%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : DAT037_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n008.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 : 300s % DateTime : Wed Aug 30 22:18:58 EDT 2023 % Result : Theorem 9.60s 2.20s % Output : Proof 14.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : DAT037_1 : TPTP v8.1.2. Released v5.0.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.33 % Computer : n008.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Thu Aug 24 14:38:02 EDT 2023 % 0.11/0.33 % CPUTime : % 0.18/0.63 ________ _____ % 0.18/0.63 ___ __ \_________(_)________________________________ % 0.18/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.63 % 0.18/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.63 (2023-06-19) % 0.18/0.63 % 0.18/0.63 (c) Philipp Rümmer, 2009-2023 % 0.18/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.63 Amanda Stjerna. % 0.18/0.63 Free software under BSD-3-Clause. % 0.18/0.63 % 0.18/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.63 % 0.18/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.65 Running up to 7 provers in parallel. % 0.18/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.18/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.12/1.20 Prover 4: Preprocessing ... % 3.12/1.21 Prover 1: Preprocessing ... % 3.12/1.26 Prover 5: Preprocessing ... % 3.12/1.26 Prover 0: Preprocessing ... % 3.57/1.26 Prover 2: Preprocessing ... % 3.57/1.27 Prover 6: Preprocessing ... % 3.57/1.27 Prover 3: Preprocessing ... % 4.74/1.67 Prover 6: Constructing countermodel ... % 4.74/1.67 Prover 5: Proving ... % 4.74/1.69 Prover 1: Constructing countermodel ... % 6.12/1.73 Prover 3: Constructing countermodel ... % 7.08/1.81 Prover 4: Constructing countermodel ... % 7.08/1.82 Prover 0: Proving ... % 7.08/1.83 Prover 2: Proving ... % 7.53/1.90 Prover 3: gave up % 7.53/1.90 Prover 1: gave up % 7.53/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.53/1.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.79/1.91 Prover 6: gave up % 7.79/1.93 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.05/1.95 Prover 7: Preprocessing ... % 8.05/1.96 Prover 8: Preprocessing ... % 8.05/1.99 Prover 9: Preprocessing ... % 9.03/2.11 Prover 8: Warning: ignoring some quantifiers % 9.03/2.12 Prover 8: Constructing countermodel ... % 9.03/2.13 Prover 7: Constructing countermodel ... % 9.60/2.18 Prover 7: gave up % 9.60/2.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.60/2.20 Prover 0: proved (1547ms) % 9.60/2.20 % 9.60/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.60/2.20 % 9.60/2.21 Prover 2: proved (1550ms) % 9.60/2.21 % 9.60/2.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.60/2.21 % 9.60/2.21 Prover 5: stopped % 9.90/2.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.90/2.22 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.90/2.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.90/2.23 Prover 10: Preprocessing ... % 9.90/2.24 Prover 9: Constructing countermodel ... % 9.90/2.25 Prover 9: stopped % 9.90/2.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.90/2.26 Prover 8: gave up % 9.90/2.27 Prover 16: Preprocessing ... % 9.90/2.29 Prover 13: Preprocessing ... % 9.90/2.30 Prover 19: Preprocessing ... % 9.90/2.30 Prover 11: Preprocessing ... % 10.60/2.45 Prover 10: Constructing countermodel ... % 10.60/2.45 Prover 13: Warning: ignoring some quantifiers % 10.60/2.46 Prover 13: Constructing countermodel ... % 10.60/2.46 Prover 16: Warning: ignoring some quantifiers % 10.60/2.47 Prover 16: Constructing countermodel ... % 10.60/2.49 Prover 10: gave up % 