TSTP Solution File: CSR012+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CSR012+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 0.96s 1.28s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : CSR012+1 : TPTP v8.1.0. Bugfixed v3.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jun 10 12:40:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 2579 was started by sandbox2 on n023.cluster.edu,
% 0.74/1.01 Fri Jun 10 12:40:53 2022
% 0.74/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2425_n023.cluster.edu".
% 0.74/1.01 ============================== end of head ===========================
% 0.74/1.01
% 0.74/1.01 ============================== INPUT =================================
% 0.74/1.01
% 0.74/1.01 % Reading from file /tmp/Prover9_2425_n023.cluster.edu
% 0.74/1.01
% 0.74/1.01 set(prolog_style_variables).
% 0.74/1.01 set(auto2).
% 0.74/1.01 % set(auto2) -> set(auto).
% 0.74/1.01 % set(auto) -> set(auto_inference).
% 0.74/1.01 % set(auto) -> set(auto_setup).
% 0.74/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01 % set(auto) -> set(auto_limits).
% 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01 % set(auto) -> set(auto_denials).
% 0.74/1.01 % set(auto) -> set(auto_process).
% 0.74/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01 % set(auto2) -> assign(stats, some).
% 0.74/1.01 % set(auto2) -> clear(echo_input).
% 0.74/1.01 % set(auto2) -> set(quiet).
% 0.74/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01 % set(auto2) -> clear(print_given).
% 0.74/1.01 assign(lrs_ticks,-1).
% 0.74/1.01 assign(sos_limit,10000).
% 0.74/1.01 assign(order,kbo).
% 0.74/1.01 set(lex_order_vars).
% 0.74/1.01 clear(print_given).
% 0.74/1.01
% 0.74/1.01 % formulas(sos). % not echoed (55 formulas)
% 0.74/1.01
% 0.74/1.01 ============================== end of input ==========================
% 0.74/1.01
% 0.74/1.01 % From the command line: assign(max_seconds, 300).
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01
% 0.74/1.01 % Formulas that are not ordinary clauses:
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 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].
% 0.74/1.01 19 (all X filling != waterLevel(X)) # label(filling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 20 (all X spilling != waterLevel(X)) # label(spilling_not_waterLevel) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 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].
% 0.74/1.01 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 28 (all X (less(X,n4) <-> less_or_equal(X,n3))) # label(less4) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 29 (all X (less(X,n5) <-> less_or_equal(X,n4))) # label(less5) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 30 (all X (less(X,n6) <-> less_or_equal(X,n5))) # label(less6) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 31 (all X (less(X,n7) <-> less_or_equal(X,n6))) # label(less7) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 32 (all X (less(X,n8) <-> less_or_equal(X,n7))) # label(less8) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 33 (all X (less(X,n9) <-> less_or_equal(X,n8))) # label(less9) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 35 (all Height -releasedAt(waterLevel(Height),n0)) # label(not_released_waterLevel_0) # label(hypothesis) # label(non_clause). [assumption].
% 0.74/1.01
% 0.74/1.01 ============================== end of process non-clausal formulas ===
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01
% 0.74/1.01 ============================== PREDICATE ELIMINATION =================
% 0.74/1.01 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)].
% 0.74/1.01 37 -stoppedIn(A,B,C) | happens(f1(A,B,C),f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.74/1.01 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.74/1.01 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.74/1.01 40 -stoppedIn(A,B,C) | terminates(f1(A,B,C),B,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 43 -startedIn(A,B,C) | happens(f3(A,C,B),f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.74/1.01 44 -startedIn(A,B,C) | less(A,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.74/1.01 45 -startedIn(A,B,C) | less(f4(A,C,B),C) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.74/1.01 46 -startedIn(A,B,C) | initiates(f3(A,C,B),B,f4(A,C,B)) # label(startedin_defn) # label(axiom). [clausify(2)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.74/1.01 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)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 48 -happens(A,B) | -releases(A,C,B) | releasedAt(C,plus(B,n1)) # label(happens_releases) # label(axiom). [clausify(11)].
% 0.96/1.28 49 releasedAt(A,B) | releases(f8(A,B),A,B) | -releasedAt(A,plus(B,n1)) # label(keep_not_released) # label(axiom). [clausify(8)].
