%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 11:48:17 EDT 2023 % Result : Theorem 19.51s 3.59s % Output : Proof 37.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM513+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.36 % Computer : n018.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Aug 25 13:55:13 EDT 2023 % 0.15/0.36 % CPUTime : % 0.22/0.64 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.81/1.31 Prover 1: Preprocessing ... % 3.81/1.31 Prover 4: Preprocessing ... % 4.33/1.35 Prover 6: Preprocessing ... % 4.33/1.35 Prover 3: Preprocessing ... % 4.33/1.35 Prover 2: Preprocessing ... % 4.33/1.35 Prover 0: Preprocessing ... % 4.33/1.35 Prover 5: Preprocessing ... % 10.41/2.25 Prover 1: Constructing countermodel ... % 10.97/2.26 Prover 3: Constructing countermodel ... % 10.97/2.26 Prover 6: Proving ... % 11.06/2.31 Prover 5: Constructing countermodel ... % 12.54/2.53 Prover 2: Proving ... % 13.21/2.59 Prover 4: Constructing countermodel ... % 13.48/2.69 Prover 0: Proving ... % 19.51/3.59 Prover 3: proved (2918ms) % 19.51/3.59 % 19.51/3.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 19.51/3.59 % 19.51/3.60 Prover 5: stopped % 20.84/3.60 Prover 0: stopped % 20.84/3.62 Prover 6: stopped % 20.84/3.62 Prover 2: stopped % 21.03/3.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 21.03/3.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.03/3.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 21.03/3.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 21.03/3.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 21.74/3.76 Prover 7: Preprocessing ... % 21.74/3.78 Prover 11: Preprocessing ... % 22.29/3.80 Prover 8: Preprocessing ... % 22.29/3.81 Prover 13: Preprocessing ... % 22.29/3.82 Prover 10: Preprocessing ... % 23.31/3.98 Prover 10: Constructing countermodel ... % 23.31/3.99 Prover 8: Warning: ignoring some quantifiers % 23.31/4.00 Prover 8: Constructing countermodel ... % 24.09/4.05 Prover 7: Constructing countermodel ... % 24.63/4.16 Prover 13: Constructing countermodel ... % 24.63/4.24 Prover 11: Constructing countermodel ... % 36.56/5.77 Prover 10: Found proof (size 128) % 36.56/5.77 Prover 10: proved (2149ms) % 36.56/5.77 Prover 4: stopped % 36.56/5.77 Prover 7: stopped % 36.56/5.77 Prover 11: stopped % 36.56/5.77 Prover 13: stopped % 36.56/5.77 Prover 1: stopped % 36.56/5.77 Prover 8: stopped % 36.56/5.77 % 36.56/5.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 36.56/5.77 % 36.56/5.78 % SZS output start Proof for theBenchmark % 36.56/5.79 Assumptions after simplification: % 36.56/5.79 --------------------------------- % 36.56/5.79 % 36.56/5.79 (mAddComm) % 36.56/5.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ % 36.56/5.82 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 36.56/5.82 (sdtpldt0(v1, v0) = v2 & $i(v2))) % 36.56/5.82 % 36.56/5.82 (mDefPrime) % 36.56/5.82 $i(sz10) & $i(sz00) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | v1 = sz10 | ~ % 36.56/5.82 $i(v1) | ~ $i(v0) | ~ isPrime0(v0) | ~ doDivides0(v1, v0) | ~ % 36.56/5.82 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = sz10 | % 36.56/5.82 v0 = sz00 | ~ $i(v0) | ~ aNaturalNumber0(v0) | isPrime0(v0) | ? [v1: $i] % 36.56/5.82 : ( ~ (v1 = v0) & ~ (v1 = sz10) & $i(v1) & doDivides0(v1, v0) & % 36.56/5.82 aNaturalNumber0(v1))) & ( ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10)) & ( % 36.56/5.82 ~ isPrime0(sz00) | ~ aNaturalNumber0(sz00)) % 36.56/5.82 % 36.56/5.82 (mDefQuot) % 36.56/5.82 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | % 36.56/5.82 v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 36.56/5.82 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 36.56/5.82 aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! % 36.56/5.82 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v0 = sz00 | ~ % 36.56/5.82 (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 36.56/5.82 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ % 36.56/5.82 aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 36.56/5.82 : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ % 36.56/5.82 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 36.56/5.82 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) % 36.56/5.82 % 36.56/5.82 (mDivAsso) % 36.56/5.83 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 36.56/5.83 : ! [v5: $i] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, v0) % 36.56/5.83 = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 36.56/5.83 ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 36.56/5.83 aNaturalNumber0(v0) | (sdtasdt0(v3, v2) = v5 & $i(v5))) % 36.56/5.83 % 36.56/5.83 (mMulAsso) % 36.56/5.