10.60/2.49 Prover 19: Warning: ignoring some quantifiers % 10.60/2.50 Prover 19: Constructing countermodel ... % 10.60/2.50 Prover 11: Constructing countermodel ... % 12.85/2.67 Prover 13: gave up % 13.00/2.72 Prover 19: gave up % 13.53/2.79 Prover 16: gave up % 13.53/2.82 Prover 4: Found proof (size 74) % 13.53/2.82 Prover 4: proved (2160ms) % 14.02/2.82 Prover 11: stopped % 14.02/2.82 % 14.02/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.02/2.82 % 14.02/2.85 % SZS output start Proof for theBenchmark % 14.02/2.85 Assumptions after simplification: % 14.02/2.85 --------------------------------- % 14.02/2.85 % 14.02/2.85 (ax1) % 14.28/2.88 collection(empty) & ! [v0: collection] : ! [v1: int] : ( ~ ($lesseq(v1, -1)) % 14.28/2.88 | ~ (count(v0) = v1) | ~ collection(v0)) & ! [v0: int] : ~ (in(v0, % 14.28/2.88 empty) = 0) % 14.28/2.88 % 14.28/2.88 (ax2) % 14.28/2.88 collection(empty) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : % 14.28/2.88 ( ~ (add(v0, v1) = v2) | ~ collection(v1) | in(v0, v2) = 0) & ! [v0: % 14.28/2.88 collection] : (v0 = empty | ~ (count(v0) = 0) | ~ collection(v0)) & ! % 14.28/2.88 [v0: int] : (v0 = 0 | ~ (count(empty) = v0)) % 14.28/2.88 % 14.28/2.88 (ax3) % 14.28/2.90 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 14.28/2.90 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (add(v0, % 14.28/2.90 v1) = v3 & count(v3) = v4 & count(v1) = $sum(v4, -1) & collection(v3))) % 14.28/2.90 & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, % 14.28/2.90 v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2) % 14.28/2.90 = v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ % 14.28/2.90 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? % 14.28/2.90 [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & % 14.28/2.90 ($difference(v5, v4) = -1 | v3 = 0))) & ! [v0: int] : ! [v1: collection] % 14.28/2.90 : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: % 14.28/2.90 int] : ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & % 14.28/2.90 in(v0, v1) = v5 & ( ~ (v5 = 0) | ~ ($difference(v4, v3) = -1)))) & ! % 14.28/2.90 [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ collection(v1) | % 14.28/2.90 ? [v2: collection] : ? [v3: int] : ? [v4: int] : ( ~ ($difference(v4, v3) % 14.28/2.90 = -1) & add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v4 & % 14.28/2.90 collection(v2))) % 14.28/2.90 % 14.28/2.90 (ax4) % 14.28/2.92 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 14.28/2.92 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ % 14.28/2.92 collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0: % 14.28/2.92 int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v3 = 0 | % 14.28/2.92 ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ collection(v1)) & ! [v0: % 14.28/2.92 int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 = v0 | % 14.28/2.92 ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, v1) % 14.28/2.92 = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ % 14.28/2.92 (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : % 14.28/2.92 ? [v5: int] : ( ~ (v5 = v4) & add(v0, v1) = v3 & count(v3) = v4 & count(v1) % 14.28/2.92 = v5 & collection(v3))) & ! [v0: int] : ! [v1: collection] : ! [v2: % 14.28/2.92 collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: any] : ? % 14.28/2.92 [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = % 14.28/2.92 v3 & ( ~ (v3 = 0) | v5 = v4))) & ! [v0: int] : ! [v1: collection] : ! % 14.28/2.92 [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : % 14.28/2.92 ? [v4: int] : ? [v5: any] : (count(v2) = v3 & count(v1) = v4 & in(v0, v1) % 