TSTP Solution File: CSR005+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CSR005+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 1.95s 2.27s
% Output : Refutation 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CSR005+2 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 10 04:18:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/1.05 ============================== Prover9 ===============================
% 0.46/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.05 Process 18251 was started by sandbox2 on n026.cluster.edu,
% 0.46/1.05 Fri Jun 10 04:18:34 2022
% 0.46/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18081_n026.cluster.edu".
% 0.46/1.05 ============================== end of head ===========================
% 0.46/1.05
% 0.46/1.05 ============================== INPUT =================================
% 0.46/1.05
% 0.46/1.05 % Reading from file /tmp/Prover9_18081_n026.cluster.edu
% 0.46/1.05
% 0.46/1.05 set(prolog_style_variables).
% 0.46/1.05 set(auto2).
% 0.46/1.05 % set(auto2) -> set(auto).
% 0.46/1.05 % set(auto) -> set(auto_inference).
% 0.46/1.05 % set(auto) -> set(auto_setup).
% 0.46/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.05 % set(auto) -> set(auto_limits).
% 0.46/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.05 % set(auto) -> set(auto_denials).
% 0.46/1.05 % set(auto) -> set(auto_process).
% 0.46/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.05 % set(auto2) -> assign(stats, some).
% 0.46/1.05 % set(auto2) -> clear(echo_input).
% 0.46/1.05 % set(auto2) -> set(quiet).
% 0.46/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.05 % set(auto2) -> clear(print_given).
% 0.46/1.05 assign(lrs_ticks,-1).
% 0.46/1.05 assign(sos_limit,10000).
% 0.46/1.05 assign(order,kbo).
% 0.46/1.05 set(lex_order_vars).
% 0.46/1.05 clear(print_given).
% 0.46/1.05
% 0.46/1.05 % formulas(sos). % not echoed (56 formulas)
% 0.46/1.05
% 0.46/1.05 ============================== end of input ==========================
% 0.46/1.05
% 0.46/1.05 % From the command line: assign(max_seconds, 300).
% 0.46/1.05
% 0.46/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.05
% 0.46/1.05 % Formulas that are not ordinary clauses:
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 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].
% 0.46/1.05 19 (all X filling != waterLevel(X)) # label(filling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 20 (all X spilling != waterLevel(X)) # label(spilling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 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].
% 0.46/1.05 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 29 (all X (less(X,n5) <-> less_or_equal(X,n4))) # label(less5) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 30 (all X (less(X,n6) <-> less_or_equal(X,n5))) # label(less6) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.05 31 (all X (less(X,n7) <-> less_or_equal(X,n6))) # label(less7) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.06 32 (all X (less(X,n8) <-> less_or_equal(X,n7))) # label(less8) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.06 33 (all X (less(X,n9) <-> less_or_equal(X,n8))) # label(less9) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.06 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.06 35 (all Height -releasedAt(waterLevel(Height),n0)) # label(not_released_waterLevel_0) # label(hypothesis) # label(non_clause). [assumption].
% 0.46/1.06
% 0.46/1.06 ============================== end of process non-clausal formulas ===
% 0.46/1.06
% 0.46/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.06
% 0.46/1.06 ============================== PREDICATE ELIMINATION =================
% 0.46/1.06 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)].
% 0.46/1.06 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.46/1.06 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.46/1.06 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.46/1.06 40 -stoppedIn(A,B,C) | terminates(f1(A,B,C),B,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 43 -startedIn(A,B,C) | happens(f3(A,C,B),f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.46/1.06 44 -startedIn(A,B,C) | less(A,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.46/1.06 45 -startedIn(A,B,C) | less(f4(A,C,B),C) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.46/1.06 46 -startedIn(A,B,C) | initiates(f3(A,C,B),B,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 0.46/1.06 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 48 -happens(A,B) | -releases(A,C,B) | releasedAt(C,plus(B,n1)) # label(happens_releases) # label(axiom). [clausify(11)].
% 1.95/2.27 49 releasedAt(A,B) | releases(f8(A,B),A,B) | -releasedAt(A,plus(B,n1)) # label(keep_not_released) # label(axiom). [clausify(8)].
% 1.95/2.27 50 -releases(A,B,C) | tapOn = A # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.95/2.27 Derived: tapOn = f8(A,B) | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(50,a,49,b)].
