%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG041+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 16:35:49 EDT 2023 % Result : Theorem 9.29s 2.00s % Output : Proof 26.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ALG041+1 : TPTP v8.1.2. Released v2.7.0. % 0.06/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n007.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 04:43:12 EDT 2023 % 0.12/0.33 % CPUTime : % 0.18/0.60 ________ _____ % 0.18/0.60 ___ __ \_________(_)________________________________ % 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.60 % 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.60 (2023-06-19) % 0.18/0.60 % 0.18/0.60 (c) Philipp Rümmer, 2009-2023 % 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.60 Amanda Stjerna. % 0.18/0.60 Free software under BSD-3-Clause. % 0.18/0.60 % 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.60 % 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.18/0.61 Running up to 7 provers in parallel. % 0.63/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.75/0.97 Prover 4: Preprocessing ... % 1.75/0.97 Prover 1: Preprocessing ... % 2.61/1.04 Prover 3: Preprocessing ... % 2.61/1.04 Prover 6: Preprocessing ... % 2.61/1.04 Prover 0: Preprocessing ... % 2.61/1.04 Prover 2: Preprocessing ... % 2.61/1.04 Prover 5: Preprocessing ... % 4.41/1.30 Prover 6: Proving ... % 4.41/1.31 Prover 1: Constructing countermodel ... % 4.41/1.31 Prover 3: Constructing countermodel ... % 4.41/1.32 Prover 5: Constructing countermodel ... % 4.88/1.36 Prover 2: Proving ... % 5.00/1.40 Prover 4: Constructing countermodel ... % 5.00/1.40 Prover 0: Proving ... % 5.29/1.43 Prover 3: gave up % 5.29/1.43 Prover 1: gave up % 5.29/1.43 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.47/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.47/1.46 Prover 7: Preprocessing ... % 5.47/1.48 Prover 8: Preprocessing ... % 6.14/1.52 Prover 7: Constructing countermodel ... % 6.14/1.55 Prover 7: gave up % 6.14/1.55 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.14/1.56 Prover 8: Warning: ignoring some quantifiers % 6.14/1.56 Prover 9: Preprocessing ... % 6.14/1.57 Prover 8: Constructing countermodel ... % 6.59/1.64 Prover 8: gave up % 6.59/1.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.16/1.66 Prover 10: Preprocessing ... % 7.26/1.70 Prover 9: Constructing countermodel ... % 7.26/1.70 Prover 10: Constructing countermodel ... % 7.54/1.71 Prover 10: gave up % 7.54/1.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.73/1.74 Prover 11: Preprocessing ... % 8.76/1.90 Prover 11: Constructing countermodel ... % 9.29/2.00 Prover 9: proved (448ms) % 9.29/2.00 % 9.29/2.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.29/2.00 % 9.29/2.00 Prover 5: stopped % 9.29/2.00 Prover 2: stopped % 9.29/2.00 Prover 6: stopped % 9.29/2.00 Prover 0: stopped % 9.29/2.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.29/2.00 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.29/2.00 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.29/2.02 Prover 19: Preprocessing ... % 9.29/2.02 Prover 13: Preprocessing ... % 9.84/2.02 Prover 16: Preprocessing ... % 9.84/2.06 Prover 13: Constructing countermodel ... % 9.84/2.07 Prover 19: Warning: ignoring some quantifiers % 10.23/2.07 Prover 19: Constructing countermodel ... % 10.23/2.09 Prover 16: Constructing countermodel ... % 25.58/4.11 Prover 11: Found proof (size 192) % 25.58/4.11 Prover 11: proved (2392ms) % 25.58/4.11 Prover 16: stopped % 25.58/4.11 Prover 4: stopped % 25.58/4.11 Prover 19: stopped % 25.58/4.11 Prover 13: stopped % 25.58/4.11 % 25.58/4.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 25.58/4.11 % 25.58/4.13 % SZS output start Proof for theBenchmark % 25.58/4.14 Assumptions after simplification: % 25.58/4.14 --------------------------------- % 25.58/4.14 % 25.58/4.14 (ax1) % 26.12/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op1(v0, v1) = v2) | ~ % 26.12/4.16 (sorti1(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 26.12/4.16 ((v4 = 0 & sorti1(v2) = 0) | ( ~ (v3 = 0) & sorti1(v1) = v3))) & ! [v0: $i] % 26.12/4.16 : ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ (sorti1(v0) = 0) | ~ $i(v1) | ~ % 26.12/4.16 $i(v0) | ? [v2: $i] : (op1(v0, v1) = v2 & sorti1(v2) = 0 & $i(v2))) % 26.12/4.16 % 26.12/4.16 (ax2) % 26.12/4.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op2(v0, v1) = v2) | ~ % 26.12/4.17 (sorti2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : % 26.12/4.17 ((v4 = 0 & sorti2(v2) = 0) | ( ~ (v3 = 0) & sorti2(v1) = v3))) & ! [v0: $i] % 26.12/4.17 : ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ (sorti2(v0) = 0) | ~ $i(v1) | ~ % 26.12/4.17 $i(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & sorti2(v2) = 0 & $i(v2))) % 26.12/4.17 % 26.12/4.17 (ax3) % 26.12/4.17 ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ( % 26.12/4.17 ~ (v2 = v0) & op1(v1, v1) = v2 & sorti1(v1) = 0 & $i(v2) & $i(v1))) % 26.12/4.17 % 26.12/4.17 (ax4) % 26.12/4.17 ? [v0: $i] : (sorti2(v0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (v2 = v0 % 26.12/4.17 | ~ (op2(v1, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & % 26.12/4.17 sorti2(v1) = v3)) & ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ $i(v1) | % 26.12/4.17 op2(v1, v1) = v0)) % 26.12/4.17 % 26.12/4.17 (co1) % 26.12/4.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~ % 26.12/4.20 (j(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: % 26.12/4.20 $i] : ? [v7: $i] : ((v7 = v6 & j(v5) = v6 & op2(v0, v2) = v5 & op1(v1, % 26.12/4.20 v3) = v6 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) = v4) | ( ~ % 26.12/4.20 (v4 = 0) & sorti2(v0) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 26.12/4.20 : ! [v3: $i] : ( ~ (j(v0) = v1) | ~ (op2(v0, v2) = v3) | ~ $i(v2) | ~ % 26.12/4.20 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 % 26.12/4.20 & j(v3) = v5 & j(v2) = v6 & op1(v1, v6) = v5 & $i(v6) & $i(v5)) | ( ~ % 26.12/4.20 (v4 = 0) & sorti2(v2) = v4) | ( ~ (v4 = 0) & sorti2(v0) = v4))) & ! % 26.12/4.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~ % 26.12/4.20 (h(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: % 26.12/4.20 $i] : ? [v7: $i] : ((v7 = v6 & h(v5) = v6 & op2(v1, v3) = v6 & op1(v0, % 26.12/4.20 v2) = v5 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti1(v2) = v4) | ( ~ % 26.12/4.20 (v4 = 0) & sorti1(v0) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 26.12/4.20 : ! [v3: $i] : ( ~ (h(v0) = v1) | ~ (op1(v0, v2) = v3) | ~ $i(v2) | ~ % 26.12/4.20 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 % 26.12/4.20 & h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v5 & $i(v6) & $i(v5)) | ( ~ % 26.12/4.20 (v4 = 0) & sorti1(v2) = v4) | ( ~ (v4 = 0) & sorti1(v0) = v4))) & ! % 26.12/4.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (j(v0) = v1) | ~ (sorti2(v2) = 0) % 26.12/4.20 | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 26.12/4.20 $i] : ((v6 = v4 & j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) % 26.12/4.20 = v4 & $i(v5) & $i(v4) & $i(v3)) | ( ~ (v3 = 0) & sorti2(v0) = v3))) & % 26.12/4.