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 36.56/5.83 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) % 36.56/5.83 | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ % 36.56/5.83 aNaturalNumber0(v0) | ? [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, % 36.56/5.83 v5) = v4 & $i(v5) & $i(v4))) % 36.56/5.83 % 36.56/5.83 (mMulCanc) % 37.45/5.83 $i(sz00) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 37.45/5.83 : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = % 37.45/5.83 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 37.45/5.83 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5: $i] : ? [v6: $i] : ( % 37.45/5.83 ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & $i(v6) & % 37.45/5.83 $i(v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = % 37.45/5.83 v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | % 37.45/5.83 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 37.45/5.83 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 37.45/5.83 % 37.45/5.83 (mMulComm) % 37.45/5.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 37.45/5.83 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 37.45/5.83 (sdtasdt0(v1, v0) = v2 & $i(v2))) % 37.45/5.83 % 37.45/5.83 (mSortsB_02) % 37.45/5.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ % 37.45/5.83 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | % 37.45/5.83 aNaturalNumber0(v2)) % 37.45/5.83 % 37.45/5.83 (mSortsC_01) % 37.45/5.83 ~ (sz10 = sz00) & $i(sz10) & $i(sz00) & aNaturalNumber0(sz10) % 37.45/5.83 % 37.45/5.83 (m__) % 37.45/5.83 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? % 37.45/5.83 [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & sdtsldt0(xk, xr) = v0 & sdtsldt0(xn, % 37.45/5.83 xr) = v1 & sdtasdt0(v1, xm) = v3 & sdtasdt0(xr, v1) = xn & sdtasdt0(xr, % 37.45/5.83 v0) = xk & sdtasdt0(xp, v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 37.45/5.83 aNaturalNumber0(v1) & aNaturalNumber0(v0)) % 37.45/5.83 % 37.45/5.83 (m__1837) % 37.45/5.83 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) & % 37.45/5.83 aNaturalNumber0(xn) % 37.45/5.83 % 37.45/5.83 (m__1860) % 37.45/5.83 $i(xp) & $i(xm) & $i(xn) & $i(sz10) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ( % 37.45/5.83 ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = % 37.45/5.83 v0 & $i(v1) & $i(v0) & isPrime0(xp) & doDivides0(xp, v0) & % 37.45/5.83 aNaturalNumber0(v1) & ! [v2: $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ % 37.45/5.83 (sdtasdt0(v2, v3) = xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | % 37.45/5.83 ~ aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ $i(v2) | % 37.45/5.83 ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2))) % 37.45/5.83 % 37.45/5.83 (m__2306) % 37.45/5.83 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk & % 37.45/5.83 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & $i(v0) & % 37.45/5.83 aNaturalNumber0(xk)) % 37.45/5.83 % 37.45/5.84 (m__2342) % 37.45/5.84 $i(xr) & $i(xk) & $i(sz10) & $i(sz00) & ? [v0: $i] : ( ~ (xr = sz10) & ~ (xr % 37.45/5.84 = sz00) & sdtasdt0(xr, v0) = xk & $i(v0) & isPrime0(xr) & doDivides0(xr, % 37.45/5.84 xk) & aNaturalNumber0(v0) & aNaturalNumber0(xr) & ! [v1: $i] : ! [v2: % 37.45/5.84 $i] : (v1 = xr | v1 = sz10 | ~ (sdtasdt0(v1, v2) = xr) | ~ $i(v2) | ~ % 37.45/5.84 $i(v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1: $i] : % 37.45/5.84 (v1 = xr | v1 = sz10 | ~ $i(v1) | ~ doDivides0(v1, xr) | ~ % 37.45/5.84 aNaturalNumber0(v1))) % 37.45/5.84 % 37.45/5.84 (m__2362) % 37.45/5.84 $i(xr) & $i(xk) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 37.45/5.84 (sdtasdt0(xr, v1) = v0 & sdtasdt0(xn, xm) = v0 & sdtpldt0(xr, v2) = xk & % 37.45/5.84 $i(v2) & $i(v1) & $i(v0) & doDivides0(xr, v0) & aNaturalNumber0(v2) & % 37.45/5.84 aNaturalNumber0(v1)) % 37.45/5.84 % 37.45/5.84 (m__2377) % 37.45/5.84 $i(xk) & $i(xp) & ? [v0: $i] : ( ~ (xk = xp) & sdtpldt0(xk, v0) = xp & $i(v0) % 37.45/5.84 & sdtlseqdt0(xk, xp) & aNaturalNumber0(v0)) % 37.45/5.84 % 37.45/5.84 (m__2487) % 37.45/5.84 $i(xr) & $i(xn) & ? [v0: $i] : (sdtasdt0(xr, v0) = xn & $i(v0) & % 37.45/5.84 doDivides0(xr, xn) & aNaturalNumber0(v0)) % 37.45/5.84 % 37.45/5.84 (m__2504) % 37.45/5.84 $i(xr) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) % 37.45/5.84 = v0 & sdtasdt0(xr, v0) = xn & sdtpldt0(v0, v1) = xn & $i(v1) & $i(v0) & % 37.45/5.84 sdtlseqdt0(v0, xn) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) % 37.45/5.84 % 37.45/5.84 (m__2576) % 37.45/5.84 $i(xr) & $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? % 37.45/5.84 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (sdtsldt0(v3, xr) = v4 & sdtsldt0(xn, % 37.45/5.84 xr) = v0 & sdtasdt0(v4, xr) = v2 & sdtasdt0(v1, xr) = v2 & sdtasdt0(v0, % 37.45/5.84 xm) = v1 & sdtasdt0(xr, v4) = v3 & sdtasdt0(xr, v0) = xn & sdtasdt0(xp, % 37.45/5.84 xk) = v3 & sdtasdt0(xn, xm) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & % 37.45/5.84 $i(v0) & aNaturalNumber0(v4) & aNaturalNumber0(v0)) % 37.45/5.84 % 37.45/5.84 (function-axioms) % 37.45/5.