%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM580+3 : TPTP v8.1.2. Released v4.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.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 11:48:44 EDT 2023 % Result : Theorem 119.43s 16.83s % Output : Proof 120.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM580+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n013.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Fri Aug 25 12:54:02 EDT 2023 % 0.16/0.35 % 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 % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 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 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.86/1.46 Prover 4: Preprocessing ... % 4.86/1.46 Prover 1: Preprocessing ... % 4.86/1.50 Prover 3: Preprocessing ... % 4.86/1.50 Prover 0: Preprocessing ... % 4.86/1.50 Prover 5: Preprocessing ... % 4.86/1.50 Prover 6: Preprocessing ... % 4.86/1.50 Prover 2: Preprocessing ... % 13.98/2.71 Prover 1: Constructing countermodel ... % 13.98/2.78 Prover 3: Constructing countermodel ... % 13.98/2.80 Prover 6: Proving ... % 16.08/2.93 Prover 5: Proving ... % 21.54/3.67 Prover 2: Proving ... % 31.30/5.02 Prover 4: Constructing countermodel ... % 37.30/5.73 Prover 0: Proving ... % 84.24/11.93 Prover 2: stopped % 84.24/11.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 84.24/12.11 Prover 7: Preprocessing ... % 87.68/12.46 Prover 7: Constructing countermodel ... % 99.52/13.97 Prover 5: stopped % 99.52/13.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 100.70/14.08 Prover 8: Preprocessing ... % 101.05/14.31 Prover 8: Warning: ignoring some quantifiers % 101.05/14.32 Prover 8: Constructing countermodel ... % 114.28/15.99 Prover 1: stopped % 114.28/15.99 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 115.20/16.09 Prover 9: Preprocessing ... % 118.31/16.46 Prover 7: Found proof (size 82) % 118.31/16.46 Prover 7: proved (4510ms) % 118.31/16.46 Prover 0: stopped % 118.31/16.46 Prover 8: stopped % 118.31/16.46 Prover 6: stopped % 118.31/16.47 Prover 4: stopped % 118.31/16.47 Prover 3: stopped % 119.43/16.82 Prover 9: Constructing countermodel ... % 119.43/16.83 Prover 9: stopped % 119.43/16.83 % 119.43/16.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 119.43/16.83 % 119.43/16.85 % SZS output start Proof for theBenchmark % 119.43/16.85 Assumptions after simplification: % 119.43/16.85 --------------------------------- % 119.43/16.85 % 119.43/16.85 (mCardCons) % 119.80/16.90 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 119.80/16.90 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2) % 119.80/16.90 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~ % 119.80/16.90 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0)))) % 119.80/16.90 % 119.80/16.90 (mCardNum) % 119.80/16.91 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) % 119.80/16.91 | ~ isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) & ! [v0: $i] % 119.80/16.91 : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v1, % 119.80/16.91 szNzAzT0) | ~ aSet0(v0) | isFinite0(v0)) % 119.80/16.91 % 119.80/16.91 (mCountNFin_01) % 119.80/16.91 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)) % 119.80/16.91 % 119.80/16.91 (mDefEmp) % 119.80/16.91 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ % 119.80/16.91 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : ( % 119.80/16.91 ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 119.80/16.91 % 119.80/16.91 (mDefSeg) % 119.80/16.92 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 119.80/16.92 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 119.80/16.92 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~ % 119.80/16.92 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i] % 119.80/16.92 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 119.80/16.92 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 119.80/16.92 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i] % 119.80/16.92 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = % 119.80/16.92 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 119.80/16.92 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 119.80/16.92 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~ % 119.80/16.92 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4: % 119.80/16.92 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 119.80/16.92 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 119.80/16.92 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, % 119.80/16.92 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( % 119.80/16.92 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) % 119.80/16.92 | aSet0(v1)) % 119.80/16.92 % 119.80/16.92 (mDefSub) % 119.80/16.