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (h(v0) = v1) | ~ (sorti1(v2) = % 26.12/4.20 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ? % 26.12/4.20 [v6: $i] : ((v6 = v4 & h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, % 26.12/4.20 v2) = v3 & $i(v5) & $i(v4) & $i(v3)) | ( ~ (v3 = 0) & sorti1(v0) = % 26.12/4.20 v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? % 26.12/4.20 [v2: int] : ? [v3: $i] : ((v3 = v0 & h(v1) = v0) | ( ~ (v2 = 0) & % 26.12/4.20 sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ % 26.12/4.20 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & sorti1(v1) = 0) | ( ~ (v2 % 26.12/4.20 = 0) & sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = % 26.12/4.20 v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ((v3 = v0 & j(v1) = v0) | ( % 26.12/4.20 ~ (v2 = 0) & sorti1(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) % 26.12/4.20 = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & sorti2(v1) = % 26.12/4.20 0) | ( ~ (v2 = 0) & sorti1(v0) = v2))) & ! [v0: $i] : ( ~ (sorti2(v0) = % 26.12/4.20 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = v1 & h(v1) = v0 & $i(v1))) & ! % 26.12/4.20 [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = v1 & % 26.12/4.20 sorti1(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) % 26.12/4.20 | ? [v1: $i] : (j(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ % 26.12/4.20 (j(v2) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? % 26.12/4.20 [v7: $i] : ((v7 = v6 & j(v5) = v6 & op2(v0, v2) = v5 & op1(v1, v3) = v6 % 26.12/4.20 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) = v4))) & ! [v2: $i] % 26.12/4.20 : ! [v3: $i] : ( ~ (op2(v0, v2) = v3) | ~ $i(v2) | ? [v4: int] : ? % 26.12/4.20 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 & j(v3) = v5 & j(v2) = % 26.12/4.20 v6 & op1(v1, v6) = v5 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) % 26.12/4.20 = v4))) & ! [v2: $i] : ( ~ (sorti2(v2) = 0) | ~ $i(v2) | ? [v3: % 26.12/4.20 $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, % 26.12/4.20 v2) = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) & ! [v0: % 26.12/4.20 $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v1) = v0 & h(v0) = % 26.12/4.20 v1 & $i(v1))) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: % 26.12/4.20 $i] : (h(v0) = v1 & sorti2(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ % 26.12/4.20 (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) = v1 & $i(v1) & ! [v2: % 26.12/4.20 $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~ $i(v2) | ? [v4: int] : ? % 26.12/4.20 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v6 & h(v5) = v6 & op2(v1, % 26.12/4.20 v3) = v6 & op1(v0, v2) = v5 & $i(v6) & $i(v5)) | ( ~ (v4 = 0) & % 26.12/4.20 sorti1(v2) = v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ (op1(v0, v2) = % 26.12/4.20 v3) | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 26.12/4.20 $i] : ((v7 = v5 & h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v5 & $i(v6) % 26.12/4.20 & $i(v5)) | ( ~ (v4 = 0) & sorti1(v2) = v4))) & ! [v2: $i] : ( ~ % 26.12/4.20 (sorti1(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 26.12/4.20 (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3 & $i(v5) % 26.12/4.20 & $i(v4) & $i(v3))))) % 26.12/4.20 % 26.12/4.20 (function-axioms) % 26.12/4.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3, % 26.12/4.20 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 26.12/4.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = % 26.12/4.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = % 26.12/4.20 v1) | ~ (j(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 26.12/4.20 v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 26.12/4.20 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (sorti2(v2) = v1) | ~ % 26.12/4.20 (sorti2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 26.12/4.20 : ! [v2: $i] : (v1 = v0 | ~ (sorti1(v2) = v1) | ~ (sorti1(v2) = v0)) % 26.12/4.20 % 26.12/4.20 Those formulas are unsatisfiable: % 26.12/4.20 --------------------------------- % 26.12/4.20 % 26.12/4.20 Begin of proof % 26.12/4.20 | % 26.12/4.20 | ALPHA: (ax1) implies: % 26.12/4.20 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ (sorti1(v0) = 0) % 26.12/4.20 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (op1(v0, v1) = v2 & % 26.12/4.20 | sorti1(v2) = 0 & $i(v2))) % 26.12/4.20 | % 26.12/4.20 | ALPHA: (ax2) implies: % 26.12/4.20 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ (sorti2(v0) = 0) % 26.12/4.20 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & % 26.12/4.20 | sorti2(v2) = 0 & $i(v2))) % 26.12/4.20 | % 26.12/4.20 | ALPHA: (co1) implies: % 26.12/4.21 | (3) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) = % 26.12/4.21 | v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~ % 26.12/4.21 | $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 26.12/4.21 | ((v7 = v6 & h(v5) = v6 & op2(v1, v3) = v6 & op1(v0, v2) = v5 & % 26.12/4.21 | $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti1(v2) = v4))) & ! % 26.12/4.21 | [v2: $i] : ! [v3: $i] : ( ~ (op1(v0, v2) = v3) | ~ $i(v2) | ? % 26.12/4.21 | [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 & % 26.12/4.21 | h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v5 & $i(v6) & $i(v5)) % 26.12/4.21 | | ( ~ (v4 = 0) & sorti1(v2) = v4))) & ! [v2: $i] : ( ~ % 26.12/4.21 | (sorti1(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? % 26.12/4.21 | [v5: $i] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, % 26.12/4.21 | v2) = v3 & $i(v5) & $i(v4) & $i(v3))))) % 26.12/4.21 | (4) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) = % 26.12/4.21 | v1 & sorti2(v1) = 0 & $i(v1))) % 26.12/4.21 | (5) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v1) = % 26.12/4.21 | v0 & h(v0) = v1 & $i(v1))) % 26.12/4.21 | (6) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = % 26.12/4.21 | v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~ % 26.12/4.21 | $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 26.12/4.21 | ((v7 = v6 & j(v5) = v6 & op2(v0, v2) = v5 & op1(v1, v3) = v6 & % 26.12/4.21 | $i(v6) & $i(v5)) | ( ~ (v4 = 0) & sorti2(v2) = v4))) & ! % 26.12/4.21 | [v2: $i] : ! [v3: $i] : ( ~ (op2(v0, v2) = v3) | ~ $i(v2) | ? % 26.12/4.21 | [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5 & % 26.12/4.21 | j(v3) = v5 & j(v2) = v6 & op1(v1, v6) = v5 & $i(v6) & $i(v5)) % 26.12/4.21 | | ( ~ (v4 = 0) & sorti2(v2) = v4))) & ! [v2: $i] : ( ~ % 26.12/4.21 | (sorti2(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? % 26.12/4.21 | [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, % 26.12/4.21 | v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) % 26.12/4.21 | (7) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = % 26.12/4.21 | v1 & sorti1(v1) = 0 & $i(v1))) % 26.12/4.21 | (8) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = % 26.12/4.21 | v1 & h(v1) = v0 & $i(v1))) % 26.12/4.21 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: int] % 26.12/4.21 | : ? [v3: $i] : ((v3 = v0 & j(v1) = v0) | ( ~ (v2 = 0) & sorti1(v0) = % 26.12/4.21 | v2))) % 26.12/4.21 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (h(v0) = v1) | ~ % 26.12/4.21 | (sorti1(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : ? [v4: % 26.12/4.21 | $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & h(v3) = v4 & h(v2) = % 26.12/4.21 | v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3 & $i(v5) & $i(v4) & % 26.12/4.21 | $i(v3)) | ( ~ (v3 = 0) & sorti1(v0) = v3))) % 26.12/4.21 | % 26.12/4.21 | ALPHA: (function-axioms) implies: % 26.12/4.21 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 