%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM604+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 11:48:54 EDT 2023 % Result : Theorem 110.37s 15.40s % Output : Proof 110.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM604+1 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n012.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 15:30:26 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.62 ________ _____ % 0.19/0.62 ___ __ \_________(_)________________________________ % 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.62 % 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.62 (2023-06-19) % 0.19/0.62 % 0.19/0.62 (c) Philipp Rümmer, 2009-2023 % 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.62 Amanda Stjerna. % 0.19/0.62 Free software under BSD-3-Clause. % 0.19/0.62 % 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.62 % 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.63 Running up to 7 provers in parallel. % 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 5.93/1.60 Prover 4: Preprocessing ... % 5.93/1.60 Prover 1: Preprocessing ... % 6.13/1.64 Prover 0: Preprocessing ... % 6.13/1.64 Prover 2: Preprocessing ... % 6.13/1.64 Prover 3: Preprocessing ... % 6.13/1.64 Prover 5: Preprocessing ... % 6.13/1.64 Prover 6: Preprocessing ... % 15.64/2.91 Prover 1: Constructing countermodel ... % 15.89/2.95 Prover 3: Constructing countermodel ... % 15.89/2.97 Prover 6: Proving ... % 16.48/3.05 Prover 5: Proving ... % 18.08/3.32 Prover 2: Proving ... % 21.50/3.78 Prover 4: Constructing countermodel ... % 22.89/3.95 Prover 0: Proving ... % 72.30/10.40 Prover 2: stopped % 72.30/10.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 73.57/10.56 Prover 7: Preprocessing ... % 76.00/10.87 Prover 7: Constructing countermodel ... % 99.73/13.98 Prover 5: stopped % 99.73/13.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.68/14.12 Prover 8: Preprocessing ... % 102.77/14.40 Prover 8: Warning: ignoring some quantifiers % 103.18/14.41 Prover 8: Constructing countermodel ... % 110.37/15.39 Prover 7: Found proof (size 125) % 110.37/15.39 Prover 7: proved (4958ms) % 110.37/15.39 Prover 6: stopped % 110.37/15.39 Prover 3: stopped % 110.37/15.39 Prover 8: stopped % 110.37/15.39 Prover 4: stopped % 110.37/15.40 Prover 1: stopped % 110.37/15.40 Prover 0: stopped % 110.37/15.40 % 110.37/15.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 110.37/15.40 % 110.77/15.41 % SZS output start Proof for theBenchmark % 110.77/15.42 Assumptions after simplification: % 110.77/15.42 --------------------------------- % 110.77/15.42 % 110.77/15.42 (mCountNFin_01) % 110.77/15.42 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 110.77/15.42 % 110.77/15.42 (mDefEmp) % 110.77/15.43 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 110.77/15.43 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 110.77/15.43 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 110.77/15.43 % 110.77/15.43 (mDefMin) % 110.77/15.45 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 % 110.77/15.45 | v0 = slcrc0 | ~ (szmzizndt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ % 110.77/15.45 aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v2, v0) | ? [v3: $i] : ($i(v3) & % 110.77/15.45 aElementOf0(v3, v0) & ~ sdtlseqdt0(v2, v3))) & ! [v0: $i] : ! [v1: $i] % 110.77/15.45 : ! [v2: $i] : (v0 = slcrc0 | ~ (szmzizndt0(v0) = v1) | ~ $i(v2) | ~ % 110.77/15.45 $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v2, v0) | % 110.77/15.45 sdtlseqdt0(v1, v2)) & ! [v0: $i] : ! [v1: $i] : (v0 = slcrc0 | ~ % 110.77/15.45 (szmzizndt0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v0, szNzAzT0) % 110.77/15.45 | aElementOf0(v1, v0)) % 110.77/15.45 % 110.77/15.45 (mDefSeg) % 110.77/15.46 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 110.77/15.46 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 110.77/15.46 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ % 110.77/15.46 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 110.77/15.46 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 110.77/15.46 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 110.77/15.46 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 110.77/15.46 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 110.77/15.46 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 110.77/15.46 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 110.77/15.46 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~ % 110.77/15.46 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: % 110.77/15.46 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 110.77/15.46 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 110.77/15.46 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, % 110.77/15.46 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( % 110.77/15.46 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 110.77/15.46 | aSet0(v1)) % 110.77/15.46 % 110.77/15.46 (mDefSub) % 110.77/15.