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 119.80/16.92 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) | % 119.80/16.92 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 119.80/16.92 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i] % 119.80/16.92 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) | % 119.80/16.92 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0))) % 119.80/16.92 % 119.80/16.92 (mEOfElem) % 119.80/16.92 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | % 119.80/16.92 ~ aSet0(v0) | aElement0(v1)) % 119.80/16.92 % 119.80/16.92 (mNATSet) % 119.80/16.92 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0) % 119.80/16.92 % 119.80/16.92 (mNatExtra) % 119.80/16.93 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ % 119.80/16.93 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & % 119.80/16.93 aElementOf0(v1, szNzAzT0))) % 119.80/16.93 % 119.80/16.93 (mSegZero) % 119.80/16.93 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0) % 119.80/16.93 % 119.80/16.93 (mSuccEquSucc) % 119.80/16.93 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 119.80/16.93 (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) % 119.80/16.93 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 119.80/16.93 % 119.80/16.93 (mZeroNum) % 119.80/16.93 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0) % 119.80/16.93 % 119.80/16.93 (m__) % 119.80/16.93 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 119.80/16.93 ? [v3: $i] : ( ~ (v3 = xK) & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & % 119.80/16.93 sbrdtbr0(v2) = v3 & sdtpldt0(xQ, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & % 119.80/16.93 $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v4: $i] : (v4 = v1 | ~ % 119.80/16.93 $i(v4) | ~ aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~ % 119.80/16.93 $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : ( ~ % 119.80/16.93 $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ % 119.80/16.93 $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) | aElementOf0(v4, v2)) % 119.80/16.93 & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 119.80/16.93 % 119.80/16.93 (m__3418) % 119.80/16.93 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0) % 119.80/16.93 % 119.80/16.93 (m__3462) % 119.80/16.93 ~ (xK = sz00) & $i(xK) & $i(sz00) % 119.80/16.93 % 119.80/16.93 (m__3520) % 119.80/16.93 ~ (xK = sz00) & $i(xK) & $i(sz00) % 119.80/16.93 % 119.80/16.93 (m__3533) % 119.80/16.93 szszuzczcdt0(xk) = xK & $i(xk) & $i(xK) & $i(szNzAzT0) & aElementOf0(xk, % 119.80/16.93 szNzAzT0) % 119.80/16.93 % 119.80/16.93 (m__3623) % 119.80/16.94 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) & % 119.80/16.94 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~ % 119.80/16.94 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~ % 119.80/16.94 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] % 119.80/16.94 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & szmzizndt0(v1) = v2 % 119.80/16.94 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & $i(v5) & $i(v4) & $i(v3) % 119.80/16.94 & $i(v2) & aSubsetOf0(v5, v3) & isCountable0(v5) & aElementOf0(v2, v1) & % 119.80/16.94 aSet0(v5) & aSet0(v3) & ~ aElementOf0(v2, v3) & ! [v6: $i] : (v6 = v2 | % 119.80/16.94 ~ $i(v6) | ~ aElementOf0(v6, v1) | ~ aElement0(v6) | aElementOf0(v6, % 119.80/16.94 v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v5) | % 119.80/16.94 aElementOf0(v6, v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v3) % 119.80/16.94 | aElementOf0(v6, v1)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, % 119.80/16.94 v3) | aElement0(v6)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, % 119.80/16.94 v1) | sdtlseqdt0(v2, v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 119.80/16.94 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 119.80/16.94 