%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM564+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 : n028.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 11:48:38 EDT 2023 % Result : Theorem 29.87s 4.90s % Output : Proof 247.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM564+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 : n028.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 09:28:35 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.61 Amanda Stjerna. % 0.19/0.61 Free software under BSD-3-Clause. % 0.19/0.61 % 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.61 % 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.62 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.23/1.32 Prover 1: Preprocessing ... % 4.23/1.32 Prover 4: Preprocessing ... % 4.23/1.37 Prover 5: Preprocessing ... % 4.23/1.37 Prover 3: Preprocessing ... % 4.23/1.38 Prover 0: Preprocessing ... % 4.23/1.38 Prover 6: Preprocessing ... % 4.23/1.39 Prover 2: Preprocessing ... % 12.95/2.49 Prover 1: Constructing countermodel ... % 13.32/2.64 Prover 6: Proving ... % 13.32/2.66 Prover 3: Constructing countermodel ... % 13.32/2.71 Prover 5: Proving ... % 15.78/2.90 Prover 2: Proving ... % 19.98/3.48 Prover 4: Constructing countermodel ... % 20.94/3.60 Prover 0: Proving ... % 29.87/4.89 Prover 3: proved (4259ms) % 29.87/4.89 % 29.87/4.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 29.87/4.90 % 29.87/4.90 Prover 2: stopped % 29.87/4.90 Prover 6: stopped % 29.87/4.90 Prover 5: stopped % 30.93/4.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 30.93/4.93 Prover 0: stopped % 30.93/4.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 30.93/4.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 30.93/4.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 30.93/4.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 32.18/5.09 Prover 8: Preprocessing ... % 32.18/5.09 Prover 7: Preprocessing ... % 32.18/5.11 Prover 11: Preprocessing ... % 32.18/5.11 Prover 10: Preprocessing ... % 32.18/5.15 Prover 13: Preprocessing ... % 33.95/5.31 Prover 10: Constructing countermodel ... % 33.95/5.34 Prover 7: Constructing countermodel ... % 33.95/5.35 Prover 8: Warning: ignoring some quantifiers % 33.95/5.36 Prover 8: Constructing countermodel ... % 34.52/5.48 Prover 13: Warning: ignoring some quantifiers % 34.52/5.50 Prover 13: Constructing countermodel ... % 39.54/6.09 Prover 11: Constructing countermodel ... % 69.74/10.07 Prover 13: stopped % 70.29/10.07 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 70.29/10.14 Prover 16: Preprocessing ... % 71.28/10.27 Prover 16: Warning: ignoring some quantifiers % 71.28/10.28 Prover 16: Constructing countermodel ... % 111.60/15.61 Prover 16: stopped % 111.60/15.63 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 112.14/15.75 Prover 19: Preprocessing ... % 114.82/15.99 Prover 1: stopped % 114.82/16.00 Prover 19: Warning: ignoring some quantifiers % 114.82/16.01 Prover 19: Constructing countermodel ... % 137.24/19.36 Prover 19: stopped % 186.50/27.70 Prover 7: stopped % 187.34/27.96 Prover 4: stopped % 228.99/38.94 Prover 11: stopped % 230.58/39.68 Prover 8: stopped % 247.02/54.12 Prover 10: Found proof (size 117) % 247.02/54.12 Prover 10: proved (49204ms) % 247.02/54.12 % 247.02/54.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 247.02/54.12 % 247.15/54.13 % SZS output start Proof for theBenchmark % 247.15/54.13 Assumptions after simplification: % 247.15/54.13 --------------------------------- % 247.15/54.13 % 247.15/54.13 (mCardCons) % 247.15/54.16 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 247.15/54.16 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2) % 247.15/54.16 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~ % 247.15/54.16 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0)))) % 247.15/54.16 % 247.15/54.16 (mCardEmpty) % 247.15/54.17 $i(sz00) & $i(slcrc0) & ! [v0: $i] : (v0 = sz00 | ~ (sbrdtbr0(slcrc0) = v0) % 247.15/54.17 | ~ aSet0(slcrc0)) & ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) % 247.15/54.17 | ~ $i(v0) | ~ aSet0(v0)) % 247.15/54.17 % 247.15/54.17 (mCardSeg) % 247.15/54.17 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) % 247.15/54.17 | ~ aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0) % 247.15/54.17 % 247.15/54.17 (mCardSubEx) % 247.15/54.17 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = % 247.15/54.17 v2) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ isFinite0(v0) | % 247.15/54.17 ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | ? [v3: $i] : (sbrdtbr0(v3) = % 247.15/54.17 v1 & $i(v3) & aSubsetOf0(v3, v0))) % 247.15/54.17 % 247.15/54.17 (mDefEmp) % 247.15/54.17 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 247.15/54.17 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 247.15/54.17 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 247.15/54.17 % 247.15/54.17 (mDefSeg) % 247.15/54.18 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 247.15/54.18 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 247.15/54.18 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ % 247.15/54.18 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 247.15/54.