% 0.96/1.28 50 -releases(A,B,C) | tapOn = A # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.96/1.28 Derived: tapOn = f8(A,B) | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(50,a,49,b)].
% 0.96/1.28 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.96/1.28 Derived: waterLevel(f11(f8(A,B),A,B)) = A | releasedAt(A,B) | -releasedAt(A,plus(B,n1)). [resolve(51,a,49,b)].
% 0.96/1.28 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.96/1.28 Derived: tapOn != A | waterLevel(B) != C | -happens(A,D) | releasedAt(C,plus(D,n1)). [resolve(52,a,48,b)].
% 0.96/1.28 Derived: tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 0.96/1.28 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)].
% 0.96/1.28 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28
% 0.96/1.28 ============================== end predicate elimination =============
% 0.96/1.28
% 0.96/1.28 Auto_denials: (non-Horn, no changes).
% 0.96/1.28
% 0.96/1.28 Term ordering decisions:
% 0.96/1.28
% 0.96/1.28 % Assigning unary symbol waterLevel kb_weight 0 and highest precedence (36).
% 0.96/1.28 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.
% 0.96/1.28
% 0.96/1.28 ============================== end of process initial clauses ========
% 0.96/1.28
% 0.96/1.28 ============================== CLAUSES FOR SEARCH ====================
% 0.96/1.28
% 0.96/1.28 ============================== end of clauses for search =============
% 0.96/1.28
% 0.96/1.28 ============================== SEARCH ================================
% 0.96/1.28
% 0.96/1.28 % Starting search at 0.03 seconds.
% 0.96/1.28
% 0.96/1.28 ============================== PROOF =================================
% 0.96/1.28 % SZS status Theorem
% 0.96/1.28 % SZS output start Refutation
% 0.96/1.28
% 0.96/1.28 % Proof 1 at 0.27 (+ 0.02) seconds.
% 0.96/1.28 % Length of proof is 88.
% 0.96/1.28 % Level of proof is 14.
% 0.96/1.28 % Maximum clause weight is 35.000.
% 0.96/1.28 % Given clauses 797.
% 0.96/1.28
% 0.96/1.28 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].
% 0.96/1.28 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].
% 0.96/1.28 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].
% 0.96/1.28 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].
% 0.96/1.28 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].
% 0.96/1.28 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].
% 0.96/1.28 21 (all X all Y (waterLevel(X) = waterLevel(Y) <-> X = Y)) # label(distinct_waterLevels) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 22 (all X all Y plus(X,Y) = plus(Y,X)) # label(symmetry_of_plus) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 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].
% 0.96/1.28 24 -(exists X less(X,n0)) # label(less0) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 25 (all X (less(X,n1) <-> less_or_equal(X,n0))) # label(less1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 26 (all X (less(X,n2) <-> less_or_equal(X,n1))) # label(less2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 27 (all X (less(X,n3) <-> less_or_equal(X,n2))) # label(less3) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 34 (all X all Y (less(X,Y) <-> -less(Y,X) & Y != X)) # label(less_property) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.28 38 -stoppedIn(A,B,C) | less(A,f2(A,B,C)) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.96/1.28 39 -stoppedIn(A,B,C) | less(f2(A,B,C),C) # label(stoppedin_defn) # label(axiom). [clausify(1)].
% 0.96/1.28 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)].
% 0.96/1.28 51 -releases(A,B,C) | waterLevel(f11(A,B,C)) = B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.96/1.28 52 releases(A,B,C) | tapOn != A | waterLevel(D) != B # label(releases_all_defn) # label(axiom). [clausify(15)].
% 0.96/1.28 54 -holdsAt(waterLevel(A),B) | plus(A,C) != D | trajectory(filling,B,waterLevel(D),C) # label(change_of_waterLevel) # label(axiom). [clausify(17)].
% 0.96/1.28 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)].
% 0.96/1.28 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)].
% 0.96/1.28 87 initiates(A,B,C) | tapOn != A | filling != B # label(initiates_all_defn) # label(axiom). [clausify(13)].