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 110.77/15.46 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 110.77/15.46 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 110.77/15.46 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 110.77/15.46 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 110.77/15.46 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 110.77/15.46 % 110.77/15.46 (mDirichlet) % 110.77/15.46 ! [v0: $i] : ! [v1: $i] : ( ~ (szDzizrdt0(v0) = v1) | ~ $i(v0) | ~ % 110.77/15.46 aFunction0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ((sdtlbdtrb0(v0, % 110.77/15.46 v1) = v4 & $i(v4) & isCountable0(v4) & aElement0(v1)) | % 110.77/15.46 (szDzozmdt0(v0) = v2 & $i(v2) & ( ~ isCountable0(v2) | (sdtlcdtrc0(v0, v2) % 110.77/15.46 = v3 & $i(v3) & ~ isFinite0(v3)))))) & ! [v0: $i] : ! [v1: $i] : % 110.77/15.46 ( ~ (szDzozmdt0(v0) = v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ % 110.77/15.46 isCountable0(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 110.77/15.46 ((szDzizrdt0(v0) = v3 & sdtlbdtrb0(v0, v3) = v4 & $i(v4) & $i(v3) & % 110.77/15.46 isCountable0(v4) & aElement0(v3)) | (sdtlcdtrc0(v0, v1) = v2 & $i(v2) & % 110.77/15.46 ~ isFinite0(v2)))) % 110.77/15.46 % 110.77/15.46 (mImgRng) % 110.77/15.46 ! [v0: $i] : ! [v1: $i] : ( ~ (szDzozmdt0(v0) = v1) | ~ $i(v0) | ~ % 110.77/15.46 aFunction0(v0) | ? [v2: $i] : (sdtlcdtrc0(v0, v1) = v2 & $i(v2) & ! [v3: % 110.77/15.46 $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(v0, v3) = v4) | ~ $i(v3) | ~ % 110.77/15.46 aElementOf0(v3, v1) | aElementOf0(v4, v2)))) % 110.77/15.46 % 110.77/15.46 (mNATSet) % 110.77/15.46 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 110.77/15.46 % 110.77/15.46 (mSegZero) % 110.77/15.46 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 110.77/15.46 % 110.77/15.46 (mSubFSet) % 110.77/15.46 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) | % 110.77/15.46 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) % 110.77/15.46 % 110.77/15.46 (mZeroNum) % 110.77/15.46 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 110.77/15.46 % 110.77/15.46 (m__) % 110.77/15.47 $i(xx) & $i(xS) & ~ aElementOf0(xx, xS) % 110.77/15.47 % 110.77/15.47 (m__3291) % 110.77/15.47 $i(xT) & isFinite0(xT) & aSet0(xT) % 110.77/15.47 % 110.77/15.47 (m__3435) % 110.77/15.47 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) % 110.77/15.47 % 110.77/15.47 (m__3623) % 110.77/15.47 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 110.77/15.47 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~ % 110.77/15.47 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 110.77/15.47 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] % 110.77/15.47 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v2) = v3 & szmzizndt0(v1) = v4 % 110.77/15.47 & szszuzczcdt0(v0) = v2 & sdtmndt0(v1, v4) = v5 & $i(v5) & $i(v4) & $i(v3) % 110.77/15.47 & $i(v2) & aSubsetOf0(v3, v5) & isCountable0(v3))) & ! [v0: $i] : ! [v1: % 110.77/15.47 $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 110.77/15.47 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, % 110.77/15.47 v0) = v2 & $i(v2) & ( ~ aSubsetOf0(v2, szNzAzT0) | ~ isCountable0(v2) | % 110.77/15.47 (sdtlpdtrp0(xN, v1) = v3 & szmzizndt0(v2) = v4 & sdtmndt0(v2, v4) = v5 & % 110.77/15.47 $i(v5) & $i(v4) & $i(v3) & aSubsetOf0(v3, v5) & isCountable0(v3))))) % 110.77/15.47 % 110.77/15.47 (m__3671) % 110.77/15.47 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 110.77/15.47 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 110.77/15.47 & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ % 110.77/15.47 aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 110.77/15.47 % 110.77/15.47 (m__4660) % 110.77/15.47 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) & % 110.77/15.47 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~ % 110.77/15.47 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 110.77/15.47 szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 110.77/15.47 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? % 110.77/15.47 [v2: $i] : (sdtlpdtrp0(xe, v0) = v2 & szmzizndt0(v1) = v2 & $i(v2))) % 110.77/15.47 % 110.77/15.47 (m__4730) % 110.77/15.48 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) & % 110.77/15.48 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | % 110.77/15.48 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 110.77/15.48 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 110.77/15.48 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 110.77/15.48 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~ % 110.77/15.48 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~ % 110.77/15.48 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) % 110.77/15.48 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 110.77/15.48 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3 % 110.77/15.48 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) & % 110.77/15.48 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ % 110.77/15.48 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~ % 110.77/15.48 aSet0(v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | % 110.77/15.48 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ? % 110.77/15.48 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v4 & sdtlpdtrp0(xC, v0) = v5 % 110.77/15.48 & sdtlpdtrp0(xN, v1) = v2 & slbdtsldtrb0(v2, xk) = v3 & $i(v5) & $i(v4) & % 110.77/15.48 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v4 | ~ % 110.77/15.48 (sdtlpdtrp0(v5, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v3) | ~ % 110.77/15.48 aSet0(v6)))) % 110.77/15.48 % 110.77/15.48 (m__4758) % 110.77/15.48 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & % 110.77/15.48 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT)) % 110.77/15.48 % 110.77/15.48 (m__4854) % 110.77/15.48 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 110.77/15.48 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) & % 110.77/15.48 aElementOf0(v0, xT)) % 110.77/15.48 % 110.77/15.48 (m__4891) % 110.77/15.48 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & % 110.77/15.48 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & % 110.77/15.48 aSet0(xO)) % 110.77/15.48 % 110.77/15.48 (m__4908) % 110.77/15.48 $i(xO) & isCountable0(xO) & aSet0(xO) % 110.77/15.48 % 110.77/15.48 (m__4982) % 110.77/15.48 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] : % 110.77/15.48 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] % 110.77/15.48 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = % 110.77/15.48 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 110.77/15.48 % 110.77/15.48 (m__5009) % 110.77/15.48 $i(xx) & $i(xO) & aElementOf0(xx, xO) % 110.77/15.48 % 110.77/15.48 (m__5034) % 110.77/15.48 sdtlpdtrp0(xe, xi) = xx & $i(xi) & $i(xx) & $i(xe) & $i(szNzAzT0) & % 110.77/15.48 aElementOf0(xi, szNzAzT0) % 110.77/15.48 % 110.77/15.48 (m__5045) % 110.77/15.48 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) & % 110.77/15.48 aSubsetOf0(v0, xS)) % 110.77/15.48 % 110.77/15.48 (function-axioms) % 110.77/15.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 110.77/15.49 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 110.77/15.49 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 110.77/15.49 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 110.77/15.49 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 110.77/15.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 110.77/15.49 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 110.77/15.49 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 110.77/15.49 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 110.77/15.49 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 110.77/15.49 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 110.77/15.49 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 110.77/15.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 110.77/15.49 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 110.77/15.49 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 110.77/15.49 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 110.77/15.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 110.77/15.49 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 110.77/15.49 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 110.77/15.49 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 110.77/15.49 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 110.77/15.49 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 110.77/15.49 v0)) % 110.77/15.49 % 110.77/15.49 Further assumptions not needed in the proof: % 110.77/15.49 -------------------------------------------- % 110.77/15.49 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 110.77/15.49 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, % 110.77/15.49 mDefDiff, mDefMax, mDefPtt, mDefRst, mDefSImg, mDefSel, mDiffCons, mDomSet, % 110.77/15.49 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, % 110.77/15.49 mFunSort, mIH, mIHSort, mImgCount, mImgElm, mLessASymm, mLessRefl, mLessRel, % 110.77/15.49 mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, % 110.77/15.49 mPttSet, mSegFin, mSegLess, mSegSucc, mSelCSet, mSelExtra, mSelFSet, mSelNSet, % 110.77/15.49 mSelSub, mSetSort, mSubASymm, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, % 110.77/15.49 mSuccNum, mZeroLess, m__3398, m__3418, m__3453, m__3462, m__3520, m__3533, % 110.77/15.49 m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411, m__4618 % 110.77/15.49 % 110.77/15.49 Those formulas are unsatisfiable: % 110.77/15.49 --------------------------------- % 110.77/15.49 % 110.77/15.49 Begin of proof % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mDefEmp) implies: % 110.77/15.49 | (1) aSet0(slcrc0) % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mCountNFin_01) implies: % 110.77/15.49 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mDefSub) implies: % 110.77/15.49 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, % 110.77/15.49 | v0) | ~ aSet0(v0) | aSet0(v1)) % 110.77/15.49 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 110.77/15.49 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 110.77/15.49 | aSet0(v0) | aElementOf0(v2, v0)) % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mNATSet) implies: % 110.77/15.49 | (5) aSet0(szNzAzT0) % 110.77/15.49 | (6) isCountable0(szNzAzT0) % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mZeroNum) implies: % 110.77/15.49 | (7) aElementOf0(sz00, szNzAzT0) % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mDefMin) implies: % 110.77/15.49 | (8) ! [v0: $i] : ! [v1: $i] : (v0 = slcrc0 | ~ (szmzizndt0(v0) = v1) | % 110.77/15.49 | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v0, szNzAzT0) | aElementOf0(v1, % 110.77/15.49 | v0)) % 110.77/15.49 | % 110.77/15.49 | ALPHA: (mDefSeg) implies: % 110.77/15.49 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = % 110.77/15.49 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ % 110.77/15.49 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3, % 110.77/15.49 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 & % 110.77/15.49 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) | % 110.77/15.49 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) & % 110.77/15.49 | aElementOf0(v3, szNzAzT0))))) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (mSegZero) implies: % 110.77/15.50 | (10) slbdtrb0(sz00) = slcrc0 % 110.77/15.50 | % 110.77/15.50 | ALPHA: (mDirichlet) implies: % 110.77/15.50 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (szDzozmdt0(v0) = v1) | ~ $i(v0) | ~ % 110.77/15.50 | aFunction0(v0) | ~ isCountable0(v1) | ? [v2: $i] : ? [v3: $i] : % 110.77/15.50 | ? [v4: $i] : ((szDzizrdt0(v0) = v3 & sdtlbdtrb0(v0, v3) = v4 & % 110.77/15.50 | $i(v4) & $i(v3) & isCountable0(v4) & aElement0(v3)) | % 110.77/15.50 | (sdtlcdtrc0(v0, v1) = v2 & $i(v2) & ~ isFinite0(v2)))) % 110.77/15.50 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (szDzizrdt0(v0) = v1) | ~ $i(v0) | ~ % 110.77/15.50 | aFunction0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 110.77/15.50 | ((sdtlbdtrb0(v0, v1) = v4 & $i(v4) & isCountable0(v4) & % 110.77/15.50 | aElement0(v1)) | (szDzozmdt0(v0) = v2 & $i(v2) & ( ~ % 110.77/15.50 | isCountable0(v2) | (sdtlcdtrc0(v0, v2) = v3 & $i(v3) & ~ % 110.77/15.50 | isFinite0(v3)))))) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__3291) implies: % 110.77/15.50 | (13) aSet0(xT) % 110.77/15.50 | (14) isFinite0(xT) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__3435) implies: % 110.77/15.50 | (15) aSubsetOf0(xS, szNzAzT0) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__3623) implies: % 110.77/15.50 | (16) $i(sz00) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__3671) implies: % 110.77/15.50 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) % 110.77/15.50 | | ~ aElementOf0(v0, szNzAzT0) | isCountable0(v1)) % 110.77/15.50 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) % 110.77/15.50 | | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4660) implies: % 110.77/15.50 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) % 110.77/15.50 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xe, v0) = % 110.77/15.50 | v2 & szmzizndt0(v1) = v2 & $i(v2))) % 110.77/15.50 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) % 110.77/15.50 | | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = % 110.77/15.50 | v2 & szmzizndt0(v2) = v1 & $i(v2) & $i(v1))) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4730) implies: % 110.77/15.50 | (21) aFunction0(xd) % 110.77/15.50 | (22) szDzozmdt0(xd) = szNzAzT0 % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4758) implies: % 110.77/15.50 | (23) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) % 110.77/15.50 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT)) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4854) implies: % 110.77/15.50 | (24) $i(xT) % 110.77/15.50 | (25) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 110.77/15.50 | = v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT)) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4891) implies: % 110.77/15.50 | (26) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) % 110.77/15.50 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO)) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4908) implies: % 110.77/15.50 | (27) isCountable0(xO) % 110.77/15.50 | % 110.77/15.50 | ALPHA: (m__4982) implies: % 110.77/15.50 | (28) $i(xd) % 110.77/15.51 | (29) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) % 110.77/15.51 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ % 110.77/15.51 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 & % 110.77/15.51 | $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0)))) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (m__5009) implies: % 110.77/15.51 | (30) $i(xO) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (m__5034) implies: % 110.77/15.51 | (31) aElementOf0(xi, szNzAzT0) % 110.77/15.51 | (32) sdtlpdtrp0(xe, xi) = xx % 110.77/15.51 | % 110.77/15.51 | ALPHA: (m__5045) implies: % 110.77/15.51 | (33) $i(xi) % 110.77/15.51 | (34) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) & aSubsetOf0(v0, xS)) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (m__) implies: % 110.77/15.51 | (35) ~ aElementOf0(xx, xS) % 110.77/15.51 | (36) $i(xS) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (function-axioms) implies: % 110.77/15.51 | (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 110.77/15.51 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) % 110.77/15.51 | (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 110.77/15.51 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0)) % 110.77/15.51 | (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 110.77/15.51 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 110.77/15.51 | (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 110.77/15.51 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) % 110.77/15.51 | (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 110.77/15.51 | (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0)) % 110.77/15.51 | % 110.77/15.51 | DELTA: instantiating (34) with fresh symbol all_76_0 gives: % 110.77/15.51 | (42) sdtlpdtrp0(xN, xi) = all_76_0 & $i(all_76_0) & aSubsetOf0(all_76_0, % 110.77/15.51 | xS) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (42) implies: % 110.77/15.51 | (43) aSubsetOf0(all_76_0, xS) % 110.77/15.51 | (44) sdtlpdtrp0(xN, xi) = all_76_0 % 110.77/15.51 | % 110.77/15.51 | DELTA: instantiating (23) with fresh symbols all_78_0, all_78_1 gives: % 110.77/15.51 | (45) sdtlcdtrc0(xd, all_78_1) = all_78_0 & szDzozmdt0(xd) = all_78_1 & % 110.77/15.51 | $i(all_78_0) & $i(all_78_1) & aSubsetOf0(all_78_0, xT) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (45) implies: % 110.77/15.51 | (46) aSubsetOf0(all_78_0, xT) % 110.77/15.51 | (47) $i(all_78_1) % 110.77/15.51 | (48) $i(all_78_0) % 110.77/15.51 | (49) szDzozmdt0(xd) = all_78_1 % 110.77/15.51 | (50) sdtlcdtrc0(xd, all_78_1) = all_78_0 % 110.77/15.51 | % 110.77/15.51 | DELTA: instantiating (25) with fresh symbols all_80_0, all_80_1 gives: % 110.77/15.51 | (51) szDzizrdt0(xd) = all_80_1 & sdtlbdtrb0(xd, all_80_1) = all_80_0 & % 110.77/15.51 | $i(all_80_0) & $i(all_80_1) & isCountable0(all_80_0) & % 110.77/15.51 | aElementOf0(all_80_1, xT) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (51) implies: % 110.77/15.51 | (52) szDzizrdt0(xd) = all_80_1 % 110.77/15.51 | % 110.77/15.51 | DELTA: instantiating (26) with fresh symbols all_82_0, all_82_1 gives: % 110.77/15.51 | (53) szDzizrdt0(xd) = all_82_1 & sdtlcdtrc0(xe, all_82_0) = xO & % 110.77/15.51 | sdtlbdtrb0(xd, all_82_1) = all_82_0 & $i(all_82_0) & $i(all_82_1) & % 110.77/15.51 | aSet0(xO) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (53) implies: % 110.77/15.51 | (54) aSet0(xO) % 110.77/15.51 | (55) sdtlbdtrb0(xd, all_82_1) = all_82_0 % 110.77/15.51 | (56) szDzizrdt0(xd) = all_82_1 % 110.77/15.51 | % 110.77/15.51 | DELTA: instantiating (29) with fresh symbols all_86_0, all_86_1 gives: % 110.77/15.51 | (57) szDzizrdt0(xd) = all_86_1 & sdtlbdtrb0(xd, all_86_1) = all_86_0 & % 110.77/15.51 | $i(all_86_0) & $i(all_86_1) & ! [v0: $i] : ( ~ $i(v0) | ~ % 110.77/15.51 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 & % 110.77/15.51 | $i(v1) & aElementOf0(v1, all_86_0) & aElementOf0(v1, szNzAzT0))) % 110.77/15.51 | % 110.77/15.51 | ALPHA: (57) implies: % 110.77/15.51 | (58) sdtlbdtrb0(xd, all_86_1) = all_86_0 % 110.77/15.51 | (59) szDzizrdt0(xd) = all_86_1 % 110.77/15.51 | % 110.77/15.51 | BETA: splitting (2) gives: % 110.77/15.51 | % 110.77/15.52 | Case 1: % 110.77/15.52 | | % 110.77/15.52 | | (60) ~ isCountable0(slcrc0) % 110.77/15.52 | | % 110.77/15.52 | | GROUND_INST: instantiating (37) with szNzAzT0, all_78_1, xd, simplifying % 110.77/15.52 | | with (22), (49) gives: % 110.77/15.52 | | (61) all_78_1 = szNzAzT0 % 110.77/15.52 | | % 110.77/15.52 | | GROUND_INST: instantiating (40) with all_82_0, all_86_0, all_82_1, xd, % 110.77/15.52 | | simplifying with (55) gives: % 110.77/15.52 | | (62) all_86_0 = all_82_0 | ~ (sdtlbdtrb0(xd, all_82_1) = all_86_0) % 110.77/15.52 | | % 110.77/15.52 | | GROUND_INST: instantiating (38) with all_82_1, all_86_1, xd, simplifying % 110.77/15.52 | | with (56), (59) gives: % 110.77/15.52 | | (63) all_86_1 = all_82_1 % 110.77/15.52 | | % 110.77/15.52 | | GROUND_INST: instantiating (38) with all_80_1, all_86_1, xd, simplifying % 110.77/15.52 | | with (52), (59) gives: % 110.77/15.52 | | (64) all_86_1 = all_80_1 % 110.77/15.52 | | % 110.77/15.52 | | PRED_UNIFY: (27), (60) imply: % 110.77/15.52 | | (65) ~ (xO = slcrc0) % 110.77/15.52 | | % 110.77/15.52 | | COMBINE_EQS: (63), (64) imply: % 110.77/15.52 | | (66) all_82_1 = all_80_1 % 110.77/15.52 | | % 110.77/15.52 | | REDUCE: (50), (61) imply: % 110.77/15.52 | | (67) sdtlcdtrc0(xd, szNzAzT0) = all_78_0 % 110.77/15.52 | | % 110.77/15.52 | | REDUCE: (58), (64) imply: % 110.77/15.52 | | (68) sdtlbdtrb0(xd, all_80_1) = all_86_0 % 110.77/15.52 | | % 110.77/15.52 | | REDUCE: (47), (61) imply: % 110.77/15.52 | | (69) $i(szNzAzT0) % 110.77/15.52 | | % 110.77/15.52 | | BETA: splitting (62) gives: % 110.77/15.52 | | % 110.77/15.52 | | Case 1: % 110.77/15.52 | | | % 110.77/15.52 | | | (70) ~ (sdtlbdtrb0(xd, all_82_1) = all_86_0) % 110.77/15.52 | | | % 110.77/15.52 | | | REDUCE: (66), (70) imply: % 110.77/15.52 | | | (71) ~ (sdtlbdtrb0(xd, all_80_1) = all_86_0) % 110.77/15.52 | | | % 110.77/15.52 | | | PRED_UNIFY: (68), (71) imply: % 110.77/15.52 | | | (72) $false % 110.77/15.52 | | | % 110.77/15.52 | | | CLOSE: (72) is inconsistent. % 110.77/15.52 | | | % 110.77/15.52 | | Case 2: % 110.77/15.52 | | | % 110.77/15.52 | | | % 