%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM574+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 : n012.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 11:48:42 EDT 2023 % Result : Theorem 155.46s 21.54s % Output : Proof 156.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM574+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n012.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 15:11:41 EDT 2023 % 0.14/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.72/1.38 Prover 4: Preprocessing ... % 4.72/1.38 Prover 1: Preprocessing ... % 4.77/1.41 Prover 0: Preprocessing ... % 4.77/1.41 Prover 5: Preprocessing ... % 4.77/1.41 Prover 2: Preprocessing ... % 4.77/1.42 Prover 6: Preprocessing ... % 4.77/1.42 Prover 3: Preprocessing ... % 13.27/2.60 Prover 3: Constructing countermodel ... % 13.27/2.61 Prover 1: Constructing countermodel ... % 13.90/2.67 Prover 6: Proving ... % 13.90/2.68 Prover 5: Proving ... % 14.18/2.86 Prover 2: Proving ... % 17.66/3.17 Prover 4: Constructing countermodel ... % 19.06/3.37 Prover 0: Proving ... % 72.21/10.39 Prover 2: stopped % 72.21/10.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 72.73/10.50 Prover 7: Preprocessing ... % 74.90/10.75 Prover 7: Constructing countermodel ... % 99.57/13.97 Prover 5: stopped % 99.57/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.35/14.12 Prover 8: Preprocessing ... % 102.55/14.37 Prover 8: Warning: ignoring some quantifiers % 102.55/14.37 Prover 8: Constructing countermodel ... % 114.86/16.01 Prover 1: stopped % 114.86/16.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.73/16.11 Prover 9: Preprocessing ... % 119.36/16.64 Prover 9: Constructing countermodel ... % 129.07/17.90 Prover 6: stopped % 129.07/17.92 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 130.13/18.03 Prover 10: Preprocessing ... % 131.24/18.14 Prover 10: Constructing countermodel ... % 155.46/21.51 Prover 10: Found proof (size 96) % 155.46/21.52 Prover 10: proved (3592ms) % 155.46/21.52 Prover 9: stopped % 155.46/21.52 Prover 3: stopped % 155.46/21.52 Prover 4: stopped % 155.46/21.53 Prover 8: stopped % 155.46/21.53 Prover 7: stopped % 155.46/21.54 Prover 0: stopped % 155.46/21.54 % 155.46/21.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 155.46/21.54 % 155.99/21.55 % SZS output start Proof for theBenchmark % 155.99/21.56 Assumptions after simplification: % 155.99/21.56 --------------------------------- % 155.99/21.56 % 155.99/21.56 (mCardCons) % 155.99/21.58 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 155.99/21.58 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2) % 155.99/21.58 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~ % 155.99/21.58 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0)))) % 155.99/21.58 % 155.99/21.58 (mCardSeg) % 155.99/21.59 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) % 155.99/21.59 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0) % 155.99/21.59 % 155.99/21.59 (mDefEmp) % 155.99/21.59 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 155.99/21.59 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 155.99/21.59 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 155.99/21.59 % 155.99/21.59 (mDefSub) % 156.14/21.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 156.14/21.59 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 156.14/21.59 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 156.14/21.59 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 156.14/21.59 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 156.14/21.59 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 156.14/21.59 % 156.14/21.59 (mEmpFin) % 156.14/21.59 $i(slcrc0) & isFinite0(slcrc0) % 156.14/21.59 % 156.14/21.59 (mNATSet) % 156.14/21.59 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 156.14/21.59 % 156.14/21.59 (mNatExtra) % 156.14/21.59 