%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM463+1 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n002.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 : Thu Aug 31 11:47:54 EDT 2023 % Result : Theorem 127.01s 17.45s % Output : Proof 128.17s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : NUM463+1 : TPTP v8.1.2. Released v4.0.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 17:56:32 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.99/1.09 Prover 1: Preprocessing ... % 2.99/1.09 Prover 4: Preprocessing ... % 3.32/1.14 Prover 5: Preprocessing ... % 3.32/1.14 Prover 3: Preprocessing ... % 3.32/1.14 Prover 6: Preprocessing ... % 3.32/1.14 Prover 2: Preprocessing ... % 3.32/1.14 Prover 0: Preprocessing ... % 7.20/1.65 Prover 1: Constructing countermodel ... % 7.78/1.73 Prover 3: Constructing countermodel ... % 7.78/1.74 Prover 6: Proving ... % 7.91/1.80 Prover 5: Constructing countermodel ... % 8.76/1.93 Prover 2: Proving ... % 8.76/1.99 Prover 4: Constructing countermodel ... % 10.02/2.07 Prover 3: gave up % 10.02/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.68/2.16 Prover 0: Proving ... % 10.68/2.16 Prover 7: Preprocessing ... % 11.42/2.28 Prover 1: gave up % 11.82/2.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.82/2.35 Prover 8: Preprocessing ... % 12.29/2.40 Prover 7: Constructing countermodel ... % 13.03/2.48 Prover 8: Warning: ignoring some quantifiers % 13.03/2.48 Prover 8: Constructing countermodel ... % 15.01/2.72 Prover 8: gave up % 15.01/2.73 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.01/2.78 Prover 9: Preprocessing ... % 18.71/3.19 Prover 9: Constructing countermodel ... % 63.96/9.05 Prover 2: stopped % 64.00/9.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 64.34/9.13 Prover 10: Preprocessing ... % 64.66/9.19 Prover 10: Constructing countermodel ... % 100.46/13.96 Prover 5: stopped % 100.46/13.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 101.29/14.04 Prover 11: Preprocessing ... % 102.85/14.28 Prover 11: Constructing countermodel ... % 127.01/17.45 Prover 7: Found proof (size 170) % 127.01/17.45 Prover 7: proved (15240ms) % 127.01/17.45 Prover 0: stopped % 127.01/17.45 Prover 6: stopped % 127.01/17.45 Prover 9: stopped % 127.01/17.45 Prover 11: stopped % 127.01/17.45 Prover 10: stopped % 127.01/17.45 Prover 4: stopped % 127.01/17.45 % 127.01/17.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 127.01/17.45 % 127.29/17.47 % SZS output start Proof for theBenchmark % 127.29/17.47 Assumptions after simplification: % 127.29/17.47 --------------------------------- % 127.29/17.47 % 127.29/17.47 (mAMDistr) % 127.29/17.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 127.29/17.52 $i] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ % 127.29/17.52 (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.29/17.52 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 127.29/17.52 [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v6, v0) = v5 % 127.29/17.52 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & % 127.29/17.52 sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & $i(v9) & $i(v8) & $i(v7) & % 127.29/17.52 $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 127.29/17.52 : ! [v4: $i] : ! [v5: $i] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, % 127.29/17.52 v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ % 127.29/17.52 $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 127.29/17.52 aNaturalNumber0(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] % 127.29/17.52 : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & % 127.29/17.52 sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6 & % 127.29/17.52 $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5))) & ! [v0: $i] : ! [v1: $i] : % 127.29/17.52 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ % 127.29/17.52 (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.29/17.52 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 127.29/17.52 [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 127.29/17.52 (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & % 127.29/17.52 sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & % 127.29/17.52 sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & % 127.29/17.52 $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 127.29/17.52 $i] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 127.29/17.52 ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 127.29/17.52 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] % 127.29/17.52 : ? [v9: $i] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & % 127.29/17.52 sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & % 127.29/17.52 sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & % 127.29/17.52 $i(v6) & $i(v5) & $i(v4))) % 127.29/17.52 % 127.29/17.52 (mAddComm) % 127.29/17.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ % 127.29/17.52 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 127.29/17.52 (sdtpldt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 127.29/17.52 : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) % 127.29/17.52 | ~ aNaturalNumber0(v0) | (sdtpldt0(v1, v0) = v2 & $i(v2))) % 127.29/17.52 % 127.29/17.52 (mDefLE) % 127.29/17.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ % 127.29/17.53 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 127.29/17.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 127.29/17.53 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ % 127.29/17.53 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtpldt0(v0, % 127.29/17.53 v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 127.29/17.53 % 127.29/17.53 (mLENTr) % 127.29/17.53 $i(sz10) & $i(sz00) & ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 127.29/17.53 aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 127.29/17.53 % 127.29/17.53 (mLETotal) % 127.29/17.53 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | % 127.29/17.53 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0: % 127.29/17.53 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0)) % 127.29/17.53 % 127.29/17.53 (mMonAdd) % 127.66/17.54 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 127.66/17.54 (sdtpldt0(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.54 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 127.66/17.54 aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = % 127.66/17.54 v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & % 127.66/17.54 sdtpldt0(v0, v2) = v5 & $i(v6) & $i(v5) & $i(v4) & sdtlseqdt0(v5, v6) & % 127.66/17.54 sdtlseqdt0(v4, v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 