% 1.95/2.27 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.95/2.27 Derived: waterLevel(f11(f8(A,B),A,B)) = A | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(51,a,49,b)].
% 1.95/2.27 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.95/2.27 Derived: tapOn != A | waterLevel(B) != C | -happens(A,D) | releasedAt(C,plus(D,n1)). [resolve(52,a,48,b)].
% 1.95/2.27 Derived: tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 1.95/2.27 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)].
% 1.95/2.27 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27
% 1.95/2.27 ============================== end predicate elimination =============
% 1.95/2.27
% 1.95/2.27 Auto_denials: (non-Horn, no changes).
% 1.95/2.27
% 1.95/2.27 Term ordering decisions:
% 1.95/2.27
% 1.95/2.27 % Assigning unary symbol waterLevel kb_weight 0 and highest precedence (36).
% 1.95/2.27 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.
% 1.95/2.27
% 1.95/2.27 ============================== end of process initial clauses ========
% 1.95/2.27
% 1.95/2.27 ============================== CLAUSES FOR SEARCH ====================
% 1.95/2.27
% 1.95/2.27 ============================== end of clauses for search =============
% 1.95/2.27
% 1.95/2.27 ============================== SEARCH ================================
% 1.95/2.27
% 1.95/2.27 % Starting search at 0.03 seconds.
% 1.95/2.27
% 1.95/2.27 ============================== PROOF =================================
% 1.95/2.27 % SZS status Theorem
% 1.95/2.27 % SZS output start Refutation
% 1.95/2.27
% 1.95/2.27 % Proof 1 at 1.21 (+ 0.03) seconds.
% 1.95/2.27 % Length of proof is 190.
% 1.95/2.27 % Level of proof is 29.
% 1.95/2.27 % Maximum clause weight is 38.000.
% 1.95/2.27 % Given clauses 2513.
% 1.95/2.27
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 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].
% 1.95/2.27 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 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].
% 1.95/2.27 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 1.95/2.27 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)].
% 1.95/2.27 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.95/2.27 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.95/2.27 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 1.95/2.27 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)].
% 1.95/2.27 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.95/2.27 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 1.95/2.27 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)].
% 1.95/2.27 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 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)].
% 1.95/2.27 62 -releasedAt(A,B) | happens(f7(A,B),B) | releasedAt(A,plus(B,n1)) # label(keep_released) # label(axiom). [clausify(7)].
% 1.95/2.27 65 -happens(A,B) | -initiates(A,C,B) | holdsAt(C,plus(B,n1)) # label(happens_holds) # label(axiom). [clausify(9)].
% 1.95/2.27 87 initiates(A,B,C) | tapOn != A | filling != B # label(initiates_all_defn) # label(axiom). [clausify(13)].
% 1.95/2.27 94 terminates(A,B,C) | overflow != A | filling != B # label(terminates_all_defn) # label(axiom). [clausify(14)].
% 1.95/2.27 98 -happens(A,B) | n0 = B | holdsAt(waterLevel(n3),B) # label(happens_all_defn) # label(axiom). [clausify(16)].
% 1.95/2.27 99 -happens(A,B) | n0 = B | holdsAt(filling,B) # label(happens_all_defn) # label(axiom). [clausify(16)].
% 1.95/2.27 101 happens(A,B) | tapOn != A | n0 != B # label(happens_all_defn) # label(axiom). [clausify(16)].
% 1.95/2.27 102 happens(A,B) | -holdsAt(waterLevel(n3),B) | -holdsAt(filling,B) | overflow != A # label(happens_all_defn) # label(axiom). [clausify(16)].
% 1.95/2.27 103 -holdsAt(waterLevel(A),B) | -holdsAt(waterLevel(C),B) | C = A # label(same_waterLevel) # label(axiom). [clausify(18)].
% 1.95/2.27 111 waterLevel(A) != waterLevel(B) | A = B # label(distinct_waterLevels) # label(axiom). [clausify(21)].
% 1.95/2.27 113 plus(n0,n0) = n0 # label(plus0_0) # label(axiom). [assumption].
% 1.95/2.27 114 plus(n0,n1) = n1 # label(plus0_1) # label(axiom). [assumption].
% 1.95/2.27 115 plus(n0,n2) = n2 # label(plus0_2) # label(axiom). [assumption].
% 1.95/2.27 117 plus(n1,n1) = n2 # label(plus1_1) # label(axiom). [assumption].
