%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : CSR004+2 : TPTP v8.1.0. Bugfixed v3.1.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.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 02:50:12 EDT 2022 % Result : Theorem 3.82s 1.58s % Output : Proof 5.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : CSR004+2 : TPTP v8.1.0. Bugfixed v3.1.0. % 0.08/0.15 % Command : ePrincess-casc -timeout=%d %s % 0.15/0.37 % Computer : n009.cluster.edu % 0.15/0.37 % Model : x86_64 x86_64 % 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.37 % Memory : 8042.1875MB % 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.37 % CPULimit : 300 % 0.15/0.37 % WCLimit : 600 % 0.15/0.37 % DateTime : Sat Jun 11 12:33:23 EDT 2022 % 0.15/0.37 % CPUTime : % 0.55/0.62 ____ _ % 0.55/0.62 ___ / __ \_____(_)___ ________ __________ % 0.55/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.55/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.55/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.55/0.62 % 0.55/0.62 A Theorem Prover for First-Order Logic % 0.55/0.62 (ePrincess v.1.0) % 0.55/0.62 % 0.55/0.62 (c) Philipp Rümmer, 2009-2015 % 0.55/0.62 (c) Peter Backeman, 2014-2015 % 0.55/0.62 (contributions by Angelo Brillout, Peter Baumgartner) % 0.55/0.62 Free software under GNU Lesser General Public License (LGPL). % 0.55/0.62 Bug reports to peter@backeman.se % 0.55/0.62 % 0.55/0.62 For more information, visit http://user.uu.se/~petba168/breu/ % 0.55/0.62 % 0.55/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.97/1.03 Prover 0: Preprocessing ... % 3.27/1.40 Prover 0: Warning: ignoring some quantifiers % 3.27/1.42 Prover 0: Constructing countermodel ... % 3.82/1.57 Prover 0: proved (899ms) % 3.82/1.58 % 3.82/1.58 No countermodel exists, formula is valid % 3.82/1.58 % SZS status Theorem for theBenchmark % 3.82/1.58 % 3.82/1.58 Generating proof ... Warning: ignoring some quantifiers % 5.47/1.92 found it (size 4) % 5.47/1.92 % 5.47/1.92 % SZS output start Proof for theBenchmark % 5.47/1.92 Assumed formulas after preprocessing and simplification: % 5.47/1.92 | (0) ? [v0] : ? [v1] : ( ~ (tapOff = overflow) & ~ (tapOff = tapOn) & ~ (spilling = filling) & ~ (overflow = tapOn) & waterLevel(n3) = v0 & waterLevel(n0) = v1 & plus(n2, n2) = n4 & plus(n2, n3) = n5 & plus(n3, n3) = n6 & plus(n1, n2) = n3 & plus(n1, n3) = n4 & plus(n1, n1) = n2 & plus(n0, n2) = n2 & plus(n0, n3) = n3 & plus(n0, n1) = n1 & plus(n0, n0) = n0 & holdsAt(v1, n0) & holdsAt(v0, n3) & holdsAt(filling, n3) & happens(tapOn, n0) & ~ releasedAt(spilling, n0) & ~ releasedAt(filling, n0) & ~ holdsAt(spilling, n0) & ~ holdsAt(filling, n0) & ~ happens(overflow, n3) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (plus(v3, v6) = v7) | ~ trajectory(v4, v3, v5, v6) | ~ initiates(v2, v4, v3) | ~ less(n0, v6) | ~ happens(v2, v3) | holdsAt(v5, v7) | stoppedIn(v3, v4, v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (plus(v3, v5) = v7) | ~ antitrajectory(v4, v3, v6, v5) | ~ terminates(v2, v4, v3) | ~ less(n0, v5) | ~ happens(v2, v3) | holdsAt(v6, v7) | startedIn(v3, v4, v7)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (waterLevel(v4) = v6) | ~ (waterLevel(v3) = v5) | ~ holdsAt(v6, v2) | ~ holdsAt(v5, v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ initiates(v5, v4, v6) | ~ less(v6, v3) | ~ less(v2, v6) | ~ happens(v5, v6) | startedIn(v2, v4, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ terminates(v5, v3, v6) | ~ less(v6, v4) | ~ less(v2, v6) | ~ happens(v5, v6) | stoppedIn(v2, v3, v4)) & ? [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (waterLevel(v4) = v6) | ~ (plus(v3, v5) = v4) | trajectory(filling, v2, v6, v5) | ? [v7] : (waterLevel(v3) = v7 & ~ holdsAt(v7, v2))) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (plus(v5, v4) = v3) | ~ (plus(v5, v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, n1) = v5) | ~ releases(v2, v4, v3) | ~ happens(v2, v3) | releasedAt(v4, v5)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, n1) = v5) | ~ releasedAt(v4, v5) | ~ initiates(v2, v4, v3) | ~ happens(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, n1) = v5) | ~ releasedAt(v4, v5) | ~ terminates(v2, v4, v3) | ~ happens(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, n1) = v5) | ~ holdsAt(v4, v5) | ~ terminates(v2, v4, v3) | ~ happens(v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v3, n1) = v5) | ~ initiates(v2, v4, v3) | ~ happens(v2, v3) | holdsAt(v4, v5)) & ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (waterLevel(v2) = v4) | ~ (waterLevel(v2) = v3)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (waterLevel(v4) = v3) | ~ (waterLevel(v4) = v2)) & ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (waterLevel(v3) = v4) | ~ (waterLevel(v2) = v4)) & ! [v2] : ! [v3] : ! [v4] : (v3 = spilling | v3 = filling | ~ initiates(v2, v3, v4) | ? [v5] : ? [v6] : ((v6 = v3 & v2 = tapOff & waterLevel(v5) = v3 & holdsAt(v3, v4)) | (v6 = v3 & v2 = overflow & waterLevel(v5) = v3 & holdsAt(v3, v4)))) & ! [v2] : ! [v3] : ! [v4] : (v3 = spilling | v2 = tapOn | ~ initiates(v2, v3, v4) | ? [v5] : ? [v6] : ((v6 = v3 & v2 = tapOff & waterLevel(v5) = v3 & holdsAt(v3, v4)) | (v6 = v3 & v2 = overflow & waterLevel(v5) = v3 & holdsAt(v3, v4)))) & ! [v2] : ! [v3] : ! [v4] : (v3 = filling | v2 = overflow | ~ initiates(v2, v3, v4) | ? [v5] : (v2 = tapOff & waterLevel(v5) = v3 & holdsAt(v3, v4))) & ! [v2] : ! [v3] : ! [v4] : (v3 = filling | ~ terminates(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : (v2 = tapOff | v2 = overflow | ~ terminates(v2, v3, v4)) & ! [v2] : ! [v3] : ! [v4] : (v2 = overflow | v2 = tapOn | ~ initiates(v2, v3, v4) | ? [v5] : (v2 = tapOff & waterLevel(v5) = v3 & holdsAt(v3, v4))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (waterLevel(v4) = v2) | ~ holdsAt(v2, v3) | initiates(tapOff, v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (waterLevel(v4) = v2) | ~ holdsAt(v2, v3) | initiates(overflow, v2, v3)) & ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, v2) = v4) | plus(v2, v3) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, n1) = v4) | ~ releasedAt(v2, v4) | releasedAt(v2, v3) | ? [v5] : (releases(v5, v2, v3) & happens(v5, v3))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, n1) = v4) | ~ releasedAt(v2, v3) | releasedAt(v2, v4) | ? [v5] : (happens(v5, v3) & (initiates(v5, v2, v3) | terminates(v5, v2, v3)))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, n1) = v4) | ~ holdsAt(v2, v4) | releasedAt(v2, v4) | holdsAt(v2, v3) | ? [v5] : (initiates(v5, v2, v3) & happens(v5, v3))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v3, n1) = v4) | ~ holdsAt(v2, v3) | releasedAt(v2, v4) | holdsAt(v2, v4) | ? [v5] : (terminates(v5, v2, v3) & happens(v5, v3))) & ! [v2] : ! [v3] : ! [v4] : ( ~ (plus(v2, v3) = v4) | plus(v3, v2) = v4) & ! [v2] : ! [v3] : ! [v4] : ( ~ releases(v2, v3, v4) | ? [v5] : (v2 = tapOn & waterLevel(v5) = v3)) & ! [v2] : ! [v3] : ! [v4] : ( ~ startedIn(v2, v4, v3) | ? [v5] : ? [v6] : (initiates(v5, v4, v6) & less(v6, v3) & less(v2, v6) & happens(v5, v6))) & ! [v2] : ! [v3] : ! [v4] : ( ~ stoppedIn(v2, v3, v4) | ? [v5] : ? [v6] : (terminates(v5, v3, v6) & less(v6, v4) & less(v2, v6) & happens(v5, v6))) & ? [v2] : ! [v3] : ! [v4] : ( ~ (waterLevel(v4) = v3) | releases(tapOn, v3, v2)) & ! [v2] : ! [v3] : (v3 = v2 | ~ less_or_equal(v2, v3) | less(v2, v3)) & ! [v2] : ! [v3] : (v3 = n0 | v2 = overflow | ~ happens(v2, v3)) & ! [v2] : ! [v3] : (v3 = n0 | ~ happens(v2, v3) | holdsAt(v0, v3)) & ! [v2] : ! [v3] : (v3 = n0 | ~ happens(v2, v3) | holdsAt(filling, v3)) & ! [v2] : ! [v3] : (v2 = overflow | v2 = tapOn | ~ happens(v2, v3)) & ! [v2] : ! [v3] : (v2 = tapOn | ~ happens(v2, v3) | holdsAt(v0, v3)) & ! [v2] : ! [v3] : (v2 = tapOn | ~ happens(v2, v3) | holdsAt(filling, v3)) & ! [v2] : ! [v3] : ( ~ (waterLevel(v2) = v3) | ~ releasedAt(v3, n0)) & ! [v2] : ! [v3] : ( ~ less(v3, v2) | ~ less(v2, v3)) & ! [v2] : ! [v3] : ( ~ less(v2, v3) | less_or_equal(v2, v3)) & ! [v2] : ~ (waterLevel(v2) = spilling) & ! [v2] : ~ (waterLevel(v2) = filling) & ! [v2] : ( ~ less_or_equal(v2, n8) | less(v2, n9)) & ! [v2] : ( ~ less_or_equal(v2, n7) | less(v2, n8)) & ! [v2] : ( ~ less_or_equal(v2, n6) | less(v2, n7)) & ! [v2] : ( ~ less_or_equal(v2, n5) | less(v2, n6)) & ! [v2] : ( ~ less_or_equal(v2, n4) | less(v2, n5)) & ! [v2] : ( ~ less_or_equal(v2, n2) | less(v2, n3)) & ! [v2] : ( ~ less_or_equal(v2, n3) | less(v2, n4)) & ! [v2] : ( ~ less_or_equal(v2, n1) | less(v2, n2)) & ! [v2] : ( ~ less_or_equal(v2, n0) | less(v2, n1)) & ! [v2] : ( ~ holdsAt(v0, v2) | ~ holdsAt(filling, v2) | happens(overflow, v2)) & ! [v2] : ~ less(v2, v2) & ! [v2] : ( ~ less(v2, n9) | less_or_equal(v2, n8)) & ! [v2] : ( ~ less(v2, n8) | less_or_equal(v2, n7)) & ! [v2] : ( ~ less(v2, n7) | less_or_equal(v2, n6)) & ! [v2] : ( ~ less(v2, n6) | less_or_equal(v2, n5)) & ! [v2] : ( ~ less(v2, n5) | less_or_equal(v2, n4)) & ! [v2] : ( ~ less(v2, n4) | less_or_equal(v2, n3)) & ! [v2] : ( ~ less(v2, n2) | less_or_equal(v2, n1)) & ! [v2] : ( ~ less(v2, n3) | less_or_equal(v2, n2)) & ! [v2] : ( ~ less(v2, n1) | less_or_equal(v2, n0)) & ! [v2] : ~ less(v2, n0) & ? [v2] : ? [v3] : (v3 = v2 | less(v3, v2) | less(v2, v3)) & ? [v2] : less_or_equal(v2, v2) & ? [v2] : initiates(overflow, spilling, v2) & ? [v2] : initiates(tapOn, filling, v2) & ? [v2] : terminates(tapOff, filling, v2) & ? [v2] : terminates(overflow, filling, v2)) % 5.47/1.97 | Instantiating (0) with all_0_0_0, all_0_1_1 yields: % 5.47/1.97 | (1) ~ (tapOff = overflow) & ~ (tapOff = tapOn) & ~ (spilling = filling) & ~ (overflow = tapOn) & waterLevel(n3) = all_0_1_1 & waterLevel(n0) = all_0_0_0 & plus(n2, n2) = n4 & plus(n2, n3) = n5 & plus(n3, n3) = n6 & plus(n1, n2) = n3 & plus(n1, n3) = n4 & plus(n1, n1) = n2 & plus(n0, n2) = n2 & plus(n0, n3) = n3 & plus(n0, n1) = n1 & plus(n0, n0) = n0 & holdsAt(all_0_0_0, n0) & holdsAt(all_0_1_1, n3) & holdsAt(filling, n3) & happens(tapOn, n0) & ~ releasedAt(spilling, n0) & ~ releasedAt(filling, n0) & ~ holdsAt(spilling, n0) & ~ holdsAt(filling, n0) & ~ happens(overflow, n3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v1, v4) = v5) | ~ trajectory(v2, v1, v3, v4) | ~ initiates(v0, v2, v1) | ~ less(n0, v4) | ~ happens(v0, v1) | holdsAt(v3, v5) | stoppedIn(v1, v2, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v1, v3) = v5) | ~ antitrajectory(v2, v1, v4, v3) | ~ terminates(v0, v2, v1) | ~ less(n0, v3) | ~ happens(v0, v1) | holdsAt(v4, v5) | startedIn(v1, v2, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (waterLevel(v2) = v4) | ~ (waterLevel(v1) = v3) | ~ holdsAt(v4, v0) | ~ holdsAt(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ initiates(v3, v2, v4) | ~ less(v4, v1) | ~ less(v0, v4) | ~ happens(v3, v4) | startedIn(v0, v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ terminates(v3, v1, v4) | ~ less(v4, v2) | ~ less(v0, v4) | ~ happens(v3, v4) | stoppedIn(v0, v1, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (waterLevel(v2) = v4) | ~ (plus(v1, v3) = v2) | trajectory(filling, v0, v4, v3) | ? [v5] : (waterLevel(v1) = v5 & ~ holdsAt(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ releases(v0, v2, v1) | ~ happens(v0, v1) | releasedAt(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ releasedAt(v2, v3) | ~ initiates(v0, v2, v1) | ~ happens(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ releasedAt(v2, v3) | ~ terminates(v0, v2, v1) | ~ happens(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ holdsAt(v2, v3) | ~ terminates(v0, v2, v1) | ~ happens(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ initiates(v0, v2, v1) | ~ happens(v0, v1) | holdsAt(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (waterLevel(v0) = v2) | ~ (waterLevel(v0) = v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (waterLevel(v2) = v1) | ~ (waterLevel(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (waterLevel(v1) = v2) | ~ (waterLevel(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = spilling | v1 = filling | ~ initiates(v0, v1, v2) | ? [v3] : ? [v4] : ((v4 = v1 & v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2)) | (v4 = v1 & v0 = overflow & waterLevel(v3) = v1 & holdsAt(v1, v2)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = spilling | v0 = tapOn | ~ initiates(v0, v1, v2) | ? [v3] : ? [v4] : ((v4 = v1 & v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2)) | (v4 = v1 & v0 = overflow & waterLevel(v3) = v1 & holdsAt(v1, v2)))) & ! [v0] : ! [v1] : ! [v2] : (v1 = filling | v0 = overflow | ~ initiates(v0, v1, v2) | ? [v3] : (v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2))) & ! [v0] : ! [v1] : ! [v2] : (v1 = filling | ~ terminates(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : (v0 = tapOff | v0 = overflow | ~ terminates(v0, v1, v2)) & ! [v0] : ! [v1] : ! [v2] : (v0 = overflow | v0 = tapOn | ~ initiates(v0, v1, v2) | ? [v3] : (v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (waterLevel(v2) = v0) | ~ holdsAt(v0, v1) | initiates(tapOff, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (waterLevel(v2) = v0) | ~ holdsAt(v0, v1) | initiates(overflow, v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, v0) = v2) | plus(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ releasedAt(v0, v2) | releasedAt(v0, v1) | ? [v3] : (releases(v3, v0, v1) & happens(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ releasedAt(v0, v1) | releasedAt(v0, v2) | ? [v3] : (happens(v3, v1) & (initiates(v3, v0, v1) | terminates(v3, v0, v1)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ holdsAt(v0, v2) | releasedAt(v0, v2) | holdsAt(v0, v1) | ? [v3] : (initiates(v3, v0, v1) & happens(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ holdsAt(v0, v1) | releasedAt(v0, v2) | holdsAt(v0, v2) | ? [v3] : (terminates(v3, v0, v1) & happens(v3, v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v0, v1) = v2) | plus(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ releases(v0, v1, v2) | ? [v3] : (v0 = tapOn & waterLevel(v3) = v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ startedIn(v0, v2, v1) | ? [v3] : ? [v4] : (initiates(v3, v2, v4) & less(v4, v1) & less(v0, v4) & happens(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ stoppedIn(v0, v1, v2) | ? [v3] : ? [v4] : (terminates(v3, v1, v4) & less(v4, v2) & less(v0, v4) & happens(v3, v4))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (waterLevel(v2) = v1) | releases(tapOn, v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ less_or_equal(v0, v1) | less(v0, v1)) & ! [v0] : ! [v1] : (v1 = n0 | v0 = overflow | ~ happens(v0, v1)) & ! [v0] : ! [v1] : (v1 = n0 | ~ happens(v0, v1) | holdsAt(all_0_1_1, v1)) & ! [v0] : ! [v1] : (v1 = n0 | ~ happens(v0, v1) | holdsAt(filling, v1)) & ! [v0] : ! [v1] : (v0 = overflow | v0 = tapOn | ~ happens(v0, v1)) & ! [v0] : ! [v1] : (v0 = tapOn | ~ happens(v0, v1) | holdsAt(all_0_1_1, v1)) & ! [v0] : ! [v1] : (v0 = tapOn | ~ happens(v0, v1) | holdsAt(filling, v1)) & ! [v0] : ! [v1] : ( ~ (waterLevel(v0) = v1) | ~ releasedAt(v1, n0)) & ! [v0] : ! [v1] : ( ~ less(v1, v0) | ~ less(v0, v1)) & ! [v0] : ! [v1] : ( ~ less(v0, v1) | less_or_equal(v0, v1)) & ! [v0] : ~ (waterLevel(v0) = spilling) & ! [v0] : ~ (waterLevel(v0) = filling) & ! [v0] : ( ~ less_or_equal(v0, n8) | less(v0, n9)) & ! [v0] : ( ~ less_or_equal(v0, n7) | less(v0, n8)) & ! [v0] : ( ~ less_or_equal(v0, n6) | less(v0, n7)) & ! [v0] : ( ~ less_or_equal(v0, n5) | less(v0, n6)) & ! [v0] : ( ~ less_or_equal(v0, n4) | less(v0, n5)) & ! [v0] : ( ~ less_or_equal(v0, n2) | less(v0, n3)) & ! [v0] : ( ~ less_or_equal(v0, n3) | less(v0, n4)) & ! [v0] : ( ~ less_or_equal(v0, n1) | less(v0, n2)) & ! [v0] : ( ~ less_or_equal(v0, n0) | less(v0, n1)) & ! [v0] : ( ~ holdsAt(all_0_1_1, v0) | ~ holdsAt(filling, v0) | happens(overflow, v0)) & ! [v0] : ~ less(v0, v0) & ! [v0] : ( ~ less(v0, n9) | less_or_equal(v0, n8)) & ! [v0] : ( ~ less(v0, n8) | less_or_equal(v0, n7)) & ! [v0] : ( ~ less(v0, n7) | less_or_equal(v0, n6)) & ! [v0] : ( ~ less(v0, n6) | less_or_equal(v0, n5)) & ! [v0] : ( ~ less(v0, n5) | less_or_equal(v0, n4)) & ! [v0] : ( ~ less(v0, n4) | less_or_equal(v0, n3)) & ! [v0] : ( ~ less(v0, n2) | less_or_equal(v0, n1)) & ! [v0] : ( ~ less(v0, n3) | less_or_equal(v0, n2)) & ! [v0] : ( ~ less(v0, n1) | less_or_equal(v0, n0)) & ! [v0] : ~ less(v0, n0) & ? [v0] : ? [v1] : (v1 = v0 | less(v1, v0) | less(v0, v1)) & ? [v0] : less_or_equal(v0, v0) & ? [v0] : initiates(overflow, spilling, v0) & ? [v0] : initiates(tapOn, filling, v0) & ? [v0] : terminates(tapOff, filling, v0) & ? [v0] : terminates(overflow, filling, v0) % 5.81/1.99 | % 5.81/1.99 | Applying alpha-rule on (1) yields: % 5.81/2.00 | (2) ! [v0] : ~ (waterLevel(v0) = spilling) % 5.81/2.00 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v1, v3) = v5) | ~ antitrajectory(v2, v1, v4, v3) | ~ terminates(v0, v2, v1) | ~ less(n0, v3) | ~ happens(v0, v1) | holdsAt(v4, v5) | startedIn(v1, v2, v5)) % 5.81/2.00 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (plus(v1, v4) = v5) | ~ trajectory(v2, v1, v3, v4) | ~ initiates(v0, v2, v1) | ~ less(n0, v4) | ~ happens(v0, v1) | holdsAt(v3, v5) | stoppedIn(v1, v2, v5)) % 5.81/2.00 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (waterLevel(v1) = v2) | ~ (waterLevel(v0) = v2)) % 5.81/2.00 | (6) ! [v0] : ! [v1] : (v0 = tapOn | ~ happens(v0, v1) | holdsAt(filling, v1)) % 5.81/2.00 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (waterLevel(v2) = v0) | ~ holdsAt(v0, v1) | initiates(tapOff, v0, v1)) % 5.81/2.00 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ holdsAt(v0, v2) | releasedAt(v0, v2) | holdsAt(v0, v1) | ? [v3] : (initiates(v3, v0, v1) & happens(v3, v1))) % 5.81/2.00 | (9) ! [v0] : ~ (waterLevel(v0) = filling) % 5.81/2.00 | (10) ! [v0] : ! [v1] : ( ~ less(v0, v1) | less_or_equal(v0, v1)) % 5.81/2.00 | (11) ! [v0] : ( ~ less(v0, n5) | less_or_equal(v0, n4)) % 5.81/2.00 | (12) ! [v0] : ( ~ less_or_equal(v0, n4) | less(v0, n5)) % 5.81/2.00 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (waterLevel(v2) = v1) | ~ (waterLevel(v2) = v0)) % 5.81/2.00 | (14) ~ (overflow = tapOn) % 5.81/2.00 | (15) ! [v0] : ( ~ less(v0, n1) | less_or_equal(v0, n0)) % 5.81/2.00 | (16) ! [v0] : ( ~ less_or_equal(v0, n0) | less(v0, n1)) % 5.81/2.00 | (17) plus(n3, n3) = n6 % 5.81/2.00 | (18) ~ releasedAt(spilling, n0) % 5.81/2.00 | (19) ! [v0] : ! [v1] : (v1 = n0 | ~ happens(v0, v1) | holdsAt(filling, v1)) % 5.81/2.00 | (20) plus(n0, n2) = n2 % 5.81/2.00 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = spilling | v1 = filling | ~ initiates(v0, v1, v2) | ? [v3] : ? [v4] : ((v4 = v1 & v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2)) | (v4 = v1 & v0 = overflow & waterLevel(v3) = v1 & holdsAt(v1, v2)))) % 5.81/2.00 | (22) plus(n0, n1) = n1 % 5.81/2.00 | (23) ! [v0] : ! [v1] : ( ~ (waterLevel(v0) = v1) | ~ releasedAt(v1, n0)) % 5.81/2.00 | (24) ! [v0] : ( ~ less(v0, n9) | less_or_equal(v0, n8)) % 5.81/2.00 | (25) ! [v0] : ( ~ less_or_equal(v0, n8) | less(v0, n9)) % 5.81/2.00 | (26) holdsAt(filling, n3) % 5.81/2.00 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ startedIn(v0, v2, v1) | ? [v3] : ? [v4] : (initiates(v3, v2, v4) & less(v4, v1) & less(v0, v4) & happens(v3, v4))) % 5.81/2.00 | (28) ~ holdsAt(spilling, n0) % 5.81/2.00 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ (waterLevel(v2) = v0) | ~ holdsAt(v0, v1) | initiates(overflow, v0, v1)) % 5.81/2.01 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ releasedAt(v0, v1) | releasedAt(v0, v2) | ? [v3] : (happens(v3, v1) & (initiates(v3, v0, v1) | terminates(v3, v0, v1)))) % 5.81/2.01 | (31) plus(n1, n1) = n2 % 5.81/2.01 | (32) ! [v0] : ! [v1] : (v0 = overflow | v0 = tapOn | ~ happens(v0, v1)) % 5.81/2.01 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ releasedAt(v0, v2) | releasedAt(v0, v1) | ? [v3] : (releases(v3, v0, v1) & happens(v3, v1))) % 5.81/2.01 | (34) ~ (tapOff = overflow) % 5.81/2.01 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = filling | ~ terminates(v0, v1, v2)) % 5.81/2.01 | (36) ! [v0] : ! [v1] : (v1 = n0 | v0 = overflow | ~ happens(v0, v1)) % 5.81/2.01 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (waterLevel(v0) = v2) | ~ (waterLevel(v0) = v1)) % 5.81/2.01 | (38) ! [v0] : ( ~ less(v0, n3) | less_or_equal(v0, n2)) % 5.81/2.01 | (39) ! [v0] : ( ~ less_or_equal(v0, n2) | less(v0, n3)) % 5.81/2.01 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ releases(v0, v2, v1) | ~ happens(v0, v1) | releasedAt(v2, v3)) % 5.81/2.01 | (41) ? [v0] : initiates(overflow, spilling, v0) % 5.81/2.01 | (42) ! [v0] : ! [v1] : (v0 = tapOn | ~ happens(v0, v1) | holdsAt(all_0_1_1, v1)) % 5.81/2.01 | (43) ! [v0] : ! [v1] : ! [v2] : (v0 = overflow | v0 = tapOn | ~ initiates(v0, v1, v2) | ? [v3] : (v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2))) % 5.81/2.01 | (44) ~ (tapOff = tapOn) % 5.81/2.01 | (45) ! [v0] : ( ~ less(v0, n4) | less_or_equal(v0, n3)) % 5.81/2.01 | (46) ! [v0] : ( ~ less_or_equal(v0, n3) | less(v0, n4)) % 5.81/2.01 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, n1) = v2) | ~ holdsAt(v0, v1) | releasedAt(v0, v2) | holdsAt(v0, v2) | ? [v3] : (terminates(v3, v0, v1) & happens(v3, v1))) % 5.81/2.01 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ releases(v0, v1, v2) | ? [v3] : (v0 = tapOn & waterLevel(v3) = v1)) % 5.81/2.01 | (49) plus(n0, n3) = n3 % 5.81/2.01 | (50) ? [v0] : ? [v1] : (v1 = v0 | less(v1, v0) | less(v0, v1)) % 5.81/2.01 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ releasedAt(v2, v3) | ~ terminates(v0, v2, v1) | ~ happens(v0, v1)) % 5.81/2.01 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ releasedAt(v2, v3) | ~ initiates(v0, v2, v1) | ~ happens(v0, v1)) % 5.81/2.01 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = spilling | v0 = tapOn | ~ initiates(v0, v1, v2) | ? [v3] : ? [v4] : ((v4 = v1 & v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2)) | (v4 = v1 & v0 = overflow & waterLevel(v3) = v1 & holdsAt(v1, v2)))) % 5.81/2.01 | (54) ? [v0] : less_or_equal(v0, v0) % 5.81/2.01 | (55) holdsAt(all_0_0_0, n0) % 5.81/2.01 | (56) ! [v0] : ! [v1] : ! [v2] : (v0 = tapOff | v0 = overflow | ~ terminates(v0, v1, v2)) % 5.81/2.01 | (57) plus(n2, n2) = n4 % 5.81/2.01 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (waterLevel(v2) = v4) | ~ (waterLevel(v1) = v3) | ~ holdsAt(v4, v0) | ~ holdsAt(v3, v0)) % 5.81/2.02 | (59) plus(n0, n0) = n0 % 5.81/2.02 | (60) ? [v0] : ! [v1] : ! [v2] : ( ~ (waterLevel(v2) = v1) | releases(tapOn, v1, v0)) % 5.81/2.02 | (61) ~ (spilling = filling) % 5.81/2.02 | (62) ! [v0] : ( ~ holdsAt(all_0_1_1, v0) | ~ holdsAt(filling, v0) | happens(overflow, v0)) % 5.81/2.02 | (63) ! [v0] : ! [v1] : ( ~ less(v1, v0) | ~ less(v0, v1)) % 5.81/2.02 | (64) plus(n2, n3) = n5 % 5.81/2.02 | (65) ? [v0] : terminates(tapOff, filling, v0) % 5.81/2.02 | (66) waterLevel(n3) = all_0_1_1 % 5.81/2.02 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ initiates(v3, v2, v4) | ~ less(v4, v1) | ~ less(v0, v4) | ~ happens(v3, v4) | startedIn(v0, v2, v1)) % 5.81/2.02 | (68) happens(tapOn, n0) % 5.81/2.02 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v0, v1) = v2) | plus(v1, v0) = v2) % 5.81/2.02 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (plus(v1, v0) = v2) | plus(v0, v1) = v2) % 5.81/2.02 | (71) ? [v0] : initiates(tapOn, filling, v0) % 5.81/2.02 | (72) ? [v0] : terminates(overflow, filling, v0) % 5.81/2.02 | (73) ! [v0] : ! [v1] : (v1 = n0 | ~ happens(v0, v1) | holdsAt(all_0_1_1, v1)) % 5.81/2.02 | (74) ~ holdsAt(filling, n0) % 5.81/2.02 | (75) ! [v0] : ~ less(v0, n0) % 5.81/2.02 | (76) waterLevel(n0) = all_0_0_0 % 5.81/2.02 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) % 5.81/2.02 | (78) holdsAt(all_0_1_1, n3) % 5.81/2.02 | (79) ! [v0] : ( ~ less(v0, n2) | less_or_equal(v0, n1)) % 5.81/2.02 | (80) ! [v0] : ( ~ less_or_equal(v0, n1) | less(v0, n2)) % 5.81/2.02 | (81) ! [v0] : ~ less(v0, v0) % 5.81/2.02 | (82) plus(n1, n2) = n3 % 5.81/2.02 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = filling | v0 = overflow | ~ initiates(v0, v1, v2) | ? [v3] : (v0 = tapOff & waterLevel(v3) = v1 & holdsAt(v1, v2))) % 5.81/2.02 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ initiates(v0, v2, v1) | ~ happens(v0, v1) | holdsAt(v2, v3)) % 5.81/2.02 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ stoppedIn(v0, v1, v2) | ? [v3] : ? [v4] : (terminates(v3, v1, v4) & less(v4, v2) & less(v0, v4) & happens(v3, v4))) % 5.81/2.02 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ terminates(v3, v1, v4) | ~ less(v4, v2) | ~ less(v0, v4) | ~ happens(v3, v4) | stoppedIn(v0, v1, v2)) % 5.81/2.02 | (87) ! [v0] : ( ~ less(v0, n7) | less_or_equal(v0, n6)) % 5.81/2.02 | (88) ! [v0] : ( ~ less_or_equal(v0, n6) | less(v0, n7)) % 5.81/2.02 | (89) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (waterLevel(v2) = v4) | ~ (plus(v1, v3) = v2) | trajectory(filling, v0, v4, v3) | ? [v5] : (waterLevel(v1) = v5 & ~ holdsAt(v5, v0))) % 5.81/2.02 | (90) plus(n1, n3) = n4 % 5.81/2.02 | (91) ! [v0] : ( ~ less(v0, n6) | less_or_equal(v0, n5)) % 5.81/2.03 | (92) ! [v0] : ( ~ less_or_equal(v0, n5) | less(v0, n6)) % 5.81/2.03 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (plus(v1, n1) = v3) | ~ holdsAt(v2, v3) | ~ terminates(v0, v2, v1) | ~ happens(v0, v1)) % 5.81/2.03 | (94) ~ releasedAt(filling, n0) % 5.81/2.03 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ less_or_equal(v0, v1) | less(v0, v1)) % 5.81/2.03 | (96) ~ happens(overflow, n3) % 5.81/2.03 | (97) ! [v0] : ( ~ less(v0, n8) | less_or_equal(v0, n7)) % 5.81/2.03 | (98) ! [v0] : ( ~ less_or_equal(v0, n7) | less(v0, n8)) % 5.81/2.03 | % 5.81/2.03 | Instantiating formula (62) with n3 and discharging atoms holdsAt(all_0_1_1, n3), holdsAt(filling, n3), ~ happens(overflow, n3), yields: % 5.81/2.03 | (99) $false % 5.81/2.03 | % 5.81/2.03 |-The branch is then unsatisfiable % 5.81/2.03 % SZS output end Proof for theBenchmark % 5.81/2.03 % 5.81/2.03 1396ms %------------------------------------------------------------------------------