127.66/17.54 $i] : (v1 = v0 | ~ (sdtpldt0(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 127.66/17.54 $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : % 127.66/17.54 ? [v6: $i] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v1) = v4 & % 127.66/17.54 sdtpldt0(v1, v2) = v6 & sdtpldt0(v0, v2) = v5 & $i(v6) & $i(v5) & $i(v4) & % 127.66/17.54 sdtlseqdt0(v5, v6) & sdtlseqdt0(v3, v4))) & ! [v0: $i] : ! [v1: $i] : ! % 127.66/17.54 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 127.66/17.54 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : % 127.66/17.54 ? [v6: $i] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & % 127.66/17.54 sdtpldt0(v2, v0) = v4 & sdtpldt0(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 127.66/17.54 sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) & ! [v0: $i] : ! [v1: $i] : ! % 127.66/17.54 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | % 127.66/17.54 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.54 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : % 127.66/17.54 ? [v6: $i] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & % 127.66/17.54 sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 127.66/17.54 sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) % 127.66/17.54 % 127.66/17.54 (mMonMul) % 127.66/17.55 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 127.66/17.55 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = % 127.66/17.55 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ % 127.66/17.55 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 127.66/17.55 sdtlseqdt0(v3, v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 127.66/17.55 : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ % 127.66/17.55 (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.55 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 127.66/17.55 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & % 127.66/17.55 sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & $i(v6) & $i(v5) & % 127.66/17.55 sdtlseqdt0(v5, v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 127.66/17.55 $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ % 127.66/17.55 (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.55 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 127.66/17.55 aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v4) & ~ (v5 = % 127.66/17.55 v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & $i(v6) & $i(v5) & % 127.66/17.55 sdtlseqdt0(v6, v4) & sdtlseqdt0(v3, v5))) & ! [v0: $i] : ! [v1: $i] : ! % 127.66/17.55 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, % 127.66/17.55 v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 127.66/17.55 $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.55 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( % 127.66/17.55 ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5 % 127.66/17.55 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v3) & sdtlseqdt0(v4, v6))) & ! [v0: % 127.66/17.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | v0 % 127.66/17.55 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) % 127.66/17.55 | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | % 127.66/17.55 ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! % 127.66/17.55 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v2 = v1 | % 127.66/17.55 v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 127.66/17.55 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ % 127.66/17.55 aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? % 127.66/17.55 [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & % 127.66/17.55 sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5) & sdtlseqdt0(v5, v6))) & ! [v0: % 127.66/17.55 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ % 127.66/17.55 (sdtasdt0(v2, v0) = v3) | ~ (sdtasdt0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) % 127.66/17.55 | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.55 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 127.66/17.55 ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | % 127.66/17.55 ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.55 sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 127.66/17.55 aNaturalNumber0(v0)) % 127.66/17.55 % 127.66/17.55 (mMulComm) % 127.66/17.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ % 127.66/17.55 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 127.66/17.55 (sdtasdt0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 127.66/17.55 : ( ~ (sdtasdt0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) % 127.66/17.55 | ~ aNaturalNumber0(v0) | (sdtasdt0(v1, v0) = v2 & $i(v2))) % 127.66/17.55 % 127.66/17.55 (mSortsB_02) % 127.66/17.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 127.66/17.55 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 127.66/17.55 aNaturalNumber0(v2)) % 127.66/17.55 % 127.66/17.55 (mSortsC_01) % 127.66/17.55 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 127.66/17.55 % 127.66/17.55 (m_MulUnit) % 127.66/17.56 $i(sz10) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) % 127.66/17.56 | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 % 127.66/17.56 | ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! % 127.66/17.56 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ $i(v0) | ~ % 127.66/17.56 aNaturalNumber0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0: $i] : ! [v1: $i] : % 127.66/17.56 ( ~ (sdtasdt0(sz10, v0) = v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | % 127.66/17.56 sdtasdt0(v0, sz10) = v0) % 127.66/17.56 % 127.66/17.56 (m_MulZero) % 127.66/17.56 $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = % 127.66/17.56 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : % 127.66/17.56 (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ % 127.66/17.56 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, sz00) = % 127.66/17.56 v1) | ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtasdt0(sz00, v0) = sz00) & ! % 127.66/17.56 [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ $i(v0) | ~ % 127.66/17.56 aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) % 127.66/17.56 % 127.66/17.56 (m__) % 127.66/17.56 $i(xn) & $i(xm) & $i(sz00) & ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm) % 127.66/17.56 = v0 & $i(v0) & ~ sdtlseqdt0(xn, v0)) % 127.66/17.56 % 127.66/17.56 (m__987) % 127.66/17.56 $i(xn) & $i(xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm) % 127.66/17.56 % 127.66/17.56 (function-axioms) % 127.66/17.