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 247.15/54.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 247.15/54.18 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 247.15/54.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 247.15/54.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 247.15/54.18 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 247.15/54.18 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~ % 247.15/54.18 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: % 247.15/54.18 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 247.15/54.18 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 247.15/54.18 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, % 247.15/54.18 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( % 247.15/54.18 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 247.15/54.18 | aSet0(v1)) % 247.15/54.18 % 247.15/54.18 (mDefSel) % 247.15/54.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: % 247.15/54.19 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | % 247.15/54.19 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ % 247.15/54.19 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 247.15/54.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ % 247.15/54.19 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 247.15/54.19 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | % 247.15/54.19 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 247.15/54.19 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ % 247.15/54.19 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ? % 247.15/54.19 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~ % 247.15/54.19 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) & % 247.15/54.19 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4, % 247.15/54.19 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( % 247.15/54.19 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~ % 247.15/54.19 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1, % 247.15/54.19 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: % 247.45/54.19 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) % 247.45/54.19 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2)) % 247.45/54.19 % 247.45/54.19 (mDefSub) % 247.45/54.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 247.45/54.19 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 247.45/54.19 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 247.45/54.19 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 247.45/54.19 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 247.45/54.19 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 247.45/54.19 % 247.45/54.19 (mEmpFin) % 247.45/54.19 $i(slcrc0) & isFinite0(slcrc0) % 247.45/54.19 % 247.45/54.19 (mLessRefl) % 247.45/54.19 $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 247.45/54.19 sdtlseqdt0(v0, v0)) % 247.45/54.19 % 247.45/54.19 (mNATSet) % 247.45/54.19 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 247.45/54.19 % 247.45/54.19 (mSegFin) % 247.45/54.20 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) % 247.45/54.20 | ~ aElementOf0(v0, szNzAzT0) | isFinite0(v1)) % 247.45/54.20 % 247.45/54.20 (mSegSucc) % 247.45/54.20 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = % 247.45/54.20 v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 247.45/54.20 aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 | % 247.45/54.20 aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 & % 247.45/54.20 $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) & ~ % 247.45/54.20 aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 & % 247.45/54.20 $i(v4) & $i(v3) & aElementOf0(v0, v4))))) % 247.45/54.20 % 247.45/54.20 (mSegZero) % 247.45/54.20 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 247.45/54.20 % 247.45/54.20 (mSubFSet) % 247.45/54.20 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, v0) | % 247.45/54.20 ~ isFinite0(v0) | ~ aSet0(v0) | isFinite0(v1)) % 247.45/54.20 % 247.45/54.20 (mSuccNum) % 247.45/54.20 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 247.45/54.20 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, % 