event exists Time (happens(Event,Time) & less(Time1,Time) & less(Time,Time2) & initiates(Event,Fluent,Time))))) # label(startedin_defn) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.77 3 (all Event all Time all Fluent all Fluent2 all Offset (happens(Event,Time) & initiates(Event,Fluent,Time) & less(n0,Offset) & trajectory(Fluent,Time,Fluent2,Offset) & -stoppedIn(Time,Fluent,plus(Time,Offset)) -> holdsAt(Fluent2,plus(Time,Offset)))) # label(change_holding) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.77 4 (all Event all Time1 all Fluent1 all Time2 all Fluent2 (happens(Event,Time1) & terminates(Event,Fluent1,Time1) & less(n0,Time2) & antitrajectory(Fluent1,Time1,Fluent2,Time2) & -startedIn(Time1,Fluent1,plus(Time1,Time2)) -> holdsAt(Fluent2,plus(Time1,Time2)))) # label(antitrajectory) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.77 5 (all Fluent all Time (holdsAt(Fluent,Time) & -releasedAt(Fluent,plus(Time,n1)) & -(exists Event (happens(Event,Time) & terminates(Event,Fluent,Time))) -> holdsAt(Fluent,plus(Time,n1)))) # label(keep_holding) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.77 6 (all Fluent all Time (-holdsAt(Fluent,Time) & -releasedAt(Fluent,plus(Time,n1)) & -(exists Event (happens(Event,Time) & initiates(Event,Fluent,Time))) -> -holdsAt(Fluent,plus(Time,n1)))) # label(keep_not_holding) # label(axiom) # label(non_clause). [assumption].
% 0.46/0.77 7 (all Fluent all Time (releasedAt(Fluent,Time) & -(exists Event (happens(Event,Time) & (initiates(Event,Fluent,Time) | terminates(Event,Fluent,Time)))) -> releasedAt(Fluent,plus(Time,n1)))) # label(keep_released) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 8 (all Fluent all Time (-releasedAt(Fluent,Time) & -(exists Event (happens(Event,Time) & releases(Event,Fluent,Time))) -> -releasedAt(Fluent,plus(Time,n1)))) # label(keep_not_released) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 9 (all Event all Time all Fluent (happens(Event,Time) & initiates(Event,Fluent,Time) -> holdsAt(Fluent,plus(Time,n1)))) # label(happens_holds) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 10 (all Event all Time all Fluent (happens(Event,Time) & terminates(Event,Fluent,Time) -> -holdsAt(Fluent,plus(Time,n1)))) # label(happens_terminates_not_holds) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 11 (all Event all Time all Fluent (happens(Event,Time) & releases(Event,Fluent,Time) -> releasedAt(Fluent,plus(Time,n1)))) # label(happens_releases) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 12 (all Event all Time all Fluent (happens(Event,Time) & (initiates(Event,Fluent,Time) | terminates(Event,Fluent,Time)) -> -releasedAt(Fluent,plus(Time,n1)))) # label(happens_not_released) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 13 (all Event all Fluent all Time (initiates(Event,Fluent,Time) <-> Event = tapOn & Fluent = filling | Event = overflow & Fluent = spilling | (exists Height (holdsAt(waterLevel(Height),Time) & Event = tapOff & Fluent = waterLevel(Height))) | (exists Height (holdsAt(waterLevel(Height),Time) & Event = overflow & Fluent = waterLevel(Height))))) # label(initiates_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 14 (all Event all Fluent all Time (terminates(Event,Fluent,Time) <-> Event = tapOff & Fluent = filling | Event = overflow & Fluent = filling)) # label(terminates_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 15 (all Event all Fluent all Time (releases(Event,Fluent,Time) <-> (exists Height (Event = tapOn & Fluent = waterLevel(Height))))) # label(releases_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 16 (all Event all Time (happens(Event,Time) <-> Event = tapOn & Time = n0 | holdsAt(waterLevel(n3),Time) & holdsAt(filling,Time) & Event = overflow)) # label(happens_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 17 (all Height1 all Time all Height2 all Offset (holdsAt(waterLevel(Height1),Time) & Height2 = plus(Height1,Offset) -> trajectory(filling,Time,waterLevel(Height2),Offset))) # label(change_of_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 18 (all Time all Height1 all Height2 (holdsAt(waterLevel(Height1),Time) & holdsAt(waterLevel(Height2),Time) -> Height1 = Height2)) # label(same_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 19 (all X filling != waterLevel(X)) # label(filling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 20 (all X spilling != waterLevel(X)) # label(spilling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 23 (all X all Y (less_or_equal(X,Y) <-> less(X,Y) | X = Y)) # label(less_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 29 (all X (less(X,n5) <-> less_or_equal(X,n4))) # label(less5) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 30 (all X (less(X,n6) <-> less_or_equal(X,n5))) # label(less6) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 31 (all X (less(X,n7) <-> less_or_equal(X,n6))) # label(less7) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 32 (all X (less(X,n8) <-> less_or_equal(X,n7))) # label(less8) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 33 (all X (less(X,n9) <-> less_or_equal(X,n8))) # label(less9) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.49/0.77 35 (all Height -releasedAt(waterLevel(Height),n0)) # label(not_released_waterLevel_0) # label(hypothesis) # label(non_clause). [assumption].