% 1.95/2.27 118 plus(n1,n2) = n3 # label(plus1_2) # label(axiom). [assumption].
% 1.95/2.27 123 plus(A,B) = plus(B,A) # label(symmetry_of_plus) # label(axiom). [clausify(22)].
% 1.95/2.27 124 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(23)].
% 1.95/2.27 125 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(23)].
% 1.95/2.27 126 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(23)].
% 1.95/2.27 127 -less(A,n0) # label(less0) # label(axiom). [clausify(24)].
% 1.95/2.27 128 -less(A,n1) | less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 1.95/2.27 129 less(A,n1) | -less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 1.95/2.27 130 -less(A,n2) | less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 1.95/2.27 131 less(A,n2) | -less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 1.95/2.27 132 -less(A,n3) | less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 1.95/2.27 133 less(A,n3) | -less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 1.95/2.27 134 -less(A,n4) | less_or_equal(A,n3) # label(less4) # label(axiom). [clausify(28)].
% 1.95/2.27 135 less(A,n4) | -less_or_equal(A,n3) # label(less4) # label(axiom). [clausify(28)].
% 1.95/2.27 146 -less(A,B) | -less(B,A) # label(less_property) # label(axiom). [clausify(34)].
% 1.95/2.27 147 -less(A,B) | B != A # label(less_property) # label(axiom). [clausify(34)].
% 1.95/2.27 148 less(A,B) | less(B,A) | B = A # label(less_property) # label(axiom). [clausify(34)].
% 1.95/2.27 149 holdsAt(waterLevel(n0),n0) # label(waterLevel_0) # label(hypothesis). [assumption].
% 1.95/2.27 155 -releasedAt(filling,n3) # label(filling_3_l1) # label(lemma). [assumption].
% 1.95/2.27 156 -holdsAt(filling,n3) # label(filling_3) # label(negated_conjecture). [assumption].
% 1.95/2.27 158 -happens(A,B) | -less(C,B) | -less(B,D) | -terminates(A,E,B) | less(C,f2(C,E,D)). [resolve(36,a,38,a)].
% 1.95/2.27 159 -happens(A,B) | -less(C,B) | -less(B,D) | -terminates(A,E,B) | less(f2(C,E,D),D). [resolve(36,a,39,a)].
% 1.95/2.27 169 tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 1.95/2.27 170 -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(E,C) != D. [resolve(53,d,54,c)].
% 1.95/2.27 171 -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(170),rewrite([123(18)])].
% 1.95/2.27 172 -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(E,C) != D. [resolve(55,d,54,c)].
% 1.95/2.27 173 -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(172),rewrite([123(15)])].
% 1.95/2.27 174 -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(E,C) != D. [resolve(56,d,54,c)].
% 1.95/2.27 175 -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(174),rewrite([123(16)])].
% 1.95/2.27 179 plus(n1,n0) = n1. [back_rewrite(114),rewrite([123(3)])].
% 1.95/2.27 181 initiates(tapOn,A,B) | filling != A. [xx_res(87,b)].
% 1.95/2.27 187 terminates(overflow,A,B) | filling != A. [xx_res(94,b)].
% 1.95/2.27 189 happens(tapOn,A) | n0 != A. [xx_res(101,b)].
% 1.95/2.27 200 less_or_equal(A,A). [xx_res(126,b)].
% 1.95/2.27 206 less(n4,A) | n4 = A | less_or_equal(A,n3). [resolve(148,a,134,a)].
% 1.95/2.27 207 less(n3,A) | n3 = A | less_or_equal(A,n2). [resolve(148,a,132,a)].
% 1.95/2.27 208 less(n2,A) | n2 = A | less_or_equal(A,n1). [resolve(148,a,130,a)].
% 1.95/2.27 209 less(n1,A) | n1 = A | less_or_equal(A,n0). [resolve(148,a,128,a)].
% 1.95/2.27 221 waterLevel(A) != B | waterLevel(f11(tapOn,B,C)) = B. [xx_res(169,a)].
% 1.95/2.27 223 initiates(tapOn,filling,A). [xx_res(181,b)].
% 1.95/2.27 230 less(n2,n3). [resolve(200,a,133,b)].
% 1.95/2.27 231 less(n1,n2). [resolve(200,a,131,b)].
% 1.95/2.27 232 less(n0,n1). [resolve(200,a,129,b)].