247.45/54.20 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~ % 247.45/54.20 aElementOf0(v0, szNzAzT0)) % 247.45/54.20 % 247.45/54.20 (m__) % 247.45/54.20 $i(xS) & $i(sz00) & $i(slcrc0) & ? [v0: $i] : (slbdtsldtrb0(xS, sz00) = v0 & % 247.45/54.20 $i(v0) & ~ aElementOf0(slcrc0, v0)) % 247.45/54.20 % 247.45/54.20 (m__3398) % 247.45/54.21 $i(xK) & $i(xT) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 247.45/54.21 [v3: $i] : ! [v4: $i] : ( ~ (sdtlcdtrc0(v3, v2) = v4) | ~ (szDzozmdt0(v3) = % 247.45/54.21 v2) | ~ (slbdtsldtrb0(v1, v0) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | % 247.45/54.21 ~ aFunction0(v3) | ~ iLess0(v0, xK) | ~ aSubsetOf0(v4, xT) | ~ % 247.45/54.21 aSubsetOf0(v1, szNzAzT0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 247.45/54.21 szNzAzT0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (slbdtsldtrb0(v6, % 247.45/54.21 v0) = v7 & $i(v7) & $i(v6) & $i(v5) & aSubsetOf0(v6, v1) & % 247.45/54.21 isCountable0(v6) & aElementOf0(v5, xT) & ! [v8: $i] : ! [v9: $i] : (v9 = % 247.45/54.21 v5 | ~ (sdtlpdtrp0(v3, v8) = v9) | ~ $i(v8) | ~ aElementOf0(v8, % 247.45/54.21 v7)))) % 247.45/54.21 % 247.45/54.21 (m__3418) % 247.45/54.21 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 247.45/54.21 % 247.45/54.21 (m__3435) % 247.45/54.21 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) % 247.45/54.21 % 247.45/54.21 (m__3453) % 247.45/54.21 $i(xc) & $i(xS) & $i(xK) & $i(xT) & ? [v0: $i] : ? [v1: $i] : % 247.45/54.21 (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) = v0 & slbdtsldtrb0(xS, xK) = v0 & % 247.45/54.21 $i(v1) & $i(v0) & aFunction0(xc) & aSubsetOf0(v1, xT)) % 247.45/54.21 % 247.45/54.21 (m__3462) % 247.45/54.21 xK = sz00 & $i(sz00) % 247.45/54.21 % 247.45/54.21 (function-axioms) % 247.45/54.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 247.45/54.22 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 247.45/54.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 247.45/54.22 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 247.45/54.22 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 247.45/54.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 247.45/54.22 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 247.45/54.22 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 247.45/54.22 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 247.45/54.22 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 247.45/54.22 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 247.45/54.22 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 247.45/54.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 247.45/54.22 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 247.45/54.22 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 247.45/54.22 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 247.45/54.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 247.45/54.22 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 247.45/54.22 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 247.45/54.22 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 247.45/54.22 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 247.45/54.22 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 247.45/54.22 v0)) % 247.45/54.22 % 247.45/54.22 Further assumptions not needed in the proof: % 247.45/54.22 -------------------------------------------- % 247.45/54.22 mCConsSet, mCDiffSet, mCardDiff, mCardNum, mCardS, mCardSub, mCntRel, mConsDiff, % 247.45/54.22 mCountNFin, mCountNFin_01, mDefCons, mDefDiff, mDefMax, mDefMin, mDefPtt, % 247.45/54.22 mDefRst, mDefSImg, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 247.45/54.22 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, % 247.45/54.22 mImgElm, mImgRng, mLessASymm, mLessRel, mLessSucc, mLessTotal, mLessTrans, % 247.45/54.22 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegLess, mSelCSet, % 247.45/54.22 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubRefl, % 247.45/54.22 mSubTrans, mSuccEquSucc, mSuccLess, mZeroLess, mZeroNum, m__3291 % 247.45/54.22 % 247.45/54.22 Those formulas are unsatisfiable: % 247.45/54.22 --------------------------------- % 247.45/54.22 % 247.45/54.22 Begin of proof % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mDefEmp) implies: % 247.45/54.22 | (1) aSet0(slcrc0) % 247.45/54.22 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mEmpFin) implies: % 247.45/54.22 | (3) isFinite0(slcrc0) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mDefSub) implies: % 247.45/54.22 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ % 247.45/54.22 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) & % 247.45/54.22 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 