% 0.49/0.77
% 0.49/0.77 ============================== end of process non-clausal formulas ===
% 0.49/0.77
% 0.49/0.77 ============================== PROCESS INITIAL CLAUSES ===============
% 0.49/0.77
% 0.49/0.77 ============================== PREDICATE ELIMINATION =================
% 0.49/0.77 36 stoppedIn(A,B,C) | -happens(D,E) | -less(A,E) | -less(E,C) | -terminates(D,B,E) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.49/0.77 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.49/0.77 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.49/0.77 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.49/0.77 40 -stoppedIn(A,B,C) | terminates(f1(A,B,C),B,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -terminates(A,E,B) | happens(f1(C,E,D),f2(C,E,D)). [resolve(36,a,37,a)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -terminates(A,E,B) | less(C,f2(C,E,D)). [resolve(36,a,38,a)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -terminates(A,E,B) | less(f2(C,E,D),D). [resolve(36,a,39,a)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -terminates(A,E,B) | terminates(f1(C,E,D),E,f2(C,E,D)). [resolve(36,a,40,a)].
% 0.49/0.77 41 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | stoppedIn(B,C,plus(B,D)) | holdsAt(E,plus(B,D)) # label(change_holding) # label(axiom). [clausify(3)].
% 0.49/0.77 Derived: -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | happens(f1(B,C,plus(B,D)),f2(B,C,plus(B,D))). [resolve(41,e,37,a)].
% 0.49/0.77 Derived: -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(B,f2(B,C,plus(B,D))). [resolve(41,e,38,a)].
% 0.49/0.77 Derived: -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(f2(B,C,plus(B,D)),plus(B,D)). [resolve(41,e,39,a)].
% 0.49/0.77 Derived: -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | terminates(f1(B,C,plus(B,D)),C,f2(B,C,plus(B,D))). [resolve(41,e,40,a)].
% 0.49/0.77 42 startedIn(A,B,C) | -happens(D,E) | -less(A,E) | -less(E,C) | -initiates(D,B,E) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.49/0.77 43 -startedIn(A,B,C) | happens(f3(A,C,B),f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.49/0.77 44 -startedIn(A,B,C) | less(A,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.49/0.77 45 -startedIn(A,B,C) | less(f4(A,C,B),C) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.49/0.77 46 -startedIn(A,B,C) | initiates(f3(A,C,B),B,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -initiates(A,E,B) | happens(f3(C,D,E),f4(C,D,E)). [resolve(42,a,43,a)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -initiates(A,E,B) | less(C,f4(C,D,E)). [resolve(42,a,44,a)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -initiates(A,E,B) | less(f4(C,D,E),D). [resolve(42,a,45,a)].
% 0.49/0.77 Derived: -happens(A,B) | -less(C,B) | -less(B,D) | -initiates(A,E,B) | initiates(f3(C,D,E),E,f4(C,D,E)). [resolve(42,a,46,a)].
% 0.49/0.77 47 -happens(A,B) | -terminates(A,C,B) | -less(n0,D) | -antitrajectory(C,B,E,D) | startedIn(B,C,plus(B,D)) | holdsAt(E,plus(B,D)) # label(antitrajectory) # label(axiom). [clausify(4)].
% 0.49/0.77 Derived: -happens(A,B) | -terminates(A,C,B) | -less(n0,D) | -antitrajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | happens(f3(B,plus(B,D),C),f4(B,plus(B,D),C)). [resolve(47,e,43,a)].
% 0.49/0.77 Derived: -happens(A,B) | -terminates(A,C,B) | -less(n0,D) | -antitrajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(B,f4(B,plus(B,D),C)). [resolve(47,e,44,a)].
% 0.81/1.13 Derived: -happens(A,B) | -terminates(A,C,B) | -less(n0,D) | -antitrajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(f4(B,plus(B,D),C),plus(B,D)). [resolve(47,e,45,a)].
% 0.81/1.13 Derived: -happens(A,B) | -terminates(A,C,B) | -less(n0,D) | -antitrajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | initiates(f3(B,plus(B,D),C),C,f4(B,plus(B,D),C)). [resolve(47,e,46,a)].
% 0.81/1.13 48 -happens(A,B) | -releases(A,C,B) | releasedAt(C,plus(B,n1)) # label(happens_releases) # label(axiom). [clausify(11)].
% 0.81/1.13 49 releasedAt(A,B) | releases(f8(A,B),A,B) | -releasedAt(A,plus(B,n1)) # label(keep_not_released) # label(axiom). [clausify(8)].
% 0.81/1.13 50 -releases(A,B,C) | tapOn = A # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.81/1.13 Derived: tapOn = f8(A,B) | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(50,a,49,b)].
% 0.81/1.13 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.81/1.13 Derived: waterLevel(f11(f8(A,B),A,B)) = A | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(51,a,49,b)].
% 0.81/1.13 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.81/1.13 Derived: tapOn != A | waterLevel(B) != C | -happens(A,D) | releasedAt(C,plus(D,n1)). [resolve(52,a,48,b)].
% 0.81/1.13 Derived: tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 0.81/1.13 53 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | happens(f1(B,C,plus(B,D)),f2(B,C,plus(B,D))). [resolve(41,e,37,a)].
% 0.81/1.13 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 0.81/1.13 Derived: -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | happens(f1(B,filling,plus(B,C)),f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(53,d,54,c)].
% 0.81/1.13 55 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(B,f2(B,C,plus(B,D))). [resolve(41,e,38,a)].
% 0.81/1.13 Derived: -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | less(B,f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(55,d,54,c)].
% 0.81/1.13 56 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(f2(B,C,plus(B,D)),plus(B,D)). [resolve(41,e,39,a)].