% 1.95/2.27 251 n2 != n3. [resolve(230,a,147,a),flip(a)].
% 1.95/2.27 255 n2 != n1. [resolve(231,a,147,a)].
% 1.95/2.27 257 less_or_equal(n1,n2). [resolve(231,a,125,b)].
% 1.95/2.27 258 n0 != n1. [resolve(232,a,147,a),flip(a)].
% 1.95/2.27 259 less_or_equal(n0,n1). [resolve(232,a,125,b)].
% 1.95/2.27 267 less(n1,n3). [resolve(257,a,133,b)].
% 1.95/2.27 268 less(n0,n2). [resolve(259,a,131,b)].
% 1.95/2.27 284 terminates(overflow,filling,A). [xx_res(187,b)].
% 1.95/2.27 288 n3 != n1. [resolve(267,a,147,a)].
% 1.95/2.27 290 less_or_equal(n1,n3). [resolve(267,a,125,b)].
% 1.95/2.27 291 n2 != n0. [resolve(268,a,147,a)].
% 1.95/2.27 292 less_or_equal(n0,n2). [resolve(268,a,125,b)].
% 1.95/2.27 297 happens(tapOn,n0). [resolve(189,b,113,a(flip)),rewrite([113(4)])].
% 1.95/2.27 299 less(n1,n4). [resolve(290,a,135,b)].
% 1.95/2.27 300 less(n0,n3). [resolve(292,a,133,b)].
% 1.95/2.27 317 n4 != n1. [resolve(299,a,147,a)].
% 1.95/2.27 318 -less(n4,n1). [resolve(299,a,146,b)].
% 1.95/2.27 320 n3 != n0. [resolve(300,a,147,a)].
% 1.95/2.27 321 less_or_equal(n0,n3). [resolve(300,a,125,b)].
% 1.95/2.27 327 less(n0,n4). [resolve(321,a,135,b)].
% 1.95/2.27 344 n4 != n0. [resolve(327,a,147,a)].
% 1.95/2.27 373 less(n4,A) | n4 = A | less(A,n3) | n3 = A. [resolve(206,c,124,a)].
% 1.95/2.27 385 less(n3,A) | n3 = A | less(A,n2) | n2 = A. [resolve(207,c,124,a)].
% 1.95/2.27 389 less(n2,A) | n2 = A | less(A,n1) | n1 = A. [resolve(208,c,124,a)].
% 1.95/2.27 398 less(n1,A) | n1 = A | n0 = A. [resolve(209,c,124,a),unit_del(c,127)].
% 1.95/2.27 419 -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(223,a,175,b)].
% 1.95/2.27 420 -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(223,a,173,b)].
% 1.95/2.27 421 -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(223,a,171,b)].
% 1.95/2.27 427 -happens(tapOn,A) | holdsAt(filling,plus(A,n1)). [resolve(223,a,65,b)].
% 1.95/2.27 441 -happens(overflow,A) | -less(B,A) | -less(A,C) | less(f2(B,filling,C),C). [resolve(284,a,159,d)].
% 1.95/2.27 442 -happens(overflow,A) | -less(B,A) | -less(A,C) | less(B,f2(B,filling,C)). [resolve(284,a,158,d)].
% 1.95/2.27 453 holdsAt(filling,n1). [resolve(427,a,297,a),rewrite([123(4),179(4)])].
% 1.95/2.27 455 releasedAt(filling,n2) | happens(f5(filling,n1),n1) | holdsAt(filling,n2). [resolve(453,a,58,a),rewrite([117(4),117(12)])].
% 1.95/2.27 456 n1 = A | n0 = A | -less(A,n1). [resolve(398,a,146,b)].
% 1.95/2.27 514 waterLevel(f11(tapOn,waterLevel(A),B)) = waterLevel(A). [xx_res(221,a)].
% 1.95/2.27 547 less(n4,A) | n4 = A | n3 = A | -less(n3,A). [resolve(373,c,146,b)].
% 1.95/2.27 553 less(n3,A) | n3 = A | n2 = A | -less(n2,A). [resolve(385,c,146,b)].
% 1.95/2.27 559 less(n2,A) | n2 = A | n1 = A | n0 = A. [resolve(389,c,456,c),merge(d)].
% 1.95/2.27 565 -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(419,a,297,a),rewrite([123(5),123(10),123(13)])].
