TSTP Solution File: CSR008+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CSR008+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 23:03:34 EDT 2022
% Result : Theorem 1.06s 1.34s
% Output : Refutation 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CSR008+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.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 : 600
% 0.13/0.34 % DateTime : Fri Jun 10 05:48:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.03 ============================== Prover9 ===============================
% 0.44/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.03 Process 8557 was started by sandbox2 on n021.cluster.edu,
% 0.44/1.03 Fri Jun 10 05:48:39 2022
% 0.44/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8404_n021.cluster.edu".
% 0.44/1.03 ============================== end of head ===========================
% 0.44/1.03
% 0.44/1.03 ============================== INPUT =================================
% 0.44/1.03
% 0.44/1.03 % Reading from file /tmp/Prover9_8404_n021.cluster.edu
% 0.44/1.03
% 0.44/1.03 set(prolog_style_variables).
% 0.44/1.03 set(auto2).
% 0.44/1.03 % set(auto2) -> set(auto).
% 0.44/1.03 % set(auto) -> set(auto_inference).
% 0.44/1.03 % set(auto) -> set(auto_setup).
% 0.44/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.03 % set(auto) -> set(auto_limits).
% 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.03 % set(auto) -> set(auto_denials).
% 0.44/1.03 % set(auto) -> set(auto_process).
% 0.44/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.03 % set(auto2) -> assign(stats, some).
% 0.44/1.03 % set(auto2) -> clear(echo_input).
% 0.44/1.03 % set(auto2) -> set(quiet).
% 0.44/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.03 % set(auto2) -> clear(print_given).
% 0.44/1.03 assign(lrs_ticks,-1).
% 0.44/1.03 assign(sos_limit,10000).
% 0.44/1.03 assign(order,kbo).
% 0.44/1.03 set(lex_order_vars).
% 0.44/1.03 clear(print_given).
% 0.44/1.03
% 0.44/1.03 % formulas(sos). % not echoed (55 formulas)
% 0.44/1.03
% 0.44/1.03 ============================== end of input ==========================
% 0.44/1.03
% 0.44/1.03 % From the command line: assign(max_seconds, 300).
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.03
% 0.44/1.03 % Formulas that are not ordinary clauses:
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 19 (all X filling != waterLevel(X)) # label(filling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 20 (all X spilling != waterLevel(X)) # label(spilling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 29 (all X (less(X,n5) <-> less_or_equal(X,n4))) # label(less5) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 30 (all X (less(X,n6) <-> less_or_equal(X,n5))) # label(less6) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 31 (all X (less(X,n7) <-> less_or_equal(X,n6))) # label(less7) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 32 (all X (less(X,n8) <-> less_or_equal(X,n7))) # label(less8) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 33 (all X (less(X,n9) <-> less_or_equal(X,n8))) # label(less9) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.04 35 (all Height -releasedAt(waterLevel(Height),n0)) # label(not_released_waterLevel_0) # label(hypothesis) # label(non_clause). [assumption].
% 0.44/1.04
% 0.44/1.04 ============================== end of process non-clausal formulas ===
% 0.44/1.04
% 0.44/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.04
% 0.44/1.04 ============================== PREDICATE ELIMINATION =================
% 0.44/1.04 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)].
% 0.44/1.04 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.44/1.04 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.44/1.04 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.44/1.04 40 -stoppedIn(A,B,C) | terminates(f1(A,B,C),B,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 43 -startedIn(A,B,C) | happens(f3(A,C,B),f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.44/1.04 44 -startedIn(A,B,C) | less(A,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.44/1.04 45 -startedIn(A,B,C) | less(f4(A,C,B),C) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.44/1.04 46 -startedIn(A,B,C) | initiates(f3(A,C,B),B,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 0.44/1.04 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 48 -happens(A,B) | -releases(A,C,B) | releasedAt(C,plus(B,n1)) # label(happens_releases) # label(axiom). [clausify(11)].
% 1.06/1.34 49 releasedAt(A,B) | releases(f8(A,B),A,B) | -releasedAt(A,plus(B,n1)) # label(keep_not_released) # label(axiom). [clausify(8)].