% 0.96/1.28 101 happens(A,B) | tapOn != A | n0 != B # label(happens_all_defn) # label(axiom). [clausify(16)].
% 0.96/1.28 111 waterLevel(A) != waterLevel(B) | A = B # label(distinct_waterLevels) # label(axiom). [clausify(21)].
% 0.96/1.28 113 plus(n0,n0) = n0 # label(plus0_0) # label(axiom). [assumption].
% 0.96/1.28 114 plus(n0,n1) = n1 # label(plus0_1) # label(axiom). [assumption].
% 0.96/1.28 123 plus(A,B) = plus(B,A) # label(symmetry_of_plus) # label(axiom). [clausify(22)].
% 0.96/1.28 124 -less_or_equal(A,B) | less(A,B) | B = A # label(less_or_equal) # label(axiom). [clausify(23)].
% 0.96/1.28 125 less_or_equal(A,B) | -less(A,B) # label(less_or_equal) # label(axiom). [clausify(23)].
% 0.96/1.28 126 less_or_equal(A,B) | B != A # label(less_or_equal) # label(axiom). [clausify(23)].
% 0.96/1.28 127 -less(A,n0) # label(less0) # label(axiom). [clausify(24)].
% 0.96/1.28 128 -less(A,n1) | less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 0.96/1.28 129 less(A,n1) | -less_or_equal(A,n0) # label(less1) # label(axiom). [clausify(25)].
% 0.96/1.28 130 -less(A,n2) | less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 0.96/1.28 131 less(A,n2) | -less_or_equal(A,n1) # label(less2) # label(axiom). [clausify(26)].
% 0.96/1.28 132 -less(A,n3) | less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 0.96/1.28 133 less(A,n3) | -less_or_equal(A,n2) # label(less3) # label(axiom). [clausify(27)].
% 0.96/1.28 146 -less(A,B) | -less(B,A) # label(less_property) # label(axiom). [clausify(34)].
% 0.96/1.28 147 -less(A,B) | B != A # label(less_property) # label(axiom). [clausify(34)].
% 0.96/1.28 148 less(A,B) | less(B,A) | B = A # label(less_property) # label(axiom). [clausify(34)].
% 0.96/1.28 149 holdsAt(waterLevel(n0),n0) # label(waterLevel_0) # label(hypothesis). [assumption].
% 0.96/1.28 155 -holdsAt(waterLevel(n1),n1) # label(waterLevel_1) # label(negated_conjecture). [assumption].
% 0.96/1.28 168 tapOn != A | waterLevel(B) != C | waterLevel(f11(A,C,D)) = C. [resolve(52,a,51,a)].
% 0.96/1.28 171 -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)].
% 0.96/1.28 172 -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)])].
% 0.96/1.28 173 -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)].
% 0.96/1.28 174 -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)])].
% 0.96/1.28 178 plus(n1,n0) = n1. [back_rewrite(114),rewrite([123(3)])].
% 0.96/1.28 179 -less(A,A). [factor(146,a,b)].
% 0.96/1.28 180 initiates(tapOn,A,B) | filling != A. [xx_res(87,b)].
% 0.96/1.28 188 happens(tapOn,A) | n0 != A. [xx_res(101,b)].
% 0.96/1.28 199 less_or_equal(A,A). [xx_res(126,b)].
% 0.96/1.28 206 less(n3,A) | n3 = A | less_or_equal(A,n2). [resolve(148,a,132,a)].
% 0.96/1.28 207 less(n2,A) | n2 = A | less_or_equal(A,n1). [resolve(148,a,130,a)].
% 0.96/1.28 208 less(n1,A) | n1 = A | less_or_equal(A,n0). [resolve(148,a,128,a)].
% 0.96/1.28 220 waterLevel(A) != B | waterLevel(f11(tapOn,B,C)) = B. [xx_res(168,a)].
% 0.96/1.28 222 initiates(tapOn,filling,A). [xx_res(180,b)].
% 0.96/1.28 231 less(n0,n1). [resolve(199,a,129,b)].
% 0.96/1.28 257 n0 != n1. [resolve(231,a,147,a),flip(a)].
% 0.96/1.28 258 less_or_equal(n0,n1). [resolve(231,a,125,b)].