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 156.14/21.59 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 156.14/21.59 aElementOf0(v1, szNzAzT0))) % 156.14/21.59 % 156.14/21.59 (mNoScLessZr) % 156.14/21.59 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 156.14/21.59 v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0)) % 156.14/21.59 % 156.14/21.59 (mSegSucc) % 156.14/21.60 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = % 156.14/21.60 v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 156.14/21.60 aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 | % 156.14/21.60 aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 & % 156.14/21.60 $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & ~ % 156.14/21.60 aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 & % 156.14/21.60 $i(v4) & $i(v3) & aElementOf0(v0, v4))))) % 156.14/21.60 % 156.14/21.60 (mSegZero) % 156.14/21.60 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 156.14/21.60 % 156.14/21.60 (mSelCSet) % 156.14/21.60 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 % 156.14/21.60 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 156.14/21.60 isCountable0(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | % 156.14/21.60 isCountable0(v2)) % 156.14/21.60 % 156.14/21.60 (mSelSub) % 156.14/21.60 $i(sz00) & $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 156.14/21.60 : ! [v3: $i] : ! [v4: $i] : (v3 = slcrc0 | v0 = sz00 | ~ (slbdtsldtrb0(v2, % 156.14/21.60 v0) = v4) | ~ (slbdtsldtrb0(v1, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 156.14/21.60 $i(v0) | ~ aSubsetOf0(v3, v4) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) % 156.14/21.60 | ~ aSet0(v1) | aSubsetOf0(v1, v2)) % 156.14/21.60 % 156.14/21.60 (mSuccNum) % 156.14/21.60 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 156.14/21.60 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, % 156.14/21.60 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~ % 156.14/21.60 aElementOf0(v0, szNzAzT0)) % 156.14/21.60 % 156.14/21.60 (mZeroNum) % 156.14/21.60 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 156.14/21.60 % 156.14/21.60 (m__) % 156.14/21.61 $i(xi) & $i(xj) & $i(xN) & ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = % 156.14/21.61 v0 & sdtlpdtrp0(xN, xj) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(xj, xi) & ~ % 156.14/21.61 aSubsetOf0(v0, v1)) % 156.14/21.61 % 156.14/21.61 (m__3418) % 156.14/21.61 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 156.14/21.61 % 156.14/21.61 (m__3435) % 156.14/21.61 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) % 156.14/21.61 % 156.14/21.61 (m__3453) % 156.14/21.61 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ? [v0: $i] : ? [v1: $i] : % 156.14/21.61 (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) = v0 & slbdtsldtrb0(xS, xK) = v0 & % 156.14/21.61 $i(v1) & $i(v0) & aFunction0(xc) & aSubsetOf0(v1, xT)) % 156.14/21.61 % 156.14/21.61 (m__3462) % 156.14/21.61 ~ (xK = sz00) & $i(xK) & $i(sz00) % 156.14/21.61 % 156.14/21.61 (m__3520) % 156.14/21.61 ~ (xK = sz00) & $i(xK) & $i(sz00) % 156.14/21.61 % 156.14/21.61 (m__3533) % 156.14/21.61 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk, % 156.14/21.61 szNzAzT0) % 156.14/21.61 % 156.14/21.61 (m__3623) % 156.14/21.61 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 156.14/21.61 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 156.14/21.61 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) % 156.14/21.61 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 156.14/21.61 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v4: $i] : ? [v5: $i] % 156.14/21.61 : (sdtlpdtrp0(xN, v4) = v5 & szszuzczcdt0(v0) = v4 & $i(v5) & $i(v4) & % 156.14/21.61 aSubsetOf0(v5, v3) & isCountable0(v5))) % 156.14/21.61 % 156.14/21.61 (m__3671) % 156.14/21.61 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 156.14/21.61 