% 1.06/1.34 50 -releases(A,B,C) | tapOn = A # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.06/1.34 Derived: tapOn = f8(A,B) | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(50,a,49,b)].
% 1.06/1.34 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.06/1.34 Derived: waterLevel(f11(f8(A,B),A,B)) = A | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(51,a,49,b)].
% 1.06/1.34 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.06/1.34 Derived: tapOn != A | waterLevel(B) != C | -happens(A,D) | releasedAt(C,plus(D,n1)). [resolve(52,a,48,b)].
% 1.06/1.34 Derived: tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 1.06/1.34 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)].
% 1.06/1.34 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34
% 1.06/1.34 ============================== end predicate elimination =============
% 1.06/1.34
% 1.06/1.34 Auto_denials: (non-Horn, no changes).
% 1.06/1.34
% 1.06/1.34 Term ordering decisions:
% 1.06/1.34
% 1.06/1.34 % Assigning unary symbol waterLevel kb_weight 0 and highest precedence (36).
% 1.06/1.34 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.
% 1.06/1.34
% 1.06/1.34 ============================== end of process initial clauses ========
% 1.06/1.34
% 1.06/1.34 ============================== CLAUSES FOR SEARCH ====================
% 1.06/1.34
% 1.06/1.34 ============================== end of clauses for search =============
% 1.06/1.34
% 1.06/1.34 ============================== SEARCH ================================
% 1.06/1.34
% 1.06/1.34 % Starting search at 0.03 seconds.
% 1.06/1.34
% 1.06/1.34 ============================== PROOF =================================
% 1.06/1.34 % SZS status Theorem
% 1.06/1.34 % SZS output start Refutation
% 1.06/1.34
% 1.06/1.34 % Proof 1 at 0.30 (+ 0.02) seconds.
% 1.06/1.34 % Length of proof is 171.
% 1.06/1.34 % Level of proof is 24.
% 1.06/1.34 % Maximum clause weight is 39.000.
% 1.06/1.34 % Given clauses 853.
% 1.06/1.34
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 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].
% 1.06/1.34 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 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].
% 1.06/1.34 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 29 (all X (less(X,n5) <-> less_or_equal(X,n4))) # label(less5) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.34 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.06/1.34 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.06/1.34 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.06/1.34 40 -stoppedIn(A,B,C) | terminates(f1(A,B,C),B,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.06/1.34 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)].
% 1.06/1.34 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.06/1.34 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.06/1.34 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)].
% 1.06/1.34 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 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)].
% 1.06/1.34 65 -happens(A,B) | -initiates(A,C,B) | holdsAt(C,plus(B,n1)) # label(happens_holds) # label(axiom). [clausify(9)].
% 1.06/1.34 66 -happens(A,B) | -terminates(A,C,B) | -holdsAt(C,plus(B,n1)) # label(happens_terminates_not_holds) # label(axiom). [clausify(10)].
% 1.06/1.34 68 -happens(A,B) | -terminates(A,C,B) | -releasedAt(C,plus(B,n1)) # label(happens_not_released) # label(axiom). [clausify(12)].
% 1.06/1.34 87 initiates(A,B,C) | tapOn != A | filling != B # label(initiates_all_defn) # label(axiom). [clausify(13)].
% 1.06/1.34 98 -happens(A,B) | n0 = B | holdsAt(waterLevel(n3),B) # label(happens_all_defn) # label(axiom). [clausify(16)].
% 1.06/1.34 101 happens(A,B) | tapOn != A | n0 != B # label(happens_all_defn) # label(axiom). [clausify(16)].
% 1.06/1.34 103 -holdsAt(waterLevel(A),B) | -holdsAt(waterLevel(C),B) | C = A # label(same_waterLevel) # label(axiom). [clausify(18)].
% 1.06/1.34 111 waterLevel(A) != waterLevel(B) | A = B # label(distinct_waterLevels) # label(axiom). [clausify(21)].
% 1.06/1.34 113 plus(n0,n0) = n0 # label(plus0_0) # label(axiom). [assumption].
