%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG178+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 : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:39:39 EDT 2023 % Result : Theorem 10.89s 2.16s % Output : Proof 44.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG178+1 : TPTP v8.1.2. Released v2.7.0. % 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n009.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Mon Aug 28 04:15:50 EDT 2023 % 0.12/0.34 % CPUTime : % 0.54/0.59 ________ _____ % 0.54/0.60 ___ __ \_________(_)________________________________ % 0.54/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.54/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.54/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.54/0.60 % 0.54/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.54/0.60 (2023-06-19) % 0.54/0.60 % 0.54/0.60 (c) Philipp Rümmer, 2009-2023 % 0.54/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.54/0.60 Amanda Stjerna. % 0.54/0.60 Free software under BSD-3-Clause. % 0.54/0.60 % 0.54/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.54/0.60 % 0.54/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.54/0.61 Running up to 7 provers in parallel. % 0.54/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.54/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.54/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.54/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.54/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.54/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.54/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.14/0.96 Prover 4: Preprocessing ... % 2.14/0.96 Prover 1: Preprocessing ... % 2.37/1.00 Prover 3: Preprocessing ... % 2.37/1.00 Prover 2: Preprocessing ... % 2.37/1.00 Prover 5: Preprocessing ... % 2.37/1.00 Prover 6: Preprocessing ... % 2.37/1.00 Prover 0: Preprocessing ... % 4.27/1.30 Prover 3: Constructing countermodel ... % 4.27/1.30 Prover 5: Constructing countermodel ... % 4.27/1.30 Prover 1: Constructing countermodel ... % 4.27/1.30 Prover 6: Proving ... % 4.27/1.31 Prover 2: Proving ... % 4.63/1.33 Prover 4: Constructing countermodel ... % 4.96/1.36 Prover 0: Proving ... % 5.61/1.46 Prover 3: gave up % 5.61/1.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 5.87/1.50 Prover 1: gave up % 5.87/1.50 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 5.87/1.51 Prover 7: Preprocessing ... % 5.87/1.52 Prover 8: Preprocessing ... % 6.36/1.56 Prover 7: Constructing countermodel ... % 6.36/1.59 Prover 8: Warning: ignoring some quantifiers % 6.36/1.59 Prover 8: Constructing countermodel ... % 6.36/1.60 Prover 7: gave up % 6.36/1.60 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 6.36/1.62 Prover 9: Preprocessing ... % 7.30/1.74 Prover 9: Constructing countermodel ... % 10.89/2.16 Prover 0: proved (1542ms) % 10.89/2.16 % 10.89/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.89/2.16 % 10.89/2.16 Prover 2: stopped % 10.89/2.16 Prover 9: stopped % 10.89/2.16 Prover 6: stopped % 10.89/2.16 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.89/2.16 Prover 5: stopped % 10.89/2.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.89/2.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.89/2.17 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.89/2.17 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.89/2.18 Prover 10: Preprocessing ... % 10.89/2.18 Prover 11: Preprocessing ... % 10.89/2.18 Prover 19: Preprocessing ... % 10.89/2.19 Prover 13: Preprocessing ... % 10.89/2.19 Prover 16: Preprocessing ... % 10.89/2.21 Prover 10: Constructing countermodel ... % 11.49/2.24 Prover 10: gave up % 11.49/2.24 Prover 13: Constructing countermodel ... % 11.49/2.25 Prover 16: Constructing countermodel ... % 11.49/2.26 Prover 19: Warning: ignoring some quantifiers % 11.49/2.26 Prover 19: Constructing countermodel ... % 11.98/2.29 Prover 11: Constructing countermodel ... % 13.13/2.51 Prover 8: gave up % 15.29/2.73 Prover 19: gave up % 42.84/6.59 Prover 4: Found proof (size 297) % 42.84/6.59 Prover 4: proved (5969ms) % 42.84/6.59 Prover 13: stopped % 42.84/6.59 Prover 11: stopped % 42.84/6.61 Prover 16: stopped % 42.84/6.61 % 42.84/6.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 42.84/6.61 % 43.37/6.66 % SZS output start Proof for theBenchmark % 43.37/6.66 Assumptions after simplification: % 43.37/6.66 --------------------------------- % 43.37/6.66 % 43.37/6.66 (ax1) % 43.37/6.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op1(v0, v1) = v2) | ~ % 43.37/6.69 (sorti1(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 43.37/6.69 (sorti1(v2) = v4 & sorti1(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] % 43.37/6.69 : ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ (sorti1(v0) = 0) | ~ $i(v1) | ~ % 43.37/6.69 $i(v0) | ? [v2: $i] : (op1(v0, v1) = v2 & sorti1(v2) = 0 & $i(v2))) % 43.37/6.69 % 43.37/6.69 (ax2) % 43.37/6.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op2(v0, v1) = v2) | ~ % 43.37/6.69 (sorti2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 43.37/6.69 (sorti2(v2) = v4 & sorti2(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] % 43.37/6.69 : ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ (sorti2(v0) = 0) | ~ $i(v1) | ~ % 43.37/6.69 $i(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & sorti2(v2) = 0 & $i(v2))) % 43.37/6.69 % 43.37/6.69 (ax3) % 43.37/6.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op1(v0, v1) = v2) | ~ % 43.37/6.70 (sorti1(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] : % 43.37/6.70 (op1(v0, v2) = v4 & sorti1(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))) & % 43.37/6.70 ! [v0: $i] : ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ (sorti1(v0) = 0) | ~ % 43.37/6.70 $i(v1) | ~ $i(v0) | ? [v2: $i] : (op1(v0, v2) = v1 & op1(v0, v1) = v2 & % 43.37/6.70 $i(v2))) % 43.37/6.70 % 43.37/6.70 (ax4) % 43.37/6.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v1) & % 43.37/6.70 op2(v0, v2) = v3 & op2(v0, v1) = v2 & sorti2(v1) = 0 & sorti2(v0) = 0 & % 43.37/6.70 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 43.37/6.70 % 43.37/6.70 (co1) % 43.64/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~ % 43.64/6.73 (j(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: % 43.64/6.73 $i] : ? [v7: $i] : (( ~ (v4 = 0) & sorti2(v0) = v4) | (j(v5) = v6 & % 43.64/6.73 op2(v0, v2) = v5 & sorti2(v2) = v4 & op1(v1, v3) = v7 & $i(v7) & $i(v6) % 43.64/6.73 & $i(v5) & ( ~ (v4 = 0) | v7 = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 43.64/6.73 [v2: $i] : ! [v3: $i] : ( ~ (j(v0) = v1) | ~ (op2(v0, v2) = v3) | ~ $i(v2) % 43.64/6.73 | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (( ~ % 43.64/6.73 (v4 = 0) & sorti2(v0) = v4) | (j(v3) = v5 & j(v2) = v6 & sorti2(v2) = v4 % 43.64/6.73 & op1(v1, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = % 43.64/6.73 v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 43.64/6.73 (h(v2) = v3) | ~ (h(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? % 43.64/6.73 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (( ~ (v4 = 0) & sorti1(v0) = v4) | % 43.64/6.73 (h(v5) = v6 & op2(v1, v3) = v7 & op1(v0, v2) = v5 & sorti1(v2) = v4 & % 43.64/6.73 $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v6)))) & ! [v0: $i] : ! % 43.64/6.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (h(v0) = v1) | ~ (op1(v0, v2) = % 43.64/6.73 v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : % 43.64/6.73 ? [v7: $i] : (( ~ (v4 = 0) & sorti1(v0) = v4) | (h(v3) = v5 & h(v2) = v6 & % 43.64/6.73 op2(v1, v6) = v7 & sorti1(v2) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 % 43.64/6.73 = 0) | v7 = v5)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 43.64/6.73 (j(v0) = v1) | ~ (sorti2(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: any] : % 43.64/6.73 ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & j(v3) = v4 & j(v2) = v5 % 43.64/6.73 & op2(v0, v2) = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3)) | ( ~ % 43.64/6.73 (v3 = 0) & sorti2(v0) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 43.64/6.73 : ( ~ (h(v0) = v1) | ~ (sorti1(v2) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: % 43.64/6.73 any] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ((v6 = v4 & h(v3) = v4 & % 43.64/6.73 h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, v2) = v3 & $i(v5) & $i(v4) & % 43.64/6.73 $i(v3)) | ( ~ (v3 = 0) & sorti1(v0) = v3))) & ! [v0: $i] : ! [v1: $i] % 43.64/6.73 : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (h(v1) = v3 & % 43.64/6.73 sorti2(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v0))) & ! [v0: $i] : ! % 43.64/6.73 [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : % 43.64/6.73 (sorti2(v0) = v2 & sorti1(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 43.64/6.73 : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 43.64/6.73 (j(v1) = v3 & sorti1(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = v0))) & ! [v0: % 43.64/6.73 $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: % 43.64/6.73 any] : (sorti2(v1) = v3 & sorti1(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! % 43.64/6.73 [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = v1 & % 43.64/6.73 h(v1) = v0 & $i(v1))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | % 43.64/6.73 ? [v1: $i] : (j(v0) = v1 & sorti1(v1) = 0 & $i(v1))) & ! [v0: $i] : ( ~ % 43.64/6.73 (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = v1 & $i(v1) & ! [v2: % 43.64/6.73 $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~ $i(v2) | ? [v4: any] : ? % 43.64/6.73 [v5: $i] : ? [v6: $i] : ? [v7: $i] : (j(v5) = v6 & op2(v0, v2) = v5 & % 43.64/6.73 sorti2(v2) = v4 & op1(v1, v3) = v7 & $i(v7) & $i(v6) & $i(v5) & ( ~ % 43.64/6.73 (v4 = 0) | v7 = v6))) & ! [v2: $i] : ! [v3: $i] : ( ~ (op2(v0, v2) % 43.64/6.73 = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: % 43.64/6.73 $i] : (j(v3) = v5 & j(v2) = v6 & sorti2(v2) = v4 & op1(v1, v6) = v7 & % 43.64/6.73 $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v5))) & ! [v2: $i] : ( % 43.64/6.73 ~ (sorti2(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] % 43.64/6.73 : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, v5) = v4 & % 43.64/6.73 $i(v5) & $i(v4) & $i(v3))))) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ % 43.64/6.73 $i(v0) | ? [v1: $i] : (j(v1) = v0 & h(v0) = v1 & $i(v1))) & ! [v0: $i] : ( % 43.64/6.73 ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) = v1 & sorti2(v1) = 0 % 43.64/6.73 & $i(v1))) & ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 43.64/6.73 : (h(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~ % 43.64/6.73 $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (h(v5) % 43.64/6.73 = v6 & op2(v1, v3) = v7 & op1(v0, v2) = v5 & sorti1(v2) = v4 & $i(v7) % 43.64/6.73 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v6))) & ! [v2: $i] : ! [v3: % 43.64/6.73 $i] : ( ~ (op1(v0, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: $i] : % 43.64/6.73 ? [v6: $i] : ? [v7: $i] : (h(v3) = v5 & h(v2) = v6 & op2(v1, v6) = v7 & % 43.64/6.73 sorti1(v2) = v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v5))) % 43.64/6.73 & ! [v2: $i] : ( ~ (sorti1(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: % 43.64/6.73 $i] : ? [v5: $i] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & % 43.64/6.73 op1(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v3))))) % 43.64/6.73 % 43.64/6.73 (function-axioms) % 43.64/6.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3, % 43.64/6.73 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 43.64/6.