%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM592+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 : n016.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 11:48:49 EDT 2023 % Result : Theorem 52.86s 7.80s % Output : Proof 193.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM592+3 : TPTP v8.1.2. Released v4.0.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n016.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 10:04:40 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 6.02/1.62 Prover 4: Preprocessing ... % 6.02/1.62 Prover 1: Preprocessing ... % 6.62/1.67 Prover 6: Preprocessing ... % 6.62/1.67 Prover 2: Preprocessing ... % 6.62/1.67 Prover 5: Preprocessing ... % 6.62/1.67 Prover 0: Preprocessing ... % 6.62/1.67 Prover 3: Preprocessing ... % 19.21/3.36 Prover 3: Constructing countermodel ... % 19.21/3.37 Prover 1: Constructing countermodel ... % 19.21/3.38 Prover 6: Proving ... % 19.86/3.52 Prover 5: Proving ... % 44.91/6.76 Prover 4: Constructing countermodel ... % 48.77/7.37 Prover 0: Proving ... % 48.77/7.40 Prover 2: Proving ... % 52.86/7.79 Prover 3: proved (7149ms) % 52.86/7.79 % 52.86/7.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 52.86/7.80 % 52.86/7.80 Prover 6: stopped % 52.86/7.81 Prover 0: stopped % 52.86/7.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 52.86/7.81 Prover 5: stopped % 52.86/7.81 Prover 2: stopped % 52.86/7.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 52.86/7.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 52.86/7.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 52.86/7.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 54.89/8.08 Prover 11: Preprocessing ... % 55.47/8.16 Prover 13: Preprocessing ... % 55.47/8.16 Prover 7: Preprocessing ... % 55.77/8.22 Prover 10: Preprocessing ... % 56.28/8.26 Prover 8: Preprocessing ... % 59.41/8.73 Prover 8: Warning: ignoring some quantifiers % 60.28/8.76 Prover 8: Constructing countermodel ... % 61.87/8.98 Prover 10: Constructing countermodel ... % 61.87/8.99 Prover 7: Constructing countermodel ... % 63.20/9.21 Prover 13: Warning: ignoring some quantifiers % 63.98/9.37 Prover 13: Constructing countermodel ... % 79.95/11.56 Prover 11: Constructing countermodel ... % 86.76/12.33 Prover 13: stopped % 87.64/12.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 88.69/12.53 Prover 16: Preprocessing ... % 91.71/12.96 Prover 16: Warning: ignoring some quantifiers % 91.71/13.03 Prover 16: Constructing countermodel ... % 115.42/16.00 Prover 1: stopped % 116.02/16.02 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 117.05/16.25 Prover 19: Preprocessing ... % 121.10/16.90 Prover 19: Warning: ignoring some quantifiers % 122.19/16.96 Prover 19: Constructing countermodel ... % 126.87/17.65 Prover 16: stopped % 142.31/19.61 Prover 19: stopped % 191.30/27.70 Prover 7: Found proof (size 34) % 191.30/27.70 Prover 7: proved (19865ms) % 191.30/27.70 Prover 4: stopped % 191.30/27.70 Prover 8: stopped % 191.30/27.71 Prover 11: stopped % 192.36/27.71 Prover 10: stopped % 192.36/27.71 % 192.36/27.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 192.36/27.71 % 192.36/27.72 % SZS output start Proof for theBenchmark % 192.36/27.72 Assumptions after simplification: % 192.36/27.72 --------------------------------- % 192.36/27.72 % 192.36/27.72 (m__) % 192.95/27.77 $i(xi) & $i(xC) & $i(xN) & $i(xk) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? % 192.95/27.77 [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xC, xi) = v3 & sdtlpdtrp0(xN, xi) = v0 & % 192.95/27.77 szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & % 192.95/27.77 $i(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v1 | % 192.95/27.77 ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ % 192.95/27.77 isCountable0(v5) | ~ aElementOf0(v7, v0) | ~ aElementOf0(v4, xT) | ~ % 192.95/27.77 aElement0(v7) | aElementOf0(v7, v2) | ? [v8: $i] : ? [v9: $i] : ( ~ (v9 % 192.95/27.77 = v4) & sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = xk & $i(v9) & $i(v8) % 192.95/27.77 & aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & aSet0(v8) & ! [v10: $i] : % 192.95/27.77 ( ~ $i(v10) | ~ aElementOf0(v10, v8) | aElementOf0(v10, v5)))) & ! % 192.95/27.77 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, % 192.95/27.77 xk) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | % 192.95/27.77 ~ aElementOf0(v7, v2) | ~ aElementOf0(v4, xT) | aElementOf0(v7, v0) | ? % 192.95/27.77 [v8: $i] : ? [v9: $i] : ( ~ (v9 = v4) & sdtlpdtrp0(v3, v8) = v9 & % 192.95/27.77 