26.12/4.21 | : (v1 = v0 | ~ (sorti1(v2) = v1) | ~ (sorti1(v2) = v0)) % 26.12/4.21 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | % 26.12/4.21 | ~ (h(v2) = v0)) % 26.12/4.22 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) | % 26.12/4.22 | ~ (j(v2) = v0)) % 26.12/4.22 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.12/4.22 | (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 26.12/4.22 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 26.12/4.22 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 26.12/4.22 | % 26.12/4.22 | DELTA: instantiating (ax4) with fresh symbol all_7_0 gives: % 26.12/4.22 | (16) sorti2(all_7_0) = 0 & $i(all_7_0) & ! [v0: $i] : ! [v1: int] : (v1 = % 26.12/4.22 | all_7_0 | ~ (op2(v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 % 26.12/4.22 | = 0) & sorti2(v0) = v2)) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | % 26.12/4.22 | ~ $i(v0) | op2(v0, v0) = all_7_0) % 26.12/4.22 | % 26.12/4.22 | ALPHA: (16) implies: % 26.12/4.22 | (17) $i(all_7_0) % 26.12/4.22 | (18) sorti2(all_7_0) = 0 % 26.12/4.22 | (19) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | op2(v0, v0) = % 26.12/4.22 | all_7_0) % 26.12/4.22 | % 26.40/4.22 | GROUND_INST: instantiating (2) with all_7_0, all_7_0, simplifying with (17), % 26.40/4.22 | (18) gives: % 26.40/4.22 | (20) ? [v0: $i] : (op2(all_7_0, all_7_0) = v0 & sorti2(v0) = 0 & $i(v0)) % 26.40/4.22 | % 26.40/4.22 | GROUND_INST: instantiating (19) with all_7_0, simplifying with (17), (18) % 26.40/4.22 | gives: % 26.40/4.22 | (21) op2(all_7_0, all_7_0) = all_7_0 % 26.40/4.22 | % 26.40/4.22 | GROUND_INST: instantiating (8) with all_7_0, simplifying with (17), (18) % 26.40/4.22 | gives: % 26.40/4.22 | (22) ? [v0: $i] : (j(all_7_0) = v0 & h(v0) = all_7_0 & $i(v0)) % 26.40/4.22 | % 26.40/4.22 | GROUND_INST: instantiating (7) with all_7_0, simplifying with (17), (18) % 26.40/4.22 | gives: % 26.40/4.22 | (23) ? [v0: $i] : (j(all_7_0) = v0 & sorti1(v0) = 0 & $i(v0)) % 26.40/4.22 | % 26.40/4.22 | GROUND_INST: instantiating (6) with all_7_0, simplifying with (17), (18) % 26.40/4.22 | gives: % 26.40/4.22 | (24) ? [v0: $i] : (j(all_7_0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 26.40/4.22 | ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : ? [v5: % 26.40/4.22 | $i] : ? [v6: $i] : ((v6 = v5 & j(v4) = v5 & op2(all_7_0, v1) = % 26.40/4.22 | v4 & op1(v0, v2) = v5 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & % 26.40/4.22 | sorti2(v1) = v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 26.40/4.22 | (op2(all_7_0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : % 26.40/4.22 | ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & j(v2) = v4 & j(v1) = v5 & % 26.40/4.22 | op1(v0, v5) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & % 26.40/4.22 | sorti2(v1) = v3))) & ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ % 26.40/4.22 | $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 & % 26.40/4.22 | j(v1) = v4 & op2(all_7_0, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & % 26.40/4.22 | $i(v3) & $i(v2)))) % 26.40/4.22 | % 26.40/4.22 | DELTA: instantiating (20) with fresh symbol all_16_0 gives: % 26.40/4.22 | (25) op2(all_7_0, all_7_0) = all_16_0 & sorti2(all_16_0) = 0 & $i(all_16_0) % 26.40/4.22 | % 26.40/4.22 | ALPHA: (25) implies: % 26.40/4.22 | (26) sorti2(all_16_0) = 0 % 26.40/4.22 | (27) op2(all_7_0, all_7_0) = all_16_0 % 26.40/4.22 | % 26.40/4.22 | DELTA: instantiating (23) with fresh symbol all_18_0 gives: % 26.40/4.23 | (28) j(all_7_0) = all_18_0 & sorti1(all_18_0) = 0 & $i(all_18_0) % 26.40/4.23 | % 26.40/4.23 | ALPHA: (28) implies: % 26.40/4.23 | (29) sorti1(all_18_0) = 0 % 26.40/4.23 | (30) j(all_7_0) = all_18_0 % 26.40/4.23 | % 26.40/4.23 | DELTA: instantiating (22) with fresh symbol all_20_0 gives: % 26.40/4.23 | (31) j(all_7_0) = all_20_0 & h(all_20_0) = all_7_0 & $i(all_20_0) % 26.40/4.23 | % 26.40/4.23 | ALPHA: (31) implies: % 26.40/4.23 | (32) h(all_20_0) = all_7_0 % 26.40/4.23 | (33) j(all_7_0) = all_20_0 % 26.40/4.23 | % 26.40/4.23 | DELTA: instantiating (24) with fresh symbol all_22_0 gives: % 26.40/4.23 | (34) j(all_7_0) = all_22_0 & $i(all_22_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.40/4.23 | (j(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] % 26.40/4.23 | : ? [v5: $i] : ((v5 = v4 & j(v3) = v4 & op2(all_7_0, v0) = v3 & % 26.40/4.23 | op1(all_22_0, v1) = v4 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & % 26.40/4.23 | sorti2(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.40/4.23 | (op2(all_7_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : % 26.40/4.23 | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & j(v1) = v3 & j(v0) = v4 & % 26.40/4.23 | op1(all_22_0, v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & % 26.40/4.23 | sorti2(v0) = v2))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ % 26.40/4.23 | $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & % 26.40/4.23 | j(v0) = v3 & op2(all_7_0, v0) = v1 & op1(all_22_0, v3) = v2 & % 26.40/4.23 | $i(v3) & $i(v2) & $i(v1))) % 26.40/4.23 | % 26.40/4.23 | ALPHA: (34) implies: % 26.40/4.23 | (35) j(all_7_0) = all_22_0 % 26.40/4.23 | (36) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 26.40/4.23 | $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_7_0, v0) = % 26.40/4.23 | v1 & op1(all_22_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1))) % 26.40/4.23 | % 26.40/4.23 | GROUND_INST: instantiating (36) with all_7_0, simplifying with (17), (18) % 26.40/4.23 | gives: % 26.40/4.23 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_0) = % 26.40/4.23 | v2 & op2(all_7_0, all_7_0) = v0 & op1(all_22_0, v2) = v1 & $i(v2) & % 26.40/4.23 | $i(v1) & $i(v0)) % 26.40/4.23 | % 26.40/4.23 | DELTA: instantiating (37) with fresh symbols all_25_0, all_25_1, all_25_2 % 26.40/4.23 | gives: % 26.40/4.23 | (38) j(all_25_2) = all_25_1 & j(all_7_0) = all_25_0 & op2(all_7_0, all_7_0) % 26.40/4.23 | = all_25_2 & op1(all_22_0, all_25_0) = all_25_1 & $i(all_25_0) & % 26.40/4.23 | $i(all_25_1) & $i(all_25_2) % 26.40/4.23 | % 26.40/4.23 | ALPHA: (38) implies: % 26.40/4.23 | (39) $i(all_25_1) % 26.40/4.23 | (40) op1(all_22_0, all_25_0) = all_25_1 % 26.40/4.23 | (41) op2(all_7_0, all_7_0) = all_25_2 % 26.40/4.23 | (42) j(all_7_0) = all_25_0 % 26.40/4.23 | (43) j(all_25_2) = all_25_1 % 26.40/4.23 | % 26.40/4.23 | GROUND_INST: instantiating (15) with all_16_0, all_25_2, all_7_0, all_7_0, % 26.40/4.23 | simplifying with (27), (41) gives: % 26.40/4.23 | (44) all_25_2 = all_16_0 % 26.40/4.23 | % 26.40/4.23 | GROUND_INST: instantiating (15) with all_7_0, all_25_2, all_7_0, all_7_0, % 26.40/4.23 | simplifying with (21), (41) gives: % 26.40/4.23 | (45) all_25_2 = all_7_0 % 26.40/4.23 | % 26.40/4.23 | GROUND_INST: instantiating (13) with all_20_0, all_22_0, all_7_0, simplifying % 26.40/4.23 | with (33), (35) gives: % 26.40/4.23 | (46) all_22_0 = all_20_0 % 26.40/4.23 | % 26.40/4.23 | GROUND_INST: instantiating (13) with all_22_0, all_25_0, all_7_0, simplifying % 26.40/4.23 | with (35), (42) gives: % 26.40/4.23 | (47) all_25_0 = all_22_0 % 26.40/4.23 | % 26.40/4.23 | GROUND_INST: instantiating (13) with all_18_0, all_25_0, all_7_0, simplifying % 26.40/4.23 | with (30), (42) gives: % 26.40/4.23 | (48) all_25_0 = all_18_0 % 26.40/4.23 | % 26.40/4.23 | COMBINE_EQS: (47), (48) imply: % 26.40/4.23 | (49) all_22_0 = all_18_0 % 26.40/4.23 | % 26.40/4.23 | SIMP: (49) implies: % 26.40/4.23 | (50) all_22_0 = all_18_0 % 26.40/4.23 | % 26.40/4.23 | COMBINE_EQS: (44), (45) imply: % 26.40/4.23 | (51) all_16_0 = all_7_0 % 26.40/4.23 | % 26.40/4.23 | COMBINE_EQS: (46), (50) imply: % 26.40/4.24 | (52) all_20_0 = all_18_0 % 26.40/4.24 | % 26.40/4.24 | SIMP: (52) implies: % 26.40/4.24 | (53) all_20_0 = all_18_0 % 26.40/4.24 | % 26.40/4.24 | REDUCE: (43), (45) imply: % 26.40/4.24 | (54) j(all_7_0) = all_25_1 % 26.40/4.24 | % 26.40/4.24 | REDUCE: (32), (53) imply: % 26.40/4.24 | (55) h(all_18_0) = all_7_0 % 26.40/4.24 | % 26.40/4.24 | REDUCE: (40), (48), (50) imply: % 26.40/4.24 | (56) op1(all_18_0, all_18_0) = all_25_1 % 26.40/4.24 | % 26.40/4.24 | GROUND_INST: instantiating (13) with all_18_0, all_25_1, all_7_0, simplifying % 26.40/4.24 | with (30), (54) gives: % 26.40/4.24 | (57) all_25_1 = all_18_0 % 26.40/4.24 | % 26.40/4.24 | REDUCE: (56), (57) imply: % 26.40/4.24 | (58) op1(all_18_0, all_18_0) = all_18_0 % 26.40/4.24 | % 26.40/4.24 | REDUCE: (39), (57) imply: % 26.40/4.24 | (59) $i(all_18_0) % 26.40/4.24 | % 26.40/4.24 | GROUND_INST: instantiating (ax3) with all_18_0, simplifying with (29), (59) % 26.40/4.24 | gives: % 26.40/4.24 | (60) ? [v0: $i] : ? [v1: any] : ( ~ (v1 = all_18_0) & op1(v0, v0) = v1 & % 26.40/4.24 | sorti1(v0) = 0 & $i(v1) & $i(v0)) % 26.40/4.24 | % 26.40/4.24 | GROUND_INST: instantiating (3) with all_18_0, simplifying with (29), (59) % 26.40/4.24 | gives: % 26.40/4.24 | (61) ? [v0: $i] : (h(all_18_0) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 26.40/4.24 | ( ~ (h(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : ? [v5: % 26.40/4.24 | $i] : ? [v6: $i] : ((v6 = v5 & h(v4) = v5 & op2(v0, v2) = v5 & % 26.40/4.24 | op1(all_18_0, v1) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & % 26.40/4.24 | sorti1(v1) = v3))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 26.40/4.24 | (op1(all_18_0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: $i] % 26.40/4.24 | : ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & h(v2) = v4 & h(v1) = v5 % 26.40/4.24 | & op2(v0, v5) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & % 26.40/4.24 | sorti1(v1) = v3))) & ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ % 26.40/4.24 | $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (h(v2) = v3 & % 26.40/4.24 | h(v1) = v4 & op2(v0, v4) = v3 & op1(all_18_0, v1) = v2 & $i(v4) % 26.40/4.24 | & $i(v3) & $i(v2)))) % 26.40/4.24 | % 26.40/4.24 | DELTA: instantiating (60) with fresh symbols all_40_0, all_40_1 gives: % 26.40/4.24 | (62) ~ (all_40_0 = all_18_0) & op1(all_40_1, all_40_1) = all_40_0 & % 26.40/4.24 | sorti1(all_40_1) = 0 & $i(all_40_0) & $i(all_40_1) % 26.40/4.24 | % 26.40/4.24 | ALPHA: (62) implies: % 26.40/4.24 | (63) ~ (all_40_0 = all_18_0) % 26.40/4.24 | (64) $i(all_40_1) % 26.40/4.24 | (65) sorti1(all_40_1) = 0 % 26.40/4.24 | (66) op1(all_40_1, all_40_1) = all_40_0 % 26.40/4.24 | % 26.40/4.24 | DELTA: instantiating (61) with fresh symbol all_42_0 gives: % 26.40/4.24 | (67) h(all_18_0) = all_42_0 & $i(all_42_0) & ! [v0: $i] : ! [v1: $i] : ( % 26.40/4.24 | ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: % 26.40/4.24 | $i] : ? [v5: $i] : ((v5 = v4 & h(v3) = v4 & op2(all_42_0, v1) = % 26.40/4.24 | v4 & op1(all_18_0, v0) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & % 26.40/4.24 | sorti1(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 26.40/4.24 | (op1(all_18_0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : % 26.40/4.24 | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & h(v1) = v3 & h(v0) = v4 & % 26.40/4.24 | op2(all_42_0, v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & % 26.40/4.24 | sorti1(v0) = v2))) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ % 26.40/4.24 | $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (h(v1) = v2 & % 26.40/4.24 | h(v0) = v3 & op2(all_42_0, v3) = v2 & op1(all_18_0, v0) = v1 & % 26.40/4.24 | $i(v3) & $i(v2) & $i(v1))) % 26.40/4.24 | % 26.40/4.24 | ALPHA: (67) implies: % 26.40/4.24 | (68) h(all_18_0) = all_42_0 % 26.40/4.25 | (69) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 26.40/4.25 | $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_42_0, v3) = % 26.40/4.25 | v2 & op1(all_18_0, v0) = v1 & $i(v3) & $i(v2) & $i(v1))) % 26.40/4.25 | (70) ! [v0: $i] : ! [v1: $i] : ( ~ (op1(all_18_0, v0) = v1) | ~ $i(v0) | % 26.40/4.25 | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & % 26.40/4.25 | h(v1) = v3 & h(v0) = v4 & op2(all_42_0, v4) = v3 & $i(v4) & % 26.40/4.25 | $i(v3)) | ( ~ (v2 = 0) & sorti1(v0) = v2))) % 26.40/4.25 | (71) ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: % 26.40/4.25 | int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v4 & h(v3) % 26.40/4.25 | = v4 & op2(all_42_0, v1) = v4 & op1(all_18_0, v0) = v3 & $i(v4) % 26.40/4.25 | & $i(v3)) | ( ~ (v2 = 0) & sorti1(v0) = v2))) % 26.40/4.25 | % 26.40/4.25 | GROUND_INST: instantiating (69) with all_18_0, simplifying with (29), (59) % 26.40/4.25 | gives: % 26.40/4.25 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & h(all_18_0) = % 26.40/4.25 | v2 & op2(all_42_0, v2) = v1 & op1(all_18_0, all_18_0) = v0 & $i(v2) % 26.40/4.25 | & $i(v1) & $i(v0)) % 26.40/4.25 | % 26.40/4.25 | GROUND_INST: instantiating (70) with all_18_0, all_18_0, simplifying with % 26.40/4.25 | (58), (59) gives: % 26.40/4.25 | (73) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v1 & % 26.40/4.25 | h(all_18_0) = v2 & h(all_18_0) = v1 & op2(all_42_0, v2) = v1 & % 26.40/4.25 | $i(v2) & $i(v1)) | ( ~ (v0 = 0) & sorti1(all_18_0) = v0)) % 26.40/4.25 | % 26.40/4.25 | GROUND_INST: instantiating (71) with all_18_0, all_7_0, simplifying with (55), % 26.40/4.25 | (59) gives: % 26.40/4.25 | (74) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = v2 & % 26.40/4.25 | h(v1) = v2 & op2(all_42_0, all_7_0) = v2 & op1(all_18_0, all_18_0) % 26.40/4.25 | = v1 & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & sorti1(all_18_0) = v0)) % 26.40/4.25 | % 26.40/4.25 | DELTA: instantiating (72) with fresh symbols all_45_0, all_45_1, all_45_2 % 26.40/4.25 | gives: % 26.40/4.25 | (75) h(all_45_2) = all_45_1 & h(all_18_0) = all_45_0 & op2(all_42_0, % 26.40/4.25 | all_45_0) = all_45_1 & op1(all_18_0, all_18_0) = all_45_2 & % 26.40/4.25 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2) % 26.40/4.25 | % 26.40/4.25 | ALPHA: (75) implies: % 26.40/4.25 | (76) $i(all_45_2) % 26.40/4.25 | (77) op1(all_18_0, all_18_0) = all_45_2 % 26.40/4.25 | (78) h(all_18_0) = all_45_0 % 26.40/4.25 | (79) h(all_45_2) = all_45_1 % 26.40/4.25 | % 26.40/4.25 | DELTA: instantiating (74) with fresh symbols all_47_0, all_47_1, all_47_2, % 26.40/4.25 | all_47_3 gives: % 26.40/4.25 | (80) (all_47_0 = all_47_1 & h(all_47_2) = all_47_1 & op2(all_42_0, all_7_0) % 26.40/4.25 | = all_47_1 & op1(all_18_0, all_18_0) = all_47_2 & $i(all_47_1) & % 26.40/4.25 | $i(all_47_2)) | ( ~ (all_47_3 = 0) & sorti1(all_18_0) = all_47_3) % 26.40/4.25 | % 26.40/4.25 | DELTA: instantiating (73) with fresh symbols all_48_0, all_48_1, all_48_2, % 26.40/4.25 | all_48_3 gives: % 26.40/4.25 | (81) (all_48_0 = all_48_2 & h(all_18_0) = all_48_1 & h(all_18_0) = all_48_2 % 26.40/4.25 | & op2(all_42_0, all_48_1) = all_48_2 & $i(all_48_1) & $i(all_48_2)) % 26.40/4.25 | | ( ~ (all_48_3 = 0) & sorti1(all_18_0) = all_48_3) % 26.40/4.25 | % 26.40/4.25 | BETA: splitting (81) gives: % 26.40/4.25 | % 26.40/4.25 | Case 1: % 26.40/4.25 | | % 26.56/4.25 | | (82) all_48_0 = all_48_2 & h(all_18_0) = all_48_1 & h(all_18_0) = % 26.56/4.25 | | all_48_2 & op2(all_42_0, all_48_1) = all_48_2 & $i(all_48_1) & % 26.56/4.25 | | $i(all_48_2) % 26.56/4.25 | | % 26.56/4.25 | | ALPHA: (82) implies: % 26.56/4.25 | | (83) h(all_18_0) = all_48_2 % 26.56/4.25 | | (84) h(all_18_0) = all_48_1 % 26.56/4.25 | | % 26.56/4.25 | | BETA: splitting (80) gives: % 26.56/4.25 | | % 26.56/4.25 | | Case 1: % 26.56/4.25 | | | % 26.56/4.25 | | | (85) all_47_0 = all_47_1 & h(all_47_2) = all_47_1 & op2(all_42_0, % 26.56/4.25 | | | all_7_0) = all_47_1 & op1(all_18_0, all_18_0) = all_47_2 & % 26.56/4.25 | | | $i(all_47_1) & $i(all_47_2) % 26.56/4.25 | | | % 26.56/4.25 | | | ALPHA: (85) implies: % 26.56/4.25 | | | (86) op1(all_18_0, all_18_0) = all_47_2 % 26.56/4.25 | | | (87) h(all_47_2) = all_47_1 % 26.56/4.25 | | | % 26.56/4.25 | | | GROUND_INST: instantiating (14) with all_18_0, all_47_2, all_18_0, % 26.56/4.25 | | | all_18_0, simplifying with (58), (86) gives: % 26.56/4.25 | | | (88) all_47_2 = all_18_0 % 26.56/4.25 | | | % 26.56/4.25 | | | GROUND_INST: instantiating (14) with all_45_2, all_47_2, all_18_0, % 26.56/4.25 | | | all_18_0, simplifying with (77), (86) gives: % 26.56/4.25 | | | (89) all_47_2 = all_45_2 % 26.56/4.25 | | | % 26.56/4.25 | | | GROUND_INST: instantiating (12) with all_7_0, all_48_2, all_18_0, % 26.56/4.25 | | | simplifying with (55), (83) gives: % 26.56/4.26 | | | (90) all_48_2 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (12) with all_45_0, all_48_2, all_18_0, % 26.56/4.26 | | | simplifying with (78), (83) gives: % 26.56/4.26 | | | (91) all_48_2 = all_45_0 % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (12) with all_45_0, all_48_1, all_18_0, % 26.56/4.26 | | | simplifying with (78), (84) gives: % 26.56/4.26 | | | (92) all_48_1 = all_45_0 % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (12) with all_42_0, all_48_1, all_18_0, % 26.56/4.26 | | | simplifying with (68), (84) gives: % 26.56/4.26 | | | (93) all_48_1 = all_42_0 % 26.56/4.26 | | | % 26.56/4.26 | | | COMBINE_EQS: (92), (93) imply: % 26.56/4.26 | | | (94) all_45_0 = all_42_0 % 26.56/4.26 | | | % 26.56/4.26 | | | SIMP: (94) implies: % 26.56/4.26 | | | (95) all_45_0 = all_42_0 % 26.56/4.26 | | | % 26.56/4.26 | | | COMBINE_EQS: (90), (91) imply: % 26.56/4.26 | | | (96) all_45_0 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | SIMP: (96) implies: % 26.56/4.26 | | | (97) all_45_0 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | COMBINE_EQS: (88), (89) imply: % 26.56/4.26 | | | (98) all_45_2 = all_18_0 % 26.56/4.26 | | | % 26.56/4.26 | | | COMBINE_EQS: (95), (97) imply: % 26.56/4.26 | | | (99) all_42_0 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | SIMP: (99) implies: % 26.56/4.26 | | | (100) all_42_0 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | REDUCE: (87), (88) imply: % 26.56/4.26 | | | (101) h(all_18_0) = all_47_1 % 26.56/4.26 | | | % 26.56/4.26 | | | REDUCE: (79), (98) imply: % 26.56/4.26 | | | (102) h(all_18_0) = all_45_1 % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (12) with all_7_0, all_47_1, all_18_0, % 26.56/4.26 | | | simplifying with (55), (101) gives: % 26.56/4.26 | | | (103) all_47_1 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (12) with all_45_1, all_47_1, all_18_0, % 26.56/4.26 | | | simplifying with (101), (102) gives: % 26.56/4.26 | | | (104) all_47_1 = all_45_1 % 26.56/4.26 | | | % 26.56/4.26 | | | COMBINE_EQS: (103), (104) imply: % 26.56/4.26 | | | (105) all_45_1 = all_7_0 % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (10) with all_18_0, all_7_0, all_40_1, % 26.56/4.26 | | | simplifying with (55), (59), (64), (65) gives: % 26.56/4.26 | | | (106) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = % 26.56/4.26 | | | v1 & h(v0) = v1 & h(all_40_1) = v2 & op2(all_7_0, v2) = v1 & % 26.56/4.26 | | | op1(all_18_0, all_40_1) = v0 & $i(v2) & $i(v1) & $i(v0)) | ( % 26.56/4.26 | | | ~ (v0 = 0) & sorti1(all_18_0) = v0)) % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (1) with all_40_1, all_40_1, simplifying with % 26.56/4.26 | | | (64), (65) gives: % 26.56/4.26 | | | (107) ? [v0: $i] : (op1(all_40_1, all_40_1) = v0 & sorti1(v0) = 0 & % 26.56/4.26 | | | $i(v0)) % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (69) with all_40_1, simplifying with (64), (65) % 26.56/4.26 | | | gives: % 26.56/4.26 | | | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & % 26.56/4.26 | | | h(all_40_1) = v2 & op2(all_42_0, v2) = v1 & op1(all_18_0, % 26.56/4.26 | | | all_40_1) = v0 & $i(v2) & $i(v1) & $i(v0)) % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (5) with all_40_1, simplifying with (64), (65) % 26.56/4.26 | | | gives: % 26.56/4.26 | | | (109) ? [v0: $i] : (j(v0) = all_40_1 & h(all_40_1) = v0 & $i(v0)) % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (4) with all_40_1, simplifying with (64), (65) % 26.56/4.26 | | | gives: % 26.56/4.26 | | | (110) ? [v0: $i] : (h(all_40_1) = v0 & sorti2(v0) = 0 & $i(v0)) % 26.56/4.26 | | | % 26.56/4.26 | | | GROUND_INST: instantiating (3) with all_40_1, simplifying with (64), (65) % 26.56/4.26 | | | gives: % 26.56/4.26 | | | (111) ? [v0: $i] : (h(all_40_1) = v0 & $i(v0) & ! [v1: $i] : ! [v2: % 26.56/4.26 | | | $i] : ( ~ (h(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? [v4: % 26.56/4.26 | | | $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & h(v4) = v5 & % 26.56/4.26 | | | op2(v0, v2) = v5 & op1(all_40_1, v1) = v4 & $i(v5) & % 26.56/4.26 | | | $i(v4)) | ( ~ (v3 = 0) & sorti1(v1) = v3))) & ! [v1: $i] % 26.56/4.26 | | | : ! [v2: $i] : ( ~ (op1(all_40_1, v1) = v2) | ~ $i(v1) | ? % 26.56/4.26 | | | [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = % 26.56/4.26 | | | v4 & h(v2) = v4 & h(v1) = v5 & op2(v0, v5) = v4 & $i(v5) % 26.56/4.26 | | | & $i(v4)) | ( ~ (v3 = 0) & sorti1(v1) = v3))) & ! [v1: % 26.56/4.26 | | | $i] : ( ~ (sorti1(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? % 26.56/4.26 | | | [v3: $i] : ? [v4: $i] : (h(v2) = v3 & h(v1) = v4 & op2(v0, % 26.56/4.26 | | | v4) = v3 & op1(all_40_1, v1) = v2 & $i(v4) & $i(v3) & % 26.56/4.26 | | | $i(v2)))) % 26.56/4.26 | | | % 26.56/4.26 | | | DELTA: instantiating (110) with fresh symbol all_70_0 gives: % 26.56/4.26 | | | (112) h(all_40_1) = all_70_0 & sorti2(all_70_0) = 0 & $i(all_70_0) % 26.56/4.26 | | | % 26.56/4.26 | | | ALPHA: (112) implies: % 26.56/4.26 | | | (113) sorti2(all_70_0) = 0 % 26.56/4.26 | | | (114) h(all_40_1) = all_70_0 % 26.56/4.26 | | | % 26.56/4.26 | | | DELTA: instantiating (109) with fresh symbol all_72_0 gives: % 26.56/4.26 | | | (115) j(all_72_0) = all_40_1 & h(all_40_1) = all_72_0 & $i(all_72_0) % 26.56/4.26 | | | % 26.56/4.26 | | | ALPHA: (115) implies: % 26.56/4.26 | | | (116) $i(all_72_0) % 26.56/4.26 | | | (117) h(all_40_1) = all_72_0 % 26.56/4.26 | | | % 26.56/4.26 | | | DELTA: instantiating (107) with fresh symbol all_74_0 gives: % 26.56/4.26 | | | (118) op1(all_40_1, all_40_1) = all_74_0 & sorti1(all_74_0) = 0 & % 26.56/4.26 | | | $i(all_74_0) % 26.56/4.26 | | | % 26.56/4.26 | | | ALPHA: (118) implies: % 26.56/4.26 | | | (119) $i(all_74_0) % 26.56/4.26 | | | (120) sorti1(all_74_0) = 0 % 26.56/4.26 | | | (121) op1(all_40_1, all_40_1) = all_74_0 % 26.56/4.26 | | | % 26.56/4.26 | | | DELTA: instantiating (108) with fresh