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) = % 43.64/6.73 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = % 43.64/6.73 v1) | ~ (j(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 43.64/6.73 v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0)) & ! [v0: MultipleValueBool] : ! % 43.64/6.73 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (sorti2(v2) = v1) | ~ % 43.64/6.73 (sorti2(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] % 43.64/6.73 : ! [v2: $i] : (v1 = v0 | ~ (sorti1(v2) = v1) | ~ (sorti1(v2) = v0)) % 43.64/6.73 % 43.64/6.73 Those formulas are unsatisfiable: % 43.64/6.73 --------------------------------- % 43.64/6.73 % 43.64/6.73 Begin of proof % 43.64/6.74 | % 43.64/6.74 | ALPHA: (ax1) implies: % 43.64/6.74 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op1(v0, v1) = v2) | ~ % 43.64/6.74 | (sorti1(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 43.64/6.74 | any] : (sorti1(v2) = v4 & sorti1(v1) = v3 & ( ~ (v3 = 0) | v4 = % 43.64/6.74 | 0))) % 43.64/6.74 | % 43.64/6.74 | ALPHA: (ax2) implies: % 43.64/6.74 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ (sorti2(v0) = 0) % 43.64/6.74 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & % 43.64/6.74 | sorti2(v2) = 0 & $i(v2))) % 43.64/6.74 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op2(v0, v1) = v2) | ~ % 43.64/6.74 | (sorti2(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: % 43.64/6.74 | any] : (sorti2(v2) = v4 & sorti2(v1) = v3 & ( ~ (v3 = 0) | v4 = % 43.64/6.74 | 0))) % 43.64/6.74 | % 43.64/6.74 | ALPHA: (ax3) implies: % 43.64/6.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op1(v0, v1) = v2) | ~ % 43.64/6.74 | (sorti1(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] % 43.64/6.74 | : (op1(v0, v2) = v4 & sorti1(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = % 43.64/6.74 | v1))) % 43.64/6.74 | % 43.64/6.74 | ALPHA: (co1) implies: % 43.64/6.74 | (5) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (h(v0) = % 43.64/6.74 | v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (h(v2) = v3) | ~ % 43.64/6.74 | $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 43.64/6.74 | (h(v5) = v6 & op2(v1, v3) = v7 & op1(v0, v2) = v5 & sorti1(v2) = % 43.64/6.74 | v4 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v6))) & ! % 43.64/6.74 | [v2: $i] : ! [v3: $i] : ( ~ (op1(v0, v2) = v3) | ~ $i(v2) | ? % 43.64/6.74 | [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (h(v3) = v5 % 43.64/6.74 | & h(v2) = v6 & op2(v1, v6) = v7 & sorti1(v2) = v4 & $i(v7) & % 43.64/6.74 | $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v5))) & ! [v2: $i] : ( ~ % 43.64/6.74 | (sorti1(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? % 43.64/6.74 | [v5: $i] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5) = v4 & op1(v0, % 43.64/6.74 | v2) = v3 & $i(v5) & $i(v4) & $i(v3))))) % 43.64/6.75 | (6) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = % 43.64/6.75 | v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (j(v2) = v3) | ~ % 43.64/6.75 | $i(v2) | ? [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : % 43.64/6.75 | (j(v5) = v6 & op2(v0, v2) = v5 & sorti2(v2) = v4 & op1(v1, v3) = % 43.64/6.75 | v7 & $i(v7) & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v6))) & ! % 43.64/6.75 | [v2: $i] : ! [v3: $i] : ( ~ (op2(v0, v2) = v3) | ~ $i(v2) | ? % 43.64/6.75 | [v4: any] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (j(v3) = v5 % 43.64/6.75 | & j(v2) = v6 & sorti2(v2) = v4 & op1(v1, v6) = v7 & $i(v7) & % 43.64/6.75 | $i(v6) & $i(v5) & ( ~ (v4 = 0) | v7 = v5))) & ! [v2: $i] : ( ~ % 43.64/6.75 | (sorti2(v2) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ? % 43.64/6.75 | [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2) = v3 & op1(v1, % 43.64/6.75 | v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) % 43.64/6.75 | (7) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = % 43.64/6.75 | v1 & sorti1(v1) = 0 & $i(v1))) % 43.64/6.75 | (8) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (j(v0) = % 43.64/6.75 | v1 & h(v1) = v0 & $i(v1))) % 43.64/6.75 | % 43.64/6.75 | ALPHA: (function-axioms) implies: % 43.64/6.75 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 43.64/6.75 | (v1 = v0 | ~ (sorti1(v2) = v1) | ~ (sorti1(v2) = v0)) % 43.64/6.75 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 43.64/6.75 | : (v1 = v0 | ~ (sorti2(v2) = v1) | ~ (sorti2(v2) = v0)) % 43.64/6.75 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) | % 43.64/6.75 | ~ (h(v2) = v0)) % 43.64/6.75 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) | % 43.64/6.75 | ~ (j(v2) = v0)) % 43.64/6.75 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.64/6.75 | (op1(v3, v2) = v1) | ~ (op1(v3, v2) = v0)) % 43.64/6.75 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 43.64/6.75 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0)) % 43.64/6.75 | % 43.64/6.75 | DELTA: instantiating (ax4) with fresh symbols all_7_0, all_7_1, all_7_2, % 43.64/6.75 | all_7_3 gives: % 43.64/6.75 | (15) ~ (all_7_0 = all_7_2) & op2(all_7_3, all_7_1) = all_7_0 & % 43.64/6.75 | op2(all_7_3, all_7_2) = all_7_1 & sorti2(all_7_2) = 0 & % 43.64/6.75 | sorti2(all_7_3) = 0 & $i(all_7_0) & $i(all_7_1) & $i(all_7_2) & % 43.64/6.75 | $i(all_7_3) % 43.64/6.75 | % 43.64/6.75 | ALPHA: (15) implies: % 43.64/6.75 | (16) ~ (all_7_0 = all_7_2) % 43.64/6.75 | (17) $i(all_7_3) % 43.64/6.75 | (18) $i(all_7_2) % 43.64/6.75 | (19) $i(all_7_1) % 43.64/6.75 | (20) $i(all_7_0) % 43.64/6.75 | (21) sorti2(all_7_3) = 0 % 43.64/6.75 | (22) sorti2(all_7_2) = 0 % 43.64/6.75 | (23) op2(all_7_3, all_7_2) = all_7_1 % 43.64/6.75 | (24) op2(all_7_3, all_7_1) = all_7_0 % 43.64/6.75 | % 43.86/6.76 | GROUND_INST: instantiating (2) with all_7_3, all_7_3, simplifying with (17), % 43.86/6.76 | (21) gives: % 43.86/6.76 | (25) ? [v0: $i] : (op2(all_7_3, all_7_3) = v0 & sorti2(v0) = 0 & $i(v0)) % 43.86/6.76 | % 43.86/6.76 | GROUND_INST: instantiating (8) with all_7_3, simplifying with (17), (21) % 43.86/6.76 | gives: % 43.86/6.76 | (26) ? [v0: $i] : (j(all_7_3) = v0 & h(v0) = all_7_3 & $i(v0)) % 43.86/6.76 | % 43.86/6.76 | GROUND_INST: instantiating (7) with all_7_3, simplifying with (17), (21) % 43.86/6.76 | gives: % 43.86/6.76 | (27) ? [v0: $i] : (j(all_7_3) = v0 & sorti1(v0) = 0 & $i(v0)) % 43.86/6.76 | % 43.86/6.76 | GROUND_INST: instantiating (6) with all_7_3, simplifying with (17), (21) % 43.86/6.76 | gives: % 43.87/6.76 | (28) ? [v0: $i] : (j(all_7_3) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 43.87/6.76 | ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: % 43.87/6.76 | $i] : ? [v6: $i] : (j(v4) = v5 & op2(all_7_3, v1) = v4 & % 43.87/6.76 | sorti2(v1) = v3 & op1(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 43.87/6.76 | ( ~ (v3 = 0) | v6 = v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 43.87/6.76 | (op2(all_7_3, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : % 43.87/6.76 | ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & j(v1) = v5 & sorti2(v1) % 43.87/6.76 | = v3 & op1(v0, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = % 43.87/6.76 | 0) | v6 = v4))) & ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ % 43.87/6.76 | $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 & % 43.87/6.76 | j(v1) = v4 & op2(all_7_3, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & % 43.87/6.76 | $i(v3) & $i(v2)))) % 43.87/6.76 | % 43.87/6.76 | GROUND_INST: instantiating (2) with all_7_2, all_7_2, simplifying with (18), % 43.87/6.76 | (22) gives: % 43.87/6.76 | (29) ? [v0: $i] : (op2(all_7_2, all_7_2) = v0 & sorti2(v0) = 0 & $i(v0)) % 43.87/6.76 | % 43.87/6.76 | GROUND_INST: instantiating (2) with all_7_3, all_7_2, simplifying with (17), % 43.87/6.76 | (18), (21), (22) gives: % 43.87/6.76 | (30) ? [v0: $i] : (op2(all_7_3, all_7_2) = v0 & sorti2(v0) = 0 & $i(v0)) % 43.87/6.76 | % 43.87/6.76 | GROUND_INST: instantiating (2) with all_7_2, all_7_3, simplifying with (17), % 43.87/6.76 | (18), (21), (22) gives: % 43.87/6.76 | (31) ? [v0: $i] : (op2(all_7_2, all_7_3) = v0 & sorti2(v0) = 0 & $i(v0)) % 43.87/6.76 | % 43.87/6.76 | GROUND_INST: instantiating (8) with all_7_2, simplifying with (18), (22) % 43.87/6.76 | gives: % 43.87/6.76 | (32) ? [v0: $i] : (j(all_7_2) = v0 & h(v0) = all_7_2 & $i(v0)) % 43.87/6.76 | % 43.87/6.76 | GROUND_INST: instantiating (7) with all_7_2, simplifying with (18), (22) % 43.87/6.76 | gives: % 43.87/6.76 | (33) ? [v0: $i] : (j(all_7_2) = v0 & sorti1(v0) = 0 & $i(v0)) % 43.87/6.76 | % 43.87/6.76 | GROUND_INST: instantiating (6) with all_7_2, simplifying with (18), (22) % 43.87/6.76 | gives: % 43.87/6.77 | (34) ? [v0: $i] : (j(all_7_2) = v0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 43.87/6.77 | ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : ? [v5: % 43.87/6.77 | $i] : ? [v6: $i] : (j(v4) = v5 & op2(all_7_2, v1) = v4 & % 43.87/6.77 | sorti2(v1) = v3 & op1(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 43.87/6.77 | ( ~ (v3 = 0) | v6 = v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 43.87/6.77 | (op2(all_7_2, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : % 43.87/6.77 | ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & j(v1) = v5 & sorti2(v1) % 43.87/6.77 | = v3 & op1(v0, v5) = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = % 43.87/6.77 | 0) | v6 = v4))) & ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ % 43.87/6.77 | $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 & % 43.87/6.77 | j(v1) = v4 & op2(all_7_2, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & % 43.87/6.77 | $i(v3) & $i(v2)))) % 43.87/6.77 | % 43.87/6.77 | GROUND_INST: instantiating (3) with all_7_3, all_7_2, all_7_1, simplifying % 43.87/6.77 | with (17), (18), (21), (23) gives: % 43.87/6.77 | (35) ? [v0: any] : ? [v1: any] : (sorti2(all_7_1) = v1 & sorti2(all_7_2) % 43.87/6.77 | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 43.87/6.77 | % 43.87/6.77 | GROUND_INST: instantiating (3) with all_7_3, all_7_1, all_7_0, simplifying % 43.87/6.77 | with (17), (19), (21), (24) gives: % 43.87/6.77 | (36) ? [v0: any] : ? [v1: any] : (sorti2(all_7_0) = v1 & sorti2(all_7_1) % 43.87/6.77 | = v0 & ( ~ (v0 = 0) | v1 = 0)) % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (33) with fresh symbol all_14_0 gives: % 43.87/6.77 | (37) j(all_7_2) = all_14_0 & sorti1(all_14_0) = 0 & $i(all_14_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (37) implies: % 43.87/6.77 | (38) sorti1(all_14_0) = 0 % 43.87/6.77 | (39) j(all_7_2) = all_14_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (32) with fresh symbol all_16_0 gives: % 43.87/6.77 | (40) j(all_7_2) = all_16_0 & h(all_16_0) = all_7_2 & $i(all_16_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (40) implies: % 43.87/6.77 | (41) $i(all_16_0) % 43.87/6.77 | (42) h(all_16_0) = all_7_2 % 43.87/6.77 | (43) j(all_7_2) = all_16_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (30) with fresh symbol all_18_0 gives: % 43.87/6.77 | (44) op2(all_7_3, all_7_2) = all_18_0 & sorti2(all_18_0) = 0 & $i(all_18_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (44) implies: % 43.87/6.77 | (45) $i(all_18_0) % 43.87/6.77 | (46) op2(all_7_3, all_7_2) = all_18_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (31) with fresh symbol all_20_0 gives: % 43.87/6.77 | (47) op2(all_7_2, all_7_3) = all_20_0 & sorti2(all_20_0) = 0 & $i(all_20_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (47) implies: % 43.87/6.77 | (48) sorti2(all_20_0) = 0 % 43.87/6.77 | (49) op2(all_7_2, all_7_3) = all_20_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (27) with fresh symbol all_22_0 gives: % 43.87/6.77 | (50) j(all_7_3) = all_22_0 & sorti1(all_22_0) = 0 & $i(all_22_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (50) implies: % 43.87/6.77 | (51) sorti1(all_22_0) = 0 % 43.87/6.77 | (52) j(all_7_3) = all_22_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (26) with fresh symbol all_24_0 gives: % 43.87/6.77 | (53) j(all_7_3) = all_24_0 & h(all_24_0) = all_7_3 & $i(all_24_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (53) implies: % 43.87/6.77 | (54) $i(all_24_0) % 43.87/6.77 | (55) j(all_7_3) = all_24_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (25) with fresh symbol all_26_0 gives: % 43.87/6.77 | (56) op2(all_7_3, all_7_3) = all_26_0 & sorti2(all_26_0) = 0 & $i(all_26_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (56) implies: % 43.87/6.77 | (57) sorti2(all_26_0) = 0 % 43.87/6.77 | (58) op2(all_7_3, all_7_3) = all_26_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (29) with fresh symbol all_28_0 gives: % 43.87/6.77 | (59) op2(all_7_2, all_7_2) = all_28_0 & sorti2(all_28_0) = 0 & $i(all_28_0) % 43.87/6.77 | % 43.87/6.77 | ALPHA: (59) implies: % 43.87/6.77 | (60) sorti2(all_28_0) = 0 % 43.87/6.77 | (61) op2(all_7_2, all_7_2) = all_28_0 % 43.87/6.77 | % 43.87/6.77 | DELTA: instantiating (36) with fresh symbols all_30_0, all_30_1 gives: % 43.87/6.78 | (62) sorti2(all_7_0) = all_30_0 & sorti2(all_7_1) = all_30_1 & ( ~ % 43.87/6.78 | (all_30_1 = 0) | all_30_0 = 0) % 43.87/6.78 | % 43.87/6.78 | ALPHA: (62) implies: % 43.87/6.78 | (63) sorti2(all_7_1) = all_30_1 % 43.87/6.78 | (64) sorti2(all_7_0) = all_30_0 % 43.87/6.78 | (65) ~ (all_30_1 = 0) | all_30_0 = 0 % 43.87/6.78 | % 43.87/6.78 | DELTA: instantiating (35) with fresh symbols all_32_0, all_32_1 gives: % 43.87/6.78 | (66) sorti2(all_7_1) = all_32_0 & sorti2(all_7_2) = all_32_1 & ( ~ % 43.87/6.78 | (all_32_1 = 0) | all_32_0 = 0) % 43.87/6.78 | % 43.87/6.78 | ALPHA: (66) implies: % 43.87/6.78 | (67) sorti2(all_7_2) = all_32_1 % 43.87/6.78 | (68) sorti2(all_7_1) = all_32_0 % 43.87/6.78 | (69) ~ (all_32_1 = 0) | all_32_0 = 0 % 43.87/6.78 | % 43.87/6.78 | DELTA: instantiating (34) with fresh symbol all_34_0 gives: % 43.87/6.78 | (70) j(all_7_2) = all_34_0 & $i(all_34_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 43.87/6.78 | (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 43.87/6.78 | : ? [v5: $i] : (j(v3) = v4 & op2(all_7_2, v0) = v3 & sorti2(v0) = % 43.87/6.78 | v2 & op1(all_34_0, v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 43.87/6.78 | 0) | v5 = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 43.87/6.78 | (op2(all_7_2, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 43.87/6.78 | ? [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) = v4 & sorti2(v0) = % 43.87/6.78 | v2 & op1(all_34_0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 43.87/6.78 | 0) | v5 = v3))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ % 43.87/6.78 | $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & % 43.87/6.78 | j(v0) = v3 & op2(all_7_2, v0) = v1 & op1(all_34_0, v3) = v2 & % 43.87/6.78 | $i(v3) & $i(v2) & $i(v1))) % 43.87/6.78 | % 43.87/6.78 | ALPHA: (70) implies: % 43.87/6.78 | (71) j(all_7_2) = all_34_0 % 43.87/6.78 | (72) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 43.87/6.78 | $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_7_2, v0) = % 43.87/6.78 | v1 & op1(all_34_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1))) % 43.87/6.78 | % 43.87/6.78 | GROUND_INST: instantiating (72) with all_7_3, simplifying with (17), (21) % 43.87/6.78 | gives: % 43.87/6.78 | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_3) = % 43.87/6.78 | v2 & op2(all_7_2, all_7_3) = v0 & op1(all_34_0, v2) = v1 & $i(v2) & % 43.87/6.78 | $i(v1) & $i(v0)) % 43.87/6.78 | % 43.87/6.78 | GROUND_INST: instantiating (72) with all_7_2, simplifying with (18), (22) % 43.87/6.78 | gives: % 43.87/6.78 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_2) = % 43.87/6.78 | v2 & op2(all_7_2, all_7_2) = v0 & op1(all_34_0, v2) = v1 & $i(v2) & % 43.87/6.78 | $i(v1) & $i(v0)) % 43.87/6.78 | % 43.87/6.78 | DELTA: instantiating (74) with fresh symbols all_37_0, all_37_1, all_37_2 % 43.87/6.78 | gives: % 43.87/6.78 | (75) j(all_37_2) = all_37_1 & j(all_7_2) = all_37_0 & op2(all_7_2, all_7_2) % 43.87/6.78 | = all_37_2 & op1(all_34_0, all_37_0) = all_37_1 & $i(all_37_0) & % 43.87/6.78 | $i(all_37_1) & $i(all_37_2) % 43.87/6.78 | % 43.87/6.78 | ALPHA: (75) implies: % 43.87/6.78 | (76) $i(all_37_2) % 43.87/6.78 | (77) op1(all_34_0, all_37_0) = all_37_1 % 43.87/6.78 | (78) op2(all_7_2, all_7_2) = all_37_2 % 43.87/6.78 | (79) j(all_7_2) = all_37_0 % 43.87/6.78 | % 43.87/6.78 | DELTA: instantiating (73) with fresh symbols all_39_0, all_39_1, all_39_2 % 43.87/6.78 | gives: % 43.87/6.78 | (80) j(all_39_2) = all_39_1 & j(all_7_3) = all_39_0 & op2(all_7_2, all_7_3) % 43.87/6.78 | = all_39_2 & op1(all_34_0, all_39_0) = all_39_1 & $i(all_39_0) & % 43.87/6.78 | $i(all_39_1) & $i(all_39_2) % 43.87/6.78 | % 43.87/6.78 | ALPHA: (80) implies: % 43.87/6.78 | (81) $i(all_39_2) % 43.87/6.78 | (82) op2(all_7_2, all_7_3) = all_39_2 % 43.87/6.78 | (83) j(all_7_3) = all_39_0 % 43.87/6.78 | % 43.87/6.78 | DELTA: instantiating (28) with fresh symbol all_41_0 gives: % 43.87/6.79 | (84) j(all_7_3) = all_41_0 & $i(all_41_0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 43.87/6.79 | (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] % 43.87/6.79 | : ? [v5: $i] : (j(v3) = v4 & op2(all_7_3, v0) = v3 & sorti2(v0) = % 43.87/6.79 | v2 & op1(all_41_0, v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 43.87/6.79 | 0) | v5 = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 43.87/6.79 | (op2(all_7_3, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : % 43.87/6.79 | ? [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) = v4 & sorti2(v0) = % 43.87/6.79 | v2 & op1(all_41_0, v4) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 43.87/6.79 | 0) | v5 = v3))) & ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ % 43.87/6.79 | $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & % 43.87/6.79 | j(v0) = v3 & op2(all_7_3, v0) = v1 & op1(all_41_0, v3) = v2 & % 43.87/6.79 | $i(v3) & $i(v2) & $i(v1))) % 43.87/6.79 | % 43.87/6.79 | ALPHA: (84) implies: % 43.87/6.79 | (85) j(all_7_3) = all_41_0 % 43.87/6.79 | (86) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 43.87/6.79 | $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_7_3, v0) = % 43.87/6.79 | v1 & op1(all_41_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1))) % 43.87/6.79 | (87) ! [v0: $i] : ! [v1: $i] : ( ~ (op2(all_7_3, v0) = v1) | ~ $i(v0) | % 43.87/6.79 | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v1) = v3 % 43.87/6.79 | & j(v0) = v4 & sorti2(v0) = v2 & op1(all_41_0, v4) = v5 & $i(v5) & % 43.87/6.79 | $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) % 43.87/6.79 | % 43.87/6.79 | GROUND_INST: instantiating (86) with all_7_3, simplifying with (17), (21) % 43.87/6.79 | gives: % 43.87/6.79 | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_3) = % 43.87/6.79 | v2 & op2(all_7_3, all_7_3) = v0 & op1(all_41_0, v2) = v1 & $i(v2) & % 43.87/6.79 | $i(v1) & $i(v0)) % 43.87/6.79 | % 43.87/6.79 | GROUND_INST: instantiating (86) with all_7_2, simplifying with (18), (22) % 43.87/6.79 | gives: % 43.87/6.79 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_2) = % 43.87/6.79 | v2 & op2(all_7_3, all_7_2) = v0 & op1(all_41_0, v2) = v1 & $i(v2) & % 43.87/6.79 | $i(v1) & $i(v0)) % 43.87/6.79 | % 43.87/6.79 | GROUND_INST: instantiating (87) with all_7_2, all_7_1, simplifying with (18), % 43.87/6.79 | (23) gives: % 43.87/6.79 | (90) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(all_7_1) = % 43.87/6.79 | v1 & j(all_7_2) = v2 & sorti2(all_7_2) = v0 & op1(all_41_0, v2) = v3 % 43.87/6.79 | & $i(v3) & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = v1)) % 43.87/6.79 | % 43.87/6.79 | GROUND_INST: instantiating (87) with all_7_1, all_7_0, simplifying with (19), % 43.87/6.79 | (24) gives: % 43.87/6.79 | (91) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(all_7_0) = % 43.87/6.79 | v1 & j(all_7_1) = v2 & sorti2(all_7_1) = v0 & op1(all_41_0, v2) = v3 % 43.87/6.79 | & $i(v3) & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v3 = v1)) % 43.87/6.79 | % 43.87/6.79 | DELTA: instantiating (89) with fresh symbols all_44_0, all_44_1, all_44_2 % 43.87/6.79 | gives: % 43.87/6.79 | (92) j(all_44_2) = all_44_1 & j(all_7_2) = all_44_0 & op2(all_7_3, all_7_2) % 43.87/6.79 | = all_44_2 & op1(all_41_0, all_44_0) = all_44_1 & $i(all_44_0) & % 43.87/6.79 | $i(all_44_1) & $i(all_44_2) % 43.87/6.79 | % 43.87/6.79 | ALPHA: (92) implies: % 43.87/6.79 | (93) op2(all_7_3, all_7_2) = all_44_2 % 43.87/6.79 | (94) j(all_7_2) = all_44_0 % 43.87/6.79 | (95) j(all_44_2) = all_44_1 % 43.87/6.79 | % 43.87/6.79 | DELTA: instantiating (88) with fresh symbols all_46_0, all_46_1, all_46_2 % 43.87/6.79 | gives: % 43.87/6.79 | (96) j(all_46_2) = all_46_1 & j(all_7_3) = all_46_0 & op2(all_7_3, all_7_3) % 43.87/6.79 | = all_46_2 & op1(all_41_0, all_46_0) = all_46_1 & $i(all_46_0) & % 43.87/6.79 | $i(all_46_1) & $i(all_46_2) % 43.87/6.79 | % 43.87/6.79 | ALPHA: (96) implies: % 43.87/6.79 | (97) $i(all_46_2) % 43.87/6.79 | (98) op2(all_7_3, all_7_3) = all_46_2 % 43.87/6.79 | (99) j(all_7_3) = all_46_0 % 43.87/6.79 | % 43.87/6.79 | DELTA: instantiating (91) with fresh symbols all_48_0, all_48_1, all_48_2, % 43.87/6.79 | all_48_3 gives: % 43.87/6.79 | (100) j(all_7_0) = all_48_2 & j(all_7_1) = all_48_1 & sorti2(all_7_1) = % 43.87/6.79 | all_48_3 & op1(all_41_0, all_48_1) = all_48_0 & $i(all_48_0) & % 43.87/6.79 | $i(all_48_1) & $i(all_48_2) & ( ~ (all_48_3 = 0) | all_48_0 = % 43.87/6.79 | all_48_2) % 43.87/6.79 | % 43.87/6.79 | ALPHA: (100) implies: % 43.87/6.79 | (101) op1(all_41_0, all_48_1) = all_48_0 % 43.87/6.79 | (102) sorti2(all_7_1) = all_48_3 % 43.87/6.79 | (103) j(all_7_1) = all_48_1 % 43.87/6.79 | (104) j(all_7_0) = all_48_2 % 43.87/6.79 | (105) ~ (all_48_3 = 0) | all_48_0 = all_48_2 % 43.87/6.79 | % 43.87/6.79 | DELTA: instantiating (90) with fresh symbols all_50_0, all_50_1, all_50_2, % 43.87/6.79 | all_50_3 gives: % 43.87/6.79 | (106) j(all_7_1) = all_50_2 & j(all_7_2) = all_50_1 & sorti2(all_7_2) = % 43.87/6.79 | all_50_3 & op1(all_41_0, all_50_1) = all_50_0 & $i(all_50_0) & % 43.87/6.79 | $i(all_50_1) & $i(all_50_2) & ( ~ (all_50_3 = 0) | all_50_0 = % 43.87/6.79 | all_50_2) % 43.87/6.79 | % 43.87/6.79 | ALPHA: (106) implies: % 43.87/6.79 | (107) op1(all_41_0, all_50_1) = all_50_0 % 43.87/6.79 | (108) sorti2(all_7_2) = all_50_3 % 43.87/6.79 | (109) j(all_7_2) = all_50_1 % 43.87/6.79 | (110) j(all_7_1) = all_50_2 % 43.87/6.79 | (111) ~ (all_50_3 = 0) | all_50_0 = all_50_2 % 43.87/6.79 | % 43.87/6.80 | GROUND_INST: instantiating (10) with 0, all_50_3, all_7_2, simplifying with % 43.87/6.80 | (22), (108) gives: % 43.87/6.80 | (112) all_50_3 = 0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (10) with all_32_1, all_50_3, all_7_2, simplifying % 43.87/6.80 | with (67), (108) gives: % 43.87/6.80 | (113) all_50_3 = all_32_1 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (10) with all_32_0, all_48_3, all_7_1, simplifying % 43.87/6.80 | with (68), (102) gives: % 43.87/6.80 | (114) all_48_3 = all_32_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (10) with all_30_1, all_48_3, all_7_1, simplifying % 43.87/6.80 | with (63), (102) gives: % 43.87/6.80 | (115) all_48_3 = all_30_1 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (14) with all_26_0, all_46_2, all_7_3, all_7_3, % 43.87/6.80 | simplifying with (58), (98) gives: % 43.87/6.80 | (116) all_46_2 = all_26_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (14) with all_7_1, all_44_2, all_7_2, all_7_3, % 43.87/6.80 | simplifying with (23), (93) gives: % 43.87/6.80 | (117) all_44_2 = all_7_1 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (14) with all_18_0, all_44_2, all_7_2, all_7_3, % 43.87/6.80 | simplifying with (46), (93) gives: % 43.87/6.80 | (118) all_44_2 = all_18_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (14) with all_20_0, all_39_2, all_7_3, all_7_2, % 43.87/6.80 | simplifying with (49), (82) gives: % 43.87/6.80 | (119) all_39_2 = all_20_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (14) with all_28_0, all_37_2, all_7_2, all_7_2, % 43.87/6.80 | simplifying with (61), (78) gives: % 43.87/6.80 | (120) all_37_2 = all_28_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_41_0, all_46_0, all_7_3, simplifying % 43.87/6.80 | with (85), (99) gives: % 43.87/6.80 | (121) all_46_0 = all_41_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_39_0, all_46_0, all_7_3, simplifying % 43.87/6.80 | with (83), (99) gives: % 43.87/6.80 | (122) all_46_0 = all_39_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_24_0, all_46_0, all_7_3, simplifying % 43.87/6.80 | with (55), (99) gives: % 43.87/6.80 | (123) all_46_0 = all_24_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_22_0, all_46_0, all_7_3, simplifying % 43.87/6.80 | with (52), (99) gives: % 43.87/6.80 | (124) all_46_0 = all_22_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_34_0, all_37_0, all_7_2, simplifying % 43.87/6.80 | with (71), (79) gives: % 43.87/6.80 | (125) all_37_0 = all_34_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_16_0, all_37_0, all_7_2, simplifying % 43.87/6.80 | with (43), (79) gives: % 43.87/6.80 | (126) all_37_0 = all_16_0 % 43.87/6.80 | % 43.87/6.80 | GROUND_INST: instantiating (12) with all_37_0, all_44_0, all_7_2, simplifying % 44.08/6.80 | with (79), (94) gives: % 44.08/6.80 | (127) all_44_0 = all_37_0 % 44.08/6.80 | % 44.08/6.80 | GROUND_INST: instantiating (12) with all_44_0, all_50_1, all_7_2, simplifying % 44.08/6.80 | with (94), (109) gives: % 44.08/6.80 | (128) all_50_1 = all_44_0 % 44.08/6.80 | % 44.08/6.80 | GROUND_INST: instantiating (12) with all_14_0, all_50_1, all_7_2, simplifying % 44.08/6.80 | with (39), (109) gives: % 44.08/6.80 | (129) all_50_1 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | GROUND_INST: instantiating (12) with all_48_1, all_50_2, all_7_1, simplifying % 44.08/6.80 | with (103), (110) gives: % 44.08/6.80 | (130) all_50_2 = all_48_1 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (128), (129) imply: % 44.08/6.80 | (131) all_44_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | SIMP: (131) implies: % 44.08/6.80 | (132) all_44_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (112), (113) imply: % 44.08/6.80 | (133) all_32_1 = 0 % 44.08/6.80 | % 44.08/6.80 | SIMP: (133) implies: % 44.08/6.80 | (134) all_32_1 = 0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (114), (115) imply: % 44.08/6.80 | (135) all_32_0 = all_30_1 % 44.08/6.80 | % 44.08/6.80 | SIMP: (135) implies: % 44.08/6.80 | (136) all_32_0 = all_30_1 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (121), (122) imply: % 44.08/6.80 | (137) all_41_0 = all_39_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (121), (124) imply: % 44.08/6.80 | (138) all_41_0 = all_22_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (121), (123) imply: % 44.08/6.80 | (139) all_41_0 = all_24_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (127), (132) imply: % 44.08/6.80 | (140) all_37_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | SIMP: (140) implies: % 44.08/6.80 | (141) all_37_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (117), (118) imply: % 44.08/6.80 | (142) all_18_0 = all_7_1 % 44.08/6.80 | % 44.08/6.80 | SIMP: (142) implies: % 44.08/6.80 | (143) all_18_0 = all_7_1 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (137), (139) imply: % 44.08/6.80 | (144) all_39_0 = all_24_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (137), (138) imply: % 44.08/6.80 | (145) all_39_0 = all_22_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (144), (145) imply: % 44.08/6.80 | (146) all_24_0 = all_22_0 % 44.08/6.80 | % 44.08/6.80 | SIMP: (146) implies: % 44.08/6.80 | (147) all_24_0 = all_22_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (125), (126) imply: % 44.08/6.80 | (148) all_34_0 = all_16_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (125), (141) imply: % 44.08/6.80 | (149) all_34_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | COMBINE_EQS: (148), (149) imply: % 44.08/6.80 | (150) all_16_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | SIMP: (150) implies: % 44.08/6.80 | (151) all_16_0 = all_14_0 % 44.08/6.80 | % 44.08/6.80 | REDUCE: (95), (117) imply: % 44.08/6.80 | (152) j(all_7_1) = all_44_1 % 44.08/6.80 | % 44.08/6.80 | REDUCE: (42), (151) imply: % 44.08/6.80 | (153) h(all_14_0) = all_7_2 % 44.08/6.80 | % 44.08/6.80 | REDUCE: (107), (129), (138) imply: % 44.08/6.80 | (154) op1(all_22_0, all_14_0) = all_50_0 % 44.08/6.80 | % 44.08/6.80 | REDUCE: (101), (138) imply: % 44.08/6.80 | (155) op1(all_22_0, all_48_1) = all_48_0 % 44.08/6.80 | % 44.08/6.80 | REDUCE: (77), (141), (149) imply: % 44.08/6.80 | (156) op1(all_14_0, all_14_0) = all_37_1 % 44.08/6.80 | % 44.08/6.80 | REDUCE: (97), (116) imply: % 44.08/6.80 | (157) $i(all_26_0) % 44.08/6.80 | % 44.08/6.80 | REDUCE: (81), (119) imply: % 44.08/6.80 | (158) $i(all_20_0) % 44.08/6.80 | % 44.08/6.80 | REDUCE: (76), (120) imply: % 44.08/6.80 | (159) $i(all_28_0) % 44.08/6.80 | % 44.08/6.80 | REDUCE: (54), (147) imply: % 44.08/6.80 | (160) $i(all_22_0) % 44.08/6.80 | % 44.08/6.80 | REDUCE: (41), (151) imply: % 44.08/6.80 | (161) $i(all_14_0) % 44.08/6.80 | % 44.08/6.80 | BETA: splitting (69) gives: % 44.08/6.80 | % 44.08/6.81 | Case 1: % 44.08/6.81 | | % 44.08/6.81 | | (162) ~ (all_32_1 = 0) % 44.08/6.81 | | % 44.08/6.81 | | REDUCE: (134), (162) imply: % 44.08/6.81 | | (163) $false % 44.08/6.81 | | % 44.08/6.81 | | CLOSE: (163) is inconsistent. % 44.08/6.81 | | % 44.08/6.81 | Case 2: % 44.08/6.81 | | % 44.08/6.81 | | (164) all_32_0 = 0 % 44.08/6.81 | | % 44.08/6.81 | | COMBINE_EQS: (136), (164) imply: % 44.08/6.81 | | (165) all_30_1 = 0 % 44.08/6.81 | | % 44.08/6.81 | | COMBINE_EQS: (115), (165) imply: % 44.08/6.81 | | (166) all_48_3 = 0 % 44.08/6.81 | | % 44.08/6.81 | | REDUCE: (63), (165) imply: % 44.08/6.81 | | (167) sorti2(all_7_1) = 0 % 44.08/6.81 | | % 44.08/6.81 | | BETA: splitting (65) gives: % 44.08/6.81 | | % 44.08/6.81 | | Case 1: % 44.08/6.81 | | | % 44.08/6.81 | | | (168) ~ (all_30_1 = 0) % 44.08/6.81 | | | % 44.08/6.81 | | | REDUCE: (165), (168) imply: % 44.08/6.81 | | | (169) $false % 44.08/6.81 | | | % 44.08/6.81 | | | CLOSE: (169) is inconsistent. % 44.08/6.81 | | | % 44.08/6.81 | | Case 2: % 44.08/6.81 | | | % 44.08/6.81 | | | (170) all_30_0 = 0 % 44.08/6.81 | | | % 44.08/6.81 | | | REDUCE: (64), (170) imply: % 44.08/6.81 | | | (171) sorti2(all_7_0) = 0 % 44.08/6.81 | | | % 44.08/6.81 | | | BETA: splitting (111) gives: % 44.08/6.81 | | | % 44.08/6.81 | | | Case 1: % 44.08/6.81 | | | | % 44.08/6.81 | | | | (172) ~ (all_50_3 = 0) % 44.08/6.81 | | | | % 44.08/6.81 | | | | REDUCE: (112), (172) imply: % 44.08/6.81 | | | | (173) $false % 44.08/6.81 | | | | % 44.08/6.81 | | | | CLOSE: (173) is inconsistent. % 44.08/6.81 | | | | % 44.08/6.81 | | | Case 2: % 44.08/6.81 | | | | % 44.08/6.81 | | | | (174) all_50_0 = all_50_2 % 44.08/6.81 | | | | % 44.08/6.81 | | | | COMBINE_EQS: (130), (174) imply: % 44.08/6.81 | | | | (175) all_50_0 = all_48_1 % 44.08/6.81 | | | | % 44.08/6.81 | | | | REDUCE: (154), (175) imply: % 44.08/6.81 | | | | (176) op1(all_22_0, all_14_0) = all_48_1 % 44.08/6.81 | | | | % 44.08/6.81 | | | | BETA: splitting (105) gives: % 44.08/6.81 | | | | % 44.08/6.81 | | | | Case 1: % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | (177) ~ (all_48_3 = 0) % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | REDUCE: (166), (177) imply: % 44.08/6.81 | | | | | (178) $false % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | CLOSE: (178) is inconsistent. % 44.08/6.81 | | | | | % 44.08/6.81 | | | | Case 2: % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | (179) all_48_0 = all_48_2 % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | REDUCE: (155), (179) imply: % 44.08/6.81 | | | | | (180) op1(all_22_0, all_48_1) = all_48_2 % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | GROUND_INST: instantiating (12) with all_48_1, all_44_1, all_7_1, % 44.08/6.81 | | | | | simplifying with (103), (152) gives: % 44.08/6.81 | | | | | (181) all_48_1 = all_44_1 % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | REDUCE: (180), (181) imply: % 44.08/6.81 | | | | | (182) op1(all_22_0, all_44_1) = all_48_2 % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | REDUCE: (176), (181) imply: % 44.08/6.81 | | | | | (183) op1(all_22_0, all_14_0) = all_44_1 % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | GROUND_INST: instantiating (5) with all_14_0, simplifying with (38), % 44.08/6.81 | | | | | (161) gives: % 44.08/6.81 | | | | | (184) ? [v0: $i] : (h(all_14_0) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.81 | | | | | [v2: $i] : ( ~ (h(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.81 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (h(v4) = v5 & % 44.08/6.81 | | | | | op2(v0, v2) = v6 & op1(all_14_0, v1) = v4 & sorti1(v1) % 44.08/6.81 | | | | | = v3 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.81 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 44.08/6.81 | | | | | (op1(all_14_0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.81 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (h(v2) = v4 & % 44.08/6.81 | | | | | h(v1) = v5 & op2(v0, v5) = v6 & sorti1(v1) = v3 & % 44.08/6.81 | | | | | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & % 44.08/6.81 | | | | | ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ $i(v1) | ? [v2: $i] % 44.08/6.81 | | | | | : ? [v3: $i] : ? [v4: $i] : (h(v2) = v3 & h(v1) = v4 & % 44.08/6.81 | | | | | op2(v0, v4) = v3 & op1(all_14_0, v1) = v2 & $i(v4) & % 44.08/6.81 | | | | | $i(v3) & $i(v2)))) % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | GROUND_INST: instantiating (5) with all_22_0, simplifying with (51), % 44.08/6.81 | | | | | (160) gives: % 44.08/6.81 | | | | | (185) ? [v0: $i] : (h(all_22_0) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.81 | | | | | [v2: $i] : ( ~ (h(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.81 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (h(v4) = v5 & % 44.08/6.81 | | | | | op2(v0, v2) = v6 & op1(all_22_0, v1) = v4 & sorti1(v1) % 44.08/6.81 | | | | | = v3 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.81 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 44.08/6.81 | | | | | (op1(all_22_0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.81 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (h(v2) = v4 & % 44.08/6.81 | | | | | h(v1) = v5 & op2(v0, v5) = v6 & sorti1(v1) = v3 & % 44.08/6.81 | | | | | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & % 44.08/6.81 | | | | | ! [v1: $i] : ( ~ (sorti1(v1) = 0) | ~ $i(v1) | ? [v2: $i] % 44.08/6.81 | | | | | : ? [v3: $i] : ? [v4: $i] : (h(v2) = v3 & h(v1) = v4 & % 44.08/6.81 | | | | | op2(v0, v4) = v3 & op1(all_22_0, v1) = v2 & $i(v4) & % 44.08/6.81 | | | | | $i(v3) & $i(v2)))) % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | GROUND_INST: instantiating (4) with all_14_0, all_14_0, all_37_1, % 44.08/6.81 | | | | | simplifying with (38), (156), (161) gives: % 44.08/6.81 | | | | | (186) ? [v0: any] : ? [v1: $i] : (op1(all_14_0, all_37_1) = v1 & % 44.08/6.81 | | | | | sorti1(all_14_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 44.08/6.81 | | | | | all_14_0)) % 44.08/6.81 | | | | | % 44.08/6.81 | | | | | GROUND_INST: instantiating (1) with all_14_0, all_14_0, all_37_1, % 44.08/6.81 | | | | | simplifying with (38), (156), (161) gives: % 44.08/6.82 | | | | | (187) ? [v0: any] : ? [v1: any] : (sorti1(all_37_1) = v1 & % 44.08/6.82 | | | | | sorti1(all_14_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (4) with all_22_0, all_14_0, all_44_1, % 44.08/6.82 | | | | | simplifying with (51), (160), (161), (183) gives: % 44.08/6.82 | | | | | (188) ? [v0: any] : ? [v1: $i] : (op1(all_22_0, all_44_1) = v1 & % 44.08/6.82 | | | | | sorti1(all_14_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = % 44.08/6.82 | | | | | all_14_0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (1) with all_22_0, all_14_0, all_44_1, % 44.08/6.82 | | | | | simplifying with (51), (160), (161), (183) gives: % 44.08/6.82 | | | | | (189) ? [v0: any] : ? [v1: any] : (sorti1(all_44_1) = v1 & % 44.08/6.82 | | | | | sorti1(all_14_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (6) with all_7_1, simplifying with (19), % 44.08/6.82 | | | | | (167) gives: % 44.08/6.82 | | | | | (190) ? [v0: $i] : (j(all_7_1) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.82 | | | | | [v2: $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.82 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v4) = v5 & % 44.08/6.82 | | | | | op2(all_7_1, v1) = v4 & sorti2(v1) = v3 & op1(v0, v2) = % 44.08/6.82 | | | | | v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.82 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ (op2(all_7_1, % 44.08/6.82 | | | | | v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : % 44.08/6.82 | | | | | ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & j(v1) = v5 & % 44.08/6.82 | | | | | sorti2(v1) = v3 & op1(v0, v5) = v6 & $i(v6) & $i(v5) & % 44.08/6.82 | | | | | $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & ! [v1: $i] : ( ~ % 44.08/6.82 | | | | | (sorti2(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] % 44.08/6.82 | | | | | : ? [v4: $i] : (j(v2) = v3 & j(v1) = v4 & op2(all_7_1, % 44.08/6.82 | | | | | v1) = v2 & op1(v0, v4) = v3 & $i(v4) & $i(v3) & % 44.08/6.82 | | | | | $i(v2)))) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (72) with all_7_0, simplifying with (20), % 44.08/6.82 | | | | | (171) gives: % 44.08/6.82 | | | | | (191) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.08/6.82 | | | | | j(all_7_0) = v2 & op2(all_7_2, all_7_0) = v0 & % 44.08/6.82 | | | | | op1(all_34_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (86) with all_7_0, simplifying with (20), % 44.08/6.82 | | | | | (171) gives: % 44.08/6.82 | | | | | (192) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.08/6.82 | | | | | j(all_7_0) = v2 & op2(all_7_3, all_7_0) = v0 & % 44.08/6.82 | | | | | op1(all_41_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (8) with all_7_0, simplifying with (20), % 44.08/6.82 | | | | | (171) gives: % 44.08/6.82 | | | | | (193) ? [v0: $i] : (j(all_7_0) = v0 & h(v0) = all_7_0 & $i(v0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (7) with all_7_0, simplifying with (20), % 44.08/6.82 | | | | | (171) gives: % 44.08/6.82 | | | | | (194) ? [v0: $i] : (j(all_7_0) = v0 & sorti1(v0) = 0 & $i(v0)) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (6) with all_7_0, simplifying with (20), % 44.08/6.82 | | | | | (171) gives: % 44.08/6.82 | | | | | (195) ? [v0: $i] : (j(all_7_0) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.82 | | | | | [v2: $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.82 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v4) = v5 & % 44.08/6.82 | | | | | op2(all_7_0, v1) = v4 & sorti2(v1) = v3 & op1(v0, v2) = % 44.08/6.82 | | | | | v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.82 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ (op2(all_7_0, % 44.08/6.82 | | | | | v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : % 44.08/6.82 | | | | | ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & j(v1) = v5 & % 44.08/6.82 | | | | | sorti2(v1) = v3 & op1(v0, v5) = v6 & $i(v6) & $i(v5) & % 44.08/6.82 | | | | | $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & ! [v1: $i] : ( ~ % 44.08/6.82 | | | | | (sorti2(v1) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] % 44.08/6.82 | | | | | : ? [v4: $i] : (j(v2) = v3 & j(v1) = v4 & op2(all_7_0, % 44.08/6.82 | | | | | v1) = v2 & op1(v0, v4) = v3 & $i(v4) & $i(v3) & % 44.08/6.82 | | | | | $i(v2)))) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (6) with all_20_0, simplifying with (48), % 44.08/6.82 | | | | | (158) gives: % 44.08/6.82 | | | | | (196) ? [v0: $i] : (j(all_20_0) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.82 | | | | | [v2: $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.82 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v4) = v5 & % 44.08/6.82 | | | | | op2(all_20_0, v1) = v4 & sorti2(v1) = v3 & op1(v0, v2) % 44.08/6.82 | | | | | = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.82 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 44.08/6.82 | | | | | (op2(all_20_0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.82 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & % 44.08/6.82 | | | | | j(v1) = v5 & sorti2(v1) = v3 & op1(v0, v5) = v6 & % 44.08/6.82 | | | | | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & % 44.08/6.82 | | | | | ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ $i(v1) | ? [v2: $i] % 44.08/6.82 | | | | | : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 & j(v1) = v4 & % 44.08/6.82 | | | | | op2(all_20_0, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & % 44.08/6.82 | | | | | $i(v3) & $i(v2)))) % 44.08/6.82 | | | | | % 44.08/6.82 | | | | | GROUND_INST: instantiating (6) with all_26_0, simplifying with (57), % 44.08/6.82 | | | | | (157) gives: % 44.08/6.83 | | | | | (197) ? [v0: $i] : (j(all_26_0) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.83 | | | | | [v2: $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.83 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v4) = v5 & % 44.08/6.83 | | | | | op2(all_26_0, v1) = v4 & sorti2(v1) = v3 & op1(v0, v2) % 44.08/6.83 | | | | | = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.83 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 44.08/6.83 | | | | | (op2(all_26_0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.83 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & % 44.08/6.83 | | | | | j(v1) = v5 & sorti2(v1) = v3 & op1(v0, v5) = v6 & % 44.08/6.83 | | | | | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & % 44.08/6.83 | | | | | ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ $i(v1) | ? [v2: $i] % 44.08/6.83 | | | | | : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 & j(v1) = v4 & % 44.08/6.83 | | | | | op2(all_26_0, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & % 44.08/6.83 | | | | | $i(v3) & $i(v2)))) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | GROUND_INST: instantiating (6) with all_28_0, simplifying with (60), % 44.08/6.83 | | | | | (159) gives: % 44.08/6.83 | | | | | (198) ? [v0: $i] : (j(all_28_0) = v0 & $i(v0) & ! [v1: $i] : ! % 44.08/6.83 | | | | | [v2: $i] : ( ~ (j(v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.83 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v4) = v5 & % 44.08/6.83 | | | | | op2(all_28_0, v1) = v4 & sorti2(v1) = v3 & op1(v0, v2) % 44.08/6.83 | | | | | = v6 & $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = % 44.08/6.83 | | | | | v5))) & ! [v1: $i] : ! [v2: $i] : ( ~ % 44.08/6.83 | | | | | (op2(all_28_0, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? % 44.08/6.83 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: $i] : (j(v2) = v4 & % 44.08/6.83 | | | | | j(v1) = v5 & sorti2(v1) = v3 & op1(v0, v5) = v6 & % 44.08/6.83 | | | | | $i(v6) & $i(v5) & $i(v4) & ( ~ (v3 = 0) | v6 = v4))) & % 44.08/6.83 | | | | | ! [v1: $i] : ( ~ (sorti2(v1) = 0) | ~ $i(v1) | ? [v2: $i] % 44.08/6.83 | | | | | : ? [v3: $i] : ? [v4: $i] : (j(v2) = v3 & j(v1) = v4 & % 44.08/6.83 | | | | | op2(all_28_0, v1) = v2 & op1(v0, v4) = v3 & $i(v4) & % 44.08/6.83 | | | | | $i(v3) & $i(v2)))) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (194) with fresh symbol all_129_0 gives: % 44.08/6.83 | | | | | (199) j(all_7_0) = all_129_0 & sorti1(all_129_0) = 0 & % 44.08/6.83 | | | | | $i(all_129_0) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (199) implies: % 44.08/6.83 | | | | | (200) j(all_7_0) = all_129_0 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (193) with fresh symbol all_133_0 gives: % 44.08/6.83 | | | | | (201) j(all_7_0) = all_133_0 & h(all_133_0) = all_7_0 & % 44.08/6.83 | | | | | $i(all_133_0) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (201) implies: % 44.08/6.83 | | | | | (202) h(all_133_0) = all_7_0 % 44.08/6.83 | | | | | (203) j(all_7_0) = all_133_0 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (187) with fresh symbols all_207_0, all_207_1 % 44.08/6.83 | | | | | gives: % 44.08/6.83 | | | | | (204) sorti1(all_37_1) = all_207_0 & sorti1(all_14_0) = all_207_1 & % 44.08/6.83 | | | | | ( ~ (all_207_1 = 0) | all_207_0 = 0) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (204) implies: % 44.08/6.83 | | | | | (205) sorti1(all_14_0) = all_207_1 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (189) with fresh symbols all_209_0, all_209_1 % 44.08/6.83 | | | | | gives: % 44.08/6.83 | | | | | (206) sorti1(all_44_1) = all_209_0 & sorti1(all_14_0) = all_209_1 & % 44.08/6.83 | | | | | ( ~ (all_209_1 = 0) | all_209_0 = 0) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (206) implies: % 44.08/6.83 | | | | | (207) sorti1(all_14_0) = all_209_1 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (186) with fresh symbols all_225_0, all_225_1 % 44.08/6.83 | | | | | gives: % 44.08/6.83 | | | | | (208) op1(all_14_0, all_37_1) = all_225_0 & sorti1(all_14_0) = % 44.08/6.83 | | | | | all_225_1 & $i(all_225_0) & ( ~ (all_225_1 = 0) | all_225_0 = % 44.08/6.83 | | | | | all_14_0) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (208) implies: % 44.08/6.83 | | | | | (209) sorti1(all_14_0) = all_225_1 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (188) with fresh symbols all_229_0, all_229_1 % 44.08/6.83 | | | | | gives: % 44.08/6.83 | | | | | (210) op1(all_22_0, all_44_1) = all_229_0 & sorti1(all_14_0) = % 44.08/6.83 | | | | | all_229_1 & $i(all_229_0) & ( ~ (all_229_1 = 0) | all_229_0 = % 44.08/6.83 | | | | | all_14_0) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (210) implies: % 44.08/6.83 | | | | | (211) sorti1(all_14_0) = all_229_1 % 44.08/6.83 | | | | | (212) op1(all_22_0, all_44_1) = all_229_0 % 44.08/6.83 | | | | | (213) ~ (all_229_1 = 0) | all_229_0 = all_14_0 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (191) with fresh symbols all_245_0, all_245_1, % 44.08/6.83 | | | | | all_245_2 gives: % 44.08/6.83 | | | | | (214) j(all_245_2) = all_245_1 & j(all_7_0) = all_245_0 & % 44.08/6.83 | | | | | op2(all_7_2, all_7_0) = all_245_2 & op1(all_34_0, all_245_0) % 44.08/6.83 | | | | | = all_245_1 & $i(all_245_0) & $i(all_245_1) & $i(all_245_2) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (214) implies: % 44.08/6.83 | | | | | (215) j(all_7_0) = all_245_0 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (192) with fresh symbols all_257_0, all_257_1, % 44.08/6.83 | | | | | all_257_2 gives: % 44.08/6.83 | | | | | (216) j(all_257_2) = all_257_1 & j(all_7_0) = all_257_0 & % 44.08/6.83 | | | | | op2(all_7_3, all_7_0) = all_257_2 & op1(all_41_0, all_257_0) % 44.08/6.83 | | | | | = all_257_1 & $i(all_257_0) & $i(all_257_1) & $i(all_257_2) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (216) implies: % 44.08/6.83 | | | | | (217) j(all_7_0) = all_257_0 % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | DELTA: instantiating (185) with fresh symbol all_382_0 gives: % 44.08/6.83 | | | | | (218) h(all_22_0) = all_382_0 & $i(all_382_0) & ! [v0: $i] : ! % 44.08/6.83 | | | | | [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.08/6.83 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (h(v3) = v4 & % 44.08/6.83 | | | | | op2(all_382_0, v1) = v5 & op1(all_22_0, v0) = v3 & % 44.08/6.83 | | | | | sorti1(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) % 44.08/6.83 | | | | | | v5 = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 44.08/6.83 | | | | | (op1(all_22_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.08/6.83 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (h(v1) = v3 & h(v0) % 44.08/6.83 | | | | | = v4 & op2(all_382_0, v4) = v5 & sorti1(v0) = v2 & $i(v5) % 44.08/6.83 | | | | | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: % 44.08/6.83 | | | | | $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 44.08/6.83 | | | | | [v2: $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & % 44.08/6.83 | | | | | op2(all_382_0, v3) = v2 & op1(all_22_0, v0) = v1 & $i(v3) % 44.08/6.83 | | | | | & $i(v2) & $i(v1))) % 44.08/6.83 | | | | | % 44.08/6.83 | | | | | ALPHA: (218) implies: % 44.08/6.83 | | | | | (219) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.08/6.83 | | | | | : ? [v2: $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & % 44.08/6.83 | | | | | op2(all_382_0, v3) = v2 & op1(all_22_0, v0) = v1 & $i(v3) % 44.08/6.83 | | | | | & $i(v2) & $i(v1))) % 44.08/6.83 | | | | | (220) ! [v0: $i] : ! [v1: $i] : ( ~ (op1(all_22_0, v0) = v1) | ~ % 44.08/6.83 | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 44.08/6.83 | | | | | $i] : (h(v1) = v3 & h(v0) = v4 & op2(all_382_0, v4) = v5 % 44.08/6.83 | | | | | & sorti1(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 44.08/6.83 | | | | | 0) | v5 = v3))) % 44.08/6.84 | | | | | (221) ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? % 44.08/6.84 | | | | | [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 44.08/6.84 | | | | | (h(v3) = v4 & op2(all_382_0, v1) = v5 & op1(all_22_0, v0) = % 44.08/6.84 | | | | | v3 & sorti1(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 % 44.08/6.84 | | | | | = 0) | v5 = v4))) % 44.08/6.84 | | | | | % 44.08/6.84 | | | | | GROUND_INST: instantiating (219) with all_14_0, simplifying with (38), % 44.08/6.84 | | | | | (161) gives: % 44.08/6.84 | | | | | (222) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & % 44.08/6.84 | | | | | h(all_14_0) = v2 & op2(all_382_0, v2) = v1 & op1(all_22_0, % 44.08/6.84 | | | | | all_14_0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 44.08/6.84 | | | | | % 44.08/6.84 | | | | | GROUND_INST: instantiating (220) with all_14_0, all_44_1, simplifying % 44.08/6.84 | | | | | with (161), (183) gives: % 44.08/6.84 | | | | | (223) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 44.08/6.84 | | | | | (h(all_44_1) = v1 & h(all_14_0) = v2 & op2(all_382_0, v2) = % 44.08/6.84 | | | | | v3 & sorti1(all_14_0) = v0 & $i(v3) & $i(v2) & $i(v1) & ( ~ % 44.08/6.84 | | | | | (v0 = 0) | v3 = v1)) % 44.08/6.84 | | | | | % 44.08/6.84 | | | | | GROUND_INST: instantiating (221) with all_14_0, all_7_2, simplifying % 44.08/6.84 | | | | | with (153), (161) gives: % 44.08/6.84 | | | | | (224) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 44.08/6.84 | | | | | (h(v1) = v2 & op2(all_382_0, all_7_2) = v3 & op1(all_22_0, % 44.08/6.84 | | | | | all_14_0) = v1 & sorti1(all_14_0) = v0 & $i(v3) & $i(v2) % 44.08/6.84 | | | | | & $i(v1) & ( ~ (v0 = 0) | v3 = v2)) % 44.08/6.84 | | | | | % 44.08/6.84 | | | | | DELTA: instantiating (198) with fresh symbol all_385_0 gives: % 44.26/6.84 | | | | | (225) j(all_28_0) = all_385_0 & $i(all_385_0) & ! [v0: $i] : ! % 44.26/6.84 | | | | | [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.84 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & % 44.26/6.84 | | | | | op2(all_28_0, v0) = v3 & sorti2(v0) = v2 & op1(all_385_0, % 44.26/6.84 | | | | | v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 % 44.26/6.84 | | | | | = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 44.26/6.84 | | | | | (op2(all_28_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.84 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) % 44.26/6.84 | | | | | = v4 & sorti2(v0) = v2 & op1(all_385_0, v4) = v5 & $i(v5) % 44.26/6.84 | | | | | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: % 44.26/6.84 | | | | | $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 44.26/6.84 | | | | | [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.84 | | | | | op2(all_28_0, v0) = v1 & op1(all_385_0, v3) = v2 & $i(v3) % 44.26/6.84 | | | | | & $i(v2) & $i(v1))) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | ALPHA: (225) implies: % 44.26/6.84 | | | | | (226) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.26/6.84 | | | | | : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.84 | | | | | op2(all_28_0, v0) = v1 & op1(all_385_0, v3) = v2 & $i(v3) % 44.26/6.84 | | | | | & $i(v2) & $i(v1))) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | GROUND_INST: instantiating (226) with all_7_0, simplifying with (20), % 44.26/6.84 | | | | | (171) gives: % 44.26/6.84 | | | | | (227) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.26/6.84 | | | | | j(all_7_0) = v2 & op2(all_28_0, all_7_0) = v0 & % 44.26/6.84 | | | | | op1(all_385_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | DELTA: instantiating (196) with fresh symbol all_388_0 gives: % 44.26/6.84 | | | | | (228) j(all_20_0) = all_388_0 & $i(all_388_0) & ! [v0: $i] : ! % 44.26/6.84 | | | | | [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.84 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & % 44.26/6.84 | | | | | op2(all_20_0, v0) = v3 & sorti2(v0) = v2 & op1(all_388_0, % 44.26/6.84 | | | | | v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 % 44.26/6.84 | | | | | = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 44.26/6.84 | | | | | (op2(all_20_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.84 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) % 44.26/6.84 | | | | | = v4 & sorti2(v0) = v2 & op1(all_388_0, v4) = v5 & $i(v5) % 44.26/6.84 | | | | | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: % 44.26/6.84 | | | | | $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 44.26/6.84 | | | | | [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.84 | | | | | op2(all_20_0, v0) = v1 & op1(all_388_0, v3) = v2 & $i(v3) % 44.26/6.84 | | | | | & $i(v2) & $i(v1))) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | ALPHA: (228) implies: % 44.26/6.84 | | | | | (229) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.26/6.84 | | | | | : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.84 | | | | | op2(all_20_0, v0) = v1 & op1(all_388_0, v3) = v2 & $i(v3) % 44.26/6.84 | | | | | & $i(v2) & $i(v1))) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | GROUND_INST: instantiating (229) with all_7_0, simplifying with (20), % 44.26/6.84 | | | | | (171) gives: % 44.26/6.84 | | | | | (230) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.26/6.84 | | | | | j(all_7_0) = v2 & op2(all_20_0, all_7_0) = v0 & % 44.26/6.84 | | | | | op1(all_388_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | DELTA: instantiating (197) with fresh symbol all_391_0 gives: % 44.26/6.84 | | | | | (231) j(all_26_0) = all_391_0 & $i(all_391_0) & ! [v0: $i] : ! % 44.26/6.84 | | | | | [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.84 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & % 44.26/6.84 | | | | | op2(all_26_0, v0) = v3 & sorti2(v0) = v2 & op1(all_391_0, % 44.26/6.84 | | | | | v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 % 44.26/6.84 | | | | | = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 44.26/6.84 | | | | | (op2(all_26_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.84 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) % 44.26/6.84 | | | | | = v4 & sorti2(v0) = v2 & op1(all_391_0, v4) = v5 & $i(v5) % 44.26/6.84 | | | | | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: % 44.26/6.84 | | | | | $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 44.26/6.84 | | | | | [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.84 | | | | | op2(all_26_0, v0) = v1 & op1(all_391_0, v3) = v2 & $i(v3) % 44.26/6.84 | | | | | & $i(v2) & $i(v1))) % 44.26/6.84 | | | | | % 44.26/6.84 | | | | | ALPHA: (231) implies: % 44.26/6.85 | | | | | (232) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.26/6.85 | | | | | : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.85 | | | | | op2(all_26_0, v0) = v1 & op1(all_391_0, v3) = v2 & $i(v3) % 44.26/6.85 | | | | | & $i(v2) & $i(v1))) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | GROUND_INST: instantiating (232) with all_7_0, simplifying with (20), % 44.26/6.85 | | | | | (171) gives: % 44.26/6.85 | | | | | (233) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.26/6.85 | | | | | j(all_7_0) = v2 & op2(all_26_0, all_7_0) = v0 & % 44.26/6.85 | | | | | op1(all_391_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | DELTA: instantiating (195) with fresh symbol all_394_0 gives: % 44.26/6.85 | | | | | (234) j(all_7_0) = all_394_0 & $i(all_394_0) & ! [v0: $i] : ! % 44.26/6.85 | | | | | [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.85 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & % 44.26/6.85 | | | | | op2(all_7_0, v0) = v3 & sorti2(v0) = v2 & op1(all_394_0, % 44.26/6.85 | | | | | v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 % 44.26/6.85 | | | | | = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (op2(all_7_0, % 44.26/6.85 | | | | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? % 44.26/6.85 | | | | | [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) = v4 & % 44.26/6.85 | | | | | sorti2(v0) = v2 & op1(all_394_0, v4) = v5 & $i(v5) & % 44.26/6.85 | | | | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] % 44.26/6.85 | | | | | : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 44.26/6.85 | | | | | $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.85 | | | | | op2(all_7_0, v0) = v1 & op1(all_394_0, v3) = v2 & $i(v3) % 44.26/6.85 | | | | | & $i(v2) & $i(v1))) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | ALPHA: (234) implies: % 44.26/6.85 | | | | | (235) j(all_7_0) = all_394_0 % 44.26/6.85 | | | | | (236) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.26/6.85 | | | | | : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.85 | | | | | op2(all_7_0, v0) = v1 & op1(all_394_0, v3) = v2 & $i(v3) % 44.26/6.85 | | | | | & $i(v2) & $i(v1))) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | GROUND_INST: instantiating (236) with all_7_0, simplifying with (20), % 44.26/6.85 | | | | | (171) gives: % 44.26/6.85 | | | | | (237) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.26/6.85 | | | | | j(all_7_0) = v2 & op2(all_7_0, all_7_0) = v0 & % 44.26/6.85 | | | | | op1(all_394_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | DELTA: instantiating (184) with fresh symbol all_397_0 gives: % 44.26/6.85 | | | | | (238) h(all_14_0) = all_397_0 & $i(all_397_0) & ! [v0: $i] : ! % 44.26/6.85 | | | | | [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.85 