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 127.66/17.56 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! % 127.66/17.56 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | % 127.66/17.56 ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 127.66/17.56 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 127.66/17.56 % 127.66/17.56 Further assumptions not needed in the proof: % 127.66/17.56 -------------------------------------------- % 127.66/17.56 mAddAsso, mAddCanc, mDefDiff, mLEAsym, mLERefl, mLETran, mMulAsso, mMulCanc, % 127.66/17.56 mNatSort, mSortsB, mSortsC, mZeroAdd, mZeroMul, m_AddZero % 127.66/17.56 % 127.66/17.56 Those formulas are unsatisfiable: % 127.66/17.56 --------------------------------- % 127.66/17.56 % 127.66/17.56 Begin of proof % 127.66/17.56 | % 127.66/17.56 | ALPHA: (mSortsC_01) implies: % 127.66/17.56 | (1) aNaturalNumber0(sz10) % 127.66/17.56 | % 127.66/17.56 | ALPHA: (mAddComm) implies: % 127.66/17.56 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v0) = v2) | % 127.66/17.56 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 127.66/17.56 | aNaturalNumber0(v0) | (sdtpldt0(v0, v1) = v2 & $i(v2))) % 127.66/17.56 | % 127.66/17.56 | ALPHA: (mMulComm) implies: % 127.66/17.56 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v1, v0) = v2) | % 127.66/17.56 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 127.66/17.56 | aNaturalNumber0(v0) | (sdtasdt0(v0, v1) = v2 & $i(v2))) % 127.66/17.56 | % 127.66/17.56 | ALPHA: (m_MulUnit) implies: % 127.66/17.56 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | % 127.66/17.56 | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 127.66/17.57 | (5) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | % 127.66/17.57 | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (m_MulZero) implies: % 127.66/17.57 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | % 127.66/17.57 | ~ $i(v0) | ~ aNaturalNumber0(v0)) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (mAMDistr) implies: % 127.66/17.57 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 127.66/17.57 | ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 127.66/17.57 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: % 127.66/17.57 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v3, v0) = % 127.66/17.57 | v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, % 127.66/17.57 | v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & % 127.66/17.57 | sdtpldt0(v5, v6) = v4 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 127.66/17.57 | & $i(v4))) % 127.66/17.57 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 127.66/17.57 | ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | % 127.66/17.57 | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 127.66/17.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: % 127.66/17.57 | $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : (sdtasdt0(v2, v0) = % 127.66/17.57 | v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, % 127.66/17.57 | v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & % 127.66/17.57 | sdtpldt0(v6, v7) = v5 & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) % 127.66/17.57 | & $i(v4))) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (mDefLE) implies: % 127.66/17.57 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, % 127.66/17.57 | v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] % 127.66/17.57 | : (sdtpldt0(v0, v2) = v1 & $i(v2) & aNaturalNumber0(v2))) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (mLETotal) implies: % 127.66/17.57 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.57 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | % 127.66/17.57 | sdtlseqdt0(v0, v1)) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (mMonAdd) implies: % 127.66/17.57 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 127.66/17.57 | (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.57 | sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 127.66/17.57 | | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 127.66/17.57 | ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, % 127.66/17.57 | v0) = v4 & sdtpldt0(v1, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 127.66/17.57 | sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) % 127.66/17.57 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 127.66/17.57 | (sdtpldt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.57 | sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 127.66/17.57 | | ~ aNaturalNumber0(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : % 127.66/17.57 | ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, % 127.66/17.57 | v0) = v4 & sdtpldt0(v0, v2) = v6 & $i(v6) & $i(v5) & $i(v4) & % 127.66/17.57 | sdtlseqdt0(v6, v3) & sdtlseqdt0(v4, v5))) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (mMonMul) implies: % 127.66/17.57 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 127.66/17.57 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, % 127.66/17.57 | v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 127.66/17.57 | sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) % 127.66/17.57 | | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) % 127.66/17.57 | % 127.66/17.57 | ALPHA: (mLENTr) implies: % 127.66/17.57 | (14) $i(sz10) % 127.66/17.58 | (15) ! [v0: $i] : (v0 = sz10 | v0 = sz00 | ~ $i(v0) | ~ % 127.66/17.58 | aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) % 127.66/17.58 | % 127.66/17.58 | ALPHA: (m__987) implies: % 127.66/17.58 | (16) aNaturalNumber0(xm) % 127.66/17.58 | (17) aNaturalNumber0(xn) % 127.66/17.58 | % 127.66/17.58 | ALPHA: (m__) implies: % 127.86/17.58 | (18) $i(xm) % 127.86/17.58 | (19) $i(xn) % 127.86/17.58 | (20) ? [v0: $i] : ( ~ (xm = sz00) & sdtasdt0(xn, xm) = v0 & $i(v0) & ~ % 127.86/17.58 | sdtlseqdt0(xn, v0)) % 127.86/17.58 | % 127.86/17.58 | ALPHA: (function-axioms) implies: % 127.86/17.58 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 127.86/17.58 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 127.86/17.58 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 127.86/17.58 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 127.86/17.58 | % 127.86/17.58 | DELTA: instantiating (20) with fresh symbol all_27_0 gives: % 127.86/17.58 | (23) ~ (xm = sz00) & sdtasdt0(xn, xm) = all_27_0 & $i(all_27_0) & ~ % 127.86/17.58 | sdtlseqdt0(xn, all_27_0) % 127.86/17.58 | % 127.86/17.58 | ALPHA: (23) implies: % 127.86/17.58 | (24) ~ (xm = sz00) % 127.86/17.58 | (25) ~ sdtlseqdt0(xn, all_27_0) % 127.86/17.58 | (26) sdtasdt0(xn, xm) = all_27_0 % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (10) with sz10, sz10, simplifying with (1), (14) % 127.86/17.58 | gives: % 127.86/17.58 | (27) sdtlseqdt0(sz10, sz10) % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (10) with