symbols all_83_0, all_83_1, all_83_2 % 26.56/4.26 | | | gives: % 26.56/4.26 | | | (122) h(all_83_2) = all_83_1 & h(all_40_1) = all_83_0 & op2(all_42_0, % 26.56/4.26 | | | all_83_0) = all_83_1 & op1(all_18_0, all_40_1) = all_83_2 & % 26.56/4.26 | | | $i(all_83_0) & $i(all_83_1) & $i(all_83_2) % 26.56/4.26 | | | % 26.56/4.26 | | | ALPHA: (122) implies: % 26.56/4.27 | | | (123) h(all_40_1) = all_83_0 % 26.56/4.27 | | | % 26.56/4.27 | | | DELTA: instantiating (106) with fresh symbols all_85_0, all_85_1, % 26.56/4.27 | | | all_85_2, all_85_3 gives: % 26.56/4.27 | | | (124) (all_85_0 = all_85_2 & h(all_85_3) = all_85_2 & h(all_40_1) = % 26.56/4.27 | | | all_85_1 & op2(all_7_0, all_85_1) = all_85_2 & op1(all_18_0, % 26.56/4.27 | | | all_40_1) = all_85_3 & $i(all_85_1) & $i(all_85_2) & % 26.56/4.27 | | | $i(all_85_3)) | ( ~ (all_85_3 = 0) & sorti1(all_18_0) = % 26.56/4.27 | | | all_85_3) % 26.56/4.27 | | | % 26.56/4.27 | | | DELTA: instantiating (111) with fresh symbol all_86_0 gives: % 26.56/4.27 | | | (125) h(all_40_1) = all_86_0 & $i(all_86_0) & ! [v0: $i] : ! [v1: $i] % 26.56/4.27 | | | : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? % 26.56/4.27 | | | [v4: $i] : ? [v5: $i] : ((v5 = v4 & h(v3) = v4 & op2(all_86_0, % 26.56/4.27 | | | v1) = v4 & op1(all_40_1, v0) = v3 & $i(v4) & $i(v3)) | ( % 26.56/4.27 | | | ~ (v2 = 0) & sorti1(v0) = v2))) & ! [v0: $i] : ! [v1: $i] % 26.56/4.27 | | | : ( ~ (op1(all_40_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? % 26.56/4.27 | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & h(v1) = v3 & % 26.56/4.27 | | | h(v0) = v4 & op2(all_86_0, v4) = v3 & $i(v4) & $i(v3)) | ( % 26.56/4.27 | | | ~ (v2 = 0) & sorti1(v0) = v2))) & ! [v0: $i] : ( ~ % 26.56/4.27 | | | (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? % 26.56/4.27 | | | [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_86_0, v3) = v2 & % 26.56/4.27 | | | op1(all_40_1, v0) = v1 & $i(v3) & $i(v2) & $i(v1))) % 26.56/4.27 | | | % 26.56/4.27 | | | ALPHA: (125) implies: % 26.56/4.27 | | | (126) h(all_40_1) = all_86_0 % 26.56/4.27 | | | (127) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 26.56/4.27 | | | [v2: $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & % 26.56/4.27 | | | op2(all_86_0, v3) = v2 & op1(all_40_1, v0) = v1 & $i(v3) & % 26.56/4.27 | | | $i(v2) & $i(v1))) % 26.56/4.27 | | | (128) ! [v0: $i] : ! [v1: $i] : ( ~ (op1(all_40_1, v0) = v1) | ~ % 26.56/4.27 | | | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 26.56/4.27 | | | : ((v5 = v3 & h(v1) = v3 & h(v0) = v4 & op2(all_86_0, v4) = v3 % 26.56/4.27 | | | & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & sorti1(v0) = v2))) % 26.56/4.27 | | | % 26.56/4.27 | | | GROUND_INST: instantiating (127) with all_18_0, simplifying with (29), % 26.56/4.27 | | | (59) gives: % 26.56/4.27 | | | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & % 26.56/4.27 | | | h(all_18_0) = v2 & op2(all_86_0, v2) = v1 & op1(all_40_1, % 26.56/4.27 | | | all_18_0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 26.56/4.27 | | | % 26.56/4.27 | | | GROUND_INST: instantiating (127) with all_40_1, simplifying with (64), % 26.56/4.27 | | | (65) gives: % 26.56/4.27 | | | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & % 26.56/4.27 | | | h(all_40_1) = v2 & op2(all_86_0, v2) = v1 & op1(all_40_1, % 26.56/4.27 | | | all_40_1) = v0 & $i(v2) & $i(v1) & $i(v0)) % 26.56/4.27 | | | % 26.56/4.27 | | | GROUND_INST: instantiating (128) with all_40_1, all_40_0, simplifying with % 26.56/4.27 | | | (64), (66) gives: % 26.56/4.27 | | | (131) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ((v3 = % 26.56/4.27 | | | v1 & h(all_40_0) = v1 & h(all_40_1) = v2 & op2(all_86_0, v2) % 26.56/4.27 | | | = v1 & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & sorti1(all_40_1) = % 26.56/4.27 | | | v0)) % 26.56/4.27 | | | % 26.56/4.27 | | | DELTA: instantiating (130) with fresh symbols all_89_0, all_89_1, all_89_2 % 26.56/4.27 | | | gives: % 26.56/4.27 | | | (132) h(all_89_2) = all_89_1 & h(all_40_1) = all_89_0 & op2(all_86_0, % 26.56/4.27 | | | all_89_0) = all_89_1 & op1(all_40_1, all_40_1) = all_89_2 & % 26.56/4.27 | | | $i(all_89_0) & $i(all_89_1) & $i(all_89_2) % 26.56/4.27 | | | % 26.56/4.27 | | | ALPHA: (132) implies: % 26.56/4.27 | | | (133) op1(all_40_1, all_40_1) = all_89_2 % 26.56/4.27 | | | (134) h(all_40_1) = all_89_0 % 26.56/4.27 | | | (135) h(all_89_2) = all_89_1 % 26.56/4.27 | | | % 26.56/4.27 | | | DELTA: instantiating (129) with fresh symbols all_91_0, all_91_1, all_91_2 % 26.56/4.27 | | | gives: % 26.56/4.27 | | | (136) h(all_91_2) = all_91_1 & h(all_18_0) = all_91_0 & op2(all_86_0, % 26.56/4.27 | | | all_91_0) = all_91_1 & op1(all_40_1, all_18_0) = all_91_2 & % 26.56/4.27 | | | $i(all_91_0) & $i(all_91_1) & $i(all_91_2) % 26.56/4.27 | | | % 26.56/4.27 | | | ALPHA: (136) implies: % 26.56/4.27 | | | (137) $i(all_91_0) % 26.56/4.27 | | | (138) h(all_18_0) = all_91_0 % 26.56/4.27 | | | % 26.56/4.27 | | | DELTA: instantiating (131) with fresh symbols all_94_0, all_94_1, % 26.56/4.27 | | | all_94_2, all_94_3 gives: % 26.56/4.27 | | | (139) (all_94_0 = all_94_2 & h(all_40_0) = all_94_2 & h(all_40_1) = % 26.56/4.27 | | | all_94_1 & op2(all_86_0, all_94_1) = all_94_2 & $i(all_94_1) & % 26.56/4.27 | | | $i(all_94_2)) | ( ~ (all_94_3 = 0) & sorti1(all_40_1) = % 26.56/4.27 | | | all_94_3) % 26.56/4.27 | | | % 26.56/4.27 | | | BETA: splitting (124) gives: % 26.56/4.27 | | | % 26.56/4.27 | | | Case 1: % 26.56/4.27 | | | | % 26.56/4.27 | | | | (140) all_85_0 = all_85_2 & h(all_85_3) = all_85_2 & h(all_40_1) = % 26.56/4.27 | | | | all_85_1 & op2(all_7_0, all_85_1) = all_85_2 & op1(all_18_0, % 26.56/4.27 | | | | all_40_1) = all_85_3 & $i(all_85_1) & $i(all_85_2) & % 26.56/4.27 | | | | $i(all_85_3) % 26.56/4.27 | | | | % 26.56/4.27 | | | | ALPHA: (140) implies: % 26.56/4.27 | | | | (141) h(all_40_1) = all_85_1 % 26.56/4.27 | | | | % 26.56/4.27 | | | | BETA: splitting (139) gives: % 26.56/4.27 | | | | % 26.56/4.27 | | | | Case 1: % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | (142) all_94_0 = all_94_2 & h(all_40_0) = all_94_2 & h(all_40_1) = % 26.56/4.27 | | | | | all_94_1 & op2(all_86_0, all_94_1) = all_94_2 & $i(all_94_1) % 26.56/4.27 | | | | | & $i(all_94_2) % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | ALPHA: (142) implies: % 26.56/4.27 | | | | | (143) op2(all_86_0, all_94_1) = all_94_2 % 26.56/4.27 | | | | | (144) h(all_40_1) = all_94_1 % 26.56/4.27 | | | | | (145) h(all_40_0) = all_94_2 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (14) with all_40_0, all_89_2, all_40_1, % 26.56/4.27 | | | | | all_40_1, simplifying with (66), (133) gives: % 26.56/4.27 | | | | | (146) all_89_2 = all_40_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (14) with all_74_0, all_89_2, all_40_1, % 26.56/4.27 | | | | | all_40_1, simplifying with (121), (133) gives: % 26.56/4.27 | | | | | (147) all_89_2 = all_74_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_7_0, all_91_0, all_18_0, % 26.56/4.27 | | | | | simplifying with (55), (138) gives: % 26.56/4.27 | | | | | (148) all_91_0 = all_7_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_83_0, all_85_1, all_40_1, % 26.56/4.27 | | | | | simplifying with (123), (141) gives: % 26.56/4.27 | | | | | (149) all_85_1 = all_83_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_83_0, all_86_0, all_40_1, % 26.56/4.27 | | | | | simplifying