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 37.45/5.84 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : ! % 37.45/5.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | % 37.45/5.84 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 37.45/5.84 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 37.45/5.84 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 37.45/5.84 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) % 37.45/5.84 % 37.45/5.84 Further assumptions not needed in the proof: % 37.45/5.84 -------------------------------------------- % 37.45/5.84 mAMDistr, mAddAsso, mAddCanc, mDefDiff, mDefDiv, mDefLE, mDivLE, mDivMin, % 37.45/5.84 mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr, mLERefl, mLETotal, mLETran, % 37.45/5.84 mMonAdd, mMonMul, mMonMul2, mNatSort, mPrimDiv, mSortsB, mSortsC, mZeroAdd, % 37.45/5.84 mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, m__1870, m__2075, m__2287, % 37.45/5.84 m__2315, m__2327, m__2449 % 37.45/5.84 % 37.45/5.84 Those formulas are unsatisfiable: % 37.45/5.84 --------------------------------- % 37.45/5.84 % 37.45/5.84 Begin of proof % 37.45/5.84 | % 37.45/5.84 | ALPHA: (mSortsC_01) implies: % 37.45/5.84 | (1) aNaturalNumber0(sz10) % 37.45/5.84 | % 37.45/5.84 | ALPHA: (mMulCanc) implies: % 37.45/5.85 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | v0 = % 37.45/5.85 | sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ % 37.45/5.85 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~ % 37.45/5.85 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) % 37.45/5.85 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 37.45/5.85 | (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, % 37.45/5.85 | v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 37.45/5.85 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) % 37.45/5.85 | | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & % 37.45/5.85 | sdtasdt0(v1, v0) = v5 & $i(v6) & $i(v5))) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (mDefQuot) implies: % 37.45/5.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v0 = % 37.45/5.85 | sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ % 37.45/5.85 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ % 37.45/5.85 | aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ % 37.45/5.85 | aNaturalNumber0(v0)) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (mDivAsso) implies: % 37.45/5.85 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 37.45/5.85 | ! [v5: $i] : (v0 = sz00 | ~ (sdtsldt0(v4, v0) = v5) | ~ (sdtsldt0(v1, % 37.45/5.85 | v0) = v2) | ~ (sdtasdt0(v3, v1) = v4) | ~ $i(v3) | ~ $i(v1) | % 37.45/5.85 | ~ $i(v0) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ % 37.45/5.85 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | (sdtasdt0(v3, v2) = v5 % 37.45/5.85 | & $i(v5))) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (mDefPrime) implies: % 37.45/5.85 | (6) ~ isPrime0(sz10) | ~ aNaturalNumber0(sz10) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__1837) implies: % 37.45/5.85 | (7) aNaturalNumber0(xn) % 37.45/5.85 | (8) aNaturalNumber0(xm) % 37.45/5.85 | (9) aNaturalNumber0(xp) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__1860) implies: % 37.45/5.85 | (10) ? [v0: $i] : ? [v1: $i] : ( ~ (xp = sz10) & ~ (xp = sz00) & % 37.45/5.85 | sdtasdt0(xp, v1) = v0 & sdtasdt0(xn, xm) = v0 & $i(v1) & $i(v0) & % 37.45/5.85 | isPrime0(xp) & doDivides0(xp, v0) & aNaturalNumber0(v1) & ! [v2: % 37.45/5.85 | $i] : ! [v3: $i] : (v2 = xp | v2 = sz10 | ~ (sdtasdt0(v2, v3) = % 37.45/5.85 | xp) | ~ $i(v3) | ~ $i(v2) | ~ aNaturalNumber0(v3) | ~ % 37.45/5.85 | aNaturalNumber0(v2)) & ! [v2: $i] : (v2 = xp | v2 = sz10 | ~ % 37.45/5.85 | $i(v2) | ~ doDivides0(v2, xp) | ~ aNaturalNumber0(v2))) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__2306) implies: % 37.45/5.85 | (11) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 & % 37.45/5.85 | sdtasdt0(xn, xm) = v0 & $i(v0) & aNaturalNumber0(xk)) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__2342) implies: % 37.45/5.85 | (12) ? [v0: $i] : ( ~ (xr = sz10) & ~ (xr = sz00) & sdtasdt0(xr, v0) = xk % 37.45/5.85 | & $i(v0) & isPrime0(xr) & doDivides0(xr, xk) & aNaturalNumber0(v0) & % 37.45/5.85 | aNaturalNumber0(xr) & ! [v1: $i] : ! [v2: $i] : (v1 = xr | v1 = % 37.45/5.85 | sz10 | ~ (sdtasdt0(v1, v2) = xr) | ~ $i(v2) | ~ $i(v1) | ~ % 37.45/5.85 | aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1: $i] : (v1 % 37.45/5.85 | = xr | v1 = sz10 | ~ $i(v1) | ~ doDivides0(v1, xr) | ~ % 37.45/5.85 | aNaturalNumber0(v1))) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__2362) implies: % 37.45/5.85 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, v1) = v0 & % 37.45/5.85 | sdtasdt0(xn, xm) = v0 & sdtpldt0(xr, v2) = xk & $i(v2) & $i(v1) & % 37.45/5.85 | $i(v0) & doDivides0(xr, v0) & aNaturalNumber0(v2) & % 37.45/5.85 | aNaturalNumber0(v1)) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__2377) implies: % 37.45/5.85 | (14) ? [v0: $i] : ( ~ (xk = xp) & sdtpldt0(xk, v0) = xp & $i(v0) & % 37.45/5.85 | sdtlseqdt0(xk, xp) & aNaturalNumber0(v0)) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__2487) implies: % 37.45/5.85 | (15) ? [v0: $i] : (sdtasdt0(xr, v0) = xn & $i(v0) & doDivides0(xr, xn) & % 37.45/5.85 | aNaturalNumber0(v0)) % 37.45/5.85 | % 37.45/5.85 | ALPHA: (m__2504) implies: % 37.45/5.86 | (16) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = xn) & sdtsldt0(xn, xr) = v0 & % 37.45/5.86 | sdtasdt0(xr, v0) = xn & sdtpldt0(v0, v1) = xn & $i(v1) & $i(v0) & % 37.45/5.86 | sdtlseqdt0(v0, xn) & aNaturalNumber0(v1) & aNaturalNumber0(v0)) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (m__2576) implies: % 37.45/5.86 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 37.45/5.86 | (sdtsldt0(v3, xr) = v4 & sdtsldt0(xn, xr) = v0 & sdtasdt0(v4, xr) = v2 % 37.45/5.86 | & sdtasdt0(v1, xr) = v2 & sdtasdt0(v0, xm) = v1 & sdtasdt0(xr, v4) = % 37.45/5.86 | v3 & sdtasdt0(xr, v0) = xn & sdtasdt0(xp, xk) = v3 & sdtasdt0(xn, % 37.45/5.86 | xm) = v2 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 37.45/5.86 | aNaturalNumber0(v4) & aNaturalNumber0(v0)) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (m__) implies: % 37.45/5.86 | (18) $i(xm) % 37.45/5.86 | (19) $i(xk) % 37.45/5.86 | (20) $i(xr) % 37.45/5.86 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) % 37.45/5.86 | & sdtsldt0(xk, xr) = v0 & sdtsldt0(xn, xr) = v1 & sdtasdt0(v1, xm) = % 37.45/5.86 | v3 & sdtasdt0(xr, v1) = xn & sdtasdt0(xr, v0) = xk & sdtasdt0(xp, % 37.45/5.86 | v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aNaturalNumber0(v1) % 37.45/5.86 | & aNaturalNumber0(v0)) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (function-axioms) implies: % 37.45/5.86 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 37.45/5.86 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) % 37.45/5.86 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 37.45/5.86 | (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) % 37.45/5.86 | % 37.45/5.86 | DELTA: instantiating (15) with fresh symbol all_40_0 gives: % 37.45/5.86 | (24) sdtasdt0(xr, all_40_0) = xn & $i(all_40_0) & doDivides0(xr, xn) & % 37.45/5.86 | aNaturalNumber0(all_40_0) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (24) implies: % 37.45/5.86 | (25) aNaturalNumber0(all_40_0) % 37.45/5.86 | (26) doDivides0(xr, xn) % 37.45/5.86 | (27) $i(all_40_0) % 37.45/5.86 | (28) sdtasdt0(xr, all_40_0) = xn % 37.45/5.86 | % 37.45/5.86 | DELTA: instantiating (11) with fresh symbol all_42_0 gives: % 37.45/5.86 | (29) sdtsldt0(all_42_0, xp) = xk & sdtasdt0(xp, xk) = all_42_0 & % 37.45/5.86 | sdtasdt0(xn, xm) = all_42_0 & $i(all_42_0) & aNaturalNumber0(xk) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (29) implies: % 37.45/5.86 | (30) aNaturalNumber0(xk) % 37.45/5.86 | (31) sdtasdt0(xn, xm) = all_42_0 % 37.45/5.86 | (32) sdtasdt0(xp, xk) = all_42_0 % 37.45/5.86 | % 37.45/5.86 | DELTA: instantiating (14) with fresh symbol all_44_0 gives: % 37.45/5.86 | (33) ~ (xk = xp) & sdtpldt0(xk, all_44_0) = xp & $i(all_44_0) & % 37.45/5.86 | sdtlseqdt0(xk, xp) & aNaturalNumber0(all_44_0) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (33) implies: % 37.45/5.86 | (34) aNaturalNumber0(all_44_0) % 37.45/5.86 | (35) $i(all_44_0) % 37.45/5.86 | (36) sdtpldt0(xk, all_44_0) = xp % 37.45/5.86 | % 37.45/5.86 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1 gives: % 37.45/5.86 | (37) ~ (all_46_1 = xn) & sdtsldt0(xn, xr) = all_46_1 & sdtasdt0(xr, % 37.45/5.86 | all_46_1) = xn & sdtpldt0(all_46_1, all_46_0) = xn & $i(all_46_0) & % 37.45/5.86 | $i(all_46_1) & sdtlseqdt0(all_46_1, xn) & aNaturalNumber0(all_46_0) & % 37.45/5.86 | aNaturalNumber0(all_46_1) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (37) implies: % 37.45/5.86 | (38) sdtsldt0(xn, xr) = all_46_1 % 37.45/5.86 | % 37.45/5.86 | DELTA: instantiating (13) with fresh symbols all_48_0, all_48_1, all_48_2 % 37.45/5.86 | gives: % 37.45/5.86 | (39) sdtasdt0(xr, all_48_1) = all_48_2 & sdtasdt0(xn, xm) = all_48_2 & % 37.45/5.86 | sdtpldt0(xr, all_48_0) = xk & $i(all_48_0) & $i(all_48_1) & % 37.45/5.86 | $i(all_48_2) & doDivides0(xr, all_48_2) & aNaturalNumber0(all_48_0) & % 37.45/5.86 | aNaturalNumber0(all_48_1) % 37.45/5.86 | % 37.45/5.86 | ALPHA: (39) implies: % 37.45/5.86 | (40) aNaturalNumber0(all_48_1) % 37.45/5.86 | (41) doDivides0(xr, all_48_2) % 37.45/5.86 | (42) $i(all_48_1) % 37.45/5.87 | (43) sdtasdt0(xn, xm) = all_48_2 % 37.45/5.87 | (44) sdtasdt0(xr, all_48_1) = all_48_2 % 37.45/5.87 | % 37.45/5.87 | DELTA: instantiating (21) with fresh symbols all_54_0, all_54_1, all_54_2, % 37.45/5.87 | all_54_3 gives: % 37.45/5.87 | (45) ~ (all_54_0 = all_54_1) & sdtsldt0(xk, xr) = all_54_3 & sdtsldt0(xn, % 37.45/5.87 | xr) = all_54_2 & sdtasdt0(all_54_2, xm) = all_54_0 & sdtasdt0(xr, % 37.45/5.87 | all_54_2) = xn & sdtasdt0(xr, all_54_3) = xk & sdtasdt0(xp, % 37.45/5.87 | all_54_3) = all_54_1 & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & % 37.45/5.87 | $i(all_54_3) & aNaturalNumber0(all_54_2) & aNaturalNumber0(all_54_3) % 37.45/5.87 | % 37.45/5.87 | ALPHA: (45) implies: % 37.45/5.87 | (46) ~ (all_54_0 = all_54_1) % 37.45/5.87 | (47) aNaturalNumber0(all_54_2) % 37.45/5.87 | (48) $i(all_54_2) % 37.45/5.87 | (49) sdtasdt0(xp, all_54_3) = all_54_1 % 37.45/5.87 | (50) sdtasdt0(xr, all_54_2) = xn % 37.45/5.87 | (51) sdtasdt0(all_54_2, xm) = all_54_0 % 37.45/5.87 | (52) sdtsldt0(xn, xr) = all_54_2 % 37.45/5.87 | (53) sdtsldt0(xk, xr) = all_54_3 % 37.45/5.87 | % 37.45/5.87 | DELTA: instantiating (17) with fresh symbols all_56_0, all_56_1, all_56_2, % 37.45/5.87 | all_56_3, all_56_4 gives: % 37.45/5.87 | (54) sdtsldt0(all_56_1, xr) = all_56_0 & sdtsldt0(xn, xr) = all_56_4 & % 37.45/5.87 | sdtasdt0(all_56_0, xr) = all_56_2 & sdtasdt0(all_56_3, xr) = all_56_2 % 37.45/5.87 | & sdtasdt0(all_56_4, xm) = all_56_3 & sdtasdt0(xr, all_56_0) = % 37.45/5.87 | all_56_1 & sdtasdt0(xr, all_56_4) = xn & sdtasdt0(xp, xk) = all_56_1 & % 37.45/5.87 | sdtasdt0(xn, xm) = all_56_2 & $i(all_56_0) & $i(all_56_1) & % 37.45/5.87 | $i(all_56_2) & $i(all_56_3) & $i(all_56_4) & aNaturalNumber0(all_56_0) % 37.45/5.87 | & aNaturalNumber0(all_56_4) % 37.45/5.87 | % 37.45/5.87 | ALPHA: (54) implies: % 37.45/5.87 | (55) aNaturalNumber0(all_56_0) % 37.45/5.87 | (56) $i(all_56_0) % 37.45/5.87 | (57) sdtasdt0(xn, xm) = all_56_2 % 37.45/5.87 | (58) sdtasdt0(xp, xk) = all_56_1 % 37.45/5.87 | (59) sdtasdt0(xr, all_56_0) = all_56_1 % 37.45/5.87 | (60) sdtasdt0(all_56_4, xm) = all_56_3 % 37.45/5.87 | (61) sdtasdt0(all_56_0, xr) = all_56_2 % 37.45/5.87 | (62) sdtsldt0(xn, xr) = all_56_4 % 37.45/5.87 | (63) sdtsldt0(all_56_1, xr) = all_56_0 % 37.45/5.87 | % 37.45/5.87 | DELTA: instantiating (12) with fresh symbol all_58_0 gives: % 37.45/5.87 | (64) ~ (xr = sz10) & ~ (xr = sz00) & sdtasdt0(xr, all_58_0) = xk & % 37.45/5.87 | $i(all_58_0) & isPrime0(xr) & doDivides0(xr, xk) & % 37.45/5.87 | aNaturalNumber0(all_58_0) & aNaturalNumber0(xr) & ! [v0: $i] : ! % 37.45/5.87 | [v1: $i] : (v0 = xr | v0 = sz10 | ~ (sdtasdt0(v0, v1) = xr) | ~ % 37.45/5.87 | $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 37.45/5.87 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xr | v0 = sz10 | ~ % 37.45/5.87 | $i(v0) | ~ doDivides0(v0, xr) | ~ aNaturalNumber0(v0)) % 37.45/5.87 | % 37.45/5.87 | ALPHA: (64) implies: % 37.45/5.87 | (65) ~ (xr = sz00) % 37.45/5.87 | (66) aNaturalNumber0(xr) % 37.45/5.87 | (67) aNaturalNumber0(all_58_0) % 37.45/5.87 | (68) doDivides0(xr, xk) % 37.95/5.87 | (69) $i(all_58_0) % 37.95/5.87 | (70) sdtasdt0(xr, all_58_0) = xk % 37.95/5.87 | % 37.95/5.87 | DELTA: instantiating (10) with fresh symbols all_61_0, all_61_1 gives: % 37.95/5.87 | (71) ~ (xp = sz10) & ~ (xp = sz00) & sdtasdt0(xp, all_61_0) = all_61_1 & % 37.95/5.87 | sdtasdt0(xn, xm) = all_61_1 & $i(all_61_0) & $i(all_61_1) & % 37.95/5.87 | isPrime0(xp) & doDivides0(xp, all_61_1) & aNaturalNumber0(all_61_0) & % 37.95/5.87 | ! [v0: $i] : ! [v1: $i] : (v0 = xp | v0 = sz10 | ~ (sdtasdt0(v0, v1) % 37.95/5.87 | = xp) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ % 37.95/5.87 | aNaturalNumber0(v0)) & ! [v0: $i] : (v0 = xp | v0 = sz10 | ~ % 37.95/5.87 | $i(v0) | ~ doDivides0(v0, xp) | ~ aNaturalNumber0(v0)) % 37.95/5.87 | % 37.95/5.87 | ALPHA: (71) implies: % 37.95/5.87 | (72) sdtasdt0(xn, xm) = all_61_1 % 37.95/5.87 | % 37.95/5.87 | BETA: splitting (6) gives: % 37.95/5.87 | % 37.95/5.87 | Case 1: % 37.95/5.87 | | % 37.95/5.87 | | (73) ~ aNaturalNumber0(sz10) % 37.95/5.87 | | % 37.95/5.87 | | PRED_UNIFY: (1), (73) imply: % 37.95/5.88 | | (74) $false % 37.95/5.88 | | % 37.95/5.88 | | CLOSE: (74) is inconsistent. % 37.95/5.88 | | % 37.95/5.88 | Case 2: % 37.95/5.88 | | % 37.95/5.88 | | % 37.95/5.88 | | GROUND_INST: instantiating (22) with all_48_2, all_56_2, xm, xn, simplifying % 37.95/5.88 | | with (43), (57) gives: % 37.95/5.88 | | (75) all_56_2 = all_48_2 % 37.95/5.88 | | % 37.95/5.88 | | GROUND_INST: instantiating (22) with all_56_2, all_61_1, xm, xn, simplifying % 37.95/5.88 | | with (57), (72) gives: % 37.95/5.88 | | (76) all_61_1 = all_56_2 % 37.95/5.88 | | % 37.95/5.88 | | GROUND_INST: instantiating (22) with all_42_0, all_61_1, xm, xn, simplifying % 37.95/5.88 | | with (31), (72) gives: % 37.95/5.88 | | (77) all_61_1 = all_42_0 % 37.95/5.88 | | % 37.95/5.88 | | GROUND_INST: instantiating (22) with all_42_0, all_56_1, xk, xp, simplifying % 37.95/5.88 | | with (32), (58) gives: % 37.95/5.88 | | (78) all_56_1 = all_42_0 % 37.95/5.88 | | % 37.95/5.88 | | GROUND_INST: instantiating (23) with all_54_2, all_56_4, xr, xn, simplifying % 37.95/5.88 | | with (52), (62) gives: % 37.95/5.88 | | (79) all_56_4 = all_54_2 % 37.95/5.88 | | % 37.98/5.88 | | GROUND_INST: instantiating (23) with all_46_1, all_56_4, xr, xn, simplifying % 37.98/5.88 | | with (38), (62) gives: % 37.98/5.88 | | (80) all_56_4 = all_46_1 % 37.98/5.88 | | % 37.98/5.88 | | COMBINE_EQS: (76), (77) imply: % 37.98/5.88 | | (81) all_56_2 = all_42_0 % 37.98/5.88 | | % 37.98/5.88 | | SIMP: (81) implies: % 37.98/5.88 | | (82) all_56_2 = all_42_0 % 37.98/5.88 | | % 37.98/5.88 | | COMBINE_EQS: (75), (82) imply: % 37.98/5.88 | | (83) all_48_2 = all_42_0 % 37.98/5.88 | | % 37.98/5.88 | | COMBINE_EQS: (79), (80) imply: % 37.98/5.88 | | (84) all_54_2 = all_46_1 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (63), (78) imply: % 37.98/5.88 | | (85) sdtsldt0(all_42_0, xr) = all_56_0 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (61), (82) imply: % 37.98/5.88 | | (86) sdtasdt0(all_56_0, xr) = all_42_0 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (60), (80) imply: % 37.98/5.88 | | (87) sdtasdt0(all_46_1, xm) = all_56_3 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (51), (84) imply: % 37.98/5.88 | | (88) sdtasdt0(all_46_1, xm) = all_54_0 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (59), (78) imply: % 37.98/5.88 | | (89) sdtasdt0(xr, all_56_0) = all_42_0 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (50), (84) imply: % 37.98/5.88 | | (90) sdtasdt0(xr, all_46_1) = xn % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (44), (83) imply: % 37.98/5.88 | | (91) sdtasdt0(xr, all_48_1) = all_42_0 % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (48), (84) imply: % 37.98/5.88 | | (92) $i(all_46_1) % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (41), (83) imply: % 37.98/5.88 | | (93) doDivides0(xr, all_42_0) % 37.98/5.88 | | % 37.98/5.88 | | REDUCE: (47), (84) imply: % 37.98/5.88 | | (94) aNaturalNumber0(all_46_1) % 37.98/5.88 | | % 37.98/5.88 | | GROUND_INST: instantiating (22) with all_54_0, all_56_3, xm, all_46_1, % 37.98/5.88 | | simplifying with (87), (88) gives: % 37.98/5.88 | | (95) all_56_3 = all_54_0 % 37.98/5.88 | | % 37.98/5.88 | | GROUND_INST: instantiating (mAddComm) with xk, all_44_0, xp, simplifying % 37.98/5.88 | | with (19), (30), (34), (35), (36) gives: % 37.98/5.88 | | (96) sdtpldt0(all_44_0, xk) = xp & $i(xp) % 37.98/5.88 | | % 37.98/5.88 | | ALPHA: (96) implies: % 37.98/5.88 | | (97) $i(xp) % 37.98/5.88 | | % 37.98/5.88 | | GROUND_INST: instantiating (mMulAsso) with xr, all_40_0, xm, xn, all_42_0, % 37.98/5.88 | | simplifying with (8), (18), (20), (25), (27), (28), (31), (66) % 37.98/5.88 | | gives: % 37.98/5.89 | | (98) ? [v0: $i] : (sdtasdt0(all_40_0, xm) = v0 & sdtasdt0(xr, v0) = % 37.98/5.89 | | all_42_0 & $i(v0) & $i(all_42_0)) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (3) with xr, all_46_1, all_40_0, xn, xn, % 37.98/5.89 | | simplifying with (20), (25), (27), (28), (66), (90), (92), (94) % 37.98/5.89 | | gives: % 37.98/5.89 | | (99) all_46_1 = all_40_0 | xr = sz00 | ? [v0: $i] : ? [v1: $i] : ( ~ % 37.98/5.89 | | (v1 = v0) & sdtasdt0(all_46_1, xr) = v0 & sdtasdt0(all_40_0, xr) = % 37.98/5.89 | | v1 & $i(v1) & $i(v0)) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (mMulAsso) with xr, all_46_1, xm, xn, all_42_0, % 37.98/5.89 | | simplifying with (8), (18), (20), (31), (66), (90), (92), (94) % 37.98/5.89 | | gives: % 37.98/5.89 | | (100) ? [v0: $i] : (sdtasdt0(all_46_1, xm) = v0 & sdtasdt0(xr, v0) = % 37.98/5.89 | | all_42_0 & $i(v0) & $i(all_42_0)) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (mMulComm) with xr, all_46_1, xn, simplifying % 37.98/5.89 | | with (20), (66), (90), (92), (94) gives: % 37.98/5.89 | | (101) sdtasdt0(all_46_1, xr) = xn & $i(xn) % 37.98/5.89 | | % 37.98/5.89 | | ALPHA: (101) implies: % 37.98/5.89 | | (102) $i(xn) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (3) with xr, all_48_1, all_56_0, all_42_0, % 37.98/5.89 | | all_42_0, simplifying with (20), (40), (42), (55), (56), (66), % 37.98/5.89 | | (89), (91) gives: % 37.98/5.89 | | (103) all_56_0 = all_48_1 | xr = sz00 | ? [v0: $i] : ? [v1: $i] : ( ~ % 37.98/5.89 | | (v1 = v0) & sdtasdt0(all_56_0, xr) = v1 & sdtasdt0(all_48_1, xr) % 37.98/5.89 | | = v0 & $i(v1) & $i(v0)) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (2) with xr, all_48_1, all_56_0, all_42_0, % 37.98/5.89 | | simplifying with (20), (40), (42), (55), (56), (66), (89), (91) % 37.98/5.89 | | gives: % 37.98/5.89 | | (104) all_56_0 = all_48_1 | xr = sz00 % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (mMulComm) with xr, all_58_0, xk, simplifying % 37.98/5.89 | | with (20), (66), (67), (69), (70) gives: % 37.98/5.89 | | (105) sdtasdt0(all_58_0, xr) = xk & $i(xk) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (mSortsB_02) with