% 0.81/1.13 Derived: -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | less(f2(B,filling,plus(B,C)),plus(B,C)) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(56,d,54,c)].
% 0.81/1.13 57 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | terminates(f1(B,C,plus(B,D)),C,f2(B,C,plus(B,D))). [resolve(41,e,40,a)].
% 0.81/1.13 Derived: -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | terminates(f1(B,filling,plus(B,C)),filling,f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(57,d,54,c)].
% 0.81/1.13
% 0.81/1.13 ============================== end predicate elimination =============
% 0.81/1.13
% 0.81/1.13 Auto_denials: (non-Horn, no changes).
% 0.81/1.13
% 0.81/1.13 Term ordering decisions:
% 0.81/1.13
% 0.81/1.13 % Assigning unary symbol waterLevel kb_weight 0 and highest precedence (36).
% 0.81/1.13 Function symbol KB weights: filling=1. n1=1. n0=1. tapOn=1. n3=1. overflow=1. spilling=1. n2=1. tapOff=1. n4=1. n5=1. n6=1. n7=1. n8=1. n9=1. plus=1. f5=1. f6=1. f7=1. f8=1. f1=1. f2=1. f3=1. f4=1. f9=1. f10=1. f11=1. waterLevel=0.
% 0.81/1.13
% 0.81/1.13 ============================== end of process initial clauses ========
% 0.81/1.13
% 0.81/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.13
% 0.81/1.13 ============================== end of clauses for search =============
% 0.81/1.13
% 0.81/1.13 ============================== SEARCH ================================
% 0.81/1.13
% 0.81/1.13 % Starting search at 0.03 seconds.
% 0.81/1.13
% 0.81/1.13 ============================== PROOF =================================
% 0.81/1.13 % SZS status Theorem
% 0.81/1.13 % SZS output start Refutation
% 0.81/1.13
% 0.81/1.13 % Proof 1 at 0.36 (+ 0.02) seconds.
% 0.81/1.13 % Length of proof is 195.
% 0.81/1.13 % Level of proof is 35.
% 0.81/1.13 % Maximum clause weight is 39.000.
% 0.81/1.13 % Given clauses 984.
% 0.81/1.13
% 0.81/1.13 1 (all Time1 all Fluent all Time2 (stoppedIn(Time1,Fluent,Time2) <-> (exists Event exists Time (happens(Event,Time) & less(Time1,Time) & less(Time,Time2) & terminates(Event,Fluent,Time))))) # label(stoppedin_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 3 (all Event all Time all Fluent all Fluent2 all Offset (happens(Event,Time) & initiates(Event,Fluent,Time) & less(n0,Offset) & trajectory(Fluent,Time,Fluent2,Offset) & -stoppedIn(Time,Fluent,plus(Time,Offset)) -> holdsAt(Fluent2,plus(Time,Offset)))) # label(change_holding) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 5 (all Fluent all Time (holdsAt(Fluent,Time) & -releasedAt(Fluent,plus(Time,n1)) & -(exists Event (happens(Event,Time) & terminates(Event,Fluent,Time))) -> holdsAt(Fluent,plus(Time,n1)))) # label(keep_holding) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 9 (all Event all Time all Fluent (happens(Event,Time) & initiates(Event,Fluent,Time) -> holdsAt(Fluent,plus(Time,n1)))) # label(happens_holds) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 10 (all Event all Time all Fluent (happens(Event,Time) & terminates(Event,Fluent,Time) -> -holdsAt(Fluent,plus(Time,n1)))) # label(happens_terminates_not_holds) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 12 (all Event all Time all Fluent (happens(Event,Time) & (initiates(Event,Fluent,Time) | terminates(Event,Fluent,Time)) -> -releasedAt(Fluent,plus(Time,n1)))) # label(happens_not_released) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 13 (all Event all Fluent all Time (initiates(Event,Fluent,Time) <-> Event = tapOn & Fluent = filling | Event = overflow & Fluent = spilling | (exists Height (holdsAt(waterLevel(Height),Time) & Event = tapOff & Fluent = waterLevel(Height))) | (exists Height (holdsAt(waterLevel(Height),Time) & Event = overflow & Fluent = waterLevel(Height))))) # label(initiates_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 15 (all Event all Fluent all Time (releases(Event,Fluent,Time) <-> (exists Height (Event = tapOn & Fluent = waterLevel(Height))))) # label(releases_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 16 (all Event all Time (happens(Event,Time) <-> Event = tapOn & Time = n0 | holdsAt(waterLevel(n3),Time) & holdsAt(filling,Time) & Event = overflow)) # label(happens_all_defn) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 17 (all Height1 all Time all Height2 all Offset (holdsAt(waterLevel(Height1),Time) & Height2 = plus(Height1,Offset) -> trajectory(filling,Time,waterLevel(Height2),Offset))) # label(change_of_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 18 (all Time all Height1 all Height2 (holdsAt(waterLevel(Height1),Time) & holdsAt(waterLevel(Height2),Time) -> Height1 = Height2)) # label(same_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 23 (all X all Y (less_or_equal(X,Y) <-> less(X,Y) | X = Y)) # label(less_or_equal) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 29 (all X (less(X,n5) <-> less_or_equal(X,n4))) # label(less5) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 30 (all X (less(X,n6) <-> less_or_equal(X,n5))) # label(less6) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.13 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.81/1.13 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.81/1.13 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.81/1.13 40 -stoppedIn(A,B,C) | terminates(f1(A,B,C),B,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.81/1.13 41 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | stoppedIn(B,C,plus(B,D)) | holdsAt(E,plus(B,D)) # label(change_holding) # label(axiom). [clausify(3)].