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (h(v3) = v4 & % 44.26/6.85 | | | | | op2(all_397_0, v1) = v5 & op1(all_14_0, v0) = v3 & % 44.26/6.85 | | | | | sorti1(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) % 44.26/6.85 | | | | | | v5 = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 44.26/6.85 | | | | | (op1(all_14_0, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.85 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (h(v1) = v3 & h(v0) % 44.26/6.85 | | | | | = v4 & op2(all_397_0, v4) = v5 & sorti1(v0) = v2 & $i(v5) % 44.26/6.85 | | | | | & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: % 44.26/6.85 | | | | | $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? % 44.26/6.85 | | | | | [v2: $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & % 44.26/6.85 | | | | | op2(all_397_0, v3) = v2 & op1(all_14_0, v0) = v1 & $i(v3) % 44.26/6.85 | | | | | & $i(v2) & $i(v1))) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | ALPHA: (238) implies: % 44.26/6.85 | | | | | (239) h(all_14_0) = all_397_0 % 44.26/6.85 | | | | | (240) ! [v0: $i] : ( ~ (sorti1(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.26/6.85 | | | | | : ? [v2: $i] : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & % 44.26/6.85 | | | | | op2(all_397_0, v3) = v2 & op1(all_14_0, v0) = v1 & $i(v3) % 44.26/6.85 | | | | | & $i(v2) & $i(v1))) % 44.26/6.85 | | | | | (241) ! [v0: $i] : ! [v1: $i] : ( ~ (op1(all_14_0, v0) = v1) | ~ % 44.26/6.85 | | | | | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 44.26/6.85 | | | | | $i] : (h(v1) = v3 & h(v0) = v4 & op2(all_397_0, v4) = v5 % 44.26/6.85 | | | | | & sorti1(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = % 44.26/6.85 | | | | | 0) | v5 = v3))) % 44.26/6.85 | | | | | (242) ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ? % 44.26/6.85 | | | | | [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : % 44.26/6.85 | | | | | (h(v3) = v4 & op2(all_397_0, v1) = v5 & op1(all_14_0, v0) = % 44.26/6.85 | | | | | v3 & sorti1(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 % 44.26/6.85 | | | | | = 0) | v5 = v4))) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | GROUND_INST: instantiating (240) with all_14_0, simplifying with (38), % 44.26/6.85 | | | | | (161) gives: % 44.26/6.85 | | | | | (243) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & % 44.26/6.85 | | | | | h(all_14_0) = v2 & op2(all_397_0, v2) = v1 & op1(all_14_0, % 44.26/6.85 | | | | | all_14_0) = v0 & $i(v2) & $i(v1) & $i(v0)) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | GROUND_INST: instantiating (241) with all_14_0, all_37_1, simplifying % 44.26/6.85 | | | | | with (156), (161) gives: % 44.26/6.85 | | | | | (244) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 44.26/6.85 | | | | | (h(all_37_1) = v1 & h(all_14_0) = v2 & op2(all_397_0, v2) = % 44.26/6.85 | | | | | v3 & sorti1(all_14_0) = v0 & $i(v3) & $i(v2) & $i(v1) & ( ~ % 44.26/6.85 | | | | | (v0 = 0) | v3 = v1)) % 44.26/6.85 | | | | | % 44.26/6.85 | | | | | GROUND_INST: instantiating (242) with all_14_0, all_7_2, simplifying % 44.26/6.85 | | | | | with (153), (161) gives: % 44.26/6.86 | | | | | (245) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 44.26/6.86 | | | | | (h(v1) = v2 & op2(all_397_0, all_7_2) = v3 & op1(all_14_0, % 44.26/6.86 | | | | | all_14_0) = v1 & sorti1(all_14_0) = v0 & $i(v3) & $i(v2) % 44.26/6.86 | | | | | & $i(v1) & ( ~ (v0 = 0) | v3 = v2)) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (190) with fresh symbol all_400_0 gives: % 44.26/6.86 | | | | | (246) j(all_7_1) = all_400_0 & $i(all_400_0) & ! [v0: $i] : ! % 44.26/6.86 | | | | | [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ? [v2: any] : ? % 44.26/6.86 | | | | | [v3: $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & % 44.26/6.86 | | | | | op2(all_7_1, v0) = v3 & sorti2(v0) = v2 & op1(all_400_0, % 44.26/6.86 | | | | | v1) = v5 & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 % 44.26/6.86 | | | | | = v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (op2(all_7_1, % 44.26/6.86 | | | | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? % 44.26/6.86 | | | | | [v4: $i] : ? [v5: $i] : (j(v1) = v3 & j(v0) = v4 & % 44.26/6.86 | | | | | sorti2(v0) = v2 & op1(all_400_0, v4) = v5 & $i(v5) & % 44.26/6.86 | | | | | $i(v4) & $i(v3) & ( ~ (v2 = 0) | v5 = v3))) & ! [v0: $i] % 44.26/6.86 | | | | | : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: % 44.26/6.86 | | | | | $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.86 | | | | | op2(all_7_1, v0) = v1 & op1(all_400_0, v3) = v2 & $i(v3) % 44.26/6.86 | | | | | & $i(v2) & $i(v1))) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (246) implies: % 44.26/6.86 | | | | | (247) ! [v0: $i] : ( ~ (sorti2(v0) = 0) | ~ $i(v0) | ? [v1: $i] % 44.26/6.86 | | | | | : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & % 44.26/6.86 | | | | | op2(all_7_1, v0) = v1 & op1(all_400_0, v3) = v2 & $i(v3) % 44.26/6.86 | | | | | & $i(v2) & $i(v1))) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (247) with all_7_0, simplifying with (20), % 44.26/6.86 | | | | | (171) gives: % 44.26/6.86 | | | | | (248) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & % 44.26/6.86 | | | | | j(all_7_0) = v2 & op2(all_7_1, all_7_0) = v0 & % 44.26/6.86 | | | | | op1(all_400_0, v2) = v1 & $i(v2) & $i(v1) & $i(v0)) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (222) with fresh symbols all_405_0, all_405_1, % 44.26/6.86 | | | | | all_405_2 gives: % 44.26/6.86 | | | | | (249) h(all_405_2) = all_405_1 & h(all_14_0) = all_405_0 & % 44.26/6.86 | | | | | op2(all_382_0, all_405_0) = all_405_1 & op1(all_22_0, % 44.26/6.86 | | | | | all_14_0) = all_405_2 & $i(all_405_0) & $i(all_405_1) & % 44.26/6.86 | | | | | $i(all_405_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (249) implies: % 44.26/6.86 | | | | | (250) h(all_14_0) = all_405_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (224) with fresh symbols all_411_0, all_411_1, % 44.26/6.86 | | | | | all_411_2, all_411_3 gives: % 44.26/6.86 | | | | | (251) h(all_411_2) = all_411_1 & op2(all_382_0, all_7_2) = % 44.26/6.86 | | | | | all_411_0 & op1(all_22_0, all_14_0) = all_411_2 & % 44.26/6.86 | | | | | sorti1(all_14_0) = all_411_3 & $i(all_411_0) & $i(all_411_1) % 44.26/6.86 | | | | | & $i(all_411_2) & ( ~ (all_411_3 = 0) | all_411_0 = % 44.26/6.86 | | | | | all_411_1) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (251) implies: % 44.26/6.86 | | | | | (252) sorti1(all_14_0) = all_411_3 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (223) with fresh symbols all_415_0, all_415_1, % 44.26/6.86 | | | | | all_415_2, all_415_3 gives: % 44.26/6.86 | | | | | (253) h(all_44_1) = all_415_2 & h(all_14_0) = all_415_1 & % 44.26/6.86 | | | | | op2(all_382_0, all_415_1) = all_415_0 & sorti1(all_14_0) = % 44.26/6.86 | | | | | all_415_3 & $i(all_415_0) & $i(all_415_1) & $i(all_415_2) & ( % 44.26/6.86 | | | | | ~ (all_415_3 = 0) | all_415_0 = all_415_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (253) implies: % 44.26/6.86 | | | | | (254) sorti1(all_14_0) = all_415_3 % 44.26/6.86 | | | | | (255) h(all_14_0) = all_415_1 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (227) with fresh symbols all_419_0, all_419_1, % 44.26/6.86 | | | | | all_419_2 gives: % 44.26/6.86 | | | | | (256) j(all_419_2) = all_419_1 & j(all_7_0) = all_419_0 & % 44.26/6.86 | | | | | op2(all_28_0, all_7_0) = all_419_2 & op1(all_385_0, % 44.26/6.86 | | | | | all_419_0) = all_419_1 & $i(all_419_0) & $i(all_419_1) & % 44.26/6.86 | | | | | $i(all_419_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (256) implies: % 44.26/6.86 | | | | | (257) j(all_7_0) = all_419_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (230) with fresh symbols all_451_0, all_451_1, % 44.26/6.86 | | | | | all_451_2 gives: % 44.26/6.86 | | | | | (258) j(all_451_2) = all_451_1 & j(all_7_0) = all_451_0 & % 44.26/6.86 | | | | | op2(all_20_0, all_7_0) = all_451_2 & op1(all_388_0, % 44.26/6.86 | | | | | all_451_0) = all_451_1 & $i(all_451_0) & $i(all_451_1) & % 44.26/6.86 | | | | | $i(all_451_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (258) implies: % 44.26/6.86 | | | | | (259) j(all_7_0) = all_451_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (233) with fresh symbols all_479_0, all_479_1, % 44.26/6.86 | | | | | all_479_2 gives: % 44.26/6.86 | | | | | (260) j(all_479_2) = all_479_1 & j(all_7_0) = all_479_0 & % 44.26/6.86 | | | | | op2(all_26_0, all_7_0) = all_479_2 & op1(all_391_0, % 44.26/6.86 | | | | | all_479_0) = all_479_1 & $i(all_479_0) & $i(all_479_1) & % 44.26/6.86 | | | | | $i(all_479_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (260) implies: % 44.26/6.86 | | | | | (261) j(all_7_0) = all_479_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (237) with fresh symbols all_507_0, all_507_1, % 44.26/6.86 | | | | | all_507_2 gives: % 44.26/6.86 | | | | | (262) j(all_507_2) = all_507_1 & j(all_7_0) = all_507_0 & % 44.26/6.86 | | | | | op2(all_7_0, all_7_0) = all_507_2 & op1(all_394_0, all_507_0) % 44.26/6.86 | | | | | = all_507_1 & $i(all_507_0) & $i(all_507_1) & $i(all_507_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (262) implies: % 44.26/6.86 | | | | | (263) j(all_7_0) = all_507_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (243) with fresh symbols all_531_0, all_531_1, % 44.26/6.86 | | | | | all_531_2 gives: % 44.26/6.86 | | | | | (264) h(all_531_2) = all_531_1 & h(all_14_0) = all_531_0 & % 44.26/6.86 | | | | | op2(all_397_0, all_531_0) = all_531_1 & op1(all_14_0, % 44.26/6.86 | | | | | all_14_0) = all_531_2 & $i(all_531_0) & $i(all_531_1) & % 44.26/6.86 | | | | | $i(all_531_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (264) implies: % 44.26/6.86 | | | | | (265) h(all_14_0) = all_531_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (244) with fresh symbols all_535_0, all_535_1, % 44.26/6.86 | | | | | all_535_2, all_535_3 gives: % 44.26/6.86 | | | | | (266) h(all_37_1) = all_535_2 & h(all_14_0) = all_535_1 & % 44.26/6.86 | | | | | op2(all_397_0, all_535_1) = all_535_0 & sorti1(all_14_0) = % 44.26/6.86 | | | | | all_535_3 & $i(all_535_0) & $i(all_535_1) & $i(all_535_2) & ( % 44.26/6.86 | | | | | ~ (all_535_3 = 0) | all_535_0 = all_535_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (266) implies: % 44.26/6.86 | | | | | (267) sorti1(all_14_0) = all_535_3 % 44.26/6.86 | | | | | (268) h(all_14_0) = all_535_1 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (245) with fresh symbols all_539_0, all_539_1, % 44.26/6.86 | | | | | all_539_2, all_539_3 gives: % 44.26/6.86 | | | | | (269) h(all_539_2) = all_539_1 & op2(all_397_0, all_7_2) = % 44.26/6.86 | | | | | all_539_0 & op1(all_14_0, all_14_0) = all_539_2 & % 44.26/6.86 | | | | | sorti1(all_14_0) = all_539_3 & $i(all_539_0) & $i(all_539_1) % 44.26/6.86 | | | | | & $i(all_539_2) & ( ~ (all_539_3 = 0) | all_539_0 = % 44.26/6.86 | | | | | all_539_1) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (269) implies: % 44.26/6.86 | | | | | (270) sorti1(all_14_0) = all_539_3 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | DELTA: instantiating (248) with fresh symbols all_543_0, all_543_1, % 44.26/6.86 | | | | | all_543_2 gives: % 44.26/6.86 | | | | | (271) j(all_543_2) = all_543_1 & j(all_7_0) = all_543_0 & % 44.26/6.86 | | | | | op2(all_7_1, all_7_0) = all_543_2 & op1(all_400_0, all_543_0) % 44.26/6.86 | | | | | = all_543_1 & $i(all_543_0) & $i(all_543_1) & $i(all_543_2) % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | ALPHA: (271) implies: % 44.26/6.86 | | | | | (272) j(all_7_0) = all_543_0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_225_1, all_229_1, all_14_0, % 