% 0.96/1.28 267 less(n0,n2). [resolve(258,a,131,b)].
% 0.96/1.28 290 n2 != n0. [resolve(267,a,147,a)].
% 0.96/1.28 291 less_or_equal(n0,n2). [resolve(267,a,125,b)].
% 0.96/1.28 296 happens(tapOn,n0). [resolve(188,b,113,a(flip)),rewrite([113(4)])].
% 0.96/1.28 299 less(n0,n3). [resolve(291,a,133,b)].
% 0.96/1.28 319 n3 != n0. [resolve(299,a,147,a)].
% 0.96/1.28 384 less(n3,A) | n3 = A | less(A,n2) | n2 = A. [resolve(206,c,124,a)].
% 0.96/1.28 388 less(n2,A) | n2 = A | less(A,n1) | n1 = A. [resolve(207,c,124,a)].
% 0.96/1.28 397 less(n1,A) | n1 = A | n0 = A. [resolve(208,c,124,a),unit_del(c,127)].
% 0.96/1.28 418 -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)].
% 0.96/1.28 419 -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)].
% 0.96/1.28 455 n1 = A | n0 = A | -less(A,n1). [resolve(397,a,146,b)].
% 0.96/1.28 513 waterLevel(f11(tapOn,waterLevel(A),B)) = waterLevel(A). [xx_res(220,a)].
% 0.96/1.28 552 less(n3,A) | n3 = A | n2 = A | -less(n2,A). [resolve(384,c,146,b)].
% 0.96/1.28 564 -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)])].
% 0.96/1.28 565 f11(tapOn,waterLevel(A),B) = A. [resolve(513,a,111,a)].
% 0.96/1.28 579 -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)])].
% 0.96/1.28 830 less(n3,A) | n3 = A | n2 = A | less(A,n1) | n1 = A. [resolve(552,d,388,a),merge(d)].
% 0.96/1.28 849 -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)].
% 0.96/1.28 870 -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)].
% 0.96/1.28 1140 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)].
% 0.96/1.28 1150 less(f2(n0,filling,n1),n1). [resolve(1140,c,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 0.96/1.28 1159 f2(n0,filling,n1) = n1 | f2(n0,filling,n1) = n0. [resolve(1150,a,455,c),flip(a),flip(b)].
% 0.96/1.28 1160 f2(n0,filling,n1) != n1. [resolve(1150,a,147,a),flip(a)].
% 0.96/1.28 1164 f2(n0,filling,n1) = n0. [back_unit_del(1159),unit_del(a,1160)].
% 0.96/1.28 1224 holdsAt(waterLevel(A),n1) | n1 != A. [resolve(870,a,830,d),rewrite([178(4),178(9),1164(8),178(9)]),flip(g),unit_del(b,179),unit_del(d,127),unit_del(e,319),unit_del(f,290),unit_del(g,257)].
% 0.96/1.28 1230 $F. [resolve(1224,b,565,a(flip)),rewrite([565(4)]),unit_del(a,155)].
% 0.96/1.28
% 0.96/1.28 % SZS output end Refutation
% 0.96/1.28 ============================== end of proof ==========================
% 0.96/1.28
% 0.96/1.28 ============================== STATISTICS ============================
% 0.96/1.28
% 0.96/1.28 Given=797. Generated=11494. Kept=1166. proofs=1.
% 0.96/1.28 Usable=785. Sos=218. Demods=15. Limbo=0, Disabled=302. Hints=0.
% 0.96/1.28 Megabytes=1.63.
% 0.96/1.28 User_CPU=0.27, System_CPU=0.02, Wall_clock=0.
% 0.96/1.28
% 0.96/1.28 ============================== end of statistics =====================
% 0.96/1.28
% 0.96/1.28 ============================== end of search =========================
% 0.96/1.28
% 0.96/1.28 THEOREM PROVED
% 0.96/1.28 % SZS status Theorem
% 0.96/1.28
% 0.96/1.28 Exiting with 1 proof.
% 0.96/1.28
% 0.96/1.28 Process 2579 exit (max_proofs) Fri Jun 10 12:40:53 2022
% 0.96/1.28 Prover9 interrupted
%------------------------------------------------------------------------------