% 0.81/1.13 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.81/1.13 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.81/1.13 53 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | happens(f1(B,C,plus(B,D)),f2(B,C,plus(B,D))). [resolve(41,e,37,a)].
% 0.81/1.13 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 0.81/1.13 55 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(B,f2(B,C,plus(B,D))). [resolve(41,e,38,a)].
% 0.81/1.13 56 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | less(f2(B,C,plus(B,D)),plus(B,D)). [resolve(41,e,39,a)].
% 0.81/1.13 57 -happens(A,B) | -initiates(A,C,B) | -less(n0,D) | -trajectory(C,B,E,D) | holdsAt(E,plus(B,D)) | terminates(f1(B,C,plus(B,D)),C,f2(B,C,plus(B,D))). [resolve(41,e,40,a)].
% 0.81/1.13 58 -holdsAt(A,B) | releasedAt(A,plus(B,n1)) | happens(f5(A,B),B) | holdsAt(A,plus(B,n1)) # label(keep_holding) # label(axiom). [clausify(5)].
% 0.81/1.13 65 -happens(A,B) | -initiates(A,C,B) | holdsAt(C,plus(B,n1)) # label(happens_holds) # label(axiom). [clausify(9)].
% 0.81/1.13 66 -happens(A,B) | -terminates(A,C,B) | -holdsAt(C,plus(B,n1)) # label(happens_terminates_not_holds) # label(axiom). [clausify(10)].
% 0.81/1.13 68 -happens(A,B) | -terminates(A,C,B) | -releasedAt(C,plus(B,n1)) # label(happens_not_released) # label(axiom). [clausify(12)].
% 0.81/1.13 87 initiates(A,B,C) | tapOn != A | filling != B # label(initiates_all_defn) # label(axiom). [clausify(13)].
% 0.81/1.13 90 initiates(A,B,C) | -holdsAt(waterLevel(D),C) | overflow != A | waterLevel(D) != B # label(initiates_all_defn) # label(axiom). [clausify(13)].
% 0.81/1.13 98 -happens(A,B) | n0 = B | holdsAt(waterLevel(n3),B) # label(happens_all_defn) # label(axiom). [clausify(16)].
% 0.81/1.13 99 -happens(A,B) | n0 = B | holdsAt(filling,B) # label(happens_all_defn) # label(axiom). [clausify(16)].
% 0.81/1.13 100 -happens(A,B) | n0 = B | overflow = A # label(happens_all_defn) # label(axiom). [clausify(16)].
% 0.81/1.13 101 happens(A,B) | tapOn != A | n0 != B # label(happens_all_defn) # label(axiom). [clausify(16)].
% 0.81/1.13 103 -holdsAt(waterLevel(A),B) | -holdsAt(waterLevel(C),B) | C = A # label(same_waterLevel) # label(axiom). [clausify(18)].
% 0.81/1.13 111 waterLevel(A) != waterLevel(B) | A = B # label(distinct_waterLevels) # label(axiom). [clausify(21)].
% 0.81/1.13 113 plus(n0,n0) = n0 # label(plus0_0) # label(axiom). [assumption].
% 0.81/1.13 114 plus(n0,n1) = n1 # label(plus0_1) # label(axiom). [assumption].
% 0.81/1.13 116 plus(n0,n3) = n3 # label(plus0_3) # label(axiom). [assumption].
% 0.81/1.13 118 plus(n1,n2) = n3 # label(plus1_2) # label(axiom). [assumption].
% 0.81/1.13 123 plus(A,B) = plus(B,A) # label(symmetry_of_plus) # label(axiom). [clausify(22)].
% 0.81/1.13 124 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(23)].
% 0.81/1.13 125 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(23)].
% 0.81/1.13 126 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(23)].
% 0.81/1.13 127 -less(A,n0) # label(less0) # label(axiom). [clausify(24)].
% 0.81/1.13 128 -less(A,n1) | less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 0.81/1.13 129 less(A,n1) | -less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 0.81/1.13 130 -less(A,n2) | less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 0.81/1.13 131 less(A,n2) | -less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 0.81/1.13 132 -less(A,n3) | less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 0.81/1.13 133 less(A,n3) | -less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 0.81/1.13 134 -less(A,n4) | less_or_equal(A,n3) # label(less4) # label(axiom). [clausify(28)].
% 0.81/1.13 135 less(A,n4) | -less_or_equal(A,n3) # label(less4) # label(axiom). [clausify(28)].
% 0.81/1.13 136 -less(A,n5) | less_or_equal(A,n4) # label(less5) # label(axiom). [clausify(29)].
% 0.81/1.13 137 less(A,n5) | -less_or_equal(A,n4) # label(less5) # label(axiom). [clausify(29)].
% 0.81/1.13 138 -less(A,n6) | less_or_equal(A,n5) # label(less6) # label(axiom). [clausify(30)].
% 0.81/1.13 139 less(A,n6) | -less_or_equal(A,n5) # label(less6) # label(axiom). [clausify(30)].
% 0.81/1.13 146 -less(A,B) | -less(B,A) # label(less_property) # label(axiom). [clausify(34)].
% 0.81/1.13 147 -less(A,B) | B != A # label(less_property) # label(axiom). [clausify(34)].