% 1.95/2.27 566 f11(tapOn,waterLevel(A),B) = A. [resolve(514,a,111,a)].
% 1.95/2.27 580 -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(420,a,297,a),rewrite([123(5),123(11)])].
% 1.95/2.27 609 -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(421,a,297,a),rewrite([123(5),123(10),123(15)])].
% 1.95/2.27 744 happens(f5(filling,n1),n1) | holdsAt(filling,n2) | happens(f7(filling,n2),n2). [resolve(455,a,62,a),rewrite([123(17),118(17)]),unit_del(d,155)].
% 1.95/2.27 830 less(n4,A) | n4 = A | n3 = A | less(A,n2) | n2 = A. [resolve(547,d,385,a),merge(d)].
% 1.95/2.27 831 less(n3,A) | n3 = A | n2 = A | less(A,n1) | n1 = A. [resolve(553,d,389,a),merge(d)].
% 1.95/2.27 833 n2 = A | n1 = A | n0 = A | -less(A,n2). [resolve(559,a,146,b)].
% 1.95/2.27 852 happens(f5(filling,n1),n1) | holdsAt(filling,n2). [resolve(744,c,99,a),flip(c),merge(d),unit_del(c,291)].
% 1.95/2.27 853 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | less(f2(n0,filling,plus(A,n0)),plus(A,n0)) | plus(A,n0) != B. [resolve(565,d,149,a)].
% 1.95/2.27 856 holdsAt(filling,n2) | holdsAt(waterLevel(n3),n1). [resolve(852,a,98,a),unit_del(b,258)].
% 1.95/2.27 857 holdsAt(filling,n2) | -holdsAt(waterLevel(A),n1) | n3 = A. [resolve(856,b,103,b)].
% 1.95/2.27 858 holdsAt(filling,n2) | happens(A,n1) | overflow != A. [resolve(856,b,102,b),unit_del(c,453)].
% 1.95/2.27 865 holdsAt(filling,n2) | happens(overflow,n1). [resolve(858,c,566,a(flip)),rewrite([566(7)])].
% 1.95/2.27 866 -less(n0,A) | holdsAt(waterLevel(B),plus(A,n0)) | less(n0,f2(n0,filling,plus(A,n0))) | plus(A,n0) != B. [resolve(580,d,149,a)].
% 1.95/2.27 868 holdsAt(filling,n2) | -less(A,n1) | -less(n1,B) | less(A,f2(A,filling,B)). [resolve(865,b,442,a)].
% 1.95/2.27 869 holdsAt(filling,n2) | -less(A,n1) | -less(n1,B) | less(f2(A,filling,B),B). [resolve(865,b,441,a)].
% 1.95/2.27 883 -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(609,d,149,a)].
% 1.95/2.27 1298 holdsAt(waterLevel(A),n1) | less(f2(n0,filling,n1),n1) | n1 != A. [resolve(853,a,831,d),rewrite([179(4),179(8),179(10),179(12)]),flip(g),unit_del(d,127),unit_del(e,320),unit_del(f,291),unit_del(g,258)].
% 1.95/2.27 1299 holdsAt(waterLevel(A),n2) | less(f2(n0,filling,n2),n2) | n2 != A. [resolve(853,a,830,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,344),unit_del(f,320),unit_del(g,291)].
% 1.95/2.27 1320 holdsAt(waterLevel(A),n1) | less(n0,f2(n0,filling,n1)) | n1 != A. [resolve(866,a,831,d),rewrite([179(4),179(9),179(12)]),flip(g),unit_del(d,127),unit_del(e,320),unit_del(f,291),unit_del(g,258)].
% 1.95/2.27 1321 holdsAt(waterLevel(A),n2) | less(n0,f2(n0,filling,n2)) | n2 != A. [resolve(866,a,830,d),rewrite([123(4),115(4),123(9),115(9),123(12),115(12)]),unit_del(d,127),unit_del(e,344),unit_del(f,320),unit_del(g,291)].
% 1.95/2.27 1356 holdsAt(waterLevel(n1),n1) | less(f2(n0,filling,n1),n1). [resolve(1298,c,566,a(flip)),rewrite([566(4)])].
% 1.95/2.27 1357 less(f2(n0,filling,n1),n1) | holdsAt(filling,n2). [resolve(1356,a,857,b),unit_del(c,288)].