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 156.14/21.61 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ % 156.14/21.61 aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 156.14/21.61 % 156.14/21.61 (m__3786) % 156.14/21.61 $i(xi) & $i(xj) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) & aElementOf0(xj, % 156.14/21.61 szNzAzT0) % 156.14/21.61 % 156.14/21.61 (m__3786_02) % 156.14/21.61 $i(xi) & $i(xj) & $i(xN) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : ( ~ % 156.14/21.61 sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~ (szszuzczcdt0(v2) = xi) | ~ $i(v2) | % 156.14/21.61 ~ aElementOf0(v2, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, % 156.14/21.61 xj) = v1 & $i(v1) & $i(v0) & aSubsetOf0(v0, v1))) % 156.14/21.61 % 156.14/21.61 (function-axioms) % 156.14/21.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 156.14/21.62 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 156.14/21.62 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 156.14/21.62 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 156.14/21.62 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 156.14/21.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 156.14/21.62 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 156.14/21.62 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 156.14/21.62 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 156.14/21.62 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 156.14/21.62 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 156.14/21.62 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 156.14/21.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 156.14/21.62 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 156.14/21.62 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 156.14/21.62 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 156.14/21.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 156.14/21.62 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 156.14/21.62 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 156.14/21.62 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 156.14/21.62 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 156.14/21.62 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 156.14/21.62 v0)) % 156.14/21.62 % 156.14/21.62 Further assumptions not needed in the proof: % 156.14/21.62 -------------------------------------------- % 156.14/21.62 mCConsSet, mCDiffSet, mCardDiff, mCardEmpty, mCardNum, mCardS, mCardSub, % 156.14/21.62 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons, mDefDiff, % 156.14/21.62 mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel, mDiffCons, % 156.14/21.62 mDirichlet, mDomSet, mEOfElem, mElmSort, mFConsSet, mFDiffSet, mFinRel, % 156.14/21.62 mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm, % 156.14/21.62 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc, % 156.14/21.62 mPttSet, mSegFin, mSegLess, mSelExtra, mSelFSet, mSelNSet, mSetSort, mSubASymm, % 156.14/21.62 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mZeroLess, m__3291, % 156.14/21.62 m__3398, m__3754 % 156.14/21.62 % 156.14/21.62 Those formulas are unsatisfiable: % 156.14/21.62 --------------------------------- % 156.14/21.62 % 156.14/21.62 Begin of proof % 156.14/21.62 | % 156.14/21.62 | ALPHA: (mDefEmp) implies: % 156.14/21.62 | (1) aSet0(slcrc0) % 156.14/21.62 | % 156.14/21.62 | ALPHA: (mEmpFin) implies: % 156.14/21.62 | (2) isFinite0(slcrc0) % 156.14/21.62 | % 156.14/21.62 | ALPHA: (mDefSub) implies: % 156.14/21.62 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 156.14/21.62 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 156.14/21.62 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 156.14/21.62 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, % 156.14/21.62 | v0) | ~ aSet0(v0) | aSet0(v1)) % 156.14/21.62 | % 156.14/21.62 | ALPHA: (mNATSet) implies: % 156.14/21.62 | (5) aSet0(szNzAzT0) % 156.14/21.62 | % 156.14/21.62 | ALPHA: (mZeroNum) implies: % 156.14/21.63 | (6) aElementOf0(sz00, szNzAzT0) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mSuccNum) implies: % 156.14/21.63 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 156.14/21.63 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0)) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mNatExtra) implies: % 156.14/21.63 | (8) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 156.14/21.63 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 156.14/21.63 | szNzAzT0))) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mNoScLessZr) implies: % 156.14/21.63 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 156.14/21.63 | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0)) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mSegZero) implies: % 156.14/21.63 | (10) slbdtrb0(sz00) = slcrc0 % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mSegSucc) implies: % 156.14/21.63 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~ % 156.14/21.63 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 156.14/21.63 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 | % 156.14/21.63 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 % 156.14/21.63 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) % 156.14/21.63 | & ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & % 156.14/21.63 | szszuzczcdt0(v1) = v3 & $i(v4) & $i(v3) & aElementOf0(v0, % 156.14/21.63 | v4))))) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mCardSeg) implies: % 156.14/21.63 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~ % 156.14/21.63 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mSelCSet) implies: % 156.14/21.63 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = sz00 | ~ % 156.14/21.63 | (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 156.14/21.63 | isCountable0(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | % 156.14/21.63 | isCountable0(v2)) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (mSelSub) implies: % 156.14/21.63 | (14) $i(slcrc0) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3418) implies: % 156.14/21.63 | (15) aElementOf0(xK, szNzAzT0) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3435) implies: % 156.14/21.63 | (16) isCountable0(xS) % 156.14/21.63 | (17) aSubsetOf0(xS, szNzAzT0) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3453) implies: % 156.14/21.63 | (18) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) % 156.14/21.63 | = v0 & slbdtsldtrb0(xS, xK) = v0 & $i(v1) & $i(v0) & aFunction0(xc) % 156.14/21.63 | & aSubsetOf0(v1, xT)) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3520) implies: % 156.14/21.63 | (19) ~ (xK = sz00) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3533) implies: % 156.14/21.63 | (20) $i(xK) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3623) implies: % 156.14/21.63 | (21) $i(sz00) % 156.14/21.63 | (22) $i(xS) % 156.14/21.63 | (23) sdtlpdtrp0(xN, sz00) = xS % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3671) implies: % 156.14/21.63 | (24) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) % 156.14/21.63 | | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3786) implies: % 156.14/21.63 | (25) aElementOf0(xj, szNzAzT0) % 156.14/21.63 | (26) aElementOf0(xi, szNzAzT0) % 156.14/21.63 | % 156.14/21.63 | ALPHA: (m__3786_02) implies: % 156.14/21.63 | (27) $i(szNzAzT0) % 156.14/21.64 | (28) ? [v0: $i] : ? [v1: $i] : ( ~ sdtlseqdt0(xj, xi) | ! [v2: $i] : ( ~ % 156.14/21.64 | (szszuzczcdt0(v2) = xi) | ~ $i(v2) | ~ aElementOf0(v2, % 156.14/21.64 | szNzAzT0)) | (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, xj) = v1 % 156.14/21.64 | & $i(v1) & $i(v0) & aSubsetOf0(v0, v1))) % 156.14/21.64 | % 156.14/21.64 | ALPHA: (m__) implies: % 156.14/21.64 | (29) $i(xj) % 156.38/21.64 | (30) $i(xi) % 156.38/21.64 | (31) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xN, xi) = v0 & sdtlpdtrp0(xN, % 156.38/21.64 | xj) = v1 & $i(v1) & $i(v0) & sdtlseqdt0(xj, xi) & ~ % 156.38/21.64 | aSubsetOf0(v0, v1)) % 156.38/21.64 | % 156.38/21.64 | ALPHA: (function-axioms) implies: % 156.38/21.64 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 156.38/21.64 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 156.38/21.64 | (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 156.38/21.64 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 156.38/21.64 | % 156.38/21.64 | DELTA: instantiating (31) with fresh symbols all_68_0, all_68_1 gives: % 156.38/21.64 | (34) sdtlpdtrp0(xN, xi) = all_68_1 & sdtlpdtrp0(xN, xj) = all_68_0 & % 156.38/21.64 | $i(all_68_0) & $i(all_68_1) & sdtlseqdt0(xj, xi) & ~ % 156.38/21.64 | aSubsetOf0(all_68_1, all_68_0) % 156.38/21.64 | % 156.38/21.64 | ALPHA: (34) implies: % 156.38/21.64 | (35) ~ aSubsetOf0(all_68_1, all_68_0) % 156.38/21.64 | (36) sdtlseqdt0(xj, xi) % 156.38/21.64 | (37) $i(all_68_0) % 156.38/21.64 | (38) sdtlpdtrp0(xN, xj) = all_68_0 % 156.38/21.64 | (39) sdtlpdtrp0(xN, xi) = all_68_1 % 156.38/21.64 | % 156.38/21.64 | DELTA: instantiating (18) with fresh symbols all_70_0, all_70_1 gives: % 156.38/21.64 | (40) sdtlcdtrc0(xc, all_70_1) = all_70_0 & szDzozmdt0(xc) = all_70_1 & % 156.38/21.64 | slbdtsldtrb0(xS, xK) = all_70_1 & $i(all_70_0) & $i(all_70_1) & % 156.38/21.64 | aFunction0(xc) & aSubsetOf0(all_70_0, xT) % 156.38/21.64 | % 156.38/21.64 | ALPHA: (40) implies: % 156.38/21.64 | (41) slbdtsldtrb0(xS, xK) = all_70_1 % 156.38/21.64 | % 156.38/21.64 | DELTA: instantiating (28) with fresh symbols all_72_0, all_72_1 gives: % 156.38/21.64 | (42) ~ sdtlseqdt0(xj, xi) | ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ % 156.38/21.64 | $i(v0) | ~ aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = % 156.38/21.64 | all_72_1 & sdtlpdtrp0(xN, xj) = all_72_0 & $i(all_72_0) & % 156.38/21.64 | $i(all_72_1) & aSubsetOf0(all_72_1, all_72_0)) % 156.38/21.64 | % 156.38/21.64 | BETA: splitting (42) gives: % 156.38/21.64 | % 156.38/21.64 | Case 1: % 156.38/21.64 | | % 156.38/21.64 | | (43) ~ sdtlseqdt0(xj, xi) % 156.38/21.64 | | % 156.38/21.64 | | PRED_UNIFY: (36), (43) imply: % 156.38/21.64 | | (44) $false % 156.38/21.64 | | % 156.38/21.64 | | CLOSE: (44) is inconsistent. % 156.38/21.64 | | % 156.38/21.64 | Case 2: % 156.38/21.64 | | % 156.38/21.65 | | (45) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~ % 156.38/21.65 | | aElementOf0(v0, szNzAzT0)) | (sdtlpdtrp0(xN, xi) = all_72_1 & % 156.38/21.65 | | sdtlpdtrp0(xN, xj) = all_72_0 & $i(all_72_0) & $i(all_72_1) & % 156.38/21.65 | | aSubsetOf0(all_72_1, all_72_0)) % 156.38/21.65 | | % 156.38/21.65 | | BETA: splitting (45) gives: % 156.38/21.65 | | % 156.38/21.65 | | Case 1: % 156.38/21.65 | | | % 156.38/21.65 | | | (46) ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = xi) | ~ $i(v0) | ~ % 156.38/21.65 | | | aElementOf0(v0, szNzAzT0)) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (8) with xj, simplifying with (25), (29) gives: % 156.38/21.65 | | | (47) xj = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) & % 156.38/21.65 | | | aElementOf0(v0, szNzAzT0)) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (8) with xi, simplifying with (26), (30) gives: % 156.38/21.65 | | | (48) xi = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) & % 156.38/21.65 | | | aElementOf0(v0, szNzAzT0)) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (4) with szNzAzT0, xS, simplifying with (5), % 156.38/21.65 | | | (17), (22), (27) gives: % 156.38/21.65 | | | (49) aSet0(xS) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (11) with sz00, sz00, slcrc0, simplifying with % 156.38/21.65 | | | (6), (10), (21) gives: % 156.38/21.65 | | | (50) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 & % 156.38/21.65 | | | szszuzczcdt0(sz00) = v0 & $i(v1) & $i(v0) & aElementOf0(sz00, % 156.38/21.65 | | | v1)) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (12) with sz00, slcrc0, simplifying with (6), % 156.38/21.65 | | | (10), (21) gives: % 156.38/21.65 | | | (51) sbrdtbr0(slcrc0) = sz00 % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (24) with xj, all_68_0, simplifying with (25), % 156.38/21.65 | | | (29), (38) gives: % 156.38/21.65 | | | (52) aSubsetOf0(all_68_0, szNzAzT0) % 156.38/21.65 | | | % 156.38/21.65 | | | DELTA: instantiating (50) with fresh symbols all_89_0, all_89_1 gives: % 156.38/21.65 | | | (53) slbdtrb0(all_89_1) = all_89_0 & szszuzczcdt0(sz00) = all_89_1 & % 156.38/21.65 | | | $i(all_89_0) & $i(all_89_1) & aElementOf0(sz00, all_89_0) % 156.38/21.65 | | | % 156.38/21.65 | | | ALPHA: (53) implies: % 156.38/21.65 | | | (54) aElementOf0(sz00, all_89_0) % 156.38/21.65 | | | (55) szszuzczcdt0(sz00) = all_89_1 % 156.38/21.65 | | | (56) slbdtrb0(all_89_1) = all_89_0 % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (13) with xS, xK, all_70_1, simplifying with % 156.38/21.65 | | | (15), (16), (20), (22), (41), (49) gives: % 156.38/21.65 | | | (57) xK = sz00 | isCountable0(all_70_1) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (4) with szNzAzT0, all_68_0, simplifying with % 156.38/21.65 | | | (5), (27), (37), (52) gives: % 156.38/21.65 | | | (58) aSet0(all_68_0) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (7) with sz00, all_89_1, simplifying with (6), % 156.38/21.65 | | | (21), (55) gives: % 156.38/21.65 | | | (59) aElementOf0(all_89_1, szNzAzT0) % 156.38/21.65 | | | % 156.38/21.65 | | | GROUND_INST: instantiating (mCardCons) with slcrc0, sz00, simplifying with % 156.38/21.65 | | | (1), (2), (14), (51) gives: % 156.38/21.66 | | | (60) ? [v0: $i] : (szszuzczcdt0(sz00) = v0 & $i(v0) & ! [v1: $i] : ! % 156.38/21.66 | | | [v2: $i] : ( ~ (sdtpldt0(slcrc0, v1) = v2) | ~ $i(v1) | ~ % 156.38/21.66 | | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, slcrc0))) % 156.38/21.66 | | | % 156.38/21.66 | | | DELTA: instantiating (60) with fresh symbol all_109_0 gives: % 156.38/21.66 | | | (61) szszuzczcdt0(sz00) = all_109_0 & $i(all_109_0) & ! [v0: $i] : ! % 156.38/21.66 | | | [v1: $i] : ( ~ (sdtpldt0(slcrc0, v0) = v1) | ~ $i(v0) | ~ % 156.38/21.66 | | | aElement0(v0) | sbrdtbr0(v1) = all_109_0 | aElementOf0(v0, % 156.38/21.66 | | | slcrc0)) % 156.38/21.66 | | | % 156.38/21.66 | | | ALPHA: (61) implies: % 156.38/21.66 | | | (62) $i(all_109_0) % 156.38/21.66 | | | (63) szszuzczcdt0(sz00) = all_109_0 % 156.38/21.66 | | | % 156.38/21.66 | | | BETA: splitting (57) gives: % 156.38/21.66 | | | % 156.38/21.66 | | | Case 1: % 156.38/21.66 | | | | % 156.38/21.66 | | | | % 156.38/21.66 | | | | GROUND_INST: instantiating (32) with all_89_1, all_109_0, sz00, % 156.38/21.66 | | | | simplifying with (55), (63) gives: % 156.38/21.66 | | | | (64) all_109_0 = all_89_1 % 156.38/21.66 | | | | % 156.38/21.66 | | | | REDUCE: (62), (64) imply: % 156.38/21.66 | | | | (65) $i(all_89_1) % 156.38/21.66 | | | | % 156.38/21.66 | | | | GROUND_INST: instantiating (3) with all_68_0, all_68_0, simplifying with % 156.38/21.66 | | | | (37), (58) gives: % 156.38/21.66 | | | | (66) aSubsetOf0(all_68_0, all_68_0) % 156.38/21.66 | | | | % 156.38/21.66 | | | | GROUND_INST: instantiating (11) with xi, all_89_1, all_89_0, simplifying % 156.38/21.66 | | | | with (26), (30), (56), (59), (65) gives: % 156.38/21.66 | | | | (67) ? [v0: $i] : ? [v1: $i] : ((all_89_1 = xi | aElementOf0(xi, % 156.38/21.66 | | | | all_89_0) | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_89_1) = % 156.38/21.66 | | | | v0 & $i(v1) & $i(v0) & ~ aElementOf0(xi, v1))) & (( ~ % 156.38/21.66 | | | | (all_89_1 = xi) & ~ aElementOf0(xi, all_89_0)) | % 156.38/21.66 | | | | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_89_1) = v0 & $i(v1) & % 156.38/21.66 | | | | $i(v0) & aElementOf0(xi, v1)))) % 156.38/21.66 | | | | % 156.38/21.66 | | | | DELTA: instantiating (67) with fresh symbols all_136_0, all_136_1 gives: % 156.38/21.66 | | | | (68) (all_89_1 = xi | aElementOf0(xi, all_89_0) | % 156.38/21.66 | | | | (slbdtrb0(all_136_1) = all_136_0 & szszuzczcdt0(all_89_1) = % 156.38/21.66 | | | | all_136_1 & $i(all_136_0) & $i(all_136_1) & ~ % 156.38/21.66 | | | | aElementOf0(xi, all_136_0))) & (( ~ (all_89_1 = xi) & ~ % 156.38/21.66 | | | | aElementOf0(xi, all_89_0)) | (slbdtrb0(all_136_1) = % 156.38/21.66 | | | | all_136_0 & szszuzczcdt0(all_89_1) = all_136_1 & % 156.38/21.66 | | | | $i(all_136_0) & $i(all_136_1) & aElementOf0(xi, all_136_0))) % 156.38/21.66 | | | | % 156.38/21.66 | | | | ALPHA: (68) implies: % 156.38/21.66 | | | | (69) ( ~ (all_89_1 = xi) & ~ aElementOf0(xi, all_89_0)) | % 156.38/21.66 | | | | (slbdtrb0(all_136_1) = all_136_0 & szszuzczcdt0(all_89_1) = % 156.38/21.66 | | | | all_136_1 & $i(all_136_0) & $i(all_136_1) & aElementOf0(xi, % 156.38/21.66 | | | | all_136_0)) % 156.38/21.66 | | | | % 156.38/21.66 | | | | BETA: splitting (48) gives: % 156.38/21.66 | | | | % 156.38/21.66 | | | | Case 1: % 156.38/21.66 | | | | | % 156.38/21.66 | | | | | (70) xi = sz00 % 156.38/21.66 | | | | | % 156.38/21.66 | | | | | REDUCE: (39), (70) imply: % 156.38/21.66 | | | | | (71) sdtlpdtrp0(xN, sz00) = all_68_1 % 156.38/21.66 | | | | | % 156.38/21.66 | | | | | REDUCE: (36), (70) imply: % 156.38/21.66 | | | | | (72) sdtlseqdt0(xj, sz00) % 156.38/21.66 | | | | | % 156.38/21.66 | | | | | BETA: splitting (69) gives: % 156.38/21.66 | | | | | % 156.38/21.66 | | | | | Case 1: % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | (73) ~ (all_89_1 = xi) & ~ aElementOf0(xi, all_89_0) % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | ALPHA: (73) implies: % 156.38/21.66 | | | | | | (74) ~ aElementOf0(xi, all_89_0) % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | REDUCE: (70), (74) imply: % 156.38/21.66 | | | | | | (75) ~ aElementOf0(sz00, all_89_0) % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | PRED_UNIFY: (54), (75) imply: % 156.38/21.66 | | | | | | (76) $false % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | CLOSE: (76) is inconsistent. % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | Case 2: % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | GROUND_INST: instantiating (33) with xS, all_68_1, sz00, xN, % 156.38/21.66 | | | | | | simplifying with (23), (71) gives: % 156.38/21.66 | | | | | | (77) all_68_1 = xS % 156.38/21.66 | | | | | | % 156.38/21.66 | | | | | | REDUCE: (35), (77) imply: % 156.38/21.67 | | | | | | (78) ~ aSubsetOf0(xS, all_68_0) % 156.38/21.67 | | | | | | % 156.38/21.67 | | | | | | BETA: splitting (47) gives: % 156.38/21.67 | | | | | | % 156.38/21.67 | | | | | | Case 1: % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | (79) xj = sz00 % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | REDUCE: (38), (79) imply: % 156.38/21.67 | | | | | | | (80) sdtlpdtrp0(xN, sz00) = all_68_0 % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | GROUND_INST: instantiating (33) with xS, all_68_0, sz00, xN, % 156.38/21.67 | | | | | | | simplifying with (23), (80) gives: % 156.38/21.67 | | | | | | | (81) all_68_0 = xS % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | REDUCE: (66), (81) imply: % 156.38/21.67 | | | | | | | (82) aSubsetOf0(xS, xS) % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | REDUCE: (78), (81) imply: % 156.38/21.67 | | | | | | | (83) ~ aSubsetOf0(xS, xS) % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | PRED_UNIFY: (82), (83) imply: % 156.38/21.67 | | | | | | | (84) $false % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | CLOSE: (84) is inconsistent. % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | Case 2: % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | (85) ? [v0: $i] : (szszuzczcdt0(v0) = xj & $i(v0) & % 156.38/21.67 | | | | | | | aElementOf0(v0, szNzAzT0)) % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | DELTA: instantiating (85) with fresh symbol all_336_0 gives: % 156.38/21.67 | | | | | | | (86) szszuzczcdt0(all_336_0) = xj & $i(all_336_0) & % 156.38/21.67 | | | | | | | aElementOf0(all_336_0, szNzAzT0) % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | ALPHA: (86) implies: % 156.38/21.67 | | | | | | | (87) aElementOf0(all_336_0, szNzAzT0) % 156.38/21.67 | | | | | | | (88) $i(all_336_0) % 156.38/21.67 | | | | | | | (89) szszuzczcdt0(all_336_0) = xj % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | GROUND_INST: instantiating (9) with all_336_0, xj, simplifying % 156.38/21.67 | | | | | | | with (72), (87), (88), (89) gives: % 156.38/21.67 | | | | | | | (90) $false % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | | CLOSE: (90) is inconsistent. % 156.38/21.67 | | | | | | | % 156.38/21.67 | | | | | | End of split % 156.38/21.67 | | | | | | % 156.38/21.67 | | | | | End of split % 156.38/21.67 | | | | | % 156.38/21.67 | | | | Case 2: % 156.38/21.67 | | | | | % 156.38/21.67 | | | | | (91) ? [v0: $i] : (szszuzczcdt0(v0) = xi & $i(v0) & % 156.38/21.67 | | | | | aElementOf0(v0, szNzAzT0)) % 156.38/21.67 | | | | | % 156.38/21.67 | | | | | DELTA: instantiating (91) with fresh symbol all_304_0 gives: % 156.38/21.67 | | | | | (92) szszuzczcdt0(all_304_0) = xi & $i(all_304_0) & % 156.38/21.67 | | | | | aElementOf0(all_304_0, szNzAzT0) % 156.38/21.67 | | | | | % 156.38/21.67 | | | | | ALPHA: (92) implies: % 156.38/21.67 | | | | | (93) aElementOf0(all_304_0, szNzAzT0) % 156.38/21.67 | | | | | (94) $i(all_304_0) % 156.38/21.67 | | | | | (95) szszuzczcdt0(all_304_0) = xi % 156.38/21.67 | | | | | % 156.38/21.67 | | | | | GROUND_INST: instantiating (46) with all_304_0, simplifying with (93), % 156.38/21.67 | | | | | (94), (95) gives: % 156.38/21.67 | | | | | (96) $false % 156.38/21.67 | | | | | % 156.38/21.67 | | | | | CLOSE: (96) is inconsistent. % 156.38/21.67 | | | | | % 156.38/21.67 | | | | End of split % 156.38/21.67 | | | | % 156.38/21.67 | | | Case 2: % 156.38/21.67 | | | | % 156.38/21.67 | | | | (97) xK = sz00 % 156.38/21.67 | | | | % 156.38/21.67 | | | | REDUCE: (19), (97) imply: % 156.38/21.67 | | | | (98) $false % 156.38/21.67 | | | | % 156.38/21.67 | | | | CLOSE: (98) is inconsistent. % 156.38/21.67 | | | | % 156.38/21.67 | | | End of split % 156.38/21.67 | | | % 156.38/21.67 | | Case 2: % 156.38/21.67 | | | % 156.38/21.67 | | | (99) sdtlpdtrp0(xN, xi) = all_72_1 & sdtlpdtrp0(xN, xj) = all_72_0 & % 156.38/21.67 | | | $i(all_72_0) & $i(all_72_1) & aSubsetOf0(all_72_1, all_72_0) % 156.38/21.67 | | | % 156.38/21.67 | | | ALPHA: (99) implies: % 156.38/21.67 | | | (100) aSubsetOf0(all_72_1, all_72_0) % 156.38/21.67 | | | (101) sdtlpdtrp0(xN, xj) = all_72_0 % 156.38/21.67 | | | (102) sdtlpdtrp0(xN, xi) = all_72_1 % 156.38/21.67 | | | % 156.38/21.67 | | | GROUND_INST: instantiating (33) with all_68_0, all_72_0, xj, xN, % 156.38/21.67 | | | simplifying with (38), (101) gives: % 156.38/21.67 | | | (103) all_72_0 = all_68_0 % 156.38/21.67 | | | % 156.38/21.67 | | | GROUND_INST: instantiating (33) with all_68_1, all_72_1, xi, xN, % 156.38/21.67 | | | simplifying with (39), (102) gives: % 156.38/21.67 | | | (104) all_72_1 = all_68_1 % 156.38/21.67 | | | % 156.38/21.67 | | | REDUCE: (100), (103), (104) imply: % 156.38/21.67 | | | (105) aSubsetOf0(all_68_1, all_68_0) % 156.38/21.67 | | | % 156.38/21.67 | | | PRED_UNIFY: (35), (105) imply: % 156.38/21.67 | | | (106) $false % 156.38/21.67 | | | % 156.38/21.67 | | | CLOSE: (106) is inconsistent. % 156.38/21.67 | | | % 156.38/21.67 | | End of split % 156.38/21.67 | | % 156.38/21.67 | End of split % 156.38/21.67 | % 156.38/21.67 End of proof % 156.38/21.68 % SZS output end Proof for theBenchmark % 156.38/21.68 % 156.38/21.68 21061ms %------------------------------------------------------------------------------