% 0.81/1.13 148 less(A,B) | less(B,A) | B = A # label(less_property) # label(axiom). [clausify(34)].
% 0.81/1.13 149 holdsAt(waterLevel(n0),n0) # label(waterLevel_0) # label(hypothesis). [assumption].
% 0.81/1.13 155 -holdsAt(waterLevel(n3),n3) # label(waterLevel_3) # label(negated_conjecture). [assumption].
% 0.81/1.13 168 tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 0.81/1.13 169 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | happens(f1(B,filling,plus(B,C)),f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(53,d,54,c)].
% 0.81/1.13 170 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | happens(f1(B,filling,plus(B,C)),f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(C,E) != D. [copy(169),rewrite([123(18)])].
% 0.81/1.13 171 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | less(B,f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(55,d,54,c)].
% 0.81/1.13 172 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | less(B,f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(C,E) != D. [copy(171),rewrite([123(15)])].
% 0.81/1.13 173 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | less(f2(B,filling,plus(B,C)),plus(B,C)) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(56,d,54,c)].
% 0.81/1.13 174 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | less(f2(B,filling,plus(B,C)),plus(B,C)) | -holdsAt(waterLevel(E),B) | plus(C,E) != D. [copy(173),rewrite([123(16)])].
% 0.81/1.13 175 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | terminates(f1(B,filling,plus(B,C)),filling,f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(E,C) != D. [resolve(57,d,54,c)].
% 0.81/1.13 176 -happens(A,B) | -initiates(A,filling,B) | -less(n0,C) | holdsAt(waterLevel(D),plus(B,C)) | terminates(f1(B,filling,plus(B,C)),filling,f2(B,filling,plus(B,C))) | -holdsAt(waterLevel(E),B) | plus(C,E) != D. [copy(175),rewrite([123(19)])].
% 0.81/1.13 178 plus(n1,n0) = n1. [back_rewrite(114),rewrite([123(3)])].
% 0.81/1.13 180 initiates(tapOn,A,B) | filling != A. [xx_res(87,b)].
% 0.81/1.13 188 happens(tapOn,A) | n0 != A. [xx_res(101,b)].
% 0.81/1.13 199 less_or_equal(A,A). [xx_res(126,b)].
% 0.81/1.13 203 less(n6,A) | n6 = A | less_or_equal(A,n5). [resolve(148,a,138,a)].
% 0.81/1.13 204 less(n5,A) | n5 = A | less_or_equal(A,n4). [resolve(148,a,136,a)].
% 0.81/1.13 205 less(n4,A) | n4 = A | less_or_equal(A,n3). [resolve(148,a,134,a)].
% 0.81/1.13 206 less(n3,A) | n3 = A | less_or_equal(A,n2). [resolve(148,a,132,a)].
% 0.81/1.13 207 less(n2,A) | n2 = A | less_or_equal(A,n1). [resolve(148,a,130,a)].
% 0.81/1.13 208 less(n1,A) | n1 = A | less_or_equal(A,n0). [resolve(148,a,128,a)].
% 0.81/1.13 220 waterLevel(A) != B | waterLevel(f11(tapOn,B,C)) = B. [xx_res(168,a)].
% 0.81/1.13 222 initiates(tapOn,filling,A). [xx_res(180,b)].
% 0.81/1.13 230 less(n1,n2). [resolve(199,a,131,b)].
% 0.81/1.13 231 less(n0,n1). [resolve(199,a,129,b)].
% 0.81/1.13 256 less_or_equal(n1,n2). [resolve(230,a,125,b)].
% 0.81/1.13 257 n0 != n1. [resolve(231,a,147,a),flip(a)].
% 0.81/1.13 258 less_or_equal(n0,n1). [resolve(231,a,125,b)].
% 0.81/1.13 266 less(n1,n3). [resolve(256,a,133,b)].
% 0.81/1.13 267 less(n0,n2). [resolve(258,a,131,b)].
% 0.81/1.13 287 n3 != n1. [resolve(266,a,147,a)].
% 0.81/1.13 290 n2 != n0. [resolve(267,a,147,a)].
% 0.81/1.13 291 less_or_equal(n0,n2). [resolve(267,a,125,b)].
% 0.81/1.13 296 happens(tapOn,n0). [resolve(188,b,113,a(flip)),rewrite([113(4)])].
% 0.81/1.13 299 less(n0,n3). [resolve(291,a,133,b)].
% 0.81/1.13 319 n3 != n0. [resolve(299,a,147,a)].
% 0.81/1.13 320 less_or_equal(n0,n3). [resolve(299,a,125,b)].
% 0.81/1.13 326 less(n0,n4). [resolve(320,a,135,b)].
% 0.81/1.13 343 n4 != n0. [resolve(326,a,147,a)].
% 0.81/1.13 344 less_or_equal(n0,n4). [resolve(326,a,125,b)].
% 0.81/1.13 351 less(n0,n5). [resolve(344,a,137,b)].
% 0.81/1.13 358 less(n6,A) | n6 = A | less(A,n5) | n5 = A. [resolve(203,c,124,a)].
% 0.81/1.13 365 n5 != n0. [resolve(351,a,147,a)].
% 0.81/1.13 366 less_or_equal(n0,n5). [resolve(351,a,125,b)].
% 0.81/1.13 367 less(n5,A) | n5 = A | less(A,n4) | n4 = A. [resolve(204,c,124,a)].
% 0.81/1.13 371 less(n0,n6). [resolve(366,a,139,b)].