sbrdtbr0(v8) = xk & $i(v9) & $i(v8) & aSubsetOf0(v8, v5) & % 192.95/27.77 aElementOf0(v8, v6) & aSet0(v8) & ! [v10: $i] : ( ~ $i(v10) | ~ % 192.95/27.77 aElementOf0(v10, v8) | aElementOf0(v10, v5)))) & ! [v4: $i] : ! [v5: % 192.95/27.77 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ % 192.95/27.77 $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v7, % 192.95/27.77 v2) | ~ aElementOf0(v4, xT) | aElement0(v7) | ? [v8: $i] : ? [v9: $i] % 192.95/27.77 : ( ~ (v9 = v4) & sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = xk & $i(v9) & % 192.95/27.77 $i(v8) & aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & aSet0(v8) & ! [v10: % 192.95/27.77 $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v8) | aElementOf0(v10, v5)))) % 192.95/27.77 & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 192.95/27.77 (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | ~ % 192.95/27.77 isCountable0(v5) | ~ aElementOf0(v7, v0) | ~ aElementOf0(v4, xT) | % 192.95/27.77 sdtlseqdt0(v1, v7) | ? [v8: $i] : ? [v9: $i] : ( ~ (v9 = v4) & % 192.95/27.77 sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = xk & $i(v9) & $i(v8) & % 192.95/27.77 aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & aSet0(v8) & ! [v10: $i] : ( % 192.95/27.77 ~ $i(v10) | ~ aElementOf0(v10, v8) | aElementOf0(v10, v5)))) & ! % 192.95/27.77 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ % 192.95/27.77 $i(v5) | ~ $i(v4) | ~ aSubsetOf0(v5, v2) | ~ isCountable0(v5) | ~ % 192.95/27.77 aElementOf0(v4, xT) | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v4) & % 192.95/27.77 sdtlpdtrp0(v3, v7) = v8 & sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & % 192.95/27.77 aSubsetOf0(v7, v5) & aElementOf0(v7, v6) & aSet0(v7) & ! [v9: $i] : ( ~ % 192.95/27.77 $i(v9) | ~ aElementOf0(v9, v7) | aElementOf0(v9, v5)))) & ! [v4: $i] % 192.95/27.77 : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) | % 192.95/27.77 ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v4, xT) | ~ % 192.95/27.77 aElementOf0(v1, v2) | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v4) & % 192.95/27.77 sdtlpdtrp0(v3, v7) = v8 & sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & % 192.95/27.77 aSubsetOf0(v7, v5) & aElementOf0(v7, v6) & aSet0(v7) & ! [v9: $i] : ( ~ % 192.95/27.77 $i(v9) | ~ aElementOf0(v9, v7) | aElementOf0(v9, v5)))) & ! [v4: $i] % 192.95/27.77 : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) | % 192.95/27.77 ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v4, xT) | ~ aSet0(v5) | % 192.95/27.77 ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v10) & $i(v7) % 192.95/27.77 & ((v8 = xk & ~ (v9 = v4) & sdtlpdtrp0(v3, v7) = v9 & sbrdtbr0(v7) = xk % 192.95/27.77 & $i(v9) & aSubsetOf0(v7, v5) & aElementOf0(v7, v6) & aSet0(v7) & ! % 192.95/27.77 [v11: $i] : ( ~ $i(v11) | ~ aElementOf0(v11, v7) | aElementOf0(v11, % 192.95/27.77 v5))) | (aElementOf0(v10, v5) & ~ aElementOf0(v10, v2))))) & ! % 192.95/27.78 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ % 192.95/27.78 $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v4, xT) | % 192.95/27.78 aElementOf0(v1, v0) | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v4) & % 192.95/27.78 sdtlpdtrp0(v3, v7) = v8 & sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & % 192.95/27.78 aSubsetOf0(v7, v5) & aElementOf0(v7, v6) & aSet0(v7) & ! [v9: $i] : ( ~ % 192.95/27.78 $i(v9) | ~ aElementOf0(v9, v7) | aElementOf0(v9, v5)))) & ! [v4: $i] % 192.95/27.78 : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) | % 192.95/27.78 ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v4, xT) | aSet0(v2) | ? % 192.95/27.78 [v7: $i] : ? [v8: $i] : ( ~ (v8 = v4) & sdtlpdtrp0(v3, v7) = v8 & % 192.95/27.78 sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & aSubsetOf0(v7, v5) & % 192.95/27.78 aElementOf0(v7, v6) & aSet0(v7) & ! [v9: $i] : ( ~ $i(v9) | ~ % 192.95/27.78 aElementOf0(v9, v7) | aElementOf0(v9, v5))))) % 192.95/27.78 % 192.95/27.78 (m__4448_02) % 192.95/27.78 $i(xd) & $i(xY) & $i(xi) & $i(xC) & $i(xN) & ? [v0: $i] : ? [v1: $i] : % 192.95/27.78 (sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & % 192.95/27.78 sdtmndt0(v0, v1) = xY & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(xY) & % 192.95/27.78 ~ aElementOf0(v1, xY) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ % 192.95/27.78 aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, xY)) & ! [v2: % 192.95/27.78 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) & ! [v2: % 192.95/27.78 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xY) | aElementOf0(v2, v0)) & ! [v2: % 192.95/27.78 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xY) | aElement0(v2))) % 192.95/27.78 % 192.95/27.78 (m__4545) % 192.95/27.79 $i(xX) & $i(xu) & $i(xd) & $i(xY) & $i(xk) & $i(xT) & ? [v0: $i] : % 192.95/27.79 (slbdtsldtrb0(xX, xk) = v0 & $i(v0) & aSubsetOf0(xX, xY) & isCountable0(xX) & % 192.95/27.79 aElementOf0(xu, xT) & aSet0(xX) & ! [v1: $i] : ! [v2: $i] : (v2 = xu | ~ % 192.95/27.79 (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ aSubsetOf0(v1, xX) | ~ % 192.95/27.79 aSet0(v1) | ? [v3: $i] : ( ~ (v3 = xk) & sbrdtbr0(v1) = v3 & $i(v3))) & % 192.95/27.79 ! [v1: $i] : ! [v2: $i] : (v2 = xu | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ % 192.95/27.79 $i(v1) | ~ aElementOf0(v1, v0) | ~ aSet0(v1)) & ! [v1: $i] : ! [v2: % 192.95/27.79 $i] : (v2 = xu | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ aSet0(v1) | % 192.95/27.79 ? [v3: $i] : ? [v4: $i] : ($i(v4) & (( ~ (v3 = xk) & sbrdtbr0(v1) = v3 & % 192.95/27.79 $i(v3)) | (aElementOf0(v4, v1) & ~ aElementOf0(v4, xX))))) & ! % 192.95/27.79 [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ % 192.95/27.79 aElementOf0(v1, v0) | ~ aSet0(v1) | sdtlpdtrp0(xd, v1) = xu) & ! [v1: % 192.95/27.79 $i] : ( ~ (sbrdtbr0(v1) = xk) | ~ $i(v1) | ~ aSubsetOf0(v1, xX) | ~ % 192.95/27.79 aSet0(v1) | sdtlpdtrp0(xd, v1) = xu) & ! [v1: $i] : ( ~ (sbrdtbr0(v1) = % 192.95/27.79 xk) | ~ $i(v1) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: $i] : ($i(v3) & % 192.95/27.79 ((v2 = xu & sdtlpdtrp0(xd, v1) = xu) | (aElementOf0(v3, v1) & ~ % 192.95/27.79 aElementOf0(v3, xX))))) & ! [v1: $i] : ( ~ $i(v1) | ~ % 192.95/27.79 aElementOf0(v1, xX) | aElementOf0(v1, xY))) % 192.95/27.79 % 192.95/27.79 (function-axioms) % 193.20/27.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 193.20/27.80 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : ! % 193.20/27.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1) % 193.20/27.80 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 193.20/27.80 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) % 193.20/27.80 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 % 193.20/27.80 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] % 193.20/27.80 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, % 193.20/27.80 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 193.20/27.80 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ % 193.20/27.80 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 193.20/27.80 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & % 193.20/27.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) | % 193.20/27.80 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 193.20/27.80 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : ! % 193.20/27.80 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) % 193.20/27.80 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 193.20/27.80 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1: % 193.20/27.80 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) % 193.20/27.80 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 193.20/27.80 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : % 193.20/27.80 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = % 193.20/27.80 v0)) % 193.20/27.80 % 193.20/27.80 Further assumptions not needed in the proof: % 193.20/27.80 -------------------------------------------- % 193.20/27.80 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS, % 193.20/27.80 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, % 193.20/27.80 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, % 193.20/27.80 mDefSeg, mDefSel, mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, % 193.20/27.80 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, % 193.20/27.80 mImgCount, mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, % 193.20/27.80 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, % 193.20/27.80 mPttSet, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, % 193.20/27.80 mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, % 193.20/27.80 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398, % 193.20/27.80 m__3418, m__3435, m__3453, m__3462, m__3520, m__3533, m__3623, m__3671, m__3754, % 193.20/27.80 m__3821, m__3965, m__4151, m__4182, m__4331, m__4423, m__4448, m__4482 % 193.20/27.80 % 193.20/27.80 Those formulas are unsatisfiable: % 193.20/27.80 --------------------------------- % 193.20/27.80 % 193.20/27.80 Begin of proof % 193.20/27.80 | % 193.20/27.80 | ALPHA: (m__4448_02) implies: % 193.20/27.80 | (1) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, % 193.20/27.80 | xi) = v0 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = xY & $i(v1) & % 193.20/27.80 | $i(v0) & aElementOf0(v1, v0) & aSet0(xY) & ~ aElementOf0(v1, xY) & % 193.20/27.80 | ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ aElementOf0(v2, v0) | ~ % 193.20/27.80 | aElement0(v2) | aElementOf0(v2, xY)) & ! [v2: $i] : ( ~ $i(v2) | % 193.20/27.80 | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) & ! [v2: $i] : ( ~ % 193.20/27.80 | $i(v2) | ~ aElementOf0(v2, xY) | aElementOf0(v2, v0)) & ! [v2: % 193.20/27.80 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xY) | aElement0(v2))) % 193.20/27.80 | % 193.20/27.80 | ALPHA: (m__4545) implies: % 193.20/27.80 | (2) $i(xu) % 193.20/27.80 | (3) $i(xX) % 193.20/27.81 | (4) ? [v0: $i] : (slbdtsldtrb0(xX, xk) = v0 & $i(v0) & aSubsetOf0(xX, xY) % 193.20/27.81 | & isCountable0(xX) & aElementOf0(xu, xT) & aSet0(xX) & ! [v1: $i] : % 193.20/27.81 | ! [v2: $i] : (v2 = xu | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ % 193.20/27.81 | aSubsetOf0(v1, xX) | ~ aSet0(v1) | ? [v3: $i] : ( ~ (v3 = xk) & % 193.20/27.81 | sbrdtbr0(v1) = v3 & $i(v3))) & ! [v1: $i] : ! [v2: $i] : (v2 = % 193.20/27.81 | xu | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ aElementOf0(v1, % 193.20/27.81 | v0) | ~ aSet0(v1)) & ! [v1: $i] : ! [v2: $i] : (v2 = xu | ~ % 193.20/27.81 | (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~ aSet0(v1) | ? [v3: $i] % 193.20/27.81 | : ? [v4: $i] : ($i(v4) & (( ~ (v3 = xk) & sbrdtbr0(v1) = v3 & % 193.20/27.81 | $i(v3)) | (aElementOf0(v4, v1) & ~ aElementOf0(v4, xX))))) & % 193.20/27.81 | ! [v1: $i] : ! [v2: $i] : ( ~ (sbrdtbr0(v1) = v2) | ~ $i(v1) | ~ % 193.20/27.81 | aElementOf0(v1, v0) | ~ aSet0(v1) | sdtlpdtrp0(xd, v1) = xu) & ! % 193.20/27.81 | [v1: $i] : ( ~ (sbrdtbr0(v1) = xk) | ~ $i(v1) | ~ aSubsetOf0(v1, % 193.20/27.81 | xX) | ~ aSet0(v1) | sdtlpdtrp0(xd, v1) = xu) & ! [v1: $i] : ( ~ % 193.20/27.81 | (sbrdtbr0(v1) = xk) | ~ $i(v1) | ~ aSet0(v1) | ? [v2: $i] : ? % 193.20/27.81 | [v3: $i] : ($i(v3) & ((v2 = xu & sdtlpdtrp0(xd, v1) = xu) | % 193.20/27.81 | (aElementOf0(v3, v1) & ~ aElementOf0(v3, xX))))) & ! [v1: $i] % 193.20/27.81 | : ( ~ $i(v1) | ~ aElementOf0(v1, xX) | aElementOf0(v1, xY))) % 193.20/27.81 | % 193.20/27.81 | ALPHA: (m__) implies: % 193.20/27.82 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xC, % 193.20/27.82 | xi) = v3 & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & % 193.20/27.82 | sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 193.20/27.82 | $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v1 | ~ % 193.20/27.82 | (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v4) | % 193.20/27.82 | ~ isCountable0(v5) | ~ aElementOf0(v7, v0) | ~ aElementOf0(v4, % 193.20/27.82 | xT) | ~ aElement0(v7) | aElementOf0(v7, v2) | ? [v8: $i] : ? % 193.20/27.82 | [v9: $i] : ( ~ (v9 = v4) & sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = % 193.20/27.82 | xk & $i(v9) & $i(v8) & aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & % 193.20/27.82 | aSet0(v8) & ! [v10: $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v8) % 193.20/27.82 | | aElementOf0(v10, v5)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 193.20/27.82 | $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v7) | % 193.20/27.82 | ~ $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v7, v2) % 193.20/27.82 | | ~ aElementOf0(v4, xT) | aElementOf0(v7, v0) | ? [v8: $i] : ? % 193.20/27.82 | [v9: $i] : ( ~ (v9 = v4) & sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = % 193.20/27.82 | xk & $i(v9) & $i(v8) & aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & % 193.20/27.82 | aSet0(v8) & ! [v10: $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v8) % 193.20/27.82 | | aElementOf0(v10, v5)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 193.20/27.82 | $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v7) | % 193.20/27.82 | ~ $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v7, v2) % 193.20/27.82 | | ~ aElementOf0(v4, xT) | aElement0(v7) | ? [v8: $i] : ? [v9: % 193.20/27.82 | $i] : ( ~ (v9 = v4) & sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = xk % 193.20/27.82 | & $i(v9) & $i(v8) & aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & % 193.20/27.82 | aSet0(v8) & ! [v10: $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v8) % 193.20/27.82 | | aElementOf0(v10, v5)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 193.20/27.82 | $i] : ! [v7: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v7) | % 193.20/27.82 | ~ $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v7, v0) % 193.20/27.82 | | ~ aElementOf0(v4, xT) | sdtlseqdt0(v1, v7) | ? [v8: $i] : ? % 193.20/27.82 | [v9: $i] : ( ~ (v9 = v4) & sdtlpdtrp0(v3, v8) = v9 & sbrdtbr0(v8) = % 193.20/27.82 | xk & $i(v9) & $i(v8) & aSubsetOf0(v8, v5) & aElementOf0(v8, v6) & % 193.20/27.82 | aSet0(v8) & ! [v10: $i] : ( ~ $i(v10) | ~ aElementOf0(v10, v8) % 193.20/27.82 | | aElementOf0(v10, v5)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 193.20/27.82 | $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 193.20/27.82 | aSubsetOf0(v5, v2) | ~ isCountable0(v5) | ~ aElementOf0(v4, xT) | % 193.20/27.82 | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v4) & sdtlpdtrp0(v3, v7) = v8 % 193.20/27.82 | & sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & aSubsetOf0(v7, v5) & % 193.20/27.82 | aElementOf0(v7, v6) & aSet0(v7) & ! [v9: $i] : ( ~ $i(v9) | ~ % 193.20/27.82 | aElementOf0(v9, v7) | aElementOf0(v9, v5)))) & ! [v4: $i] : ! % 193.20/27.82 | [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) % 193.20/27.82 | | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v4, xT) | ~ % 193.20/27.82 | aElementOf0(v1, v2) | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v4) & % 193.20/27.82 | sdtlpdtrp0(v3, v7) = v8 & sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & % 193.20/27.82 | aSubsetOf0(v7, v5) & aElementOf0(v7, v6) & aSet0(v7) & ! [v9: % 193.20/27.82 | $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v7) | aElementOf0(v9, % 193.20/27.82 | v5)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ % 193.20/27.82 | (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 193.20/27.82 | isCountable0(v5) | ~ aElementOf0(v4, xT) | ~ aSet0(v5) | ? [v7: % 193.20/27.82 | $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ($i(v10) & % 193.20/27.82 | $i(v7) & ((v8 = xk & ~ (v9 = v4) & sdtlpdtrp0(v3, v7) = v9 & % 193.20/27.82 | sbrdtbr0(v7) = xk & $i(v9) & aSubsetOf0(v7, v5) & % 193.20/27.82 | aElementOf0(v7, v6) & aSet0(v7) & ! [v11: $i] : ( ~ $i(v11) % 193.20/27.82 | | ~ aElementOf0(v11, v7) | aElementOf0(v11, v5))) | % 193.20/27.82 | (aElementOf0(v10, v5) & ~ aElementOf0(v10, v2))))) & ! [v4: % 193.20/27.82 | $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | % 193.20/27.82 | ~ $i(v5) | ~ $i(v4) | ~ isCountable0(v5) | ~ aElementOf0(v4, % 193.20/27.82 | xT) | aElementOf0(v1, v0) | ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = % 193.20/27.82 | v4) & sdtlpdtrp0(v3, v7) = v8 & sbrdtbr0(v7) = xk & $i(v8) & % 193.20/27.82 | $i(v7) & aSubsetOf0(v7, v5) & aElementOf0(v7, v6) & aSet0(v7) & % 193.20/27.82 | ! [v9: $i] : ( ~ $i(v9) | ~ aElementOf0(v9, v7) | % 193.20/27.82 | aElementOf0(v9, v5)))) & ! [v4: $i] : ! [v5: $i] : ! [v6: % 193.20/27.82 | $i] : ( ~ (slbdtsldtrb0(v5, xk) = v6) | ~ $i(v5) | ~ $i(v4) | ~ % 193.20/27.82 | isCountable0(v5) | ~ aElementOf0(v4, xT) | aSet0(v2) | ? [v7: $i] % 193.20/27.82 | : ? [v8: $i] : ( ~ (v8 = v4) & sdtlpdtrp0(v3, v7) = v8 & % 193.20/27.82 | sbrdtbr0(v7) = xk & $i(v8) & $i(v7) & aSubsetOf0(v7, v5) & % 193.20/27.82 | aElementOf0(v7, v6) & aSet0(v7) & ! [v9: $i] : ( ~ $i(v9) | ~ % 193.20/27.82 | aElementOf0(v9, v7) | aElementOf0(v9, v5))))) % 193.20/27.82 | % 193.20/27.82 | ALPHA: (function-axioms) implies: % 193.20/27.82 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) % 193.20/27.82 | = v1) | ~ (szmzizndt0(v2) = v0)) % 193.20/27.82 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 193.20/27.82 | (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) % 193.20/27.82 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 193.20/27.82 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) % 193.20/27.82 | % 193.20/27.82 | DELTA: instantiating (1) with fresh symbols all_73_0, all_73_1 gives: % 193.20/27.83 | (9) sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, xi) = all_73_1 & % 193.20/27.83 | szmzizndt0(all_73_1) = all_73_0 & sdtmndt0(all_73_1, all_73_0) = xY & % 193.20/27.83 | $i(all_73_0) & $i(all_73_1) & aElementOf0(all_73_0, all_73_1) & % 193.20/27.83 | aSet0(xY) & ~ aElementOf0(all_73_0, xY) & ! [v0: any] : (v0 = % 193.20/27.83 | all_73_0 | ~ $i(v0) | ~ aElementOf0(v0, all_73_1) | ~ % 193.20/27.83 | aElement0(v0) | aElementOf0(v0, xY)) & ! [v0: $i] : ( ~ $i(v0) | ~ % 193.20/27.83 | aElementOf0(v0, all_73_1) | sdtlseqdt0(all_73_0, v0)) & ! [v0: $i] : % 193.20/27.83 | ( ~ $i(v0) | ~ aElementOf0(v0, xY) | aElementOf0(v0, all_73_1)) & ! % 193.20/27.83 