% 1.06/1.34 114 plus(n0,n1) = n1 # label(plus0_1) # label(axiom). [assumption].
% 1.06/1.34 115 plus(n0,n2) = n2 # label(plus0_2) # label(axiom). [assumption].
% 1.06/1.34 117 plus(n1,n1) = n2 # label(plus1_1) # label(axiom). [assumption].
% 1.06/1.34 123 plus(A,B) = plus(B,A) # label(symmetry_of_plus) # label(axiom). [clausify(22)].
% 1.06/1.34 124 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(23)].
% 1.06/1.34 125 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(23)].
% 1.06/1.34 126 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(23)].
% 1.06/1.34 127 -less(A,n0) # label(less0) # label(axiom). [clausify(24)].
% 1.06/1.34 128 -less(A,n1) | less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 1.06/1.34 129 less(A,n1) | -less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 1.06/1.34 130 -less(A,n2) | less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 1.06/1.34 131 less(A,n2) | -less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 1.06/1.34 132 -less(A,n3) | less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 1.06/1.34 133 less(A,n3) | -less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 1.06/1.34 134 -less(A,n4) | less_or_equal(A,n3) # label(less4) # label(axiom). [clausify(28)].
% 1.06/1.34 135 less(A,n4) | -less_or_equal(A,n3) # label(less4) # label(axiom). [clausify(28)].
% 1.06/1.34 136 -less(A,n5) | less_or_equal(A,n4) # label(less5) # label(axiom). [clausify(29)].
% 1.06/1.34 137 less(A,n5) | -less_or_equal(A,n4) # label(less5) # label(axiom). [clausify(29)].
% 1.06/1.34 146 -less(A,B) | -less(B,A) # label(less_property) # label(axiom). [clausify(34)].
% 1.06/1.34 147 -less(A,B) | B != A # label(less_property) # label(axiom). [clausify(34)].
% 1.06/1.34 148 less(A,B) | less(B,A) | B = A # label(less_property) # label(axiom). [clausify(34)].
% 1.06/1.34 149 holdsAt(waterLevel(n0),n0) # label(waterLevel_0) # label(hypothesis). [assumption].
% 1.06/1.34 155 -holdsAt(waterLevel(n2),n2) # label(waterLevel_2) # label(negated_conjecture). [assumption].
% 1.06/1.34 168 tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 1.06/1.34 169 -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)].
% 1.06/1.34 170 -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)])].
% 1.06/1.34 171 -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)].
% 1.06/1.34 172 -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)])].
% 1.06/1.34 173 -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)].
% 1.06/1.34 174 -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)])].
% 1.06/1.34 175 -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)].
% 1.06/1.34 176 -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)])].
% 1.06/1.34 178 plus(n1,n0) = n1. [back_rewrite(114),rewrite([123(3)])].
% 1.06/1.34 179 -less(A,A). [factor(146,a,b)].
% 1.06/1.34 180 initiates(tapOn,A,B) | filling != A. [xx_res(87,b)].
% 1.06/1.34 188 happens(tapOn,A) | n0 != A. [xx_res(101,b)].
% 1.06/1.34 199 less_or_equal(A,A). [xx_res(126,b)].
% 1.06/1.34 204 less(n5,A) | n5 = A | less_or_equal(A,n4). [resolve(148,a,136,a)].
% 1.06/1.34 205 less(n4,A) | n4 = A | less_or_equal(A,n3). [resolve(148,a,134,a)].
% 1.06/1.34 206 less(n3,A) | n3 = A | less_or_equal(A,n2). [resolve(148,a,132,a)].
% 1.06/1.34 207 less(n2,A) | n2 = A | less_or_equal(A,n1). [resolve(148,a,130,a)].
% 1.06/1.34 208 less(n1,A) | n1 = A | less_or_equal(A,n0). [resolve(148,a,128,a)].
% 1.06/1.34 220 waterLevel(A) != B | waterLevel(f11(tapOn,B,C)) = B. [xx_res(168,a)].
% 1.06/1.34 222 initiates(tapOn,filling,A). [xx_res(180,b)].
% 1.06/1.34 230 less(n1,n2). [resolve(199,a,131,b)].