14.28/2.92 = v5 & ( ~ (v4 = v3) | v5 = 0))) & ! [v0: int] : ! [v1: collection] : ( % 14.28/2.92 ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] % 14.28/2.92 : (add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v3 & collection(v2))) % 14.28/2.92 % 14.28/2.92 (ax5) % 14.28/2.93 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ! % 14.28/2.93 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = % 14.28/2.93 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) % 14.28/2.93 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : ( % 14.28/2.93 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, % 14.28/2.93 v1) = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | % 14.28/2.93 ~ (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] % 14.28/2.93 : ? [v5: int] : ( ~ ($difference(v5, v4) = 1) & remove(v0, v1) = v3 & % 14.28/2.93 count(v3) = v4 & count(v1) = v5 & collection(v3))) & ! [v0: int] : ! % 14.28/2.93 [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ % 14.28/2.93 (in(v0, v2) = 0) | ~ collection(v1)) & ! [v0: int] : ! [v1: collection] : % 14.28/2.93 ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: % 14.28/2.93 any] : ? [v4: int] : ? [v5: int] : (count(v2) = v4 & count(v1) = v5 & % 14.28/2.93 in(v0, v1) = v3 & ( ~ (v3 = 0) | $difference(v5, v4) = 1))) & ! [v0: int] % 14.28/2.93 : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ % 14.28/2.93 collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: any] : (count(v2) = % 14.28/2.93 v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ ($difference(v4, v3) = 1) | v5 % 14.28/2.93 = 0))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.28/2.93 collection(v1) | ? [v2: collection] : ? [v3: int] : (remove(v0, v1) = v2 & % 14.28/2.93 count(v2) = v3 & count(v1) = $sum(v3, 1) & collection(v2))) % 14.28/2.93 % 14.28/2.93 (ax6) % 14.28/2.93 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = % 14.28/2.94 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (remove(v0, % 14.28/2.94 v1) = v3 & count(v3) = v4 & count(v1) = v4 & collection(v3))) & ! [v0: % 14.28/2.94 int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) % 14.28/2.94 | ~ collection(v1) | ? [v3: any] : ? [v4: int] : ? [v5: int] : % 14.28/2.94 (count(v2) = v4 & count(v1) = v5 & in(v0, v1) = v3 & (v5 = v4 | v3 = 0))) & % 14.28/2.94 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 14.28/2.94 = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: any] : % 14.28/2.94 (count(v2) = v3 & count(v1) = v4 & in(v0, v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = % 14.28/2.94 v3)))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | % 14.28/2.94 ~ collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] : ( ~ % 14.28/2.94 (v4 = v3) & remove(v0, v1) = v2 & count(v2) = v3 & count(v1) = v4 & % 14.28/2.94 collection(v2))) % 14.28/2.94 % 14.28/2.94 (ax7) % 14.28/2.94 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) % 14.28/2.94 = v2) | ~ collection(v1) | ? [v3: any] : ? [v4: collection] : (add(v0, % 14.28/2.94 v2) = v4 & in(v0, v1) = v3 & collection(v4) & ( ~ (v3 = 0) | v4 = v1))) % 14.28/2.94 & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.28/2.94 collection(v1) | ? [v2: collection] : (remove(v0, v1) = v2 & add(v0, v2) = % 14.28/2.94 v1 & collection(v2))) % 14.28/2.94 % 14.28/2.94 (co1) % 14.28/2.94 ? [v0: collection] : (count(v0) = 1 & in(5, v0) = 0 & in(2, v0) = 0 & % 14.28/2.94 collection(v0)) % 14.28/2.94 % 14.28/2.94 (function-axioms) % 14.28/2.94 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] % 14.28/2.94 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0: % 14.28/2.94 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1 % 14.28/2.94 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0: % 14.28/2.