xm, xm, simplifying with (16), (18) % 127.86/17.58 | gives: % 127.86/17.58 | (28) sdtlseqdt0(xm, xm) % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (15) with xm, simplifying with (16), (18) gives: % 127.86/17.58 | (29) xm = sz10 | xm = sz00 | sdtlseqdt0(sz10, xm) % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (10) with xn, xn, simplifying with (17), (19) % 127.86/17.58 | gives: % 127.86/17.58 | (30) sdtlseqdt0(xn, xn) % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (3) with xm, xn, all_27_0, simplifying with (16), % 127.86/17.58 | (17), (18), (19), (26) gives: % 127.86/17.58 | (31) sdtasdt0(xm, xn) = all_27_0 & $i(all_27_0) % 127.86/17.58 | % 127.86/17.58 | ALPHA: (31) implies: % 127.86/17.58 | (32) $i(all_27_0) % 127.86/17.58 | (33) sdtasdt0(xm, xn) = all_27_0 % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (mSortsB_02) with xn, xm, all_27_0, simplifying % 127.86/17.58 | with (16), (17), (18), (19), (26) gives: % 127.86/17.58 | (34) aNaturalNumber0(all_27_0) % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (5) with xn, all_27_0, simplifying with (17), (19) % 127.86/17.58 | gives: % 127.86/17.58 | (35) all_27_0 = xn | ~ (sdtasdt0(xn, sz10) = all_27_0) % 127.86/17.58 | % 127.86/17.58 | GROUND_INST: instantiating (6) with xm, all_27_0, simplifying with (16), (18) % 127.86/17.58 | gives: % 127.86/17.58 | (36) all_27_0 = sz00 | ~ (sdtasdt0(sz00, xm) = all_27_0) % 127.86/17.58 | % 127.86/17.58 | PRED_UNIFY: (25), (30) imply: % 127.86/17.58 | (37) ~ (all_27_0 = xn) % 127.86/17.58 | % 127.86/17.58 | BETA: splitting (35) gives: % 127.86/17.58 | % 127.86/17.58 | Case 1: % 127.86/17.58 | | % 127.86/17.58 | | (38) ~ (sdtasdt0(xn, sz10) = all_27_0) % 127.86/17.58 | | % 127.86/17.58 | | PRED_UNIFY: (26), (38) imply: % 127.86/17.58 | | (39) ~ (xm = sz10) % 127.86/17.58 | | % 127.86/17.58 | | BETA: splitting (29) gives: % 127.86/17.58 | | % 127.86/17.59 | | Case 1: % 127.86/17.59 | | | % 127.86/17.59 | | | (40) sdtlseqdt0(sz10, xm) % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (10) with xn, all_27_0, simplifying with (17), % 127.86/17.59 | | | (19), (25), (32), (34) gives: % 127.86/17.59 | | | (41) sdtlseqdt0(all_27_0, xn) % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (9) with sz10, sz10, simplifying with (1), % 127.86/17.59 | | | (14), (27) gives: % 127.86/17.59 | | | (42) ? [v0: $i] : (sdtpldt0(sz10, v0) = sz10 & $i(v0) & % 127.86/17.59 | | | aNaturalNumber0(v0)) % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (9) with sz10, xm, simplifying with (1), (14), % 127.86/17.59 | | | (16), (18), (40) gives: % 127.86/17.59 | | | (43) ? [v0: $i] : (sdtpldt0(sz10, v0) = xm & $i(v0) & % 127.86/17.59 | | | aNaturalNumber0(v0)) % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (9) with xm, xm, simplifying with (16), (18), % 127.86/17.59 | | | (28) gives: % 127.86/17.59 | | | (44) ? [v0: $i] : (sdtpldt0(xm, v0) = xm & $i(v0) & % 127.86/17.59 | | | aNaturalNumber0(v0)) % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (9) with xn, xn, simplifying with (17), (19), % 127.86/17.59 | | | (30) gives: % 127.86/17.59 | | | (45) ? [v0: $i] : (sdtpldt0(xn, v0) = xn & $i(v0) & % 127.86/17.59 | | | aNaturalNumber0(v0)) % 127.86/17.59 | | | % 127.86/17.59 | | | DELTA: instantiating (45) with fresh symbol all_57_0 gives: % 127.86/17.59 | | | (46) sdtpldt0(xn, all_57_0) = xn & $i(all_57_0) & % 127.86/17.59 | | | aNaturalNumber0(all_57_0) % 127.86/17.59 | | | % 127.86/17.59 | | | ALPHA: (46) implies: % 127.86/17.59 | | | (47) aNaturalNumber0(all_57_0) % 127.86/17.59 | | | (48) $i(all_57_0) % 127.86/17.59 | | | (49) sdtpldt0(xn, all_57_0) = xn % 127.86/17.59 | | | % 127.86/17.59 | | | DELTA: instantiating (44) with fresh symbol all_59_0 gives: % 127.86/17.59 | | | (50) sdtpldt0(xm, all_59_0) = xm & $i(all_59_0) & % 127.86/17.59 | | | aNaturalNumber0(all_59_0) % 127.86/17.59 | | | % 127.86/17.59 | | | ALPHA: (50) implies: % 127.86/17.59 | | | (51) aNaturalNumber0(all_59_0) % 127.86/17.59 | | | (52) $i(all_59_0) % 127.86/17.59 | | | (53) sdtpldt0(xm, all_59_0) = xm % 127.86/17.59 | | | % 127.86/17.59 | | | DELTA: instantiating (42) with fresh symbol all_61_0 gives: % 127.86/17.59 | | | (54) sdtpldt0(sz10, all_61_0) = sz10 & $i(all_61_0) & % 127.86/17.59 | | | aNaturalNumber0(all_61_0) % 127.86/17.59 | | | % 127.86/17.59 | | | ALPHA: (54) implies: % 127.86/17.59 | | | (55) aNaturalNumber0(all_61_0) % 127.86/17.59 | | | (56) $i(all_61_0) % 127.86/17.59 | | | (57) sdtpldt0(sz10, all_61_0) = sz10 % 127.86/17.59 | | | % 127.86/17.59 | | | DELTA: instantiating (43) with fresh symbol all_65_0 gives: % 127.86/17.59 | | | (58) sdtpldt0(sz10, all_65_0) = xm & $i(all_65_0) & % 127.86/17.59 | | | aNaturalNumber0(all_65_0) % 127.86/17.59 | | | % 127.86/17.59 | | | ALPHA: (58) implies: % 127.86/17.59 | | | (59) aNaturalNumber0(all_65_0) % 127.86/17.59 | | | (60) $i(all_65_0) % 127.86/17.59 | | | (61) sdtpldt0(sz10, all_65_0) = xm % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (9) with all_27_0, xn, simplifying with (17), % 127.86/17.59 | | | (19), (32), (34), (41) gives: % 127.86/17.59 | | | (62) ? [v0: $i] : (sdtpldt0(all_27_0, v0) = xn & $i(v0) & % 127.86/17.59 | | | aNaturalNumber0(v0)) % 127.86/17.59 | | | % 127.86/17.59 | | | GROUND_INST: instantiating (11) with sz10, xm, all_61_0, sz10, simplifying % 127.86/17.59 | | | with (1), (14), (16), (18), (40), (55), (56), (57) gives: % 127.86/17.59 | | | (63) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 127.86/17.59 | | | sz10) & ~ (v1 = v0) & sdtpldt0(all_61_0, xm) = v1 & % 127.86/17.59 | | | sdtpldt0(all_61_0, sz10) = v0 & sdtpldt0(xm, all_61_0) = v2 & % 127.86/17.59 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(sz10, % 127.86/17.59 | | | v2)) % 127.86/17.59 | | | % 127.86/17.60 | | | GROUND_INST: instantiating (2) with all_61_0, sz10, sz10, simplifying with % 127.86/17.60 | | | (1), (14), (55), (56), (57) gives: % 127.86/17.60 | | | (64) sdtpldt0(all_61_0, sz10) = sz10 % 127.86/17.60 | | | % 127.86/17.60 | | | GROUND_INST: instantiating (7) with xn, sz10, all_65_0, xm, all_27_0, % 127.86/17.60 | | | simplifying with (1), (14), (17), (19), (26), (59), (60), % 127.86/17.60 | | | (61) gives: % 127.86/17.60 | | | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 127.86/17.60 | | | $i] : (sdtasdt0(all_65_0, xn) = v4 & sdtasdt0(xn, all_65_0) = v1 % 127.86/17.60 | | | & sdtasdt0(xn, sz10) = v0 & sdtasdt0(xm, xn) = v2 & % 127.86/17.60 | | | sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, % 127.86/17.60 | | | v1) = all_27_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 127.86/17.60 | | | $i(all_27_0)) % 127.86/17.60 | | | % 127.86/17.60 | | | GROUND_INST: instantiating (8) with xn, sz10, all_65_0, xm, all_27_0, % 127.86/17.60 | | | simplifying with (1), (14), (17), (19), (33), (59), (60), % 127.86/17.60 | | | (61) gives: % 127.86/17.60 | | | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 127.86/17.60 | | | $i] : (sdtasdt0(all_65_0, xn) = v4 & sdtasdt0(xn, all_65_0) = v2 % 127.86/17.60 | | | & sdtasdt0(xn, xm) = v0 & sdtasdt0(xn, sz10) = v1 & % 127.86/17.60 | | | sdtasdt0(sz10, xn) = v3 & sdtpldt0(v3, v4) = all_27_0 & % 127.86/17.60 | | | sdtpldt0(v1, v2) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 127.86/17.60 | | | $i(v0) & $i(all_27_0)) % 127.86/17.60 | | | % 127.86/17.60 | | | GROUND_INST: instantiating (11) with sz10, xm, all_65_0, xm, simplifying % 127.86/17.60 | | | with (1), (14), (16), (18), (40), (59), (60), (61) gives: % 127.86/17.60 | | | (67) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 127.86/17.60 | | | xm) & ~ (v1 = v0) & sdtpldt0(all_65_0, xm) = v1 & % 127.86/17.60 | | | sdtpldt0(all_65_0, sz10) = v0 & sdtpldt0(xm, all_65_0) = v2 & % 127.86/17.60 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, % 127.86/17.60 | | | v2)) % 127.86/17.60 | | | % 127.86/17.60 | | | GROUND_INST: instantiating (2) with all_65_0, sz10, xm, simplifying with % 127.86/17.60 | | | (1), (14), (59), (60), (61) gives: % 127.86/17.60 | | | (68) sdtpldt0(all_65_0, sz10) = xm & $i(xm) % 127.86/17.60 | | | % 127.86/17.60 | | | GROUND_INST: instantiating (7) with xn, xm, all_59_0, xm, all_27_0, % 127.86/17.60 | | | simplifying with (16), (17), (18), (19), (26), (51), (52), % 127.86/17.60 | | | (53) gives: % 127.86/17.60 | | | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 127.86/17.60 | | | $i] : (sdtasdt0(all_59_0, xn) = v4 & sdtasdt0(xn, all_59_0) = v1 % 127.86/17.60 | | | & sdtasdt0(xn, xm) = v0 & sdtasdt0(xm, xn) = v3 & sdtasdt0(xm, % 127.86/17.60 | | | xn) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_27_0 % 127.86/17.60 | | | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_27_0)) % 127.86/17.60 | | | % 127.86/17.61 | | | GROUND_INST: instantiating (8) with xn, xm, all_59_0, xm, all_27_0, % 127.86/17.61 | | | simplifying with (16), (17), (18), (19), (33), (51), (52), % 127.86/17.61 | | | (53) gives: % 127.86/17.61 | | | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 127.86/17.61 | | | $i] : (sdtasdt0(all_59_0, xn) = v4 & sdtasdt0(xn, all_59_0) = v2 % 127.86/17.61 | | | & sdtasdt0(xn, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtasdt0(xm, % 127.86/17.61 | | | xn) = v3 & sdtpldt0(v3, v4) = all_27_0 & sdtpldt0(v1, v2) = v0 % 127.86/17.61 | | | & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & $i(all_27_0)) % 127.86/17.61 | | | % 127.86/17.61 | | | GROUND_INST: instantiating (12) with sz10, xm, all_59_0, xm, simplifying % 127.86/17.61 | | | with (1), (14), (16), (18), (40), (51), (52), (53) gives: % 127.86/17.61 | | | (71) xm = sz10 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = % 127.86/17.61 | | | xm) & ~ (v1 = v0) & sdtpldt0(all_59_0, xm) = v1 & % 127.86/17.61 | | | sdtpldt0(all_59_0, sz10) = v0 & sdtpldt0(sz10, all_59_0) = v2 & % 127.86/17.61 | | | $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v2, xm) & sdtlseqdt0(v0, % 127.86/17.61 | | | v1)) % 127.86/17.61 | | | % 127.86/17.61 | | | GROUND_INST: instantiating (2) with all_59_0, xm, xm, simplifying with % 127.86/17.61 | | | (16), (18), (51), (52), (53) gives: % 127.86/17.61 | | | (72) sdtpldt0(all_59_0, xm) = xm % 127.86/17.61 | | | % 127.86/17.61 | | | GROUND_INST: instantiating (8) with xm, xn, all_57_0, xn, all_27_0, % 127.86/17.61 | | | simplifying with (16), (17), (18), (19), (26), (47), (48), % 127.86/17.61 | | | (49) gives: % 127.86/17.61 | | | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 127.86/17.61 | | | $i] : (sdtasdt0(all_57_0, xm) = v4 & sdtasdt0(xn, xm) = v3 & % 127.86/17.61 | | | sdtasdt0(xm, all_57_0) = v2 & sdtasdt0(xm, xn) = v1 & % 127.86/17.61 | | | sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = all_27_0 & % 127.86/17.61 | | | sdtpldt0(v1, v2) = v0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 127.86/17.61 | | | $i(v0) & $i(all_27_0)) % 127.86/17.61 | | | % 127.86/17.61 | | | GROUND_INST: instantiating (7) with xm, xn, all_57_0, xn, all_27_0, % 127.86/17.61 | | | simplifying with (16), (17), (18), (19), (33), (47), (48), % 127.86/17.61 | | | (49) gives: % 127.86/17.61 | | | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: % 127.86/17.61 | | | $i] : (sdtasdt0(all_57_0, xm) = v4 & sdtasdt0(xn, xm) = v3 & % 127.86/17.61 | | | sdtasdt0(xn, xm) = v2 & sdtasdt0(xm, all_57_0) = v1 & % 127.86/17.61 | | | sdtasdt0(xm, xn) = v0 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) % 127.86/17.61 | | | = all_27_0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 127.86/17.61 | | | $i(all_27_0)) % 127.86/17.61 | | | % 127.86/17.61 | | | DELTA: instantiating (62) with fresh symbol all_77_0 gives: % 127.86/17.61 | | | (75) sdtpldt0(all_27_0, all_77_0) = xn & $i(all_77_0) & % 127.86/17.61 | | | aNaturalNumber0(all_77_0) % 127.86/17.61 | | | % 127.86/17.61 | | | ALPHA: (75) implies: % 127.86/17.62 | | | (76) aNaturalNumber0(all_77_0) % 127.86/17.62 | | | (77) $i(all_77_0) % 127.86/17.62 | | | (78) sdtpldt0(all_27_0, all_77_0) = xn % 127.86/17.62 | | | % 127.86/17.62 | | | DELTA: instantiating (74) with fresh symbols all_89_0, all_89_1, all_89_2, % 127.86/17.62 | | | all_89_3, all_89_4 gives: % 127.86/17.62 | | | (79) sdtasdt0(all_57_0, xm) = all_89_0 & sdtasdt0(xn, xm) = all_89_1 & % 127.86/17.62 | | | sdtasdt0(xn, xm) = all_89_2 & sdtasdt0(xm, all_57_0) = all_89_3 & % 127.86/17.62 | | | sdtasdt0(xm, xn) = all_89_4 & sdtpldt0(all_89_1, all_89_0) = % 127.86/17.62 | | | all_89_2 & sdtpldt0(all_89_4, all_89_3) = all_27_0 & $i(all_89_0) % 127.86/17.62 | | | & $i(all_89_1) & $i(all_89_2) & $i(all_89_3) & $i(all_89_4) & % 127.86/17.62 | | | $i(all_27_0) % 127.86/17.62 | | | % 127.86/17.62 | | | ALPHA: (79) implies: % 127.86/17.62 | | | (80) $i(all_89_4) % 127.86/17.62 | | | (81) sdtasdt0(xm, xn) = all_89_4 % 127.86/17.62 | | | (82) sdtasdt0(xn, xm) = all_89_2 % 127.86/17.62 | | | (83) sdtasdt0(xn, xm) = all_89_1 % 127.86/17.62 | | | % 127.86/17.62 | | | DELTA: instantiating (73) with fresh symbols all_91_0, all_91_1, all_91_2, % 127.86/17.62 | | | all_91_3, all_91_4 gives: % 127.86/17.62 | | | (84) sdtasdt0(all_57_0, xm) = all_91_0 & sdtasdt0(xn, xm) = all_91_1 & % 127.86/17.62 | | | sdtasdt0(xm, all_57_0) = all_91_2 & sdtasdt0(xm, xn) = all_91_3 & % 127.86/17.62 | | | sdtasdt0(xm, xn) = all_91_4 & sdtpldt0(all_91_1, all_91_0) = % 127.86/17.62 | | | all_27_0 & sdtpldt0(all_91_3, all_91_2) = all_91_4 & $i(all_91_0) % 127.86/17.62 | | | & $i(all_91_1) & $i(all_91_2) & $i(all_91_3) & $i(all_91_4) & % 127.86/17.62 | | | $i(all_27_0) % 127.86/17.62 | | | % 127.86/17.62 | | | ALPHA: (84) implies: % 127.86/17.62 | | | (85) sdtasdt0(xm, xn) = all_91_4 % 127.86/17.62 | | | (86) sdtasdt0(xm, xn) = all_91_3 % 127.86/17.62 | | | (87) sdtasdt0(xn, xm) = all_91_1 % 127.86/17.62 | | | % 127.86/17.62 | | | DELTA: instantiating (66) with fresh symbols all_93_0, all_93_1, all_93_2, % 127.86/17.62 | | | all_93_3, all_93_4 gives: % 127.86/17.62 | | | (88) sdtasdt0(all_65_0, xn) = all_93_0 & sdtasdt0(xn, all_65_0) = % 127.86/17.62 | | | all_93_2 & sdtasdt0(xn, xm) = all_93_4 & sdtasdt0(xn, sz10) = % 127.86/17.62 | | | all_93_3 & sdtasdt0(sz10, xn) = all_93_1 & sdtpldt0(all_93_1, % 127.86/17.62 | | | all_93_0) = all_27_0 & sdtpldt0(all_93_3, all_93_2) = all_93_4 & % 127.86/17.62 | | | $i(all_93_0) & $i(all_93_1) & $i(all_93_2) & $i(all_93_3) & % 127.86/17.62 | | | $i(all_93_4) & $i(all_27_0) % 127.86/17.62 | | | % 127.86/17.62 | | | ALPHA: (88) implies: % 127.86/17.62 | | | (89) sdtasdt0(sz10, xn) = all_93_1 % 127.86/17.62 | | | (90) sdtasdt0(xn, sz10) = all_93_3 % 127.86/17.62 | | | (91) sdtasdt0(xn, xm) = all_93_4 % 127.86/17.62 | | | % 127.86/17.62 | | | DELTA: instantiating (65) with fresh symbols all_95_0, all_95_1, all_95_2, % 127.86/17.62 | | | all_95_3, all_95_4 gives: % 127.86/17.62 | | | (92) sdtasdt0(all_65_0, xn) = all_95_0 & sdtasdt0(xn, all_65_0) = % 127.86/17.62 | | | all_95_3 & sdtasdt0(xn, sz10) = all_95_4 & sdtasdt0(xm, xn) = % 127.86/17.62 | | | all_95_2 & sdtasdt0(sz10, xn) = all_95_1 & sdtpldt0(all_95_1, % 127.86/17.62 | | | all_95_0) = all_95_2 & sdtpldt0(all_95_4, all_95_3) = all_27_0 & % 127.86/17.62 | | | $i(all_95_0) & $i(all_95_1) & $i(all_95_2) & $i(all_95_3) & % 127.86/17.62 | | | $i(all_95_4) & $i(all_27_0) % 127.86/17.62 | | | % 127.86/17.62 | | | ALPHA: (92) implies: % 127.86/17.62 | | | (93) sdtasdt0(sz10, xn) = all_95_1 % 127.86/17.62 | | | (94) sdtasdt0(xm, xn) = all_95_2 % 127.86/17.62 | | | (95) sdtasdt0(xn, sz10) = all_95_4 % 127.86/17.62 | | | % 127.86/17.62 | | | DELTA: instantiating (70) with fresh symbols all_97_0, all_97_1, all_97_2, % 127.86/17.62 | | | all_97_3, all_97_4 gives: % 127.86/17.62 | | | (96) sdtasdt0(all_59_0, xn) = all_97_0 & sdtasdt0(xn, all_59_0) = % 127.86/17.62 | | | all_97_2 & sdtasdt0(xn, xm) = all_97_3 & sdtasdt0(xn, xm) = % 127.86/17.62 | | | all_97_4 & sdtasdt0(xm, xn) = all_97_1 & sdtpldt0(all_97_1, % 127.86/17.62 | | | all_97_0) = all_27_0 & sdtpldt0(all_97_3, all_97_2) = all_97_4 & % 127.86/17.62 | | | $i(all_97_0) & $i(all_97_1) & $i(all_97_2) & $i(all_97_3) & % 127.86/17.62 | | | $i(all_97_4) & $i(all_27_0) % 127.86/17.62 | | | % 127.86/17.62 | | | ALPHA: (96) implies: % 127.86/17.62 | | | (97) sdtasdt0(xm, xn) = all_97_1 % 127.86/17.62 | | | (98) sdtasdt0(xn, xm) = all_97_4 % 127.86/17.62 | | | (99) sdtasdt0(xn, xm) = all_97_3 % 127.86/17.62 | | | % 127.86/17.62 | | | DELTA: instantiating (69) with fresh symbols all_99_0, all_99_1, all_99_2, % 127.86/17.62 | | | all_99_3, all_99_4 gives: % 127.86/17.62 | | | (100) sdtasdt0(all_59_0, xn) = all_99_0 & sdtasdt0(xn, all_59_0) = % 127.86/17.62 | | | all_99_3 & sdtasdt0(xn, xm) = all_99_4 & sdtasdt0(xm, xn) = % 127.86/17.62 | | | all_99_1 & sdtasdt0(xm, xn) = all_99_2 & sdtpldt0(all_99_1, % 127.86/17.62 | | | all_99_0) = all_99_2 & sdtpldt0(all_99_4, all_99_3) = all_27_0 % 127.86/17.62 | | | & $i(all_99_0) & $i(all_99_1) & $i(all_99_2) & $i(all_99_3) & % 127.86/17.62 | | | $i(all_99_4) & $i(all_27_0) % 127.86/17.62 | | | % 127.86/17.62 | | | ALPHA: (100) implies: % 127.86/17.62 | | | (101) sdtasdt0(xm, xn) = all_99_2 % 127.86/17.62 | | | (102) sdtasdt0(xm, xn) = all_99_1 % 127.86/17.62 | | | (103) sdtasdt0(xn, xm) = all_99_4 % 127.86/17.62 | | | % 127.86/17.62 | | | BETA: splitting (71) gives: % 127.86/17.62 | | | % 127.86/17.62 | | | Case 1: % 127.86/17.62 | | | | % 127.86/17.62 | | | | (104) xm = sz10 % 127.86/17.62 | | | | % 127.86/17.62 | | | | REDUCE: (39), (104) imply: % 127.86/17.62 | | | | (105) $false % 127.86/17.62 | | | | % 127.86/17.62 | | | | CLOSE: (105) is inconsistent. % 127.86/17.62 | | | | % 127.86/17.63 | | | Case 2: % 127.86/17.63 | | | | % 127.86/17.63 | | | | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = xm) & ~ % 127.86/17.63 | | | | (v1 = v0) & sdtpldt0(all_59_0, xm) = v1 & sdtpldt0(all_59_0, % 127.86/17.63 | | | | sz10) = v0 & sdtpldt0(sz10, all_59_0) = v2 & $i(v2) & % 127.86/17.63 | | | | $i(v1) & $i(v0) & sdtlseqdt0(v2, xm) & sdtlseqdt0(v0, v1)) % 127.86/17.63 | | | | % 127.86/17.63 | | | | DELTA: instantiating (106) with fresh symbols all_108_0, all_108_1, % 127.86/17.63 | | | | all_108_2 gives: % 127.86/17.63 | | | | (107) ~ (all_108_0 = xm) & ~ (all_108_1 = all_108_2) & % 127.86/17.63 | | | | sdtpldt0(all_59_0, xm) = all_108_1 & sdtpldt0(all_59_0, sz10) = % 127.86/17.63 | | | | all_108_2 & sdtpldt0(sz10, all_59_0) = all_108_0 & % 127.86/17.63 | | | | $i(all_108_0) & $i(all_108_1) & $i(all_108_2) & % 127.86/17.63 | | | | sdtlseqdt0(all_108_0, xm) & sdtlseqdt0(all_108_2, all_108_1) % 127.86/17.63 | | | | % 127.86/17.63 | | | | ALPHA: (107) implies: % 127.86/17.63 | | | | (108) $i(all_108_1) % 127.86/17.63 | | | | (109) sdtpldt0(all_59_0, xm) = all_108_1 % 127.86/17.63 | | | | % 127.86/17.63 | | | | BETA: splitting (63) gives: % 127.86/17.63 | | | | % 127.86/17.63 | | | | Case 1: % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | (110) xm = sz10 % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | REDUCE: (39), (110) imply: % 127.86/17.63 | | | | | (111) $false % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | CLOSE: (111) is inconsistent. % 127.86/17.63 | | | | | % 127.86/17.63 | | | | Case 2: % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = sz10) & % 127.86/17.63 | | | | | ~ (v1 = v0) & sdtpldt0(all_61_0, xm) = v1 & % 127.86/17.63 | | | | | sdtpldt0(all_61_0, sz10) = v0 & sdtpldt0(xm, all_61_0) = v2 % 127.86/17.63 | | | | | & $i(v2) & $i(v1) & $i(v0) & sdtlseqdt0(v0, v1) & % 127.86/17.63 | | | | | sdtlseqdt0(sz10, v2)) % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | DELTA: instantiating (112) with fresh symbols all_123_0, all_123_1, % 127.86/17.63 | | | | | all_123_2 gives: % 127.86/17.63 | | | | | (113) ~ (all_123_0 = sz10) & ~ (all_123_1 = all_123_2) & % 127.86/17.63 | | | | | sdtpldt0(all_61_0, xm) = all_123_1 & sdtpldt0(all_61_0, sz10) % 127.86/17.63 | | | | | = all_123_2 & sdtpldt0(xm, all_61_0) = all_123_0 & % 127.86/17.63 | | | | | $i(all_123_0) & $i(all_123_1) & $i(all_123_2) & % 127.86/17.63 | | | | | sdtlseqdt0(all_123_2, all_123_1) & sdtlseqdt0(sz10, % 127.86/17.63 | | | | | all_123_0) % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | ALPHA: (113) implies: % 127.86/17.63 | | | | | (114) $i(all_123_2) % 127.86/17.63 | | | | | (115) sdtpldt0(all_61_0, sz10) = all_123_2 % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | BETA: splitting (67) gives: % 127.86/17.63 | | | | | % 127.86/17.63 | | | | | Case 1: % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | (116) xm = sz10 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | REDUCE: (39), (116) imply: % 127.86/17.63 | | | | | | (117) $false % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | CLOSE: (117) is inconsistent. % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | Case 2: % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (21) with xm, all_108_1, xm, all_59_0, % 127.86/17.63 | | | | | | simplifying with (72), (109) gives: % 127.86/17.63 | | | | | | (118) all_108_1 = xm % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (21) with sz10, all_123_2, sz10, % 127.86/17.63 | | | | | | all_61_0, simplifying with (64), (115) gives: % 127.86/17.63 | | | | | | (119) all_123_2 = sz10 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_93_1, all_95_1, xn, sz10, % 127.86/17.63 | | | | | | simplifying with (89), (93) gives: % 127.86/17.63 | | | | | | (120) all_95_1 = all_93_1 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_89_4, all_91_3, xn, xm, % 127.86/17.63 | | | | | | simplifying with (81), (86) gives: % 127.86/17.63 | | | | | | (121) all_91_3 = all_89_4 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_27_0, all_99_2, xn, xm, % 127.86/17.63 | | | | | | simplifying with (33), (101) gives: % 127.86/17.63 | | | | | | (122) all_99_2 = all_27_0 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_97_1, all_99_2, xn, xm, % 127.86/17.63 | | | | | | simplifying with (97), (101) gives: % 127.86/17.63 | | | | | | (123) all_99_2 = all_97_1 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_91_3, all_99_2, xn, xm, % 127.86/17.63 | | | | | | simplifying with (86), (101) gives: % 127.86/17.63 | | | | | | (124) all_99_2 = all_91_3 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_91_4, all_99_2, xn, xm, % 127.86/17.63 | | | | | | simplifying with (85), (101) gives: % 127.86/17.63 | | | | | | (125) all_99_2 = all_91_4 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_99_2, all_99_1, xn, xm, % 127.86/17.63 | | | | | | simplifying with (101), (102) gives: % 127.86/17.63 | | | | | | (126) all_99_1 = all_99_2 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_95_2, all_99_1, xn, xm, % 127.86/17.63 | | | | | | simplifying with (94), (102) gives: % 127.86/17.63 | | | | | | (127) all_99_1 = all_95_2 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_93_3, all_95_4, sz10, xn, % 127.86/17.63 | | | | | | simplifying with (90), (95) gives: % 127.86/17.63 | | | | | | (128) all_95_4 = all_93_3 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | PRED_UNIFY: (38), (95) imply: % 127.86/17.63 | | | | | | (129) ~ (all_95_4 = all_27_0) % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_89_1, all_91_1, xm, xn, % 127.86/17.63 | | | | | | simplifying with (83), (87) gives: % 127.86/17.63 | | | | | | (130) all_91_1 = all_89_1 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_27_0, all_93_4, xm, xn, % 127.86/17.63 | | | | | | simplifying with (26), (91) gives: % 127.86/17.63 | | | | | | (131) all_93_4 = all_27_0 % 127.86/17.63 | | | | | | % 127.86/17.63 | | | | | | GROUND_INST: instantiating (22) with all_91_1, all_93_4, xm, xn, % 127.86/17.63 | | | | | | simplifying with (87), (91) gives: % 127.86/17.63 | | | | | | (132) all_93_4 = all_91_1 % 127.86/17.63 | | | | | | % 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_89_1, all_97_4, xm, xn, % 127.86/17.64 | | | | | | simplifying with (83), (98) gives: % 127.86/17.64 | | | | | | (133) all_97_4 = all_89_1 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_97_3, all_99_4, xm, xn, % 127.86/17.64 | | | | | | simplifying with (99), (103) gives: % 127.86/17.64 | | | | | | (134) all_99_4 = all_97_3 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_97_4, all_99_4, xm, xn, % 127.86/17.64 | | | | | | simplifying with (98), (103) gives: % 127.86/17.64 | | | | | | (135) all_99_4 = all_97_4 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | GROUND_INST: instantiating (22) with all_89_2, all_99_4, xm, xn, % 127.86/17.64 | | | | | | simplifying with (82), (103) gives: % 127.86/17.64 | | | | | | (136) all_99_4 = all_89_2 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (126), (127) imply: % 127.86/17.64 | | | | | | (137) all_99_2 = all_95_2 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | SIMP: (137) implies: % 127.86/17.64 | | | | | | (138) all_99_2 = all_95_2 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (123), (124) imply: % 127.86/17.64 | | | | | | (139) all_97_1 = all_91_3 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (122), (123) imply: % 127.86/17.64 | | | | | | (140) all_97_1 = all_27_0 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (123), (125) imply: % 127.86/17.64 | | | | | | (141) all_97_1 = all_91_4 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (123), (138) imply: % 127.86/17.64 | | | | | | (142) all_97_1 = all_95_2 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (134), (135) imply: % 127.86/17.64 | | | | | | (143) all_97_3 = all_97_4 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (134), (136) imply: % 127.86/17.64 | | | | | | (144) all_97_3 = all_89_2 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (141), (142) imply: % 127.86/17.64 | | | | | | (145) all_95_2 = all_91_4 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (139), (142) imply: % 127.86/17.64 | | | | | | (146) all_95_2 = all_91_3 % 127.86/17.64 | | | | | | % 127.86/17.64 | | | | | | COMBINE_EQS: (140), (142) imply: % 128.17/17.64 | | | | | | (147) all_95_2 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (143), (144) imply: % 128.17/17.64 | | | | | | (148) all_97_4 = all_89_2 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | SIMP: (148) implies: % 128.17/17.64 | | | | | | (149) all_97_4 = all_89_2 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (133), (149) imply: % 128.17/17.64 | | | | | | (150) all_89_1 = all_89_2 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | SIMP: (150) implies: % 128.17/17.64 | | | | | | (151) all_89_1 = all_89_2 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (145), (147) imply: % 128.17/17.64 | | | | | | (152) all_91_4 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (145), (146) imply: % 128.17/17.64 | | | | | | (153) all_91_3 = all_91_4 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | SIMP: (153) implies: % 128.17/17.64 | | | | | | (154) all_91_3 = all_91_4 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (131), (132) imply: % 128.17/17.64 | | | | | | (155) all_91_1 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | SIMP: (155) implies: % 128.17/17.64 | | | | | | (156) all_91_1 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (130), (156) imply: % 128.17/17.64 | | | | | | (157) all_89_1 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | SIMP: (157) implies: % 128.17/17.64 | | | | | | (158) all_89_1 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (121), (154) imply: % 128.17/17.64 | | | | | | (159) all_91_4 = all_89_4 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | SIMP: (159) implies: % 128.17/17.64 | | | | | | (160) all_91_4 = all_89_4 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (152), (160) imply: % 128.17/17.64 | | | | | | (161) all_89_4 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | COMBINE_EQS: (151), (158) imply: % 128.17/17.64 | | | | | | (162) all_89_2 = all_27_0 % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | REDUCE: (128), (129) imply: % 128.17/17.64 | | | | | | (163) ~ (all_93_3 = all_27_0) % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | GROUND_INST: instantiating (2) with all_77_0, all_27_0, xn, % 128.17/17.64 | | | | | | simplifying with (32), (34), (76), (77), (78) gives: % 128.17/17.64 | | | | | | (164) sdtpldt0(all_77_0, all_27_0) = xn & $i(xn) % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | GROUND_INST: instantiating (13) with xn, sz10, xm, all_93_1, % 128.17/17.64 | | | | | | all_27_0, simplifying with (1), (14), (16), (17), (18), % 128.17/17.64 | | | | | | (19), (33), (40), (89) gives: % 128.17/17.64 | | | | | | (165) xn = sz00 | xm = sz10 | sdtlseqdt0(all_93_1, all_27_0) % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | GROUND_INST: instantiating (4) with xn, all_93_1, simplifying with % 128.17/17.64 | | | | | | (17), (19), (89) gives: % 128.17/17.64 | | | | | | (166) all_93_1 = xn % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | GROUND_INST: instantiating (5) with xn, all_93_3, simplifying with % 128.17/17.64 | | | | | | (17), (19), (90) gives: % 128.17/17.64 | | | | | | (167) all_93_3 = xn % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | REDUCE: (163), (167) imply: % 128.17/17.64 | | | | | | (168) ~ (all_27_0 = xn) % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | BETA: splitting (165) gives: % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | | Case 1: % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | (169) sdtlseqdt0(all_93_1, all_27_0) % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | REDUCE: (166), (169) imply: % 128.17/17.64 | | | | | | | (170) sdtlseqdt0(xn, all_27_0) % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | PRED_UNIFY: (25), (170) imply: % 128.17/17.64 | | | | | | | (171) $false % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | CLOSE: (171) is inconsistent. % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | Case 2: % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | (172) xn = sz00 | xm = sz10 % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | BETA: splitting (172) gives: % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | | Case 1: % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | (173) xn = sz00 % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | REDUCE: (37), (173) imply: % 128.17/17.64 | | | | | | | | (174) ~ (all_27_0 = sz00) % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | REDUCE: (26), (173) imply: % 128.17/17.64 | | | | | | | | (175) sdtasdt0(sz00, xm) = all_27_0 % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | BETA: splitting (36) gives: % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | Case 1: % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | | (176) ~ (sdtasdt0(sz00, xm) = all_27_0) % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | | PRED_UNIFY: (175), (176) imply: % 128.17/17.64 | | | | | | | | | (177) $false % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | | CLOSE: (177) is inconsistent. % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | Case 2: % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | | (178) all_27_0 = sz00 % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | | REDUCE: (174), (178) imply: % 128.17/17.64 | | | | | | | | | (179) $false % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | | CLOSE: (179) is inconsistent. % 128.17/17.64 | | | | | | | | | % 128.17/17.64 | | | | | | | | End of split % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | Case 2: % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | (180) xm = sz10 % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | REDUCE: (39), (180) imply: % 128.17/17.64 | | | | | | | | (181) $false % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | | CLOSE: (181) is inconsistent. % 128.17/17.64 | | | | | | | | % 128.17/17.64 | | | | | | | End of split % 128.17/17.64 | | | | | | | % 128.17/17.64 | | | | | | End of split % 128.17/17.64 | | | | | | % 128.17/17.64 | | | | | End of split % 128.17/17.64 | | | | | % 128.17/17.65 | | | | End of split % 128.17/17.65 | | | | % 128.17/17.65 | | | End of split % 128.17/17.65 | | | % 128.17/17.65 | | Case 2: % 128.17/17.65 | | | % 128.17/17.65 | | | (182) xm = sz10 | xm = sz00 % 128.17/17.65 | | | % 128.17/17.65 | | | BETA: splitting (182) gives: % 128.17/17.65 | | | % 128.17/17.65 | | | Case 1: % 128.17/17.65 | | | | % 128.17/17.65 | | | | (183) xm = sz00 % 128.17/17.65 | | | | % 128.17/17.65 | | | | REDUCE: (24), (183) imply: % 128.17/17.65 | | | | (184) $false % 128.17/17.65 | | | | % 128.17/17.65 | | | | CLOSE: (184) is inconsistent. % 128.17/17.65 | | | | % 128.17/17.65 | | | Case 2: % 128.17/17.65 | | | | % 128.17/17.65 | | | | (185) xm = sz10 % 128.17/17.65 | | | | % 128.17/17.65 | | | | REDUCE: (39), (185) imply: % 128.17/17.65 | | | | (186) $false % 128.17/17.65 | | | | % 128.17/17.65 | | | | CLOSE: (186) is inconsistent. % 128.17/17.65 | | | | % 128.17/17.65 | | | End of split % 128.17/17.65 | | | % 128.17/17.65 | | End of split % 128.17/17.65 | | % 128.17/17.65 | Case 2: % 128.17/17.65 | | % 128.17/17.65 | | (187) all_27_0 = xn % 128.17/17.65 | | % 128.17/17.65 | | REDUCE: (37), (187) imply: % 128.17/17.65 | | (188) $false % 128.17/17.65 | | % 128.17/17.65 | | CLOSE: (188) is inconsistent. % 128.17/17.65 | | % 128.17/17.65 | End of split % 128.17/17.65 | % 128.17/17.65 End of proof % 128.17/17.65 % SZS output end Proof for theBenchmark % 128.17/17.65 % 128.17/17.65 17051ms %------------------------------------------------------------------------------