% 0.81/1.13 372 less(n4,A) | n4 = A | less(A,n3) | n3 = A. [resolve(205,c,124,a)].
% 0.81/1.13 382 n6 != n0. [resolve(371,a,147,a)].
% 0.81/1.13 384 less(n3,A) | n3 = A | less(A,n2) | n2 = A. [resolve(206,c,124,a)].
% 0.81/1.13 388 less(n2,A) | n2 = A | less(A,n1) | n1 = A. [resolve(207,c,124,a)].
% 0.81/1.13 397 less(n1,A) | n1 = A | n0 = A. [resolve(208,c,124,a),unit_del(c,127)].
% 0.81/1.13 417 -happens(tapOn,A) | -less(n0,B) | holdsAt(waterLevel(C),plus(A,B)) | terminates(f1(A,filling,plus(A,B)),filling,f2(A,filling,plus(A,B))) | -holdsAt(waterLevel(D),A) | plus(B,D) != C. [resolve(222,a,176,b)].
% 0.81/1.13 418 -happens(tapOn,A) | -less(n0,B) | holdsAt(waterLevel(C),plus(A,B)) | less(f2(A,filling,plus(A,B)),plus(A,B)) | -holdsAt(waterLevel(D),A) | plus(B,D) != C. [resolve(222,a,174,b)].
% 0.81/1.13 419 -happens(tapOn,A) | -less(n0,B) | holdsAt(waterLevel(C),plus(A,B)) | less(A,f2(A,filling,plus(A,B))) | -holdsAt(waterLevel(D),A) | plus(B,D) != C. [resolve(222,a,172,b)].
% 0.81/1.13 420 -happens(tapOn,A) | -less(n0,B) | holdsAt(waterLevel(C),plus(A,B)) | happens(f1(A,filling,plus(A,B)),f2(A,filling,plus(A,B))) | -holdsAt(waterLevel(D),A) | plus(B,D) != C. [resolve(222,a,170,b)].
% 0.81/1.13 455 n1 = A | n0 = A | -less(A,n1). [resolve(397,a,146,b)].
% 0.81/1.13 513 waterLevel(f11(tapOn,waterLevel(A),B)) = waterLevel(A). [xx_res(220,a)].
% 0.81/1.13 536 less(n6,A) | n6 = A | n5 = A | -less(n5,A). [resolve(358,c,146,b)].
% 0.81/1.13 541 less(n5,A) | n5 = A | n4 = A | -less(n4,A). [resolve(367,c,146,b)].
% 0.81/1.13 544 n4 = A | less(A,n3) | n3 = A | -less(A,n4). [resolve(372,a,146,b)].
% 0.81/1.13 552 less(n3,A) | n3 = A | n2 = A | -less(n2,A). [resolve(384,c,146,b)].
% 0.81/1.13 558 less(n2,A) | n2 = A | n1 = A | n0 = A. [resolve(388,c,455,c),merge(d)].
% 0.81/1.13 562 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | terminates(f1(n0,filling,plus(A,n0)),filling,f2(n0,filling,plus(A,n0))) | -holdsAt(waterLevel(C),n0) | plus(A,C) != B. [resolve(417,a,296,a),rewrite([123(5),123(10),123(16)])].
% 0.81/1.13 564 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | less(f2(n0,filling,plus(A,n0)),plus(A,n0)) | -holdsAt(waterLevel(C),n0) | plus(A,C) != B. [resolve(418,a,296,a),rewrite([123(5),123(10),123(13)])].
% 0.81/1.13 565 f11(tapOn,waterLevel(A),B) = A. [resolve(513,a,111,a)].
% 0.81/1.13 579 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | less(n0,f2(n0,filling,plus(A,n0))) | -holdsAt(waterLevel(C),n0) | plus(A,C) != B. [resolve(419,a,296,a),rewrite([123(5),123(11)])].
% 0.81/1.13 608 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | happens(f1(n0,filling,plus(A,n0)),f2(n0,filling,plus(A,n0))) | -holdsAt(waterLevel(C),n0) | plus(A,C) != B. [resolve(420,a,296,a),rewrite([123(5),123(10),123(15)])].
% 0.81/1.13 808 less(n6,A) | n6 = A | n5 = A | less(A,n4) | n4 = A. [resolve(536,d,367,a),merge(d)].
% 0.81/1.13 823 less(n5,A) | n5 = A | n4 = A | less(A,n3) | n3 = A. [resolve(541,d,372,a),merge(d)].
% 0.81/1.13 830 less(n3,A) | n3 = A | n2 = A | less(A,n1) | n1 = A. [resolve(552,d,388,a),merge(d)].
% 0.81/1.13 831 n2 = A | n1 = A | n0 = A | less(n3,A) | n3 = A. [resolve(558,a,552,d),merge(f)].
% 0.81/1.13 834 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | terminates(f1(n0,filling,plus(A,n0)),filling,f2(n0,filling,plus(A,n0))) | plus(A,n0) != B. [resolve(562,d,149,a)].
% 0.81/1.13 849 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | less(f2(n0,filling,plus(A,n0)),plus(A,n0)) | plus(A,n0) != B. [resolve(564,d,149,a)].
% 0.81/1.13 867 less(n6,A) | n6 = A | n5 = A | n4 = A | less(A,n3) | n3 = A. [resolve(808,d,544,d),merge(e)].
% 0.81/1.13 870 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | less(n0,f2(n0,filling,plus(A,n0))) | plus(A,n0) != B. [resolve(579,d,149,a)].