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : ! % 14.28/2.94 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 14.28/2.94 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) | % 14.28/2.94 ~ (count(v2) = v0)) % 14.28/2.94 % 14.28/2.94 Those formulas are unsatisfiable: % 14.28/2.94 --------------------------------- % 14.28/2.94 % 14.28/2.94 Begin of proof % 14.28/2.95 | % 14.28/2.95 | ALPHA: (ax1) implies: % 14.28/2.95 | (1) ! [v0: int] : ~ (in(v0, empty) = 0) % 14.28/2.95 | % 14.28/2.95 | ALPHA: (ax2) implies: % 14.28/2.95 | (2) ! [v0: collection] : (v0 = empty | ~ (count(v0) = 0) | ~ % 14.28/2.95 | collection(v0)) % 14.28/2.95 | % 14.28/2.95 | ALPHA: (ax3) implies: % 14.65/2.95 | (3) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.65/2.95 | collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] : % 14.65/2.95 | ( ~ ($difference(v4, v3) = -1) & add(v0, v1) = v2 & count(v2) = v3 & % 14.65/2.95 | count(v1) = v4 & collection(v2))) % 14.65/2.95 | % 14.65/2.95 | ALPHA: (ax4) implies: % 14.65/2.95 | (4) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.65/2.96 | collection(v1) | ? [v2: collection] : ? [v3: int] : (add(v0, v1) = % 14.65/2.96 | v2 & count(v2) = v3 & count(v1) = v3 & collection(v2))) % 14.65/2.96 | (5) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] % 14.65/2.96 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ % 14.65/2.96 | collection(v1) | in(v0, v1) = 0) % 14.65/2.96 | % 14.65/2.96 | ALPHA: (ax5) implies: % 14.65/2.96 | (6) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.65/2.96 | collection(v1) | ? [v2: collection] : ? [v3: int] : (remove(v0, v1) % 14.65/2.96 | = v2 & count(v2) = v3 & count(v1) = $sum(v3, 1) & collection(v2))) % 14.65/2.96 | % 14.65/2.96 | ALPHA: (ax6) implies: % 14.65/2.96 | (7) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.65/2.96 | collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] : % 14.65/2.96 | ( ~ (v4 = v3) & remove(v0, v1) = v2 & count(v2) = v3 & count(v1) = v4 % 14.65/2.96 | & collection(v2))) % 14.65/2.96 | % 14.65/2.96 | ALPHA: (ax7) implies: % 14.65/2.96 | (8) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ % 14.65/2.96 | collection(v1) | ? [v2: collection] : (remove(v0, v1) = v2 & add(v0, % 14.65/2.96 | v2) = v1 & collection(v2))) % 14.65/2.96 | % 14.65/2.96 | ALPHA: (function-axioms) implies: % 14.65/2.96 | (9) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ % 14.65/2.96 | (count(v2) = v1) | ~ (count(v2) = v0)) % 14.65/2.96 | (10) ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! % 14.65/2.97 | [v3: int] : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = % 14.65/2.97 | v0)) % 14.65/2.97 | % 14.65/2.97 | DELTA: instantiating (co1) with fresh symbol all_13_0 gives: % 14.65/2.97 | (11) count(all_13_0) = 1 & in(5, all_13_0) = 0 & in(2, all_13_0) = 0 & % 14.65/2.97 | collection(all_13_0) % 14.65/2.97 | % 14.65/2.97 | ALPHA: (11) implies: % 14.65/2.97 | (12) collection(all_13_0) % 14.65/2.97 | (13) in(2, all_13_0) = 0 % 14.65/2.97 | (14) in(5, all_13_0) = 0 % 14.65/2.97 | (15) count(all_13_0) = 1 % 14.65/2.97 | % 14.77/2.97 | GROUND_INST: instantiating (3) with 2, all_13_0, simplifying with (12), (13) % 14.77/2.97 | gives: % 14.77/2.98 | (16) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ % 14.77/2.98 | ($difference(v2, v1) = -1) & add(2, all_13_0) = v0 & count(v0) = v1 % 14.77/2.98 | & count(all_13_0) = v2 & collection(v0)) % 14.77/2.98 | % 14.77/2.98 | GROUND_INST: instantiating (7) with 2, all_13_0, simplifying with (12), (13) % 14.77/2.98 | gives: % 14.77/2.98 | (17) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & % 14.77/2.98 | remove(2, all_13_0) = v0 & count(v0) = v1 & count(all_13_0) = v2 & % 14.77/2.98 | collection(v0)) % 14.77/2.98 | % 14.77/2.98 | GROUND_INST: instantiating (6) with 2, all_13_0, simplifying with (12), (13) % 14.77/2.98 | gives: % 14.77/2.98 | (18) ? [v0: collection] : ? [v1: int] : (remove(2, all_13_0) = v0 & % 14.77/2.98 | count(v0) = v1 & count(all_13_0) = $sum(v1, 1) & collection(v0)) % 14.77/2.98 | % 14.77/2.98 | GROUND_INST: instantiating (4) with 2, all_13_0, simplifying with (12), (13) % 14.77/2.98 | gives: % 14.77/2.98 | (19) ? [v0: collection] : ? [v1: int] : (add(2, all_13_0) = v0 & % 14.77/2.98 | count(v0) = v1 & count(all_13_0) = v1 & collection(v0)) % 14.77/2.98 | % 14.77/2.98 | GROUND_INST: instantiating (8) with 2, all_13_0, simplifying with (12), (13) % 14.77/2.98 | gives: % 14.77/2.98 | (20) ? [v0: collection] : (remove(2, all_13_0) = v0 & add(2, v0) = % 14.77/2.98 | all_13_0 & collection(v0)) % 14.77/2.98 | % 14.77/2.98 | GROUND_INST: instantiating (3) with 5, all_13_0, simplifying with (12), (14) % 14.77/2.98 | gives: % 14.77/2.98 | (21) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ % 14.77/2.99 | ($difference(v2, v1) = -1) & add(5, all_13_0) = v0 & count(v0) = v1 % 14.77/2.99 | & count(all_13_0) = v2 & collection(v0)) % 14.77/2.99 | % 14.77/2.99 | GROUND_INST: instantiating (7) with 5, all_13_0, simplifying with (12), (14) % 14.77/2.99 | gives: % 14.77/2.99 | (22) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) & % 14.77/2.99 | remove(5, all_13_0) = v0 & count(v0) = v1 & count(all_13_0) = v2 & % 14.77/2.99 | collection(v0)) % 14.77/2.99 | % 14.77/2.99 | GROUND_INST: instantiating (6) with 5, all_13_0, simplifying with (12), (14) % 14.77/2.99 | gives: % 14.77/2.99 | (23) ? [v0: collection] : ? [v1: int] : (remove(5, all_13_0) = v0 & % 14.77/2.99 | count(v0) = v1 & count(all_13_0) = $sum(v1, 1) & collection(v0)) % 14.77/2.99 | % 14.77/2.99 | GROUND_INST: instantiating (4) with 5, all_13_0, simplifying with (12), (14) % 14.77/2.99 | gives: % 14.77/2.99 | (24) ? [v0: collection] : ? [v1: int] : (add(5, all_13_0) = v0 & % 14.77/2.99 | count(v0) = v1 & count(all_13_0) = v1 & collection(v0)) % 14.77/2.99 | % 14.77/2.99 | DELTA: instantiating (20) with fresh symbol all_22_0 gives: % 14.77/2.99 | (25) remove(2, all_13_0) = all_22_0 & add(2, all_22_0) = all_13_0 & % 14.77/2.99 | collection(all_22_0) % 14.77/2.99 | % 14.77/2.99 | ALPHA: (25) implies: % 14.77/2.99 | (26) add(2, all_22_0) = all_13_0 % 14.77/2.99 | (27) remove(2, all_13_0) = all_22_0 % 14.77/2.99 | % 14.77/2.99 | DELTA: instantiating (19) with fresh symbols all_24_0, all_24_1 gives: % 14.77/2.99 | (28) add(2, all_13_0) = all_24_1 & count(all_24_1) = all_24_0 & % 14.77/2.99 | count(all_13_0) = all_24_0 & collection(all_24_1) % 14.77/2.99 | % 14.77/2.99 | ALPHA: (28) implies: % 14.77/2.99 | (29) count(all_13_0) = all_24_0 % 14.77/2.99 | % 14.77/2.99 | DELTA: instantiating (18) with fresh symbols all_26_0, all_26_1 gives: % 14.77/2.99 | (30) remove(2, all_13_0) = all_26_1 & count(all_26_1) = all_26_0 & % 14.77/2.99 | count(all_13_0) = $sum(all_26_0, 1) & collection(all_26_1) % 14.77/2.99 | % 14.77/2.99 | ALPHA: (30) implies: % 14.77/2.99 | (31) collection(all_26_1) % 14.77/3.00 | (32) count(all_13_0) = $sum(all_26_0, 1) % 14.77/3.00 | (33) count(all_26_1) = all_26_0 % 14.77/3.00 | (34) remove(2, all_13_0) = all_26_1 % 14.77/3.00 | % 14.77/3.00 | DELTA: instantiating (23) with fresh symbols all_28_0, all_28_1 gives: % 14.77/3.00 | (35) remove(5, all_13_0) = all_28_1 & count(all_28_1) = all_28_0 & % 14.77/3.00 | count(all_13_0) = $sum(all_28_0, 1) & collection(all_28_1) % 14.77/3.00 | % 14.77/3.00 | ALPHA: (35) implies: % 14.77/3.00 | (36) count(all_13_0) = $sum(all_28_0, 1) % 14.77/3.00 | % 14.77/3.00 | DELTA: instantiating (24) with fresh symbols all_30_0, all_30_1 gives: % 14.77/3.00 | (37) add(5, all_13_0) = all_30_1 & count(all_30_1) = all_30_0 & % 14.77/3.00 | count(all_13_0) = all_30_0 & collection(all_30_1) % 14.77/3.00 | % 14.77/3.00 | ALPHA: (37) implies: % 14.77/3.00 | (38) count(all_13_0) = all_30_0 % 14.77/3.00 | % 14.77/3.00 | DELTA: instantiating (22) with fresh symbols all_32_0, all_32_1, all_32_2 % 14.77/3.00 | gives: % 14.77/3.00 | (39) ~ (all_32_0 = all_32_1) & remove(5, all_13_0) = all_32_2 & % 14.77/3.00 | count(all_32_2) = all_32_1 & count(all_13_0) = all_32_0 & % 14.77/3.00 | collection(all_32_2) % 14.77/3.00 | % 14.77/3.00 | ALPHA: (39) implies: % 14.77/3.00 | (40) count(all_13_0) = all_32_0 % 14.77/3.00 | % 14.77/3.00 | DELTA: instantiating (21) with fresh symbols all_34_0, all_34_1, all_34_2 % 14.77/3.00 | gives: % 14.77/3.00 | (41) ~ ($difference(all_34_0, all_34_1) = -1) & add(5, all_13_0) = % 14.77/3.00 | all_34_2 & count(all_34_2) = all_34_1 & count(all_13_0) = all_34_0 & % 14.77/3.00 | collection(all_34_2) % 14.77/3.00 | % 14.77/3.00 | ALPHA: (41) implies: % 14.77/3.00 | (42) count(all_13_0) = all_34_0 % 14.77/3.00 | % 14.77/3.00 | DELTA: instantiating (17) with fresh symbols all_36_0, all_36_1, all_36_2 % 14.77/3.00 | gives: % 14.77/3.01 | (43) ~ (all_36_0 = all_36_1) & remove(2, all_13_0) = all_36_2 & % 14.77/3.01 | count(all_36_2) = all_36_1 & count(all_13_0) = all_36_0 & % 14.77/3.01 | collection(all_36_2) % 14.77/3.01 | % 14.77/3.01 | ALPHA: (43) implies: % 14.77/3.01 | (44) count(all_13_0) = all_36_0 % 14.77/3.01 | (45) count(all_36_2) = all_36_1 % 14.77/3.01 | (46) remove(2, all_13_0) = all_36_2 % 14.77/3.01 | % 14.77/3.01 | DELTA: instantiating (16) with fresh symbols all_38_0, all_38_1, all_38_2 % 14.77/3.01 | gives: % 14.77/3.01 | (47) ~ ($difference(all_38_0, all_38_1) = -1) & add(2, all_13_0) = % 14.77/3.01 | all_38_2 & count(all_38_2) = all_38_1 & count(all_13_0) = all_38_0 & % 14.77/3.01 | collection(all_38_2) % 14.77/3.01 | % 14.77/3.01 | ALPHA: (47) implies: % 14.77/3.01 | (48) count(all_13_0) = all_38_0 % 14.77/3.01 | % 14.77/3.01 | GROUND_INST: instantiating (9) with 1, $sum(all_26_0, 1), all_13_0, % 14.77/3.01 | simplifying with (15), (32) gives: % 14.77/3.01 | (49) all_26_0 = 0 % 14.77/3.01 | % 14.77/3.01 | GROUND_INST: instantiating (9) with $sum(all_26_0, 1), $sum(all_28_0, 1), % 14.77/3.01 | all_13_0, simplifying with (32), (36) gives: % 14.77/3.01 | (50) all_28_0 = all_26_0 % 14.77/3.01 | % 14.77/3.01 | GROUND_INST: instantiating (9) with all_32_0, all_34_0, all_13_0, simplifying % 14.77/3.01 | with (40), (42) gives: % 14.77/3.01 | (51) all_34_0 = all_32_0 % 14.77/3.01 | % 14.77/3.01 | GROUND_INST: instantiating (9) with all_32_0, all_36_0, all_13_0, simplifying % 14.77/3.01 | with (40), (44) gives: % 14.77/3.01 | (52) all_36_0 = all_32_0 % 14.77/3.01 | % 14.77/3.01 | GROUND_INST: instantiating (9) with all_30_0, all_36_0, all_13_0, simplifying % 14.77/3.01 | with (38), (44) gives: % 14.77/3.01 | (53) all_36_0 = all_30_0 % 14.77/3.01 | % 14.77/3.01 | GROUND_INST: instantiating (9) with $sum(all_28_0, 1), all_36_0, all_13_0, % 14.77/3.02 | simplifying with (36), (44) gives: % 14.77/3.02 | (54) $difference(all_36_0, all_28_0) = 1 % 14.77/3.02 | % 14.77/3.02 | GROUND_INST: instantiating (9) with all_34_0, all_38_0, all_13_0, simplifying % 14.77/3.02 | with (42), (48) gives: % 14.77/3.02 | (55) all_38_0 = all_34_0 % 14.77/3.02 | % 14.77/3.02 | GROUND_INST: instantiating (9) with all_24_0, all_38_0, all_13_0, simplifying % 14.77/3.02 | with (29), (48) gives: % 14.77/3.02 | (56) all_38_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | GROUND_INST: instantiating (10) with all_26_1, all_36_2, all_13_0, 2, % 14.77/3.02 | simplifying with (34), (46) gives: % 14.77/3.02 | (57) all_36_2 = all_26_1 % 14.77/3.02 | % 14.77/3.02 | GROUND_INST: instantiating (10) with all_22_0, all_36_2, all_13_0, 2, % 14.77/3.02 | simplifying with (27), (46) gives: % 14.77/3.02 | (58) all_36_2 = all_22_0 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (55), (56) imply: % 14.77/3.02 | (59) all_34_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | SIMP: (59) implies: % 14.77/3.02 | (60) all_34_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (52), (53) imply: % 14.77/3.02 | (61) all_32_0 = all_30_0 % 14.77/3.02 | % 14.77/3.02 | SIMP: (61) implies: % 14.77/3.02 | (62) all_32_0 = all_30_0 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (53), (54) imply: % 14.77/3.02 | (63) $difference(all_30_0, all_28_0) = 1 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (57), (58) imply: % 14.77/3.02 | (64) all_26_1 = all_22_0 % 14.77/3.02 | % 14.77/3.02 | SIMP: (64) implies: % 14.77/3.02 | (65) all_26_1 = all_22_0 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (51), (60) imply: % 14.77/3.02 | (66) all_32_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | SIMP: (66) implies: % 14.77/3.02 | (67) all_32_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (62), (67) imply: % 14.77/3.02 | (68) all_30_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | SIMP: (68) implies: % 14.77/3.02 | (69) all_30_0 = all_24_0 % 14.77/3.02 | % 14.77/3.02 | COMBINE_EQS: (63), (69) imply: % 14.77/3.03 | (70) $difference(all_28_0, all_24_0) = -1 % 14.77/3.03 | % 14.77/3.03 | SIMP: (70) implies: % 14.77/3.03 | (71) $difference(all_28_0, all_24_0) = -1 % 14.77/3.03 | % 14.77/3.03 | COMBINE_EQS: (50), (71) imply: % 14.77/3.03 | (72) $difference(all_26_0, all_24_0) = -1 % 14.77/3.03 | % 14.77/3.03 | SIMP: (72) implies: % 14.77/3.03 | (73) $difference(all_26_0, all_24_0) = -1 % 14.77/3.03 | % 14.77/3.03 | COMBINE_EQS: (49), (73) imply: % 14.77/3.03 | (74) all_24_0 = 1 % 14.77/3.03 | % 14.77/3.03 | REDUCE: (45), (58) imply: % 14.77/3.03 | (75) count(all_22_0) = all_36_1 % 14.77/3.03 | % 14.77/3.03 | REDUCE: (33), (49), (65) imply: % 14.77/3.03 | (76) count(all_22_0) = 0 % 14.77/3.03 | % 14.77/3.03 | REDUCE: (31), (65) imply: % 14.77/3.03 | (77) collection(all_22_0) % 14.77/3.03 | % 14.77/3.03 | GROUND_INST: instantiating (9) with 0, all_36_1, all_22_0, simplifying with % 14.77/3.03 | (75), (76) gives: % 14.77/3.03 | (78) all_36_1 = 0 % 14.77/3.03 | % 14.77/3.03 | GROUND_INST: instantiating (2) with all_22_0, simplifying with (76), (77) % 14.77/3.03 | gives: % 14.77/3.03 | (79) all_22_0 = empty % 14.77/3.03 | % 14.77/3.03 | GROUND_INST: instantiating (5) with 5, all_22_0, 2, all_13_0, simplifying with % 14.77/3.03 | (14), (26), (77) gives: % 14.77/3.03 | (80) in(5, all_22_0) = 0 % 14.77/3.03 | % 14.77/3.03 | REDUCE: (79), (80) imply: % 14.77/3.03 | (81) in(5, empty) = 0 % 14.77/3.03 | % 14.77/3.03 | GROUND_INST: instantiating (1) with 5, simplifying with (81) gives: % 14.77/3.03 | (82) $false % 14.77/3.04 | % 14.77/3.04 | CLOSE: (82) is inconsistent. % 14.77/3.04 | % 14.77/3.04 End of proof % 14.77/3.04 % SZS output end Proof for theBenchmark % 14.77/3.04 % 14.77/3.04 2408ms %------------------------------------------------------------------------------