44.26/6.86 | | | | | simplifying with (209), (211) gives: % 44.26/6.86 | | | | | (273) all_229_1 = all_225_1 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with 0, all_415_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (38), (254) gives: % 44.26/6.86 | | | | | (274) all_415_3 = 0 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_225_1, all_415_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (209), (254) gives: % 44.26/6.86 | | | | | (275) all_415_3 = all_225_1 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_209_1, all_415_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (207), (254) gives: % 44.26/6.86 | | | | | (276) all_415_3 = all_209_1 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_207_1, all_535_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (205), (267) gives: % 44.26/6.86 | | | | | (277) all_535_3 = all_207_1 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_535_3, all_539_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (267), (270) gives: % 44.26/6.86 | | | | | (278) all_539_3 = all_535_3 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_411_3, all_539_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (252), (270) gives: % 44.26/6.86 | | | | | (279) all_539_3 = all_411_3 % 44.26/6.86 | | | | | % 44.26/6.86 | | | | | GROUND_INST: instantiating (9) with all_229_1, all_539_3, all_14_0, % 44.26/6.86 | | | | | simplifying with (211), (270) gives: % 44.26/6.86 | | | | | (280) all_539_3 = all_229_1 % 44.26/6.86 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (13) with all_48_2, all_229_0, all_44_1, % 44.26/6.87 | | | | | all_22_0, simplifying with (182), (212) gives: % 44.26/6.87 | | | | | (281) all_229_0 = all_48_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (11) with all_415_1, all_531_0, all_14_0, % 44.26/6.87 | | | | | simplifying with (255), (265) gives: % 44.26/6.87 | | | | | (282) all_531_0 = all_415_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (11) with all_405_0, all_531_0, all_14_0, % 44.26/6.87 | | | | | simplifying with (250), (265) gives: % 44.26/6.87 | | | | | (283) all_531_0 = all_405_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (11) with all_397_0, all_531_0, all_14_0, % 44.26/6.87 | | | | | simplifying with (239), (265) gives: % 44.26/6.87 | | | | | (284) all_531_0 = all_397_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (11) with all_7_2, all_535_1, all_14_0, % 44.26/6.87 | | | | | simplifying with (153), (268) gives: % 44.26/6.87 | | | | | (285) all_535_1 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (11) with all_415_1, all_535_1, all_14_0, % 44.26/6.87 | | | | | simplifying with (255), (268) gives: % 44.26/6.87 | | | | | (286) all_535_1 = all_415_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_245_0, all_257_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (215), (217) gives: % 44.26/6.87 | | | | | (287) all_257_0 = all_245_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_257_0, all_419_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (217), (257) gives: % 44.26/6.87 | | | | | (288) all_419_0 = all_257_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_419_0, all_451_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (257), (259) gives: % 44.26/6.87 | | | | | (289) all_451_0 = all_419_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_48_2, all_479_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (104), (261) gives: % 44.26/6.87 | | | | | (290) all_479_0 = all_48_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_245_0, all_479_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (215), (261) gives: % 44.26/6.87 | | | | | (291) all_479_0 = all_245_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_133_0, all_479_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (203), (261) gives: % 44.26/6.87 | | | | | (292) all_479_0 = all_133_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_451_0, all_507_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (259), (263) gives: % 44.26/6.87 | | | | | (293) all_507_0 = all_451_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_129_0, all_507_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (200), (263) gives: % 44.26/6.87 | | | | | (294) all_507_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_419_0, all_543_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (257), (272) gives: % 44.26/6.87 | | | | | (295) all_543_0 = all_419_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | GROUND_INST: instantiating (12) with all_394_0, all_543_0, all_7_0, % 44.26/6.87 | | | | | simplifying with (235), (272) gives: % 44.26/6.87 | | | | | (296) all_543_0 = all_394_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (295), (296) imply: % 44.26/6.87 | | | | | (297) all_419_0 = all_394_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (297) implies: % 44.26/6.87 | | | | | (298) all_419_0 = all_394_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (278), (279) imply: % 44.26/6.87 | | | | | (299) all_535_3 = all_411_3 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (299) implies: % 44.26/6.87 | | | | | (300) all_535_3 = all_411_3 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (279), (280) imply: % 44.26/6.87 | | | | | (301) all_411_3 = all_229_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (285), (286) imply: % 44.26/6.87 | | | | | (302) all_415_1 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (302) implies: % 44.26/6.87 | | | | | (303) all_415_1 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (277), (300) imply: % 44.26/6.87 | | | | | (304) all_411_3 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (304) implies: % 44.26/6.87 | | | | | (305) all_411_3 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (282), (283) imply: % 44.26/6.87 | | | | | (306) all_415_1 = all_405_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (306) implies: % 44.26/6.87 | | | | | (307) all_415_1 = all_405_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (283), (284) imply: % 44.26/6.87 | | | | | (308) all_405_0 = all_397_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (293), (294) imply: % 44.26/6.87 | | | | | (309) all_451_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (309) implies: % 44.26/6.87 | | | | | (310) all_451_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (291), (292) imply: % 44.26/6.87 | | | | | (311) all_245_0 = all_133_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (311) implies: % 44.26/6.87 | | | | | (312) all_245_0 = all_133_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (290), (292) imply: % 44.26/6.87 | | | | | (313) all_133_0 = all_48_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (289), (310) imply: % 44.26/6.87 | | | | | (314) all_419_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (314) implies: % 44.26/6.87 | | | | | (315) all_419_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (298), (315) imply: % 44.26/6.87 | | | | | (316) all_394_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (288), (298) imply: % 44.26/6.87 | | | | | (317) all_394_0 = all_257_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (303), (307) imply: % 44.26/6.87 | | | | | (318) all_405_0 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (318) implies: % 44.26/6.87 | | | | | (319) all_405_0 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (275), (276) imply: % 44.26/6.87 | | | | | (320) all_225_1 = all_209_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (320) implies: % 44.26/6.87 | | | | | (321) all_225_1 = all_209_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (274), (276) imply: % 44.26/6.87 | | | | | (322) all_209_1 = 0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (301), (305) imply: % 44.26/6.87 | | | | | (323) all_229_1 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (323) implies: % 44.26/6.87 | | | | | (324) all_229_1 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (308), (319) imply: % 44.26/6.87 | | | | | (325) all_397_0 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (325) implies: % 44.26/6.87 | | | | | (326) all_397_0 = all_7_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (316), (317) imply: % 44.26/6.87 | | | | | (327) all_257_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (327) implies: % 44.26/6.87 | | | | | (328) all_257_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (287), (328) imply: % 44.26/6.87 | | | | | (329) all_245_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (329) implies: % 44.26/6.87 | | | | | (330) all_245_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (312), (330) imply: % 44.26/6.87 | | | | | (331) all_133_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (331) implies: % 44.26/6.87 | | | | | (332) all_133_0 = all_129_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (273), (324) imply: % 44.26/6.87 | | | | | (333) all_225_1 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (333) implies: % 44.26/6.87 | | | | | (334) all_225_1 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (321), (334) imply: % 44.26/6.87 | | | | | (335) all_209_1 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | SIMP: (335) implies: % 44.26/6.87 | | | | | (336) all_209_1 = all_207_1 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (322), (336) imply: % 44.26/6.87 | | | | | (337) all_207_1 = 0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (313), (332) imply: % 44.26/6.87 | | | | | (338) all_129_0 = all_48_2 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | COMBINE_EQS: (324), (337) imply: % 44.26/6.87 | | | | | (339) all_229_1 = 0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | REDUCE: (202), (313) imply: % 44.26/6.87 | | | | | (340) h(all_48_2) = all_7_0 % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | BETA: splitting (213) gives: % 44.26/6.87 | | | | | % 44.26/6.87 | | | | | Case 1: % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | (341) ~ (all_229_1 = 0) % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | REDUCE: (339), (341) imply: % 44.26/6.87 | | | | | | (342) $false % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | CLOSE: (342) is inconsistent. % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | Case 2: % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | (343) all_229_0 = all_14_0 % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | COMBINE_EQS: (281), (343) imply: % 44.26/6.87 | | | | | | (344) all_48_2 = all_14_0 % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | SIMP: (344) implies: % 44.26/6.87 | | | | | | (345) all_48_2 = all_14_0 % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | REDUCE: (340), (345) imply: % 44.26/6.87 | | | | | | (346) h(all_14_0) = all_7_0 % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | GROUND_INST: instantiating (11) with all_7_2, all_7_0, all_14_0, % 44.26/6.87 | | | | | | simplifying with (153), (346) gives: % 44.26/6.87 | | | | | | (347) all_7_0 = all_7_2 % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | REDUCE: (16), (347) imply: % 44.26/6.87 | | | | | | (348) $false % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | | CLOSE: (348) is inconsistent. % 44.26/6.87 | | | | | | % 44.26/6.87 | | | | | End of split % 44.26/6.87 | | | | | % 44.26/6.87 | | | | End of split % 44.26/6.87 | | | | % 44.26/6.87 | | | End of split % 44.26/6.87 | | | % 44.26/6.87 | | End of split % 44.26/6.87 | | % 44.26/6.87 | End of split % 44.26/6.87 | % 44.26/6.87 End of proof % 44.26/6.87 % SZS output end Proof for theBenchmark % 44.26/6.87 % 44.26/6.87 6278ms %------------------------------------------------------------------------------