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xY) | aElement0(v0)) % 193.20/27.83 | % 193.20/27.83 | ALPHA: (9) implies: % 193.20/27.83 | (10) sdtmndt0(all_73_1, all_73_0) = xY % 193.20/27.83 | (11) szmzizndt0(all_73_1) = all_73_0 % 193.20/27.83 | (12) sdtlpdtrp0(xN, xi) = all_73_1 % 193.20/27.83 | (13) sdtlpdtrp0(xC, xi) = xd % 193.20/27.83 | % 193.20/27.83 | DELTA: instantiating (4) with fresh symbol all_76_0 gives: % 193.20/27.83 | (14) slbdtsldtrb0(xX, xk) = all_76_0 & $i(all_76_0) & aSubsetOf0(xX, xY) & % 193.20/27.83 | isCountable0(xX) & aElementOf0(xu, xT) & aSet0(xX) & ! [v0: $i] : ! % 193.20/27.83 | [v1: $i] : (v1 = xu | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ % 193.20/27.83 | aSubsetOf0(v0, xX) | ~ aSet0(v0) | ? [v2: $i] : ( ~ (v2 = xk) & % 193.20/27.83 | sbrdtbr0(v0) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : (v1 = % 193.20/27.83 | xu | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, % 193.20/27.83 | all_76_0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : (v1 = xu | % 193.20/27.83 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aSet0(v0) | ? [v2: % 193.20/27.83 | $i] : ? [v3: $i] : ($i(v3) & (( ~ (v2 = xk) & sbrdtbr0(v0) = v2 & % 193.20/27.83 | $i(v2)) | (aElementOf0(v3, v0) & ~ aElementOf0(v3, xX))))) & % 193.20/27.83 | ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ % 193.20/27.83 | aElementOf0(v0, all_76_0) | ~ aSet0(v0) | sdtlpdtrp0(xd, v0) = xu) % 193.20/27.83 | & ! [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ % 193.20/27.83 | aSubsetOf0(v0, xX) | ~ aSet0(v0) | sdtlpdtrp0(xd, v0) = xu) & ! % 193.20/27.83 | [v0: $i] : ( ~ (sbrdtbr0(v0) = xk) | ~ $i(v0) | ~ aSet0(v0) | ? % 193.20/27.83 | [v1: $i] : ? [v2: $i] : ($i(v2) & ((v1 = xu & sdtlpdtrp0(xd, v0) = % 193.20/27.83 | xu) | (aElementOf0(v2, v0) & ~ aElementOf0(v2, xX))))) & ! % 193.20/27.83 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xX) | aElementOf0(v0, xY)) % 193.20/27.83 | % 193.20/27.83 | ALPHA: (14) implies: % 193.20/27.83 | (15) aElementOf0(xu, xT) % 193.20/27.83 | (16) isCountable0(xX) % 193.20/27.83 | (17) aSubsetOf0(xX, xY) % 193.20/27.83 | (18) slbdtsldtrb0(xX, xk) = all_76_0 % 193.20/27.83 | (19) ! [v0: $i] : ! [v1: $i] : (v1 = xu | ~ (sdtlpdtrp0(xd, v0) = v1) | % 193.20/27.83 | ~ $i(v0) | ~ aElementOf0(v0, all_76_0) | ~ aSet0(v0)) % 193.20/27.83 | % 193.20/27.83 | DELTA: instantiating (5) with fresh symbols all_85_0, all_85_1, all_85_2, % 193.20/27.83 | all_85_3 gives: % 193.20/27.85 | (20) sdtlpdtrp0(xC, xi) = all_85_0 & sdtlpdtrp0(xN, xi) = all_85_3 & % 193.20/27.85 | szmzizndt0(all_85_3) = all_85_2 & sdtmndt0(all_85_3, all_85_2) = % 193.20/27.85 | all_85_1 & $i(all_85_0) & $i(all_85_1) & $i(all_85_2) & $i(all_85_3) & % 193.20/27.85 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : (v3 = % 193.20/27.85 | all_85_2 | ~ (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v3) | ~ $i(v1) | % 193.20/27.85 | ~ $i(v0) | ~ isCountable0(v1) | ~ aElementOf0(v3, all_85_3) | ~ % 193.20/27.85 | aElementOf0(v0, xT) | ~ aElement0(v3) | aElementOf0(v3, all_85_1) | % 193.20/27.85 | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v0) & sdtlpdtrp0(all_85_0, v4) % 193.20/27.85 | = v5 & sbrdtbr0(v4) = xk & $i(v5) & $i(v4) & aSubsetOf0(v4, v1) & % 193.20/27.85 | aElementOf0(v4, v2) & aSet0(v4) & ! [v6: $i] : ( ~ $i(v6) | ~ % 193.20/27.85 | aElementOf0(v6, v4) | aElementOf0(v6, v1)))) & ! [v0: $i] : ! % 193.20/27.85 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtsldtrb0(v1, xk) = v2) % 193.20/27.85 | | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ isCountable0(v1) | ~ % 193.20/27.85 | aElementOf0(v3, all_85_1) | ~ aElementOf0(v0, xT) | aElementOf0(v3, % 193.20/27.85 | all_85_3) | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v0) & % 193.20/27.85 | sdtlpdtrp0(all_85_0, v4) = v5 & sbrdtbr0(v4) = xk & $i(v5) & % 193.20/27.85 | $i(v4) & aSubsetOf0(v4, v1) & aElementOf0(v4, v2) & aSet0(v4) & ! % 193.20/27.85 | [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v4) | aElementOf0(v6, % 193.20/27.85 | v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] % 193.20/27.85 | : ( ~ (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 193.20/27.85 | | ~ isCountable0(v1) | ~ aElementOf0(v3, all_85_1) | ~ % 193.20/27.85 | aElementOf0(v0, xT) | aElement0(v3) | ? [v4: $i] : ? [v5: $i] : ( % 193.20/27.85 | ~ (v5 = v0) & sdtlpdtrp0(all_85_0, v4) = v5 & sbrdtbr0(v4) = xk & % 193.20/27.85 | $i(v5) & $i(v4) & aSubsetOf0(v4, v1) & aElementOf0(v4, v2) & % 193.20/27.85 | aSet0(v4) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v4) | % 193.20/27.85 | aElementOf0(v6, v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 193.20/27.85 | : ! [v3: $i] : ( ~ (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v3) | ~ % 193.20/27.85 | $i(v1) | ~ $i(v0) | ~ isCountable0(v1) | ~ aElementOf0(v3, % 193.20/27.85 | all_85_3) | ~ aElementOf0(v0, xT) | sdtlseqdt0(all_85_2, v3) | ? % 193.20/27.85 | [v4: $i] : ? [v5: $i] : ( ~ (v5 = v0) & sdtlpdtrp0(all_85_0, v4) = % 193.20/27.85 | v5 & sbrdtbr0(v4) = xk & $i(v5) & $i(v4) & aSubsetOf0(v4, v1) & % 193.20/27.85 | aElementOf0(v4, v2) & aSet0(v4) & ! [v6: $i] : ( ~ $i(v6) | ~ % 193.20/27.85 | aElementOf0(v6, v4) | aElementOf0(v6, v1)))) & ! [v0: $i] : ! % 193.20/27.85 | [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v1) | % 193.20/27.85 | ~ $i(v0) | ~ aSubsetOf0(v1, all_85_1) | ~ isCountable0(v1) | ~ % 193.20/27.85 | aElementOf0(v0, xT) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v0) & % 193.20/27.85 | sdtlpdtrp0(all_85_0, v3) = v4 & sbrdtbr0(v3) = xk & $i(v4) & % 193.20/27.85 | $i(v3) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2) & aSet0(v3) & ! % 193.20/27.85 | [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v3) | aElementOf0(v5, % 193.20/27.85 | v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 193.20/27.85 | (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 193.20/27.85 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ~ aElementOf0(all_85_2, % 193.20/27.85 | all_85_1) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v0) & % 193.20/27.85 | sdtlpdtrp0(all_85_0, v3) = v4 & sbrdtbr0(v3) = xk & $i(v4) & % 193.20/27.85 | $i(v3) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2) & aSet0(v3) & ! % 193.20/27.85 | [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v3) | aElementOf0(v5, % 193.20/27.85 | v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 193.20/27.85 | (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 193.20/27.85 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ~ aSet0(v1) | ? [v3: % 193.20/27.85 | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & $i(v3) & % 193.20/27.85 | ((v4 = xk & ~ (v5 = v0) & sdtlpdtrp0(all_85_0, v3) = v5 & % 193.20/27.85 | sbrdtbr0(v3) = xk & $i(v5) & aSubsetOf0(v3, v1) & % 193.20/27.85 | aElementOf0(v3, v2) & aSet0(v3) & ! [v7: $i] : ( ~ $i(v7) | % 193.20/27.85 | ~ aElementOf0(v7, v3) | aElementOf0(v7, v1))) | % 193.20/27.85 | (aElementOf0(v6, v1) & ~ aElementOf0(v6, all_85_1))))) & ! % 193.20/27.85 | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xk) = v2) % 193.20/27.85 | | ~ $i(v1) | ~ $i(v0) | ~ isCountable0(v1) | ~ aElementOf0(v0, % 193.20/27.85 | xT) | aElementOf0(all_85_2, all_85_3) | ? [v3: $i] : ? [v4: $i] % 193.20/27.85 | : ( ~ (v4 = v0) & sdtlpdtrp0(all_85_0, v3) = v4 & sbrdtbr0(v3) = xk % 193.20/27.85 | & $i(v4) & $i(v3) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2) & % 193.20/27.85 | aSet0(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v3) | % 193.46/27.85 | aElementOf0(v5, v1)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 193.46/27.85 | : ( ~ (slbdtsldtrb0(v1, xk) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 193.46/27.85 | isCountable0(v1) | ~ aElementOf0(v0, xT) | aSet0(all_85_1) | ? % 193.46/27.85 | [v3: $i] : ? [v4: $i] : ( ~ (v4 = v0) & sdtlpdtrp0(all_85_0, v3) = % 193.46/27.85 | v4 & sbrdtbr0(v3) = xk & $i(v4) & $i(v3) & aSubsetOf0(v3, v1) & % 193.46/27.85 | aElementOf0(v3, v2) & aSet0(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ % 193.46/27.85 | aElementOf0(v5, v3) | aElementOf0(v5, v1)))) % 193.46/27.85 | % 193.46/27.85 | ALPHA: (20) implies: % 193.46/27.85 | (21) sdtmndt0(all_85_3, all_85_2) = all_85_1 % 193.46/27.85 | (22) szmzizndt0(all_85_3) = all_85_2 % 193.46/27.85 | (23) sdtlpdtrp0(xN, xi) = all_85_3 % 193.46/27.85 | (24) sdtlpdtrp0(xC, xi) = all_85_0 % 193.46/27.85 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v1, xk) = % 193.46/27.85 | v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, all_85_1) | ~ % 193.46/27.85 | isCountable0(v1) | ~ aElementOf0(v0, xT) | ? [v3: $i] : ? [v4: % 193.46/27.85 | $i] : ( ~ (v4 = v0) & sdtlpdtrp0(all_85_0, v3) = v4 & sbrdtbr0(v3) % 193.46/27.85 | = xk & $i(v4) & $i(v3) & aSubsetOf0(v3, v1) & aElementOf0(v3, v2) % 193.46/27.85 | & aSet0(v3) & ! [v5: $i] : ( ~ $i(v5) | ~ aElementOf0(v5, v3) | % 193.47/27.85 | aElementOf0(v5, v1)))) % 193.47/27.85 | % 193.47/27.85 | GROUND_INST: instantiating (6) with all_73_0, all_85_2, all_73_1, simplifying % 193.47/27.85 | with (11) gives: % 193.47/27.85 | (26) all_85_2 = all_73_0 | ~ (szmzizndt0(all_73_1) = all_85_2) % 