with (123), (126) gives: % 26.56/4.27 | | | | | (150) all_86_0 = all_83_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_70_0, all_86_0, all_40_1, % 26.56/4.27 | | | | | simplifying with (114), (126) gives: % 26.56/4.27 | | | | | (151) all_86_0 = all_70_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_85_1, all_89_0, all_40_1, % 26.56/4.27 | | | | | simplifying with (134), (141) gives: % 26.56/4.27 | | | | | (152) all_89_0 = all_85_1 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_89_0, all_94_1, all_40_1, % 26.56/4.27 | | | | | simplifying with (134), (144) gives: % 26.56/4.27 | | | | | (153) all_94_1 = all_89_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | GROUND_INST: instantiating (12) with all_72_0, all_94_1, all_40_1, % 26.56/4.27 | | | | | simplifying with (117), (144) gives: % 26.56/4.27 | | | | | (154) all_94_1 = all_72_0 % 26.56/4.27 | | | | | % 26.56/4.27 | | | | | COMBINE_EQS: (153), (154) imply: % 26.56/4.28 | | | | | (155) all_89_0 = all_72_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | SIMP: (155) implies: % 26.56/4.28 | | | | | (156) all_89_0 = all_72_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | COMBINE_EQS: (152), (156) imply: % 26.56/4.28 | | | | | (157) all_85_1 = all_72_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | SIMP: (157) implies: % 26.56/4.28 | | | | | (158) all_85_1 = all_72_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | COMBINE_EQS: (146), (147) imply: % 26.56/4.28 | | | | | (159) all_74_0 = all_40_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | COMBINE_EQS: (150), (151) imply: % 26.56/4.28 | | | | | (160) all_83_0 = all_70_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | SIMP: (160) implies: % 26.56/4.28 | | | | | (161) all_83_0 = all_70_0 % 26.56/4.28 | | | | | % 26.56/4.28 | | | | | COMBINE_EQS: (149), (158) imply: % 26.56/4.29 | | | | | (162) all_83_0 = all_72_0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | SIMP: (162) implies: % 26.56/4.29 | | | | | (163) all_83_0 = all_72_0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | COMBINE_EQS: (161), (163) imply: % 26.56/4.29 | | | | | (164) all_72_0 = all_70_0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | COMBINE_EQS: (154), (164) imply: % 26.56/4.29 | | | | | (165) all_94_1 = all_70_0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | REDUCE: (135), (146) imply: % 26.56/4.29 | | | | | (166) h(all_40_0) = all_89_1 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | REDUCE: (143), (151), (165) imply: % 26.56/4.29 | | | | | (167) op2(all_70_0, all_70_0) = all_94_2 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | REDUCE: (120), (159) imply: % 26.56/4.29 | | | | | (168) sorti1(all_40_0) = 0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | REDUCE: (119), (159) imply: % 26.56/4.29 | | | | | (169) $i(all_40_0) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | REDUCE: (116), (164) imply: % 26.56/4.29 | | | | | (170) $i(all_70_0) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | GROUND_INST: instantiating (12) with all_94_2, all_89_1, all_40_0, % 26.56/4.29 | | | | | simplifying with (145), (166) gives: % 26.56/4.29 | | | | | (171) all_94_2 = all_89_1 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | REDUCE: (167), (171) imply: % 26.56/4.29 | | | | | (172) op2(all_70_0, all_70_0) = all_89_1 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | GROUND_INST: instantiating (19) with all_70_0, simplifying with (113), % 26.56/4.29 | | | | | (170) gives: % 26.56/4.29 | | | | | (173) op2(all_70_0, all_70_0) = all_7_0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | GROUND_INST: instantiating (6) with all_70_0, simplifying with (113), % 26.56/4.29 | | | | | (170) gives: % 26.56/4.29 | | | | | (174) ? [v0: $i] : (j(all_70_0) = v0 & $i(v0) & ! [v1: $i] : ! % 26.56/4.29 | | | | | [v2: $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: int] : ? % 26.56/4.29 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v5 & j(v4) % 26.56/4.29 | | | | | = v5 & op2(all_70_0, v1) = v4 & op1(v0, v2) = v5 & % 26.56/4.29 | | | | | $i(v5) & $i(v4)) | ( ~ (v3 = 0) & sorti2(v1) = v3))) % 26.56/4.29 | | | | | & ! [v1: $i] : ! [v2: $i] : ( ~ (op2(all_70_0, v1) = v2) % 26.56/4.29 | | | | | | ~ $i(v1) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : % 26.56/4.29 | | | | | ? [v6: $i] : ((v6 = v4 & j(v2) = v4 & j(v1) = v5 & % 26.56/4.29 | | | | | op1(v0, v5) = v4 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & % 26.56/4.29 | | | | | sorti2(v1) = v3))) & ! [v1: $i] : ( ~ (sorti2(v1) = % 26.56/4.29 | | | | | 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: % 26.56/4.29 | | | | | $i] : (j(v2) = v3 & j(v1) = v4 & op2(all_70_0, v1) = v2 % 26.56/4.29 | | | | | & op1(v0, v4) = v3 & $i(v4) & $i(v3) & $i(v2)))) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | GROUND_INST: instantiating (9) with all_40_0, all_89_1, simplifying % 26.56/4.29 | | | | | with (166), (169) gives: % 26.56/4.29 | | | | | (175) ? [v0: int] : ? [v1: int] : ((v1 = all_40_0 & j(all_89_1) = % 26.56/4.29 | | | | | all_40_0) | ( ~ (v0 = 0) & sorti1(all_40_0) = v0)) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | DELTA: instantiating (175) with fresh symbols all_213_0, all_213_1 % 26.56/4.29 | | | | | gives: % 26.56/4.29 | | | | | (176) (all_213_0 = all_40_0 & j(all_89_1) = all_40_0) | ( ~ % 26.56/4.29 | | | | | (all_213_1 = 0) & sorti1(all_40_0) = all_213_1) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | DELTA: instantiating (174) with fresh symbol all_311_0 gives: % 26.56/4.29 | | | | | (177) j(all_70_0) = all_311_0 & $i(all_311_0) & ! [v0: $i] : ! % 26.56/4.29 | | | | | [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? % 26.56/4.29 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v4 & j(v3) = % 26.56/4.29 | | | | | v4 & op2(all_70_0, v0) = v3 & op1(all_311_0, v1) = v4 & % 26.56/4.29 | | | | | $i(v4) & $i(v3)) | ( ~ (v2 = 0) & sorti2(v0) = v2))) & % 26.56/4.29 | | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (op2(all_70_0, v0) = v1) | ~ % 26.56/4.29 | | | | | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 26.56/4.29 | | | | | $i] : ((v5 = v3 & j(v1) = v3 & j(v0) = v4 & % 26.56/4.29 | | | | | op1(all_311_0, v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = % 26.56/4.29 | | | | | 0) & sorti2(v0) = v2))) & ! [v0: $i] : ( ~ % 26.56/4.29 | | | | | (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : % 26.56/4.29 | | | | | ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_70_0, v0) = % 26.56/4.29 | | | | | v1 & op1(all_311_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1))) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | ALPHA: (177) implies: % 26.56/4.29 | | | | | (178) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 26.56/4.29 | | | | | : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 26.56/4.29 | | | | | op2(all_70_0, v0) = v1 & op1(all_311_0, v3) = v2 & $i(v3) % 26.56/4.29 | | | | | & $i(v2) & $i(v1))) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | GROUND_INST: instantiating (178) with all_7_0, simplifying with (17), % 26.56/4.29 | | | | | (18) gives: % 26.56/4.29 | | | | | (179) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 26.56/4.29 | | | | | j(all_7_0) = v2 & op2(all_70_0, all_7_0) = v0 & % 26.56/4.29 | | | | | op1(all_311_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | DELTA: instantiating (179) with fresh symbols all_328_0, all_328_1, % 26.56/4.29 | | | | | all_328_2 gives: % 26.56/4.29 | | | | | (180) j(all_328_2) = all_328_1 & j(all_7_0) = all_328_0 & % 26.56/4.29 | | | | | op2(all_70_0, all_7_0) = all_328_2 & op1(all_311_0, % 26.56/4.29 | | | | | all_328_0) = all_328_1 & $i(all_328_0) & $i(all_328_1) & % 26.56/4.29 | | | | | $i(all_328_2) % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | ALPHA: (180) implies: % 26.56/4.29 | | | | | (181) j(all_7_0) = all_328_0 % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | BETA: splitting (176) gives: % 26.56/4.29 | | | | | % 26.56/4.29 | | | | | Case 1: % 26.56/4.29 | | | | | | % 26.56/4.29 | | | | | | % 26.56/4.29 | | | | | | GROUND_INST: instantiating (15) with all_89_1, all_7_0, all_70_0, % 26.56/4.29 | | | | | | all_70_0, simplifying with (172), (173) gives: % 26.56/4.29 | | | | | | (182) all_89_1 = all_7_0 % 26.56/4.29 | | | | | | % 26.56/4.29 | | | | | | BETA: splitting (176) gives: % 26.56/4.29 | | | | | | % 26.56/4.29 | | | | | | Case 1: % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | (183) all_213_0 = all_40_0 & j(all_89_1) = all_40_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | ALPHA: (183) implies: % 26.56/4.29 | | | | | | | (184) j(all_89_1) = all_40_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | REDUCE: (182), (184) imply: % 26.56/4.29 | | | | | | | (185) j(all_7_0) = all_40_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | GROUND_INST: instantiating (13) with all_18_0, all_328_0, all_7_0, % 26.56/4.29 | | | | | | | simplifying with (30), (181) gives: % 26.56/4.29 | | | | | | | (186) all_328_0 = all_18_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | GROUND_INST: instantiating (13) with all_40_0, all_328_0, all_7_0, % 26.56/4.29 | | | | | | | simplifying with (181), (185) gives: % 26.56/4.29 | | | | | | | (187) all_328_0 = all_40_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | COMBINE_EQS: (186), (187) imply: % 26.56/4.29 | | | | | | | (188) all_40_0 = all_18_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | SIMP: (188) implies: % 26.56/4.29 | | | | | | | (189) all_40_0 = all_18_0 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | REDUCE: (63), (189) imply: % 26.56/4.29 | | | | | | | (190) $false % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | CLOSE: (190) is inconsistent. % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | Case 2: % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | (191) ~ (all_213_1 = 0) & sorti1(all_40_0) = all_213_1 % 26.56/4.29 | | | | | | | % 26.56/4.29 | | | | | | | ALPHA: (191) implies: % 26.56/4.30 | | | | | | | (192) ~ (all_213_1 = 0) % 26.56/4.30 | | | | | | | (193) sorti1(all_40_0) = all_213_1 % 26.56/4.30 | | | | | | | % 26.56/4.30 | | | | | | | REF_CLOSE: (11), (168), (192), (193) are inconsistent by sub-proof % 26.56/4.30 | | | | | | | #1. % 26.56/4.30 | | | | | | | % 26.56/4.30 | | | | | | End of split % 26.56/4.30 | | | | | | % 26.56/4.30 | | | | | Case 2: % 26.56/4.30 | | | | | | % 26.56/4.30 | | | | | | (194) ~ (all_213_1 = 0) & sorti1(all_40_0) = all_213_1 % 26.56/4.30 | | | | | | % 26.56/4.30 | | | | | | ALPHA: (194) implies: % 26.56/4.30 | | | | | | (195) ~ (all_213_1 = 0) % 26.56/4.30 | | | | | | (196) sorti1(all_40_0) = all_213_1 % 26.56/4.30 | | | | | | % 26.56/4.30 | | | | | | REF_CLOSE: (11), (168), (195), (196) are inconsistent by sub-proof % 26.56/4.30 | | | | | | #1. % 26.56/4.30 | | | | | | % 26.56/4.30 | | | | | End of split % 26.56/4.30 | | | | | % 26.56/4.30 | | | | Case 2: % 26.56/4.30 | | | | | % 26.56/4.30 | | | | | (197) ~ (all_94_3 = 0) & sorti1(all_40_1) = all_94_3 % 26.56/4.30 | | | | | % 26.56/4.30 | | | | | ALPHA: (197) implies: % 26.56/4.30 | | | | | (198) ~ (all_94_3 = 0) % 26.56/4.30 | | | | | (199) sorti1(all_40_1) = all_94_3 % 26.56/4.30 | | | | | % 26.56/4.30 | | | | | GROUND_INST: instantiating (11) with 0, all_94_3, all_40_1, % 26.56/4.30 | | | | | simplifying with (65), (199) gives: % 26.56/4.30 | | | | | (200) all_94_3 = 0 % 26.56/4.30 | | | | | % 26.56/4.30 | | | | | REDUCE: (198), (200) imply: % 26.56/4.30 | | | | | (201) $false % 26.56/4.30 | | | | | % 26.56/4.30 | | | | | CLOSE: (201) is inconsistent. % 26.56/4.30 | | | | | % 26.56/4.30 | | | | End of split % 26.56/4.30 | | | | % 26.56/4.30 | | | Case 2: % 26.56/4.30 | | | | % 26.56/4.30 | | | | (202) ~ (all_85_3 = 0) & sorti1(all_18_0) = all_85_3 % 26.56/4.30 | | | | % 26.56/4.30 | | | | ALPHA: (202) implies: % 26.56/4.30 | | | | (203) ~ (all_85_3 = 0) % 26.56/4.30 | | | | (204) sorti1(all_18_0) = all_85_3 % 26.56/4.30 | | | | % 26.56/4.30 | | | | GROUND_INST: instantiating (11) with 0, all_85_3, all_18_0, simplifying % 26.56/4.30 | | | | with (29), (204) gives: % 26.56/4.30 | | | | (205) all_85_3 = 0 % 26.56/4.30 | | | | % 26.56/4.30 | | | | REDUCE: (203), (205) imply: % 26.56/4.30 | | | | (206) $false % 26.56/4.30 | | | | % 26.56/4.30 | | | | CLOSE: (206) is inconsistent. % 26.56/4.30 | | | | % 26.56/4.30 | | | End of split % 26.56/4.30 | | | % 26.56/4.30 | | Case 2: % 26.56/4.30 | | | % 26.56/4.30 | | | (207) ~ (all_47_3 = 0) & sorti1(all_18_0) = all_47_3 % 26.56/4.30 | | | % 26.56/4.30 | | | ALPHA: (207) implies: % 26.56/4.30 | | | (208) ~ (all_47_3 = 0) % 26.56/4.30 | | | (209) sorti1(all_18_0) = all_47_3 % 26.56/4.30 | | | % 26.56/4.30 | | | GROUND_INST: instantiating (11) with 0, all_47_3, all_18_0, simplifying % 26.56/4.30 | | | with (29), (209) gives: % 26.56/4.30 | | | (210) all_47_3 = 0 % 26.56/4.30 | | | % 26.56/4.30 | | | REDUCE: (208), (210) imply: % 26.56/4.30 | | | (211) $false % 26.56/4.30 | | | % 26.56/4.30 | | | CLOSE: (211) is inconsistent. % 26.56/4.30 | | | % 26.56/4.30 | | End of split % 26.56/4.30 | | % 26.56/4.30 | Case 2: % 26.56/4.30 | | % 26.56/4.30 | | (212) ~ (all_48_3 = 0) & sorti1(all_18_0) = all_48_3 % 26.56/4.30 | | % 26.56/4.30 | | ALPHA: (212) implies: % 26.56/4.30 | | (213) ~ (all_48_3 = 0) % 26.56/4.30 | | (214) sorti1(all_18_0) = all_48_3 % 26.56/4.30 | | % 26.56/4.30 | | GROUND_INST: instantiating (11) with 0, all_48_3, all_18_0, simplifying with % 26.56/4.30 | | (29), (214) gives: % 26.56/4.30 | | (215) all_48_3 = 0 % 26.56/4.30 | | % 26.56/4.30 | | REDUCE: (213), (215) imply: % 26.56/4.30 | | (216) $false % 26.56/4.30 | | % 26.56/4.30 | | CLOSE: (216) is inconsistent. % 26.56/4.30 | | % 26.56/4.30 | End of split % 26.56/4.30 | % 26.56/4.30 End of proof % 26.56/4.30 % 26.56/4.30 Sub-proof #1 shows that the following formulas are inconsistent: % 26.56/4.30 ---------------------------------------------------------------- % 26.56/4.30 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 26.56/4.30 (v1 = v0 | ~ (sorti1(v2) = v1) | ~ (sorti1(v2) = v0)) % 26.56/4.30 (2) sorti1(all_40_0) = all_213_1 % 26.56/4.30 (3) sorti1(all_40_0) = 0 % 26.56/4.30 (4) ~ (all_213_1 = 0) % 26.56/4.30 % 26.56/4.30 Begin of proof % 26.56/4.30 | % 26.56/4.30 | GROUND_INST: instantiating (1) with 0, all_213_1, all_40_0, simplifying with % 26.56/4.30 | (2), (3) gives: % 26.56/4.30 | (5) all_213_1 = 0 % 26.56/4.30 | % 26.56/4.30 | REDUCE: (4), (5) imply: % 26.56/4.30 | (6) $false % 26.56/4.30 | % 26.56/4.30 | CLOSE: (6) is inconsistent. % 26.56/4.30 | % 26.56/4.30 End of proof % 26.56/4.30 % SZS output end Proof for theBenchmark % 26.56/4.30 % 26.56/4.30 3701ms %------------------------------------------------------------------------------