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: $i] : ? % 119.80/16.94 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 & % 119.80/16.94 szmzizndt0(v1) = v2 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & % 119.80/16.94 $i(v5) & $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v5, v3) & % 119.80/16.94 isCountable0(v5) & aElementOf0(v2, v1) & aSet0(v5) & aSet0(v3) & ~ % 119.80/16.94 aElementOf0(v2, v3) & ! [v7: $i] : (v7 = v2 | ~ $i(v7) | ~ % 119.80/16.94 aElementOf0(v7, v1) | ~ aElement0(v7) | aElementOf0(v7, v3)) & ! % 119.80/16.94 [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v5) | aElementOf0(v7, v3)) % 119.80/16.94 & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | aElementOf0(v7, % 119.80/16.94 v1)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | % 119.80/16.94 aElement0(v7)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v1) | % 119.80/16.94 sdtlseqdt0(v2, v7))) | (aElementOf0(v6, v1) & ~ aElementOf0(v6, % 119.80/16.94 szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = % 119.80/16.94 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] % 119.80/16.94 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (sdtlpdtrp0(xN, v0) = v2 & % 119.80/16.94 $i(v6) & $i(v2) & ( ~ isCountable0(v2) | (sdtlpdtrp0(xN, v1) = v5 & % 119.80/16.94 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v5) & $i(v4) & $i(v3) % 119.80/16.94 & aSubsetOf0(v5, v4) & isCountable0(v5) & aElementOf0(v3, v2) & % 119.80/16.94 aSet0(v5) & aSet0(v4) & ~ aElementOf0(v3, v4) & ! [v7: $i] : (v7 = % 119.80/16.94 v3 | ~ $i(v7) | ~ aElementOf0(v7, v2) | ~ aElement0(v7) | % 119.80/16.94 aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, % 119.80/16.94 v5) | aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ % 119.80/16.94 aElementOf0(v7, v4) | aElementOf0(v7, v2)) & ! [v7: $i] : ( ~ % 119.80/16.94 $i(v7) | ~ aElementOf0(v7, v4) | aElement0(v7)) & ! [v7: $i] : ( ~ % 119.80/16.94 $i(v7) | ~ aElementOf0(v7, v2) | sdtlseqdt0(v3, v7))) | ( ~ % 119.80/16.94 aSubsetOf0(v2, szNzAzT0) & ( ~ aSet0(v2) | (aElementOf0(v6, v2) & ~ % 119.80/16.94 aElementOf0(v6, szNzAzT0))))))) % 119.80/16.94 % 119.80/16.94 (m__3671) % 119.80/16.95 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 119.80/16.95 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | % 119.80/16.95 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : ! % 119.80/16.95 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 119.80/16.95 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 119.80/16.95 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 119.80/16.95 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 119.80/16.95 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1)) % 119.80/16.95 % 119.80/16.95 (m__3989) % 119.80/16.95 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0) % 119.80/16.95 % 119.80/16.95 (m__3989_02) % 119.80/16.95 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 119.80/16.95 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & % 119.80/16.95 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & % 119.80/16.95 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & % 119.80/16.95 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & ! % 119.80/16.95 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4) % 119.80/16.95 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 119.80/16.95 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) % 119.80/16.95 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) | % 119.80/16.95 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | % 119.80/16.95 aElementOf0(v4, v2))) % 119.80/16.95 % 119.80/16.95 (function-axioms) % 119.80/16.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 119.80/16.96 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 119.80/16.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 119.80/16.96 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 119.80/16.96 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 119.80/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 119.80/16.96 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 119.80/16.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 119.80/16.96 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 119.80/16.96 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 119.80/16.96 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 119.80/16.96 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 119.80/16.