193.47/27.85 | % 193.47/27.85 | GROUND_INST: instantiating (8) with all_73_1, all_85_3, xi, xN, simplifying % 193.47/27.85 | with (12), (23) gives: % 193.47/27.85 | (27) all_85_3 = all_73_1 % 193.47/27.85 | % 193.47/27.85 | GROUND_INST: instantiating (8) with xd, all_85_0, xi, xC, simplifying with % 193.47/27.85 | (13), (24) gives: % 193.47/27.85 | (28) all_85_0 = xd % 193.47/27.85 | % 193.47/27.85 | REDUCE: (22), (27) imply: % 193.47/27.85 | (29) szmzizndt0(all_73_1) = all_85_2 % 193.47/27.85 | % 193.47/27.85 | REDUCE: (21), (27) imply: % 193.47/27.85 | (30) sdtmndt0(all_73_1, all_85_2) = all_85_1 % 193.47/27.85 | % 193.47/27.85 | BETA: splitting (26) gives: % 193.47/27.85 | % 193.47/27.85 | Case 1: % 193.47/27.85 | | % 193.47/27.85 | | (31) ~ (szmzizndt0(all_73_1) = all_85_2) % 193.47/27.85 | | % 193.47/27.85 | | PRED_UNIFY: (29), (31) imply: % 193.47/27.85 | | (32) $false % 193.47/27.85 | | % 193.47/27.85 | | CLOSE: (32) is inconsistent. % 193.47/27.85 | | % 193.47/27.86 | Case 2: % 193.47/27.86 | | % 193.47/27.86 | | (33) all_85_2 = all_73_0 % 193.47/27.86 | | % 193.47/27.86 | | REDUCE: (30), (33) imply: % 193.47/27.86 | | (34) sdtmndt0(all_73_1, all_73_0) = all_85_1 % 193.47/27.86 | | % 193.47/27.86 | | GROUND_INST: instantiating (7) with xY, all_85_1, all_73_0, all_73_1, % 193.47/27.86 | | simplifying with (10), (34) gives: % 193.47/27.86 | | (35) all_85_1 = xY % 193.47/27.86 | | % 193.47/27.86 | | GROUND_INST: instantiating (25) with xu, xX, all_76_0, simplifying with (2), % 193.47/27.86 | | (3), (15), (16), (18) gives: % 193.47/27.86 | | (36) ~ aSubsetOf0(xX, all_85_1) | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = % 193.47/27.86 | | xu) & sdtlpdtrp0(all_85_0, v0) = v1 & sbrdtbr0(v0) = xk & $i(v1) % 193.47/27.86 | | & $i(v0) & aSubsetOf0(v0, xX) & aElementOf0(v0, all_76_0) & % 193.47/27.86 | | aSet0(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | % 193.47/27.86 | | aElementOf0(v2, xX))) % 193.47/27.86 | | % 193.47/27.86 | | BETA: splitting (36) gives: % 193.47/27.86 | | % 193.47/27.86 | | Case 1: % 193.47/27.86 | | | % 193.47/27.86 | | | (37) ~ aSubsetOf0(xX, all_85_1) % 193.47/27.86 | | | % 193.47/27.86 | | | REDUCE: (35), (37) imply: % 193.47/27.86 | | | (38) ~ aSubsetOf0(xX, xY) % 193.47/27.86 | | | % 193.47/27.86 | | | PRED_UNIFY: (17), (38) imply: % 193.47/27.86 | | | (39) $false % 193.47/27.86 | | | % 193.47/27.86 | | | CLOSE: (39) is inconsistent. % 193.47/27.86 | | | % 193.47/27.86 | | Case 2: % 193.47/27.86 | | | % 193.47/27.86 | | | (40) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xu) & sdtlpdtrp0(all_85_0, % 193.47/27.86 | | | v0) = v1 & sbrdtbr0(v0) = xk & $i(v1) & $i(v0) & % 193.47/27.86 | | | aSubsetOf0(v0, xX) & aElementOf0(v0, all_76_0) & aSet0(v0) & ! % 193.47/27.86 | | | [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | aElementOf0(v2, % 193.47/27.86 | | | xX))) % 193.47/27.86 | | | % 193.47/27.86 | | | DELTA: instantiating (40) with fresh symbols all_192_0, all_192_1 gives: % 193.47/27.86 | | | (41) ~ (all_192_0 = xu) & sdtlpdtrp0(all_85_0, all_192_1) = all_192_0 % 193.47/27.86 | | | & sbrdtbr0(all_192_1) = xk & $i(all_192_0) & $i(all_192_1) & % 193.47/27.86 | | | aSubsetOf0(all_192_1, xX) & aElementOf0(all_192_1, all_76_0) & % 193.47/27.86 | | | aSet0(all_192_1) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, % 193.47/27.86 | | | all_192_1) | aElementOf0(v0, xX)) % 193.47/27.86 | | | % 193.47/27.86 | | | ALPHA: (41) implies: % 193.47/27.86 | | | (42) ~ (all_192_0 = xu) % 193.47/27.86 | | | (43) aSet0(all_192_1) % 193.47/27.86 | | | (44) aElementOf0(all_192_1, all_76_0) % 193.47/27.86 | | | (45) $i(all_192_1) % 193.47/27.86 | | | (46) sdtlpdtrp0(all_85_0, all_192_1) = all_192_0 % 193.47/27.86 | | | % 193.47/27.86 | | | REDUCE: (28), (46) imply: % 193.47/27.86 | | | (47) sdtlpdtrp0(xd, all_192_1) = all_192_0 % 193.47/27.86 | | | % 193.47/27.86 | | | GROUND_INST: instantiating (19) with all_192_1, all_192_0, simplifying % 193.47/27.86 | | | with (43), (44), (45), (47) gives: % 193.47/27.86 | | | (48) all_192_0 = xu % 193.47/27.86 | | | % 193.47/27.86 | | | REDUCE: (42), (48) imply: % 193.47/27.86 | | | (49) $false % 193.47/27.86 | | | % 193.47/27.86 | | | CLOSE: (49) is inconsistent. % 193.47/27.86 | | | % 193.47/27.87 | | End of split % 193.47/27.87 | | % 193.47/27.87 | End of split % 193.47/27.87 | % 193.47/27.87 End of proof % 193.47/27.87 % SZS output end Proof for theBenchmark % 193.47/27.87 % 193.47/27.87 27259ms %------------------------------------------------------------------------------