% 0.81/1.13 886 n2 = A | n1 = A | n0 = A | n3 = A | -less(A,n3). [resolve(831,d,146,b)].
% 0.81/1.13 888 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | happens(f1(n0,filling,plus(A,n0)),f2(n0,filling,plus(A,n0))) | plus(A,n0) != B. [resolve(608,d,149,a)].
% 0.81/1.13 920 holdsAt(waterLevel(A),n3) | terminates(f1(n0,filling,n3),filling,f2(n0,filling,n3)) | n3 != A. [resolve(834,a,823,d),rewrite([123(4),116(4),123(8),116(8),123(13),116(13),123(16),116(16)]),unit_del(d,127),unit_del(e,365),unit_del(f,343),unit_del(g,319)].
% 0.81/1.13 956 terminates(f1(n0,filling,n3),filling,f2(n0,filling,n3)). [resolve(920,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 0.81/1.13 962 -happens(f1(n0,filling,n3),f2(n0,filling,n3)) | -releasedAt(filling,plus(n1,f2(n0,filling,n3))). [resolve(956,a,68,b),rewrite([123(16)])].
% 0.81/1.13 963 -happens(f1(n0,filling,n3),f2(n0,filling,n3)) | -holdsAt(filling,plus(n1,f2(n0,filling,n3))). [resolve(956,a,66,b),rewrite([123(16)])].
% 0.81/1.13 1139 holdsAt(waterLevel(A),n1) | less(f2(n0,filling,n1),n1) | n1 != A. [resolve(849,a,830,d),rewrite([178(4),178(8),178(10),178(12)]),flip(g),unit_del(d,127),unit_del(e,319),unit_del(f,290),unit_del(g,257)].
% 0.81/1.13 1141 holdsAt(waterLevel(A),n3) | less(f2(n0,filling,n3),n3) | n3 != A. [resolve(849,a,823,d),rewrite([123(4),116(4),123(8),116(8),123(10),116(10),123(12),116(12)]),unit_del(d,127),unit_del(e,365),unit_del(f,343),unit_del(g,319)].
% 0.81/1.13 1149 holdsAt(waterLevel(n1),n1) | less(f2(n0,filling,n1),n1). [resolve(1139,c,565,a(flip)),rewrite([565(4)])].
% 0.81/1.13 1150 less(f2(n0,filling,n1),n1) | -holdsAt(waterLevel(A),n1) | n1 = A. [resolve(1149,a,103,b)].
% 0.81/1.13 1168 less(f2(n0,filling,n3),n3). [resolve(1141,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 0.81/1.13 1169 f2(n0,filling,n3) = n2 | f2(n0,filling,n3) = n1 | f2(n0,filling,n3) = n0 | f2(n0,filling,n3) = n3. [resolve(1168,a,886,e),flip(a),flip(b),flip(c),flip(d)].
% 0.81/1.13 1178 f2(n0,filling,n3) != n3. [resolve(1168,a,147,a),flip(a)].
% 0.81/1.13 1190 f2(n0,filling,n3) = n2 | f2(n0,filling,n3) = n1 | f2(n0,filling,n3) = n0. [back_unit_del(1169),unit_del(d,1178)].
% 0.81/1.13 1225 holdsAt(waterLevel(A),n3) | less(n0,f2(n0,filling,n3)) | n3 != A. [resolve(870,a,867,e),rewrite([123(4),116(4),123(9),116(9),123(12),116(12)]),unit_del(d,127),unit_del(e,382),unit_del(f,365),unit_del(g,343),unit_del(h,319)].
% 0.81/1.13 1229 holdsAt(waterLevel(A),n1) | less(n0,f2(n0,filling,n1)) | n1 != A. [resolve(870,a,830,d),rewrite([178(4),178(9),178(12)]),flip(g),unit_del(d,127),unit_del(e,319),unit_del(f,290),unit_del(g,257)].
% 0.81/1.13 1245 less(n0,f2(n0,filling,n3)). [resolve(1225,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 0.81/1.13 1249 f2(n0,filling,n3) != n0. [resolve(1245,a,147,a)].
% 0.81/1.13 1251 f2(n0,filling,n3) = n2 | f2(n0,filling,n3) = n1. [back_unit_del(1190),unit_del(c,1249)].
% 0.81/1.13 1268 holdsAt(waterLevel(n1),n1) | less(n0,f2(n0,filling,n1)). [resolve(1229,c,565,a(flip)),rewrite([565(4)])].
% 0.81/1.13 1269 less(n0,f2(n0,filling,n1)) | -holdsAt(waterLevel(A),n1) | n1 = A. [resolve(1268,a,103,b)].
% 0.81/1.13 1279 holdsAt(waterLevel(A),n3) | happens(f1(n0,filling,n3),f2(n0,filling,n3)) | n3 != A. [resolve(888,a,867,e),rewrite([123(4),116(4),123(8),116(8),123(12),116(12),123(15),116(15)]),unit_del(d,127),unit_del(e,382),unit_del(f,365),unit_del(g,343),unit_del(h,319)].
% 0.81/1.13 1393 happens(f1(n0,filling,n3),f2(n0,filling,n3)). [resolve(1279,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 0.81/1.13 1395 -holdsAt(filling,plus(n1,f2(n0,filling,n3))). [back_unit_del(963),unit_del(a,1393)].
% 0.81/1.13 1396 -releasedAt(filling,plus(n1,f2(n0,filling,n3))). [back_unit_del(962),unit_del(a,1393)].
