%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWX032+1 : TPTP v9.1.0. Released v9.1.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n028.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 : Tue Apr 1 02:15:29 AM UTC 2025 % Result : Theorem 151.74s 20.54s % Output : Proof 153.78s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWX032+1 : TPTP v9.1.0. Released v9.1.0. % 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n028.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 Mar 31 14:22:19 EDT 2025 % 0.12/0.34 % CPUTime : % 0.60/0.60 ________ _____ % 0.60/0.60 ___ __ \_________(_)________________________________ % 0.60/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.60/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.60/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.60/0.60 % 0.60/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.60/0.60 (2023-06-19) % 0.60/0.60 % 0.60/0.60 (c) Philipp Rümmer, 2009-2023 % 0.60/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.60/0.60 Amanda Stjerna. % 0.60/0.60 Free software under BSD-3-Clause. % 0.60/0.60 % 0.60/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.60/0.60 % 0.60/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.63/0.61 Running up to 7 provers in parallel. % 0.63/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.63/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.63/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.63/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.63/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.63/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.63/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.00/1.22 Prover 1: Preprocessing ... % 4.00/1.22 Prover 4: Preprocessing ... % 4.14/1.25 Prover 3: Preprocessing ... % 4.14/1.25 Prover 6: Preprocessing ... % 4.14/1.25 Prover 2: Preprocessing ... % 4.14/1.25 Prover 5: Preprocessing ... % 4.14/1.25 Prover 0: Preprocessing ... % 9.55/2.00 Prover 5: Proving ... % 10.25/2.08 Prover 1: Warning: ignoring some quantifiers % 10.37/2.10 Prover 4: Warning: ignoring some quantifiers % 10.37/2.11 Prover 1: Constructing countermodel ... % 10.52/2.12 Prover 3: Warning: ignoring some quantifiers % 10.52/2.15 Prover 2: Proving ... % 10.52/2.16 Prover 3: Constructing countermodel ... % 10.52/2.19 Prover 4: Constructing countermodel ... % 11.23/2.24 Prover 6: Proving ... % 11.23/2.26 Prover 0: Proving ... % 73.55/10.27 Prover 2: stopped % 73.55/10.27 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.91/10.34 Prover 7: Preprocessing ... % 75.37/10.51 Prover 7: Warning: ignoring some quantifiers % 75.37/10.53 Prover 7: Constructing countermodel ... % 102.20/13.96 Prover 5: stopped % 102.20/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 102.91/14.07 Prover 8: Preprocessing ... % 103.74/14.19 Prover 8: Warning: ignoring some quantifiers % 103.74/14.20 Prover 8: Constructing countermodel ... % 117.67/15.97 Prover 1: stopped % 117.67/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 117.67/16.01 Prover 9: Preprocessing ... % 119.32/16.17 Prover 9: Warning: ignoring some quantifiers % 119.43/16.18 Prover 9: Constructing countermodel ... % 131.76/17.87 Prover 6: stopped % 131.76/17.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 132.33/17.96 Prover 10: Preprocessing ... % 133.32/18.03 Prover 10: Warning: ignoring some quantifiers % 133.32/18.04 Prover 10: Constructing countermodel ... % 151.74/20.51 Prover 8: Found proof (size 4086) % 151.74/20.52 Prover 8: proved (6455ms) % 151.74/20.52 Prover 9: stopped % 151.74/20.52 Prover 3: stopped % 151.74/20.52 Prover 0: stopped % 151.74/20.52 Prover 10: stopped % 151.74/20.53 Prover 7: stopped % 151.74/20.53 Prover 4: stopped % 151.74/20.53 % 151.74/20.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 151.74/20.54 % 151.89/20.59 % SZS output start Proof for theBenchmark % 151.89/20.60 Assumptions after simplification: % 151.89/20.60 --------------------------------- % 151.89/20.60 % 151.89/20.60 (corollary-(plus:successor)) % 151.89/20.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, v1) = v3) % 151.89/20.63 | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? % 151.89/20.63 [v6: $i] : (@+(v0, v1) = v5 & nat_succeeds(v0) = v4 & s(v5) = v6 & $i(v6) & % 151.89/20.63 $i(v5) & ( ~ (v4 = 0) | v6 = v3))) % 151.89/20.63 % 151.89/20.63 (corollary-(plus:types)) % 151.89/20.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (@+(v0, v1) = v2) | ~ $i(v1) | % 151.89/20.63 ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : (nat_succeeds(v2) = % 151.89/20.63 v5 & nat_succeeds(v1) = v4 & nat_succeeds(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 % 151.89/20.63 = 0) | v5 = 0))) % 151.89/20.63 % 151.89/20.63 (corollary-(plus:zero)) % 151.89/20.63 $i(0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ % 151.89/20.63 $i(v0)) % 151.89/20.63 % 151.89/20.63 (id1) % 151.89/20.63 $i(0) & ! [v0: $i] : ( ~ (s(v0) = 0) | ~ $i(v0)) % 151.89/20.63 % 151.89/20.63 (id2) % 151.89/20.63 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | ~ % 151.89/20.63 (s(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 151.89/20.63 % 151.89/20.63 (id27) % 151.89/20.64 $i(0) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (nat_succeeds(v0) = v1) | ~ % 151.89/20.64 $i(v0) | ( ~ (v0 = 0) & ! [v2: $i] : ( ~ (nat_succeeds(v2) = 0) | ~ $i(v2) % 151.89/20.64 | ? [v3: $i] : ( ~ (v3 = v0) & s(v2) = v3 & $i(v3))))) & ! [v0: $i] : % 151.89/20.64 (v0 = 0 | ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: $i] : % 151.89/20.64 (nat_succeeds(v1) = 0 & s(v1) = v0 & $i(v1))) % 151.89/20.64 % 151.89/20.64 (id3) % 151.89/20.64 gr(0) = 0 & $i(0) % 151.89/20.64 % 151.89/20.64 (id4) % 151.89/20.64 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (gr(v0) = v1) | ~ $i(v0) | ? [v2: % 151.89/20.64 $i] : ? [v3: int] : ( ~ (v3 = 0) & gr(v2) = v3 & s(v0) = v2 & $i(v2))) & % 151.89/20.64 ! [v0: $i] : ( ~ (gr(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (gr(v1) = 0 & s(v0) % 151.89/20.64 = v1 & $i(v1))) % 151.89/20.64 % 151.89/20.64 (induction) % 152.19/20.65 $i(0) & ( ? [v0: $i] : ($i(v0) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 152.19/20.65 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & @+(v3, v2) = v4 & % 152.19/20.65 @+(v1, v2) = v5 & @+(v0, v5) = v6 & @+(v0, v1) = v3 & nat_succeeds(v2) = % 152.19/20.65 0 & nat_succeeds(v1) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 152.19/20.65 $i(v1)) & (v0 = 0 | ? [v1: $i] : (nat_succeeds(v1) = 0 & s(v1) = v0 & % 152.19/20.65 $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ % 152.19/20.65 (@+(v4, v3) = v5) | ~ (@+(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | % 152.19/20.65 ? [v6: any] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (@+(v2, v3) % 152.19/20.65 = v8 & @+(v1, v8) = v9 & nat_succeeds(v3) = v6 & nat_succeeds(v2) % 152.19/20.65 = v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = % 152.19/20.65 v5)))))) | ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) % 152.19/20.65 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (@+(v3, v2) % 152.19/20.65 = v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? [v5: any] : % 152.19/20.65 ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (@+(v1, v2) = v7 & @+(v0, v7) % 152.19/20.65 = v8 & nat_succeeds(v2) = v5 & nat_succeeds(v1) = v6 & $i(v8) & $i(v7) % 152.19/20.65 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4))))) % 152.19/20.65 % 152.19/20.65 (theorem-(plus:associative)) % 152.19/20.65 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 152.19/20.65 $i] : ? [v6: $i] : ( ~ (v6 = v4) & @+(v3, v2) = v4 & @+(v1, v2) = v5 & % 152.19/20.65 @+(v0, v5) = v6 & @+(v0, v1) = v3 & nat_succeeds(v2) = 0 & nat_succeeds(v1) % 152.19/20.65 = 0 & nat_succeeds(v0) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 152.19/20.65 $i(v1) & $i(v0)) % 152.19/20.65 % 152.19/20.65 (function-axioms) % 152.19/20.66 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 152.19/20.66 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (plus_terminates(v4, v3, v2) = v1) | ~ % 152.19/20.66 (plus_terminates(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 152.19/20.66 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 152.19/20.66 (plus_fails(v4, v3, v2) = v1) | ~ (plus_fails(v4, v3, v2) = v0)) & ! [v0: % 152.19/20.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 152.19/20.66 : ! [v4: $i] : (v1 = v0 | ~ (plus_succeeds(v4, v3, v2) = v1) | ~ % 152.19/20.66 (plus_succeeds(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 152.19/20.66 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 152.19/20.66 (times_terminates(v4, v3, v2) = v1) | ~ (times_terminates(v4, v3, v2) = % 152.19/20.66 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 152.19/20.66 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (times_succeeds(v4, v3, v2) % 152.19/20.66 = v1) | ~ (times_succeeds(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] % 152.19/20.66 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = % 152.19/20.66 v0 | ~ (times_fails(v4, v3, v2) = v1) | ~ (times_fails(v4, v3, v2) = v0)) % 152.19/20.66 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.19/20.66 (@*(v3, v2) = v1) | ~ (@*(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 152.19/20.66 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (@+(v3, v2) = v1) | ~ (@+(v3, v2) = % 152.19/20.66 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 152.19/20.66 $i] : ! [v3: $i] : (v1 = v0 | ~ (@<_terminates(v3, v2) = v1) | ~ % 152.19/20.66 (@<_terminates(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 152.19/20.66 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.19/20.66 (@<_succeeds(v3, v2) = v1) | ~ (@<_succeeds(v3, v2) = v0)) & ! [v0: % 152.19/20.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 152.19/20.66 : (v1 = v0 | ~ (@<_fails(v3, v2) = v1) | ~ (@<_fails(v3, v2) = v0)) & ! % 152.19/20.66 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 152.19/20.66 $i] : (v1 = v0 | ~ (@=<_terminates(v3, v2) = v1) | ~ (@=<_terminates(v3, % 152.19/20.66 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : % 152.19/20.66 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (@=<_succeeds(v3, v2) = v1) | ~ % 152.19/20.66 (@=<_succeeds(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 152.19/20.66 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.19/20.66 (@=<_fails(v3, v2) = v1) | ~ (@=<_fails(v3, v2) = v0)) & ! [v0: % 152.19/20.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 152.19/20.66 ~ (nat_terminates(v2) = v1) | ~ (nat_terminates(v2) = v0)) & ! [v0: % 152.19/20.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 152.19/20.66 ~ (nat_fails(v2) = v1) | ~ (nat_fails(v2) = v0)) & ! [v0: % 152.19/20.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 152.19/20.66 ~ (nat_succeeds(v2) = v1) | ~ (nat_succeeds(v2) = v0)) & ! [v0: % 152.19/20.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 152.19/20.66 ~ (gr(v2) = v1) | ~ (gr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 152.19/20.66 $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ (s(v2) = v0)) & ? [v0: $i] : ? [v1: % 152.19/20.66 $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : (plus_terminates(v2, v1, % 152.19/20.66 v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 152.19/20.66 MultipleValueBool] : (plus_fails(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: % 152.19/20.66 $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : (plus_succeeds(v2, v1, v0) % 152.19/20.66 = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] % 152.19/20.66 : (times_terminates(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 152.19/20.66 $i] : ? [v3: MultipleValueBool] : (times_succeeds(v2, v1, v0) = v3) & ? % 152.19/20.66 [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: MultipleValueBool] : % 152.19/20.66 (times_fails(v2, v1, v0) = v3) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 152.19/20.66 MultipleValueBool] : (@<_terminates(v1, v0) = v2) & ? [v0: $i] : ? [v1: % 152.19/20.66 $i] : ? [v2: MultipleValueBool] : (@<_succeeds(v1, v0) = v2) & ? [v0: $i] % 152.19/20.66 : ? [v1: $i] : ? [v2: MultipleValueBool] : (@<_fails(v1, v0) = v2) & ? [v0: % 152.19/20.66 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (@=<_terminates(v1, v0) = % 152.19/20.66 v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : % 152.19/20.66 (@=<_succeeds(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 152.19/20.66 MultipleValueBool] : (@=<_fails(v1, v0) = v2) & ? [v0: $i] : ? [v1: $i] : % 152.19/20.66 ? [v2: $i] : (@*(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 152.19/20.66 $i] : (@+(v1, v0) = v2 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] % 152.19/20.66 : (nat_terminates(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 152.19/20.66 (nat_fails(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : % 152.19/20.66 (nat_succeeds(v0) = v1) & ? [v0: $i] : ? [v1: MultipleValueBool] : (gr(v0) = % 152.19/20.66 v1) & ? [v0: $i] : ? [v1: $i] : (s(v0) = v1 & $i(v1)) % 152.19/20.66 % 152.19/20.66 Further assumptions not needed in the proof: % 152.19/20.66 -------------------------------------------- % 152.19/20.66 (@*)/2, (@+)/2, id10, id11, id12, id13, id14, id15, id16, id17, id18, id19, % 152.19/20.66 id20, id21, id22, id23, id24, id25, id26, id28, id29, id5, id6, id7, id8, id9, % 152.19/20.66 lemma-(nat:ground), lemma-(nat:termination), lemma-(plus:existence), % 152.19/20.66 lemma-(plus:ground:1), lemma-(plus:ground:2), lemma-(plus:ground:3), % 152.19/20.66 lemma-(plus:termination:1), lemma-(plus:termination:2), % 152.19/20.66 lemma-(plus:termination:3), lemma-(plus:types:1), lemma-(plus:types:2), % 152.19/20.66 lemma-(plus:types:3), lemma-(plus:uniqueness) % 152.19/20.66 % 152.19/20.66 Those formulas are unsatisfiable: % 152.19/20.66 --------------------------------- % 152.19/20.66 % 152.19/20.66 Begin of proof % 152.19/20.66 | % 152.19/20.66 | ALPHA: (id1) implies: % 152.19/20.66 | (1) ! [v0: $i] : ( ~ (s(v0) = 0) | ~ $i(v0)) % 152.19/20.66 | % 152.19/20.66 | ALPHA: (id3) implies: % 152.19/20.66 | (2) gr(0) = 0 % 152.19/20.66 | % 152.19/20.66 | ALPHA: (id4) implies: % 152.19/20.66 | (3) ! [v0: $i] : ( ~ (gr(v0) = 0) | ~ $i(v0) | ? [v1: $i] : (gr(v1) = 0 % 152.19/20.66 | & s(v0) = v1 & $i(v1))) % 152.19/20.66 | % 152.19/20.66 | ALPHA: (id27) implies: % 152.19/20.67 | (4) ! [v0: $i] : (v0 = 0 | ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 152.19/20.67 | $i] : (nat_succeeds(v1) = 0 & s(v1) = v0 & $i(v1))) % 152.19/20.67 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (nat_succeeds(v0) = v1) | ~ % 152.19/20.67 | $i(v0) | ( ~ (v0 = 0) & ! [v2: $i] : ( ~ (nat_succeeds(v2) = 0) | ~ % 152.19/20.67 | $i(v2) | ? [v3: $i] : ( ~ (v3 = v0) & s(v2) = v3 & $i(v3))))) % 152.19/20.67 | % 152.19/20.67 | ALPHA: (corollary-(plus:zero)) implies: % 152.19/20.67 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ $i(v0)) % 152.19/20.67 | % 152.19/20.67 | ALPHA: (induction) implies: % 152.19/20.67 | (7) $i(0) % 152.19/20.67 | (8) ? [v0: $i] : ($i(v0) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? % 152.19/20.67 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & @+(v3, v2) = % 152.19/20.67 | v4 & @+(v1, v2) = v5 & @+(v0, v5) = v6 & @+(v0, v1) = v3 & % 152.19/20.67 | nat_succeeds(v2) = 0 & nat_succeeds(v1) = 0 & $i(v6) & $i(v5) & % 152.19/20.67 | $i(v4) & $i(v3) & $i(v2) & $i(v1)) & (v0 = 0 | ? [v1: $i] : % 152.19/20.67 | (nat_succeeds(v1) = 0 & s(v1) = v0 & $i(v1) & ! [v2: $i] : ! [v3: % 152.19/20.67 | $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (@+(v4, v3) = v5) | ~ % 152.19/20.67 | (@+(v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? % 152.19/20.67 | [v7: any] : ? [v8: $i] : ? [v9: $i] : (@+(v2, v3) = v8 & % 152.19/20.67 | @+(v1, v8) = v9 & nat_succeeds(v3) = v6 & nat_succeeds(v2) = % 152.19/20.67 | v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = % 152.19/20.67 | v5)))))) | ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 152.19/20.67 | $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 152.19/20.67 | (@+(v3, v2) = v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 152.19/20.67 | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (@+(v1, % 152.19/20.67 | v2) = v7 & @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & % 152.19/20.67 | nat_succeeds(v1) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 152.19/20.67 | 0) | v8 = v4)))) % 152.19/20.67 | % 152.19/20.67 | ALPHA: (function-axioms) implies: % 152.19/20.67 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 152.19/20.67 | ~ (s(v2) = v0)) % 152.19/20.67 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 152.19/20.67 | : (v1 = v0 | ~ (nat_succeeds(v2) = v1) | ~ (nat_succeeds(v2) = v0)) % 152.19/20.67 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 152.19/20.67 | (@+(v3, v2) = v1) | ~ (@+(v3, v2) = v0)) % 152.19/20.67 | % 152.19/20.67 | DELTA: instantiating (theorem-(plus:associative)) with fresh symbols all_89_0, % 152.19/20.67 | all_89_1, all_89_2, all_89_3, all_89_4, all_89_5, all_89_6 gives: % 152.19/20.68 | (12) ~ (all_89_0 = all_89_2) & @+(all_89_3, all_89_4) = all_89_2 & % 152.19/20.68 | @+(all_89_5, all_89_4) = all_89_1 & @+(all_89_6, all_89_1) = all_89_0 % 152.19/20.68 | & @+(all_89_6, all_89_5) = all_89_3 & nat_succeeds(all_89_4) = 0 & % 152.19/20.68 | nat_succeeds(all_89_5) = 0 & nat_succeeds(all_89_6) = 0 & $i(all_89_0) % 152.19/20.68 | & $i(all_89_1) & $i(all_89_2) & $i(all_89_3) & $i(all_89_4) & % 152.19/20.68 | $i(all_89_5) & $i(all_89_6) % 152.19/20.68 | % 152.19/20.68 | ALPHA: (12) implies: % 152.19/20.68 | (13) ~ (all_89_0 = all_89_2) % 152.19/20.68 | (14) $i(all_89_6) % 152.19/20.68 | (15) $i(all_89_5) % 152.19/20.68 | (16) $i(all_89_4) % 152.19/20.68 | (17) $i(all_89_3) % 152.19/20.68 | (18) $i(all_89_2) % 152.19/20.68 | (19) $i(all_89_1) % 152.19/20.68 | (20) $i(all_89_0) % 152.19/20.68 | (21) nat_succeeds(all_89_6) = 0 % 152.19/20.68 | (22) nat_succeeds(all_89_5) = 0 % 152.19/20.68 | (23) nat_succeeds(all_89_4) = 0 % 152.19/20.68 | (24) @+(all_89_6, all_89_5) = all_89_3 % 152.19/20.68 | (25) @+(all_89_6, all_89_1) = all_89_0 % 152.19/20.68 | (26) @+(all_89_5, all_89_4) = all_89_1 % 152.19/20.68 | (27) @+(all_89_3, all_89_4) = all_89_2 % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (3) with 0, simplifying with (2), (7) gives: % 152.19/20.68 | (28) ? [v0: $i] : (gr(v0) = 0 & s(0) = v0 & $i(v0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (4) with all_89_6, simplifying with (14), (21) % 152.19/20.68 | gives: % 152.19/20.68 | (29) all_89_6 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_89_6 % 152.19/20.68 | & $i(v0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (4) with all_89_5, simplifying with (15), (22) % 152.19/20.68 | gives: % 152.19/20.68 | (30) all_89_5 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_89_5 % 152.19/20.68 | & $i(v0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (4) with all_89_4, simplifying with (16), (23) % 152.19/20.68 | gives: % 152.19/20.68 | (31) all_89_4 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_89_4 % 152.19/20.68 | & $i(v0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (corollary-(plus:types)) with all_89_6, all_89_5, % 152.19/20.68 | all_89_3, simplifying with (14), (15), (24) gives: % 152.19/20.68 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (nat_succeeds(all_89_3) = % 152.19/20.68 | v2 & nat_succeeds(all_89_5) = v1 & nat_succeeds(all_89_6) = v0 & ( ~ % 152.19/20.68 | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (corollary-(plus:types)) with all_89_6, all_89_1, % 152.19/20.68 | all_89_0, simplifying with (14), (19), (25) gives: % 152.19/20.68 | (33) ? [v0: any] : ? [v1: any] : ? [v2: any] : (nat_succeeds(all_89_0) = % 152.19/20.68 | v2 & nat_succeeds(all_89_1) = v1 & nat_succeeds(all_89_6) = v0 & ( ~ % 152.19/20.68 | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (corollary-(plus:types)) with all_89_5, all_89_4, % 152.19/20.68 | all_89_1, simplifying with (15), (16), (26) gives: % 152.19/20.68 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : (nat_succeeds(all_89_1) = % 152.19/20.68 | v2 & nat_succeeds(all_89_4) = v1 & nat_succeeds(all_89_5) = v0 & ( ~ % 152.19/20.68 | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.19/20.68 | % 152.19/20.68 | GROUND_INST: instantiating (corollary-(plus:types)) with all_89_3, all_89_4, % 152.19/20.68 | all_89_2, simplifying with (16), (17), (27) gives: % 152.19/20.69 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : (nat_succeeds(all_89_2) = % 152.19/20.69 | v2 & nat_succeeds(all_89_3) = v0 & nat_succeeds(all_89_4) = v1 & ( ~ % 152.19/20.69 | (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.19/20.69 | % 152.19/20.69 | DELTA: instantiating (28) with fresh symbol all_96_0 gives: % 152.19/20.69 | (36) gr(all_96_0) = 0 & s(0) = all_96_0 & $i(all_96_0) % 152.19/20.69 | % 152.19/20.69 | ALPHA: (36) implies: % 152.19/20.69 | (37) s(0) = all_96_0 % 152.19/20.69 | % 152.19/20.69 | DELTA: instantiating (35) with fresh symbols all_98_0, all_98_1, all_98_2 % 152.19/20.69 | gives: % 152.19/20.69 | (38) nat_succeeds(all_89_2) = all_98_0 & nat_succeeds(all_89_3) = all_98_2 % 152.19/20.69 | & nat_succeeds(all_89_4) = all_98_1 & ( ~ (all_98_1 = 0) | ~ % 152.19/20.69 | (all_98_2 = 0) | all_98_0 = 0) % 152.19/20.69 | % 152.19/20.69 | ALPHA: (38) implies: % 152.19/20.69 | (39) nat_succeeds(all_89_4) = all_98_1 % 152.19/20.69 | (40) nat_succeeds(all_89_3) = all_98_2 % 152.19/20.69 | (41) nat_succeeds(all_89_2) = all_98_0 % 152.19/20.69 | (42) ~ (all_98_1 = 0) | ~ (all_98_2 = 0) | all_98_0 = 0 % 152.19/20.69 | % 152.19/20.69 | DELTA: instantiating (34) with fresh symbols all_100_0, all_100_1, all_100_2 % 152.19/20.69 | gives: % 152.19/20.69 | (43) nat_succeeds(all_89_1) = all_100_0 & nat_succeeds(all_89_4) = % 152.19/20.69 | all_100_1 & nat_succeeds(all_89_5) = all_100_2 & ( ~ (all_100_1 = 0) | % 152.19/20.69 | ~ (all_100_2 = 0) | all_100_0 = 0) % 152.19/20.69 | % 152.19/20.69 | ALPHA: (43) implies: % 152.42/20.69 | (44) nat_succeeds(all_89_5) = all_100_2 % 152.42/20.69 | (45) nat_succeeds(all_89_4) = all_100_1 % 152.42/20.69 | (46) nat_succeeds(all_89_1) = all_100_0 % 152.42/20.69 | (47) ~ (all_100_1 = 0) | ~ (all_100_2 = 0) | all_100_0 = 0 % 152.42/20.69 | % 152.42/20.69 | DELTA: instantiating (33) with fresh symbols all_102_0, all_102_1, all_102_2 % 152.42/20.69 | gives: % 152.42/20.69 | (48) nat_succeeds(all_89_0) = all_102_0 & nat_succeeds(all_89_1) = % 152.42/20.69 | all_102_1 & nat_succeeds(all_89_6) = all_102_2 & ( ~ (all_102_1 = 0) | % 152.42/20.69 | ~ (all_102_2 = 0) | all_102_0 = 0) % 152.42/20.69 | % 152.42/20.69 | ALPHA: (48) implies: % 152.42/20.69 | (49) nat_succeeds(all_89_6) = all_102_2 % 152.42/20.69 | (50) nat_succeeds(all_89_1) = all_102_1 % 152.42/20.69 | (51) nat_succeeds(all_89_0) = all_102_0 % 152.42/20.69 | (52) ~ (all_102_1 = 0) | ~ (all_102_2 = 0) | all_102_0 = 0 % 152.42/20.69 | % 152.42/20.69 | DELTA: instantiating (32) with fresh symbols all_104_0, all_104_1, all_104_2 % 152.42/20.69 | gives: % 152.42/20.69 | (53) nat_succeeds(all_89_3) = all_104_0 & nat_succeeds(all_89_5) = % 152.42/20.69 | all_104_1 & nat_succeeds(all_89_6) = all_104_2 & ( ~ (all_104_1 = 0) | % 152.42/20.69 | ~ (all_104_2 = 0) | all_104_0 = 0) % 152.42/20.69 | % 152.42/20.69 | ALPHA: (53) implies: % 152.42/20.69 | (54) nat_succeeds(all_89_6) = all_104_2 % 152.42/20.69 | (55) nat_succeeds(all_89_5) = all_104_1 % 152.42/20.69 | (56) nat_succeeds(all_89_3) = all_104_0 % 152.42/20.69 | (57) ~ (all_104_1 = 0) | ~ (all_104_2 = 0) | all_104_0 = 0 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with 0, all_104_2, all_89_6, simplifying with % 152.42/20.69 | (21), (54) gives: % 152.42/20.69 | (58) all_104_2 = 0 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with all_102_2, all_104_2, all_89_6, % 152.42/20.69 | simplifying with (49), (54) gives: % 152.42/20.69 | (59) all_104_2 = all_102_2 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with 0, all_104_1, all_89_5, simplifying with % 152.42/20.69 | (22), (55) gives: % 152.42/20.69 | (60) all_104_1 = 0 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with all_100_2, all_104_1, all_89_5, % 152.42/20.69 | simplifying with (44), (55) gives: % 152.42/20.69 | (61) all_104_1 = all_100_2 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with 0, all_100_1, all_89_4, simplifying with % 152.42/20.69 | (23), (45) gives: % 152.42/20.69 | (62) all_100_1 = 0 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with all_98_1, all_100_1, all_89_4, % 152.42/20.69 | simplifying with (39), (45) gives: % 152.42/20.69 | (63) all_100_1 = all_98_1 % 152.42/20.69 | % 152.42/20.69 | GROUND_INST: instantiating (10) with all_98_2, all_104_0, all_89_3, % 152.42/20.69 | simplifying with (40), (56) gives: % 152.42/20.69 | (64) all_104_0 = all_98_2 % 152.42/20.69 | % 152.42/20.70 | GROUND_INST: instantiating (10) with all_100_0, all_102_1, all_89_1, % 152.42/20.70 | simplifying with (46), (50) gives: % 152.42/20.70 | (65) all_102_1 = all_100_0 % 152.42/20.70 | % 152.42/20.70 | COMBINE_EQS: (60), (61) imply: % 152.42/20.70 | (66) all_100_2 = 0 % 152.42/20.70 | % 152.42/20.70 | COMBINE_EQS: (58), (59) imply: % 152.42/20.70 | (67) all_102_2 = 0 % 152.42/20.70 | % 152.42/20.70 | COMBINE_EQS: (62), (63) imply: % 152.42/20.70 | (68) all_98_1 = 0 % 152.42/20.70 | % 152.42/20.70 | SIMP: (68) implies: % 152.42/20.70 | (69) all_98_1 = 0 % 152.42/20.70 | % 152.42/20.70 | BETA: splitting (57) gives: % 152.42/20.70 | % 152.42/20.70 | Case 1: % 152.42/20.70 | | % 152.42/20.70 | | (70) ~ (all_104_1 = 0) % 152.42/20.70 | | % 152.42/20.70 | | REDUCE: (60), (70) imply: % 152.42/20.70 | | (71) $false % 152.42/20.70 | | % 152.42/20.70 | | CLOSE: (71) is inconsistent. % 152.42/20.70 | | % 152.42/20.70 | Case 2: % 152.42/20.70 | | % 152.42/20.70 | | (72) ~ (all_104_2 = 0) | all_104_0 = 0 % 152.42/20.70 | | % 152.42/20.70 | | BETA: splitting (47) gives: % 152.42/20.70 | | % 152.42/20.70 | | Case 1: % 152.42/20.70 | | | % 152.42/20.70 | | | (73) ~ (all_100_1 = 0) % 152.42/20.70 | | | % 152.42/20.70 | | | REDUCE: (62), (73) imply: % 152.42/20.70 | | | (74) $false % 152.42/20.70 | | | % 152.42/20.70 | | | CLOSE: (74) is inconsistent. % 152.42/20.70 | | | % 152.42/20.70 | | Case 2: % 152.42/20.70 | | | % 152.42/20.70 | | | (75) ~ (all_100_2 = 0) | all_100_0 = 0 % 152.42/20.70 | | | % 152.42/20.70 | | | BETA: splitting (75) gives: % 152.42/20.70 | | | % 152.42/20.70 | | | Case 1: % 152.42/20.70 | | | | % 152.42/20.70 | | | | (76) ~ (all_100_2 = 0) % 152.42/20.70 | | | | % 152.42/20.70 | | | | REDUCE: (66), (76) imply: % 152.42/20.70 | | | | (77) $false % 152.42/20.70 | | | | % 152.42/20.70 | | | | CLOSE: (77) is inconsistent. % 152.42/20.70 | | | | % 152.42/20.70 | | | Case 2: % 152.42/20.70 | | | | % 152.42/20.70 | | | | (78) all_100_0 = 0 % 152.42/20.70 | | | | % 152.42/20.70 | | | | COMBINE_EQS: (65), (78) imply: % 152.42/20.70 | | | | (79) all_102_1 = 0 % 152.42/20.70 | | | | % 152.42/20.70 | | | | REDUCE: (46), (78) imply: % 152.42/20.70 | | | | (80) nat_succeeds(all_89_1) = 0 % 152.42/20.70 | | | | % 152.42/20.70 | | | | BETA: splitting (72) gives: % 152.42/20.70 | | | | % 152.42/20.70 | | | | Case 1: % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | (81) ~ (all_104_2 = 0) % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | REDUCE: (58), (81) imply: % 152.42/20.70 | | | | | (82) $false % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | CLOSE: (82) is inconsistent. % 152.42/20.70 | | | | | % 152.42/20.70 | | | | Case 2: % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | (83) all_104_0 = 0 % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | COMBINE_EQS: (64), (83) imply: % 152.42/20.70 | | | | | (84) all_98_2 = 0 % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | REDUCE: (40), (84) imply: % 152.42/20.70 | | | | | (85) nat_succeeds(all_89_3) = 0 % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | BETA: splitting (52) gives: % 152.42/20.70 | | | | | % 152.42/20.70 | | | | | Case 1: % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | | (86) ~ (all_102_1 = 0) % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | | REDUCE: (79), (86) imply: % 152.42/20.70 | | | | | | (87) $false % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | | CLOSE: (87) is inconsistent. % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | Case 2: % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | | (88) ~ (all_102_2 = 0) | all_102_0 = 0 % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | | BETA: splitting (88) gives: % 152.42/20.70 | | | | | | % 152.42/20.70 | | | | | | Case 1: % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | (89) ~ (all_102_2 = 0) % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | REDUCE: (67), (89) imply: % 152.42/20.70 | | | | | | | (90) $false % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | CLOSE: (90) is inconsistent. % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | Case 2: % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | (91) all_102_0 = 0 % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | REDUCE: (51), (91) imply: % 152.42/20.70 | | | | | | | (92) nat_succeeds(all_89_0) = 0 % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | BETA: splitting (42) gives: % 152.42/20.70 | | | | | | | % 152.42/20.70 | | | | | | | Case 1: % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | | (93) ~ (all_98_1 = 0) % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | | REDUCE: (69), (93) imply: % 152.42/20.70 | | | | | | | | (94) $false % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | | CLOSE: (94) is inconsistent. % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | Case 2: % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | | (95) ~ (all_98_2 = 0) | all_98_0 = 0 % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | | BETA: splitting (95) gives: % 152.42/20.70 | | | | | | | | % 152.42/20.70 | | | | | | | | Case 1: % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | | (96) ~ (all_98_2 = 0) % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | | REDUCE: (84), (96) imply: % 152.42/20.70 | | | | | | | | | (97) $false % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | | CLOSE: (97) is inconsistent. % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | Case 2: % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | | (98) all_98_0 = 0 % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | | REDUCE: (41), (98) imply: % 152.42/20.70 | | | | | | | | | (99) nat_succeeds(all_89_2) = 0 % 152.42/20.70 | | | | | | | | | % 152.42/20.70 | | | | | | | | | GROUND_INST: instantiating (4) with all_89_3, simplifying with % 152.42/20.70 | | | | | | | | | (17), (85) gives: % 152.42/20.71 | | | | | | | | | (100) all_89_3 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & % 152.42/20.71 | | | | | | | | | s(v0) = all_89_3 & $i(v0)) % 152.42/20.71 | | | | | | | | | % 152.42/20.71 | | | | | | | | | GROUND_INST: instantiating (4) with all_89_2, simplifying with % 152.42/20.71 | | | | | | | | | (18), (99) gives: % 152.42/20.71 | | | | | | | | | (101) all_89_2 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & % 152.42/20.71 | | | | | | | | | s(v0) = all_89_2 & $i(v0)) % 152.42/20.71 | | | | | | | | | % 152.42/20.71 | | | | | | | | | GROUND_INST: instantiating (4) with all_89_1, simplifying with % 152.42/20.71 | | | | | | | | | (19), (80) gives: % 152.42/20.71 | | | | | | | | | (102) all_89_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & % 152.42/20.71 | | | | | | | | | s(v0) = all_89_1 & $i(v0)) % 152.42/20.71 | | | | | | | | | % 152.42/20.71 | | | | | | | | | GROUND_INST: instantiating (4) with all_89_0, simplifying with % 152.42/20.71 | | | | | | | | | (20), (92) gives: % 152.42/20.71 | | | | | | | | | (103) all_89_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & % 152.42/20.71 | | | | | | | | | s(v0) = all_89_0 & $i(v0)) % 152.42/20.71 | | | | | | | | | % 152.42/20.71 | | | | | | | | | BETA: splitting (8) gives: % 152.42/20.71 | | | | | | | | | % 152.42/20.71 | | | | | | | | | Case 1: % 152.42/20.71 | | | | | | | | | | % 152.42/20.71 | | | | | | | | | | (104) ? [v0: $i] : ($i(v0) & ? [v1: $i] : ? [v2: $i] : % 152.42/20.71 | | | | | | | | | | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: % 152.42/20.71 | | | | | | | | | | $i] : ( ~ (v6 = v4) & @+(v3, v2) = v4 & @+(v1, % 152.42/20.71 | | | | | | | | | | v2) = v5 & @+(v0, v5) = v6 & @+(v0, v1) = v3 % 152.42/20.71 | | | | | | | | | | & nat_succeeds(v2) = 0 & nat_succeeds(v1) = 0 & % 152.42/20.71 | | | | | | | | | | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & % 152.42/20.71 | | | | | | | | | | $i(v1)) & (v0 = 0 | ? [v1: $i] : % 152.42/20.71 | | | | | | | | | | (nat_succeeds(v1) = 0 & s(v1) = v0 & $i(v1) & % 152.42/20.71 | | | | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! % 152.42/20.71 | | | | | | | | | | [v5: $i] : ( ~ (@+(v4, v3) = v5) | ~ (@+(v1, % 152.42/20.71 | | | | | | | | | | v2) = v4) | ~ $i(v3) | ~ $i(v2) | ? % 152.42/20.71 | | | | | | | | | | [v6: any] : ? [v7: any] : ? [v8: $i] : ? % 152.42/20.71 | | | | | | | | | | [v9: $i] : (@+(v2, v3) = v8 & @+(v1, v8) = % 152.42/20.71 | | | | | | | | | | v9 & nat_succeeds(v3) = v6 & % 152.42/20.71 | | | | | | | | | | nat_succeeds(v2) = v7 & $i(v9) & $i(v8) & % 152.42/20.71 | | | | | | | | | | ( ~ (v7 = 0) | ~ (v6 = 0) | v9 = % 152.42/20.71 | | | | | | | | | | v5)))))) % 152.42/20.71 | | | | | | | | | | % 152.42/20.71 | | | | | | | | | | DELTA: instantiating (104) with fresh symbol all_154_0 % 152.42/20.71 | | | | | | | | | | gives: % 152.42/20.72 | | | | | | | | | | (105) $i(all_154_0) & ? [v0: $i] : ? [v1: $i] : ? [v2: % 152.42/20.72 | | | | | | | | | | $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( % 152.42/20.72 | | | | | | | | | | ~ (v5 = v3) & @+(v2, v1) = v3 & @+(v0, v1) = v4 & % 152.42/20.72 | | | | | | | | | | @+(all_154_0, v4) = v5 & @+(all_154_0, v0) = v2 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(v1) = 0 & nat_succeeds(v0) = 0 & % 152.42/20.72 | | | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 152.42/20.72 | | | | | | | | | | $i(v0)) & (all_154_0 = 0 | ? [v0: $i] : % 152.42/20.72 | | | | | | | | | | (nat_succeeds(v0) = 0 & s(v0) = all_154_0 & % 152.42/20.72 | | | | | | | | | | $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: % 152.42/20.72 | | | | | | | | | | $i] : ! [v4: $i] : ( ~ (@+(v3, v2) = v4) | % 152.42/20.72 | | | | | | | | | | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 152.42/20.72 | | | | | | | | | | ? [v5: any] : ? [v6: any] : ? [v7: $i] : % 152.42/20.72 | | | | | | | | | | ? [v8: $i] : (@+(v1, v2) = v7 & @+(v0, v7) = % 152.42/20.72 | | | | | | | | | | v8 & nat_succeeds(v2) = v5 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(v1) = v6 & $i(v8) & $i(v7) & ( % 152.42/20.72 | | | | | | | | | | ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4))))) % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | ALPHA: (105) implies: % 152.42/20.72 | | | | | | | | | | (106) $i(all_154_0) % 152.42/20.72 | | | | | | | | | | (107) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 % 152.42/20.72 | | | | | | | | | | & s(v0) = all_154_0 & $i(v0) & ! [v1: $i] : ! % 152.42/20.72 | | | | | | | | | | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 152.42/20.72 | | | | | | | | | | (@+(v3, v2) = v4) | ~ (@+(v0, v1) = v3) | ~ % 152.42/20.72 | | | | | | | | | | $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: % 152.42/20.72 | | | | | | | | | | any] : ? [v7: $i] : ? [v8: $i] : (@+(v1, % 152.42/20.72 | | | | | | | | | | v2) = v7 & @+(v0, v7) = v8 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(v2) = v5 & nat_succeeds(v1) = v6 % 152.42/20.72 | | | | | | | | | | & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = % 152.42/20.72 | | | | | | | | | | 0) | v8 = v4)))) % 152.42/20.72 | | | | | | | | | | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: % 152.42/20.72 | | | | | | | | | | $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v3) & % 152.42/20.72 | | | | | | | | | | @+(v2, v1) = v3 & @+(v0, v1) = v4 & @+(all_154_0, % 152.42/20.72 | | | | | | | | | | v4) = v5 & @+(all_154_0, v0) = v2 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(v1) = 0 & nat_succeeds(v0) = 0 & % 152.42/20.72 | | | | | | | | | | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 152.42/20.72 | | | | | | | | | | $i(v0)) % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | DELTA: instantiating (108) with fresh symbols all_156_0, % 152.42/20.72 | | | | | | | | | | all_156_1, all_156_2, all_156_3, all_156_4, all_156_5 % 152.42/20.72 | | | | | | | | | | gives: % 152.42/20.72 | | | | | | | | | | (109) ~ (all_156_0 = all_156_2) & @+(all_156_3, % 152.42/20.72 | | | | | | | | | | all_156_4) = all_156_2 & @+(all_156_5, all_156_4) % 152.42/20.72 | | | | | | | | | | = all_156_1 & @+(all_154_0, all_156_1) = all_156_0 % 152.42/20.72 | | | | | | | | | | & @+(all_154_0, all_156_5) = all_156_3 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(all_156_4) = 0 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(all_156_5) = 0 & $i(all_156_0) & % 152.42/20.72 | | | | | | | | | | $i(all_156_1) & $i(all_156_2) & $i(all_156_3) & % 152.42/20.72 | | | | | | | | | | $i(all_156_4) & $i(all_156_5) % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | ALPHA: (109) implies: % 152.42/20.72 | | | | | | | | | | (110) ~ (all_156_0 = all_156_2) % 152.42/20.72 | | | | | | | | | | (111) $i(all_156_5) % 152.42/20.72 | | | | | | | | | | (112) $i(all_156_4) % 152.42/20.72 | | | | | | | | | | (113) $i(all_156_3) % 152.42/20.72 | | | | | | | | | | (114) $i(all_156_1) % 152.42/20.72 | | | | | | | | | | (115) nat_succeeds(all_156_5) = 0 % 152.42/20.72 | | | | | | | | | | (116) nat_succeeds(all_156_4) = 0 % 152.42/20.72 | | | | | | | | | | (117) @+(all_154_0, all_156_5) = all_156_3 % 152.42/20.72 | | | | | | | | | | (118) @+(all_154_0, all_156_1) = all_156_0 % 152.42/20.72 | | | | | | | | | | (119) @+(all_156_5, all_156_4) = all_156_1 % 152.42/20.72 | | | | | | | | | | (120) @+(all_156_3, all_156_4) = all_156_2 % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | GROUND_INST: instantiating (4) with all_156_5, simplifying with % 152.42/20.72 | | | | | | | | | | (111), (115) gives: % 152.42/20.72 | | | | | | | | | | (121) all_156_5 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 % 152.42/20.72 | | | | | | | | | | & s(v0) = all_156_5 & $i(v0)) % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | GROUND_INST: instantiating (4) with all_156_4, simplifying with % 152.42/20.72 | | | | | | | | | | (112), (116) gives: % 152.42/20.72 | | | | | | | | | | (122) all_156_4 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 % 152.42/20.72 | | | | | | | | | | & s(v0) = all_156_4 & $i(v0)) % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.42/20.72 | | | | | | | | | | all_154_0, all_156_5, all_156_3, simplifying with % 152.42/20.72 | | | | | | | | | | (106), (111), (117) gives: % 152.42/20.72 | | | | | | | | | | (123) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.42/20.72 | | | | | | | | | | (nat_succeeds(all_156_3) = v2 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(all_156_5) = v1 & % 152.42/20.72 | | | | | | | | | | nat_succeeds(all_154_0) = v0 & ( ~ (v1 = 0) | ~ % 152.42/20.72 | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.42/20.72 | | | | | | | | | | % 152.42/20.72 | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.42/20.72 | | | | | | | | | | all_154_0, all_156_1, all_156_0, simplifying with % 152.42/20.72 | | | | | | | | | | (106), (114), (118) gives: % 152.42/20.73 | | | | | | | | | | (124) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.42/20.73 | | | | | | | | | | (nat_succeeds(all_156_0) = v2 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_1) = v1 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_154_0) = v0 & ( ~ (v1 = 0) | ~ % 152.42/20.73 | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.42/20.73 | | | | | | | | | | all_156_5, all_156_4, all_156_1, simplifying with % 152.42/20.73 | | | | | | | | | | (111), (112), (119) gives: % 152.42/20.73 | | | | | | | | | | (125) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.42/20.73 | | | | | | | | | | (nat_succeeds(all_156_1) = v2 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_4) = v1 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_5) = v0 & ( ~ (v1 = 0) | ~ % 152.42/20.73 | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.42/20.73 | | | | | | | | | | all_156_3, all_156_4, all_156_2, simplifying with % 152.42/20.73 | | | | | | | | | | (112), (113), (120) gives: % 152.42/20.73 | | | | | | | | | | (126) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.42/20.73 | | | | | | | | | | (nat_succeeds(all_156_2) = v2 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_3) = v0 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 152.42/20.73 | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | DELTA: instantiating (126) with fresh symbols all_165_0, % 152.42/20.73 | | | | | | | | | | all_165_1, all_165_2 gives: % 152.42/20.73 | | | | | | | | | | (127) nat_succeeds(all_156_2) = all_165_0 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_3) = all_165_2 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_4) = all_165_1 & ( ~ % 152.42/20.73 | | | | | | | | | | (all_165_1 = 0) | ~ (all_165_2 = 0) | all_165_0 % 152.42/20.73 | | | | | | | | | | = 0) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | ALPHA: (127) implies: % 152.42/20.73 | | | | | | | | | | (128) nat_succeeds(all_156_4) = all_165_1 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | DELTA: instantiating (125) with fresh symbols all_167_0, % 152.42/20.73 | | | | | | | | | | all_167_1, all_167_2 gives: % 152.42/20.73 | | | | | | | | | | (129) nat_succeeds(all_156_1) = all_167_0 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_4) = all_167_1 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_5) = all_167_2 & ( ~ % 152.42/20.73 | | | | | | | | | | (all_167_1 = 0) | ~ (all_167_2 = 0) | all_167_0 % 152.42/20.73 | | | | | | | | | | = 0) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | ALPHA: (129) implies: % 152.42/20.73 | | | | | | | | | | (130) nat_succeeds(all_156_5) = all_167_2 % 152.42/20.73 | | | | | | | | | | (131) nat_succeeds(all_156_4) = all_167_1 % 152.42/20.73 | | | | | | | | | | (132) nat_succeeds(all_156_1) = all_167_0 % 152.42/20.73 | | | | | | | | | | (133) ~ (all_167_1 = 0) | ~ (all_167_2 = 0) | all_167_0 % 152.42/20.73 | | | | | | | | | | = 0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | DELTA: instantiating (123) with fresh symbols all_169_0, % 152.42/20.73 | | | | | | | | | | all_169_1, all_169_2 gives: % 152.42/20.73 | | | | | | | | | | (134) nat_succeeds(all_156_3) = all_169_0 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_5) = all_169_1 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_154_0) = all_169_2 & ( ~ % 152.42/20.73 | | | | | | | | | | (all_169_1 = 0) | ~ (all_169_2 = 0) | all_169_0 % 152.42/20.73 | | | | | | | | | | = 0) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | ALPHA: (134) implies: % 152.42/20.73 | | | | | | | | | | (135) nat_succeeds(all_154_0) = all_169_2 % 152.42/20.73 | | | | | | | | | | (136) nat_succeeds(all_156_5) = all_169_1 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | DELTA: instantiating (124) with fresh symbols all_171_0, % 152.42/20.73 | | | | | | | | | | all_171_1, all_171_2 gives: % 152.42/20.73 | | | | | | | | | | (137) nat_succeeds(all_156_0) = all_171_0 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_156_1) = all_171_1 & % 152.42/20.73 | | | | | | | | | | nat_succeeds(all_154_0) = all_171_2 & ( ~ % 152.42/20.73 | | | | | | | | | | (all_171_1 = 0) | ~ (all_171_2 = 0) | all_171_0 % 152.42/20.73 | | | | | | | | | | = 0) % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | ALPHA: (137) implies: % 152.42/20.73 | | | | | | | | | | (138) nat_succeeds(all_154_0) = all_171_2 % 152.42/20.73 | | | | | | | | | | (139) nat_succeeds(all_156_1) = all_171_1 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (10) with all_169_2, all_171_2, % 152.42/20.73 | | | | | | | | | | all_154_0, simplifying with (135), (138) gives: % 152.42/20.73 | | | | | | | | | | (140) all_171_2 = all_169_2 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_169_1, all_156_5, % 152.42/20.73 | | | | | | | | | | simplifying with (115), (136) gives: % 152.42/20.73 | | | | | | | | | | (141) all_169_1 = 0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (10) with all_167_2, all_169_1, % 152.42/20.73 | | | | | | | | | | all_156_5, simplifying with (130), (136) gives: % 152.42/20.73 | | | | | | | | | | (142) all_169_1 = all_167_2 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_167_1, all_156_4, % 152.42/20.73 | | | | | | | | | | simplifying with (116), (131) gives: % 152.42/20.73 | | | | | | | | | | (143) all_167_1 = 0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (10) with all_165_1, all_167_1, % 152.42/20.73 | | | | | | | | | | all_156_4, simplifying with (128), (131) gives: % 152.42/20.73 | | | | | | | | | | (144) all_167_1 = all_165_1 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | GROUND_INST: instantiating (10) with all_167_0, all_171_1, % 152.42/20.73 | | | | | | | | | | all_156_1, simplifying with (132), (139) gives: % 152.42/20.73 | | | | | | | | | | (145) all_171_1 = all_167_0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | COMBINE_EQS: (141), (142) imply: % 152.42/20.73 | | | | | | | | | | (146) all_167_2 = 0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | SIMP: (146) implies: % 152.42/20.73 | | | | | | | | | | (147) all_167_2 = 0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | COMBINE_EQS: (143), (144) imply: % 152.42/20.73 | | | | | | | | | | (148) all_165_1 = 0 % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | BETA: splitting (133) gives: % 152.42/20.73 | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | Case 1: % 152.42/20.73 | | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | | (149) ~ (all_167_1 = 0) % 152.42/20.73 | | | | | | | | | | | % 152.42/20.73 | | | | | | | | | | | REDUCE: (143), (149) imply: % 152.42/20.73 | | | | | | | | | | | (150) $false % 152.42/20.73 | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | CLOSE: (150) is inconsistent. % 152.42/20.74 | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | Case 2: % 152.42/20.74 | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | (151) ~ (all_167_2 = 0) | all_167_0 = 0 % 152.42/20.74 | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | BETA: splitting (151) gives: % 152.42/20.74 | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | Case 1: % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | (152) ~ (all_167_2 = 0) % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | REDUCE: (147), (152) imply: % 152.42/20.74 | | | | | | | | | | | | (153) $false % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | Case 2: % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | (154) all_167_0 = 0 % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | REDUCE: (132), (154) imply: % 152.42/20.74 | | | | | | | | | | | | (155) nat_succeeds(all_156_1) = 0 % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_154_0, all_169_2, % 152.42/20.74 | | | | | | | | | | | | simplifying with (106), (135) gives: % 152.42/20.74 | | | | | | | | | | | | (156) all_169_2 = 0 | ( ~ (all_154_0 = 0) & ! [v0: $i] % 152.42/20.74 | | | | | | | | | | | | : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? % 152.42/20.74 | | | | | | | | | | | | [v1: any] : ( ~ (v1 = all_154_0) & s(v0) = v1 % 152.42/20.74 | | | | | | | | | | | | & $i(v1)))) % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_156_1, simplifying with % 152.42/20.74 | | | | | | | | | | | | (114), (155) gives: % 152.42/20.74 | | | | | | | | | | | | (157) all_156_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.42/20.74 | | | | | | | | | | | | 0 & s(v0) = all_156_1 & $i(v0)) % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | BETA: splitting (29) gives: % 152.42/20.74 | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | Case 1: % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | (158) all_89_6 = 0 % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | REDUCE: (25), (158) imply: % 152.42/20.74 | | | | | | | | | | | | | (159) @+(0, all_89_1) = all_89_0 % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | REDUCE: (24), (158) imply: % 152.42/20.74 | | | | | | | | | | | | | (160) @+(0, all_89_5) = all_89_3 % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | BETA: splitting (30) gives: % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | Case 1: % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | (161) all_89_5 = 0 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (160), (161) imply: % 152.42/20.74 | | | | | | | | | | | | | | (162) @+(0, 0) = all_89_3 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_89_3, simplifying % 152.42/20.74 | | | | | | | | | | | | | | with (7), (162) gives: % 152.42/20.74 | | | | | | | | | | | | | | (163) all_89_3 = 0 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (162), (163) imply: % 152.42/20.74 | | | | | | | | | | | | | | (164) @+(0, 0) = 0 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 152.42/20.74 | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 152.42/20.74 | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 152.42/20.74 | | | | | | | | | | | | | | (164), (corollary-(plus:successor)), % 152.42/20.74 | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 152.42/20.74 | | | | | | | | | | | | | | by sub-proof #7. % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | Case 2: % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_5, all_89_3, % 152.42/20.74 | | | | | | | | | | | | | | simplifying with (15), (160) gives: % 152.42/20.74 | | | | | | | | | | | | | | (165) all_89_3 = all_89_5 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_1, all_89_0, % 152.42/20.74 | | | | | | | | | | | | | | simplifying with (19), (159) gives: % 152.42/20.74 | | | | | | | | | | | | | | (166) all_89_0 = all_89_1 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (13), (166) imply: % 152.42/20.74 | | | | | | | | | | | | | | (167) ~ (all_89_1 = all_89_2) % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (27), (165) imply: % 152.42/20.74 | | | | | | | | | | | | | | (168) @+(all_89_5, all_89_4) = all_89_2 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_1, all_89_2, % 152.42/20.74 | | | | | | | | | | | | | | all_89_4, all_89_5, simplifying with (26), (168) % 152.42/20.74 | | | | | | | | | | | | | | gives: % 152.42/20.74 | | | | | | | | | | | | | | (169) all_89_1 = all_89_2 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (167), (169) imply: % 152.42/20.74 | | | | | | | | | | | | | | (170) $false % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | End of split % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | Case 2: % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | (171) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.42/20.74 | | | | | | | | | | | | | all_89_6 & $i(v0)) % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | DELTA: instantiating (171) with fresh symbol all_217_0 % 152.42/20.74 | | | | | | | | | | | | | gives: % 152.42/20.74 | | | | | | | | | | | | | (172) nat_succeeds(all_217_0) = 0 & s(all_217_0) = % 152.42/20.74 | | | | | | | | | | | | | all_89_6 & $i(all_217_0) % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | ALPHA: (172) implies: % 152.42/20.74 | | | | | | | | | | | | | (173) $i(all_217_0) % 152.42/20.74 | | | | | | | | | | | | | (174) s(all_217_0) = all_89_6 % 152.42/20.74 | | | | | | | | | | | | | (175) nat_succeeds(all_217_0) = 0 % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | BETA: splitting (31) gives: % 152.42/20.74 | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | Case 1: % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | (176) all_89_4 = 0 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (27), (176) imply: % 152.42/20.74 | | | | | | | | | | | | | | (177) @+(all_89_3, 0) = all_89_2 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | REDUCE: (26), (176) imply: % 152.42/20.74 | | | | | | | | | | | | | | (178) @+(all_89_5, 0) = all_89_1 % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | BETA: splitting (30) gives: % 152.42/20.74 | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | Case 1: % 152.42/20.74 | | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | | (179) all_89_5 = 0 % 152.42/20.74 | | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | | REDUCE: (178), (179) imply: % 152.42/20.74 | | | | | | | | | | | | | | | (180) @+(0, 0) = all_89_1 % 152.42/20.74 | | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_89_1, simplifying % 152.42/20.74 | | | | | | | | | | | | | | | with (7), (180) gives: % 152.42/20.74 | | | | | | | | | | | | | | | (181) all_89_1 = 0 % 152.42/20.74 | | | | | | | | | | | | | | | % 152.42/20.74 | | | | | | | | | | | | | | | REDUCE: (180), (181) imply: % 152.42/20.75 | | | | | | | | | | | | | | | (182) @+(0, 0) = 0 % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 152.42/20.75 | | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 152.42/20.75 | | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 152.42/20.75 | | | | | | | | | | | | | | | (182), (corollary-(plus:successor)), % 152.42/20.75 | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 152.42/20.75 | | | | | | | | | | | | | | | by sub-proof #7. % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | Case 2: % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | (183) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.42/20.75 | | | | | | | | | | | | | | | all_89_5 & $i(v0)) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | DELTA: instantiating (183) with fresh symbol all_231_0 % 152.42/20.75 | | | | | | | | | | | | | | | gives: % 152.42/20.75 | | | | | | | | | | | | | | | (184) nat_succeeds(all_231_0) = 0 & s(all_231_0) = % 152.42/20.75 | | | | | | | | | | | | | | | all_89_5 & $i(all_231_0) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | ALPHA: (184) implies: % 152.42/20.75 | | | | | | | | | | | | | | | (185) $i(all_231_0) % 152.42/20.75 | | | | | | | | | | | | | | | (186) s(all_231_0) = all_89_5 % 152.42/20.75 | | | | | | | | | | | | | | | (187) nat_succeeds(all_231_0) = 0 % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.42/20.75 | | | | | | | | | | | | | | | all_217_0, all_89_1, all_89_6, all_89_0, % 152.42/20.75 | | | | | | | | | | | | | | | simplifying with (19), (25), (173), (174) gives: % 152.42/20.75 | | | | | | | | | | | | | | | (188) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.42/20.75 | | | | | | | | | | | | | | | (@+(all_217_0, all_89_1) = v1 & % 152.42/20.75 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & s(v1) = v2 & % 152.42/20.75 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_0)) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.42/20.75 | | | | | | | | | | | | | | | all_217_0, all_89_5, all_89_6, all_89_3, % 152.42/20.75 | | | | | | | | | | | | | | | simplifying with (15), (24), (173), (174) gives: % 152.42/20.75 | | | | | | | | | | | | | | | (189) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.42/20.75 | | | | | | | | | | | | | | | (@+(all_217_0, all_89_5) = v1 & % 152.42/20.75 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & s(v1) = v2 & % 152.42/20.75 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_3)) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_217_0, simplifying with % 152.42/20.75 | | | | | | | | | | | | | | | (173), (175) gives: % 152.42/20.75 | | | | | | | | | | | | | | | (190) all_217_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.42/20.75 | | | | | | | | | | | | | | | 0 & s(v0) = all_217_0 & $i(v0)) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_231_0, simplifying with % 152.42/20.75 | | | | | | | | | | | | | | | (185), (187) gives: % 152.42/20.75 | | | | | | | | | | | | | | | (191) all_231_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.42/20.75 | | | | | | | | | | | | | | | 0 & s(v0) = all_231_0 & $i(v0)) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.42/20.75 | | | | | | | | | | | | | | | all_231_0, 0, all_89_5, all_89_1, simplifying with % 152.42/20.75 | | | | | | | | | | | | | | | (7), (178), (185), (186) gives: % 152.42/20.75 | | | | | | | | | | | | | | | (192) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.42/20.75 | | | | | | | | | | | | | | | (@+(all_231_0, 0) = v1 & nat_succeeds(all_231_0) = % 152.42/20.75 | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 152.42/20.75 | | | | | | | | | | | | | | | | v2 = all_89_1)) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | DELTA: instantiating (189) with fresh symbols all_240_0, % 152.42/20.75 | | | | | | | | | | | | | | | all_240_1, all_240_2 gives: % 152.42/20.75 | | | | | | | | | | | | | | | (193) @+(all_217_0, all_89_5) = all_240_1 & % 152.42/20.75 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_240_2 & s(all_240_1) % 152.42/20.75 | | | | | | | | | | | | | | | = all_240_0 & $i(all_240_0) & $i(all_240_1) & ( ~ % 152.42/20.75 | | | | | | | | | | | | | | | (all_240_2 = 0) | all_240_0 = all_89_3) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | ALPHA: (193) implies: % 152.42/20.75 | | | | | | | | | | | | | | | (194) $i(all_240_1) % 152.42/20.75 | | | | | | | | | | | | | | | (195) s(all_240_1) = all_240_0 % 152.42/20.75 | | | | | | | | | | | | | | | (196) nat_succeeds(all_217_0) = all_240_2 % 152.42/20.75 | | | | | | | | | | | | | | | (197) @+(all_217_0, all_89_5) = all_240_1 % 152.42/20.75 | | | | | | | | | | | | | | | (198) ~ (all_240_2 = 0) | all_240_0 = all_89_3 % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | DELTA: instantiating (188) with fresh symbols all_242_0, % 152.42/20.75 | | | | | | | | | | | | | | | all_242_1, all_242_2 gives: % 152.42/20.75 | | | | | | | | | | | | | | | (199) @+(all_217_0, all_89_1) = all_242_1 & % 152.42/20.75 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_242_2 & s(all_242_1) % 152.42/20.75 | | | | | | | | | | | | | | | = all_242_0 & $i(all_242_0) & $i(all_242_1) & ( ~ % 152.42/20.75 | | | | | | | | | | | | | | | (all_242_2 = 0) | all_242_0 = all_89_0) % 152.42/20.75 | | | | | | | | | | | | | | | % 152.42/20.75 | | | | | | | | | | | | | | | ALPHA: (199) implies: % 152.42/20.75 | | | | | | | | | | | | | | | (200) $i(all_242_1) % 152.42/20.75 | | | | | | | | | | | | | | | (201) s(all_242_1) = all_242_0 % 152.42/20.75 | | | | | | | | | | | | | | | (202) nat_succeeds(all_217_0) = all_242_2 % 152.74/20.75 | | | | | | | | | | | | | | | (203) @+(all_217_0, all_89_1) = all_242_1 % 152.74/20.75 | | | | | | | | | | | | | | | (204) ~ (all_242_2 = 0) | all_242_0 = all_89_0 % 152.74/20.75 | | | | | | | | | | | | | | | % 152.74/20.75 | | | | | | | | | | | | | | | DELTA: instantiating (192) with fresh symbols all_244_0, % 152.74/20.75 | | | | | | | | | | | | | | | all_244_1, all_244_2 gives: % 152.74/20.75 | | | | | | | | | | | | | | | (205) @+(all_231_0, 0) = all_244_1 & % 152.74/20.75 | | | | | | | | | | | | | | | nat_succeeds(all_231_0) = all_244_2 & s(all_244_1) % 152.74/20.75 | | | | | | | | | | | | | | | = all_244_0 & $i(all_244_0) & $i(all_244_1) & ( ~ % 152.74/20.75 | | | | | | | | | | | | | | | (all_244_2 = 0) | all_244_0 = all_89_1) % 152.74/20.75 | | | | | | | | | | | | | | | % 152.74/20.75 | | | | | | | | | | | | | | | ALPHA: (205) implies: % 152.74/20.75 | | | | | | | | | | | | | | | (206) $i(all_244_1) % 152.74/20.75 | | | | | | | | | | | | | | | (207) $i(all_244_0) % 152.74/20.76 | | | | | | | | | | | | | | | (208) s(all_244_1) = all_244_0 % 152.74/20.76 | | | | | | | | | | | | | | | (209) nat_succeeds(all_231_0) = all_244_2 % 152.74/20.76 | | | | | | | | | | | | | | | (210) @+(all_231_0, 0) = all_244_1 % 152.74/20.76 | | | | | | | | | | | | | | | (211) ~ (all_244_2 = 0) | all_244_0 = all_89_1 % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_242_2, all_217_0, % 152.74/20.76 | | | | | | | | | | | | | | | simplifying with (175), (202) gives: % 152.74/20.76 | | | | | | | | | | | | | | | (212) all_242_2 = 0 % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_240_2, all_242_2, % 152.74/20.76 | | | | | | | | | | | | | | | all_217_0, simplifying with (196), (202) gives: % 152.74/20.76 | | | | | | | | | | | | | | | (213) all_242_2 = all_240_2 % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_244_2, all_231_0, % 152.74/20.76 | | | | | | | | | | | | | | | simplifying with (187), (209) gives: % 152.74/20.76 | | | | | | | | | | | | | | | (214) all_244_2 = 0 % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | COMBINE_EQS: (212), (213) imply: % 152.74/20.76 | | | | | | | | | | | | | | | (215) all_240_2 = 0 % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | SIMP: (215) implies: % 152.74/20.76 | | | | | | | | | | | | | | | (216) all_240_2 = 0 % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 152.74/20.76 | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | Case 1: % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | (217) ~ (all_244_2 = 0) % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | REDUCE: (214), (217) imply: % 152.74/20.76 | | | | | | | | | | | | | | | | (218) $false % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent. % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | Case 2: % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | (219) all_244_0 = all_89_1 % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | REDUCE: (208), (219) imply: % 152.74/20.76 | | | | | | | | | | | | | | | | (220) s(all_244_1) = all_89_1 % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 152.74/20.76 | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | Case 1: % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | (221) ~ (all_242_2 = 0) % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | REDUCE: (212), (221) imply: % 152.74/20.76 | | | | | | | | | | | | | | | | | (222) $false % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | Case 2: % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | (223) all_242_0 = all_89_0 % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | REDUCE: (201), (223) imply: % 152.74/20.76 | | | | | | | | | | | | | | | | | (224) s(all_242_1) = all_89_0 % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 152.74/20.76 | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | Case 1: % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | (225) ~ (all_240_2 = 0) % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | REDUCE: (216), (225) imply: % 152.74/20.76 | | | | | | | | | | | | | | | | | | (226) $false % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent. % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | Case 2: % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | (227) all_240_0 = all_89_3 % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | REDUCE: (195), (227) imply: % 152.74/20.76 | | | | | | | | | | | | | | | | | | (228) s(all_240_1) = all_89_3 % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.74/20.76 | | | | | | | | | | | | | | | | | | all_240_1, 0, all_89_3, all_89_2, simplifying with % 152.74/20.76 | | | | | | | | | | | | | | | | | | (7), (177), (194), (228) gives: % 152.74/20.76 | | | | | | | | | | | | | | | | | | (229) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.74/20.76 | | | | | | | | | | | | | | | | | | (@+(all_240_1, 0) = v1 & nat_succeeds(all_240_1) = % 152.74/20.76 | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 152.74/20.76 | | | | | | | | | | | | | | | | | | | v2 = all_89_2)) % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.74/20.76 | | | | | | | | | | | | | | | | | | all_217_0, all_89_5, all_240_1, simplifying with % 152.74/20.76 | | | | | | | | | | | | | | | | | | (15), (173), (197) gives: % 152.74/20.76 | | | | | | | | | | | | | | | | | | (230) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.74/20.76 | | | | | | | | | | | | | | | | | | (nat_succeeds(all_240_1) = v2 & % 152.74/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & % 152.74/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_5) = v1 & ( ~ (v1 = 0) | ~ % 152.74/20.76 | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.74/20.76 | | | | | | | | | | | | | | | | | | all_217_0, all_89_1, all_242_1, simplifying with % 152.74/20.76 | | | | | | | | | | | | | | | | | | (19), (173), (203) gives: % 152.74/20.76 | | | | | | | | | | | | | | | | | | (231) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.74/20.76 | | | | | | | | | | | | | | | | | | (nat_succeeds(all_242_1) = v2 & % 152.74/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & % 152.74/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_1) = v1 & ( ~ (v1 = 0) | ~ % 152.74/20.76 | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_269_0, % 152.74/20.76 | | | | | | | | | | | | | | | | | | all_269_1, all_269_2 gives: % 152.74/20.76 | | | | | | | | | | | | | | | | | | (232) nat_succeeds(all_242_1) = all_269_0 & % 152.74/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_269_2 & % 152.74/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_1) = all_269_1 & ( ~ % 152.74/20.76 | | | | | | | | | | | | | | | | | | (all_269_1 = 0) | ~ (all_269_2 = 0) | all_269_0 % 152.74/20.76 | | | | | | | | | | | | | | | | | | = 0) % 152.74/20.76 | | | | | | | | | | | | | | | | | | % 152.74/20.76 | | | | | | | | | | | | | | | | | | ALPHA: (232) implies: % 152.78/20.76 | | | | | | | | | | | | | | | | | | (233) nat_succeeds(all_89_1) = all_269_1 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (234) nat_succeeds(all_217_0) = all_269_2 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (235) nat_succeeds(all_242_1) = all_269_0 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (236) ~ (all_269_1 = 0) | ~ (all_269_2 = 0) | % 152.78/20.76 | | | | | | | | | | | | | | | | | | all_269_0 = 0 % 152.78/20.76 | | | | | | | | | | | | | | | | | | % 152.78/20.76 | | | | | | | | | | | | | | | | | | DELTA: instantiating (230) with fresh symbols all_271_0, % 152.78/20.76 | | | | | | | | | | | | | | | | | | all_271_1, all_271_2 gives: % 152.78/20.76 | | | | | | | | | | | | | | | | | | (237) nat_succeeds(all_240_1) = all_271_0 & % 152.78/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_271_2 & % 152.78/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_5) = all_271_1 & ( ~ % 152.78/20.76 | | | | | | | | | | | | | | | | | | (all_271_1 = 0) | ~ (all_271_2 = 0) | all_271_0 % 152.78/20.76 | | | | | | | | | | | | | | | | | | = 0) % 152.78/20.76 | | | | | | | | | | | | | | | | | | % 152.78/20.76 | | | | | | | | | | | | | | | | | | ALPHA: (237) implies: % 152.78/20.76 | | | | | | | | | | | | | | | | | | (238) nat_succeeds(all_89_5) = all_271_1 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (239) nat_succeeds(all_217_0) = all_271_2 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (240) nat_succeeds(all_240_1) = all_271_0 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (241) ~ (all_271_1 = 0) | ~ (all_271_2 = 0) | % 152.78/20.76 | | | | | | | | | | | | | | | | | | all_271_0 = 0 % 152.78/20.76 | | | | | | | | | | | | | | | | | | % 152.78/20.76 | | | | | | | | | | | | | | | | | | DELTA: instantiating (229) with fresh symbols all_275_0, % 152.78/20.76 | | | | | | | | | | | | | | | | | | all_275_1, all_275_2 gives: % 152.78/20.76 | | | | | | | | | | | | | | | | | | (242) @+(all_240_1, 0) = all_275_1 & % 152.78/20.76 | | | | | | | | | | | | | | | | | | nat_succeeds(all_240_1) = all_275_2 & s(all_275_1) % 152.78/20.76 | | | | | | | | | | | | | | | | | | = all_275_0 & $i(all_275_0) & $i(all_275_1) & ( ~ % 152.78/20.76 | | | | | | | | | | | | | | | | | | (all_275_2 = 0) | all_275_0 = all_89_2) % 152.78/20.76 | | | | | | | | | | | | | | | | | | % 152.78/20.76 | | | | | | | | | | | | | | | | | | ALPHA: (242) implies: % 152.78/20.76 | | | | | | | | | | | | | | | | | | (243) $i(all_275_1) % 152.78/20.76 | | | | | | | | | | | | | | | | | | (244) s(all_275_1) = all_275_0 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (245) nat_succeeds(all_240_1) = all_275_2 % 152.78/20.76 | | | | | | | | | | | | | | | | | | (246) @+(all_240_1, 0) = all_275_1 % 152.78/20.77 | | | | | | | | | | | | | | | | | | (247) ~ (all_275_2 = 0) | all_275_0 = all_89_2 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_271_1, all_89_5, % 152.78/20.77 | | | | | | | | | | | | | | | | | | simplifying with (22), (238) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (248) all_271_1 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_269_1, all_89_1, % 152.78/20.77 | | | | | | | | | | | | | | | | | | simplifying with (80), (233) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (249) all_269_1 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_271_2, all_217_0, % 152.78/20.77 | | | | | | | | | | | | | | | | | | simplifying with (175), (239) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (250) all_271_2 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_269_2, all_271_2, % 152.78/20.77 | | | | | | | | | | | | | | | | | | all_217_0, simplifying with (234), (239) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (251) all_271_2 = all_269_2 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_271_0, all_275_2, % 152.78/20.77 | | | | | | | | | | | | | | | | | | all_240_1, simplifying with (240), (245) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (252) all_275_2 = all_271_0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (251) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (253) all_269_2 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | SIMP: (253) implies: % 152.78/20.77 | | | | | | | | | | | | | | | | | | (254) all_269_2 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | (255) ~ (all_271_1 = 0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | REDUCE: (248), (255) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | (256) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | CLOSE: (256) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | (257) ~ (all_271_2 = 0) | all_271_0 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | (258) ~ (all_269_1 = 0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (258) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | (259) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | (260) ~ (all_269_2 = 0) | all_269_0 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | (261) ~ (all_271_2 = 0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | REDUCE: (250), (261) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | (262) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | (263) all_271_0 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (263) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | (264) all_275_2 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | (265) ~ (all_275_2 = 0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (264), (265) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | (266) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | (267) all_275_0 = all_89_2 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (244), (267) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | (268) s(all_275_1) = all_89_2 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | (269) ~ (all_269_2 = 0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (254), (269) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | (270) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (270) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | (271) all_269_0 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (235), (271) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | (272) nat_succeeds(all_242_1) = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (273) all_89_0 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (273) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (274) s(all_242_1) = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_242_1, simplifying with % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (200), (274) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (275) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (275) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (276) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | all_89_0 & $i(v0)) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (276) with fresh symbol all_315_0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (277) nat_succeeds(all_315_0) = 0 & s(all_315_0) = % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | all_89_0 & $i(all_315_0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (278) $i(all_315_0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (279) s(all_315_0) = all_89_0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | (280) nat_succeeds(all_315_0) = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_89_2 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (281) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (282) s(all_275_1) = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_275_1, simplifying with % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (243), (282) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (283) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (283) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (284) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | all_89_2 & $i(v0)) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (284) with fresh symbol all_323_0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (285) nat_succeeds(all_323_0) = 0 & s(all_323_0) = % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | all_89_2 & $i(all_323_0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (286) $i(all_323_0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | (287) s(all_323_0) = all_89_2 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_89_1 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (220), (288) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (289) s(all_244_1) = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_244_1, simplifying with % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (289) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (290) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (291) ~ (all_89_1 = 0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_89_3 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (228), (292) imply: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) s(all_240_1) = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_240_1, simplifying with % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (293) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) $false % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent. % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3 & $i(v0)) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (295) with fresh symbol all_339_0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) nat_succeeds(all_339_0) = 0 & s(all_339_0) = % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3 & $i(all_339_0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) $i(all_339_0) % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) s(all_339_0) = all_89_3 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_154_0 = 0 % 152.78/20.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (299) imply: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) @+(0, all_156_1) = all_156_0 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (299) imply: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) @+(0, all_156_5) = all_156_3 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (110), (111), (114), (119), (120), % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300), (301) are inconsistent by sub-proof #10. % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) ~ (all_154_0 = 0) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (@+(v3, v2) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ? [v8: $i] : (@+(v1, v2) = v7 & % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(v1) = v6 & $i(v8) & $i(v7) & ( % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (303) with fresh symbol all_347_0 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) nat_succeeds(all_347_0) = 0 & s(all_347_0) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_347_0) & ! [v0: $i] : ! [v1: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1) = v3) | ~ (@+(all_347_0, v0) = v2) | ~ % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | : ? [v6: $i] : ? [v7: $i] : (@+(v0, v1) = v6 & % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(all_347_0, v6) = v7 & nat_succeeds(v1) = v4 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(v0) = v5 & $i(v7) & $i(v6) & ( % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v5 = 0) | ~ (v4 = 0) | v7 = v3))) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) $i(all_347_0) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) s(all_347_0) = all_154_0 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) nat_succeeds(all_347_0) = 0 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ( ~ (@+(v2, v1) = v3) | ~ (@+(all_347_0, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ? [v5: any] : ? [v6: $i] : ? [v7: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : (@+(v0, v1) = v6 & @+(all_347_0, v6) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v7 & nat_succeeds(v1) = v4 & nat_succeeds(v0) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | v7 = v3))) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_156_5 = 0 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (309) imply: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) @+(0, all_156_4) = all_156_1 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (309) imply: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) @+(all_154_0, 0) = all_156_3 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (309) imply: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) nat_succeeds(0) = 0 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_242_1, all_315_0, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_0, simplifying with (200), (224), (278), % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) all_315_0 = all_242_1 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_275_1, all_323_0, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_2, simplifying with (243), (268), (286), % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_323_0 = all_275_1 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_339_0, 0, all_89_3, all_89_2, simplifying with % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7), (177), (297), (298) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_339_0, 0) = v1 & nat_succeeds(all_339_0) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_89_2)) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_240_1, all_339_0, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3, simplifying with (194), (228), (297), % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_339_0 = all_240_1 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, all_156_1, all_154_0, all_156_0, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (305), (306) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (317) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_347_0, all_156_1) = v1 & % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & s(v1) = v2 & % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_242_1, simplifying with % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200), (272) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_242_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_242_1 & $i(v0)) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_315_0, simplifying with % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (280) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (319) all_315_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_315_0 & $i(v0)) % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_4, all_156_1, % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (310) gives: % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_156_1 = all_156_4 % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, 0, all_154_0, all_156_3, simplifying % 152.78/20.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (7), (305), (306), (311) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (321) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_347_0, 0) = v1 & nat_succeeds(all_347_0) = % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_156_3)) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, 0, all_156_3, simplifying with (7), % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (311) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (322) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_156_3) = v2 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_154_0) = v0 & nat_succeeds(0) = % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1, 0, all_275_1, simplifying with (7), % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (246) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (323) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_275_1) = v2 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_240_1) = v0 & nat_succeeds(0) = % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (323) with fresh symbols all_372_0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_372_1, all_372_2 gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (324) nat_succeeds(all_275_1) = all_372_0 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_240_1) = all_372_2 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_372_1 & ( ~ (all_372_1 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_372_2 = 0) | all_372_0 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (325) nat_succeeds(0) = all_372_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (322) with fresh symbols all_374_0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_374_1, all_374_2 gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (326) nat_succeeds(all_156_3) = all_374_0 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_154_0) = all_374_2 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_374_1 & ( ~ (all_374_1 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_374_2 = 0) | all_374_0 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (327) nat_succeeds(0) = all_374_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (328) nat_succeeds(all_154_0) = all_374_2 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (321) with fresh symbols all_376_0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, all_376_2 gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (329) @+(all_347_0, 0) = all_376_1 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_376_2 & s(all_376_1) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_376_0 & $i(all_376_0) & $i(all_376_1) & ( ~ % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_376_2 = 0) | all_376_0 = all_156_3) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (330) $i(all_376_1) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (331) s(all_376_1) = all_376_0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (332) nat_succeeds(all_347_0) = all_376_2 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (333) @+(all_347_0, 0) = all_376_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (334) ~ (all_376_2 = 0) | all_376_0 = all_156_3 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (317) with fresh symbols all_378_0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, all_378_2 gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (335) @+(all_347_0, all_156_1) = all_378_1 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_378_2 & s(all_378_1) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_378_0 & $i(all_378_0) & $i(all_378_1) & ( ~ % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_378_2 = 0) | all_378_0 = all_156_0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (336) s(all_378_1) = all_378_0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (337) nat_succeeds(all_347_0) = all_378_2 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (338) @+(all_347_0, all_156_1) = all_378_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (339) ~ (all_378_2 = 0) | all_378_0 = all_156_0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (315) with fresh symbols all_380_0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_380_1, all_380_2 gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (340) @+(all_339_0, 0) = all_380_1 & % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_339_0) = all_380_2 & s(all_380_1) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_380_0 & $i(all_380_0) & $i(all_380_1) & ( ~ % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_380_2 = 0) | all_380_0 = all_89_2) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (341) @+(all_339_0, 0) = all_380_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (320), (338) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (342) @+(all_347_0, all_156_4) = all_378_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (316), (341) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (343) @+(all_240_1, 0) = all_380_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (320) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (344) @+(all_154_0, all_156_4) = all_156_0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (310), (320) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (345) @+(0, all_156_4) = all_156_4 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_374_1, 0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (312), (327) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (346) all_374_1 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_372_1, all_374_1, 0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (325), (327) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (347) all_374_1 = all_372_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_169_2, all_374_2, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (135), (328) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (348) all_374_2 = all_169_2 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_378_2, all_347_0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (307), (337) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_378_2 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_376_2, all_378_2, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, simplifying with (332), (337) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_378_2 = all_376_2 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_275_1, all_380_1, 0, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1, simplifying with (246), (343) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (351) all_380_1 = all_275_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (350) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (352) all_376_2 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (352) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (353) all_376_2 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (347) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (354) all_372_1 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (354) implies: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (355) all_372_1 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (356) ~ (all_378_2 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (356) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (357) $false % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (357) is inconsistent. % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_378_0 = all_156_0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (358) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (359) s(all_378_1) = all_156_0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (360) ~ (all_376_2 = 0) % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (353), (360) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (361) $false % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (361) is inconsistent. % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_376_0 = all_156_3 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (331), (362) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (363) s(all_376_1) = all_156_3 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_169_2 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (364) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (365) nat_succeeds(all_154_0) = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (366) all_217_0 = 0 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (366) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (367) @+(0, all_89_1) = all_242_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (366) imply: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (368) @+(0, all_89_5) = all_240_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_5, all_240_1, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (368) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (369) all_240_1 = all_89_5 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_1, all_242_1, % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (367) gives: % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (370) all_242_1 = all_89_1 % 152.78/20.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (370) imply: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371) all_315_0 = all_89_1 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (369) imply: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372) @+(all_89_5, 0) = all_275_1 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (370) imply: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (373) s(all_89_1) = all_89_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (178), (268), (291), (319), % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371), (372), (373) are inconsistent by sub-proof % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #5. % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (374) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(v0)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (374) with fresh symbol all_458_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375) nat_succeeds(all_458_0) = 0 & s(all_458_0) = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(all_458_0) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376) $i(all_458_0) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (377) s(all_458_0) = all_217_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378) nat_succeeds(all_458_0) = 0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, all_156_4, all_156_3, all_156_2, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (120), (330), (363) gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (379) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_376_1, all_156_4) = v1 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_376_1) = v0 & s(v1) = v2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_2)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_458_0, all_89_1, all_217_0, all_242_1, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (203), (376), (377) gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (380) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_458_0, all_89_1) = v1 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_458_0) = v0 & s(v1) = v2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_242_1)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_458_0, all_89_5, all_217_0, all_240_1, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (197), (376), (377) gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (381) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_458_0, all_89_5) = v1 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_458_0) = v0 & s(v1) = v2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (365) gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (382) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, 0, all_376_1, simplifying with (7), % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305), (333) gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (383) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_376_1) = v2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & nat_succeeds(0) = % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, all_156_4, all_378_1, simplifying with % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (305), (342) gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (384) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_378_1) = v2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (384) with fresh symbols all_476_0, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_476_1, all_476_2 gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (385) nat_succeeds(all_378_1) = all_476_0 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_476_2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_476_1 & ( ~ % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_476_1 = 0) | ~ (all_476_2 = 0) | all_476_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386) nat_succeeds(all_156_4) = all_476_1 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387) nat_succeeds(all_347_0) = all_476_2 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (383) with fresh symbols all_478_0, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_478_1, all_478_2 gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (388) nat_succeeds(all_376_1) = all_478_0 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_478_2 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_478_1 & ( ~ (all_478_1 = 0) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_478_2 = 0) | all_478_0 = 0) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389) nat_succeeds(0) = all_478_1 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (390) nat_succeeds(all_347_0) = all_478_2 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) nat_succeeds(all_376_1) = all_478_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) ~ (all_478_1 = 0) | ~ (all_478_2 = 0) | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_478_0 = 0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (381) with fresh symbols all_480_0, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_480_1, all_480_2 gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) @+(all_458_0, all_89_5) = all_480_1 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_458_0) = all_480_2 & s(all_480_1) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_480_0 & $i(all_480_0) & $i(all_480_1) & ( ~ % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_480_2 = 0) | all_480_0 = all_240_1) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (393) implies: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) nat_succeeds(all_458_0) = all_480_2 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (380) with fresh symbols all_482_0, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_482_1, all_482_2 gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) @+(all_458_0, all_89_1) = all_482_1 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_458_0) = all_482_2 & s(all_482_1) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_482_0 & $i(all_482_0) & $i(all_482_1) & ( ~ % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_482_2 = 0) | all_482_0 = all_242_1) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) $i(all_482_1) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) s(all_482_1) = all_482_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) nat_succeeds(all_458_0) = all_482_2 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) ~ (all_482_2 = 0) | all_482_0 = all_242_1 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (379) with fresh symbols all_486_0, % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_486_1, all_486_2 gives: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) @+(all_376_1, all_156_4) = all_486_1 & % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_376_1) = all_486_2 & s(all_486_1) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_486_0 & $i(all_486_0) & $i(all_486_1) & ( ~ % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_486_2 = 0) | all_486_0 = all_156_2) % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies: % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) s(all_486_1) = all_486_0 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) nat_succeeds(all_376_1) = all_486_2 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) @+(all_376_1, all_156_4) = all_486_1 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) ~ (all_486_2 = 0) | all_486_0 = all_156_2 % 152.78/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (382) gives: % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_154_0 = 0 % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (405) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (406) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (407) with fresh symbol all_492_0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) nat_succeeds(all_492_0) = 0 & s(all_492_0) = % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_492_0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (408) implies: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) $i(all_492_0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) s(all_492_0) = all_154_0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_478_1, 0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (312), (389) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_478_1 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_476_1, all_156_4, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (386) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_476_1 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_478_2, all_347_0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (307), (390) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) all_478_2 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_476_2, all_478_2, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, simplifying with (387), (390) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_478_2 = all_476_2 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_478_0, all_486_2, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, simplifying with (391), (402) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_486_2 = all_478_0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_482_2, all_458_0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (378), (398) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_482_2 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_480_2, all_482_2, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_458_0, simplifying with (394), (398) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) all_482_2 = all_480_2 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (416), (417) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_480_2 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (414) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_476_2 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) ~ (all_482_2 = 0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (416), (420) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (421) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_482_0 = all_242_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (422) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) s(all_482_1) = all_242_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) ~ (all_478_1 = 0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (411), (424) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (425) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) ~ (all_478_2 = 0) | all_478_0 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) ~ (all_478_2 = 0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (413), (427) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (428) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) all_478_0 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (429) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) all_486_2 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) ~ (all_486_2 = 0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (430), (431) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (432) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_486_0 = all_156_2 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (401), (433) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) s(all_486_1) = all_156_2 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) all_242_1 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (423), (435) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) s(all_482_1) = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_482_1, simplifying with % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396), (436) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (437) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) ~ (all_242_1 = 0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) all_315_0 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (439) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_242_1 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (438), (440) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) $false % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (441) is inconsistent. % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_492_0, all_156_4, all_154_0, all_156_0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (344), (409), (410) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_492_0, all_156_4) = v1 & % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_492_0) = v0 & s(v1) = v2 & % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_347_0, all_492_0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (305), (306), (409), % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) all_492_0 = all_347_0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (308) with 0, all_156_4, all_376_1, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_486_1, simplifying with (7), (112), (333), % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_347_0, v2) = v3 & @+(0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(0) = v1 & $i(v3) & $i(v2) & ( ~ % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = all_486_1)) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (442) with fresh symbols all_620_0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_620_1, all_620_2 gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) @+(all_492_0, all_156_4) = all_620_1 & % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_492_0) = all_620_2 & s(all_620_1) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_620_0 & $i(all_620_0) & $i(all_620_1) & ( ~ % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_620_2 = 0) | all_620_0 = all_156_0) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) @+(all_492_0, all_156_4) = all_620_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (444) with fresh symbols all_632_0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_632_1, all_632_2, all_632_3 gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) @+(all_347_0, all_632_1) = all_632_0 & @+(0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = all_632_1 & nat_succeeds(all_156_4) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_632_3 & nat_succeeds(0) = all_632_2 & % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_632_0) & $i(all_632_1) & ( ~ (all_632_2 = % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_632_3 = 0) | all_632_0 = % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_486_1) % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) nat_succeeds(0) = all_632_2 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) nat_succeeds(all_156_4) = all_632_3 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) @+(0, all_156_4) = all_632_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) @+(all_347_0, all_632_1) = all_632_0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) ~ (all_632_2 = 0) | ~ (all_632_3 = 0) | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_632_0 = all_486_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (443), (446) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) @+(all_347_0, all_156_4) = all_620_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_632_2, 0, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (312), (448) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_632_2 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_632_3, all_156_4, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (449) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_632_3 = 0 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_4, all_632_1, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, 0, simplifying with (345), (450) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_632_1 = all_156_4 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_378_1, all_620_1, % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_347_0, simplifying with (342), % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) gives: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_620_1 = all_378_1 % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (451), (456) imply: % 152.99/20.