% 1.06/1.34 231 less(n0,n1). [resolve(199,a,129,b)].
% 1.06/1.34 256 less_or_equal(n1,n2). [resolve(230,a,125,b)].
% 1.06/1.34 257 n0 != n1. [resolve(231,a,147,a),flip(a)].
% 1.06/1.34 258 less_or_equal(n0,n1). [resolve(231,a,125,b)].
% 1.06/1.34 266 less(n1,n3). [resolve(256,a,133,b)].
% 1.06/1.34 267 less(n0,n2). [resolve(258,a,131,b)].
% 1.06/1.34 287 n3 != n1. [resolve(266,a,147,a)].
% 1.06/1.34 290 n2 != n0. [resolve(267,a,147,a)].
% 1.06/1.34 291 less_or_equal(n0,n2). [resolve(267,a,125,b)].
% 1.06/1.34 296 happens(tapOn,n0). [resolve(188,b,113,a(flip)),rewrite([113(4)])].
% 1.06/1.34 299 less(n0,n3). [resolve(291,a,133,b)].
% 1.06/1.34 319 n3 != n0. [resolve(299,a,147,a)].
% 1.06/1.34 320 less_or_equal(n0,n3). [resolve(299,a,125,b)].
% 1.06/1.34 326 less(n0,n4). [resolve(320,a,135,b)].
% 1.06/1.34 343 n4 != n0. [resolve(326,a,147,a)].
% 1.06/1.34 344 less_or_equal(n0,n4). [resolve(326,a,125,b)].
% 1.06/1.34 351 less(n0,n5). [resolve(344,a,137,b)].
% 1.06/1.34 365 n5 != n0. [resolve(351,a,147,a)].
% 1.06/1.34 367 less(n5,A) | n5 = A | less(A,n4) | n4 = A. [resolve(204,c,124,a)].
% 1.06/1.34 372 less(n4,A) | n4 = A | less(A,n3) | n3 = A. [resolve(205,c,124,a)].
% 1.06/1.34 384 less(n3,A) | n3 = A | less(A,n2) | n2 = A. [resolve(206,c,124,a)].
% 1.06/1.34 388 less(n2,A) | n2 = A | less(A,n1) | n1 = A. [resolve(207,c,124,a)].
% 1.06/1.34 397 less(n1,A) | n1 = A | n0 = A. [resolve(208,c,124,a),unit_del(c,127)].
% 1.06/1.34 417 -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)].
% 1.06/1.34 418 -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)].
% 1.06/1.34 419 -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)].
% 1.06/1.34 420 -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)].
% 1.06/1.34 426 -happens(tapOn,A) | holdsAt(filling,plus(A,n1)). [resolve(222,a,65,b)].
% 1.06/1.34 452 holdsAt(filling,n1). [resolve(426,a,296,a),rewrite([123(4),178(4)])].
% 1.06/1.34 454 releasedAt(filling,n2) | happens(f5(filling,n1),n1) | holdsAt(filling,n2). [resolve(452,a,58,a),rewrite([117(4),117(12)])].
% 1.06/1.34 455 n1 = A | n0 = A | -less(A,n1). [resolve(397,a,146,b)].
% 1.06/1.34 513 waterLevel(f11(tapOn,waterLevel(A),B)) = waterLevel(A). [xx_res(220,a)].
% 1.06/1.34 541 less(n5,A) | n5 = A | n4 = A | -less(n4,A). [resolve(367,c,146,b)].
% 1.06/1.34 546 less(n4,A) | n4 = A | n3 = A | -less(n3,A). [resolve(372,c,146,b)].
% 1.06/1.34 550 n3 = A | less(A,n2) | n2 = A | -less(A,n3). [resolve(384,a,146,b)].
% 1.06/1.34 552 less(n3,A) | n3 = A | n2 = A | -less(n2,A). [resolve(384,c,146,b)].
% 1.06/1.34 558 less(n2,A) | n2 = A | n1 = A | n0 = A. [resolve(388,c,455,c),merge(d)].
% 1.06/1.34 562 -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)])].
% 1.06/1.34 564 -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)])].