all_46_1, xm, all_54_0, % 37.98/5.89 | | simplifying with (8), (18), (88), (92), (94) gives: % 37.98/5.89 | | (106) aNaturalNumber0(all_54_0) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (mSortsB_02) with all_56_0, xr, all_42_0, % 37.98/5.89 | | simplifying with (20), (55), (56), (66), (86) gives: % 37.98/5.89 | | (107) aNaturalNumber0(all_42_0) % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (4) with xr, xn, all_46_1, all_40_0, simplifying % 37.98/5.89 | | with (7), (20), (25), (26), (27), (28), (38), (66), (102) % 37.98/5.89 | | gives: % 37.98/5.89 | | (108) all_46_1 = all_40_0 | xr = sz00 % 37.98/5.89 | | % 37.98/5.89 | | GROUND_INST: instantiating (5) with xr, xk, all_54_3, xp, all_42_0, % 37.98/5.89 | | all_56_0, simplifying with (9), (19), (20), (30), (32), (53), % 37.98/5.89 | | (66), (68), (85), (97) gives: % 37.98/5.89 | | (109) xr = sz00 | (sdtasdt0(xp, all_54_3) = all_56_0 & $i(all_56_0)) % 37.98/5.89 | | % 37.98/5.89 | | DELTA: instantiating (100) with fresh symbol all_105_0 gives: % 37.98/5.89 | | (110) sdtasdt0(all_46_1, xm) = all_105_0 & sdtasdt0(xr, all_105_0) = % 37.98/5.89 | | all_42_0 & $i(all_105_0) & $i(all_42_0) % 37.98/5.89 | | % 37.98/5.89 | | ALPHA: (110) implies: % 37.98/5.89 | | (111) $i(all_105_0) % 37.98/5.89 | | (112) sdtasdt0(xr, all_105_0) = all_42_0 % 37.98/5.89 | | (113) sdtasdt0(all_46_1, xm) = all_105_0 % 37.98/5.89 | | % 37.98/5.89 | | DELTA: instantiating (98) with fresh symbol all_111_0 gives: % 37.98/5.89 | | (114) sdtasdt0(all_40_0, xm) = all_111_0 & sdtasdt0(xr, all_111_0) = % 37.98/5.89 | | all_42_0 & $i(all_111_0) & $i(all_42_0) % 37.98/5.89 | | % 37.98/5.89 | | ALPHA: (114) implies: % 37.98/5.89 | | (115) $i(all_42_0) % 37.98/5.89 | | (116) sdtasdt0(all_40_0, xm) = all_111_0 % 37.98/5.89 | | % 37.98/5.89 | | BETA: splitting (99) gives: % 37.98/5.90 | | % 37.98/5.90 | | Case 1: % 37.98/5.90 | | | % 37.98/5.90 | | | (117) xr = sz00 % 37.98/5.90 | | | % 37.98/5.90 | | | REDUCE: (65), (117) imply: % 37.98/5.90 | | | (118) $false % 37.98/5.90 | | | % 37.98/5.90 | | | CLOSE: (118) is inconsistent. % 37.98/5.90 | | | % 37.98/5.90 | | Case 2: % 37.98/5.90 | | | % 37.98/5.90 | | | (119) all_46_1 = all_40_0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & % 37.98/5.90 | | | sdtasdt0(all_46_1, xr) = v0 & sdtasdt0(all_40_0, xr) = v1 & % 37.98/5.90 | | | $i(v1) & $i(v0)) % 37.98/5.90 | | | % 37.98/5.90 | | | BETA: splitting (119) gives: % 37.98/5.90 | | | % 37.98/5.90 | | | Case 1: % 37.98/5.90 | | | | % 37.98/5.90 | | | | (120) all_46_1 = all_40_0 % 37.98/5.90 | | | | % 37.98/5.90 | | | | REDUCE: (113), (120) imply: % 37.98/5.90 | | | | (121) sdtasdt0(all_40_0, xm) = all_105_0 % 37.98/5.90 | | | | % 37.98/5.90 | | | | REDUCE: (88), (120) imply: % 37.98/5.90 | | | | (122) sdtasdt0(all_40_0, xm) = all_54_0 % 37.98/5.90 | | | | % 37.98/5.90 | | | | BETA: splitting (103) gives: % 37.98/5.90 | | | | % 37.98/5.90 | | | | Case 1: % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | (123) xr = sz00 % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | REDUCE: (65), (123) imply: % 37.98/5.90 | | | | | (124) $false % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | CLOSE: (124) is inconsistent. % 37.98/5.90 | | | | | % 37.98/5.90 | | | | Case 2: % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | (125) all_56_0 = all_48_1 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 37.98/5.90 | | | | | v0) & sdtasdt0(all_56_0, xr) = v1 & sdtasdt0(all_48_1, % 37.98/5.90 | | | | | xr) = v0 & $i(v1) & $i(v0)) % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | BETA: splitting (125) gives: % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | Case 1: % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | (126) all_56_0 = all_48_1 % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | REDUCE: (85), (126) imply: % 37.98/5.90 | | | | | | (127) sdtsldt0(all_42_0, xr) = all_48_1 % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | BETA: splitting (109) gives: % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | Case 1: % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | (128) xr = sz00 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (65), (128) imply: % 37.98/5.90 | | | | | | | (129) $false % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | CLOSE: (129) is inconsistent. % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | Case 2: % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | (130) sdtasdt0(xp, all_54_3) = all_56_0 & $i(all_56_0) % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | ALPHA: (130) implies: % 37.98/5.90 | | | | | | | (131) sdtasdt0(xp, all_54_3) = all_56_0 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (126), (131) imply: % 37.98/5.90 | | | | | | | (132) sdtasdt0(xp, all_54_3) = all_48_1 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | GROUND_INST: instantiating (22) with all_54_1, all_48_1, all_54_3, % 37.98/5.90 | | | | | | | xp, simplifying with (49), (132) gives: % 37.98/5.90 | | | | | | | (133) all_54_1 = all_48_1 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | GROUND_INST: instantiating (22) with all_105_0, all_111_0, xm, % 37.98/5.90 | | | | | | | all_40_0, simplifying with (116), (121) gives: % 37.98/5.90 | | | | | | | (134) all_111_0 = all_105_0 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | GROUND_INST: instantiating (22) with all_54_0, all_111_0, xm, % 37.98/5.90 | | | | | | | all_40_0, simplifying with (116), (122) gives: % 37.98/5.90 | | | | | | | (135) all_111_0 = all_54_0 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | COMBINE_EQS: (134), (135) imply: % 37.98/5.90 | | | | | | | (136) all_105_0 = all_54_0 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (46), (133) imply: % 37.98/5.90 | | | | | | | (137) ~ (all_54_0 = all_48_1) % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (112), (136) imply: % 37.98/5.90 | | | | | | | (138) sdtasdt0(xr, all_54_0) = all_42_0 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (111), (136) imply: % 37.98/5.90 | | | | | | | (139) $i(all_54_0) % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | GROUND_INST: instantiating (4) with xr, all_42_0, all_48_1, % 37.98/5.90 | | | | | | | all_54_0, simplifying with (20), (66), (93), (106), % 37.98/5.90 | | | | | | | (107), (115), (127), (138), (139) gives: % 37.98/5.90 | | | | | | | (140) all_54_0 = all_48_1 | xr = sz00 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | BETA: splitting (140) gives: % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | Case 1: % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | | (141) xr = sz00 % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | | REDUCE: (65), (141) imply: % 37.98/5.90 | | | | | | | | (142) $false % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | | CLOSE: (142) is inconsistent. % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | Case 2: % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | | (143) all_54_0 = all_48_1 % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | | REDUCE: (137), (143) imply: % 37.98/5.90 | | | | | | | | (144) $false % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | | CLOSE: (144) is inconsistent. % 37.98/5.90 | | | | | | | | % 37.98/5.90 | | | | | | | End of split % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | End of split % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | Case 2: % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | (145) ~ (all_56_0 = all_48_1) % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | BETA: splitting (104) gives: % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | | Case 1: % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | (146) xr = sz00 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (65), (146) imply: % 37.98/5.90 | | | | | | | (147) $false % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | CLOSE: (147) is inconsistent. % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | Case 2: % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | (148) all_56_0 = all_48_1 % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | REDUCE: (145), (148) imply: % 37.98/5.90 | | | | | | | (149) $false % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | | CLOSE: (149) is inconsistent. % 37.98/5.90 | | | | | | | % 37.98/5.90 | | | | | | End of split % 37.98/5.90 | | | | | | % 37.98/5.90 | | | | | End of split % 37.98/5.90 | | | | | % 37.98/5.90 | | | | End of split % 37.98/5.90 | | | | % 37.98/5.90 | | | Case 2: % 37.98/5.90 | | | | % 37.98/5.90 | | | | (150) ~ (all_46_1 = all_40_0) % 37.98/5.90 | | | | % 37.98/5.90 | | | | BETA: splitting (108) gives: % 37.98/5.90 | | | | % 37.98/5.90 | | | | Case 1: % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | (151) xr = sz00 % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | REDUCE: (65), (151) imply: % 37.98/5.90 | | | | | (152) $false % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | CLOSE: (152) is inconsistent. % 37.98/5.90 | | | | | % 37.98/5.90 | | | | Case 2: % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | (153) all_46_1 = all_40_0 % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | REDUCE: (150), (153) imply: % 37.98/5.90 | | | | | (154) $false % 37.98/5.90 | | | | | % 37.98/5.90 | | | | | CLOSE: (154) is inconsistent. % 37.98/5.90 | | | | | % 37.98/5.90 | | | | End of split % 37.98/5.90 | | | | % 37.98/5.90 | | | End of split % 37.98/5.90 | | | % 37.98/5.90 | | End of split % 37.98/5.90 | | % 37.98/5.90 | End of split % 37.98/5.90 | % 37.98/5.90 End of proof % 37.98/5.90 % SZS output end Proof for theBenchmark % 38.10/5.90 % 38.10/5.90 5265ms %------------------------------------------------------------------------------