110.77/15.52 | | | GROUND_INST: instantiating (3) with szNzAzT0, xS, simplifying with (5), % 110.77/15.52 | | | (15), (36), (69) gives: % 110.77/15.52 | | | (73) aSet0(xS) % 110.77/15.52 | | | % 110.77/15.52 | | | GROUND_INST: instantiating (mSubFSet) with xT, all_78_0, simplifying with % 110.77/15.52 | | | (13), (14), (24), (46), (48) gives: % 110.77/15.52 | | | (74) isFinite0(all_78_0) % 110.77/15.52 | | | % 110.77/15.52 | | | GROUND_INST: instantiating (9) with sz00, slcrc0, xO, simplifying with % 110.77/15.52 | | | (7), (10), (16), (30), (54) gives: % 110.77/15.52 | | | (75) xO = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ % 110.77/15.52 | | | aElementOf0(v0, xO) | ~ aElementOf0(v0, szNzAzT0) | % 110.77/15.52 | | | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) & % 110.77/15.52 | | | (aElementOf0(v0, xO) | (szszuzczcdt0(v0) = v1 & $i(v1) & % 110.77/15.52 | | | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0)))) % 110.77/15.52 | | | % 110.77/15.52 | | | GROUND_INST: instantiating (11) with xd, szNzAzT0, simplifying with (6), % 110.77/15.52 | | | (21), (22), (28) gives: % 110.77/15.52 | | | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((szDzizrdt0(xd) = v1 & % 110.77/15.52 | | | sdtlbdtrb0(xd, v1) = v2 & $i(v2) & $i(v1) & isCountable0(v2) & % 110.77/15.52 | | | aElement0(v1)) | (sdtlcdtrc0(xd, szNzAzT0) = v0 & $i(v0) & ~ % 110.77/15.52 | | | isFinite0(v0))) % 110.77/15.52 | | | % 110.77/15.52 | | | GROUND_INST: instantiating (mImgRng) with xd, szNzAzT0, simplifying with % 110.77/15.52 | | | (21), (22), (28) gives: % 110.77/15.53 | | | (77) ? [v0: $i] : (sdtlcdtrc0(xd, szNzAzT0) = v0 & $i(v0) & ! [v1: % 110.77/15.53 | | | $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) % 110.77/15.53 | | | | ~ aElementOf0(v1, szNzAzT0) | aElementOf0(v2, v0))) % 110.77/15.53 | | | % 110.77/15.53 | | | GROUND_INST: instantiating (18) with xi, all_76_0, simplifying with (31), % 110.77/15.53 | | | (33), (44) gives: % 110.77/15.53 | | | (78) aSubsetOf0(all_76_0, szNzAzT0) % 110.77/15.53 | | | % 110.77/15.53 | | | GROUND_INST: instantiating (17) with xi, all_76_0, simplifying with (31), % 110.77/15.53 | | | (33), (44) gives: % 110.77/15.53 | | | (79) isCountable0(all_76_0) % 110.77/15.53 | | | % 110.77/15.53 | | | GROUND_INST: instantiating (19) with xi, all_76_0, simplifying with (31), % 110.77/15.53 | | | (33), (44) gives: % 110.77/15.53 | | | (80) ? [v0: $i] : (sdtlpdtrp0(xe, xi) = v0 & szmzizndt0(all_76_0) = v0 % 110.77/15.53 | | | & $i(v0)) % 110.77/15.53 | | | % 110.77/15.53 | | | GROUND_INST: instantiating (20) with xi, xx, simplifying with (31), (32), % 110.77/15.53 | | | (33) gives: % 110.77/15.53 | | | (81) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = xx & % 110.77/15.53 | | | $i(v0) & $i(xx)) % 110.77/15.53 | | | % 110.77/15.53 | | | GROUND_INST: instantiating (12) with xd, all_80_1, simplifying with (21), % 110.77/15.53 | | | (28), (52) gives: % 110.77/15.53 | | | (82) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((sdtlbdtrb0(xd, % 110.77/15.53 | | | all_80_1) = v2 & $i(v2) & isCountable0(v2) & % 110.77/15.53 | | | aElement0(all_80_1)) | (szDzozmdt0(xd) = v0 & $i(v0) & ( ~ % 110.77/15.53 | | | isCountable0(v0) | (sdtlcdtrc0(xd, v0) = v1 & $i(v1) & ~ % 110.77/15.53 | | | isFinite0(v1))))) % 110.77/15.53 | | | % 110.77/15.53 | | | DELTA: instantiating (80) with fresh symbol all_114_0 gives: % 110.77/15.53 | | | (83) sdtlpdtrp0(xe, xi) = all_114_0 & szmzizndt0(all_76_0) = all_114_0 % 110.77/15.53 | | | & $i(all_114_0) % 110.77/15.53 | | | % 110.77/15.53 | | | ALPHA: (83) implies: % 110.77/15.53 | | | (84) $i(all_114_0) % 110.77/15.53 | | | (85) szmzizndt0(all_76_0) = all_114_0 % 110.77/15.53 | | | (86) sdtlpdtrp0(xe, xi) = all_114_0 % 110.77/15.53 | | | % 110.77/15.53 | | | DELTA: instantiating (81) with fresh symbol all_118_0 gives: % 110.77/15.53 | | | (87) sdtlpdtrp0(xN, xi) = all_118_0 & szmzizndt0(all_118_0) = xx & % 110.77/15.53 | | | $i(all_118_0) & $i(xx) % 110.77/15.53 | | | % 110.77/15.53 | | | ALPHA: (87) implies: % 110.77/15.53 | | | (88) $i(all_118_0) % 110.77/15.53 | | | (89) sdtlpdtrp0(xN, xi) = all_118_0 % 110.77/15.53 | | | % 110.77/15.53 | | | DELTA: instantiating (77) with fresh symbol all_128_0 gives: % 110.77/15.53 | | | (90) sdtlcdtrc0(xd, szNzAzT0) = all_128_0 & $i(all_128_0) & ! [v0: $i] % 110.77/15.53 | | | : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 110.77/15.53 | | | aElementOf0(v0, szNzAzT0) | aElementOf0(v1, all_128_0)) % 110.77/15.53 | | | % 110.77/15.53 | | | ALPHA: (90) implies: % 110.77/15.53 | | | (91) sdtlcdtrc0(xd, szNzAzT0) = all_128_0 % 110.77/15.53 | | | % 110.77/15.53 | | | DELTA: instantiating (76) with fresh symbols all_141_0, all_141_1, % 110.77/15.53 | | | all_141_2 gives: % 110.77/15.53 | | | (92) (szDzizrdt0(xd) = all_141_1 & sdtlbdtrb0(xd, all_141_1) = % 110.77/15.53 | | | all_141_0 & $i(all_141_0) & $i(all_141_1) & % 110.77/15.53 | | | isCountable0(all_141_0) & aElement0(all_141_1)) | % 110.77/15.53 | | | (sdtlcdtrc0(xd, szNzAzT0) = all_141_2 & $i(all_141_2) & ~ % 110.77/15.53 | | | isFinite0(all_141_2)) % 110.77/15.53 | | | % 110.77/15.53 | | | DELTA: instantiating (82) with