% 1.06/1.34 565 f11(tapOn,waterLevel(A),B) = A. [resolve(513,a,111,a)].
% 1.06/1.34 579 -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)])].
% 1.06/1.34 608 -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)])].
% 1.06/1.34 823 less(n5,A) | n5 = A | n4 = A | less(A,n3) | n3 = A. [resolve(541,d,372,a),merge(d)].
% 1.06/1.34 829 less(n4,A) | n4 = A | n3 = A | less(A,n2) | n2 = A. [resolve(546,d,384,a),merge(d)].
% 1.06/1.34 830 less(n3,A) | n3 = A | n2 = A | less(A,n1) | n1 = A. [resolve(552,d,388,a),merge(d)].
% 1.06/1.34 832 n2 = A | n1 = A | n0 = A | -less(A,n2). [resolve(558,a,146,b)].
% 1.06/1.34 834 -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)].
% 1.06/1.34 849 -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)].
% 1.06/1.34 870 -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)].
% 1.06/1.34 873 less(n5,A) | n5 = A | n4 = A | n3 = A | less(A,n2) | n2 = A. [resolve(823,d,550,d),merge(e)].
% 1.06/1.34 888 -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)].
% 1.06/1.34 919 holdsAt(waterLevel(A),n2) | terminates(f1(n0,filling,n2),filling,f2(n0,filling,n2)) | n2 != A. [resolve(834,a,829,d),rewrite([123(4),115(4),123(8),115(8),123(13),115(13),123(16),115(16)]),unit_del(d,127),unit_del(e,343),unit_del(f,319),unit_del(g,290)].
% 1.06/1.34 941 terminates(f1(n0,filling,n2),filling,f2(n0,filling,n2)). [resolve(919,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 1.06/1.34 947 -happens(f1(n0,filling,n2),f2(n0,filling,n2)) | -releasedAt(filling,plus(n1,f2(n0,filling,n2))). [resolve(941,a,68,b),rewrite([123(16)])].
% 1.06/1.34 948 -happens(f1(n0,filling,n2),f2(n0,filling,n2)) | -holdsAt(filling,plus(n1,f2(n0,filling,n2))). [resolve(941,a,66,b),rewrite([123(16)])].
% 1.06/1.34 1138 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)].
% 1.06/1.34 1139 holdsAt(waterLevel(A),n2) | less(f2(n0,filling,n2),n2) | n2 != A. [resolve(849,a,829,d),rewrite([123(4),115(4),123(8),115(8),123(10),115(10),123(12),115(12)]),unit_del(d,127),unit_del(e,343),unit_del(f,319),unit_del(g,290)].
% 1.06/1.34 1148 holdsAt(waterLevel(n1),n1) | less(f2(n0,filling,n1),n1). [resolve(1138,c,565,a(flip)),rewrite([565(4)])].
% 1.06/1.34 1149 less(f2(n0,filling,n1),n1) | -holdsAt(waterLevel(A),n1) | n1 = A. [resolve(1148,a,103,b)].
% 1.06/1.34 1154 less(f2(n0,filling,n2),n2). [resolve(1139,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 1.06/1.34 1155 f2(n0,filling,n2) = n2 | f2(n0,filling,n2) = n1 | f2(n0,filling,n2) = n0. [resolve(1154,a,832,d),flip(a),flip(b),flip(c)].
% 1.06/1.34 1164 f2(n0,filling,n2) != n2. [resolve(1154,a,147,a),flip(a)].
% 1.06/1.34 1176 f2(n0,filling,n2) = n1 | f2(n0,filling,n2) = n0. [back_unit_del(1155),unit_del(a,1164)].
% 1.06/1.34 1223 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)].
% 1.06/1.34 1224 holdsAt(waterLevel(A),n2) | less(n0,f2(n0,filling,n2)) | n2 != A. [resolve(870,a,829,d),rewrite([123(4),115(4),123(9),115(9),123(12),115(12)]),unit_del(d,127),unit_del(e,343),unit_del(f,319),unit_del(g,290)].
