TSTP Solution File: NUM592+3 by Princess---230619
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%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------