fresh symbols all_145_0, all_145_1, % 110.77/15.53 | | | all_145_2 gives: % 110.77/15.53 | | | (93) (sdtlbdtrb0(xd, all_80_1) = all_145_0 & $i(all_145_0) & % 110.77/15.53 | | | isCountable0(all_145_0) & aElement0(all_80_1)) | (szDzozmdt0(xd) % 110.77/15.53 | | | = all_145_2 & $i(all_145_2) & ( ~ isCountable0(all_145_2) | % 110.77/15.53 | | | (sdtlcdtrc0(xd, all_145_2) = all_145_1 & $i(all_145_1) & ~ % 110.77/15.53 | | | isFinite0(all_145_1)))) % 110.77/15.53 | | | % 110.77/15.53 | | | BETA: splitting (75) gives: % 110.77/15.53 | | | % 110.77/15.53 | | | Case 1: % 110.77/15.53 | | | | % 110.77/15.53 | | | | (94) xO = slcrc0 % 110.77/15.53 | | | | % 110.77/15.53 | | | | REDUCE: (65), (94) imply: % 110.77/15.53 | | | | (95) $false % 110.77/15.53 | | | | % 110.77/15.53 | | | | CLOSE: (95) is inconsistent. % 110.77/15.53 | | | | % 110.77/15.53 | | | Case 2: % 110.77/15.53 | | | | % 110.77/15.53 | | | | % 110.77/15.53 | | | | PRED_UNIFY: (60), (79) imply: % 110.77/15.53 | | | | (96) ~ (all_76_0 = slcrc0) % 110.77/15.53 | | | | % 110.77/15.53 | | | | GROUND_INST: instantiating (39) with all_76_0, all_118_0, xi, xN, % 110.77/15.53 | | | | simplifying with (44), (89) gives: % 110.77/15.53 | | | | (97) all_118_0 = all_76_0 % 110.77/15.53 | | | | % 110.77/15.53 | | | | GROUND_INST: instantiating (39) with xx, all_114_0, xi, xe, simplifying % 110.77/15.53 | | | | with (32), (86) gives: % 110.77/15.53 | | | | (98) all_114_0 = xx % 110.77/15.53 | | | | % 110.77/15.53 | | | | GROUND_INST: instantiating (41) with all_78_0, all_128_0, szNzAzT0, xd, % 110.77/15.53 | | | | simplifying with (67), (91) gives: % 110.77/15.53 | | | | (99) all_128_0 = all_78_0 % 110.77/15.53 | | | | % 110.77/15.53 | | | | REDUCE: (85), (98) imply: % 110.77/15.53 | | | | (100) szmzizndt0(all_76_0) = xx % 110.77/15.53 | | | | % 110.77/15.53 | | | | REDUCE: (88), (97) imply: % 110.77/15.53 | | | | (101) $i(all_76_0) % 110.77/15.53 | | | | % 110.77/15.53 | | | | REDUCE: (84), (98) imply: % 110.77/15.53 | | | | (102) $i(xx) % 110.77/15.53 | | | | % 110.77/15.53 | | | | BETA: splitting (92) gives: % 110.77/15.53 | | | | % 110.77/15.53 | | | | Case 1: % 110.77/15.53 | | | | | % 110.77/15.53 | | | | | (103) szDzizrdt0(xd) = all_141_1 & sdtlbdtrb0(xd, all_141_1) = % 110.77/15.53 | | | | | all_141_0 & $i(all_141_0) & $i(all_141_1) & % 110.77/15.53 | | | | | isCountable0(all_141_0) & aElement0(all_141_1) % 110.77/15.53 | | | | | % 110.77/15.53 | | | | | ALPHA: (103) implies: % 110.77/15.53 | | | | | (104) sdtlbdtrb0(xd, all_141_1) = all_141_0 % 110.77/15.53 | | | | | (105) szDzizrdt0(xd) = all_141_1 % 110.77/15.53 | | | | | % 110.77/15.53 | | | | | BETA: splitting (93) gives: % 110.77/15.53 | | | | | % 110.77/15.53 | | | | | Case 1: % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | (106) sdtlbdtrb0(xd, all_80_1) = all_145_0 & $i(all_145_0) & % 110.77/15.53 | | | | | | isCountable0(all_145_0) & aElement0(all_80_1) % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | ALPHA: (106) implies: % 110.77/15.53 | | | | | | (107) sdtlbdtrb0(xd, all_80_1) = all_145_0 % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | GROUND_INST: instantiating (40) with all_145_0, all_141_0, all_80_1, % 110.77/15.53 | | | | | | xd, simplifying with (107) gives: % 110.77/15.53 | | | | | | (108) all_145_0 = all_141_0 | ~ (sdtlbdtrb0(xd, all_80_1) = % 110.77/15.53 | | | | | | all_141_0) % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | GROUND_INST: instantiating (38) with all_80_1, all_141_1, xd, % 110.77/15.53 | | | | | | simplifying with (52), (105) gives: % 110.77/15.53 | | | | | | (109) all_141_1 = all_80_1 % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | REDUCE: (104), (109) imply: % 110.77/15.53 | | | | | | (110) sdtlbdtrb0(xd, all_80_1) = all_141_0 % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | BETA: splitting (108) gives: % 110.77/15.53 | | | | | | % 110.77/15.53 | | | | | | Case 1: % 110.77/15.53 | | | | | | | % 110.77/15.53 | | | | | | | (111) ~ (sdtlbdtrb0(xd, all_80_1) = all_141_0) % 110.77/15.53 | | | | | | | % 110.77/15.53 | | | | | | | PRED_UNIFY: (110), (111) imply: % 110.77/15.53 | | | | | | | (112) $false % 110.77/15.53 | | | | | | | % 110.77/15.54 | | | | | | | CLOSE: (112) is inconsistent. % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | Case 2: % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | GROUND_INST: instantiating (4) with xS, all_76_0, xx, simplifying % 110.77/15.54 | | | | | | | with (35), (36), (43), (73), (101), (102) gives: % 110.77/15.54 | | | | | | | (113) ~ aElementOf0(xx, all_76_0) % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | GROUND_INST: instantiating (8) with all_76_0, xx, simplifying with % 110.77/15.54 | | | | | | | (78), (100), (101), (102) gives: % 110.77/15.54 | | | | | | | (114) all_76_0 = slcrc0 | aElementOf0(xx, all_76_0) % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | BETA: splitting (114) gives: % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | Case 1: % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | | (115) aElementOf0(xx, all_76_0) % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | | PRED_UNIFY: (113), (115) imply: % 110.77/15.54 | | | | | | | | (116) $false % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | | CLOSE: (116) is inconsistent. % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | Case 2: % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | | (117) all_76_0 = slcrc0 % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | | REDUCE: (96), (117) imply: % 110.77/15.54 | | | | | | | | (118) $false % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | | CLOSE: (118) is inconsistent. % 110.77/15.54 | | | | | | | | % 110.77/15.54 | | | | | | | End of split % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | End of split % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | Case 2: % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | | (119) szDzozmdt0(xd) = all_145_2 & $i(all_145_2) & ( ~ % 110.77/15.54 | | | | | | isCountable0(all_145_2) | (sdtlcdtrc0(xd, all_145_2) = % 110.77/15.54 | | | | | | all_145_1 & $i(all_145_1) & ~ isFinite0(all_145_1))) % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | | ALPHA: (119) implies: % 110.77/15.54 | | | | | | (120) szDzozmdt0(xd) = all_145_2 % 110.77/15.54 | | | | | | (121) ~ isCountable0(all_145_2) | (sdtlcdtrc0(xd, all_145_2) = % 110.77/15.54 | | | | | | all_145_1 & $i(all_145_1) & ~ isFinite0(all_145_1)) % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | | GROUND_INST: instantiating (37) with szNzAzT0, all_145_2, xd, % 110.77/15.54 | | | | | | simplifying with (22), (120) gives: % 110.77/15.54 | | | | | | (122) all_145_2 = szNzAzT0 % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | | BETA: splitting (121) gives: % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | | Case 1: % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | (123) ~ isCountable0(all_145_2) % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | REDUCE: (122), (123) imply: % 110.77/15.54 | | | | | | | (124) ~ isCountable0(szNzAzT0) % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | PRED_UNIFY: (6), (124) imply: % 110.77/15.54 | | | | | | | (125) $false % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | CLOSE: (125) is inconsistent. % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | Case 2: % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | (126) sdtlcdtrc0(xd, all_145_2) = all_145_1 & $i(all_145_1) & % 110.77/15.54 | | | | | | | ~ isFinite0(all_145_1) % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | ALPHA: (126) implies: % 110.77/15.54 | | | | | | | (127) ~ isFinite0(all_145_1) % 110.77/15.54 | | | | | | | (128) sdtlcdtrc0(xd, all_145_2) = all_145_1 % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | REDUCE: (122), (128) imply: % 110.77/15.54 | | | | | | | (129) sdtlcdtrc0(xd, szNzAzT0) = all_145_1 % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | GROUND_INST: instantiating (41) with all_78_0, all_145_1, % 110.77/15.54 | | | | | | | szNzAzT0, xd, simplifying with (67), (129) gives: % 110.77/15.54 | | | | | | | (130) all_145_1 = all_78_0 % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | PRED_UNIFY: (74), (127) imply: % 110.77/15.54 | | | | | | | (131) ~ (all_145_1 = all_78_0) % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | REDUCE: (130), (131) imply: % 110.77/15.54 | | | | | | | (132) $false % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | | CLOSE: (132) is inconsistent. % 110.77/15.54 | | | | | | | % 110.77/15.54 | | | | | | End of split % 110.77/15.54 | | | | | | % 110.77/15.54 | | | | | End of split % 110.77/15.54 | | | | | % 110.77/15.54 | | | | Case 2: % 110.77/15.54 | | | | | % 110.77/15.54 | | | | | (133) sdtlcdtrc0(xd, szNzAzT0) = all_141_2 & $i(all_141_2) & ~ % 110.77/15.54 | | | | | isFinite0(all_141_2) % 110.77/15.54 | | | | | % 110.77/15.54 | | | | | ALPHA: (133) implies: % 110.77/15.54 | | | | | (134) ~ isFinite0(all_141_2) % 110.77/15.54 | | | | | (135) sdtlcdtrc0(xd, szNzAzT0) = all_141_2 % 110.77/15.54 | | | | | % 110.77/15.54 | | | | | GROUND_INST: instantiating (41) with all_78_0, all_141_2, szNzAzT0, % 110.77/15.54 | | | | | xd, simplifying with (67), (135) gives: % 110.77/15.54 | | | | | (136) all_141_2 = all_78_0 % 110.77/15.54 | | | | | % 110.77/15.54 | | | | | PRED_UNIFY: (74), (134) imply: % 110.77/15.54 | | | | | (137) ~ (all_141_2 = all_78_0) % 110.77/15.54 | | | | | % 110.77/15.54 | | | | | REDUCE: (136), (137) imply: % 110.77/15.54 | | | | | (138) $false % 110.77/15.54 | | | | | % 110.77/15.54 | | | | | CLOSE: (138) is inconsistent. % 110.77/15.54 | | | | | % 110.77/15.54 | | | | End of split % 110.77/15.54 | | | | % 110.77/15.54 | | | End of split % 110.77/15.54 | | | % 110.77/15.54 | | End of split % 110.77/15.54 | | % 110.77/15.54 | Case 2: % 110.77/15.54 | | % 110.77/15.54 | | (139) ~ aSet0(slcrc0) % 110.77/15.54 | | % 110.77/15.54 | | PRED_UNIFY: (1), (139) imply: % 110.77/15.54 | | (140) $false % 110.77/15.54 | | % 110.77/15.54 | | CLOSE: (140) is inconsistent. % 110.77/15.54 | | % 110.77/15.54 | End of split % 110.77/15.54 | % 110.77/15.54 End of proof % 110.77/15.54 % SZS output end Proof for theBenchmark % 110.77/15.54 % 110.77/15.54 14920ms %------------------------------------------------------------------------------