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) @+(all_347_0, all_156_4) = all_632_0 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) ~ (all_632_2 = 0) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (454), (459) imply: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) $false % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (460) is inconsistent. % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) ~ (all_632_3 = 0) | all_632_0 = all_486_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) ~ (all_632_3 = 0) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (455), (462) imply: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) $false % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (463) is inconsistent. % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_632_0 = all_486_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (458), (464) imply: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) @+(all_347_0, all_156_4) = all_486_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_378_1, all_486_1, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_347_0, simplifying with (342), % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_486_1 = all_378_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (466) imply: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) s(all_378_1) = all_156_2 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, simplifying with (359), (467) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_156_0 = all_156_2 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (468) imply: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) $false % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (469) is inconsistent. % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (470) implies: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (305), (306), (307), (471) are inconsistent % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #4. % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_5 & $i(v0)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (472) with fresh symbol all_364_0 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) nat_succeeds(all_364_0) = 0 & s(all_364_0) = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_5 & $i(all_364_0) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) $i(all_364_0) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) s(all_364_0) = all_156_5 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_242_1, all_315_0, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_0, simplifying with (200), (224), (278), % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) all_315_0 = all_242_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_275_1, all_323_0, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_2, simplifying with (243), (268), (286), % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_323_0 = all_275_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_339_0, 0, all_89_3, all_89_2, simplifying with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7), (177), (297), (298) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_339_0, 0) = v1 & nat_succeeds(all_339_0) = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_89_2)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_240_1, all_339_0, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3, simplifying with (194), (228), (297), % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_339_0 = all_240_1 % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, all_156_1, all_154_0, all_156_0, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (305), (306) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_347_0, all_156_1) = v1 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & s(v1) = v2 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, all_156_5, all_154_0, all_156_3, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (111), (117), (305), (306) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_347_0, all_156_5) = v1 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & s(v1) = v2 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_3)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_364_0, all_156_4, all_156_5, all_156_1, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (119), (474), (475) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_364_0, all_156_4) = v1 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_364_0) = v0 & s(v1) = v2 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_242_1, simplifying with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200), (272) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_242_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_242_1 & $i(v0)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_315_0, simplifying with % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278), (280) gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_315_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_315_0 & $i(v0)) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (480) with fresh symbols all_376_0, % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, all_376_2 gives: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) @+(all_347_0, all_156_1) = all_376_1 & % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_376_2 & s(all_376_1) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_376_0 & $i(all_376_0) & $i(all_376_1) & ( ~ % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_376_2 = 0) | all_376_0 = all_156_0) % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies: % 152.99/20.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) s(all_376_1) = all_376_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) nat_succeeds(all_347_0) = all_376_2 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) @+(all_347_0, all_156_1) = all_376_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_376_2 = 0) | all_376_0 = all_156_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (478) with fresh symbols all_378_0, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, all_378_2 gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) @+(all_339_0, 0) = all_378_1 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_339_0) = all_378_2 & s(all_378_1) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_378_0 & $i(all_378_0) & $i(all_378_1) & ( ~ % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_378_2 = 0) | all_378_0 = all_89_2) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) @+(all_339_0, 0) = all_378_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (482) with fresh symbols all_380_0, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_380_1, all_380_2 gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) @+(all_364_0, all_156_4) = all_380_1 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_364_0) = all_380_2 & s(all_380_1) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_380_0 & $i(all_380_0) & $i(all_380_1) & ( ~ % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_380_2 = 0) | all_380_0 = all_156_1) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) @+(all_364_0, all_156_4) = all_380_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (481) with fresh symbols all_382_0, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_382_2 gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) @+(all_347_0, all_156_5) = all_382_1 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_382_2 & s(all_382_1) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_382_0 & $i(all_382_0) & $i(all_382_1) & ( ~ % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_382_2 = 0) | all_382_0 = all_156_3) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) $i(all_382_1) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) s(all_382_1) = all_382_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) nat_succeeds(all_347_0) = all_382_2 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) @+(all_347_0, all_156_5) = all_382_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) ~ (all_382_2 = 0) | all_382_0 = all_156_3 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (479), (491) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) @+(all_240_1, 0) = all_378_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_382_2, all_347_0, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (307), (497) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_382_2 = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_376_2, all_382_2, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, simplifying with (487), (497) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_382_2 = all_376_2 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_275_1, all_378_1, 0, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_240_1, simplifying with (246), (500) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_378_1 = all_275_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (501), (502) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_376_2 = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (499) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) ~ (all_382_2 = 0) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (501), (505) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) $false % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (506) is inconsistent. % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_382_0 = all_156_3 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (496), (507) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) s(all_382_1) = all_156_3 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (489) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) ~ (all_376_2 = 0) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (504), (509) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) $false % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (510) is inconsistent. % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_376_0 = all_156_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (486), (511) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) s(all_376_1) = all_156_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_169_2 = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (513) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) nat_succeeds(all_154_0) = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_217_0 = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (203), (515) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) @+(0, all_89_1) = all_242_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (197), (515) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) @+(0, all_89_5) = all_240_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_231_0 = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (518) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) @+(0, 0) = all_244_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_244_1, simplifying % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (7), (519) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_244_1 = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (519), (520) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) @+(0, 0) = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (corollary-(plus:successor)), % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #7. % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_5, all_240_1, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (517) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_240_1 = all_89_5 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_1, all_242_1, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (516) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_242_1 = all_89_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (523) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) all_315_0 = all_89_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (522) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) @+(all_89_5, 0) = all_275_1 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (523) imply: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) s(all_89_1) = all_89_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (178), (268), (291), (484), % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524), (525), (526) are inconsistent by sub-proof % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #5. % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(v0)) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (527) with fresh symbol all_464_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) nat_succeeds(all_464_0) = 0 & s(all_464_0) = % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(all_464_0) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (528) implies: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) $i(all_464_0) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) s(all_464_0) = all_217_0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) nat_succeeds(all_464_0) = 0 % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_156_4, all_156_3, all_156_2, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (120), (495), (508) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_382_1, all_156_4) = v1 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_382_1) = v0 & s(v1) = v2 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_2)) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_464_0, all_89_1, all_217_0, all_242_1, % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (203), (529), (530) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_464_0, all_89_1) = v1 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_464_0) = v0 & s(v1) = v2 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_242_1)) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (514) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, all_156_5, all_382_1, simplifying with % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (305), (498) gives: % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_382_1) = v2 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = v1 & ( ~ (v1 = 0) | ~ % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.99/20.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, all_156_1, all_376_1, simplifying with % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (305), (488) gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_376_1) = v2 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = v0 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = v1 & ( ~ (v1 = 0) | ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_364_0, all_156_4, all_380_1, simplifying with % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (474), (493) gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_380_1) = v2 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_364_0) = v0 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (537) with fresh symbols all_482_0, % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_482_1, all_482_2 gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) nat_succeeds(all_380_1) = all_482_0 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_364_0) = all_482_2 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_482_1 & ( ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_482_1 = 0) | ~ (all_482_2 = 0) | all_482_0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (538) implies: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) nat_succeeds(all_156_4) = all_482_1 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (536) with fresh symbols all_484_0, % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_484_1, all_484_2 gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) nat_succeeds(all_376_1) = all_484_0 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_484_2 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = all_484_1 & ( ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_484_1 = 0) | ~ (all_484_2 = 0) | all_484_0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (540) implies: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) nat_succeeds(all_347_0) = all_484_2 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (535) with fresh symbols all_486_0, % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_486_1, all_486_2 gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) nat_succeeds(all_382_1) = all_486_0 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_347_0) = all_486_2 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_486_1 & ( ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_486_1 = 0) | ~ (all_486_2 = 0) | all_486_0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) nat_succeeds(all_156_5) = all_486_1 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) nat_succeeds(all_347_0) = all_486_2 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) nat_succeeds(all_382_1) = all_486_0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) ~ (all_486_1 = 0) | ~ (all_486_2 = 0) | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_486_0 = 0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (533) with fresh symbols all_490_0, % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_490_1, all_490_2 gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) @+(all_464_0, all_89_1) = all_490_1 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_464_0) = all_490_2 & s(all_490_1) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_490_0 & $i(all_490_0) & $i(all_490_1) & ( ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_490_2 = 0) | all_490_0 = all_242_1) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (547) implies: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) $i(all_490_1) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) s(all_490_1) = all_490_0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) nat_succeeds(all_464_0) = all_490_2 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) ~ (all_490_2 = 0) | all_490_0 = all_242_1 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (532) with fresh symbols all_494_0, % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_494_1, all_494_2 gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) @+(all_382_1, all_156_4) = all_494_1 & % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_382_1) = all_494_2 & s(all_494_1) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_494_0 & $i(all_494_0) & $i(all_494_1) & ( ~ % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_494_2 = 0) | all_494_0 = all_156_2) % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (552) implies: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) s(all_494_1) = all_494_0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) nat_succeeds(all_382_1) = all_494_2 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) @+(all_382_1, all_156_4) = all_494_1 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) ~ (all_494_2 = 0) | all_494_0 = all_156_2 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) all_154_0 = 0 % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (557) imply: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) $false % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (558) is inconsistent. % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 152.99/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (559) with fresh symbol all_500_0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) nat_succeeds(all_500_0) = 0 & s(all_500_0) = % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_500_0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) $i(all_500_0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) s(all_500_0) = all_154_0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_486_1, all_156_5, % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (543) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_486_1 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_482_1, all_156_4, % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (539) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_482_1 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_486_2, all_347_0, % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (307), (544) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) all_486_2 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_484_2, all_486_2, % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_347_0, simplifying with (541), (544) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_486_2 = all_484_2 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_486_0, all_494_2, % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, simplifying with (545), (554) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_494_2 = all_486_0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_490_2, all_464_0, % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (531), (550) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_490_2 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (565), (566) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_484_2 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (551) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) ~ (all_490_2 = 0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (570) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) $false % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (571) is inconsistent. % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) all_490_0 = all_242_1 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (572) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) s(all_490_1) = all_242_1 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) ~ (all_486_1 = 0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (574) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) $false % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (575) is inconsistent. % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) ~ (all_486_2 = 0) | all_486_0 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) ~ (all_486_2 = 0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (577) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) $false % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (578) is inconsistent. % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) all_486_0 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (567), (579) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_494_2 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) ~ (all_494_2 = 0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (581) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) $false % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (582) is inconsistent. % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_494_0 = all_156_2 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (583) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) s(all_494_1) = all_156_2 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_315_0 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (476), (585) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) all_242_1 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (586) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) s(all_490_1) = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_490_1, simplifying with % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548), (587) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) $false % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (588) is inconsistent. % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) ~ (all_315_0 = 0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (476), (589) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) ~ (all_242_1 = 0) % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_242_1 = 0 % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (590), (591) imply: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) $false % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (592) is inconsistent. % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_500_0, all_156_1, all_154_0, all_156_0, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (561), (562) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_500_0, all_156_1) = v1 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_500_0) = v0 & s(v1) = v2 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_347_0, all_500_0, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (305), (306), (561), % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) all_500_0 = all_347_0 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (308) with all_156_5, all_156_4, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_494_1, simplifying with (111), % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (498), (555) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_347_0, v2) = v3 & @+(all_156_5, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(all_156_5) = v1 & $i(v3) & $i(v2) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_494_1)) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (593) with fresh symbols all_644_0, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_644_1, all_644_2 gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) @+(all_500_0, all_156_1) = all_644_1 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_500_0) = all_644_2 & s(all_644_1) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_644_0 & $i(all_644_0) & $i(all_644_1) & ( ~ % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_644_2 = 0) | all_644_0 = all_156_0) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) @+(all_500_0, all_156_1) = all_644_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (595) with fresh symbols all_646_0, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_646_1, all_646_2, all_646_3 gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) @+(all_347_0, all_646_1) = all_646_0 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(all_156_5, all_156_4) = all_646_1 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_646_3 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_646_2 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_646_0) & $i(all_646_1) & ( ~ (all_646_2 = % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_646_3 = 0) | all_646_0 = % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_494_1) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (598) implies: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) nat_succeeds(all_156_5) = all_646_2 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) nat_succeeds(all_156_4) = all_646_3 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) @+(all_156_5, all_156_4) = all_646_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) @+(all_347_0, all_646_1) = all_646_0 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) ~ (all_646_2 = 0) | ~ (all_646_3 = 0) | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_646_0 = all_494_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (597) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) @+(all_347_0, all_156_1) = all_644_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_646_2, all_156_5, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (599) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) all_646_2 = 0 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_646_3, all_156_4, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (600) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_646_3 = 0 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_646_1, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (119), % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_646_1 = all_156_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_376_1, all_644_1, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_347_0, simplifying with (488), % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) all_644_1 = all_376_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (602), (607) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) @+(all_347_0, all_156_1) = all_646_0 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (603) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) ~ (all_646_2 = 0) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (605), (610) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) $false % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (611) is inconsistent. % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) ~ (all_646_3 = 0) | all_646_0 = all_494_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (612) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) ~ (all_646_3 = 0) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (606), (613) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) $false % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (614) is inconsistent. % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) all_646_0 = all_494_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (609), (615) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) @+(all_347_0, all_156_1) = all_494_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_376_1, all_494_1, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_347_0, simplifying with (488), % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_494_1 = all_376_1 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (617) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) s(all_376_1) = all_156_2 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, simplifying with (512), (618) gives: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_156_0 = all_156_2 % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (619) imply: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) $false % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (620) is inconsistent. % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (621) implies: % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (305), (306), (307), (622) are inconsistent % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #4. % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | End of split % 153.14/20.85 | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | Case 2: % 153.14/20.85 | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | (623) ~ (all_89_4 = 0) % 153.14/20.85 | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | BETA: splitting (30) gives: % 153.14/20.85 | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | Case 1: % 153.14/20.85 | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | (624) all_89_5 = 0 % 153.14/20.85 | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | REDUCE: (26), (624) imply: % 153.14/20.85 | | | | | | | | | | | | | | | (625) @+(0, all_89_4) = all_89_1 % 153.14/20.85 | | | | | | | | | | | | | | | % 153.14/20.85 | | | | | | | | | | | | | | | REDUCE: (24), (624) imply: % 153.14/20.85 | | | | | | | | | | | | | | | (626) @+(all_89_6, 0) = all_89_3 % 153.14/20.85 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.86 | | | | | | | | | | | | | | | all_217_0, all_89_1, all_89_6, all_89_0, % 153.14/20.86 | | | | | | | | | | | | | | | simplifying with (19), (25), (173), (174) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (627) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.86 | | | | | | | | | | | | | | | (@+(all_217_0, all_89_1) = v1 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & s(v1) = v2 & % 153.14/20.86 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_0)) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_217_0, simplifying with % 153.14/20.86 | | | | | | | | | | | | | | | (173), (175) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (628) all_217_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.86 | | | | | | | | | | | | | | | 0 & s(v0) = all_217_0 & $i(v0)) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_4, all_89_1, % 153.14/20.86 | | | | | | | | | | | | | | | simplifying with (16), (625) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (629) all_89_1 = all_89_4 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.86 | | | | | | | | | | | | | | | all_217_0, 0, all_89_6, all_89_3, simplifying with % 153.14/20.86 | | | | | | | | | | | | | | | (7), (173), (174), (626) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (630) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.86 | | | | | | | | | | | | | | | (@+(all_217_0, 0) = v1 & nat_succeeds(all_217_0) = % 153.14/20.86 | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.14/20.86 | | | | | | | | | | | | | | | | v2 = all_89_3)) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | DELTA: instantiating (627) with fresh symbols all_241_0, % 153.14/20.86 | | | | | | | | | | | | | | | all_241_1, all_241_2 gives: % 153.14/20.86 | | | | | | | | | | | | | | | (631) @+(all_217_0, all_89_1) = all_241_1 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_241_2 & s(all_241_1) % 153.14/20.86 | | | | | | | | | | | | | | | = all_241_0 & $i(all_241_0) & $i(all_241_1) & ( ~ % 153.14/20.86 | | | | | | | | | | | | | | | (all_241_2 = 0) | all_241_0 = all_89_0) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | ALPHA: (631) implies: % 153.14/20.86 | | | | | | | | | | | | | | | (632) $i(all_241_1) % 153.14/20.86 | | | | | | | | | | | | | | | (633) @+(all_217_0, all_89_1) = all_241_1 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | DELTA: instantiating (630) with fresh symbols all_243_0, % 153.14/20.86 | | | | | | | | | | | | | | | all_243_1, all_243_2 gives: % 153.14/20.86 | | | | | | | | | | | | | | | (634) @+(all_217_0, 0) = all_243_1 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_243_2 & s(all_243_1) % 153.14/20.86 | | | | | | | | | | | | | | | = all_243_0 & $i(all_243_0) & $i(all_243_1) & ( ~ % 153.14/20.86 | | | | | | | | | | | | | | | (all_243_2 = 0) | all_243_0 = all_89_3) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | ALPHA: (634) implies: % 153.14/20.86 | | | | | | | | | | | | | | | (635) @+(all_217_0, 0) = all_243_1 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | REDUCE: (629), (633) imply: % 153.14/20.86 | | | | | | | | | | | | | | | (636) @+(all_217_0, all_89_4) = all_241_1 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | REDUCE: (625), (629) imply: % 153.14/20.86 | | | | | | | | | | | | | | | (637) @+(0, all_89_4) = all_89_4 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.86 | | | | | | | | | | | | | | | all_217_0, 0, all_243_1, simplifying with (7), % 153.14/20.86 | | | | | | | | | | | | | | | (173), (635) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (638) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.86 | | | | | | | | | | | | | | | (nat_succeeds(all_243_1) = v2 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & nat_succeeds(0) = % 153.14/20.86 | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.86 | | | | | | | | | | | | | | | all_217_0, all_89_4, all_241_1, simplifying with % 153.14/20.86 | | | | | | | | | | | | | | | (16), (173), (636) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (639) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.86 | | | | | | | | | | | | | | | (nat_succeeds(all_241_1) = v2 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_89_4) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.86 | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | DELTA: instantiating (639) with fresh symbols all_271_0, % 153.14/20.86 | | | | | | | | | | | | | | | all_271_1, all_271_2 gives: % 153.14/20.86 | | | | | | | | | | | | | | | (640) nat_succeeds(all_241_1) = all_271_0 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_271_2 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_89_4) = all_271_1 & ( ~ % 153.14/20.86 | | | | | | | | | | | | | | | (all_271_1 = 0) | ~ (all_271_2 = 0) | all_271_0 % 153.14/20.86 | | | | | | | | | | | | | | | = 0) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | ALPHA: (640) implies: % 153.14/20.86 | | | | | | | | | | | | | | | (641) nat_succeeds(all_89_4) = all_271_1 % 153.14/20.86 | | | | | | | | | | | | | | | (642) nat_succeeds(all_217_0) = all_271_2 % 153.14/20.86 | | | | | | | | | | | | | | | (643) nat_succeeds(all_241_1) = all_271_0 % 153.14/20.86 | | | | | | | | | | | | | | | (644) ~ (all_271_1 = 0) | ~ (all_271_2 = 0) | % 153.14/20.86 | | | | | | | | | | | | | | | all_271_0 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | DELTA: instantiating (638) with fresh symbols all_273_0, % 153.14/20.86 | | | | | | | | | | | | | | | all_273_1, all_273_2 gives: % 153.14/20.86 | | | | | | | | | | | | | | | (645) nat_succeeds(all_243_1) = all_273_0 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_273_2 & % 153.14/20.86 | | | | | | | | | | | | | | | nat_succeeds(0) = all_273_1 & ( ~ (all_273_1 = 0) % 153.14/20.86 | | | | | | | | | | | | | | | | ~ (all_273_2 = 0) | all_273_0 = 0) % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | ALPHA: (645) implies: % 153.14/20.86 | | | | | | | | | | | | | | | (646) nat_succeeds(all_217_0) = all_273_2 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_271_1, all_89_4, % 153.14/20.86 | | | | | | | | | | | | | | | simplifying with (23), (641) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (647) all_271_1 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_273_2, all_217_0, % 153.14/20.86 | | | | | | | | | | | | | | | simplifying with (175), (646) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (648) all_273_2 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_271_2, all_273_2, % 153.14/20.86 | | | | | | | | | | | | | | | all_217_0, simplifying with (642), (646) gives: % 153.14/20.86 | | | | | | | | | | | | | | | (649) all_273_2 = all_271_2 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | COMBINE_EQS: (648), (649) imply: % 153.14/20.86 | | | | | | | | | | | | | | | (650) all_271_2 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | SIMP: (650) implies: % 153.14/20.86 | | | | | | | | | | | | | | | (651) all_271_2 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | BETA: splitting (644) gives: % 153.14/20.86 | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | Case 1: % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | (652) ~ (all_271_1 = 0) % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | REDUCE: (647), (652) imply: % 153.14/20.86 | | | | | | | | | | | | | | | | (653) $false % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | CLOSE: (653) is inconsistent. % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | Case 2: % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | (654) ~ (all_271_2 = 0) | all_271_0 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | BETA: splitting (654) gives: % 153.14/20.86 | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | Case 1: % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | (655) ~ (all_271_2 = 0) % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | REDUCE: (651), (655) imply: % 153.14/20.86 | | | | | | | | | | | | | | | | | (656) $false % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | CLOSE: (656) is inconsistent. % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | Case 2: % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | (657) all_271_0 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | REDUCE: (643), (657) imply: % 153.14/20.86 | | | | | | | | | | | | | | | | | (658) nat_succeeds(all_241_1) = 0 % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 153.14/20.86 | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | (659) all_154_0 = 0 % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | REDUCE: (118), (659) imply: % 153.14/20.86 | | | | | | | | | | | | | | | | | | (660) @+(0, all_156_1) = all_156_0 % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | REDUCE: (117), (659) imply: % 153.14/20.86 | | | | | | | | | | | | | | | | | | (661) @+(0, all_156_5) = all_156_3 % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (110), (111), (114), (119), (120), % 153.14/20.86 | | | | | | | | | | | | | | | | | | (660), (661) are inconsistent by sub-proof #10. % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | (662) ~ (all_154_0 = 0) % 153.14/20.86 | | | | | | | | | | | | | | | | | | (663) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.86 | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 153.14/20.86 | | | | | | | | | | | | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (@+(v3, v2) = % 153.14/20.86 | | | | | | | | | | | | | | | | | | v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ % 153.14/20.86 | | | | | | | | | | | | | | | | | | $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: % 153.14/20.86 | | | | | | | | | | | | | | | | | | $i] : ? [v8: $i] : (@+(v1, v2) = v7 & % 153.14/20.86 | | | | | | | | | | | | | | | | | | @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & % 153.14/20.86 | | | | | | | | | | | | | | | | | | nat_succeeds(v1) = v6 & $i(v8) & $i(v7) & ( % 153.14/20.86 | | | | | | | | | | | | | | | | | | ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))) % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | DELTA: instantiating (663) with fresh symbol all_331_0 % 153.14/20.86 | | | | | | | | | | | | | | | | | | gives: % 153.14/20.86 | | | | | | | | | | | | | | | | | | (664) nat_succeeds(all_331_0) = 0 & s(all_331_0) = % 153.14/20.86 | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_331_0) & ! [v0: $i] : ! [v1: % 153.14/20.86 | | | | | | | | | | | | | | | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, % 153.14/20.86 | | | | | | | | | | | | | | | | | | v1) = v3) | ~ (@+(all_331_0, v0) = v2) | ~ % 153.14/20.86 | | | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 153.14/20.86 | | | | | | | | | | | | | | | | | | : ? [v6: $i] : ? [v7: $i] : (@+(v0, v1) = v6 & % 153.14/20.86 | | | | | | | | | | | | | | | | | | @+(all_331_0, v6) = v7 & nat_succeeds(v1) = v4 % 153.14/20.86 | | | | | | | | | | | | | | | | | | & nat_succeeds(v0) = v5 & $i(v7) & $i(v6) & ( % 153.14/20.86 | | | | | | | | | | | | | | | | | | ~ (v5 = 0) | ~ (v4 = 0) | v7 = v3))) % 153.14/20.86 | | | | | | | | | | | | | | | | | | % 153.14/20.86 | | | | | | | | | | | | | | | | | | ALPHA: (664) implies: % 153.14/20.86 | | | | | | | | | | | | | | | | | | (665) $i(all_331_0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | (666) s(all_331_0) = all_154_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | (667) nat_succeeds(all_331_0) = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | (668) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 153.14/20.87 | | | | | | | | | | | | | | | | | | $i] : ( ~ (@+(v2, v1) = v3) | ~ (@+(all_331_0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 153.14/20.87 | | | | | | | | | | | | | | | | | | any] : ? [v5: any] : ? [v6: $i] : ? [v7: % 153.14/20.87 | | | | | | | | | | | | | | | | | | $i] : (@+(v0, v1) = v6 & @+(all_331_0, v6) = % 153.14/20.87 | | | | | | | | | | | | | | | | | | v7 & nat_succeeds(v1) = v4 & nat_succeeds(v0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | = v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 % 153.14/20.87 | | | | | | | | | | | | | | | | | | = 0) | v7 = v3))) % 153.14/20.87 | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | (669) all_156_5 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | REDUCE: (119), (669) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | (670) @+(0, all_156_4) = all_156_1 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | REDUCE: (117), (669) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | (671) @+(all_154_0, 0) = all_156_3 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | REDUCE: (115), (669) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | (672) nat_succeeds(0) = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (673) all_156_4 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (670), (673) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (674) @+(0, 0) = all_156_1 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_156_1, simplifying % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | with (7), (674) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (675) all_156_1 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (674), (675) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (676) @+(0, 0) = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (676), (corollary-(plus:successor)), % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | by sub-proof #7. % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_1, all_154_0, all_156_0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (665), (666) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (677) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (@+(all_331_0, all_156_1) = v1 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & s(v1) = v2 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_241_1, simplifying with % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (632), (658) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (678) all_241_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_241_1 & $i(v0)) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_331_0, simplifying with % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (665), (667) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (679) all_331_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_331_0 & $i(v0)) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_4, all_156_1, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | simplifying with (112), (670) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (680) all_156_1 = all_156_4 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_331_0, 0, all_154_0, all_156_3, simplifying % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | with (7), (665), (666), (671) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (681) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (@+(all_331_0, 0) = v1 & nat_succeeds(all_331_0) = % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | v2 = all_156_3)) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_154_0, 0, all_156_3, simplifying with (7), % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (106), (671) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (682) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_156_3) = v2 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_154_0) = v0 & nat_succeeds(0) = % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (682) with fresh symbols all_358_0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_358_1, all_358_2 gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (683) nat_succeeds(all_156_3) = all_358_0 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_154_0) = all_358_2 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_358_1 & ( ~ (all_358_1 = 0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | ~ (all_358_2 = 0) | all_358_0 = 0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (683) implies: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (684) nat_succeeds(0) = all_358_1 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (685) nat_succeeds(all_154_0) = all_358_2 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (681) with fresh symbols all_360_0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_360_1, all_360_2 gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (686) @+(all_331_0, 0) = all_360_1 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_360_2 & s(all_360_1) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | = all_360_0 & $i(all_360_0) & $i(all_360_1) & ( ~ % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (all_360_2 = 0) | all_360_0 = all_156_3) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (686) implies: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (687) $i(all_360_1) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (688) s(all_360_1) = all_360_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (689) nat_succeeds(all_331_0) = all_360_2 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (690) @+(all_331_0, 0) = all_360_1 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (691) ~ (all_360_2 = 0) | all_360_0 = all_156_3 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (677) with fresh symbols all_362_0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_362_1, all_362_2 gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (692) @+(all_331_0, all_156_1) = all_362_1 & % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_362_2 & s(all_362_1) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | = all_362_0 & $i(all_362_0) & $i(all_362_1) & ( ~ % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (all_362_2 = 0) | all_362_0 = all_156_0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (692) implies: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (693) $i(all_362_1) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (694) s(all_362_1) = all_362_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (695) nat_succeeds(all_331_0) = all_362_2 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (696) @+(all_331_0, all_156_1) = all_362_1 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (697) ~ (all_362_2 = 0) | all_362_0 = all_156_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (680), (696) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (698) @+(all_331_0, all_156_4) = all_362_1 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (680) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (699) @+(all_154_0, all_156_4) = all_156_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | REDUCE: (670), (680) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (700) @+(0, all_156_4) = all_156_4 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_358_1, 0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | simplifying with (672), (684) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (701) all_358_1 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_169_2, all_358_2, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (135), (685) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (702) all_358_2 = all_169_2 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_362_2, all_331_0, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | simplifying with (667), (695) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (703) all_362_2 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_360_2, all_362_2, % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | all_331_0, simplifying with (689), (695) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (704) all_362_2 = all_360_2 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (703), (704) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (705) all_360_2 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | SIMP: (705) implies: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | (706) all_360_2 = 0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (697) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | (707) ~ (all_362_2 = 0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | REDUCE: (703), (707) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | (708) $false % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | CLOSE: (708) is inconsistent. % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | (709) all_362_0 = all_156_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | REDUCE: (694), (709) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | (710) s(all_362_1) = all_156_0 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (691) gives: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | (711) ~ (all_360_2 = 0) % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (706), (711) imply: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | (712) $false % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (712) is inconsistent. % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | (713) all_360_0 = all_156_3 % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.87 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (688), (713) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | (714) s(all_360_1) = all_156_3 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | (715) all_169_2 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (715) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | (716) nat_succeeds(all_154_0) = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (717) all_217_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (636), (717) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (718) @+(0, all_89_4) = all_241_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (635), (717) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (719) @+(0, 0) = all_243_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_4, all_241_1, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_89_4, 0, simplifying with (637), (718) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (720) all_241_1 = all_89_4 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (10), (11), (37), (106), % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (112), (114), (115), (116), % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (117), (118), (119), (120), (121), (135), (155), % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (156), (623), (678), (719), (720), % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:successor)), % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #3. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (721) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(v0)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (721) with fresh symbol all_438_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (722) nat_succeeds(all_438_0) = 0 & s(all_438_0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(all_438_0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (722) implies: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (723) $i(all_438_0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (724) s(all_438_0) = all_217_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, all_156_4, all_156_3, all_156_2, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (120), (687), (714) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (725) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_360_1, all_156_4) = v1 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = v0 & s(v1) = v2 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_156_2)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_438_0, 0, all_217_0, all_243_1, simplifying % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | with (7), (635), (723), (724) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (726) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_438_0, 0) = v1 & nat_succeeds(all_438_0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_243_1)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (106), (716) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (727) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, 0, all_360_1, simplifying with (7), % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (665), (690) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (728) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_360_1) = v2 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & nat_succeeds(0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_4, all_362_1, simplifying with % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (112), (665), (698) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (729) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_362_1) = v2 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (729) with fresh symbols all_462_0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_462_1, all_462_2 gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (730) nat_succeeds(all_362_1) = all_462_0 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_462_2 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_462_1 & ( ~ % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (all_462_1 = 0) | ~ (all_462_2 = 0) | all_462_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (730) implies: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (731) nat_succeeds(all_156_4) = all_462_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (732) nat_succeeds(all_331_0) = all_462_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (733) nat_succeeds(all_362_1) = all_462_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (734) ~ (all_462_1 = 0) | ~ (all_462_2 = 0) | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_462_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (728) with fresh symbols all_464_0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_464_1, all_464_2 gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (735) nat_succeeds(all_360_1) = all_464_0 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_464_2 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_464_1 & ( ~ (all_464_1 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_464_2 = 0) | all_464_0 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (735) implies: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (736) nat_succeeds(0) = all_464_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (737) nat_succeeds(all_331_0) = all_464_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (738) nat_succeeds(all_360_1) = all_464_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (739) ~ (all_464_1 = 0) | ~ (all_464_2 = 0) | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_464_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (726) with fresh symbols all_466_0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_466_1, all_466_2 gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (740) @+(all_438_0, 0) = all_466_1 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_438_0) = all_466_2 & s(all_466_1) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | = all_466_0 & $i(all_466_0) & $i(all_466_1) & ( ~ % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (all_466_2 = 0) | all_466_0 = all_243_1) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (740) implies: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (741) @+(all_438_0, 0) = all_466_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (725) with fresh symbols all_468_0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | all_468_1, all_468_2 gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (742) @+(all_360_1, all_156_4) = all_468_1 & % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = all_468_2 & s(all_468_1) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | = all_468_0 & $i(all_468_0) & $i(all_468_1) & ( ~ % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (all_468_2 = 0) | all_468_0 = all_156_2) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (742) implies: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (743) s(all_468_1) = all_468_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (744) nat_succeeds(all_360_1) = all_468_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (745) @+(all_360_1, all_156_4) = all_468_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | (746) ~ (all_468_2 = 0) | all_468_0 = all_156_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_154_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (662), (747) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (748) $false % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (748) is inconsistent. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (749) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (749) with fresh symbol all_476_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (750) nat_succeeds(all_476_0) = 0 & s(all_476_0) = % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_476_0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (750) implies: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (751) $i(all_476_0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (752) s(all_476_0) = all_154_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_464_1, 0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (672), (736) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_464_1 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_462_1, all_156_4, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (731) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_462_1 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_464_2, all_331_0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (667), (737) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (755) all_464_2 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_462_2, all_464_2, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, simplifying with (732), (737) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_464_2 = all_462_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_464_0, all_468_2, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, simplifying with (738), (744) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_468_2 = all_464_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (755), (756) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | (758) all_462_2 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (734) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (759) ~ (all_462_1 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (754), (759) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (760) $false % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (760) is inconsistent. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (761) ~ (all_462_2 = 0) | all_462_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (761) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) ~ (all_462_2 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (758), (762) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) $false % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (763) is inconsistent. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_462_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (733), (764) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) nat_succeeds(all_362_1) = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (739) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) ~ (all_464_1 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (753), (766) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) $false % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (767) is inconsistent. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) ~ (all_464_2 = 0) | all_464_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) ~ (all_464_2 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (755), (769) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) $false % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (770) is inconsistent. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) all_464_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (757), (771) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_468_2 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (746) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) ~ (all_468_2 = 0) % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (772), (773) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) $false % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (774) is inconsistent. % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) all_468_0 = all_156_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (743), (775) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) s(all_468_1) = all_156_2 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (679) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_331_0 = 0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (698), (777) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) @+(0, all_156_4) = all_362_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (690), (777) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) @+(0, 0) = all_360_1 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (666), (777) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) s(0) = all_154_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_96_0, all_154_0, 0, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (37), (780) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) all_154_0 = all_96_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_4, all_362_1, % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, 0, simplifying with (700), (778) gives: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_362_1 = all_156_4 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (752), (781) imply: % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) s(all_476_0) = all_96_0 % 153.14/20.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with 0, all_476_0, all_96_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (7), (37), (751), (783) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) all_476_0 = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_360_1, simplifying % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (7), (779) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_360_1 = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (779), (785) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) @+(0, 0) = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786), (corollary-(plus:successor)), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #7. % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_476_0, all_156_4, all_154_0, all_156_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (699), (751), (752) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_476_0, all_156_4) = v1 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_476_0) = v0 & s(v1) = v2 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_331_0, all_476_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (665), (666), (751), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_476_0 = all_331_0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (668) with 0, all_156_4, all_360_1, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_468_1, simplifying with (7), (112), (690), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_331_0, v2) = v3 & @+(0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(0) = v1 & $i(v3) & $i(v2) & ( ~ % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = all_468_1)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_438_0, 0, all_466_1, simplifying with (7), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723), (741) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_466_1) = v2 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_438_0) = v0 & nat_succeeds(0) = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (790) with fresh symbols all_578_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_578_1, all_578_2 gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) nat_succeeds(all_466_1) = all_578_0 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_438_0) = all_578_2 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_578_1 & ( ~ (all_578_1 = 0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_578_2 = 0) | all_578_0 = 0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) nat_succeeds(0) = all_578_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (787) with fresh symbols all_582_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_582_1, all_582_2 gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) @+(all_476_0, all_156_4) = all_582_1 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_476_0) = all_582_2 & s(all_582_1) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_582_0 & $i(all_582_0) & $i(all_582_1) & ( ~ % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_582_2 = 0) | all_582_0 = all_156_0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (793) implies: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) @+(all_476_0, all_156_4) = all_582_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (789) with fresh symbols all_596_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_596_1, all_596_2, all_596_3 gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) @+(all_331_0, all_596_1) = all_596_0 & @+(0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = all_596_1 & nat_succeeds(all_156_4) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_596_3 & nat_succeeds(0) = all_596_2 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_596_0) & $i(all_596_1) & ( ~ (all_596_2 = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_596_3 = 0) | all_596_0 = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_468_1) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (795) implies: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) nat_succeeds(0) = all_596_2 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) nat_succeeds(all_156_4) = all_596_3 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) @+(0, all_156_4) = all_596_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) @+(all_331_0, all_596_1) = all_596_0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) ~ (all_596_2 = 0) | ~ (all_596_3 = 0) | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_596_0 = all_468_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (788), (794) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) @+(all_331_0, all_156_4) = all_582_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_596_2, 0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (672), (796) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_596_2 = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_578_1, all_596_2, 0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (792), (796) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_596_2 = all_578_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_596_3, all_156_4, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (797) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) all_596_3 = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_4, all_596_1, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, 0, simplifying with (700), (798) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) all_596_1 = all_156_4 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_362_1, all_582_1, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_331_0, simplifying with (698), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_582_1 = all_362_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (802), (803) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_578_1 = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (799), (805) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) @+(all_331_0, all_156_4) = all_596_0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (800) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) ~ (all_596_2 = 0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (802), (809) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) $false % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (810) is inconsistent. % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) ~ (all_596_3 = 0) | all_596_0 = all_468_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (811) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) ~ (all_596_3 = 0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (804), (812) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) $false % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (813) is inconsistent. % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_596_0 = all_468_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (808), (814) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) @+(all_331_0, all_156_4) = all_468_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_362_1, all_468_1, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_331_0, simplifying with (698), % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_468_1 = all_362_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (776), (816) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) s(all_362_1) = all_156_2 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_362_1, simplifying with (710), (817) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_156_0 = all_156_2 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (818) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) $false % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (819) is inconsistent. % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | (820) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (820) implies: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | (821) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (665), (666), (667), (821) are inconsistent % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.89 | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | (822) ~ (all_156_5 = 0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | (823) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | all_156_5 & $i(v0)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | DELTA: instantiating (823) with fresh symbol all_340_0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | (824) nat_succeeds(all_340_0) = 0 & s(all_340_0) = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | all_156_5 & $i(all_340_0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | ALPHA: (824) implies: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | (825) $i(all_340_0) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | (826) s(all_340_0) = all_156_5 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (827) all_156_4 = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (827) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (828) @+(all_156_3, 0) = all_156_2 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (827) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (829) @+(all_156_5, 0) = all_156_1 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (827) imply: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (830) nat_succeeds(0) = 0 % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_1, all_154_0, all_156_0, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (665), (666) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (831) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (@+(all_331_0, all_156_1) = v1 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & s(v1) = v2 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_5, all_154_0, all_156_3, % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | simplifying with (111), (117), (665), (666) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (832) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (@+(all_331_0, all_156_5) = v1 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & s(v1) = v2 & % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | all_156_3)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_241_1, simplifying with % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (632), (658) gives: % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (833) all_241_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_241_1 & $i(v0)) % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_331_0, simplifying with % 153.14/20.89 | | | | | | | | | | | | | | | | | | | | (665), (667) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (834) all_331_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_331_0 & $i(v0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_340_0, 0, all_156_5, all_156_1, simplifying % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | with (7), (825), (826), (829) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (835) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (@+(all_340_0, 0) = v1 & nat_succeeds(all_340_0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | v2 = all_156_1)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_156_3, 0, all_156_2, simplifying with (7), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (113), (828) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (836) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_156_2) = v2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_3) = v0 & nat_succeeds(0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (836) with fresh symbols all_358_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_358_1, all_358_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (837) nat_succeeds(all_156_2) = all_358_0 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_3) = all_358_2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_358_1 & ( ~ (all_358_1 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | ~ (all_358_2 = 0) | all_358_0 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (837) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (838) nat_succeeds(0) = all_358_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (832) with fresh symbols all_360_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_360_1, all_360_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (839) @+(all_331_0, all_156_5) = all_360_1 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_360_2 & s(all_360_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | = all_360_0 & $i(all_360_0) & $i(all_360_1) & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (all_360_2 = 0) | all_360_0 = all_156_3) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (839) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (840) $i(all_360_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (841) s(all_360_1) = all_360_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (842) nat_succeeds(all_331_0) = all_360_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (843) @+(all_331_0, all_156_5) = all_360_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (844) ~ (all_360_2 = 0) | all_360_0 = all_156_3 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (831) with fresh symbols all_362_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_362_1, all_362_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (845) @+(all_331_0, all_156_1) = all_362_1 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_362_2 & s(all_362_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | = all_362_0 & $i(all_362_0) & $i(all_362_1) & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (all_362_2 = 0) | all_362_0 = all_156_0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (845) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (846) s(all_362_1) = all_362_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (847) nat_succeeds(all_331_0) = all_362_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (848) @+(all_331_0, all_156_1) = all_362_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (849) ~ (all_362_2 = 0) | all_362_0 = all_156_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (835) with fresh symbols all_364_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_364_1, all_364_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (850) @+(all_340_0, 0) = all_364_1 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = all_364_2 & s(all_364_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | = all_364_0 & $i(all_364_0) & $i(all_364_1) & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (all_364_2 = 0) | all_364_0 = all_156_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (850) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (851) @+(all_340_0, 0) = all_364_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_358_1, 0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | simplifying with (830), (838) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (852) all_358_1 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_362_2, all_331_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | simplifying with (667), (847) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (853) all_362_2 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_360_2, all_362_2, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | all_331_0, simplifying with (842), (847) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (854) all_362_2 = all_360_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (853), (854) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | (855) all_360_2 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (849) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | (856) ~ (all_362_2 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (853), (856) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | (857) $false % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | CLOSE: (857) is inconsistent. % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | (858) all_362_0 = all_156_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (846), (858) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | (859) s(all_362_1) = all_156_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (844) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | (860) ~ (all_360_2 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (855), (860) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | (861) $false % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (861) is inconsistent. % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | (862) all_360_0 = all_156_3 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (841), (862) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | (863) s(all_360_1) = all_156_3 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | (864) all_169_2 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (864) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | (865) nat_succeeds(all_154_0) = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (866) all_217_0 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (636), (866) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (867) @+(0, all_89_4) = all_241_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (635), (866) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (868) @+(0, 0) = all_243_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_4, all_241_1, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_89_4, 0, simplifying with (637), (867) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (869) all_241_1 = all_89_4 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (10), (11), (37), (106), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (107), (110), (111), (112), (114), (115), (116), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (117), (118), (119), (120), (121), (135), (155), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (156), (623), (833), (868), (869), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:successor)), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #3. % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (870) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(v0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (870) with fresh symbol all_450_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (871) nat_succeeds(all_450_0) = 0 & s(all_450_0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(all_450_0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (871) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (872) $i(all_450_0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (873) s(all_450_0) = all_217_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, 0, all_156_3, all_156_2, simplifying % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | with (7), (828), (840), (863) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (874) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_360_1, 0) = v1 & nat_succeeds(all_360_1) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_156_2)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_450_0, 0, all_217_0, all_243_1, simplifying % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | with (7), (635), (872), (873) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (875) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_450_0, 0) = v1 & nat_succeeds(all_450_0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_243_1)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (106), (865) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (876) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_5, all_360_1, simplifying with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (111), (665), (843) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (877) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_360_1) = v2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_1, all_362_1, simplifying with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (114), (665), (848) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (878) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_362_1) = v2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_340_0, 0, all_364_1, simplifying with (7), % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (825), (851) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (879) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_364_1) = v2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = v0 & nat_succeeds(0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (879) with fresh symbols all_474_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_474_1, all_474_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (880) nat_succeeds(all_364_1) = all_474_0 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = all_474_2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_474_1 & ( ~ (all_474_1 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_474_2 = 0) | all_474_0 = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (880) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (881) nat_succeeds(0) = all_474_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (877) with fresh symbols all_476_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_476_1, all_476_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (882) nat_succeeds(all_360_1) = all_476_0 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_476_2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_476_1 & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (all_476_1 = 0) | ~ (all_476_2 = 0) | all_476_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (882) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (883) nat_succeeds(all_156_5) = all_476_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (884) nat_succeeds(all_331_0) = all_476_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (885) nat_succeeds(all_360_1) = all_476_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (886) ~ (all_476_1 = 0) | ~ (all_476_2 = 0) | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_476_0 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (878) with fresh symbols all_478_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_478_1, all_478_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (887) nat_succeeds(all_362_1) = all_478_0 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_478_2 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = all_478_1 & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (all_478_1 = 0) | ~ (all_478_2 = 0) | all_478_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (887) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (888) nat_succeeds(all_331_0) = all_478_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (875) with fresh symbols all_480_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_480_1, all_480_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (889) @+(all_450_0, 0) = all_480_1 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_450_0) = all_480_2 & s(all_480_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | = all_480_0 & $i(all_480_0) & $i(all_480_1) & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (all_480_2 = 0) | all_480_0 = all_243_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (889) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (890) @+(all_450_0, 0) = all_480_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (874) with fresh symbols all_484_0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | all_484_1, all_484_2 gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (891) @+(all_360_1, 0) = all_484_1 & % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = all_484_2 & s(all_484_1) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | = all_484_0 & $i(all_484_0) & $i(all_484_1) & ( ~ % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (all_484_2 = 0) | all_484_0 = all_156_2) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (891) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (892) s(all_484_1) = all_484_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (893) nat_succeeds(all_360_1) = all_484_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (894) @+(all_360_1, 0) = all_484_1 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | (895) ~ (all_484_2 = 0) | all_484_0 = all_156_2 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (876) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (896) all_154_0 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (662), (896) imply: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (897) $false % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (897) is inconsistent. % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (898) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (898) with fresh symbol all_490_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (899) nat_succeeds(all_490_0) = 0 & s(all_490_0) = % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_490_0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (899) implies: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (900) $i(all_490_0) % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (901) s(all_490_0) = all_154_0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (902) nat_succeeds(all_490_0) = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_474_1, 0, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (830), (881) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_474_1 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_476_1, all_156_5, % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (883) gives: % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | (904) all_476_1 = 0 % 153.14/20.90 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_478_2, all_331_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (667), (888) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | (905) all_478_2 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_476_2, all_478_2, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, simplifying with (884), (888) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_478_2 = all_476_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_476_0, all_484_2, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, simplifying with (885), (893) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_484_2 = all_476_0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (905), (906) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_476_2 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (886) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (909) ~ (all_476_1 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (904), (909) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (910) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (910) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (911) ~ (all_476_2 = 0) | all_476_0 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) ~ (all_476_2 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (908), (912) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (913) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) all_476_0 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (907), (914) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) all_484_2 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (895) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) ~ (all_484_2 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (915), (916) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (917) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_484_0 = all_156_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (892), (918) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) s(all_484_1) = all_156_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (834) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_331_0 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (848), (920) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) @+(0, all_156_1) = all_362_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (843), (920) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) @+(0, all_156_5) = all_360_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_5, all_360_1, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (111), (922) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_360_1 = all_156_5 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_1, all_362_1, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (921) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) all_362_1 = all_156_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (894), (923) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) @+(all_156_5, 0) = all_484_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (859), (924) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) s(all_156_1) = all_156_0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_484_1, 0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_5, simplifying with (829), (925) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) all_484_1 = all_156_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (919), (927) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) s(all_156_1) = all_156_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (110), (926), (928) are inconsistent by % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) ~ (all_331_0 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_490_0, all_156_1, all_154_0, all_156_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (900), (901) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_490_0, all_156_1) = v1 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_490_0) = v0 & s(v1) = v2 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_331_0, all_490_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (665), (666), (900), % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_490_0 = all_331_0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_490_0, simplifying with % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900), (902) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_490_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_490_0 & $i(v0)) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (668) with all_156_5, 0, all_360_1, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_484_1, simplifying with (7), (111), (843), % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_331_0, v2) = v3 & @+(all_156_5, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) = v2 & nat_succeeds(all_156_5) = v1 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = v0 & $i(v3) & $i(v2) & ( ~ (v1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | ~ (v0 = 0) | v3 = all_484_1)) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, 0, all_484_1, simplifying with (7), % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840), (894) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_484_1) = v2 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = v0 & nat_succeeds(0) = % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_450_0, 0, all_480_1, simplifying with (7), % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872), (890) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_480_1) = v2 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_450_0) = v0 & nat_succeeds(0) = % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (935) with fresh symbols all_588_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_588_1, all_588_2 gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) nat_succeeds(all_480_1) = all_588_0 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_450_0) = all_588_2 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_588_1 & ( ~ (all_588_1 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_588_2 = 0) | all_588_0 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (936) implies: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) nat_succeeds(0) = all_588_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (934) with fresh symbols all_590_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_590_1, all_590_2 gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) nat_succeeds(all_484_1) = all_590_0 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = all_590_2 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_590_1 & ( ~ (all_590_1 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_590_2 = 0) | all_590_0 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (938) implies: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) nat_succeeds(0) = all_590_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (930) with fresh symbols all_606_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_606_1, all_606_2 gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) @+(all_490_0, all_156_1) = all_606_1 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_490_0) = all_606_2 & s(all_606_1) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_606_0 & $i(all_606_0) & $i(all_606_1) & ( ~ % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_606_2 = 0) | all_606_0 = all_156_0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (940) implies: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) @+(all_490_0, all_156_1) = all_606_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (933) with fresh symbols all_608_0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_608_1, all_608_2, all_608_3 gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) @+(all_331_0, all_608_1) = all_608_0 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(all_156_5, 0) = all_608_1 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_608_2 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_608_3 & $i(all_608_0) & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_608_1) & ( ~ (all_608_2 = 0) | ~ % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_608_3 = 0) | all_608_0 = all_484_1) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (942) implies: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) nat_succeeds(0) = all_608_3 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) nat_succeeds(all_156_5) = all_608_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) @+(all_156_5, 0) = all_608_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) @+(all_331_0, all_608_1) = all_608_0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) ~ (all_608_2 = 0) | ~ (all_608_3 = 0) | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_608_0 = all_484_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (931), (941) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) @+(all_331_0, all_156_1) = all_606_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (932) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_490_0 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (931), (949) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_331_0 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (929), (950) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (951) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_590_1, 0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (830), (939) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) all_590_1 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_590_1, all_608_3, 0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (939), (943) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) all_608_3 = all_590_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_588_1, all_608_3, 0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (937), (943) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) all_608_3 = all_588_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_608_2, all_156_5, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (944) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_608_2 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_608_1, 0, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_5, simplifying with (829), (945) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_608_1 = all_156_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_362_1, all_606_1, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_331_0, simplifying with (848), % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_606_1 = all_362_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (953), (954) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) all_590_1 = all_588_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (958) implies: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_590_1 = all_588_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (952), (959) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_588_1 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (954), (960) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_608_3 = 0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (946), (956) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) @+(all_331_0, all_156_1) = all_608_0 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (947) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) ~ (all_608_2 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (955), (963) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (964) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) ~ (all_608_3 = 0) | all_608_0 = all_484_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (965) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) ~ (all_608_3 = 0) % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (961), (966) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (967) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_608_0 = all_484_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (962), (968) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) @+(all_331_0, all_156_1) = all_484_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_362_1, all_484_1, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_331_0, simplifying with (848), % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_484_1 = all_362_1 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (919), (970) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) s(all_362_1) = all_156_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_362_1, simplifying with (859), (971) gives: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_156_0 = all_156_2 % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (972) imply: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) $false % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (973) is inconsistent. % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | (974) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 153.14/20.91 | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (974) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (975) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (665), (666), (667), (975) are inconsistent % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (976) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_156_4 & $i(v0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (976) with fresh symbol all_348_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (977) nat_succeeds(all_348_0) = 0 & s(all_348_0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_156_4 & $i(all_348_0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (977) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (978) $i(all_348_0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (979) s(all_348_0) = all_156_4 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (980) nat_succeeds(all_348_0) = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_1, all_154_0, all_156_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (665), (666) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (981) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (@+(all_331_0, all_156_1) = v1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & s(v1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_5, all_154_0, all_156_3, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | simplifying with (111), (117), (665), (666) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (982) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (@+(all_331_0, all_156_5) = v1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & s(v1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_156_3)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_340_0, all_156_4, all_156_5, all_156_1, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | simplifying with (112), (119), (825), (826) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (983) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (@+(all_340_0, all_156_4) = v1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = v0 & s(v1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_156_1)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_331_0, simplifying with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (665), (667) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (984) all_331_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_331_0 & $i(v0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_348_0, simplifying with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (978), (980) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (985) all_348_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_348_0 & $i(v0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (982) with fresh symbols all_360_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_360_1, all_360_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (986) @+(all_331_0, all_156_5) = all_360_1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_360_2 & s(all_360_1) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | = all_360_0 & $i(all_360_0) & $i(all_360_1) & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (all_360_2 = 0) | all_360_0 = all_156_3) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (986) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (987) $i(all_360_1) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (988) s(all_360_1) = all_360_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (989) nat_succeeds(all_331_0) = all_360_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (990) @+(all_331_0, all_156_5) = all_360_1 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (991) ~ (all_360_2 = 0) | all_360_0 = all_156_3 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (981) with fresh symbols all_362_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_362_1, all_362_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (992) @+(all_331_0, all_156_1) = all_362_1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_362_2 & s(all_362_1) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | = all_362_0 & $i(all_362_0) & $i(all_362_1) & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (all_362_2 = 0) | all_362_0 = all_156_0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (992) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (993) s(all_362_1) = all_362_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (994) nat_succeeds(all_331_0) = all_362_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (995) @+(all_331_0, all_156_1) = all_362_1 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (996) ~ (all_362_2 = 0) | all_362_0 = all_156_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (983) with fresh symbols all_364_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_364_1, all_364_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (997) @+(all_340_0, all_156_4) = all_364_1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = all_364_2 & s(all_364_1) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | = all_364_0 & $i(all_364_0) & $i(all_364_1) & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (all_364_2 = 0) | all_364_0 = all_156_1) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (997) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (998) @+(all_340_0, all_156_4) = all_364_1 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_362_2, all_331_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | simplifying with (667), (994) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (999) all_362_2 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_360_2, all_362_2, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | all_331_0, simplifying with (989), (994) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (1000) all_362_2 = all_360_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (999), (1000) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | (1001) all_360_2 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | BETA: splitting (996) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | (1002) ~ (all_362_2 = 0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (999), (1002) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | (1003) $false % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1003) is inconsistent. % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | (1004) all_362_0 = all_156_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | REDUCE: (993), (1004) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | (1005) s(all_362_1) = all_156_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (991) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | (1006) ~ (all_360_2 = 0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1001), (1006) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | (1007) $false % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1007) is inconsistent. % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | (1008) all_360_0 = all_156_3 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (988), (1008) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | (1009) s(all_360_1) = all_156_3 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1010) all_169_2 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1010) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1011) nat_succeeds(all_154_0) = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_360_1, all_156_4, all_156_3, all_156_2, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (120), (987), (1009) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1012) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (@+(all_360_1, all_156_4) = v1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = v0 & s(v1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_156_2)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (106), (1011) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1013) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_5, all_360_1, simplifying with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (111), (665), (990) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1014) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_360_1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_331_0, all_156_1, all_362_1, simplifying with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (114), (665), (995) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1015) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_362_1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = v0 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_340_0, all_156_4, all_364_1, simplifying with % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (112), (825), (998) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1016) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_364_1) = v2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = v0 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1016) with fresh symbols all_468_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_468_1, all_468_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1017) nat_succeeds(all_364_1) = all_468_0 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_340_0) = all_468_2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_468_1 & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (all_468_1 = 0) | ~ (all_468_2 = 0) | all_468_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1017) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1018) nat_succeeds(all_156_4) = all_468_1 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1015) with fresh symbols all_470_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_470_1, all_470_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1019) nat_succeeds(all_362_1) = all_470_0 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_470_2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = all_470_1 & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (all_470_1 = 0) | ~ (all_470_2 = 0) | all_470_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1019) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1020) nat_succeeds(all_331_0) = all_470_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1014) with fresh symbols all_472_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_472_1, all_472_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1021) nat_succeeds(all_360_1) = all_472_0 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_331_0) = all_472_2 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_472_1 & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (all_472_1 = 0) | ~ (all_472_2 = 0) | all_472_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1021) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1022) nat_succeeds(all_156_5) = all_472_1 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1023) nat_succeeds(all_331_0) = all_472_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1024) nat_succeeds(all_360_1) = all_472_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1025) ~ (all_472_1 = 0) | ~ (all_472_2 = 0) | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_472_0 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1012) with fresh symbols all_476_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | all_476_1, all_476_2 gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1026) @+(all_360_1, all_156_4) = all_476_1 & % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = all_476_2 & s(all_476_1) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | = all_476_0 & $i(all_476_0) & $i(all_476_1) & ( ~ % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (all_476_2 = 0) | all_476_0 = all_156_2) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1026) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1027) s(all_476_1) = all_476_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1028) nat_succeeds(all_360_1) = all_476_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1029) @+(all_360_1, all_156_4) = all_476_1 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | (1030) ~ (all_476_2 = 0) | all_476_0 = all_156_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1013) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1031) all_154_0 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (662), (1031) imply: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1032) $false % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1032) is inconsistent. % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1033) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1033) with fresh symbol all_484_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1034) nat_succeeds(all_484_0) = 0 & s(all_484_0) = % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_484_0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1034) implies: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1035) $i(all_484_0) % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1036) s(all_484_0) = all_154_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1037) nat_succeeds(all_484_0) = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_472_1, all_156_5, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (1022) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_472_1 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_468_1, all_156_4, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (1018) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1039) all_468_1 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_472_2, all_331_0, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (667), (1023) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_472_2 = 0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_470_2, all_472_2, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | all_331_0, simplifying with (1020), (1023) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1041) all_472_2 = all_470_2 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_472_0, all_476_2, % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, simplifying with (1024), (1028) gives: % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | (1042) all_476_2 = all_472_0 % 153.14/20.92 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1040), (1041) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | (1043) all_470_2 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1025) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1044) ~ (all_472_1 = 0) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1038), (1044) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1045) $false % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1045) is inconsistent. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | (1046) ~ (all_472_2 = 0) | all_472_0 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) ~ (all_472_2 = 0) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1040), (1047) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) $false % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1048) is inconsistent. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) all_472_0 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1042), (1049) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_476_2 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1024), (1049) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) nat_succeeds(all_360_1) = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1030) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) ~ (all_476_2 = 0) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1050), (1052) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) $false % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1053) is inconsistent. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_476_0 = all_156_2 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1027), (1054) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) s(all_476_1) = all_156_2 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) all_331_0 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (995), (1056) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) @+(0, all_156_1) = all_362_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (990), (1056) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) @+(0, all_156_5) = all_360_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (666), (1056) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) s(0) = all_154_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_96_0, all_154_0, 0, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (37), (1059) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) all_154_0 = all_96_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (985) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_348_0 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (979), (1061) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) s(0) = all_156_4 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_96_0, all_156_4, 0, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (37), (1062) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_156_4 = all_96_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1029), (1063) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) @+(all_360_1, all_96_0) = all_476_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1063) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) @+(all_156_5, all_96_0) = all_156_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_360_1, simplifying with % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987), (1051) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_360_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_360_1 & $i(v0)) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_5, all_360_1, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (111), (1058) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) all_360_1 = all_156_5 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_1, all_362_1, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (1057) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_362_1 = all_156_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1064), (1067) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) @+(all_156_5, all_96_0) = all_476_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1005), (1068) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) s(all_156_1) = all_156_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1066) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_360_1 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1067), (1071) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) all_156_5 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1072) implies: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_156_5 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (822), (1073) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) $false % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1074) is inconsistent. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_476_1, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_96_0, all_156_5, simplifying with (1065), % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_476_1 = all_156_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1055), (1075) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) s(all_156_1) = all_156_2 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (110), (1070), (1076) are inconsistent by % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_360_1, simplifying with % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987), (1051) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) all_360_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_360_1 & $i(v0)) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_5, all_360_1, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (111), (1058) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) all_360_1 = all_156_5 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_1, all_362_1, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (1057) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) all_362_1 = all_156_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1029), (1078) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) @+(all_156_5, all_156_4) = all_476_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1005), (1079) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) s(all_156_1) = all_156_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1077) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_360_1 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1078), (1082) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_156_5 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1083) implies: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_156_5 = 0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (822), (1084) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) $false % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1085) is inconsistent. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_476_1, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (119), % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_476_1 = all_156_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1055), (1086) imply: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) s(all_156_1) = all_156_2 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (110), (1081), (1087) are inconsistent by % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) ~ (all_331_0 = 0) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_484_0, all_156_1, all_154_0, all_156_0, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (1035), (1036) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_484_0, all_156_1) = v1 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_484_0) = v0 & s(v1) = v2 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_331_0, all_484_0, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (665), (666), (1035), % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_484_0 = all_331_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_484_0, simplifying with % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035), (1037) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) all_484_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_484_0 & $i(v0)) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (668) with all_156_5, all_156_4, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, all_476_1, simplifying with (111), % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (990), (1029) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_331_0, v2) = v3 & @+(all_156_5, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(all_156_5) = v1 & $i(v3) & $i(v2) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_476_1)) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_360_1, all_156_4, all_476_1, simplifying with % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (987), (1029) gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_476_1) = v2 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = v0 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1093) with fresh symbols all_590_0, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_590_1, all_590_2 gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) nat_succeeds(all_476_1) = all_590_0 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_360_1) = all_590_2 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_590_1 & ( ~ % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_590_1 = 0) | ~ (all_590_2 = 0) | all_590_0 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1094) implies: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) nat_succeeds(all_156_4) = all_590_1 % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1089) with fresh symbols all_594_0, % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_594_1, all_594_2 gives: % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) @+(all_484_0, all_156_1) = all_594_1 & % 153.14/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_484_0) = all_594_2 & s(all_594_1) % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_594_0 & $i(all_594_0) & $i(all_594_1) & ( ~ % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_594_2 = 0) | all_594_0 = all_156_0) % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1096) implies: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) @+(all_484_0, all_156_1) = all_594_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1092) with fresh symbols all_608_0, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_608_1, all_608_2, all_608_3 gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) @+(all_331_0, all_608_1) = all_608_0 & % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(all_156_5, all_156_4) = all_608_1 & % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_608_3 & % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_608_2 & % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_608_0) & $i(all_608_1) & ( ~ (all_608_2 = % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_608_3 = 0) | all_608_0 = % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_476_1) % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1098) implies: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) nat_succeeds(all_156_5) = all_608_2 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) nat_succeeds(all_156_4) = all_608_3 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) @+(all_156_5, all_156_4) = all_608_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) @+(all_331_0, all_608_1) = all_608_0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) ~ (all_608_2 = 0) | ~ (all_608_3 = 0) | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_608_0 = all_476_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1090), (1097) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) @+(all_331_0, all_156_1) = all_594_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1091) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) all_484_0 = 0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1090), (1105) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_331_0 = 0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1088), (1106) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) $false % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1107) is inconsistent. % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_608_2, all_156_5, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (1099) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) all_608_2 = 0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_608_3, all_156_4, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (1100) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_608_3 = 0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_590_1, all_608_3, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, simplifying with (1095), (1100) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_608_3 = all_590_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_608_1, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (119), % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_608_1 = all_156_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_362_1, all_594_1, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_331_0, simplifying with (995), % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_594_1 = all_362_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1109), (1110) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) all_590_1 = 0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1102), (1111) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) @+(all_331_0, all_156_1) = all_608_0 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1103) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) ~ (all_608_2 = 0) % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1108), (1115) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) $false % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1116) is inconsistent. % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) ~ (all_608_3 = 0) | all_608_0 = all_476_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1117) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) ~ (all_608_3 = 0) % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1109), (1118) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) $false % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1119) is inconsistent. % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_608_0 = all_476_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1114), (1120) imply: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) @+(all_331_0, all_156_1) = all_476_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_362_1, all_476_1, % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_331_0, simplifying with (995), % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) gives: % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_476_1 = all_362_1 % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1055), (1122) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) s(all_362_1) = all_156_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_362_1, simplifying with (1005), (1123) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_156_0 = all_156_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1124) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) $false % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1125) is inconsistent. % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | (1126) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1126) implies: % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | (1127) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (665), (666), (667), (1127) are inconsistent % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | End of split % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | Case 2: % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | (1128) ~ (all_89_5 = 0) % 153.53/20.94 | | | | | | | | | | | | | | | (1129) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.94 | | | | | | | | | | | | | | | all_89_5 & $i(v0)) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | DELTA: instantiating (1129) with fresh symbol all_233_0 % 153.53/20.94 | | | | | | | | | | | | | | | gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1130) nat_succeeds(all_233_0) = 0 & s(all_233_0) = % 153.53/20.94 | | | | | | | | | | | | | | | all_89_5 & $i(all_233_0) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | ALPHA: (1130) implies: % 153.53/20.94 | | | | | | | | | | | | | | | (1131) $i(all_233_0) % 153.53/20.94 | | | | | | | | | | | | | | | (1132) s(all_233_0) = all_89_5 % 153.53/20.94 | | | | | | | | | | | | | | | (1133) nat_succeeds(all_233_0) = 0 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.94 | | | | | | | | | | | | | | | all_217_0, all_89_1, all_89_6, all_89_0, % 153.53/20.94 | | | | | | | | | | | | | | | simplifying with (19), (25), (173), (174) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1134) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.94 | | | | | | | | | | | | | | | (@+(all_217_0, all_89_1) = v1 & % 153.53/20.94 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & s(v1) = v2 & % 153.53/20.94 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_0)) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.94 | | | | | | | | | | | | | | | all_217_0, all_89_5, all_89_6, all_89_3, % 153.53/20.94 | | | | | | | | | | | | | | | simplifying with (15), (24), (173), (174) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1135) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.94 | | | | | | | | | | | | | | | (@+(all_217_0, all_89_5) = v1 & % 153.53/20.94 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & s(v1) = v2 & % 153.53/20.94 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_3)) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.94 | | | | | | | | | | | | | | | all_233_0, all_89_4, all_89_5, all_89_1, % 153.53/20.94 | | | | | | | | | | | | | | | simplifying with (16), (26), (1131), (1132) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1136) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.94 | | | | | | | | | | | | | | | (@+(all_233_0, all_89_4) = v1 & % 153.53/20.94 | | | | | | | | | | | | | | | nat_succeeds(all_233_0) = v0 & s(v1) = v2 & % 153.53/20.94 | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_1)) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_217_0, simplifying with % 153.53/20.94 | | | | | | | | | | | | | | | (173), (175) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1137) all_217_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.94 | | | | | | | | | | | | | | | 0 & s(v0) = all_217_0 & $i(v0)) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_233_0, simplifying with % 153.53/20.94 | | | | | | | | | | | | | | | (1131), (1133) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1138) all_233_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.94 | | | | | | | | | | | | | | | 0 & s(v0) = all_233_0 & $i(v0)) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | DELTA: instantiating (1135) with fresh symbols all_242_0, % 153.53/20.94 | | | | | | | | | | | | | | | all_242_1, all_242_2 gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1139) @+(all_217_0, all_89_5) = all_242_1 & % 153.53/20.94 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_242_2 & s(all_242_1) % 153.53/20.94 | | | | | | | | | | | | | | | = all_242_0 & $i(all_242_0) & $i(all_242_1) & ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | (all_242_2 = 0) | all_242_0 = all_89_3) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | ALPHA: (1139) implies: % 153.53/20.94 | | | | | | | | | | | | | | | (1140) $i(all_242_1) % 153.53/20.94 | | | | | | | | | | | | | | | (1141) s(all_242_1) = all_242_0 % 153.53/20.94 | | | | | | | | | | | | | | | (1142) nat_succeeds(all_217_0) = all_242_2 % 153.53/20.94 | | | | | | | | | | | | | | | (1143) @+(all_217_0, all_89_5) = all_242_1 % 153.53/20.94 | | | | | | | | | | | | | | | (1144) ~ (all_242_2 = 0) | all_242_0 = all_89_3 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | DELTA: instantiating (1134) with fresh symbols all_244_0, % 153.53/20.94 | | | | | | | | | | | | | | | all_244_1, all_244_2 gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1145) @+(all_217_0, all_89_1) = all_244_1 & % 153.53/20.94 | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_244_2 & s(all_244_1) % 153.53/20.94 | | | | | | | | | | | | | | | = all_244_0 & $i(all_244_0) & $i(all_244_1) & ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | (all_244_2 = 0) | all_244_0 = all_89_0) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | ALPHA: (1145) implies: % 153.53/20.94 | | | | | | | | | | | | | | | (1146) $i(all_244_1) % 153.53/20.94 | | | | | | | | | | | | | | | (1147) s(all_244_1) = all_244_0 % 153.53/20.94 | | | | | | | | | | | | | | | (1148) nat_succeeds(all_217_0) = all_244_2 % 153.53/20.94 | | | | | | | | | | | | | | | (1149) @+(all_217_0, all_89_1) = all_244_1 % 153.53/20.94 | | | | | | | | | | | | | | | (1150) ~ (all_244_2 = 0) | all_244_0 = all_89_0 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | DELTA: instantiating (1136) with fresh symbols all_246_0, % 153.53/20.94 | | | | | | | | | | | | | | | all_246_1, all_246_2 gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1151) @+(all_233_0, all_89_4) = all_246_1 & % 153.53/20.94 | | | | | | | | | | | | | | | nat_succeeds(all_233_0) = all_246_2 & s(all_246_1) % 153.53/20.94 | | | | | | | | | | | | | | | = all_246_0 & $i(all_246_0) & $i(all_246_1) & ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | (all_246_2 = 0) | all_246_0 = all_89_1) % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | ALPHA: (1151) implies: % 153.53/20.94 | | | | | | | | | | | | | | | (1152) $i(all_246_1) % 153.53/20.94 | | | | | | | | | | | | | | | (1153) $i(all_246_0) % 153.53/20.94 | | | | | | | | | | | | | | | (1154) s(all_246_1) = all_246_0 % 153.53/20.94 | | | | | | | | | | | | | | | (1155) nat_succeeds(all_233_0) = all_246_2 % 153.53/20.94 | | | | | | | | | | | | | | | (1156) @+(all_233_0, all_89_4) = all_246_1 % 153.53/20.94 | | | | | | | | | | | | | | | (1157) ~ (all_246_2 = 0) | all_246_0 = all_89_1 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_244_2, all_217_0, % 153.53/20.94 | | | | | | | | | | | | | | | simplifying with (175), (1148) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1158) all_244_2 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_242_2, all_244_2, % 153.53/20.94 | | | | | | | | | | | | | | | all_217_0, simplifying with (1142), (1148) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1159) all_244_2 = all_242_2 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_246_2, all_233_0, % 153.53/20.94 | | | | | | | | | | | | | | | simplifying with (1133), (1155) gives: % 153.53/20.94 | | | | | | | | | | | | | | | (1160) all_246_2 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | COMBINE_EQS: (1158), (1159) imply: % 153.53/20.94 | | | | | | | | | | | | | | | (1161) all_242_2 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | SIMP: (1161) implies: % 153.53/20.94 | | | | | | | | | | | | | | | (1162) all_242_2 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | BETA: splitting (1144) gives: % 153.53/20.94 | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | Case 1: % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | (1163) ~ (all_242_2 = 0) % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | REDUCE: (1162), (1163) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | (1164) $false % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | CLOSE: (1164) is inconsistent. % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | Case 2: % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | (1165) all_242_0 = all_89_3 % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | REDUCE: (1141), (1165) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | (1166) s(all_242_1) = all_89_3 % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | BETA: splitting (1157) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | Case 1: % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | (1167) ~ (all_246_2 = 0) % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | REDUCE: (1160), (1167) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | | (1168) $false % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | CLOSE: (1168) is inconsistent. % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | Case 2: % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | (1169) all_246_0 = all_89_1 % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | REDUCE: (1154), (1169) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | | (1170) s(all_246_1) = all_89_1 % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | BETA: splitting (1150) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1171) ~ (all_244_2 = 0) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | REDUCE: (1158), (1171) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1172) $false % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | CLOSE: (1172) is inconsistent. % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1173) all_244_0 = all_89_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | REDUCE: (1147), (1173) imply: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1174) s(all_244_1) = all_89_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_242_1, all_89_4, all_89_3, all_89_2, % 153.53/20.94 | | | | | | | | | | | | | | | | | | simplifying with (16), (27), (1140), (1166) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1175) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.94 | | | | | | | | | | | | | | | | | | (@+(all_242_1, all_89_4) = v1 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_242_1) = v0 & s(v1) = v2 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_2)) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_217_0, all_89_5, all_242_1, simplifying with % 153.53/20.94 | | | | | | | | | | | | | | | | | | (15), (173), (1143) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1176) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.94 | | | | | | | | | | | | | | | | | | (nat_succeeds(all_242_1) = v2 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_5) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_217_0, all_89_1, all_244_1, simplifying with % 153.53/20.94 | | | | | | | | | | | | | | | | | | (19), (173), (1149) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1177) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.94 | | | | | | | | | | | | | | | | | | (nat_succeeds(all_244_1) = v2 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = v0 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_1) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | DELTA: instantiating (1177) with fresh symbols all_271_0, % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_271_1, all_271_2 gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1178) nat_succeeds(all_244_1) = all_271_0 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_271_2 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_1) = all_271_1 & ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | (all_271_1 = 0) | ~ (all_271_2 = 0) | all_271_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | ALPHA: (1178) implies: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1179) nat_succeeds(all_89_1) = all_271_1 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1180) nat_succeeds(all_217_0) = all_271_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1181) nat_succeeds(all_244_1) = all_271_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1182) ~ (all_271_1 = 0) | ~ (all_271_2 = 0) | % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_271_0 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | DELTA: instantiating (1176) with fresh symbols all_273_0, % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_273_1, all_273_2 gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1183) nat_succeeds(all_242_1) = all_273_0 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_217_0) = all_273_2 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_89_5) = all_273_1 & ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | (all_273_1 = 0) | ~ (all_273_2 = 0) | all_273_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | ALPHA: (1183) implies: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1184) nat_succeeds(all_89_5) = all_273_1 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1185) nat_succeeds(all_217_0) = all_273_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1186) nat_succeeds(all_242_1) = all_273_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1187) ~ (all_273_1 = 0) | ~ (all_273_2 = 0) | % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_273_0 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | DELTA: instantiating (1175) with fresh symbols all_277_0, % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_277_1, all_277_2 gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1188) @+(all_242_1, all_89_4) = all_277_1 & % 153.53/20.94 | | | | | | | | | | | | | | | | | | nat_succeeds(all_242_1) = all_277_2 & s(all_277_1) % 153.53/20.94 | | | | | | | | | | | | | | | | | | = all_277_0 & $i(all_277_0) & $i(all_277_1) & ( ~ % 153.53/20.94 | | | | | | | | | | | | | | | | | | (all_277_2 = 0) | all_277_0 = all_89_2) % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | ALPHA: (1188) implies: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1189) $i(all_277_1) % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1190) s(all_277_1) = all_277_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1191) nat_succeeds(all_242_1) = all_277_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1192) @+(all_242_1, all_89_4) = all_277_1 % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1193) ~ (all_277_2 = 0) | all_277_0 = all_89_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_273_1, all_89_5, % 153.53/20.94 | | | | | | | | | | | | | | | | | | simplifying with (22), (1184) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1194) all_273_1 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_271_1, all_89_1, % 153.53/20.94 | | | | | | | | | | | | | | | | | | simplifying with (80), (1179) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1195) all_271_1 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_273_2, all_217_0, % 153.53/20.94 | | | | | | | | | | | | | | | | | | simplifying with (175), (1185) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1196) all_273_2 = 0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_271_2, all_273_2, % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_217_0, simplifying with (1180), (1185) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1197) all_273_2 = all_271_2 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_273_0, all_277_2, % 153.53/20.94 | | | | | | | | | | | | | | | | | | all_242_1, simplifying with (1186), (1191) gives: % 153.53/20.94 | | | | | | | | | | | | | | | | | | (1198) all_277_2 = all_273_0 % 153.53/20.94 | | | | | | | | | | | | | | | | | | % 153.53/20.94 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1196), (1197) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | (1199) all_271_2 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | SIMP: (1199) implies: % 153.53/20.95 | | | | | | | | | | | | | | | | | | (1200) all_271_2 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | BETA: splitting (1182) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | (1201) ~ (all_271_1 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | REDUCE: (1195), (1201) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | (1202) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | CLOSE: (1202) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | (1203) ~ (all_271_2 = 0) | all_271_0 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (1187) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | (1204) ~ (all_273_1 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | REDUCE: (1194), (1204) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | (1205) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | CLOSE: (1205) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | (1206) ~ (all_273_2 = 0) | all_273_0 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1206) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | (1207) ~ (all_273_2 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1196), (1207) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | (1208) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1208) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | (1209) all_273_0 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1198), (1209) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | (1210) all_277_2 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1193) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | (1211) ~ (all_277_2 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1210), (1211) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | (1212) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1212) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | (1213) all_277_0 = all_89_2 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1190), (1213) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | (1214) s(all_277_1) = all_89_2 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1203) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | (1215) ~ (all_271_2 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1200), (1215) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | (1216) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1216) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | (1217) all_271_0 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1181), (1217) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | (1218) nat_succeeds(all_244_1) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1219) all_89_2 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1214), (1219) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1220) s(all_277_1) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_277_1, simplifying with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1189), (1220) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1221) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1221) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1222) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | all_89_2 & $i(v0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1222) with fresh symbol all_317_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1223) nat_succeeds(all_317_0) = 0 & s(all_317_0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | all_89_2 & $i(all_317_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1223) implies: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1224) $i(all_317_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1225) s(all_317_0) = all_89_2 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | (1226) nat_succeeds(all_317_0) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1227) all_89_3 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1166), (1227) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1228) s(all_242_1) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_242_1, simplifying with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1140), (1228) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1229) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1229) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1230) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3 & $i(v0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1230) with fresh symbol all_325_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1231) nat_succeeds(all_325_0) = 0 & s(all_325_0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3 & $i(all_325_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1231) implies: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1232) $i(all_325_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1233) s(all_325_0) = all_89_3 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | (1234) nat_succeeds(all_325_0) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) all_89_0 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1174), (1235) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) s(all_244_1) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_244_1, simplifying with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1146), (1236) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1237) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_0 & $i(v0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1238) with fresh symbol all_333_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) nat_succeeds(all_333_0) = 0 & s(all_333_0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_0 & $i(all_333_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1239) implies: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) $i(all_333_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) s(all_333_0) = all_89_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) nat_succeeds(all_333_0) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) all_89_1 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1170), (1243) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) s(all_246_1) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_246_1, simplifying with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152), (1244) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) $false % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1245) is inconsistent. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_1 & $i(v0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1246) with fresh symbol all_341_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) nat_succeeds(all_341_0) = 0 & s(all_341_0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_1 & $i(all_341_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1247) implies: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) $i(all_341_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) s(all_341_0) = all_89_1 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) nat_succeeds(all_341_0) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) all_154_0 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1251) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) @+(0, all_156_1) = all_156_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (1251) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) @+(0, all_156_5) = all_156_3 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (110), (111), (114), (119), (120), % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252), (1253) are inconsistent by sub-proof #10. % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) ~ (all_154_0 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (@+(v3, v2) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ? [v8: $i] : (@+(v1, v2) = v7 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(v1) = v6 & $i(v8) & $i(v7) & ( % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1255) with fresh symbol all_349_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) nat_succeeds(all_349_0) = 0 & s(all_349_0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_349_0) & ! [v0: $i] : ! [v1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1) = v3) | ~ (@+(all_349_0, v0) = v2) | ~ % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | : ? [v6: $i] : ? [v7: $i] : (@+(v0, v1) = v6 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(all_349_0, v6) = v7 & nat_succeeds(v1) = v4 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(v0) = v5 & $i(v7) & $i(v6) & ( % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (v5 = 0) | ~ (v4 = 0) | v7 = v3))) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1256) implies: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) $i(all_349_0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) s(all_349_0) = all_154_0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) nat_succeeds(all_349_0) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : ( ~ (@+(v2, v1) = v3) | ~ (@+(all_349_0, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ? [v5: any] : ? [v6: $i] : ? [v7: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i] : (@+(v0, v1) = v6 & @+(all_349_0, v6) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | v7 & nat_succeeds(v1) = v4 & nat_succeeds(v0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) | v7 = v3))) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) all_156_5 = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1261) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) @+(0, all_156_4) = all_156_1 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (1261) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) @+(all_154_0, 0) = all_156_3 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (1261) imply: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) nat_succeeds(0) = 0 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_277_1, all_317_0, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_2, simplifying with (1189), (1214), (1224), % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) all_317_0 = all_277_1 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_325_0, all_89_4, all_89_3, all_89_2, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (16), (27), (1232), (1233) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_325_0, all_89_4) = v1 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_325_0) = v0 & s(v1) = v2 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_2)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_242_1, all_325_0, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3, simplifying with (1140), (1166), (1232), % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) all_325_0 = all_242_1 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, all_156_1, all_154_0, all_156_0, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (1257), (1258) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_349_0, all_156_1) = v1 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & s(v1) = v2 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_317_0, simplifying with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224), (1226) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1269) all_317_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_317_0 & $i(v0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_349_0, simplifying with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257), (1259) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) all_349_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_349_0 & $i(v0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_4, all_156_1, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (1262) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) all_156_1 = all_156_4 % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, 0, all_154_0, all_156_3, simplifying % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (7), (1257), (1258), (1263) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_349_0, 0) = v1 & nat_succeeds(all_349_0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v0 & s(v1) = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v2 = all_156_3)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, 0, all_156_3, simplifying with (7), % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (1263) gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_156_3) = v2 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_154_0) = v0 & nat_succeeds(0) = % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1273) with fresh symbols all_376_0, % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_376_1, all_376_2 gives: % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) nat_succeeds(all_156_3) = all_376_0 & % 153.53/20.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_154_0) = all_376_2 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_376_1 & ( ~ (all_376_1 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_376_2 = 0) | all_376_0 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1274) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) nat_succeeds(0) = all_376_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) nat_succeeds(all_154_0) = all_376_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1268) with fresh symbols all_378_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, all_378_2 gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) @+(all_349_0, all_156_1) = all_378_1 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_378_2 & s(all_378_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_378_0 & $i(all_378_0) & $i(all_378_1) & ( ~ % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_378_2 = 0) | all_378_0 = all_156_0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1277) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) $i(all_378_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) s(all_378_1) = all_378_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) nat_succeeds(all_349_0) = all_378_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) @+(all_349_0, all_156_1) = all_378_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) ~ (all_378_2 = 0) | all_378_0 = all_156_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1266) with fresh symbols all_380_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_380_1, all_380_2 gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) @+(all_325_0, all_89_4) = all_380_1 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_325_0) = all_380_2 & s(all_380_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_380_0 & $i(all_380_0) & $i(all_380_1) & ( ~ % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_380_2 = 0) | all_380_0 = all_89_2) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1283) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) $i(all_380_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) @+(all_325_0, all_89_4) = all_380_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1272) with fresh symbols all_382_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_382_2 gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) @+(all_349_0, 0) = all_382_1 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_382_2 & s(all_382_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_382_0 & $i(all_382_0) & $i(all_382_1) & ( ~ % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_382_2 = 0) | all_382_0 = all_156_3) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1286) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) $i(all_382_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) s(all_382_1) = all_382_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) nat_succeeds(all_349_0) = all_382_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) @+(all_349_0, 0) = all_382_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) ~ (all_382_2 = 0) | all_382_0 = all_156_3 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1271), (1281) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) @+(all_349_0, all_156_4) = all_378_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1267), (1285) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) @+(all_242_1, all_89_4) = all_380_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1271) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) @+(all_154_0, all_156_4) = all_156_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1262), (1271) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) @+(0, all_156_4) = all_156_4 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_376_1, 0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1264), (1275) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_376_1 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_169_2, all_376_2, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (135), (1276) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_376_2 = all_169_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_382_2, all_349_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1259), (1289) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) all_382_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_378_2, all_382_2, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, simplifying with (1280), (1289) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_382_2 = all_378_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_277_1, all_380_1, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_4, all_242_1, simplifying with (1192), % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_380_1 = all_277_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1298), (1299) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1301) all_378_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1301) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302) all_378_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1291) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1303) ~ (all_382_2 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1298), (1303) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1304) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1304) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) all_382_0 = all_156_3 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1288), (1305) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) s(all_382_1) = all_156_3 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1282) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) ~ (all_378_2 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1302), (1307) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1308) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) all_378_0 = all_156_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1279), (1309) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) s(all_378_1) = all_156_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) all_169_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1311) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) nat_succeeds(all_154_0) = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_156_4, all_156_3, all_156_2, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (120), (1287), (1306) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_382_1, all_156_4) = v1 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_382_1) = v0 & s(v1) = v2 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_2)) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (1312) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, 0, all_382_1, simplifying with (7), % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257), (1290) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_382_1) = v2 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & nat_succeeds(0) = % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0)) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, all_156_4, all_378_1, simplifying with % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (1257), (1292) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_378_1) = v2 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1316) with fresh symbols all_488_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_488_1, all_488_2 gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) nat_succeeds(all_378_1) = all_488_0 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_488_2 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_488_1 & ( ~ % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_488_1 = 0) | ~ (all_488_2 = 0) | all_488_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1317) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) nat_succeeds(all_156_4) = all_488_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) nat_succeeds(all_349_0) = all_488_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) nat_succeeds(all_378_1) = all_488_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) ~ (all_488_1 = 0) | ~ (all_488_2 = 0) | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_488_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1315) with fresh symbols all_490_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_490_1, all_490_2 gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) nat_succeeds(all_382_1) = all_490_0 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_490_2 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(0) = all_490_1 & ( ~ (all_490_1 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_490_2 = 0) | all_490_0 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1322) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) nat_succeeds(0) = all_490_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) nat_succeeds(all_349_0) = all_490_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) nat_succeeds(all_382_1) = all_490_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) ~ (all_490_1 = 0) | ~ (all_490_2 = 0) | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_490_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1313) with fresh symbols all_498_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1, all_498_2 gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) @+(all_382_1, all_156_4) = all_498_1 & % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_382_1) = all_498_2 & s(all_498_1) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_498_0 & $i(all_498_0) & $i(all_498_1) & ( ~ % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_498_2 = 0) | all_498_0 = all_156_2) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1327) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) s(all_498_1) = all_498_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) nat_succeeds(all_382_1) = all_498_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) @+(all_382_1, all_156_4) = all_498_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) ~ (all_498_2 = 0) | all_498_0 = all_156_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1314) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) all_154_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1254), (1332) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1333) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1334) with fresh symbol all_504_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) nat_succeeds(all_504_0) = 0 & s(all_504_0) = % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_504_0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1335) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) $i(all_504_0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) s(all_504_0) = all_154_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) nat_succeeds(all_504_0) = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_490_1, 0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1264), (1323) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_490_1 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_488_1, all_156_4, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (1318) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_488_1 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_490_2, all_349_0, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1259), (1324) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_490_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_488_2, all_490_2, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, simplifying with (1319), (1324) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) all_490_2 = all_488_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_490_0, all_498_2, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, simplifying with (1325), (1329) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) all_498_2 = all_490_0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1341), (1342) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) all_488_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1321) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) ~ (all_488_1 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1340), (1345) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1346) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) ~ (all_488_2 = 0) | all_488_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1347) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) ~ (all_488_2 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1344), (1348) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1349) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) all_488_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1320), (1350) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) nat_succeeds(all_378_1) = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1326) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) ~ (all_490_1 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1339), (1352) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1353) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) ~ (all_490_2 = 0) | all_490_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1354) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) ~ (all_490_2 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1341), (1355) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1356) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) all_490_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (1357) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_498_2 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1331) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) ~ (all_498_2 = 0) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1358), (1359) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) $false % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1360) is inconsistent. % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) all_498_0 = all_156_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1328), (1361) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) s(all_498_1) = all_156_2 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1270) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1363) all_349_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1292), (1363) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1364) @+(0, all_156_4) = all_378_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1290), (1363) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) @+(0, 0) = all_382_1 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_4, all_378_1, % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, 0, simplifying with (1295), (1364) % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) all_378_1 = all_156_4 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1269) gives: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) all_317_0 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1265), (1367) imply: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_277_1 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1368) implies: % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) all_277_1 = 0 % 153.53/20.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_382_1, simplifying % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (7), (1365) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) all_382_1 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1365), (1370) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) @+(0, 0) = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371), (corollary-(plus:successor)), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #7. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_382_1, simplifying % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (7), (1365) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_382_1 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1365), (1372) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373) @+(0, 0) = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (10), (11), (37), (106), (107), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (112), (114), (115), (116), (117), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (118), (119), (120), (121), (135), (155), (156), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373), (corollary-(plus:successor)), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (corollary-(plus:types)), (id2) are inconsistent % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #7. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1374) ~ (all_349_0 = 0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_504_0, all_156_4, all_154_0, all_156_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (1294), (1336), (1337) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1375) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_504_0, all_156_4) = v1 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_504_0) = v0 & s(v1) = v2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_349_0, all_504_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (1257), (1258), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336), (1337) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_504_0 = all_349_0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_504_0, simplifying with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336), (1338) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_504_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_504_0 & $i(v0)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1260) with 0, all_156_4, all_382_1, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1, simplifying with (7), (112), (1290), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1378) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_349_0, v2) = v3 & @+(0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(0) = v1 & $i(v3) & $i(v2) & ( ~ % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = all_498_1)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_156_4, all_498_1, simplifying with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (1287), (1330) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1379) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_498_1) = v2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_382_1) = v0 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1379) with fresh symbols all_628_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_628_1, all_628_2 gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1380) nat_succeeds(all_498_1) = all_628_0 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_382_1) = all_628_2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_628_1 & ( ~ % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_628_1 = 0) | ~ (all_628_2 = 0) | all_628_0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1380) implies: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1381) nat_succeeds(all_156_4) = all_628_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1375) with fresh symbols all_636_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_636_1, all_636_2 gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1382) @+(all_504_0, all_156_4) = all_636_1 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_504_0) = all_636_2 & s(all_636_1) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_636_0 & $i(all_636_0) & $i(all_636_1) & ( ~ % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_636_2 = 0) | all_636_0 = all_156_0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1382) implies: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1383) @+(all_504_0, all_156_4) = all_636_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1378) with fresh symbols all_644_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_644_1, all_644_2, all_644_3 gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1384) @+(all_349_0, all_644_1) = all_644_0 & @+(0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = all_644_1 & nat_succeeds(all_156_4) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_644_3 & nat_succeeds(0) = all_644_2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_644_0) & $i(all_644_1) & ( ~ (all_644_2 = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_644_3 = 0) | all_644_0 = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1384) implies: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1385) nat_succeeds(0) = all_644_2 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1386) nat_succeeds(all_156_4) = all_644_3 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1387) @+(0, all_156_4) = all_644_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1388) @+(all_349_0, all_644_1) = all_644_0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1389) ~ (all_644_2 = 0) | ~ (all_644_3 = 0) | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_644_0 = all_498_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1376), (1383) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1390) @+(all_349_0, all_156_4) = all_636_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1377) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1391) all_504_0 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1376), (1391) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1392) all_349_0 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1374), (1392) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1393) $false % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1393) is inconsistent. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_644_2, 0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1264), (1385) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1394) all_644_2 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_644_3, all_156_4, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (1386) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1395) all_644_3 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_628_1, all_644_3, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, simplifying with (1381), (1386) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1396) all_644_3 = all_628_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_4, all_644_1, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, 0, simplifying with (1295), (1387) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) all_644_1 = all_156_4 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_378_1, all_636_1, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_349_0, simplifying with (1292), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1390) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) all_636_1 = all_378_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1395), (1396) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) all_628_1 = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1388), (1397) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400) @+(all_349_0, all_156_4) = all_644_0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1389) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1401) ~ (all_644_2 = 0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1394), (1401) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1402) $false % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1402) is inconsistent. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1403) ~ (all_644_3 = 0) | all_644_0 = all_498_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1403) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1404) ~ (all_644_3 = 0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1395), (1404) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1405) $false % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1405) is inconsistent. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1406) all_644_0 = all_498_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1400), (1406) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) @+(all_349_0, all_156_4) = all_498_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_378_1, all_498_1, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_349_0, simplifying with (1292), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408) all_498_1 = all_378_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1362), (1408) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409) s(all_378_1) = all_156_2 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, simplifying with (1310), (1409) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1410) all_156_0 = all_156_2 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1410) imply: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411) $false % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1411) is inconsistent. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1412) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1412) implies: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1413) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1257), (1258), (1259), (1413) are % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1414) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_5 & $i(v0)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1414) with fresh symbol all_366_0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415) nat_succeeds(all_366_0) = 0 & s(all_366_0) = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_5 & $i(all_366_0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1415) implies: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1416) $i(all_366_0) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1417) s(all_366_0) = all_156_5 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418) nat_succeeds(all_366_0) = 0 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_277_1, all_317_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_2, simplifying with (1189), (1214), (1224), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) all_317_0 = all_277_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_325_0, all_89_4, all_89_3, all_89_2, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (16), (27), (1232), (1233) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1420) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_325_0, all_89_4) = v1 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_325_0) = v0 & s(v1) = v2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_89_2)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_242_1, all_325_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_3, simplifying with (1140), (1166), (1232), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421) all_325_0 = all_242_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_244_1, all_333_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_0, simplifying with (1146), (1174), (1240), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422) all_333_0 = all_244_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_246_1, all_341_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_1, simplifying with (1152), (1170), (1248), % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1423) all_341_0 = all_246_1 % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, all_156_1, all_154_0, all_156_0, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (1257), (1258) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_349_0, all_156_1) = v1 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & s(v1) = v2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, all_156_5, all_154_0, all_156_3, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (111), (117), (1257), (1258) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_349_0, all_156_5) = v1 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & s(v1) = v2 & % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_3)) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_0, all_156_4, all_156_5, all_156_1, % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (119), (1416), (1417) % 153.53/20.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_366_0, all_156_4) = v1 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_366_0) = v0 & s(v1) = v2 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_244_1, simplifying with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146), (1218) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) all_244_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_244_1 & $i(v0)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_325_0, simplifying with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232), (1234) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_325_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_325_0 & $i(v0)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_333_0, simplifying with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1240), (1242) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) all_333_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_333_0 & $i(v0)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_341_0, simplifying with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248), (1250) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) all_341_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_341_0 & $i(v0)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_349_0, simplifying with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257), (1259) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) all_349_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_349_0 & $i(v0)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1424) with fresh symbols all_378_0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, all_378_2 gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) @+(all_349_0, all_156_1) = all_378_1 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_378_2 & s(all_378_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_378_0 & $i(all_378_0) & $i(all_378_1) & ( ~ % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_378_2 = 0) | all_378_0 = all_156_0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1432) implies: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) $i(all_378_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) s(all_378_1) = all_378_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1435) nat_succeeds(all_349_0) = all_378_2 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1436) @+(all_349_0, all_156_1) = all_378_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437) ~ (all_378_2 = 0) | all_378_0 = all_156_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1420) with fresh symbols all_380_0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_380_1, all_380_2 gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) @+(all_325_0, all_89_4) = all_380_1 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_325_0) = all_380_2 & s(all_380_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_380_0 & $i(all_380_0) & $i(all_380_1) & ( ~ % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_380_2 = 0) | all_380_0 = all_89_2) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1438) implies: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) @+(all_325_0, all_89_4) = all_380_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1426) with fresh symbols all_382_0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_382_1, all_382_2 gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) @+(all_366_0, all_156_4) = all_382_1 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_366_0) = all_382_2 & s(all_382_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_382_0 & $i(all_382_0) & $i(all_382_1) & ( ~ % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_382_2 = 0) | all_382_0 = all_156_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1440) implies: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) $i(all_382_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) $i(all_382_0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) s(all_382_1) = all_382_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) nat_succeeds(all_366_0) = all_382_2 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) @+(all_366_0, all_156_4) = all_382_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) ~ (all_382_2 = 0) | all_382_0 = all_156_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1425) with fresh symbols all_384_0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_384_1, all_384_2 gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) @+(all_349_0, all_156_5) = all_384_1 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_384_2 & s(all_384_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_384_0 & $i(all_384_0) & $i(all_384_1) & ( ~ % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_384_2 = 0) | all_384_0 = all_156_3) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1447) implies: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) $i(all_384_1) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) s(all_384_1) = all_384_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) nat_succeeds(all_349_0) = all_384_2 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) @+(all_349_0, all_156_5) = all_384_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) ~ (all_384_2 = 0) | all_384_0 = all_156_3 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1421), (1439) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) @+(all_242_1, all_89_4) = all_380_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_384_2, all_349_0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1259), (1450) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) all_384_2 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_378_2, all_384_2, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, simplifying with (1435), (1450) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) all_384_2 = all_378_2 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_382_2, all_366_0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1418), (1444) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) all_382_2 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_277_1, all_380_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_4, all_242_1, simplifying with (1192), % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_380_1 = all_277_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1454), (1455) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) all_378_2 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1452) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) ~ (all_384_2 = 0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1454), (1459) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) $false % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1460) is inconsistent. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) all_384_0 = all_156_3 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1449), (1461) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) s(all_384_1) = all_156_3 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1437) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) ~ (all_378_2 = 0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1458), (1463) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) $false % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1464) is inconsistent. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_378_0 = all_156_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1434), (1465) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) s(all_378_1) = all_156_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1446) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) ~ (all_382_2 = 0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1456), (1467) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) $false % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1468) is inconsistent. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_382_0 = all_156_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1443), (1469) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) s(all_382_1) = all_156_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_169_2 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1471) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) nat_succeeds(all_154_0) = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_156_1 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1470), (1473) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) s(all_382_1) = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_382_1, simplifying with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441), (1474) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) $false % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1475) is inconsistent. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) ~ (all_156_1 = 0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1137) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_217_0 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1149), (1477) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) @+(0, all_89_1) = all_244_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1143), (1477) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) @+(0, all_89_5) = all_242_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (1477) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) s(0) = all_89_6 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_96_0, all_89_6, 0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (37), (1480) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_96_0 = all_89_6 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1138) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) all_233_0 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1156), (1482) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) @+(0, all_89_4) = all_246_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1132), (1482) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) s(0) = all_89_5 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_89_6, all_89_5, 0, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1480), (1484) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) all_89_5 = all_89_6 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (1485) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) @+(all_89_6, all_89_4) = all_89_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1479), (1485) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) @+(0, all_89_6) = all_242_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_6, all_242_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (14), (1487) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_242_1 = all_89_6 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_4, all_246_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (16), (1483) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) all_246_1 = all_89_4 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_1, all_244_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (1478) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) all_244_1 = all_89_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1423), (1489) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) all_341_0 = all_89_4 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1192), (1488) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) @+(all_89_6, all_89_4) = all_277_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1174), (1490) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) s(all_89_1) = all_89_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1430) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_341_0 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1491), (1494) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_89_4 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (623), (1495) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) $false % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1496) is inconsistent. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_1, all_277_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_4, all_89_6, simplifying with (1486), % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) all_277_1 = all_89_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1214), (1497) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) s(all_89_1) = all_89_2 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (1493), (1498) are inconsistent by % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_5, all_242_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (1479) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_242_1 = all_89_5 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_89_1, all_244_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (1478) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) all_244_1 = all_89_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1421), (1499) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_325_0 = all_89_5 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1192), (1499) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) @+(all_89_5, all_89_4) = all_277_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1174), (1500) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) s(all_89_1) = all_89_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1428) gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) all_325_0 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1501), (1504) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_89_5 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1505) implies: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_89_5 = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1128), (1506) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) $false % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1507) is inconsistent. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_1, all_277_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_89_4, all_89_5, simplifying with (26), (1502) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_277_1 = all_89_1 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1214), (1508) imply: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) s(all_89_1) = all_89_2 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (1503), (1509) are inconsistent by % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #6. % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(v0)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1510) with fresh symbol all_462_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) nat_succeeds(all_462_0) = 0 & s(all_462_0) = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_217_0 & $i(all_462_0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1511) implies: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) $i(all_462_0) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) s(all_462_0) = all_217_0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) nat_succeeds(all_462_0) = 0 % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_384_1, all_156_4, all_156_3, all_156_2, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (112), (120), (1448), (1462) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_384_1, all_156_4) = v1 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_384_1) = v0 & s(v1) = v2 & % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_2)) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_462_0, all_89_1, all_217_0, all_244_1, % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (19), (1149), (1512), (1513) % 153.53/20.