247.45/54.22 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, % 247.45/54.22 | v0) | ~ aSet0(v0) | aSet0(v1)) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mNATSet) implies: % 247.45/54.22 | (6) aSet0(szNzAzT0) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mSuccNum) implies: % 247.45/54.22 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) | % 247.45/54.22 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0)) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mLessRefl) implies: % 247.45/54.22 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 247.45/54.22 | sdtlseqdt0(v0, v0)) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mCardEmpty) implies: % 247.45/54.22 | (9) ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~ % 247.45/54.22 | aSet0(v0)) % 247.45/54.22 | % 247.45/54.22 | ALPHA: (mCardSubEx) implies: % 247.45/54.23 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v0) = v2) | ~ % 247.45/54.23 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ isFinite0(v0) | ~ % 247.45/54.23 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | ? [v3: $i] : % 247.45/54.23 | (sbrdtbr0(v3) = v1 & $i(v3) & aSubsetOf0(v3, v0))) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (mDefSeg) implies: % 247.45/54.23 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ % 247.45/54.23 | $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (mSegFin) implies: % 247.45/54.23 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~ % 247.45/54.23 | aElementOf0(v0, szNzAzT0) | isFinite0(v1)) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (mSegZero) implies: % 247.45/54.23 | (13) slbdtrb0(sz00) = slcrc0 % 247.45/54.23 | % 247.45/54.23 | ALPHA: (mSegSucc) implies: % 247.45/54.23 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtrb0(v1) = v2) | ~ % 247.45/54.23 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ % 247.45/54.23 | aElementOf0(v0, szNzAzT0) | ? [v3: $i] : ? [v4: $i] : ((v1 = v0 | % 247.45/54.23 | aElementOf0(v0, v2) | (slbdtrb0(v3) = v4 & szszuzczcdt0(v1) = v3 % 247.45/54.23 | & $i(v4) & $i(v3) & ~ aElementOf0(v0, v4))) & (( ~ (v1 = v0) % 247.45/54.23 | & ~ aElementOf0(v0, v2)) | (slbdtrb0(v3) = v4 & % 247.45/54.23 | szszuzczcdt0(v1) = v3 & $i(v4) & $i(v3) & aElementOf0(v0, % 247.45/54.23 | v4))))) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (mCardSeg) implies: % 247.45/54.23 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ $i(v0) | ~ % 247.45/54.23 | aElementOf0(v0, szNzAzT0) | sbrdtbr0(v1) = v0) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (mDefSel) implies: % 247.45/54.23 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 247.45/54.23 | (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | % 247.45/54.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ % 247.45/54.23 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (m__3418) implies: % 247.45/54.23 | (17) aElementOf0(xK, szNzAzT0) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (m__3435) implies: % 247.45/54.23 | (18) aSubsetOf0(xS, szNzAzT0) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (m__3453) implies: % 247.45/54.23 | (19) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xc, v0) = v1 & szDzozmdt0(xc) % 247.45/54.23 | = v0 & slbdtsldtrb0(xS, xK) = v0 & $i(v1) & $i(v0) & aFunction0(xc) % 247.45/54.23 | & aSubsetOf0(v1, xT)) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (m__3398) implies: % 247.45/54.23 | (20) $i(szNzAzT0) % 247.45/54.23 | (21) $i(xK) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (m__3462) implies: % 247.45/54.23 | (22) xK = sz00 % 247.45/54.23 | % 247.45/54.23 | ALPHA: (m__) implies: % 247.45/54.23 | (23) $i(slcrc0) % 247.45/54.23 | (24) $i(xS) % 247.45/54.23 | (25) ? [v0: $i] : (slbdtsldtrb0(xS, sz00) = v0 & $i(v0) & ~ % 247.45/54.23 | aElementOf0(slcrc0, v0)) % 247.45/54.23 | % 247.45/54.23 | ALPHA: (function-axioms) implies: % 247.45/54.24 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 247.45/54.24 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 247.45/54.24 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) % 247.45/54.24 | = v1) | ~ (slbdtrb0(v2) = v0)) % 247.45/54.24 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 247.45/54.24 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) % 247.45/54.24 | % 247.45/54.24 | DELTA: instantiating (25) with fresh symbol all_65_0 gives: % 247.45/54.24 | (29) slbdtsldtrb0(xS, sz00) = all_65_0 & $i(all_65_0) & ~ % 247.45/54.24 | aElementOf0(slcrc0, all_65_0) % 247.45/54.24 | % 247.45/54.24 | ALPHA: (29) implies: % 247.45/54.24 | (30) ~ aElementOf0(slcrc0, all_65_0) % 247.45/54.24 | (31) slbdtsldtrb0(xS, sz00) = all_65_0 % 247.45/54.24 | % 247.45/54.24 | DELTA: instantiating (19) with fresh symbols all_67_0, all_67_1 gives: % 247.45/54.24 | (32) sdtlcdtrc0(xc, all_67_1) = all_67_0 & szDzozmdt0(xc) = all_67_1 & % 247.45/54.24 | slbdtsldtrb0(xS, xK) = all_67_1 & $i(all_67_0) & $i(all_67_1) & % 247.45/54.24 | aFunction0(xc) & aSubsetOf0(all_67_0, xT) % 247.45/54.24 | % 247.45/54.24 | ALPHA: (32) implies: % 247.45/54.24 | (33) $i(all_67_1) % 247.45/54.24 | (34) slbdtsldtrb0(xS, xK) = all_67_1 % 247.45/54.24 | % 247.45/54.24 | REDUCE: (22), (34) imply: % 247.45/54.24 | (35) slbdtsldtrb0(xS, sz00) = all_67_1 % 247.45/54.24 | % 247.45/54.24 | REDUCE: (21), (22) imply: % 247.45/54.24 | (36) $i(sz00) % 247.45/54.24 | % 247.45/54.24 | REDUCE: (17), (22) imply: % 247.45/54.24 | (37) aElementOf0(sz00, szNzAzT0) % 247.45/54.24 | % 247.45/54.24 | GROUND_INST: instantiating (28) with all_65_0, all_67_1, sz00, xS, simplifying % 247.45/54.24 | with (31), (35) gives: % 247.45/54.24 | (38) all_67_1 = all_65_0 % 247.45/54.24 | % 247.45/54.24 | REDUCE: (33), (38) imply: % 247.45/54.24 | (39) $i(all_65_0) % 247.45/54.24 | % 247.45/54.24 | GROUND_INST: instantiating (8) with sz00, simplifying with (36), (37) gives: % 247.45/54.24 | (40) sdtlseqdt0(sz00, sz00) % 247.45/54.24 | % 247.45/54.24 | GROUND_INST: instantiating (5) with szNzAzT0, xS, simplifying with (6), (18), % 247.45/54.24 | (20), (24) gives: % 247.45/54.24 | (41) aSet0(xS) % 247.45/54.24 | % 247.45/54.24 | GROUND_INST: instantiating (14) with sz00, sz00, slcrc0, simplifying with % 247.45/54.24 | (13), (36), (37) gives: % 247.45/54.24 | (42) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 & szszuzczcdt0(sz00) = % 247.45/54.24 | v0 & $i(v1) & $i(v0) & aElementOf0(sz00, v1)) % 247.45/54.24 | % 247.45/54.24 | GROUND_INST: instantiating (15) with sz00, slcrc0, simplifying with (13), % 247.45/54.24 | (36), (37) gives: % 247.45/54.24 | (43) sbrdtbr0(slcrc0) = sz00 % 247.45/54.24 | % 247.45/54.24 | DELTA: instantiating (42) with fresh symbols all_83_0, all_83_1 gives: % 247.45/54.24 | (44) slbdtrb0(all_83_1) = all_83_0 & szszuzczcdt0(sz00) = all_83_1 & % 247.45/54.24 | $i(all_83_0) & $i(all_83_1) & aElementOf0(sz00, all_83_0) % 247.45/54.24 | % 247.45/54.24 | ALPHA: (44) implies: % 247.45/54.24 | (45) aElementOf0(sz00, all_83_0) % 247.45/54.24 | (46) $i(all_83_0) % 247.45/54.24 | (47) szszuzczcdt0(sz00) = all_83_1 % 247.45/54.24 | (48) slbdtrb0(all_83_1) = all_83_0 % 247.45/54.24 | % 247.45/54.25 | GROUND_INST: instantiating (4) with xS, slcrc0, simplifying with (1), (23), % 247.45/54.25 | (24), (41) gives: % 247.45/54.25 | (49) aSubsetOf0(slcrc0, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, % 247.45/54.25 | slcrc0) & ~ aElementOf0(v0, xS)) % 247.45/54.25 | % 247.45/54.25 | GROUND_INST: instantiating (7) with sz00, all_83_1, simplifying with (36), % 247.45/54.25 | (37), (47) gives: % 247.45/54.25 | (50) aElementOf0(all_83_1, szNzAzT0) % 247.45/54.25 | % 247.45/54.25 | GROUND_INST: instantiating (10) with slcrc0, sz00, sz00, simplifying with (1), % 247.45/54.25 | (3), (23), (36), (37), (40), (43) gives: % 247.45/54.25 | (51) ? [v0: $i] : (sbrdtbr0(v0) = sz00 & $i(v0) & aSubsetOf0(v0, slcrc0)) % 247.45/54.25 | % 247.45/54.25 | GROUND_INST: instantiating (mCardCons) with slcrc0, sz00, simplifying with % 247.45/54.25 | (1), (3), (23), (43) gives: % 247.45/54.25 | (52) ? [v0: $i] : (szszuzczcdt0(sz00) = v0 & $i(v0) & ! [v1: $i] : ! % 247.45/54.25 | [v2: $i] : ( ~ (sdtpldt0(slcrc0, v1) = v2) | ~ $i(v1) | ~ % 247.45/54.25 | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, slcrc0))) % 247.45/54.25 | % 247.45/54.25 | DELTA: instantiating (51) with fresh symbol all_91_0 gives: % 247.45/54.25 | (53) sbrdtbr0(all_91_0) = sz00 & $i(all_91_0) & aSubsetOf0(all_91_0, % 247.45/54.25 | slcrc0) % 247.45/54.25 | % 247.45/54.25 | ALPHA: (53) implies: % 247.45/54.25 | (54) aSubsetOf0(all_91_0, slcrc0) % 247.45/54.25 | (55) $i(all_91_0) % 247.45/54.25 | (56) sbrdtbr0(all_91_0) = sz00 % 247.45/54.25 | % 247.45/54.25 | DELTA: instantiating (52) with fresh symbol all_93_0 gives: % 247.45/54.25 | (57) szszuzczcdt0(sz00) = all_93_0 & $i(all_93_0) & ! [v0: $i] : ! [v1: % 247.45/54.25 | $i] : ( ~ (sdtpldt0(slcrc0, v0) = v1) | ~ $i(v0) | ~ aElement0(v0) % 247.45/54.25 | | sbrdtbr0(v1) = all_93_0 | aElementOf0(v0, slcrc0)) % 247.45/54.25 | % 247.45/54.25 | ALPHA: (57) implies: % 247.45/54.25 | (58) $i(all_93_0) % 247.45/54.25 | (59) szszuzczcdt0(sz00) = all_93_0 % 247.45/54.25 | % 247.45/54.25 | GROUND_INST: instantiating (26) with all_83_1, all_93_0, sz00, simplifying % 247.45/54.25 | with (47), (59) gives: % 247.45/54.25 | (60) all_93_0 = all_83_1 % 247.45/54.25 | % 247.45/54.25 | REDUCE: (58), (60) imply: % 247.45/54.25 | (61) $i(all_83_1) % 247.45/54.25 | % 247.45/54.25 | GROUND_INST: instantiating (14) with all_83_1, all_83_1, all_83_0, simplifying % 247.45/54.25 | with (48), (50), (61) gives: % 247.45/54.25 | (62) ? [v0: $i] : ? [v1: $i] : (slbdtrb0(v0) = v1 & % 247.45/54.25 | szszuzczcdt0(all_83_1) = v0 & $i(v1) & $i(v0) & % 247.45/54.25 | aElementOf0(all_83_1, v1)) % 247.45/54.25 | % 247.45/54.25 | GROUND_INST: instantiating (14) with sz00, all_83_1, all_83_0, simplifying % 247.45/54.25 | with (36), (37), (48), (50), (61) gives: % 247.45/54.26 | (63) ? [v0: $i] : ? [v1: $i] : ((all_83_1 = sz00 | aElementOf0(sz00, % 247.45/54.26 | all_83_0) | (slbdtrb0(v0) = v1 & szszuzczcdt0(all_83_1) = v0 & % 247.45/54.26 | $i(v1) & $i(v0) & ~ aElementOf0(sz00, v1))) & (( ~ (all_83_1 = % 247.45/54.26 | sz00) & ~ aElementOf0(sz00, all_83_0)) | (slbdtrb0(v0) = v1 & % 247.45/54.26 | szszuzczcdt0(all_83_1) = v0 & $i(v1) & $i(v0) & % 247.45/54.26 | aElementOf0(sz00, v1)))) % 247.45/54.26 | % 247.45/54.26 | GROUND_INST: instantiating (11) with all_83_1, all_83_0, simplifying with % 247.45/54.26 | (46), (48), (50), (61) gives: % 247.45/54.26 | (64) aSet0(all_83_0) % 247.45/54.26 | % 247.45/54.26 | GROUND_INST: instantiating (15) with all_83_1, all_83_0, simplifying with % 247.45/54.26 | (48), (50), (61) gives: % 247.45/54.26 | (65) sbrdtbr0(all_83_0) = all_83_1 % 247.45/54.26 | % 247.45/54.26 | GROUND_INST: instantiating (12) with all_83_1, all_83_0, simplifying with % 247.45/54.26 | (48), (50), (61) gives: % 247.45/54.26 | (66) isFinite0(all_83_0) % 247.45/54.26 | % 247.45/54.26 | GROUND_INST: instantiating (mSubFSet) with slcrc0, all_91_0, simplifying with % 247.45/54.26 | (1), (3), (23), (54), (55) gives: % 247.45/54.26 | (67) isFinite0(all_91_0) % 247.45/54.26 | % 247.45/54.26 | GROUND_INST: instantiating (5) with slcrc0, all_91_0, simplifying with (1), % 247.45/54.26 | (23), (54), (55) gives: % 247.45/54.26 | (68) aSet0(all_91_0) % 247.45/54.26 | % 247.45/54.26 | DELTA: instantiating (62) with fresh symbols all_106_0, all_106_1 gives: % 247.45/54.26 | (69) slbdtrb0(all_106_1) = all_106_0 & szszuzczcdt0(all_83_1) = all_106_1 & % 247.45/54.26 | $i(all_106_0) & $i(all_106_1) & aElementOf0(all_83_1, all_106_0) % 247.45/54.26 | % 247.45/54.26 | ALPHA: (69) implies: % 247.45/54.26 | (70) aElementOf0(all_83_1, all_106_0) % 247.45/54.26 | (71) szszuzczcdt0(all_83_1) = all_106_1 % 247.45/54.26 | (72) slbdtrb0(all_106_1) = all_106_0 % 247.45/54.26 | % 247.45/54.26 | DELTA: instantiating (63) with fresh symbols all_108_0, all_108_1 gives: % 247.45/54.26 | (73) (all_83_1 = sz00 | aElementOf0(sz00, all_83_0) | (slbdtrb0(all_108_1) % 247.45/54.26 | = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1 & $i(all_108_0) & % 247.45/54.26 | $i(all_108_1) & ~ aElementOf0(sz00, all_108_0))) & (( ~ (all_83_1 % 247.45/54.26 | = sz00) & ~ aElementOf0(sz00, all_83_0)) | (slbdtrb0(all_108_1) % 247.45/54.26 | = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1 & $i(all_108_0) & % 247.45/54.26 | $i(all_108_1) & aElementOf0(sz00, all_108_0))) % 247.45/54.26 | % 247.45/54.26 | ALPHA: (73) implies: % 247.45/54.26 | (74) ( ~ (all_83_1 = sz00) & ~ aElementOf0(sz00, all_83_0)) | % 247.45/54.26 | (slbdtrb0(all_108_1) = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1 % 247.45/54.26 | & $i(all_108_0) & $i(all_108_1) & aElementOf0(sz00, all_108_0)) % 247.45/54.26 | % 247.45/54.26 | BETA: splitting (74) gives: % 247.45/54.26 | % 247.45/54.26 | Case 1: % 247.45/54.26 | | % 247.45/54.26 | | (75) ~ (all_83_1 = sz00) & ~ aElementOf0(sz00, all_83_0) % 247.45/54.26 | | % 247.45/54.26 | | ALPHA: (75) implies: % 247.45/54.26 | | (76) ~ aElementOf0(sz00, all_83_0) % 247.45/54.26 | | % 247.45/54.26 | | PRED_UNIFY: (45), (76) imply: % 247.45/54.26 | | (77) $false % 247.45/54.27 | | % 247.45/54.27 | | CLOSE: (77) is inconsistent. % 247.45/54.27 | | % 247.45/54.27 | Case 2: % 247.45/54.27 | | % 247.45/54.27 | | (78) slbdtrb0(all_108_1) = all_108_0 & szszuzczcdt0(all_83_1) = all_108_1 % 247.45/54.27 | | & $i(all_108_0) & $i(all_108_1) & aElementOf0(sz00, all_108_0) % 247.45/54.27 | | % 247.45/54.27 | | ALPHA: (78) implies: % 247.45/54.27 | | (79) szszuzczcdt0(all_83_1) = all_108_1 % 247.45/54.27 | | (80) slbdtrb0(all_108_1) = all_108_0 % 247.45/54.27 | | % 247.45/54.27 | | GROUND_INST: instantiating (26) with all_106_1, all_108_1, all_83_1, % 247.45/54.27 | | simplifying with (71), (79) gives: % 247.45/54.27 | | (81) all_108_1 = all_106_1 % 247.45/54.27 | | % 247.45/54.27 | | REDUCE: (80), (81) imply: % 247.45/54.27 | | (82) slbdtrb0(all_106_1) = all_108_0 % 247.45/54.27 | | % 247.45/54.27 | | GROUND_INST: instantiating (27) with all_106_0, all_108_0, all_106_1, % 247.45/54.27 | | simplifying with (72), (82) gives: % 247.45/54.27 | | (83) all_108_0 = all_106_0 % 247.45/54.27 | | % 247.45/54.27 | | GROUND_INST: instantiating (9) with all_91_0, simplifying with (55), (56), % 247.45/54.27 | | (68) gives: % 247.45/54.27 | | (84) all_91_0 = slcrc0 % 247.45/54.27 | | % 247.45/54.27 | | GROUND_INST: instantiating (10) with all_91_0, sz00, sz00, simplifying with % 247.45/54.27 | | (36), (37), (40), (55), (56), (67), (68) gives: % 247.45/54.27 | | (85) ? [v0: $i] : (sbrdtbr0(v0) = sz00 & $i(v0) & aSubsetOf0(v0, % 247.45/54.27 | | all_91_0)) % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (mCardCons) with all_91_0, sz00, simplifying with % 247.45/54.28 | | (55), (56), (67), (68) gives: % 247.45/54.28 | | (86) ? [v0: $i] : (szszuzczcdt0(sz00) = v0 & $i(v0) & ! [v1: $i] : ! % 247.45/54.28 | | [v2: $i] : ( ~ (sdtpldt0(all_91_0, v1) = v2) | ~ $i(v1) | ~ % 247.45/54.28 | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, all_91_0))) % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (7) with all_83_1, all_106_1, simplifying with % 247.45/54.28 | | (50), (61), (71) gives: % 247.45/54.28 | | (87) aElementOf0(all_106_1, szNzAzT0) % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (mCardCons) with all_83_0, all_83_1, simplifying % 247.45/54.28 | | with (46), (64), (65), (66) gives: % 247.45/54.28 | | (88) ? [v0: $i] : (szszuzczcdt0(all_83_1) = v0 & $i(v0) & ! [v1: $i] : % 247.45/54.28 | | ! [v2: $i] : ( ~ (sdtpldt0(all_83_0, v1) = v2) | ~ $i(v1) | ~ % 247.45/54.28 | | aElement0(v1) | sbrdtbr0(v2) = v0 | aElementOf0(v1, all_83_0))) % 247.45/54.28 | | % 247.45/54.28 | | DELTA: instantiating (85) with fresh symbol all_128_0 gives: % 247.45/54.28 | | (89) sbrdtbr0(all_128_0) = sz00 & $i(all_128_0) & aSubsetOf0(all_128_0, % 247.45/54.28 | | all_91_0) % 247.45/54.28 | | % 247.45/54.28 | | ALPHA: (89) implies: % 247.45/54.28 | | (90) aSubsetOf0(all_128_0, all_91_0) % 247.45/54.28 | | (91) $i(all_128_0) % 247.45/54.28 | | (92) sbrdtbr0(all_128_0) = sz00 % 247.45/54.28 | | % 247.45/54.28 | | DELTA: instantiating (86) with fresh symbol all_134_0 gives: % 247.45/54.28 | | (93) szszuzczcdt0(sz00) = all_134_0 & $i(all_134_0) & ! [v0: $i] : ! % 247.45/54.28 | | [v1: $i] : ( ~ (sdtpldt0(all_91_0, v0) = v1) | ~ $i(v0) | ~ % 247.45/54.28 | | aElement0(v0) | sbrdtbr0(v1) = all_134_0 | aElementOf0(v0, % 247.45/54.28 | | all_91_0)) % 247.45/54.28 | | % 247.45/54.28 | | ALPHA: (93) implies: % 247.45/54.28 | | (94) $i(all_134_0) % 247.45/54.28 | | (95) szszuzczcdt0(sz00) = all_134_0 % 247.45/54.28 | | % 247.45/54.28 | | DELTA: instantiating (88) with fresh symbol all_137_0 gives: % 247.45/54.28 | | (96) szszuzczcdt0(all_83_1) = all_137_0 & $i(all_137_0) & ! [v0: $i] : % 247.45/54.28 | | ! [v1: $i] : ( ~ (sdtpldt0(all_83_0, v0) = v1) | ~ $i(v0) | ~ % 247.45/54.28 | | aElement0(v0) | sbrdtbr0(v1) = all_137_0 | aElementOf0(v0, % 247.45/54.28 | | all_83_0)) % 247.45/54.28 | | % 247.45/54.28 | | ALPHA: (96) implies: % 247.45/54.28 | | (97) $i(all_137_0) % 247.45/54.28 | | (98) szszuzczcdt0(all_83_1) = all_137_0 % 247.45/54.28 | | % 247.45/54.28 | | REDUCE: (84), (90) imply: % 247.45/54.28 | | (99) aSubsetOf0(all_128_0, slcrc0) % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (26) with all_83_1, all_134_0, sz00, simplifying % 247.45/54.28 | | with (47), (95) gives: % 247.45/54.28 | | (100) all_134_0 = all_83_1 % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (26) with all_106_1, all_137_0, all_83_1, % 247.45/54.28 | | simplifying with (71), (98) gives: % 247.45/54.28 | | (101) all_137_0 = all_106_1 % 247.45/54.28 | | % 247.45/54.28 | | REDUCE: (97), (101) imply: % 247.45/54.28 | | (102) $i(all_106_1) % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (14) with all_83_1, all_106_1, all_106_0, % 247.45/54.28 | | simplifying with (50), (61), (72), (87), (102) gives: % 247.45/54.28 | | (103) ? [v0: $i] : ? [v1: $i] : ((all_106_1 = all_83_1 | % 247.45/54.28 | | aElementOf0(all_83_1, all_106_0) | (slbdtrb0(v0) = v1 & % 247.45/54.28 | | szszuzczcdt0(all_106_1) = v0 & $i(v1) & $i(v0) & ~ % 247.45/54.28 | | aElementOf0(all_83_1, v1))) & (( ~ (all_106_1 = all_83_1) & % 247.45/54.28 | | ~ aElementOf0(all_83_1, all_106_0)) | (slbdtrb0(v0) = v1 & % 247.45/54.28 | | szszuzczcdt0(all_106_1) = v0 & $i(v1) & $i(v0) & % 247.45/54.28 | | aElementOf0(all_83_1, v1)))) % 247.45/54.28 | | % 247.45/54.28 | | GROUND_INST: instantiating (5) with slcrc0, all_128_0, simplifying with (1), % 247.45/54.28 | | (23), (91), (99) gives: % 247.45/54.28 | | (104) aSet0(all_128_0) % 247.45/54.28 | | % 247.45/54.28 | | DELTA: instantiating (103) with fresh symbols all_153_0, all_153_1 gives: % 247.45/54.28 | | (105) (all_106_1 = all_83_1 | aElementOf0(all_83_1, all_106_0) | % 247.45/54.28 | | (slbdtrb0(all_153_1) = all_153_0 & szszuzczcdt0(all_106_1) = % 247.45/54.28 | | all_153_1 & $i(all_153_0) & $i(all_153_1) & ~ % 247.45/54.28 | | aElementOf0(all_83_1, all_153_0))) & (( ~ (all_106_1 = % 247.45/54.28 | | all_83_1) & ~ aElementOf0(all_83_1, all_106_0)) | % 247.45/54.28 | | (slbdtrb0(all_153_1) = all_153_0 & szszuzczcdt0(all_106_1) = % 247.45/54.28 | | all_153_1 & $i(all_153_0) & $i(all_153_1) & % 247.45/54.28 | | aElementOf0(all_83_1, all_153_0))) % 247.45/54.28 | | % 247.45/54.28 | | ALPHA: (105) implies: % 247.45/54.28 | | (106) ( ~ (all_106_1 = all_83_1) & ~ aElementOf0(all_83_1, all_106_0)) | % 247.45/54.28 | | (slbdtrb0(all_153_1) = all_153_0 & szszuzczcdt0(all_106_1) = % 247.45/54.28 | | all_153_1 & $i(all_153_0) & $i(all_153_1) & aElementOf0(all_83_1, % 247.45/54.28 | | all_153_0)) % 247.45/54.28 | | % 247.45/54.28 | | BETA: splitting (106) gives: % 247.45/54.28 | | % 247.45/54.28 | | Case 1: % 247.45/54.28 | | | % 247.45/54.28 | | | (107) ~ (all_106_1 = all_83_1) & ~ aElementOf0(all_83_1, all_106_0) % 247.45/54.28 | | | % 247.45/54.28 | | | ALPHA: (107) implies: % 247.45/54.28 | | | (108) ~ aElementOf0(all_83_1, all_106_0) % 247.45/54.28 | | | % 247.45/54.28 | | | PRED_UNIFY: (70), (108) imply: % 247.45/54.29 | | | (109) $false % 247.45/54.29 | | | % 247.45/54.29 | | | CLOSE: (109) is inconsistent. % 247.45/54.29 | | | % 247.45/54.29 | | Case 2: % 247.45/54.29 | | | % 247.45/54.29 | | | % 247.45/54.29 | | | GROUND_INST: instantiating (9) with all_128_0, simplifying with (91), % 247.45/54.29 | | | (92), (104) gives: % 247.45/54.29 | | | (110) all_128_0 = slcrc0 % 247.45/54.29 | | | % 247.45/54.29 | | | GROUND_INST: instantiating (4) with xS, all_128_0, simplifying with (24), % 247.45/54.29 | | | (41), (91), (104) gives: % 247.45/54.29 | | | (111) aSubsetOf0(all_128_0, xS) | ? [v0: $i] : ($i(v0) & % 247.45/54.29 | | | aElementOf0(v0, all_128_0) & ~ aElementOf0(v0, xS)) % 247.45/54.29 | | | % 247.45/54.29 | | | BETA: splitting (49) gives: % 247.45/54.29 | | | % 247.45/54.29 | | | Case 1: % 247.45/54.29 | | | | % 247.45/54.29 | | | | (112) aSubsetOf0(slcrc0, xS) % 247.45/54.29 | | | | % 247.45/54.29 | | | | GROUND_INST: instantiating (16) with xS, sz00, all_65_0, slcrc0, % 247.45/54.29 | | | | simplifying with (23), (24), (30), (31), (36), (37), (39), % 247.45/54.29 | | | | (41), (43), (112) gives: % 247.45/54.29 | | | | (113) $false % 247.45/54.29 | | | | % 247.45/54.29 | | | | CLOSE: (113) is inconsistent. % 247.45/54.29 | | | | % 247.45/54.29 | | | Case 2: % 247.45/54.29 | | | | % 247.45/54.29 | | | | (114) ~ aSubsetOf0(slcrc0, xS) % 247.45/54.29 | | | | % 247.45/54.29 | | | | BETA: splitting (111) gives: % 247.45/54.29 | | | | % 247.45/54.29 | | | | Case 1: % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | (115) aSubsetOf0(all_128_0, xS) % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | REDUCE: (110), (115) imply: % 247.45/54.29 | | | | | (116) aSubsetOf0(slcrc0, xS) % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | PRED_UNIFY: (114), (116) imply: % 247.45/54.29 | | | | | (117) $false % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | CLOSE: (117) is inconsistent. % 247.45/54.29 | | | | | % 247.45/54.29 | | | | Case 2: % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | (118) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_128_0) & ~ % 247.45/54.29 | | | | | aElementOf0(v0, xS)) % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | DELTA: instantiating (118) with fresh symbol all_402_0 gives: % 247.45/54.29 | | | | | (119) $i(all_402_0) & aElementOf0(all_402_0, all_128_0) & ~ % 247.45/54.29 | | | | | aElementOf0(all_402_0, xS) % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | ALPHA: (119) implies: % 247.45/54.29 | | | | | (120) aElementOf0(all_402_0, all_128_0) % 247.45/54.29 | | | | | (121) $i(all_402_0) % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | REDUCE: (110), (120) imply: % 247.45/54.29 | | | | | (122) aElementOf0(all_402_0, slcrc0) % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | GROUND_INST: instantiating (2) with all_402_0, simplifying with (121), % 247.45/54.29 | | | | | (122) gives: % 247.45/54.29 | | | | | (123) $false % 247.45/54.29 | | | | | % 247.45/54.29 | | | | | CLOSE: (123) is inconsistent. % 247.45/54.29 | | | | | % 247.45/54.29 | | | | End of split % 247.45/54.29 | | | | % 247.45/54.29 | | | End of split % 247.45/54.29 | | | % 247.45/54.29 | | End of split % 247.45/54.29 | | % 247.45/54.29 | End of split % 247.45/54.29 | % 247.45/54.29 End of proof % 247.45/54.29 % SZS output end Proof for theBenchmark % 247.45/54.29 % 247.45/54.29 53685ms %------------------------------------------------------------------------------