% 1.95/2.27 1358 less(f2(n0,filling,n1),n1) | -holdsAt(waterLevel(A),n1) | n1 = A. [resolve(1356,a,103,b)].
% 1.95/2.27 1364 less(f2(n0,filling,n1),n1) | happens(f5(filling,n2),n2). [resolve(1357,b,58,a),rewrite([123(10),118(10),123(18),118(18)]),unit_del(b,155),unit_del(d,156)].
% 1.95/2.27 1367 less(f2(n0,filling,n1),n1) | holdsAt(waterLevel(n3),n2). [resolve(1364,b,98,a),flip(b),unit_del(b,291)].
% 1.95/2.27 1370 holdsAt(filling,n2) | -less(n1,A) | less(n0,f2(n0,filling,A)). [resolve(868,b,232,a)].
% 1.95/2.27 1392 less(f2(n0,filling,n1),n1) | -holdsAt(waterLevel(A),n2) | n3 = A. [resolve(1367,b,103,b)].
% 1.95/2.27 1416 holdsAt(filling,n2) | -less(n1,A) | less(f2(n0,filling,A),A). [resolve(869,b,232,a)].
% 1.95/2.27 1645 holdsAt(filling,n2) | less(n0,f2(n0,filling,n2)). [resolve(1370,b,830,d),unit_del(c,318),unit_del(d,317),unit_del(e,288),unit_del(f,255)].
% 1.95/2.27 1664 holdsAt(waterLevel(A),n2) | happens(f1(n0,filling,n2),f2(n0,filling,n2)) | n2 != A. [resolve(883,a,830,d),rewrite([123(4),115(4),123(8),115(8),123(12),115(12),123(15),115(15)]),unit_del(d,127),unit_del(e,344),unit_del(f,320),unit_del(g,291)].
% 1.95/2.27 1674 less(n0,f2(n0,filling,n2)) | happens(f5(filling,n2),n2). [resolve(1645,a,58,a),rewrite([123(10),118(10),123(18),118(18)]),unit_del(b,155),unit_del(d,156)].
% 1.95/2.27 1706 less(n0,f2(n0,filling,n2)) | holdsAt(waterLevel(n3),n2). [resolve(1674,b,98,a),flip(b),unit_del(b,291)].
% 1.95/2.27 1709 less(n0,f2(n0,filling,n2)) | -holdsAt(waterLevel(A),n2) | n3 = A. [resolve(1706,b,103,b)].
% 1.95/2.27 2012 holdsAt(filling,n2) | less(f2(n0,filling,n2),n2). [resolve(1416,b,830,d),unit_del(c,318),unit_del(d,317),unit_del(e,288),unit_del(f,255)].
% 1.95/2.27 2031 less(f2(n0,filling,n2),n2) | happens(f5(filling,n2),n2). [resolve(2012,a,58,a),rewrite([123(10),118(10),123(18),118(18)]),unit_del(b,155),unit_del(d,156)].
% 1.95/2.27 2094 less(f2(n0,filling,n2),n2) | holdsAt(waterLevel(n3),n2). [resolve(2031,b,98,a),flip(b),unit_del(b,291)].
% 1.95/2.27 2097 less(f2(n0,filling,n2),n2) | -holdsAt(waterLevel(A),n2) | n3 = A. [resolve(2094,b,103,b)].
% 1.95/2.27 4848 holdsAt(waterLevel(n2),n2) | less(f2(n0,filling,n2),n2). [resolve(1299,c,566,a(flip)),rewrite([566(4)])].
% 1.95/2.27 5029 holdsAt(waterLevel(n1),n1) | less(n0,f2(n0,filling,n1)). [resolve(1320,c,566,a(flip)),rewrite([566(4)])].
% 1.95/2.27 5033 less(n0,f2(n0,filling,n1)) | holdsAt(filling,n2). [resolve(5029,a,857,b),unit_del(c,288)].
% 1.95/2.27 5034 less(n0,f2(n0,filling,n1)) | -holdsAt(waterLevel(A),n1) | n1 = A. [resolve(5029,a,103,b)].
% 1.95/2.27 5040 less(n0,f2(n0,filling,n1)) | happens(f5(filling,n2),n2). [resolve(5033,b,58,a),rewrite([123(10),118(10),123(18),118(18)]),unit_del(b,155),unit_del(d,156)].