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_462_0, all_89_1) = v1 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_462_0) = v0 & s(v1) = v2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_244_1)) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_462_0, all_89_5, all_217_0, all_242_1, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (15), (1143), (1512), (1513) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_462_0, all_89_5) = v1 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_462_0) = v0 & s(v1) = v2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_242_1)) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_154_0, simplifying with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (1472) gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_154_0 & $i(v0)) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, all_156_5, all_384_1, simplifying with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (111), (1257), (1451) gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1519) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_384_1) = v2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, all_156_1, all_378_1, simplifying with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (1257), (1436) gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_378_1) = v2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = v0 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:types)) with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_366_0, all_156_4, all_382_1, simplifying with % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (1416), (1445) gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(all_382_1) = v2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_366_0) = v0 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1521) with fresh symbols all_488_0, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_488_1, all_488_2 gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1522) nat_succeeds(all_382_1) = all_488_0 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_366_0) = all_488_2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_488_1 & ( ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_488_1 = 0) | ~ (all_488_2 = 0) | all_488_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1522) implies: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1523) nat_succeeds(all_156_4) = all_488_1 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1520) with fresh symbols all_490_0, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_490_1, all_490_2 gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1524) nat_succeeds(all_378_1) = all_490_0 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_490_2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_1) = all_490_1 & ( ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_490_1 = 0) | ~ (all_490_2 = 0) | all_490_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1524) implies: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1525) nat_succeeds(all_156_1) = all_490_1 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526) nat_succeeds(all_349_0) = all_490_2 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1527) nat_succeeds(all_378_1) = all_490_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1528) ~ (all_490_1 = 0) | ~ (all_490_2 = 0) | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_490_0 = 0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1519) with fresh symbols all_492_0, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_492_1, all_492_2 gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529) nat_succeeds(all_384_1) = all_492_0 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_349_0) = all_492_2 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_492_1 & ( ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_492_1 = 0) | ~ (all_492_2 = 0) | all_492_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = 0) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1529) implies: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) nat_succeeds(all_156_5) = all_492_1 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) nat_succeeds(all_349_0) = all_492_2 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) nat_succeeds(all_384_1) = all_492_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) ~ (all_492_1 = 0) | ~ (all_492_2 = 0) | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_492_0 = 0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1515) with fresh symbols all_496_0, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_496_1, all_496_2 gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) @+(all_384_1, all_156_4) = all_496_1 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_384_1) = all_496_2 & s(all_496_1) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_496_0 & $i(all_496_0) & $i(all_496_1) & ( ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_496_2 = 0) | all_496_0 = all_156_2) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1534) implies: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) s(all_496_1) = all_496_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) nat_succeeds(all_384_1) = all_496_2 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) @+(all_384_1, all_156_4) = all_496_1 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) ~ (all_496_2 = 0) | all_496_0 = all_156_2 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1517) with fresh symbols all_498_0, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_498_1, all_498_2 gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) @+(all_462_0, all_89_5) = all_498_1 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_462_0) = all_498_2 & s(all_498_1) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_498_0 & $i(all_498_0) & $i(all_498_1) & ( ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_498_2 = 0) | all_498_0 = all_242_1) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1539) implies: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) nat_succeeds(all_462_0) = all_498_2 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1516) with fresh symbols all_500_0, % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_500_1, all_500_2 gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) @+(all_462_0, all_89_1) = all_500_1 & % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_462_0) = all_500_2 & s(all_500_1) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_500_0 & $i(all_500_0) & $i(all_500_1) & ( ~ % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_500_2 = 0) | all_500_0 = all_244_1) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1541) implies: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) $i(all_500_1) % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) s(all_500_1) = all_500_0 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) nat_succeeds(all_462_0) = all_500_2 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) ~ (all_500_2 = 0) | all_500_0 = all_244_1 % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1518) gives: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.53/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) all_154_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1254), (1546) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1547) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(v0)) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1548) with fresh symbol all_506_0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) nat_succeeds(all_506_0) = 0 & s(all_506_0) = % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0 & $i(all_506_0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1549) implies: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) $i(all_506_0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) s(all_506_0) = all_154_0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) nat_succeeds(all_506_0) = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_492_1, all_156_5, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (1530) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_492_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_488_1, all_156_4, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (1523) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_488_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_490_1, all_156_1, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (155), (1525) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) all_490_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_492_2, all_349_0, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1259), (1531) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_492_2 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_490_2, all_492_2, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_349_0, simplifying with (1526), (1531) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_492_2 = all_490_2 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_492_0, all_496_2, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_384_1, simplifying with (1532), (1536) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_496_2 = all_492_0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_500_2, all_462_0, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (1514), (1544) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_500_2 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_498_2, all_500_2, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_462_0, simplifying with (1540), (1544) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_500_2 = all_498_2 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1559), (1560) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_498_2 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1556), (1557) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) all_490_2 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1545) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) ~ (all_500_2 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1559), (1563) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1564) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) all_500_0 = all_244_1 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1543), (1565) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) s(all_500_1) = all_244_1 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1528) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) ~ (all_490_1 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1555), (1567) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1568) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) ~ (all_490_2 = 0) | all_490_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1569) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) ~ (all_490_2 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1562), (1570) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1571) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) all_490_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1527), (1572) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) nat_succeeds(all_378_1) = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1533) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) ~ (all_492_1 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1553), (1574) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1575) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) ~ (all_492_2 = 0) | all_492_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1576) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) ~ (all_492_2 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1556), (1577) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1578) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) all_492_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1558), (1579) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_496_2 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1538) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) ~ (all_496_2 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1580), (1581) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1582) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_496_0 = all_156_2 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1535), (1583) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) s(all_496_1) = all_156_2 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1431) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_349_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1436), (1585) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) @+(0, all_156_1) = all_378_1 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1451), (1585) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) @+(0, all_156_5) = all_384_1 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) all_244_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1566), (1588) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) s(all_500_1) = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_500_1, simplifying with % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542), (1589) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1590) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1590) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1591) ~ (all_244_1 = 0) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1429) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_333_0 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1422), (1592) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1593) all_244_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1591), (1593) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1594) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_378_1, simplifying with % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433), (1573) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) all_378_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_378_1 & $i(v0)) % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_5, all_384_1, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (111), (1587) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) all_384_1 = all_156_5 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_156_1, all_378_1, % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (1586) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1597) all_378_1 = all_156_1 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1537), (1596) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) @+(all_156_5, all_156_4) = all_496_1 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1466), (1597) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1599) s(all_156_1) = all_156_0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1595) gives: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1600) all_378_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1597), (1600) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_156_1 = 0 % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1476), (1601) imply: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1602) $false % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1602) is inconsistent. % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/20.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_496_1, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (119), % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603) all_496_1 = all_156_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1584), (1603) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1604) s(all_156_1) = all_156_2 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (110), (1599), (1604) are inconsistent by % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1605) ~ (all_349_0 = 0) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (corollary-(plus:successor)) with % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_506_0, all_156_1, all_154_0, all_156_0, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (114), (118), (1550), (1551) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1606) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (@+(all_506_0, all_156_1) = v1 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_506_0) = v0 & s(v1) = v2 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_0)) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (id2) with all_349_0, all_506_0, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_154_0, simplifying with (1257), (1258), % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550), (1551) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607) all_506_0 = all_349_0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_506_0, simplifying with % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550), (1552) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) all_506_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0 & s(v0) = all_506_0 & $i(v0)) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (1260) with all_156_5, all_156_4, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_384_1, all_496_1, simplifying with (111), % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (112), (1451), (1537) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | [v3: $i] : (@+(all_349_0, v2) = v3 & @+(all_156_5, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & nat_succeeds(all_156_5) = v1 & $i(v3) & $i(v2) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_496_1)) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1606) with fresh symbols all_642_0, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_642_1, all_642_2 gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) @+(all_506_0, all_156_1) = all_642_1 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_506_0) = all_642_2 & s(all_642_1) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_642_0 & $i(all_642_0) & $i(all_642_1) & ( ~ % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_642_2 = 0) | all_642_0 = all_156_0) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1610) implies: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) @+(all_506_0, all_156_1) = all_642_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (1609) with fresh symbols all_650_0, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_650_1, all_650_2, all_650_3 gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) @+(all_349_0, all_650_1) = all_650_0 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | @+(all_156_5, all_156_4) = all_650_1 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_4) = all_650_3 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | nat_succeeds(all_156_5) = all_650_2 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_650_0) & $i(all_650_1) & ( ~ (all_650_2 = % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 0) | ~ (all_650_3 = 0) | all_650_0 = % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_496_1) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1612) implies: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) nat_succeeds(all_156_5) = all_650_2 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) nat_succeeds(all_156_4) = all_650_3 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) @+(all_156_5, all_156_4) = all_650_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) @+(all_349_0, all_650_1) = all_650_0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) ~ (all_650_2 = 0) | ~ (all_650_3 = 0) | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_650_0 = all_496_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1607), (1611) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) @+(all_349_0, all_156_1) = all_642_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1608) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) all_506_0 = 0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1607), (1619) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_349_0 = 0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1620) implies: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_349_0 = 0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1605), (1621) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) $false % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1622) is inconsistent. % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_650_2, all_156_5, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (115), (1613) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) all_650_2 = 0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_650_3, all_156_4, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (116), (1614) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_650_3 = 0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_156_1, all_650_1, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (119), % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_650_1 = all_156_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_378_1, all_642_1, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_349_0, simplifying with (1436), % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) all_642_1 = all_378_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1616), (1625) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) @+(all_349_0, all_156_1) = all_650_0 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1617) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) ~ (all_650_2 = 0) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1623), (1628) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) $false % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1629) is inconsistent. % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) ~ (all_650_3 = 0) | all_650_0 = all_496_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1630) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) ~ (all_650_3 = 0) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1624), (1631) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) $false % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1632) is inconsistent. % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_650_0 = all_496_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1627), (1633) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) @+(all_349_0, all_156_1) = all_496_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_378_1, all_496_1, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_156_1, all_349_0, simplifying with (1436), % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_496_1 = all_378_1 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1584), (1635) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) s(all_378_1) = all_156_2 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with all_156_0, all_156_2, % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_378_1, simplifying with (1466), (1636) gives: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_156_0 = all_156_2 % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (1637) imply: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) $false % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1638) is inconsistent. % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v1))) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1639) implies: % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | s(v0) = v1 & $i(v1))) % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1257), (1258), (1259), (1640) are % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | End of split % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | (1641) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ % 153.78/21.00 | | | | | | | | | | $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 153.78/21.00 | | | | | | | | | | : ! [v4: $i] : ( ~ (@+(v3, v2) = v4) | ~ % 153.78/21.00 | | | | | | | | | | (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ? % 153.78/21.00 | | | | | | | | | | [v5: any] : ? [v6: any] : ? [v7: $i] : ? % 153.78/21.00 | | | | | | | | | | [v8: $i] : (@+(v1, v2) = v7 & @+(v0, v7) = v8 % 153.78/21.00 | | | | | | | | | | & nat_succeeds(v2) = v5 & nat_succeeds(v1) = % 153.78/21.00 | | | | | | | | | | v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 % 153.78/21.00 | | | | | | | | | | = 0) | v8 = v4)))) % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | GROUND_INST: instantiating (1641) with all_89_6, simplifying % 153.78/21.00 | | | | | | | | | | with (14), (21) gives: % 153.78/21.00 | | | | | | | | | | (1642) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 153.78/21.00 | | | | | | | | | | $i] : ( ~ (@+(v2, v1) = v3) | ~ (@+(all_89_6, % 153.78/21.00 | | | | | | | | | | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 153.78/21.00 | | | | | | | | | | any] : ? [v5: any] : ? [v6: $i] : ? [v7: % 153.78/21.00 | | | | | | | | | | $i] : (@+(v0, v1) = v6 & @+(all_89_6, v6) = v7 % 153.78/21.00 | | | | | | | | | | & nat_succeeds(v1) = v4 & nat_succeeds(v0) = % 153.78/21.00 | | | | | | | | | | v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = % 153.78/21.00 | | | | | | | | | | 0) | v7 = v3))) % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | GROUND_INST: instantiating (1642) with all_89_5, all_89_4, % 153.78/21.00 | | | | | | | | | | all_89_3, all_89_2, simplifying with (15), (16), % 153.78/21.00 | | | | | | | | | | (24), (27) gives: % 153.78/21.00 | | | | | | | | | | (1643) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.78/21.00 | | | | | | | | | | [v3: $i] : (@+(all_89_5, all_89_4) = v2 & % 153.78/21.00 | | | | | | | | | | @+(all_89_6, v2) = v3 & nat_succeeds(all_89_4) = % 153.78/21.00 | | | | | | | | | | v0 & nat_succeeds(all_89_5) = v1 & $i(v3) & % 153.78/21.00 | | | | | | | | | | $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = % 153.78/21.00 | | | | | | | | | | all_89_2)) % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | DELTA: instantiating (1643) with fresh symbols all_162_0, % 153.78/21.00 | | | | | | | | | | all_162_1, all_162_2, all_162_3 gives: % 153.78/21.00 | | | | | | | | | | (1644) @+(all_89_5, all_89_4) = all_162_1 & @+(all_89_6, % 153.78/21.00 | | | | | | | | | | all_162_1) = all_162_0 & nat_succeeds(all_89_4) % 153.78/21.00 | | | | | | | | | | = all_162_3 & nat_succeeds(all_89_5) = all_162_2 & % 153.78/21.00 | | | | | | | | | | $i(all_162_0) & $i(all_162_1) & ( ~ (all_162_2 = % 153.78/21.00 | | | | | | | | | | 0) | ~ (all_162_3 = 0) | all_162_0 = % 153.78/21.00 | | | | | | | | | | all_89_2) % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | ALPHA: (1644) implies: % 153.78/21.00 | | | | | | | | | | (1645) nat_succeeds(all_89_5) = all_162_2 % 153.78/21.00 | | | | | | | | | | (1646) nat_succeeds(all_89_4) = all_162_3 % 153.78/21.00 | | | | | | | | | | (1647) @+(all_89_6, all_162_1) = all_162_0 % 153.78/21.00 | | | | | | | | | | (1648) @+(all_89_5, all_89_4) = all_162_1 % 153.78/21.00 | | | | | | | | | | (1649) ~ (all_162_2 = 0) | ~ (all_162_3 = 0) | % 153.78/21.00 | | | | | | | | | | all_162_0 = all_89_2 % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_162_2, all_89_5, % 153.78/21.00 | | | | | | | | | | simplifying with (22), (1645) gives: % 153.78/21.00 | | | | | | | | | | (1650) all_162_2 = 0 % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_162_3, all_89_4, % 153.78/21.00 | | | | | | | | | | simplifying with (23), (1646) gives: % 153.78/21.00 | | | | | | | | | | (1651) all_162_3 = 0 % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_1, all_162_1, % 153.78/21.00 | | | | | | | | | | all_89_4, all_89_5, simplifying with (26), (1648) % 153.78/21.00 | | | | | | | | | | gives: % 153.78/21.00 | | | | | | | | | | (1652) all_162_1 = all_89_1 % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | REDUCE: (1647), (1652) imply: % 153.78/21.00 | | | | | | | | | | (1653) @+(all_89_6, all_89_1) = all_162_0 % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | BETA: splitting (1649) gives: % 153.78/21.00 | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | Case 1: % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | (1654) ~ (all_162_2 = 0) % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | REDUCE: (1650), (1654) imply: % 153.78/21.00 | | | | | | | | | | | (1655) $false % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | CLOSE: (1655) is inconsistent. % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | (1656) ~ (all_162_3 = 0) | all_162_0 = all_89_2 % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | BETA: splitting (1656) gives: % 153.78/21.00 | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | Case 1: % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | (1657) ~ (all_162_3 = 0) % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | REDUCE: (1651), (1657) imply: % 153.78/21.00 | | | | | | | | | | | | (1658) $false % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | CLOSE: (1658) is inconsistent. % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | Case 2: % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | (1659) all_162_0 = all_89_2 % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.00 | | | | | | | | | | | | REDUCE: (1653), (1659) imply: % 153.78/21.00 | | | | | | | | | | | | (1660) @+(all_89_6, all_89_1) = all_89_2 % 153.78/21.00 | | | | | | | | | | | | % 153.78/21.01 | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_89_0, all_89_2, % 153.78/21.01 | | | | | | | | | | | | all_89_1, all_89_6, simplifying with (25), (1660) % 153.78/21.01 | | | | | | | | | | | | gives: % 153.78/21.01 | | | | | | | | | | | | (1661) all_89_0 = all_89_2 % 153.78/21.01 | | | | | | | | | | | | % 153.78/21.01 | | | | | | | | | | | | REDUCE: (13), (1661) imply: % 153.78/21.01 | | | | | | | | | | | | (1662) $false % 153.78/21.01 | | | | | | | | | | | | % 153.78/21.01 | | | | | | | | | | | | CLOSE: (1662) is inconsistent. % 153.78/21.01 | | | | | | | | | | | | % 153.78/21.01 | | | | | | | | | | | End of split % 153.78/21.01 | | | | | | | | | | | % 153.78/21.01 | | | | | | | | | | End of split % 153.78/21.01 | | | | | | | | | | % 153.78/21.01 | | | | | | | | | End of split % 153.78/21.01 | | | | | | | | | % 153.78/21.01 | | | | | | | | End of split % 153.78/21.01 | | | | | | | | % 153.78/21.01 | | | | | | | End of split % 153.78/21.01 | | | | | | | % 153.78/21.01 | | | | | | End of split % 153.78/21.01 | | | | | | % 153.78/21.01 | | | | | End of split % 153.78/21.01 | | | | | % 153.78/21.01 | | | | End of split % 153.78/21.01 | | | | % 153.78/21.01 | | | End of split % 153.78/21.01 | | | % 153.78/21.01 | | End of split % 153.78/21.01 | | % 153.78/21.01 | End of split % 153.78/21.01 | % 153.78/21.01 End of proof % 153.78/21.01 % 153.78/21.01 Sub-proof #1 shows that the following formulas are inconsistent: % 153.78/21.01 ---------------------------------------------------------------- % 153.78/21.01 (1) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ % 153.78/21.01 (v1 = all_154_0) & s(v0) = v1 & $i(v1))) % 153.78/21.01 (2) s(all_349_0) = all_154_0 % 153.78/21.01 (3) nat_succeeds(all_349_0) = 0 % 153.78/21.01 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.01 (s(v2) = v0)) % 153.78/21.01 (5) $i(all_349_0) % 153.78/21.01 % 153.78/21.01 Begin of proof % 153.78/21.01 | % 153.78/21.01 | GROUND_INST: instantiating (1) with all_349_0, simplifying with (3), (5) % 153.78/21.01 | gives: % 153.78/21.01 | (6) ? [v0: any] : ( ~ (v0 = all_154_0) & s(all_349_0) = v0 & $i(v0)) % 153.78/21.01 | % 153.78/21.01 | DELTA: instantiating (6) with fresh symbol all_433_0 gives: % 153.78/21.01 | (7) ~ (all_433_0 = all_154_0) & s(all_349_0) = all_433_0 & $i(all_433_0) % 153.78/21.01 | % 153.78/21.01 | ALPHA: (7) implies: % 153.78/21.01 | (8) ~ (all_433_0 = all_154_0) % 153.78/21.01 | (9) s(all_349_0) = all_433_0 % 153.78/21.01 | % 153.78/21.01 | GROUND_INST: instantiating (4) with all_154_0, all_433_0, all_349_0, % 153.78/21.01 | simplifying with (2), (9) gives: % 153.78/21.01 | (10) all_433_0 = all_154_0 % 153.78/21.01 | % 153.78/21.01 | REDUCE: (8), (10) imply: % 153.78/21.01 | (11) $false % 153.78/21.01 | % 153.78/21.01 | CLOSE: (11) is inconsistent. % 153.78/21.01 | % 153.78/21.01 End of proof % 153.78/21.01 % 153.78/21.01 Sub-proof #2 shows that the following formulas are inconsistent: % 153.78/21.01 ---------------------------------------------------------------- % 153.78/21.01 (1) nat_succeeds(all_331_0) = 0 % 153.78/21.01 (2) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ % 153.78/21.01 (v1 = all_154_0) & s(v0) = v1 & $i(v1))) % 153.78/21.01 (3) $i(all_331_0) % 153.78/21.01 (4) s(all_331_0) = all_154_0 % 153.78/21.01 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.01 (s(v2) = v0)) % 153.78/21.01 % 153.78/21.01 Begin of proof % 153.78/21.01 | % 153.78/21.01 | GROUND_INST: instantiating (2) with all_331_0, simplifying with (1), (3) % 153.78/21.01 | gives: % 153.78/21.01 | (6) ? [v0: any] : ( ~ (v0 = all_154_0) & s(all_331_0) = v0 & $i(v0)) % 153.78/21.01 | % 153.78/21.01 | DELTA: instantiating (6) with fresh symbol all_415_0 gives: % 153.78/21.01 | (7) ~ (all_415_0 = all_154_0) & s(all_331_0) = all_415_0 & $i(all_415_0) % 153.78/21.01 | % 153.78/21.01 | ALPHA: (7) implies: % 153.78/21.01 | (8) ~ (all_415_0 = all_154_0) % 153.78/21.01 | (9) s(all_331_0) = all_415_0 % 153.78/21.01 | % 153.78/21.01 | GROUND_INST: instantiating (5) with all_154_0, all_415_0, all_331_0, % 153.78/21.01 | simplifying with (4), (9) gives: % 153.78/21.01 | (10) all_415_0 = all_154_0 % 153.78/21.01 | % 153.78/21.01 | REDUCE: (8), (10) imply: % 153.78/21.01 | (11) $false % 153.78/21.01 | % 153.78/21.01 | CLOSE: (11) is inconsistent. % 153.78/21.01 | % 153.78/21.01 End of proof % 153.78/21.01 % 153.78/21.01 Sub-proof #3 shows that the following formulas are inconsistent: % 153.78/21.01 ---------------------------------------------------------------- % 153.78/21.01 (1) $i(0) % 153.78/21.01 (2) @+(all_154_0, all_156_5) = all_156_3 % 153.78/21.01 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, v1) = % 153.78/21.01 v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 153.78/21.01 [v5: $i] : ? [v6: $i] : (@+(v0, v1) = v5 & nat_succeeds(v0) = v4 & % 153.78/21.01 s(v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = v3))) % 153.78/21.01 (4) $i(all_156_4) % 153.78/21.01 (5) @+(all_156_3, all_156_4) = all_156_2 % 153.78/21.01 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (@+(v0, v1) = v2) | ~ % 153.78/21.01 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 153.78/21.01 (nat_succeeds(v2) = v5 & nat_succeeds(v1) = v4 & nat_succeeds(v0) = v3 % 153.78/21.01 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 153.78/21.01 (7) s(0) = all_96_0 % 153.78/21.01 (8) @+(all_154_0, all_156_1) = all_156_0 % 153.78/21.01 (9) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ $i(v0)) % 153.78/21.01 (10) all_241_1 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_241_1 % 153.78/21.01 & $i(v0)) % 153.78/21.01 (11) $i(all_156_1) % 153.78/21.01 (12) nat_succeeds(all_156_5) = 0 % 153.78/21.01 (13) all_241_1 = all_89_4 % 153.78/21.01 (14) nat_succeeds(all_154_0) = all_169_2 % 153.78/21.01 (15) ~ (all_156_0 = all_156_2) % 153.78/21.01 (16) all_169_2 = 0 | ( ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.78/21.01 (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 153.78/21.01 all_154_0) & s(v0) = v1 & $i(v1)))) % 153.78/21.01 (17) $i(all_156_5) % 153.78/21.01 (18) nat_succeeds(all_156_1) = 0 % 153.78/21.01 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 153.78/21.01 ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 153.78/21.01 (20) @+(0, 0) = all_243_1 % 153.78/21.01 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.78/21.01 (@+(v3, v2) = v1) | ~ (@+(v3, v2) = v0)) % 153.78/21.01 (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 153.78/21.01 (v1 = v0 | ~ (nat_succeeds(v2) = v1) | ~ (nat_succeeds(v2) = v0)) % 153.78/21.01 (23) @+(all_156_5, all_156_4) = all_156_1 % 153.78/21.01 (24) ! [v0: $i] : (v0 = 0 | ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.78/21.01 $i] : (nat_succeeds(v1) = 0 & s(v1) = v0 & $i(v1))) % 153.78/21.01 (25) nat_succeeds(all_156_4) = 0 % 153.78/21.01 (26) $i(all_154_0) % 153.78/21.01 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 153.78/21.01 ~ (s(v2) = v0)) % 153.78/21.01 (28) ~ (all_89_4 = 0) % 153.78/21.01 (29) all_156_5 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_156_5 % 153.78/21.01 & $i(v0)) % 153.78/21.01 (30) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_154_0 % 153.78/21.01 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 153.78/21.01 (@+(v3, v2) = v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 153.78/21.01 ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (@+(v1, v2) % 153.78/21.01 = v7 & @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & nat_succeeds(v1) % 153.78/21.01 = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))) % 153.78/21.01 % 153.78/21.01 Begin of proof % 153.78/21.01 | % 153.78/21.01 | BETA: splitting (10) gives: % 153.78/21.01 | % 153.78/21.01 | Case 1: % 153.78/21.01 | | % 153.78/21.01 | | (31) all_241_1 = 0 % 153.78/21.01 | | % 153.78/21.01 | | COMBINE_EQS: (13), (31) imply: % 153.78/21.01 | | (32) all_89_4 = 0 % 153.78/21.01 | | % 153.78/21.01 | | REDUCE: (28), (32) imply: % 153.78/21.01 | | (33) $false % 153.78/21.01 | | % 153.78/21.01 | | CLOSE: (33) is inconsistent. % 153.78/21.01 | | % 153.78/21.01 | Case 2: % 153.78/21.01 | | % 153.78/21.01 | | % 153.78/21.01 | | GROUND_INST: instantiating (9) with 0, all_243_1, simplifying with (1), (20) % 153.78/21.01 | | gives: % 153.78/21.01 | | (34) all_243_1 = 0 % 153.78/21.01 | | % 153.78/21.01 | | REDUCE: (20), (34) imply: % 153.78/21.01 | | (35) @+(0, 0) = 0 % 153.78/21.01 | | % 153.78/21.01 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15), % 153.78/21.01 | | (16), (17), (18), (19), (21), (22), (23), (24), (25), (26), (27), % 153.78/21.01 | | (29), (30), (35) are inconsistent by sub-proof #7. % 153.78/21.01 | | % 153.78/21.01 | End of split % 153.78/21.01 | % 153.78/21.01 End of proof % 153.78/21.01 % 153.78/21.01 Sub-proof #4 shows that the following formulas are inconsistent: % 153.78/21.01 ---------------------------------------------------------------- % 153.78/21.01 (1) s(all_347_0) = all_154_0 % 153.78/21.01 (2) $i(all_347_0) % 153.78/21.01 (3) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ % 153.78/21.01 (v1 = all_154_0) & s(v0) = v1 & $i(v1))) % 153.78/21.01 (4) nat_succeeds(all_347_0) = 0 % 153.78/21.01 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.01 (s(v2) = v0)) % 153.78/21.01 % 153.78/21.01 Begin of proof % 153.78/21.01 | % 153.78/21.01 | GROUND_INST: instantiating (3) with all_347_0, simplifying with (2), (4) % 153.78/21.01 | gives: % 153.78/21.01 | (6) ? [v0: any] : ( ~ (v0 = all_154_0) & s(all_347_0) = v0 & $i(v0)) % 153.78/21.01 | % 153.78/21.01 | DELTA: instantiating (6) with fresh symbol all_435_0 gives: % 153.78/21.01 | (7) ~ (all_435_0 = all_154_0) & s(all_347_0) = all_435_0 & $i(all_435_0) % 153.78/21.01 | % 153.78/21.01 | ALPHA: (7) implies: % 153.78/21.01 | (8) ~ (all_435_0 = all_154_0) % 153.78/21.01 | (9) s(all_347_0) = all_435_0 % 153.78/21.01 | % 153.78/21.01 | GROUND_INST: instantiating (5) with all_154_0, all_435_0, all_347_0, % 153.78/21.01 | simplifying with (1), (9) gives: % 153.78/21.01 | (10) all_435_0 = all_154_0 % 153.78/21.01 | % 153.78/21.01 | REDUCE: (8), (10) imply: % 153.78/21.01 | (11) $false % 153.78/21.01 | % 153.78/21.01 | CLOSE: (11) is inconsistent. % 153.78/21.01 | % 153.78/21.01 End of proof % 153.78/21.01 % 153.78/21.01 Sub-proof #5 shows that the following formulas are inconsistent: % 153.78/21.01 ---------------------------------------------------------------- % 153.78/21.01 (1) s(all_89_1) = all_89_0 % 153.78/21.01 (2) all_315_0 = all_89_1 % 153.78/21.01 (3) @+(all_89_5, 0) = all_275_1 % 153.78/21.01 (4) ~ (all_89_1 = 0) % 153.78/21.01 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.78/21.01 (@+(v3, v2) = v1) | ~ (@+(v3, v2) = v0)) % 153.78/21.01 (6) @+(all_89_5, 0) = all_89_1 % 153.78/21.01 (7) ~ (all_89_0 = all_89_2) % 153.78/21.01 (8) all_315_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_315_0 & % 153.78/21.01 $i(v0)) % 153.78/21.01 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.01 (s(v2) = v0)) % 153.78/21.01 (10) s(all_275_1) = all_89_2 % 153.78/21.01 % 153.78/21.01 Begin of proof % 153.78/21.01 | % 153.78/21.01 | BETA: splitting (8) gives: % 153.78/21.01 | % 153.78/21.01 | Case 1: % 153.78/21.01 | | % 153.78/21.01 | | (11) all_315_0 = 0 % 153.78/21.01 | | % 153.78/21.01 | | COMBINE_EQS: (2), (11) imply: % 153.78/21.01 | | (12) all_89_1 = 0 % 153.78/21.01 | | % 153.78/21.01 | | REDUCE: (4), (12) imply: % 153.78/21.01 | | (13) $false % 153.78/21.01 | | % 153.78/21.01 | | CLOSE: (13) is inconsistent. % 153.78/21.01 | | % 153.78/21.01 | Case 2: % 153.78/21.01 | | % 153.78/21.01 | | % 153.78/21.01 | | GROUND_INST: instantiating (5) with all_89_1, all_275_1, 0, all_89_5, % 153.78/21.01 | | simplifying with (3), (6) gives: % 153.78/21.01 | | (14) all_275_1 = all_89_1 % 153.78/21.01 | | % 153.78/21.01 | | REDUCE: (10), (14) imply: % 153.78/21.01 | | (15) s(all_89_1) = all_89_2 % 153.78/21.01 | | % 153.78/21.01 | | REF_CLOSE: (1), (7), (9), (15) are inconsistent by sub-proof #6. % 153.78/21.01 | | % 153.78/21.01 | End of split % 153.78/21.01 | % 153.78/21.01 End of proof % 153.78/21.01 % 153.78/21.02 Sub-proof #6 shows that the following formulas are inconsistent: % 153.78/21.02 ---------------------------------------------------------------- % 153.78/21.02 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.02 (s(v2) = v0)) % 153.78/21.02 (2) s(all_89_1) = all_89_0 % 153.78/21.02 (3) s(all_89_1) = all_89_2 % 153.78/21.02 (4) ~ (all_89_0 = all_89_2) % 153.78/21.02 % 153.78/21.02 Begin of proof % 153.78/21.02 | % 153.78/21.02 | GROUND_INST: instantiating (1) with all_89_0, all_89_2, all_89_1, simplifying % 153.78/21.02 | with (2), (3) gives: % 153.78/21.02 | (5) all_89_0 = all_89_2 % 153.78/21.02 | % 153.78/21.02 | REDUCE: (4), (5) imply: % 153.78/21.02 | (6) $false % 153.78/21.02 | % 153.78/21.02 | CLOSE: (6) is inconsistent. % 153.78/21.02 | % 153.78/21.02 End of proof % 153.78/21.02 % 153.78/21.02 Sub-proof #7 shows that the following formulas are inconsistent: % 153.78/21.02 ---------------------------------------------------------------- % 153.78/21.02 (1) @+(all_154_0, all_156_5) = all_156_3 % 153.78/21.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, v1) = % 153.78/21.02 v3) | ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 153.78/21.02 [v5: $i] : ? [v6: $i] : (@+(v0, v1) = v5 & nat_succeeds(v0) = v4 & % 153.78/21.02 s(v5) = v6 & $i(v6) & $i(v5) & ( ~ (v4 = 0) | v6 = v3))) % 153.78/21.02 (3) $i(all_156_4) % 153.78/21.02 (4) @+(all_156_3, all_156_4) = all_156_2 % 153.78/21.02 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (@+(v0, v1) = v2) | ~ % 153.78/21.02 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : % 153.78/21.02 (nat_succeeds(v2) = v5 & nat_succeeds(v1) = v4 & nat_succeeds(v0) = v3 % 153.78/21.02 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) % 153.78/21.02 (6) s(0) = all_96_0 % 153.78/21.02 (7) @+(all_154_0, all_156_1) = all_156_0 % 153.78/21.02 (8) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ $i(v0)) % 153.78/21.02 (9) $i(all_156_1) % 153.78/21.02 (10) nat_succeeds(all_156_5) = 0 % 153.78/21.02 (11) nat_succeeds(all_154_0) = all_169_2 % 153.78/21.02 (12) ~ (all_156_0 = all_156_2) % 153.78/21.02 (13) all_169_2 = 0 | ( ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ % 153.78/21.02 (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = % 153.78/21.02 all_154_0) & s(v0) = v1 & $i(v1)))) % 153.78/21.02 (14) $i(all_156_5) % 153.78/21.02 (15) nat_succeeds(all_156_1) = 0 % 153.78/21.02 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v1) = v2) | % 153.78/21.02 ~ (s(v0) = v2) | ~ $i(v1) | ~ $i(v0)) % 153.78/21.02 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.78/21.02 (@+(v3, v2) = v1) | ~ (@+(v3, v2) = v0)) % 153.78/21.02 (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 153.78/21.02 (v1 = v0 | ~ (nat_succeeds(v2) = v1) | ~ (nat_succeeds(v2) = v0)) % 153.78/21.02 (19) @+(all_156_5, all_156_4) = all_156_1 % 153.78/21.02 (20) ! [v0: $i] : (v0 = 0 | ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: % 153.78/21.02 $i] : (nat_succeeds(v1) = 0 & s(v1) = v0 & $i(v1))) % 153.78/21.02 (21) nat_succeeds(all_156_4) = 0 % 153.78/21.02 (22) @+(0, 0) = 0 % 153.78/21.02 (23) $i(all_154_0) % 153.78/21.02 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | % 153.78/21.02 ~ (s(v2) = v0)) % 153.78/21.02 (25) all_156_5 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_156_5 % 153.78/21.02 & $i(v0)) % 153.78/21.02 (26) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_154_0 % 153.78/21.02 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 153.78/21.02 (@+(v3, v2) = v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 153.78/21.02 ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (@+(v1, v2) % 153.78/21.02 = v7 & @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & nat_succeeds(v1) % 153.78/21.02 = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v4)))) % 153.78/21.02 % 153.78/21.02 Begin of proof % 153.78/21.02 | % 153.78/21.02 | BETA: splitting (26) gives: % 153.78/21.02 | % 153.78/21.02 | Case 1: % 153.78/21.02 | | % 153.78/21.02 | | (27) all_154_0 = 0 % 153.78/21.02 | | % 153.78/21.02 | | REDUCE: (7), (27) imply: % 153.78/21.02 | | (28) @+(0, all_156_1) = all_156_0 % 153.78/21.02 | | % 153.78/21.02 | | REDUCE: (1), (27) imply: % 153.78/21.02 | | (29) @+(0, all_156_5) = all_156_3 % 153.78/21.02 | | % 153.78/21.02 | | REF_CLOSE: (4), (8), (9), (12), (14), (17), (19), (28), (29) are % 153.78/21.02 | | inconsistent by sub-proof #10. % 153.78/21.02 | | % 153.78/21.02 | Case 2: % 153.78/21.02 | | % 153.78/21.02 | | (30) ~ (all_154_0 = 0) % 153.78/21.02 | | (31) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_154_0 & $i(v0) & % 153.78/21.02 | | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (@+(v3, % 153.78/21.02 | | v2) = v4) | ~ (@+(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 153.78/21.02 | | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8: $i] : (@+(v1, % 153.78/21.02 | | v2) = v7 & @+(v0, v7) = v8 & nat_succeeds(v2) = v5 & % 153.78/21.02 | | nat_succeeds(v1) = v6 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ % 153.78/21.02 | | (v5 = 0) | v8 = v4)))) % 153.78/21.02 | | % 153.78/21.02 | | DELTA: instantiating (31) with fresh symbol all_310_0 gives: % 153.78/21.02 | | (32) nat_succeeds(all_310_0) = 0 & s(all_310_0) = all_154_0 & % 153.78/21.02 | | $i(all_310_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 153.78/21.02 | | $i] : ( ~ (@+(v2, v1) = v3) | ~ (@+(all_310_0, v0) = v2) | ~ % 153.78/21.02 | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : % 153.78/21.02 | | ? [v7: $i] : (@+(v0, v1) = v6 & @+(all_310_0, v6) = v7 & % 153.78/21.02 | | nat_succeeds(v1) = v4 & nat_succeeds(v0) = v5 & $i(v7) & $i(v6) % 153.78/21.02 | | & ( ~ (v5 = 0) | ~ (v4 = 0) | v7 = v3))) % 153.78/21.02 | | % 153.78/21.02 | | ALPHA: (32) implies: % 153.78/21.02 | | (33) $i(all_310_0) % 153.78/21.02 | | (34) s(all_310_0) = all_154_0 % 153.78/21.02 | | (35) nat_succeeds(all_310_0) = 0 % 153.78/21.02 | | (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (@+(v2, % 153.78/21.02 | | v1) = v3) | ~ (@+(all_310_0, v0) = v2) | ~ $i(v1) | ~ % 153.78/21.02 | | $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : % 153.78/21.02 | | (@+(v0, v1) = v6 & @+(all_310_0, v6) = v7 & nat_succeeds(v1) = v4 % 153.78/21.02 | | & nat_succeeds(v0) = v5 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ % 153.78/21.02 | | (v4 = 0) | v7 = v3))) % 153.78/21.02 | | % 153.78/21.02 | | GROUND_INST: instantiating (2) with all_310_0, all_156_1, all_154_0, % 153.78/21.02 | | all_156_0, simplifying with (7), (9), (33), (34) gives: % 153.78/21.02 | | (37) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (@+(all_310_0, all_156_1) % 153.78/21.02 | | = v1 & nat_succeeds(all_310_0) = v0 & s(v1) = v2 & $i(v2) & $i(v1) % 153.78/21.02 | | & ( ~ (v0 = 0) | v2 = all_156_0)) % 153.78/21.02 | | % 153.78/21.02 | | GROUND_INST: instantiating (2) with all_310_0, all_156_5, all_154_0, % 153.78/21.02 | | all_156_3, simplifying with (1), (14), (33), (34) gives: % 153.78/21.02 | | (38) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (@+(all_310_0, all_156_5) % 153.78/21.02 | | = v1 & nat_succeeds(all_310_0) = v0 & s(v1) = v2 & $i(v2) & $i(v1) % 153.78/21.02 | | & ( ~ (v0 = 0) | v2 = all_156_3)) % 153.78/21.02 | | % 153.78/21.02 | | GROUND_INST: instantiating (20) with all_310_0, simplifying with (33), (35) % 153.78/21.02 | | gives: % 153.78/21.02 | | (39) all_310_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = % 153.78/21.02 | | all_310_0 & $i(v0)) % 153.78/21.02 | | % 153.78/21.02 | | DELTA: instantiating (38) with fresh symbols all_323_0, all_323_1, all_323_2 % 153.78/21.02 | | gives: % 153.78/21.02 | | (40) @+(all_310_0, all_156_5) = all_323_1 & nat_succeeds(all_310_0) = % 153.78/21.02 | | all_323_2 & s(all_323_1) = all_323_0 & $i(all_323_0) & $i(all_323_1) % 153.78/21.02 | | & ( ~ (all_323_2 = 0) | all_323_0 = all_156_3) % 153.78/21.02 | | % 153.78/21.02 | | ALPHA: (40) implies: % 153.78/21.02 | | (41) $i(all_323_1) % 153.78/21.02 | | (42) s(all_323_1) = all_323_0 % 153.78/21.02 | | (43) nat_succeeds(all_310_0) = all_323_2 % 153.78/21.02 | | (44) @+(all_310_0, all_156_5) = all_323_1 % 153.78/21.02 | | (45) ~ (all_323_2 = 0) | all_323_0 = all_156_3 % 153.78/21.02 | | % 153.78/21.02 | | DELTA: instantiating (37) with fresh symbols all_325_0, all_325_1, all_325_2 % 153.78/21.02 | | gives: % 153.78/21.02 | | (46) @+(all_310_0, all_156_1) = all_325_1 & nat_succeeds(all_310_0) = % 153.78/21.02 | | all_325_2 & s(all_325_1) = all_325_0 & $i(all_325_0) & $i(all_325_1) % 153.78/21.02 | | & ( ~ (all_325_2 = 0) | all_325_0 = all_156_0) % 153.78/21.02 | | % 153.78/21.02 | | ALPHA: (46) implies: % 153.78/21.02 | | (47) s(all_325_1) = all_325_0 % 153.78/21.02 | | (48) nat_succeeds(all_310_0) = all_325_2 % 153.78/21.02 | | (49) @+(all_310_0, all_156_1) = all_325_1 % 153.78/21.02 | | (50) ~ (all_325_2 = 0) | all_325_0 = all_156_0 % 153.78/21.02 | | % 153.78/21.02 | | GROUND_INST: instantiating (18) with 0, all_325_2, all_310_0, simplifying % 153.78/21.02 | | with (35), (48) gives: % 153.78/21.02 | | (51) all_325_2 = 0 % 153.78/21.02 | | % 153.78/21.02 | | GROUND_INST: instantiating (18) with all_323_2, all_325_2, all_310_0, % 153.78/21.02 | | simplifying with (43), (48) gives: % 153.78/21.02 | | (52) all_325_2 = all_323_2 % 153.78/21.02 | | % 153.78/21.02 | | COMBINE_EQS: (51), (52) imply: % 153.78/21.02 | | (53) all_323_2 = 0 % 153.78/21.02 | | % 153.78/21.02 | | BETA: splitting (45) gives: % 153.78/21.02 | | % 153.78/21.02 | | Case 1: % 153.78/21.02 | | | % 153.78/21.02 | | | (54) ~ (all_323_2 = 0) % 153.78/21.02 | | | % 153.78/21.02 | | | REDUCE: (53), (54) imply: % 153.78/21.02 | | | (55) $false % 153.78/21.02 | | | % 153.78/21.02 | | | CLOSE: (55) is inconsistent. % 153.78/21.02 | | | % 153.78/21.02 | | Case 2: % 153.78/21.02 | | | % 153.78/21.02 | | | (56) all_323_0 = all_156_3 % 153.78/21.02 | | | % 153.78/21.02 | | | REDUCE: (42), (56) imply: % 153.78/21.02 | | | (57) s(all_323_1) = all_156_3 % 153.78/21.02 | | | % 153.78/21.02 | | | BETA: splitting (50) gives: % 153.78/21.02 | | | % 153.78/21.02 | | | Case 1: % 153.78/21.02 | | | | % 153.78/21.02 | | | | (58) ~ (all_325_2 = 0) % 153.78/21.02 | | | | % 153.78/21.02 | | | | REDUCE: (51), (58) imply: % 153.78/21.02 | | | | (59) $false % 153.78/21.02 | | | | % 153.78/21.02 | | | | CLOSE: (59) is inconsistent. % 153.78/21.02 | | | | % 153.78/21.02 | | | Case 2: % 153.78/21.02 | | | | % 153.78/21.02 | | | | (60) all_325_0 = all_156_0 % 153.78/21.02 | | | | % 153.78/21.02 | | | | REDUCE: (47), (60) imply: % 153.78/21.02 | | | | (61) s(all_325_1) = all_156_0 % 153.78/21.02 | | | | % 153.78/21.02 | | | | BETA: splitting (25) gives: % 153.78/21.02 | | | | % 153.78/21.02 | | | | Case 1: % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | (62) all_156_5 = 0 % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | REDUCE: (44), (62) imply: % 153.78/21.02 | | | | | (63) @+(all_310_0, 0) = all_323_1 % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | REDUCE: (19), (62) imply: % 153.78/21.02 | | | | | (64) @+(0, all_156_4) = all_156_1 % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | REDUCE: (10), (62) imply: % 153.78/21.02 | | | | | (65) nat_succeeds(0) = 0 % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | REDUCE: (14), (62) imply: % 153.78/21.02 | | | | | (66) $i(0) % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | BETA: splitting (13) gives: % 153.78/21.02 | | | | | % 153.78/21.02 | | | | | Case 1: % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | (67) all_169_2 = 0 % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | REDUCE: (11), (67) imply: % 153.78/21.02 | | | | | | (68) nat_succeeds(all_154_0) = 0 % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | GROUND_INST: instantiating (2) with all_323_1, all_156_4, all_156_3, % 153.78/21.02 | | | | | | all_156_2, simplifying with (3), (4), (41), (57) gives: % 153.78/21.02 | | | | | | (69) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (@+(all_323_1, % 153.78/21.02 | | | | | | all_156_4) = v1 & nat_succeeds(all_323_1) = v0 & s(v1) = % 153.78/21.02 | | | | | | v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_156_2)) % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | GROUND_INST: instantiating (20) with all_154_0, simplifying with % 153.78/21.02 | | | | | | (23), (68) gives: % 153.78/21.02 | | | | | | (70) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) % 153.78/21.02 | | | | | | = all_154_0 & $i(v0)) % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | GROUND_INST: instantiating (8) with all_156_4, all_156_1, % 153.78/21.02 | | | | | | simplifying with (3), (64) gives: % 153.78/21.02 | | | | | | (71) all_156_1 = all_156_4 % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | GROUND_INST: instantiating (5) with all_310_0, 0, all_323_1, % 153.78/21.02 | | | | | | simplifying with (33), (63), (66) gives: % 153.78/21.02 | | | | | | (72) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.78/21.02 | | | | | | (nat_succeeds(all_323_1) = v2 & nat_succeeds(all_310_0) = v0 % 153.78/21.02 | | | | | | & nat_succeeds(0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = % 153.78/21.02 | | | | | | 0)) % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | GROUND_INST: instantiating (5) with all_310_0, all_156_1, all_325_1, % 153.78/21.02 | | | | | | simplifying with (9), (33), (49) gives: % 153.78/21.02 | | | | | | (73) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.78/21.02 | | | | | | (nat_succeeds(all_325_1) = v2 & nat_succeeds(all_310_0) = v0 % 153.78/21.02 | | | | | | & nat_succeeds(all_156_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 153.78/21.02 | | | | | | 0) | v2 = 0)) % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | DELTA: instantiating (72) with fresh symbols all_425_0, all_425_1, % 153.78/21.02 | | | | | | all_425_2 gives: % 153.78/21.02 | | | | | | (74) nat_succeeds(all_323_1) = all_425_0 & % 153.78/21.02 | | | | | | nat_succeeds(all_310_0) = all_425_2 & nat_succeeds(0) = % 153.78/21.02 | | | | | | all_425_1 & ( ~ (all_425_1 = 0) | ~ (all_425_2 = 0) | % 153.78/21.02 | | | | | | all_425_0 = 0) % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | ALPHA: (74) implies: % 153.78/21.02 | | | | | | (75) nat_succeeds(0) = all_425_1 % 153.78/21.02 | | | | | | (76) nat_succeeds(all_310_0) = all_425_2 % 153.78/21.02 | | | | | | (77) nat_succeeds(all_323_1) = all_425_0 % 153.78/21.02 | | | | | | (78) ~ (all_425_1 = 0) | ~ (all_425_2 = 0) | all_425_0 = 0 % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | DELTA: instantiating (73) with fresh symbols all_427_0, all_427_1, % 153.78/21.02 | | | | | | all_427_2 gives: % 153.78/21.02 | | | | | | (79) nat_succeeds(all_325_1) = all_427_0 & % 153.78/21.02 | | | | | | nat_succeeds(all_310_0) = all_427_2 & % 153.78/21.02 | | | | | | nat_succeeds(all_156_1) = all_427_1 & ( ~ (all_427_1 = 0) | % 153.78/21.02 | | | | | | ~ (all_427_2 = 0) | all_427_0 = 0) % 153.78/21.02 | | | | | | % 153.78/21.02 | | | | | | ALPHA: (79) implies: % 153.78/21.02 | | | | | | (80) nat_succeeds(all_156_1) = all_427_1 % 153.78/21.03 | | | | | | (81) nat_succeeds(all_310_0) = all_427_2 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | DELTA: instantiating (69) with fresh symbols all_429_0, all_429_1, % 153.78/21.03 | | | | | | all_429_2 gives: % 153.78/21.03 | | | | | | (82) @+(all_323_1, all_156_4) = all_429_1 & % 153.78/21.03 | | | | | | nat_succeeds(all_323_1) = all_429_2 & s(all_429_1) = % 153.78/21.03 | | | | | | all_429_0 & $i(all_429_0) & $i(all_429_1) & ( ~ (all_429_2 = % 153.78/21.03 | | | | | | 0) | all_429_0 = all_156_2) % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | ALPHA: (82) implies: % 153.78/21.03 | | | | | | (83) s(all_429_1) = all_429_0 % 153.78/21.03 | | | | | | (84) nat_succeeds(all_323_1) = all_429_2 % 153.78/21.03 | | | | | | (85) @+(all_323_1, all_156_4) = all_429_1 % 153.78/21.03 | | | | | | (86) ~ (all_429_2 = 0) | all_429_0 = all_156_2 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | REDUCE: (49), (71) imply: % 153.78/21.03 | | | | | | (87) @+(all_310_0, all_156_4) = all_325_1 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | REDUCE: (7), (71) imply: % 153.78/21.03 | | | | | | (88) @+(all_154_0, all_156_4) = all_156_0 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | REDUCE: (64), (71) imply: % 153.78/21.03 | | | | | | (89) @+(0, all_156_4) = all_156_4 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | REDUCE: (71), (80) imply: % 153.78/21.03 | | | | | | (90) nat_succeeds(all_156_4) = all_427_1 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | BETA: splitting (70) gives: % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | Case 1: % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | (91) all_154_0 = 0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | REDUCE: (30), (91) imply: % 153.78/21.03 | | | | | | | (92) $false % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | CLOSE: (92) is inconsistent. % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | Case 2: % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | (93) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_154_0 & % 153.78/21.03 | | | | | | | $i(v0)) % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | DELTA: instantiating (93) with fresh symbol all_435_0 gives: % 153.78/21.03 | | | | | | | (94) nat_succeeds(all_435_0) = 0 & s(all_435_0) = all_154_0 & % 153.78/21.03 | | | | | | | $i(all_435_0) % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | ALPHA: (94) implies: % 153.78/21.03 | | | | | | | (95) $i(all_435_0) % 153.78/21.03 | | | | | | | (96) s(all_435_0) = all_154_0 % 153.78/21.03 | | | | | | | (97) nat_succeeds(all_435_0) = 0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | GROUND_INST: instantiating (18) with 0, all_425_1, 0, simplifying % 153.78/21.03 | | | | | | | with (65), (75) gives: % 153.78/21.03 | | | | | | | (98) all_425_1 = 0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | GROUND_INST: instantiating (18) with 0, all_427_1, all_156_4, % 153.78/21.03 | | | | | | | simplifying with (21), (90) gives: % 153.78/21.03 | | | | | | | (99) all_427_1 = 0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | GROUND_INST: instantiating (18) with 0, all_427_2, all_310_0, % 153.78/21.03 | | | | | | | simplifying with (35), (81) gives: % 153.78/21.03 | | | | | | | (100) all_427_2 = 0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | GROUND_INST: instantiating (18) with all_425_2, all_427_2, % 153.78/21.03 | | | | | | | all_310_0, simplifying with (76), (81) gives: % 153.78/21.03 | | | | | | | (101) all_427_2 = all_425_2 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | GROUND_INST: instantiating (18) with all_425_0, all_429_2, % 153.78/21.03 | | | | | | | all_323_1, simplifying with (77), (84) gives: % 153.78/21.03 | | | | | | | (102) all_429_2 = all_425_0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | COMBINE_EQS: (100), (101) imply: % 153.78/21.03 | | | | | | | (103) all_425_2 = 0 % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | BETA: splitting (78) gives: % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | | (104) ~ (all_425_1 = 0) % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | | REDUCE: (98), (104) imply: % 153.78/21.03 | | | | | | | | (105) $false % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | | CLOSE: (105) is inconsistent. % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | | (106) ~ (all_425_2 = 0) | all_425_0 = 0 % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | | BETA: splitting (106) gives: % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | (107) ~ (all_425_2 = 0) % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | REDUCE: (103), (107) imply: % 153.78/21.03 | | | | | | | | | (108) $false % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | CLOSE: (108) is inconsistent. % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | (109) all_425_0 = 0 % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | COMBINE_EQS: (102), (109) imply: % 153.78/21.03 | | | | | | | | | (110) all_429_2 = 0 % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | BETA: splitting (86) gives: % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | (111) ~ (all_429_2 = 0) % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | REDUCE: (110), (111) imply: % 153.78/21.03 | | | | | | | | | | (112) $false % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | CLOSE: (112) is inconsistent. % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | (113) all_429_0 = all_156_2 % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | REDUCE: (83), (113) imply: % 153.78/21.03 | | | | | | | | | | (114) s(all_429_1) = all_156_2 % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | BETA: splitting (39) gives: % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | (115) all_310_0 = 0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (63), (115) imply: % 153.78/21.03 | | | | | | | | | | | (116) @+(0, 0) = all_323_1 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (34), (115) imply: % 153.78/21.03 | | | | | | | | | | | (117) s(0) = all_154_0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_96_0, all_154_0, 0, % 153.78/21.03 | | | | | | | | | | | simplifying with (6), (117) gives: % 153.78/21.03 | | | | | | | | | | | (118) all_154_0 = all_96_0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_323_1, 0, 0, % 153.78/21.03 | | | | | | | | | | | simplifying with (22), (116) gives: % 153.78/21.03 | | | | | | | | | | | (119) all_323_1 = 0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (88), (118) imply: % 153.78/21.03 | | | | | | | | | | | (120) @+(all_96_0, all_156_4) = all_156_0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (57), (119) imply: % 153.78/21.03 | | | | | | | | | | | (121) s(0) = all_156_3 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_96_0, all_156_3, 0, % 153.78/21.03 | | | | | | | | | | | simplifying with (6), (121) gives: % 153.78/21.03 | | | | | | | | | | | (122) all_156_3 = all_96_0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (4), (122) imply: % 153.78/21.03 | | | | | | | | | | | (123) @+(all_96_0, all_156_4) = all_156_2 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (17) with all_156_0, all_156_2, % 153.78/21.03 | | | | | | | | | | | all_156_4, all_96_0, simplifying with (120), (123) % 153.78/21.03 | | | | | | | | | | | gives: % 153.78/21.03 | | | | | | | | | | | (124) all_156_0 = all_156_2 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (12), (124) imply: % 153.78/21.03 | | | | | | | | | | | (125) $false % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | CLOSE: (125) is inconsistent. % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | (126) ~ (all_310_0 = 0) % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (16) with all_310_0, all_435_0, % 153.78/21.03 | | | | | | | | | | | all_154_0, simplifying with (33), (34), (95), (96) % 153.78/21.03 | | | | | | | | | | | gives: % 153.78/21.03 | | | | | | | | | | | (127) all_435_0 = all_310_0 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_435_0, simplifying % 153.78/21.03 | | | | | | | | | | | with (95), (97) gives: % 153.78/21.03 | | | | | | | | | | | (128) all_435_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.78/21.03 | | | | | | | | | | | 0 & s(v0) = all_435_0 & $i(v0)) % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_435_0, all_156_4, % 153.78/21.03 | | | | | | | | | | | all_154_0, all_156_0, simplifying with (3), (88), % 153.78/21.03 | | | | | | | | | | | (95), (96) gives: % 153.78/21.03 | | | | | | | | | | | (129) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.78/21.03 | | | | | | | | | | | (@+(all_435_0, all_156_4) = v1 & % 153.78/21.03 | | | | | | | | | | | nat_succeeds(all_435_0) = v0 & s(v1) = v2 & % 153.78/21.03 | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.78/21.03 | | | | | | | | | | | all_156_0)) % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | GROUND_INST: instantiating (36) with 0, all_156_4, all_323_1, % 153.78/21.03 | | | | | | | | | | | all_429_1, simplifying with (3), (63), (66), (85) % 153.78/21.03 | | | | | | | | | | | gives: % 153.78/21.03 | | | | | | | | | | | (130) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.78/21.03 | | | | | | | | | | | [v3: $i] : (@+(all_310_0, v2) = v3 & @+(0, % 153.78/21.03 | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.78/21.03 | | | | | | | | | | | & nat_succeeds(0) = v1 & $i(v3) & $i(v2) & ( ~ % 153.78/21.03 | | | | | | | | | | | (v1 = 0) | ~ (v0 = 0) | v3 = all_429_1)) % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | DELTA: instantiating (129) with fresh symbols all_518_0, % 153.78/21.03 | | | | | | | | | | | all_518_1, all_518_2 gives: % 153.78/21.03 | | | | | | | | | | | (131) @+(all_435_0, all_156_4) = all_518_1 & % 153.78/21.03 | | | | | | | | | | | nat_succeeds(all_435_0) = all_518_2 & s(all_518_1) % 153.78/21.03 | | | | | | | | | | | = all_518_0 & $i(all_518_0) & $i(all_518_1) & ( ~ % 153.78/21.03 | | | | | | | | | | | (all_518_2 = 0) | all_518_0 = all_156_0) % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | ALPHA: (131) implies: % 153.78/21.03 | | | | | | | | | | | (132) @+(all_435_0, all_156_4) = all_518_1 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | DELTA: instantiating (130) with fresh symbols all_530_0, % 153.78/21.03 | | | | | | | | | | | all_530_1, all_530_2, all_530_3 gives: % 153.78/21.03 | | | | | | | | | | | (133) @+(all_310_0, all_530_1) = all_530_0 & @+(0, % 153.78/21.03 | | | | | | | | | | | all_156_4) = all_530_1 & nat_succeeds(all_156_4) % 153.78/21.03 | | | | | | | | | | | = all_530_3 & nat_succeeds(0) = all_530_2 & % 153.78/21.03 | | | | | | | | | | | $i(all_530_0) & $i(all_530_1) & ( ~ (all_530_2 = % 153.78/21.03 | | | | | | | | | | | 0) | ~ (all_530_3 = 0) | all_530_0 = % 153.78/21.03 | | | | | | | | | | | all_429_1) % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | ALPHA: (133) implies: % 153.78/21.03 | | | | | | | | | | | (134) nat_succeeds(0) = all_530_2 % 153.78/21.03 | | | | | | | | | | | (135) nat_succeeds(all_156_4) = all_530_3 % 153.78/21.03 | | | | | | | | | | | (136) @+(0, all_156_4) = all_530_1 % 153.78/21.03 | | | | | | | | | | | (137) @+(all_310_0, all_530_1) = all_530_0 % 153.78/21.03 | | | | | | | | | | | (138) ~ (all_530_2 = 0) | ~ (all_530_3 = 0) | % 153.78/21.03 | | | | | | | | | | | all_530_0 = all_429_1 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | REDUCE: (127), (132) imply: % 153.78/21.03 | | | | | | | | | | | (139) @+(all_310_0, all_156_4) = all_518_1 % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | BETA: splitting (128) gives: % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | (140) all_435_0 = 0 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | COMBINE_EQS: (127), (140) imply: % 153.78/21.03 | | | | | | | | | | | | (141) all_310_0 = 0 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | SIMP: (141) implies: % 153.78/21.03 | | | | | | | | | | | | (142) all_310_0 = 0 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | REDUCE: (126), (142) imply: % 153.78/21.03 | | | | | | | | | | | | (143) $false % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | CLOSE: (143) is inconsistent. % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_530_2, 0, % 153.78/21.03 | | | | | | | | | | | | simplifying with (65), (134) gives: % 153.78/21.03 | | | | | | | | | | | | (144) all_530_2 = 0 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_530_3, all_156_4, % 153.78/21.03 | | | | | | | | | | | | simplifying with (21), (135) gives: % 153.78/21.03 | | | | | | | | | | | | (145) all_530_3 = 0 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_156_4, all_530_1, % 153.78/21.03 | | | | | | | | | | | | all_156_4, 0, simplifying with (89), (136) gives: % 153.78/21.03 | | | | | | | | | | | | (146) all_530_1 = all_156_4 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_325_1, all_518_1, % 153.78/21.03 | | | | | | | | | | | | all_156_4, all_310_0, simplifying with (87), (139) % 153.78/21.03 | | | | | | | | | | | | gives: % 153.78/21.03 | | | | | | | | | | | | (147) all_518_1 = all_325_1 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | REDUCE: (137), (146) imply: % 153.78/21.03 | | | | | | | | | | | | (148) @+(all_310_0, all_156_4) = all_530_0 % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | BETA: splitting (138) gives: % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | (149) ~ (all_530_2 = 0) % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | REDUCE: (144), (149) imply: % 153.78/21.03 | | | | | | | | | | | | | (150) $false % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | CLOSE: (150) is inconsistent. % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | (151) ~ (all_530_3 = 0) | all_530_0 = all_429_1 % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | BETA: splitting (151) gives: % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | Case 1: % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | (152) ~ (all_530_3 = 0) % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | REDUCE: (145), (152) imply: % 153.78/21.03 | | | | | | | | | | | | | | (153) $false % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | CLOSE: (153) is inconsistent. % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | Case 2: % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | (154) all_530_0 = all_429_1 % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | REDUCE: (148), (154) imply: % 153.78/21.03 | | | | | | | | | | | | | | (155) @+(all_310_0, all_156_4) = all_429_1 % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_325_1, all_429_1, % 153.78/21.03 | | | | | | | | | | | | | | all_156_4, all_310_0, simplifying with (87), (155) % 153.78/21.03 | | | | | | | | | | | | | | gives: % 153.78/21.03 | | | | | | | | | | | | | | (156) all_429_1 = all_325_1 % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | REDUCE: (114), (156) imply: % 153.78/21.03 | | | | | | | | | | | | | | (157) s(all_325_1) = all_156_2 % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_156_0, all_156_2, % 153.78/21.03 | | | | | | | | | | | | | | all_325_1, simplifying with (61), (157) gives: % 153.78/21.03 | | | | | | | | | | | | | | (158) all_156_0 = all_156_2 % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | REDUCE: (12), (158) imply: % 153.78/21.03 | | | | | | | | | | | | | | (159) $false % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | | CLOSE: (159) is inconsistent. % 153.78/21.03 | | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | | End of split % 153.78/21.03 | | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | | End of split % 153.78/21.03 | | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | | End of split % 153.78/21.03 | | | | | | | | | | | % 153.78/21.03 | | | | | | | | | | End of split % 153.78/21.03 | | | | | | | | | | % 153.78/21.03 | | | | | | | | | End of split % 153.78/21.03 | | | | | | | | | % 153.78/21.03 | | | | | | | | End of split % 153.78/21.03 | | | | | | | | % 153.78/21.03 | | | | | | | End of split % 153.78/21.03 | | | | | | | % 153.78/21.03 | | | | | | End of split % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | Case 2: % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | (160) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ (nat_succeeds(v0) = % 153.78/21.03 | | | | | | 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.78/21.03 | | | | | | s(v0) = v1 & $i(v1))) % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | ALPHA: (160) implies: % 153.78/21.03 | | | | | | (161) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? % 153.78/21.03 | | | | | | [v1: any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & $i(v1))) % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | REF_CLOSE: (24), (33), (34), (35), (161) are inconsistent by % 153.78/21.03 | | | | | | sub-proof #9. % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | End of split % 153.78/21.03 | | | | | % 153.78/21.03 | | | | Case 2: % 153.78/21.03 | | | | | % 153.78/21.03 | | | | | (162) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_156_5 & % 153.78/21.03 | | | | | $i(v0)) % 153.78/21.03 | | | | | % 153.78/21.03 | | | | | DELTA: instantiating (162) with fresh symbol all_357_0 gives: % 153.78/21.03 | | | | | (163) nat_succeeds(all_357_0) = 0 & s(all_357_0) = all_156_5 & % 153.78/21.03 | | | | | $i(all_357_0) % 153.78/21.03 | | | | | % 153.78/21.03 | | | | | ALPHA: (163) implies: % 153.78/21.03 | | | | | (164) $i(all_357_0) % 153.78/21.03 | | | | | (165) s(all_357_0) = all_156_5 % 153.78/21.03 | | | | | % 153.78/21.03 | | | | | BETA: splitting (13) gives: % 153.78/21.03 | | | | | % 153.78/21.03 | | | | | Case 1: % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | (166) all_169_2 = 0 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | REDUCE: (11), (166) imply: % 153.78/21.03 | | | | | | (167) nat_succeeds(all_154_0) = 0 % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | GROUND_INST: instantiating (2) with all_323_1, all_156_4, all_156_3, % 153.78/21.03 | | | | | | all_156_2, simplifying with (3), (4), (41), (57) gives: % 153.78/21.03 | | | | | | (168) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (@+(all_323_1, % 153.78/21.03 | | | | | | all_156_4) = v1 & nat_succeeds(all_323_1) = v0 & s(v1) % 153.78/21.03 | | | | | | = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_156_2)) % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | GROUND_INST: instantiating (2) with all_357_0, all_156_4, all_156_5, % 153.78/21.03 | | | | | | all_156_1, simplifying with (3), (19), (164), (165) % 153.78/21.03 | | | | | | gives: % 153.78/21.03 | | | | | | (169) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (@+(all_357_0, % 153.78/21.03 | | | | | | all_156_4) = v1 & nat_succeeds(all_357_0) = v0 & s(v1) % 153.78/21.03 | | | | | | = v2 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_156_1)) % 153.78/21.03 | | | | | | % 153.78/21.03 | | | | | | GROUND_INST: instantiating (20) with all_154_0, simplifying with % 153.78/21.03 | | | | | | (23), (167) gives: % 153.78/21.04 | | | | | | (170) all_154_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) % 153.78/21.04 | | | | | | = all_154_0 & $i(v0)) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | GROUND_INST: instantiating (5) with all_310_0, all_156_5, all_323_1, % 153.78/21.04 | | | | | | simplifying with (14), (33), (44) gives: % 153.78/21.04 | | | | | | (171) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.78/21.04 | | | | | | (nat_succeeds(all_323_1) = v2 & nat_succeeds(all_310_0) = % 153.78/21.04 | | | | | | v0 & nat_succeeds(all_156_5) = v1 & ( ~ (v1 = 0) | ~ (v0 % 153.78/21.04 | | | | | | = 0) | v2 = 0)) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | GROUND_INST: instantiating (5) with all_310_0, all_156_1, all_325_1, % 153.78/21.04 | | | | | | simplifying with (9), (33), (49) gives: % 153.78/21.04 | | | | | | (172) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.78/21.04 | | | | | | (nat_succeeds(all_325_1) = v2 & nat_succeeds(all_310_0) = % 153.78/21.04 | | | | | | v0 & nat_succeeds(all_156_1) = v1 & ( ~ (v1 = 0) | ~ (v0 % 153.78/21.04 | | | | | | = 0) | v2 = 0)) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | DELTA: instantiating (172) with fresh symbols all_426_0, all_426_1, % 153.78/21.04 | | | | | | all_426_2 gives: % 153.78/21.04 | | | | | | (173) nat_succeeds(all_325_1) = all_426_0 & % 153.78/21.04 | | | | | | nat_succeeds(all_310_0) = all_426_2 & % 153.78/21.04 | | | | | | nat_succeeds(all_156_1) = all_426_1 & ( ~ (all_426_1 = 0) | % 153.78/21.04 | | | | | | ~ (all_426_2 = 0) | all_426_0 = 0) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | ALPHA: (173) implies: % 153.78/21.04 | | | | | | (174) nat_succeeds(all_310_0) = all_426_2 % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | DELTA: instantiating (171) with fresh symbols all_428_0, all_428_1, % 153.78/21.04 | | | | | | all_428_2 gives: % 153.78/21.04 | | | | | | (175) nat_succeeds(all_323_1) = all_428_0 & % 153.78/21.04 | | | | | | nat_succeeds(all_310_0) = all_428_2 & % 153.78/21.04 | | | | | | nat_succeeds(all_156_5) = all_428_1 & ( ~ (all_428_1 = 0) | % 153.78/21.04 | | | | | | ~ (all_428_2 = 0) | all_428_0 = 0) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | ALPHA: (175) implies: % 153.78/21.04 | | | | | | (176) nat_succeeds(all_156_5) = all_428_1 % 153.78/21.04 | | | | | | (177) nat_succeeds(all_310_0) = all_428_2 % 153.78/21.04 | | | | | | (178) nat_succeeds(all_323_1) = all_428_0 % 153.78/21.04 | | | | | | (179) ~ (all_428_1 = 0) | ~ (all_428_2 = 0) | all_428_0 = 0 % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | DELTA: instantiating (169) with fresh symbols all_430_0, all_430_1, % 153.78/21.04 | | | | | | all_430_2 gives: % 153.78/21.04 | | | | | | (180) @+(all_357_0, all_156_4) = all_430_1 & % 153.78/21.04 | | | | | | nat_succeeds(all_357_0) = all_430_2 & s(all_430_1) = % 153.78/21.04 | | | | | | all_430_0 & $i(all_430_0) & $i(all_430_1) & ( ~ (all_430_2 % 153.78/21.04 | | | | | | = 0) | all_430_0 = all_156_1) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | ALPHA: (180) implies: % 153.78/21.04 | | | | | | (181) @+(all_357_0, all_156_4) = all_430_1 % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | DELTA: instantiating (168) with fresh symbols all_432_0, all_432_1, % 153.78/21.04 | | | | | | all_432_2 gives: % 153.78/21.04 | | | | | | (182) @+(all_323_1, all_156_4) = all_432_1 & % 153.78/21.04 | | | | | | nat_succeeds(all_323_1) = all_432_2 & s(all_432_1) = % 153.78/21.04 | | | | | | all_432_0 & $i(all_432_0) & $i(all_432_1) & ( ~ (all_432_2 % 153.78/21.04 | | | | | | = 0) | all_432_0 = all_156_2) % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | ALPHA: (182) implies: % 153.78/21.04 | | | | | | (183) s(all_432_1) = all_432_0 % 153.78/21.04 | | | | | | (184) nat_succeeds(all_323_1) = all_432_2 % 153.78/21.04 | | | | | | (185) @+(all_323_1, all_156_4) = all_432_1 % 153.78/21.04 | | | | | | (186) ~ (all_432_2 = 0) | all_432_0 = all_156_2 % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | BETA: splitting (170) gives: % 153.78/21.04 | | | | | | % 153.78/21.04 | | | | | | Case 1: % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | (187) all_154_0 = 0 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | REDUCE: (30), (187) imply: % 153.78/21.04 | | | | | | | (188) $false % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | CLOSE: (188) is inconsistent. % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | Case 2: % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | (189) ? [v0: $i] : (nat_succeeds(v0) = 0 & s(v0) = all_154_0 & % 153.78/21.04 | | | | | | | $i(v0)) % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | DELTA: instantiating (189) with fresh symbol all_438_0 gives: % 153.78/21.04 | | | | | | | (190) nat_succeeds(all_438_0) = 0 & s(all_438_0) = all_154_0 & % 153.78/21.04 | | | | | | | $i(all_438_0) % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | ALPHA: (190) implies: % 153.78/21.04 | | | | | | | (191) $i(all_438_0) % 153.78/21.04 | | | | | | | (192) s(all_438_0) = all_154_0 % 153.78/21.04 | | | | | | | (193) nat_succeeds(all_438_0) = 0 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | GROUND_INST: instantiating (18) with 0, all_428_1, all_156_5, % 153.78/21.04 | | | | | | | simplifying with (10), (176) gives: % 153.78/21.04 | | | | | | | (194) all_428_1 = 0 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | GROUND_INST: instantiating (18) with 0, all_428_2, all_310_0, % 153.78/21.04 | | | | | | | simplifying with (35), (177) gives: % 153.78/21.04 | | | | | | | (195) all_428_2 = 0 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | GROUND_INST: instantiating (18) with all_426_2, all_428_2, % 153.78/21.04 | | | | | | | all_310_0, simplifying with (174), (177) gives: % 153.78/21.04 | | | | | | | (196) all_428_2 = all_426_2 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | GROUND_INST: instantiating (18) with all_428_0, all_432_2, % 153.78/21.04 | | | | | | | all_323_1, simplifying with (178), (184) gives: % 153.78/21.04 | | | | | | | (197) all_432_2 = all_428_0 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | COMBINE_EQS: (195), (196) imply: % 153.78/21.04 | | | | | | | (198) all_426_2 = 0 % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | BETA: splitting (179) gives: % 153.78/21.04 | | | | | | | % 153.78/21.04 | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | | (199) ~ (all_428_1 = 0) % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | | REDUCE: (194), (199) imply: % 153.78/21.04 | | | | | | | | (200) $false % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | | CLOSE: (200) is inconsistent. % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | | (201) ~ (all_428_2 = 0) | all_428_0 = 0 % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | | BETA: splitting (201) gives: % 153.78/21.04 | | | | | | | | % 153.78/21.04 | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | (202) ~ (all_428_2 = 0) % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | REDUCE: (195), (202) imply: % 153.78/21.04 | | | | | | | | | (203) $false % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | CLOSE: (203) is inconsistent. % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | (204) all_428_0 = 0 % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | COMBINE_EQS: (197), (204) imply: % 153.78/21.04 | | | | | | | | | (205) all_432_2 = 0 % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | BETA: splitting (186) gives: % 153.78/21.04 | | | | | | | | | % 153.78/21.04 | | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | (206) ~ (all_432_2 = 0) % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | REDUCE: (205), (206) imply: % 153.78/21.04 | | | | | | | | | | (207) $false % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | CLOSE: (207) is inconsistent. % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | (208) all_432_0 = all_156_2 % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | REDUCE: (183), (208) imply: % 153.78/21.04 | | | | | | | | | | (209) s(all_432_1) = all_156_2 % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | BETA: splitting (39) gives: % 153.78/21.04 | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | (210) all_310_0 = 0 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (49), (210) imply: % 153.78/21.04 | | | | | | | | | | | (211) @+(0, all_156_1) = all_325_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (44), (210) imply: % 153.78/21.04 | | | | | | | | | | | (212) @+(0, all_156_5) = all_323_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (34), (210) imply: % 153.78/21.04 | | | | | | | | | | | (213) s(0) = all_154_0 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_96_0, all_154_0, 0, % 153.78/21.04 | | | | | | | | | | | simplifying with (6), (213) gives: % 153.78/21.04 | | | | | | | | | | | (214) all_154_0 = all_96_0 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (30), (214) imply: % 153.78/21.04 | | | | | | | | | | | (215) ~ (all_96_0 = 0) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (167), (214) imply: % 153.78/21.04 | | | | | | | | | | | (216) nat_succeeds(all_96_0) = 0 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (23), (214) imply: % 153.78/21.04 | | | | | | | | | | | (217) $i(all_96_0) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_96_0, simplifying with % 153.78/21.04 | | | | | | | | | | | (216), (217) gives: % 153.78/21.04 | | | | | | | | | | | (218) all_96_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = 0 % 153.78/21.04 | | | | | | | | | | | & s(v0) = all_96_0 & $i(v0)) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_156_5, all_323_1, % 153.78/21.04 | | | | | | | | | | | simplifying with (14), (212) gives: % 153.78/21.04 | | | | | | | | | | | (219) all_323_1 = all_156_5 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_156_1, all_325_1, % 153.78/21.04 | | | | | | | | | | | simplifying with (9), (211) gives: % 153.78/21.04 | | | | | | | | | | | (220) all_325_1 = all_156_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (185), (219) imply: % 153.78/21.04 | | | | | | | | | | | (221) @+(all_156_5, all_156_4) = all_432_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (61), (220) imply: % 153.78/21.04 | | | | | | | | | | | (222) s(all_156_1) = all_156_0 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | BETA: splitting (218) gives: % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | (223) all_96_0 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | REDUCE: (215), (223) imply: % 153.78/21.04 | | | | | | | | | | | | (224) $false % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | CLOSE: (224) is inconsistent. % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_156_1, all_432_1, % 153.78/21.04 | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (19), (221) % 153.78/21.04 | | | | | | | | | | | | gives: % 153.78/21.04 | | | | | | | | | | | | (225) all_432_1 = all_156_1 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | REDUCE: (209), (225) imply: % 153.78/21.04 | | | | | | | | | | | | (226) s(all_156_1) = all_156_2 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | REF_CLOSE: (12), (24), (222), (226) are inconsistent by % 153.78/21.04 | | | | | | | | | | | | sub-proof #8. % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | End of split % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | (227) ~ (all_310_0 = 0) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (2) with all_438_0, all_156_1, % 153.78/21.04 | | | | | | | | | | | all_154_0, all_156_0, simplifying with (7), (9), % 153.78/21.04 | | | | | | | | | | | (191), (192) gives: % 153.78/21.04 | | | | | | | | | | | (228) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : % 153.78/21.04 | | | | | | | | | | | (@+(all_438_0, all_156_1) = v1 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_438_0) = v0 & s(v1) = v2 & % 153.78/21.04 | | | | | | | | | | | $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = % 153.78/21.04 | | | | | | | | | | | all_156_0)) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (16) with all_310_0, all_438_0, % 153.78/21.04 | | | | | | | | | | | all_154_0, simplifying with (33), (34), (191), % 153.78/21.04 | | | | | | | | | | | (192) gives: % 153.78/21.04 | | | | | | | | | | | (229) all_438_0 = all_310_0 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (20) with all_438_0, simplifying % 153.78/21.04 | | | | | | | | | | | with (191), (193) gives: % 153.78/21.04 | | | | | | | | | | | (230) all_438_0 = 0 | ? [v0: $i] : (nat_succeeds(v0) = % 153.78/21.04 | | | | | | | | | | | 0 & s(v0) = all_438_0 & $i(v0)) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (36) with all_156_5, all_156_4, % 153.78/21.04 | | | | | | | | | | | all_323_1, all_432_1, simplifying with (3), (14), % 153.78/21.04 | | | | | | | | | | | (44), (185) gives: % 153.78/21.04 | | | | | | | | | | | (231) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? % 153.78/21.04 | | | | | | | | | | | [v3: $i] : (@+(all_310_0, v2) = v3 & @+(all_156_5, % 153.78/21.04 | | | | | | | | | | | all_156_4) = v2 & nat_succeeds(all_156_4) = v0 % 153.78/21.04 | | | | | | | | | | | & nat_succeeds(all_156_5) = v1 & $i(v3) & $i(v2) % 153.78/21.04 | | | | | | | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0) | v3 = all_432_1)) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_323_1, all_156_4, % 153.78/21.04 | | | | | | | | | | | all_432_1, simplifying with (3), (41), (185) % 153.78/21.04 | | | | | | | | | | | gives: % 153.78/21.04 | | | | | | | | | | | (232) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.78/21.04 | | | | | | | | | | | (nat_succeeds(all_432_1) = v2 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_323_1) = v0 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.78/21.04 | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_357_0, all_156_4, % 153.78/21.04 | | | | | | | | | | | all_430_1, simplifying with (3), (164), (181) % 153.78/21.04 | | | | | | | | | | | gives: % 153.78/21.04 | | | | | | | | | | | (233) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 153.78/21.04 | | | | | | | | | | | (nat_succeeds(all_430_1) = v2 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_357_0) = v0 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_156_4) = v1 & ( ~ (v1 = 0) | ~ % 153.78/21.04 | | | | | | | | | | | (v0 = 0) | v2 = 0)) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_519_0, % 153.78/21.04 | | | | | | | | | | | all_519_1, all_519_2 gives: % 153.78/21.04 | | | | | | | | | | | (234) nat_succeeds(all_430_1) = all_519_0 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_357_0) = all_519_2 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_156_4) = all_519_1 & ( ~ % 153.78/21.04 | | | | | | | | | | | (all_519_1 = 0) | ~ (all_519_2 = 0) | all_519_0 % 153.78/21.04 | | | | | | | | | | | = 0) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | ALPHA: (234) implies: % 153.78/21.04 | | | | | | | | | | | (235) nat_succeeds(all_156_4) = all_519_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | DELTA: instantiating (232) with fresh symbols all_521_0, % 153.78/21.04 | | | | | | | | | | | all_521_1, all_521_2 gives: % 153.78/21.04 | | | | | | | | | | | (236) nat_succeeds(all_432_1) = all_521_0 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_323_1) = all_521_2 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_156_4) = all_521_1 & ( ~ % 153.78/21.04 | | | | | | | | | | | (all_521_1 = 0) | ~ (all_521_2 = 0) | all_521_0 % 153.78/21.04 | | | | | | | | | | | = 0) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | ALPHA: (236) implies: % 153.78/21.04 | | | | | | | | | | | (237) nat_succeeds(all_156_4) = all_521_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | DELTA: instantiating (228) with fresh symbols all_523_0, % 153.78/21.04 | | | | | | | | | | | all_523_1, all_523_2 gives: % 153.78/21.04 | | | | | | | | | | | (238) @+(all_438_0, all_156_1) = all_523_1 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_438_0) = all_523_2 & s(all_523_1) % 153.78/21.04 | | | | | | | | | | | = all_523_0 & $i(all_523_0) & $i(all_523_1) & ( ~ % 153.78/21.04 | | | | | | | | | | | (all_523_2 = 0) | all_523_0 = all_156_0) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | ALPHA: (238) implies: % 153.78/21.04 | | | | | | | | | | | (239) @+(all_438_0, all_156_1) = all_523_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | DELTA: instantiating (231) with fresh symbols all_539_0, % 153.78/21.04 | | | | | | | | | | | all_539_1, all_539_2, all_539_3 gives: % 153.78/21.04 | | | | | | | | | | | (240) @+(all_310_0, all_539_1) = all_539_0 & % 153.78/21.04 | | | | | | | | | | | @+(all_156_5, all_156_4) = all_539_1 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_156_4) = all_539_3 & % 153.78/21.04 | | | | | | | | | | | nat_succeeds(all_156_5) = all_539_2 & % 153.78/21.04 | | | | | | | | | | | $i(all_539_0) & $i(all_539_1) & ( ~ (all_539_2 = % 153.78/21.04 | | | | | | | | | | | 0) | ~ (all_539_3 = 0) | all_539_0 = % 153.78/21.04 | | | | | | | | | | | all_432_1) % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | ALPHA: (240) implies: % 153.78/21.04 | | | | | | | | | | | (241) nat_succeeds(all_156_5) = all_539_2 % 153.78/21.04 | | | | | | | | | | | (242) nat_succeeds(all_156_4) = all_539_3 % 153.78/21.04 | | | | | | | | | | | (243) @+(all_156_5, all_156_4) = all_539_1 % 153.78/21.04 | | | | | | | | | | | (244) @+(all_310_0, all_539_1) = all_539_0 % 153.78/21.04 | | | | | | | | | | | (245) ~ (all_539_2 = 0) | ~ (all_539_3 = 0) | % 153.78/21.04 | | | | | | | | | | | all_539_0 = all_432_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | REDUCE: (229), (239) imply: % 153.78/21.04 | | | | | | | | | | | (246) @+(all_310_0, all_156_1) = all_523_1 % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | BETA: splitting (230) gives: % 153.78/21.04 | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | (247) all_438_0 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | COMBINE_EQS: (229), (247) imply: % 153.78/21.04 | | | | | | | | | | | | (248) all_310_0 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | SIMP: (248) implies: % 153.78/21.04 | | | | | | | | | | | | (249) all_310_0 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | REDUCE: (227), (249) imply: % 153.78/21.04 | | | | | | | | | | | | (250) $false % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | CLOSE: (250) is inconsistent. % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_539_2, all_156_5, % 153.78/21.04 | | | | | | | | | | | | simplifying with (10), (241) gives: % 153.78/21.04 | | | | | | | | | | | | (251) all_539_2 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (18) with 0, all_539_3, all_156_4, % 153.78/21.04 | | | | | | | | | | | | simplifying with (21), (242) gives: % 153.78/21.04 | | | | | | | | | | | | (252) all_539_3 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_521_1, all_539_3, % 153.78/21.04 | | | | | | | | | | | | all_156_4, simplifying with (237), (242) gives: % 153.78/21.04 | | | | | | | | | | | | (253) all_539_3 = all_521_1 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_519_1, all_539_3, % 153.78/21.04 | | | | | | | | | | | | all_156_4, simplifying with (235), (242) gives: % 153.78/21.04 | | | | | | | | | | | | (254) all_539_3 = all_519_1 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_156_1, all_539_1, % 153.78/21.04 | | | | | | | | | | | | all_156_4, all_156_5, simplifying with (19), (243) % 153.78/21.04 | | | | | | | | | | | | gives: % 153.78/21.04 | | | | | | | | | | | | (255) all_539_1 = all_156_1 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_325_1, all_523_1, % 153.78/21.04 | | | | | | | | | | | | all_156_1, all_310_0, simplifying with (49), (246) % 153.78/21.04 | | | | | | | | | | | | gives: % 153.78/21.04 | | | | | | | | | | | | (256) all_523_1 = all_325_1 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | COMBINE_EQS: (252), (253) imply: % 153.78/21.04 | | | | | | | | | | | | (257) all_521_1 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | COMBINE_EQS: (253), (254) imply: % 153.78/21.04 | | | | | | | | | | | | (258) all_521_1 = all_519_1 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | COMBINE_EQS: (257), (258) imply: % 153.78/21.04 | | | | | | | | | | | | (259) all_519_1 = 0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | REDUCE: (244), (255) imply: % 153.78/21.04 | | | | | | | | | | | | (260) @+(all_310_0, all_156_1) = all_539_0 % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | BETA: splitting (245) gives: % 153.78/21.04 | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | (261) ~ (all_539_2 = 0) % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | REDUCE: (251), (261) imply: % 153.78/21.04 | | | | | | | | | | | | | (262) $false % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | CLOSE: (262) is inconsistent. % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | Case 2: % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | (263) ~ (all_539_3 = 0) | all_539_0 = all_432_1 % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | BETA: splitting (263) gives: % 153.78/21.04 | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | Case 1: % 153.78/21.04 | | | | | | | | | | | | | | % 153.78/21.04 | | | | | | | | | | | | | | (264) ~ (all_539_3 = 0) % 153.78/21.04 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | REDUCE: (252), (264) imply: % 153.78/21.05 | | | | | | | | | | | | | | (265) $false % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | Case 2: % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | (266) all_539_0 = all_432_1 % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | REDUCE: (260), (266) imply: % 153.78/21.05 | | | | | | | | | | | | | | (267) @+(all_310_0, all_156_1) = all_432_1 % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_325_1, all_432_1, % 153.78/21.05 | | | | | | | | | | | | | | all_156_1, all_310_0, simplifying with (49), (267) % 153.78/21.05 | | | | | | | | | | | | | | gives: % 153.78/21.05 | | | | | | | | | | | | | | (268) all_432_1 = all_325_1 % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | REDUCE: (209), (268) imply: % 153.78/21.05 | | | | | | | | | | | | | | (269) s(all_325_1) = all_156_2 % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_156_0, all_156_2, % 153.78/21.05 | | | | | | | | | | | | | | all_325_1, simplifying with (61), (269) gives: % 153.78/21.05 | | | | | | | | | | | | | | (270) all_156_0 = all_156_2 % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | REDUCE: (12), (270) imply: % 153.78/21.05 | | | | | | | | | | | | | | (271) $false % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | | CLOSE: (271) is inconsistent. % 153.78/21.05 | | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | | End of split % 153.78/21.05 | | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | | End of split % 153.78/21.05 | | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | | End of split % 153.78/21.05 | | | | | | | | | | | % 153.78/21.05 | | | | | | | | | | End of split % 153.78/21.05 | | | | | | | | | | % 153.78/21.05 | | | | | | | | | End of split % 153.78/21.05 | | | | | | | | | % 153.78/21.05 | | | | | | | | End of split % 153.78/21.05 | | | | | | | | % 153.78/21.05 | | | | | | | End of split % 153.78/21.05 | | | | | | | % 153.78/21.05 | | | | | | End of split % 153.78/21.05 | | | | | | % 153.78/21.05 | | | | | Case 2: % 153.78/21.05 | | | | | | % 153.78/21.05 | | | | | | (272) ~ (all_154_0 = 0) & ! [v0: $i] : ( ~ (nat_succeeds(v0) = % 153.78/21.05 | | | | | | 0) | ~ $i(v0) | ? [v1: any] : ( ~ (v1 = all_154_0) & % 153.78/21.05 | | | | | | s(v0) = v1 & $i(v1))) % 153.78/21.05 | | | | | | % 153.78/21.05 | | | | | | ALPHA: (272) implies: % 153.78/21.05 | | | | | | (273) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? % 153.78/21.05 | | | | | | [v1: any] : ( ~ (v1 = all_154_0) & s(v0) = v1 & $i(v1))) % 153.78/21.05 | | | | | | % 153.78/21.05 | | | | | | REF_CLOSE: (24), (33), (34), (35), (273) are inconsistent by % 153.78/21.05 | | | | | | sub-proof #9. % 153.78/21.05 | | | | | | % 153.78/21.05 | | | | | End of split % 153.78/21.05 | | | | | % 153.78/21.05 | | | | End of split % 153.78/21.05 | | | | % 153.78/21.05 | | | End of split % 153.78/21.05 | | | % 153.78/21.05 | | End of split % 153.78/21.05 | | % 153.78/21.05 | End of split % 153.78/21.05 | % 153.78/21.05 End of proof % 153.78/21.05 % 153.78/21.05 Sub-proof #8 shows that the following formulas are inconsistent: % 153.78/21.05 ---------------------------------------------------------------- % 153.78/21.05 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.05 (s(v2) = v0)) % 153.78/21.05 (2) s(all_156_1) = all_156_0 % 153.78/21.05 (3) s(all_156_1) = all_156_2 % 153.78/21.05 (4) ~ (all_156_0 = all_156_2) % 153.78/21.05 % 153.78/21.05 Begin of proof % 153.78/21.05 | % 153.78/21.05 | GROUND_INST: instantiating (1) with all_156_0, all_156_2, all_156_1, % 153.78/21.05 | simplifying with (2), (3) gives: % 153.78/21.05 | (5) all_156_0 = all_156_2 % 153.78/21.05 | % 153.78/21.05 | REDUCE: (4), (5) imply: % 153.78/21.05 | (6) $false % 153.78/21.05 | % 153.78/21.05 | CLOSE: (6) is inconsistent. % 153.78/21.05 | % 153.78/21.05 End of proof % 153.78/21.05 % 153.78/21.05 Sub-proof #9 shows that the following formulas are inconsistent: % 153.78/21.05 ---------------------------------------------------------------- % 153.78/21.05 (1) ! [v0: $i] : ( ~ (nat_succeeds(v0) = 0) | ~ $i(v0) | ? [v1: any] : ( ~ % 153.78/21.05 (v1 = all_154_0) & s(v0) = v1 & $i(v1))) % 153.78/21.05 (2) s(all_310_0) = all_154_0 % 153.78/21.05 (3) nat_succeeds(all_310_0) = 0 % 153.78/21.05 (4) $i(all_310_0) % 153.78/21.05 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (s(v2) = v1) | ~ % 153.78/21.05 (s(v2) = v0)) % 153.78/21.05 % 153.78/21.05 Begin of proof % 153.78/21.05 | % 153.78/21.05 | GROUND_INST: instantiating (1) with all_310_0, simplifying with (3), (4) % 153.78/21.05 | gives: % 153.78/21.05 | (6) ? [v0: any] : ( ~ (v0 = all_154_0) & s(all_310_0) = v0 & $i(v0)) % 153.78/21.05 | % 153.78/21.05 | DELTA: instantiating (6) with fresh symbol all_404_0 gives: % 153.78/21.05 | (7) ~ (all_404_0 = all_154_0) & s(all_310_0) = all_404_0 & $i(all_404_0) % 153.78/21.05 | % 153.78/21.05 | ALPHA: (7) implies: % 153.78/21.05 | (8) ~ (all_404_0 = all_154_0) % 153.78/21.05 | (9) s(all_310_0) = all_404_0 % 153.78/21.05 | % 153.78/21.05 | GROUND_INST: instantiating (5) with all_154_0, all_404_0, all_310_0, % 153.78/21.05 | simplifying with (2), (9) gives: % 153.78/21.05 | (10) all_404_0 = all_154_0 % 153.78/21.05 | % 153.78/21.05 | REDUCE: (8), (10) imply: % 153.78/21.05 | (11) $false % 153.78/21.05 | % 153.78/21.05 | CLOSE: (11) is inconsistent. % 153.78/21.05 | % 153.78/21.05 End of proof % 153.78/21.05 % 153.78/21.05 Sub-proof #10 shows that the following formulas are inconsistent: % 153.78/21.05 ---------------------------------------------------------------- % 153.78/21.05 (1) @+(all_156_3, all_156_4) = all_156_2 % 153.78/21.05 (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (@+(0, v0) = v1) | ~ $i(v0)) % 153.78/21.05 (3) $i(all_156_1) % 153.78/21.05 (4) ~ (all_156_0 = all_156_2) % 153.78/21.05 (5) $i(all_156_5) % 153.78/21.05 (6) @+(0, all_156_1) = all_156_0 % 153.78/21.05 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 153.78/21.05 (@+(v3, v2) = v1) | ~ (@+(v3, v2) = v0)) % 153.78/21.05 (8) @+(all_156_5, all_156_4) = all_156_1 % 153.78/21.05 (9) @+(0, all_156_5) = all_156_3 % 153.78/21.05 % 153.78/21.05 Begin of proof % 153.78/21.05 | % 153.78/21.05 | GROUND_INST: instantiating (2) with all_156_5, all_156_3, simplifying with % 153.78/21.05 | (5), (9) gives: % 153.78/21.05 | (10) all_156_3 = all_156_5 % 153.78/21.05 | % 153.78/21.05 | GROUND_INST: instantiating (2) with all_156_1, all_156_0, simplifying with % 153.78/21.05 | (3), (6) gives: % 153.78/21.05 | (11) all_156_0 = all_156_1 % 153.78/21.05 | % 153.78/21.05 | REDUCE: (4), (11) imply: % 153.78/21.05 | (12) ~ (all_156_1 = all_156_2) % 153.78/21.05 | % 153.78/21.05 | REDUCE: (1), (10) imply: % 153.78/21.05 | (13) @+(all_156_5, all_156_4) = all_156_2 % 153.78/21.05 | % 153.78/21.05 | GROUND_INST: instantiating (7) with all_156_1, all_156_2, all_156_4, % 153.78/21.05 | all_156_5, simplifying with (8), (13) gives: % 153.78/21.05 | (14) all_156_1 = all_156_2 % 153.78/21.05 | % 153.78/21.05 | REDUCE: (12), (14) imply: % 153.78/21.05 | (15) $false % 153.78/21.05 | % 153.78/21.05 | CLOSE: (15) is inconsistent. % 153.78/21.05 | % 153.78/21.05 End of proof % 153.78/21.05 % SZS output end Proof for theBenchmark % 153.78/21.05 % 153.78/21.05 20449ms %------------------------------------------------------------------------------