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 119.80/16.96 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 119.80/16.96 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 119.80/16.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 119.80/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 119.80/16.96 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 119.80/16.96 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 119.80/16.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 119.80/16.96 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 119.80/16.96 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 119.80/16.96 v0)) % 119.80/16.96 % 119.80/16.96 Further assumptions not needed in the proof: % 119.80/16.96 -------------------------------------------- % 119.80/16.96 mCConsSet, mCDiffSet, mCardDiff, mCardEmpty, mCardS, mCardSeg, mCardSub, % 119.80/16.96 mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons, mDefDiff, mDefMax, % 119.80/16.96 mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSel, mDiffCons, mDirichlet, mDomSet, % 119.80/16.96 mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, % 119.80/16.96 mIHSort, mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, % 119.80/16.96 mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatNSucc, mNoScLessZr, mPttSet, % 119.80/16.96 mSegFin, mSegLess, mSegSucc, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, % 119.80/16.96 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccLess, mSuccNum, % 119.80/16.96 mZeroLess, m__3291, m__3398, m__3435, m__3453, m__3754, m__3821 % 119.80/16.96 % 119.80/16.96 Those formulas are unsatisfiable: % 119.80/16.96 --------------------------------- % 119.80/16.96 % 119.80/16.96 Begin of proof % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mDefEmp) implies: % 119.80/16.96 | (1) aSet0(slcrc0) % 119.80/16.96 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0)) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mCountNFin_01) implies: % 119.80/16.96 | (3) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mDefSub) implies: % 119.80/16.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ % 119.80/16.96 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ % 119.80/16.96 | aSet0(v0) | aElementOf0(v2, v0)) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mNATSet) implies: % 119.80/16.96 | (5) aSet0(szNzAzT0) % 119.80/16.96 | (6) isCountable0(szNzAzT0) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mZeroNum) implies: % 119.80/16.96 | (7) aElementOf0(sz00, szNzAzT0) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mSuccEquSucc) implies: % 119.80/16.96 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 119.80/16.96 | (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ % 119.80/16.96 | $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0)) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mNatExtra) implies: % 119.80/16.96 | (9) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | % 119.80/16.96 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1, % 119.80/16.96 | szNzAzT0))) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mCardNum) implies: % 119.80/16.96 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 119.80/16.96 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | isFinite0(v0)) % 119.80/16.96 | % 119.80/16.96 | ALPHA: (mDefSeg) implies: % 119.80/16.96 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) % 119.80/16.96 | = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ % 119.80/16.96 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ % 119.80/16.96 | aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) | % 119.80/16.97 | (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) & % 119.80/16.97 | (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & % 119.80/16.97 | sdtlseqdt0(v4, v0) & aElementOf0(v3, szNzAzT0))))) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (mSegZero) implies: % 119.80/16.97 | (12) slbdtrb0(sz00) = slcrc0 % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3418) implies: % 119.80/16.97 | (13) aElementOf0(xK, szNzAzT0) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3520) implies: % 119.80/16.97 | (14) ~ (xK = sz00) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3533) implies: % 119.80/16.97 | (15) aElementOf0(xk, szNzAzT0) % 119.80/16.97 | (16) szszuzczcdt0(xk) = xK % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3623) implies: % 119.80/16.97 | (17) $i(sz00) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3671) implies: % 119.80/16.97 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlpdtrp0(xN, v0) = % 119.80/16.97 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~ % 119.80/16.97 | aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3989) implies: % 119.80/16.97 | (19) aElementOf0(xi, szNzAzT0) % 119.80/16.97 | (20) $i(szNzAzT0) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__3989_02) implies: % 119.80/16.97 | (21) $i(xk) % 119.80/16.97 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 119.80/16.97 | (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) % 119.80/16.97 | = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & % 119.80/16.97 | $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & % 119.80/16.97 | aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) % 119.80/16.97 | & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ % 119.80/16.97 | aElement0(v4) | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | % 119.80/16.97 | ~ aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ % 119.80/16.97 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : ( % 119.80/16.97 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: % 119.80/16.97 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2))) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (m__) implies: % 119.80/16.97 | (23) $i(xK) % 119.80/16.97 | (24) $i(xi) % 119.80/16.97 | (25) $i(xQ) % 119.80/16.97 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = xK) % 119.80/16.97 | & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = v3 % 119.80/16.97 | & sdtpldt0(xQ, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 119.80/16.97 | aElementOf0(v1, v0) & aSet0(v2) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) % 119.80/16.97 | | ~ aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : ( % 119.80/16.97 | ~ $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : % 119.80/16.97 | ( ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4: % 119.80/16.97 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) | % 119.80/16.97 | aElementOf0(v4, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2))) % 119.80/16.97 | % 119.80/16.97 | ALPHA: (function-axioms) implies: % 119.80/16.97 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 119.80/16.97 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0)) % 119.80/16.97 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) % 119.80/16.97 | = v1) | ~ (sbrdtbr0(v2) = v0)) % 119.80/16.98 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 119.80/16.98 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0)) % 119.80/16.98 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 119.80/16.98 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 119.80/16.98 | % 119.80/16.98 | DELTA: instantiating (26) with fresh symbols all_70_0, all_70_1, all_70_2, % 119.80/16.98 | all_70_3 gives: % 119.80/16.98 | (31) ~ (all_70_0 = xK) & sdtlpdtrp0(xN, xi) = all_70_3 & % 119.80/16.98 | szmzizndt0(all_70_3) = all_70_2 & sbrdtbr0(all_70_1) = all_70_0 & % 119.80/16.98 | sdtpldt0(xQ, all_70_2) = all_70_1 & $i(all_70_0) & $i(all_70_1) & % 119.80/16.98 | $i(all_70_2) & $i(all_70_3) & aElementOf0(all_70_2, all_70_3) & % 119.80/16.98 | aSet0(all_70_1) & ! [v0: any] : (v0 = all_70_2 | ~ $i(v0) | ~ % 119.80/16.98 | aElementOf0(v0, all_70_1) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ % 119.80/16.98 | $i(v0) | ~ aElementOf0(v0, all_70_1) | aElement0(v0)) & ! [v0: $i] % 119.80/16.98 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_3) | sdtlseqdt0(all_70_2, % 119.80/16.98 | v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ % 119.80/16.98 | aElement0(v0) | aElementOf0(v0, all_70_1)) & ( ~ aElement0(all_70_2) % 119.80/16.98 | | aElementOf0(all_70_2, all_70_1)) % 119.80/16.98 | % 119.80/16.98 | ALPHA: (31) implies: % 119.80/16.98 | (32) ~ (all_70_0 = xK) % 119.80/16.98 | (33) aSet0(all_70_1) % 119.80/16.98 | (34) $i(all_70_1) % 119.80/16.98 | (35) sdtpldt0(xQ, all_70_2) = all_70_1 % 119.80/16.98 | (36) sbrdtbr0(all_70_1) = all_70_0 % 119.80/16.98 | (37) szmzizndt0(all_70_3) = all_70_2 % 119.80/16.98 | (38) sdtlpdtrp0(xN, xi) = all_70_3 % 119.80/16.98 | (39) ~ aElement0(all_70_2) | aElementOf0(all_70_2, all_70_1) % 119.80/16.98 | % 119.80/16.98 | DELTA: instantiating (22) with fresh symbols all_73_0, all_73_1, all_73_2, % 119.80/16.98 | all_73_3 gives: % 119.80/16.98 | (40) sdtlpdtrp0(xN, xi) = all_73_3 & slbdtsldtrb0(all_73_1, xk) = all_73_0 % 119.80/16.98 | & szmzizndt0(all_73_3) = all_73_2 & sbrdtbr0(xQ) = xk & % 119.80/16.98 | sdtmndt0(all_73_3, all_73_2) = all_73_1 & $i(all_73_0) & $i(all_73_1) % 119.80/16.98 | & $i(all_73_2) & $i(all_73_3) & aSubsetOf0(xQ, all_73_1) & % 119.80/16.98 | aElementOf0(all_73_2, all_73_3) & aElementOf0(xQ, all_73_0) & % 119.80/16.98 | aSet0(all_73_1) & aSet0(xQ) & ~ aElementOf0(all_73_2, all_73_1) & ! % 119.80/16.98 | [v0: any] : (v0 = all_73_2 | ~ $i(v0) | ~ aElementOf0(v0, all_73_3) % 119.80/16.98 | | ~ aElement0(v0) | aElementOf0(v0, all_73_1)) & ! [v0: $i] : ( ~ % 119.80/16.98 | $i(v0) | ~ aElementOf0(v0, all_73_1) | aElementOf0(v0, all_73_3)) & % 119.80/16.98 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_73_1) | % 119.80/16.98 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 119.80/16.98 | all_73_3) | sdtlseqdt0(all_73_2, v0)) & ! [v0: $i] : ( ~ $i(v0) | % 119.80/16.98 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_73_1)) % 119.80/16.98 | % 119.80/16.98 | ALPHA: (40) implies: % 119.80/16.98 | (41) ~ aElementOf0(all_73_2, all_73_1) % 119.80/16.98 | (42) aSet0(xQ) % 119.80/16.98 | (43) aSet0(all_73_1) % 119.80/16.98 | (44) aElementOf0(all_73_2, all_73_3) % 119.80/16.98 | (45) aSubsetOf0(xQ, all_73_1) % 119.80/16.99 | (46) $i(all_73_2) % 119.80/16.99 | (47) $i(all_73_1) % 119.80/16.99 | (48) sbrdtbr0(xQ) = xk % 119.80/16.99 | (49) szmzizndt0(all_73_3) = all_73_2 % 119.80/16.99 | (50) sdtlpdtrp0(xN, xi) = all_73_3 % 119.80/16.99 | % 119.80/16.99 | BETA: splitting (3) gives: % 119.80/16.99 | % 119.80/16.99 | Case 1: % 119.80/16.99 | | % 119.80/16.99 | | (51) ~ isCountable0(slcrc0) % 119.80/16.99 | | % 119.80/16.99 | | GROUND_INST: instantiating (29) with all_70_2, all_73_2, all_70_3, % 119.80/16.99 | | simplifying with (37) gives: % 119.80/16.99 | | (52) all_73_2 = all_70_2 | ~ (szmzizndt0(all_70_3) = all_73_2) % 119.80/16.99 | | % 119.80/16.99 | | GROUND_INST: instantiating (30) with all_70_3, all_73_3, xi, xN, simplifying % 119.80/16.99 | | with (38), (50) gives: % 119.80/16.99 | | (53) all_73_3 = all_70_3 % 119.80/16.99 | | % 119.80/16.99 | | PRED_UNIFY: (6), (51) imply: % 119.80/16.99 | | (54) ~ (szNzAzT0 = slcrc0) % 119.80/16.99 | | % 119.80/16.99 | | REDUCE: (49), (53) imply: % 119.80/16.99 | | (55) szmzizndt0(all_70_3) = all_73_2 % 119.80/16.99 | | % 119.80/16.99 | | REDUCE: (44), (53) imply: % 119.80/16.99 | | (56) aElementOf0(all_73_2, all_70_3) % 119.80/16.99 | | % 119.80/16.99 | | BETA: splitting (52) gives: % 119.80/16.99 | | % 119.80/16.99 | | Case 1: % 119.80/16.99 | | | % 120.23/16.99 | | | (57) ~ (szmzizndt0(all_70_3) = all_73_2) % 120.23/16.99 | | | % 120.23/16.99 | | | PRED_UNIFY: (55), (57) imply: % 120.23/16.99 | | | (58) $false % 120.23/16.99 | | | % 120.23/16.99 | | | CLOSE: (58) is inconsistent. % 120.23/16.99 | | | % 120.23/16.99 | | Case 2: % 120.23/16.99 | | | % 120.23/16.99 | | | (59) all_73_2 = all_70_2 % 120.23/16.99 | | | % 120.23/16.99 | | | REDUCE: (46), (59) imply: % 120.23/16.99 | | | (60) $i(all_70_2) % 120.23/16.99 | | | % 120.23/16.99 | | | REDUCE: (56), (59) imply: % 120.23/16.99 | | | (61) aElementOf0(all_70_2, all_70_3) % 120.23/16.99 | | | % 120.23/16.99 | | | REDUCE: (41), (59) imply: % 120.23/16.99 | | | (62) ~ aElementOf0(all_70_2, all_73_1) % 120.23/16.99 | | | % 120.23/16.99 | | | GROUND_INST: instantiating (9) with xK, simplifying with (13), (23) gives: % 120.23/17.00 | | | (63) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & % 120.23/17.00 | | | aElementOf0(v0, szNzAzT0)) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (mEOfElem) with szNzAzT0, all_70_2, simplifying % 120.23/17.00 | | | with (5), (20), (60) gives: % 120.23/17.00 | | | (64) ~ aElementOf0(all_70_2, szNzAzT0) | aElement0(all_70_2) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (2) with all_70_2, simplifying with (60) gives: % 120.23/17.00 | | | (65) ~ aElementOf0(all_70_2, slcrc0) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (4) with all_73_1, xQ, all_70_2, simplifying % 120.23/17.00 | | | with (25), (43), (45), (47), (60), (62) gives: % 120.23/17.00 | | | (66) ~ aElementOf0(all_70_2, xQ) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (10) with xQ, xk, simplifying with (15), (25), % 120.23/17.00 | | | (42), (48) gives: % 120.23/17.00 | | | (67) isFinite0(xQ) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (11) with sz00, slcrc0, all_70_1, simplifying % 120.23/17.00 | | | with (7), (12), (17), (33), (34) gives: % 120.23/17.00 | | | (68) all_70_1 = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ % 120.23/17.00 | | | aElementOf0(v0, all_70_1) | ~ aElementOf0(v0, szNzAzT0) | % 120.23/17.00 | | | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) & % 120.23/17.00 | | | (aElementOf0(v0, all_70_1) | (szszuzczcdt0(v0) = v1 & $i(v1) & % 120.23/17.00 | | | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0)))) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (11) with sz00, slcrc0, szNzAzT0, simplifying % 120.23/17.00 | | | with (5), (7), (12), (17), (20) gives: % 120.23/17.00 | | | (69) szNzAzT0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : (szszuzczcdt0(v0) % 120.23/17.00 | | | = v1 & $i(v1) & $i(v0) & aElementOf0(v0, szNzAzT0) & ~ % 120.23/17.00 | | | sdtlseqdt0(v1, sz00)) % 120.23/17.00 | | | % 120.23/17.00 | | | GROUND_INST: instantiating (18) with xi, all_70_3, all_70_2, simplifying % 120.23/17.00 | | | with (19), (24), (38), (60), (61) gives: % 120.23/17.00 | | | (70) aElementOf0(all_70_2, szNzAzT0) % 120.23/17.00 | | | % 120.23/17.00 | | | BETA: splitting (64) gives: % 120.23/17.00 | | | % 120.23/17.00 | | | Case 1: % 120.23/17.00 | | | | % 120.23/17.00 | | | | (71) ~ aElementOf0(all_70_2, szNzAzT0) % 120.23/17.00 | | | | % 120.23/17.00 | | | | PRED_UNIFY: (70), (71) imply: % 120.23/17.00 | | | | (72) $false % 120.23/17.00 | | | | % 120.23/17.00 | | | | CLOSE: (72) is inconsistent. % 120.23/17.00 | | | | % 120.23/17.00 | | | Case 2: % 120.23/17.00 | | | | % 120.23/17.00 | | | | (73) aElement0(all_70_2) % 120.23/17.00 | | | | % 120.23/17.00 | | | | BETA: splitting (63) gives: % 120.23/17.00 | | | | % 120.23/17.00 | | | | Case 1: % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | (74) xK = sz00 % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | REDUCE: (14), (74) imply: % 120.23/17.00 | | | | | (75) $false % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | CLOSE: (75) is inconsistent. % 120.23/17.00 | | | | | % 120.23/17.00 | | | | Case 2: % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | (76) ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) & % 120.23/17.00 | | | | | aElementOf0(v0, szNzAzT0)) % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | DELTA: instantiating (76) with fresh symbol all_137_0 gives: % 120.23/17.00 | | | | | (77) szszuzczcdt0(all_137_0) = xK & $i(all_137_0) & % 120.23/17.00 | | | | | aElementOf0(all_137_0, szNzAzT0) % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | ALPHA: (77) implies: % 120.23/17.00 | | | | | (78) aElementOf0(all_137_0, szNzAzT0) % 120.23/17.00 | | | | | (79) $i(all_137_0) % 120.23/17.00 | | | | | (80) szszuzczcdt0(all_137_0) = xK % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | BETA: splitting (39) gives: % 120.23/17.00 | | | | | % 120.23/17.00 | | | | | Case 1: % 120.23/17.00 | | | | | | % 120.23/17.00 | | | | | | (81) aElementOf0(all_70_2, all_70_1) % 120.23/17.00 | | | | | | % 120.23/17.00 | | | | | | BETA: splitting (69) gives: % 120.23/17.00 | | | | | | % 120.23/17.00 | | | | | | Case 1: % 120.23/17.00 | | | | | | | % 120.23/17.00 | | | | | | | (82) szNzAzT0 = slcrc0 % 120.23/17.00 | | | | | | | % 120.23/17.00 | | | | | | | REDUCE: (54), (82) imply: % 120.23/17.00 | | | | | | | (83) $false % 120.23/17.00 | | | | | | | % 120.23/17.00 | | | | | | | CLOSE: (83) is inconsistent. % 120.23/17.00 | | | | | | | % 120.23/17.00 | | | | | | Case 2: % 120.23/17.00 | | | | | | | % 120.23/17.00 | | | | | | | % 120.23/17.01 | | | | | | | PRED_UNIFY: (65), (81) imply: % 120.23/17.01 | | | | | | | (84) ~ (all_70_1 = slcrc0) % 120.23/17.01 | | | | | | | % 120.23/17.01 | | | | | | | BETA: splitting (68) gives: % 120.23/17.01 | | | | | | | % 120.23/17.01 | | | | | | | Case 1: % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | (85) all_70_1 = slcrc0 % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | REDUCE: (84), (85) imply: % 120.23/17.01 | | | | | | | | (86) $false % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | CLOSE: (86) is inconsistent. % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | Case 2: % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (mCardCons) with xQ, xk, simplifying % 120.23/17.01 | | | | | | | | with (25), (42), (48), (67) gives: % 120.23/17.01 | | | | | | | | (87) ? [v0: $i] : (szszuzczcdt0(xk) = v0 & $i(v0) & ! [v1: % 120.23/17.01 | | | | | | | | $i] : ! [v2: $i] : ( ~ (sdtpldt0(xQ, v1) = v2) | ~ % 120.23/17.01 | | | | | | | | $i(v1) | ~ aElement0(v1) | sbrdtbr0(v2) = v0 | % 120.23/17.01 | | | | | | | | aElementOf0(v1, xQ))) % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (8) with all_137_0, xk, xK, % 120.23/17.01 | | | | | | | | simplifying with (15), (16), (21), (78), (79), (80) % 120.23/17.01 | | | | | | | | gives: % 120.23/17.01 | | | | | | | | (88) all_137_0 = xk % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | DELTA: instantiating (87) with fresh symbol all_211_0 gives: % 120.23/17.01 | | | | | | | | (89) szszuzczcdt0(xk) = all_211_0 & $i(all_211_0) & ! [v0: % 120.23/17.01 | | | | | | | | $i] : ! [v1: $i] : ( ~ (sdtpldt0(xQ, v0) = v1) | ~ % 120.23/17.01 | | | | | | | | $i(v0) | ~ aElement0(v0) | sbrdtbr0(v1) = all_211_0 | % 120.23/17.01 | | | | | | | | aElementOf0(v0, xQ)) % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | ALPHA: (89) implies: % 120.23/17.01 | | | | | | | | (90) szszuzczcdt0(xk) = all_211_0 % 120.23/17.01 | | | | | | | | (91) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(xQ, v0) = v1) % 120.23/17.01 | | | | | | | | | ~ $i(v0) | ~ aElement0(v0) | sbrdtbr0(v1) = % 120.23/17.01 | | | | | | | | all_211_0 | aElementOf0(v0, xQ)) % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (91) with all_70_2, all_70_1, % 120.23/17.01 | | | | | | | | simplifying with (35), (60), (66), (73) gives: % 120.23/17.01 | | | | | | | | (92) sbrdtbr0(all_70_1) = all_211_0 % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (27) with xK, all_211_0, xk, % 120.23/17.01 | | | | | | | | simplifying with (16), (90) gives: % 120.23/17.01 | | | | | | | | (93) all_211_0 = xK % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | GROUND_INST: instantiating (28) with all_70_0, all_211_0, % 120.23/17.01 | | | | | | | | all_70_1, simplifying with (36), (92) gives: % 120.23/17.01 | | | | | | | | (94) all_211_0 = all_70_0 % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | COMBINE_EQS: (93), (94) imply: % 120.23/17.01 | | | | | | | | (95) all_70_0 = xK % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | SIMP: (95) implies: % 120.23/17.01 | | | | | | | | (96) all_70_0 = xK % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | REDUCE: (32), (96) imply: % 120.23/17.01 | | | | | | | | (97) $false % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | | CLOSE: (97) is inconsistent. % 120.23/17.01 | | | | | | | | % 120.23/17.01 | | | | | | | End of split % 120.23/17.01 | | | | | | | % 120.23/17.01 | | | | | | End of split % 120.23/17.01 | | | | | | % 120.23/17.01 | | | | | Case 2: % 120.23/17.01 | | | | | | % 120.23/17.01 | | | | | | (98) ~ aElement0(all_70_2) % 120.23/17.01 | | | | | | % 120.23/17.01 | | | | | | PRED_UNIFY: (73), (98) imply: % 120.23/17.01 | | | | | | (99) $false % 120.23/17.01 | | | | | | % 120.23/17.01 | | | | | | CLOSE: (99) is inconsistent. % 120.23/17.01 | | | | | | % 120.23/17.01 | | | | | End of split % 120.23/17.01 | | | | | % 120.23/17.01 | | | | End of split % 120.23/17.01 | | | | % 120.23/17.01 | | | End of split % 120.23/17.01 | | | % 120.23/17.01 | | End of split % 120.23/17.01 | | % 120.23/17.01 | Case 2: % 120.23/17.01 | | % 120.23/17.01 | | (100) ~ aSet0(slcrc0) % 120.23/17.01 | | % 120.23/17.01 | | PRED_UNIFY: (1), (100) imply: % 120.23/17.01 | | (101) $false % 120.23/17.01 | | % 120.23/17.01 | | CLOSE: (101) is inconsistent. % 120.23/17.01 | | % 120.23/17.01 | End of split % 120.23/17.01 | % 120.23/17.01 End of proof % 120.23/17.01 % SZS output end Proof for theBenchmark % 120.23/17.01 % 120.23/17.01 16396ms %------------------------------------------------------------------------------