% 1.95/2.27 5043 less(n0,f2(n0,filling,n1)) | holdsAt(waterLevel(n3),n2). [resolve(5040,b,98,a),flip(b),unit_del(b,291)].
% 1.95/2.27 5046 less(n0,f2(n0,filling,n1)) | -holdsAt(waterLevel(A),n2) | n3 = A. [resolve(5043,b,103,b)].
% 1.95/2.27 5760 holdsAt(waterLevel(n2),n2) | less(n0,f2(n0,filling,n2)). [resolve(1321,c,566,a(flip)),rewrite([566(4)])].
% 1.95/2.27 6327 less(n0,f2(n0,filling,n2)). [resolve(1709,b,5760,a),flip(b),merge(c),unit_del(b,251)].
% 1.95/2.27 6332 f2(n0,filling,n2) != n0. [resolve(6327,a,147,a)].
% 1.95/2.27 6454 less(f2(n0,filling,n2),n2). [resolve(2097,b,4848,a),flip(b),merge(c),unit_del(b,251)].
% 1.95/2.27 6455 f2(n0,filling,n2) = n2 | f2(n0,filling,n2) = n1. [resolve(6454,a,833,d),flip(a),flip(b),flip(c),unit_del(c,6332)].
% 1.95/2.27 6463 f2(n0,filling,n2) != n2. [resolve(6454,a,147,a),flip(a)].
% 1.95/2.27 6474 f2(n0,filling,n2) = n1. [back_unit_del(6455),unit_del(a,6463)].
% 1.95/2.27 6480 holdsAt(waterLevel(A),n2) | happens(f1(n0,filling,n2),n1) | n2 != A. [back_rewrite(1664),rewrite([6474(11)])].
% 1.95/2.27 6746 holdsAt(waterLevel(n2),n2) | happens(f1(n0,filling,n2),n1). [resolve(6480,c,566,a(flip)),rewrite([566(4)])].
% 1.95/2.27 6749 holdsAt(waterLevel(n2),n2) | holdsAt(waterLevel(n3),n1). [resolve(6746,b,98,a),unit_del(b,258)].
% 1.95/2.27 6759 holdsAt(waterLevel(n3),n1) | less(n0,f2(n0,filling,n1)). [resolve(6749,a,5046,b),flip(c),unit_del(c,251)].
% 1.95/2.27 6762 holdsAt(waterLevel(n3),n1) | less(f2(n0,filling,n1),n1). [resolve(6749,a,1392,b),flip(c),unit_del(c,251)].
% 1.95/2.27 7010 less(n0,f2(n0,filling,n1)). [resolve(6759,a,5034,b),flip(c),merge(b),unit_del(b,288)].
% 1.95/2.27 7015 f2(n0,filling,n1) != n0. [resolve(7010,a,147,a)].
% 1.95/2.27 7028 less(f2(n0,filling,n1),n1). [resolve(6762,a,1358,b),flip(c),merge(b),unit_del(b,288)].
% 1.95/2.27 7119 f2(n0,filling,n1) = n1. [resolve(7028,a,456,c),flip(a),flip(b),unit_del(b,7015)].
% 1.95/2.27 7120 $F. [resolve(7028,a,147,a),rewrite([7119(5)]),xx(a)].
% 1.95/2.27
% 1.95/2.27 % SZS output end Refutation
% 1.95/2.27 ============================== end of proof ==========================
% 1.95/2.27
% 1.95/2.27 ============================== STATISTICS ============================
% 1.95/2.27
% 1.95/2.27 Given=2513. Generated=34236. Kept=7056. proofs=1.
% 1.95/2.27 Usable=1374. Sos=1254. Demods=19. Limbo=90, Disabled=4478. Hints=0.
% 1.95/2.27 Megabytes=7.06.
% 1.95/2.27 User_CPU=1.21, System_CPU=0.03, Wall_clock=1.
% 1.95/2.27
% 1.95/2.27 ============================== end of statistics =====================
% 1.95/2.27
% 1.95/2.27 ============================== end of search =========================
% 1.95/2.27
% 1.95/2.27 THEOREM PROVED
% 1.95/2.27 % SZS status Theorem
% 1.95/2.27
% 1.95/2.27 Exiting with 1 proof.
% 1.95/2.27
% 1.95/2.27 Process 18251 exit (max_proofs) Fri Jun 10 04:18:35 2022
% 1.95/2.28 Prover9 interrupted
%------------------------------------------------------------------------------