% 1.06/1.34 1270 holdsAt(waterLevel(n1),n1) | less(n0,f2(n0,filling,n1)). [resolve(1223,c,565,a(flip)),rewrite([565(4)])].
% 1.06/1.34 1275 less(n0,f2(n0,filling,n1)) | -holdsAt(waterLevel(A),n1) | n1 = A. [resolve(1270,a,103,b)].
% 1.06/1.34 1280 less(n0,f2(n0,filling,n2)). [resolve(1224,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 1.06/1.34 1286 f2(n0,filling,n2) = n1. [para(1176(b,1),1280(a,2)),unit_del(b,179)].
% 1.06/1.34 1288 -happens(f1(n0,filling,n2),n1) | -holdsAt(filling,n2). [back_rewrite(948),rewrite([1286(8),1286(12),117(10)])].
% 1.06/1.34 1289 -happens(f1(n0,filling,n2),n1) | -releasedAt(filling,n2). [back_rewrite(947),rewrite([1286(8),1286(12),117(10)])].
% 1.06/1.34 1296 holdsAt(waterLevel(A),n2) | happens(f1(n0,filling,n2),n1) | n2 != A. [resolve(888,a,873,e),rewrite([123(4),115(4),123(8),115(8),123(12),115(12),1286(11),123(12),115(12)]),unit_del(d,127),unit_del(e,365),unit_del(f,343),unit_del(g,319),unit_del(h,290)].
% 1.06/1.34 1306 -happens(f1(n0,filling,n2),n1) | happens(f5(filling,n1),n1) | holdsAt(filling,n2). [resolve(1289,b,454,a)].
% 1.06/1.34 1318 happens(f1(n0,filling,n2),n1). [resolve(1296,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 1.06/1.34 1319 happens(f5(filling,n1),n1) | holdsAt(filling,n2). [back_unit_del(1306),unit_del(a,1318)].
% 1.06/1.34 1326 -holdsAt(filling,n2). [back_unit_del(1288),unit_del(a,1318)].
% 1.06/1.34 1329 happens(f5(filling,n1),n1). [back_unit_del(1319),unit_del(b,1326)].
% 1.06/1.34 1332 holdsAt(waterLevel(n3),n1). [resolve(1329,a,98,a),unit_del(a,257)].
% 1.06/1.34 1362 less(n0,f2(n0,filling,n1)). [resolve(1332,a,1275,b),flip(b),unit_del(b,287)].
% 1.06/1.34 1363 less(f2(n0,filling,n1),n1). [resolve(1332,a,1149,b),flip(b),unit_del(b,287)].
% 1.06/1.34 1381 f2(n0,filling,n1) != n0. [resolve(1362,a,147,a)].
% 1.06/1.34 1391 f2(n0,filling,n1) = n1. [resolve(1363,a,455,c),flip(a),flip(b),unit_del(b,1381)].
% 1.06/1.34 1392 $F. [resolve(1363,a,147,a),rewrite([1391(5)]),xx(a)].
% 1.06/1.34
% 1.06/1.34 % SZS output end Refutation
% 1.06/1.34 ============================== end of proof ==========================
% 1.06/1.34
% 1.06/1.34 ============================== STATISTICS ============================
% 1.06/1.34
% 1.06/1.34 Given=853. Generated=12674. Kept=1328. proofs=1.
% 1.06/1.34 Usable=724. Sos=167. Demods=18. Limbo=9, Disabled=567. Hints=0.
% 1.06/1.34 Megabytes=1.76.
% 1.06/1.34 User_CPU=0.30, System_CPU=0.02, Wall_clock=1.
% 1.06/1.34
% 1.06/1.34 ============================== end of statistics =====================
% 1.06/1.34
% 1.06/1.34 ============================== end of search =========================
% 1.06/1.34
% 1.06/1.34 THEOREM PROVED
% 1.06/1.34 % SZS status Theorem
% 1.06/1.34
% 1.06/1.34 Exiting with 1 proof.
% 1.06/1.34
% 1.06/1.34 Process 8557 exit (max_proofs) Fri Jun 10 05:48:40 2022
% 1.06/1.34 Prover9 interrupted
%------------------------------------------------------------------------------