% 0.81/1.13 1402 f1(n0,filling,n3) = overflow. [resolve(1393,a,100,a),flip(a),flip(b),unit_del(a,1249)].
% 0.81/1.13 1403 holdsAt(filling,f2(n0,filling,n3)). [resolve(1393,a,99,a),flip(a),unit_del(a,1249)].
% 0.81/1.13 1404 holdsAt(waterLevel(n3),f2(n0,filling,n3)). [resolve(1393,a,98,a),flip(a),unit_del(a,1249)].
% 0.81/1.13 1406 happens(overflow,f2(n0,filling,n3)). [back_rewrite(1393),rewrite([1402(4)])].
% 0.81/1.13 1414 happens(f5(filling,f2(n0,filling,n3)),f2(n0,filling,n3)). [resolve(1403,a,58,a),rewrite([123(7),123(26)]),unit_del(a,1396),unit_del(c,1395)].
% 0.81/1.13 1423 initiates(A,B,f2(n0,filling,n3)) | overflow != A | waterLevel(n3) != B. [resolve(1404,a,90,b)].
% 0.81/1.13 1467 f5(filling,f2(n0,filling,n3)) = overflow. [resolve(1414,a,100,a),flip(a),flip(b),unit_del(a,1249)].
% 0.81/1.13 1469 f2(n0,filling,n3) = n1 | f5(filling,n2) = overflow. [para(1251(a,1),1467(a,1,2))].
% 0.81/1.13 1480 f5(filling,n2) = overflow | holdsAt(waterLevel(n3),n1). [para(1469(a,1),1404(a,2))].
% 0.81/1.13 1507 f5(filling,n2) = overflow | less(n0,f2(n0,filling,n1)). [resolve(1480,b,1269,b),flip(c),unit_del(c,287)].
% 0.81/1.13 1508 f5(filling,n2) = overflow | less(f2(n0,filling,n1),n1). [resolve(1480,b,1150,b),flip(c),unit_del(c,287)].
% 0.81/1.13 1531 f5(filling,n2) = overflow | f2(n0,filling,n1) != n0. [resolve(1507,b,147,a)].
% 0.81/1.13 1544 f5(filling,n2) = overflow | less_or_equal(f2(n0,filling,n1),n0). [resolve(1508,b,128,a)].
% 0.81/1.13 1573 f5(filling,n2) = overflow | f2(n0,filling,n1) = n0. [resolve(1544,b,124,a),flip(c),unit_del(b,127)].
% 0.81/1.13 1578 f5(filling,n2) = overflow. [resolve(1573,b,1531,b),merge(b)].
% 0.81/1.13 1664 initiates(overflow,A,f2(n0,filling,n3)) | waterLevel(n3) != A. [resolve(1423,b,1578,a(flip)),rewrite([1578(3)])].
% 0.81/1.13 1666 initiates(overflow,waterLevel(n3),f2(n0,filling,n3)). [resolve(1664,b,565,a(flip)),rewrite([565(6)])].
% 0.81/1.13 1675 holdsAt(waterLevel(n3),plus(n1,f2(n0,filling,n3))). [resolve(1666,a,65,b),rewrite([123(14)]),unit_del(a,1406)].
% 0.81/1.13 1684 f2(n0,filling,n3) = n1. [para(1251(a,1),1675(a,2,2)),rewrite([118(11)]),unit_del(b,155)].
% 0.81/1.13 1713 holdsAt(waterLevel(n3),n1). [back_rewrite(1404),rewrite([1684(6)])].
% 0.81/1.13 1736 less(n0,f2(n0,filling,n1)). [resolve(1713,a,1269,b),flip(b),unit_del(b,287)].
% 0.81/1.13 1737 less(f2(n0,filling,n1),n1). [resolve(1713,a,1150,b),flip(b),unit_del(b,287)].
% 0.81/1.13 1780 f2(n0,filling,n1) != n0. [resolve(1736,a,147,a)].
% 0.81/1.13 1793 f2(n0,filling,n1) = n1. [resolve(1737,a,455,c),flip(a),flip(b),unit_del(b,1780)].
% 0.81/1.13 1794 $F. [resolve(1737,a,147,a),rewrite([1793(5)]),xx(a)].
% 0.81/1.13
% 0.81/1.13 % SZS output end Refutation
% 0.81/1.13 ============================== end of proof ==========================
% 0.81/1.13
% 0.81/1.13 ============================== STATISTICS ============================
% 0.81/1.13
% 0.81/1.13 Given=984. Generated=14346. Kept=1730. proofs=1.
% 0.81/1.13 Usable=735. Sos=184. Demods=22. Limbo=9, Disabled=941. Hints=0.
% 0.81/1.13 Megabytes=2.13.
% 0.81/1.13 User_CPU=0.36, System_CPU=0.02, Wall_clock=0.
% 0.81/1.13
% 0.81/1.13 ============================== end of statistics =====================
% 0.81/1.13
% 0.81/1.13 ============================== end of search =========================
% 0.81/1.13
% 0.81/1.13 THEOREM PROVED
% 0.81/1.13 % SZS status Theorem
% 0.81/1.13
% 0.81/1.13 Exiting with 1 proof.
% 0.81/1.13
% 0.81/1.13 Process 28926 exit (max_proofs) Sat Jun 11 12:18:10 2022
% 0.81/1.13 Prover9 interrupted
%------------------------------------------------------------------------------