TSTP Solution File: NUM621+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM621+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 : n019.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 11:49:02 EDT 2023
% Result : Theorem 145.52s 20.16s
% Output : Proof 146.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM621+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 : n019.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 08:22:58 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.56/1.65 Prover 4: Preprocessing ...
% 6.56/1.65 Prover 1: Preprocessing ...
% 6.56/1.67 Prover 5: Preprocessing ...
% 6.56/1.67 Prover 0: Preprocessing ...
% 6.56/1.67 Prover 3: Preprocessing ...
% 6.56/1.67 Prover 2: Preprocessing ...
% 6.56/1.67 Prover 6: Preprocessing ...
% 18.89/3.31 Prover 1: Constructing countermodel ...
% 18.89/3.31 Prover 3: Constructing countermodel ...
% 19.38/3.38 Prover 6: Proving ...
% 21.88/3.71 Prover 5: Proving ...
% 47.45/7.08 Prover 4: Constructing countermodel ...
% 50.33/7.48 Prover 2: Proving ...
% 54.06/8.10 Prover 0: Proving ...
% 99.60/13.96 Prover 5: stopped
% 99.60/13.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 100.53/14.13 Prover 7: Preprocessing ...
% 103.47/14.46 Prover 2: stopped
% 103.47/14.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 104.85/14.68 Prover 8: Preprocessing ...
% 106.53/14.91 Prover 7: Constructing countermodel ...
% 107.18/15.02 Prover 8: Warning: ignoring some quantifiers
% 107.18/15.04 Prover 8: Constructing countermodel ...
% 114.14/16.00 Prover 1: stopped
% 114.14/16.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 116.10/16.17 Prover 9: Preprocessing ...
% 129.07/17.88 Prover 6: stopped
% 129.07/17.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.78/18.12 Prover 10: Preprocessing ...
% 133.88/18.56 Prover 9: Constructing countermodel ...
% 134.47/18.71 Prover 10: Constructing countermodel ...
% 144.87/20.13 Prover 10: Found proof (size 92)
% 144.87/20.13 Prover 10: proved (2248ms)
% 144.87/20.13 Prover 7: stopped
% 144.87/20.13 Prover 9: stopped
% 144.87/20.13 Prover 8: stopped
% 144.87/20.13 Prover 3: stopped
% 144.87/20.15 Prover 4: stopped
% 144.87/20.16 Prover 0: stopped
% 145.52/20.16
% 145.52/20.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 145.52/20.16
% 145.52/20.18 % SZS output start Proof for theBenchmark
% 145.52/20.19 Assumptions after simplification:
% 145.52/20.19 ---------------------------------
% 145.52/20.19
% 145.52/20.19 (mCountNFin_01)
% 145.52/20.19 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 145.52/20.19
% 145.52/20.19 (mDefEmp)
% 145.52/20.19 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 145.52/20.19 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 145.52/20.19 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 145.52/20.19
% 145.52/20.19 (mMinMin)
% 146.34/20.22 $i(szNzAzT0) & $i(slcrc0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 146.34/20.22 $i] : (v3 = v2 | v1 = slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~
% 146.34/20.22 (szmzizndt0(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0)
% 146.34/20.22 | ~ aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~ aElementOf0(v2,
% 146.34/20.22 v1))
% 146.34/20.22
% 146.34/20.22 (m__)
% 146.34/20.22 $i(xm) & $i(xx) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 146.34/20.22 ? [v3: $i] : (sdtlpdtrp0(xN, v2) = v3 & sdtlpdtrp0(xN, xm) = v1 &
% 146.34/20.22 sdtlpdtrp0(xN, xn) = v0 & szszuzczcdt0(xn) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 146.34/20.22 $i(v0) & aSubsetOf0(v0, v1) & ~ aElementOf0(xx, v3) & ! [v4: $i] : ( ~
% 146.34/20.22 $i(v4) | ~ aElementOf0(v4, v0) | aElementOf0(v4, v1)))
% 146.34/20.22
% 146.34/20.22 (m__3671)
% 146.34/20.22 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 146.34/20.22 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 146.34/20.22 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 146.34/20.22 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 146.34/20.22 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 146.34/20.22 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 146.34/20.22 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 146.34/20.22 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 146.34/20.22
% 146.34/20.22 (m__4660)
% 146.34/20.23 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 146.34/20.23 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 146.34/20.23 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 146.34/20.23 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 146.34/20.23 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 146.34/20.23
% 146.34/20.23 (m__4730)
% 146.34/20.23 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 146.34/20.23 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 146.34/20.23 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 146.34/20.23 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 146.34/20.23 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 146.34/20.23 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 146.34/20.23 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~
% 146.34/20.23 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) &
% 146.34/20.23 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 146.34/20.23 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7:
% 146.34/20.23 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6)
% 146.34/20.23 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) =
% 146.34/20.23 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3)))))))
% 146.34/20.23
% 146.34/20.23 (m__4758)
% 146.34/20.23 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 146.34/20.23 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & !
% 146.34/20.23 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 146.34/20.23 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 146.34/20.23 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 146.34/20.23 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 &
% 146.34/20.23 $i(v3) & aElementOf0(v3, v0))))
% 146.34/20.23
% 146.34/20.23 (m__4854)
% 146.34/20.24 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 146.34/20.24 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 146.34/20.24 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 146.34/20.24 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 146.34/20.24 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 146.34/20.24 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 146.34/20.24 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 146.34/20.24 aElementOf0(v3, v1)))
% 146.34/20.24
% 146.34/20.24 (m__4891)
% 146.34/20.24 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 146.34/20.24 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 146.34/20.24 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 146.34/20.24 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 146.34/20.24 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 146.34/20.24 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 146.34/20.24 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 146.34/20.24 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 146.34/20.24 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 146.34/20.24 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 146.34/20.24 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 146.34/20.24 aElementOf0(v4, v1))))
% 146.34/20.24
% 146.34/20.24 (m__5093)
% 146.34/20.24 $i(xQ) & $i(xO) & $i(slcrc0) & ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) &
% 146.34/20.24 aElementOf0(v0, xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) |
% 146.34/20.24 aElementOf0(v1, xO)))
% 146.34/20.24
% 146.34/20.24 (m__5106)
% 146.34/20.24 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) |
% 146.34/20.24 ~ aElementOf0(v0, xQ) | aElementOf0(v0, szNzAzT0))
% 146.34/20.24
% 146.34/20.24 (m__5147)
% 146.34/20.24 szmzizndt0(xQ) = xp & $i(xp) & $i(xQ) & aElementOf0(xp, xQ) & ! [v0: $i] : (
% 146.34/20.24 ~ $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(xp, v0))
% 146.34/20.24
% 146.34/20.24 (m__5164)
% 146.34/20.24 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 146.34/20.24 $i(v0) & aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 146.34/20.24 $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) | aElementOf0(v1, xP))
% 146.34/20.24 & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElementOf0(v1, xQ)) &
% 146.34/20.24 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1:
% 146.34/20.24 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 146.34/20.24
% 146.34/20.24 (m__5309)
% 146.34/20.24 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 146.34/20.24 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd,
% 146.34/20.24 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1)
% 146.34/20.24 & $i(v0) & aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn,
% 146.34/20.24 szNzAzT0))
% 146.34/20.24
% 146.34/20.24 (m__5348)
% 146.34/20.25 $i(xx) & $i(xP) & $i(xQ) & ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 &
% 146.34/20.25 $i(v0) & aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx))
% 146.34/20.25
% 146.34/20.25 (m__5389)
% 146.34/20.25 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) &
% 146.34/20.25 aElementOf0(xm, szNzAzT0)
% 146.34/20.25
% 146.34/20.25 (m__5401)
% 146.34/20.25 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) &
% 146.34/20.25 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 146.34/20.25
% 146.34/20.25 (m__5442)
% 146.34/20.25 $i(xm) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 146.34/20.25 $i] : (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn)
% 146.34/20.25 = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~
% 146.34/20.25 aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2))
% 146.34/20.25
% 146.34/20.25 (function-axioms)
% 146.34/20.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 146.34/20.25 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 146.34/20.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 146.34/20.25 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 146.34/20.25 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 146.34/20.25 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 146.34/20.25 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 146.34/20.25 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 146.34/20.25 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 146.34/20.25 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 146.34/20.25 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 146.34/20.25 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 146.34/20.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 146.34/20.25 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 146.34/20.25 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 146.34/20.25 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 146.34/20.25 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 146.34/20.25 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 146.34/20.25 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 146.34/20.25 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 146.34/20.25 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 146.34/20.25 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 146.34/20.25 v0))
% 146.34/20.25
% 146.34/20.25 Further assumptions not needed in the proof:
% 146.34/20.25 --------------------------------------------
% 146.34/20.25 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 146.34/20.25 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 146.34/20.25 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 146.34/20.25 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 146.34/20.25 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 146.34/20.25 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 146.34/20.25 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 146.34/20.25 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 146.34/20.25 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 146.34/20.25 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 146.34/20.25 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331,
% 146.34/20.25 m__4411, m__4618, m__4908, m__4982, m__4998, m__5078, m__5116, m__5173, m__5182,
% 146.34/20.25 m__5195, m__5208, m__5217, m__5270, m__5321, m__5365
% 146.34/20.25
% 146.34/20.25 Those formulas are unsatisfiable:
% 146.34/20.25 ---------------------------------
% 146.34/20.25
% 146.34/20.25 Begin of proof
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (mDefEmp) implies:
% 146.34/20.26 | (1) aSet0(slcrc0)
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (mCountNFin_01) implies:
% 146.34/20.26 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (mMinMin) implies:
% 146.34/20.26 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | v1 =
% 146.34/20.26 | slcrc0 | v0 = slcrc0 | ~ (szmzizndt0(v1) = v3) | ~ (szmzizndt0(v0)
% 146.34/20.26 | = v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 146.34/20.26 | aSubsetOf0(v0, szNzAzT0) | ~ aElementOf0(v3, v0) | ~
% 146.34/20.26 | aElementOf0(v2, v1))
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (m__3671) implies:
% 146.34/20.26 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 146.34/20.26 | ~ aElementOf0(v0, szNzAzT0) | isCountable0(v1))
% 146.34/20.26 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 146.34/20.26 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0))
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (m__4660) implies:
% 146.34/20.26 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 146.34/20.26 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 146.34/20.26 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & !
% 146.34/20.26 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 146.34/20.26 | v3))))
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (m__4730) implies:
% 146.34/20.26 | (7) szDzozmdt0(xd) = szNzAzT0
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (m__4758) implies:
% 146.34/20.26 | (8) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) =
% 146.34/20.26 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] :
% 146.34/20.26 | ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) |
% 146.34/20.26 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 146.34/20.26 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2:
% 146.34/20.26 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 146.34/20.26 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 146.34/20.26 |
% 146.34/20.26 | ALPHA: (m__4854) implies:
% 146.34/20.26 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 146.34/20.26 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 146.34/20.26 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i]
% 146.34/20.26 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 146.34/20.27 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 146.34/20.27 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 146.34/20.27 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0)
% 146.34/20.27 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1)))
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__4891) implies:
% 146.34/20.27 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 146.34/20.27 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 146.34/20.27 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i]
% 146.34/20.27 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 146.34/20.27 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 146.34/20.27 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 146.34/20.27 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 146.34/20.27 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 146.34/20.27 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 146.34/20.27 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 146.34/20.27 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 146.34/20.27 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 146.34/20.27 | $i(v4) & aElementOf0(v4, v1))))
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5093) implies:
% 146.34/20.27 | (11) ? [v0: $i] : ( ~ (xQ = slcrc0) & $i(v0) & aElementOf0(v0, xQ) & !
% 146.34/20.27 | [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1,
% 146.34/20.27 | xO)))
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5106) implies:
% 146.34/20.27 | (12) aSubsetOf0(xQ, szNzAzT0)
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5147) implies:
% 146.34/20.27 | (13) szmzizndt0(xQ) = xp
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5164) implies:
% 146.34/20.27 | (14) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 146.34/20.27 | aSet0(xP) & ~ aElementOf0(v0, xP) & ! [v1: $i] : (v1 = v0 | ~
% 146.34/20.27 | $i(v1) | ~ aElementOf0(v1, xQ) | ~ aElement0(v1) |
% 146.34/20.27 | aElementOf0(v1, xP)) & ! [v1: $i] : ( ~ $i(v1) | ~
% 146.34/20.27 | aElementOf0(v1, xP) | aElementOf0(v1, xQ)) & ! [v1: $i] : ( ~
% 146.34/20.27 | $i(v1) | ~ aElementOf0(v1, xP) | aElement0(v1)) & ! [v1: $i] : (
% 146.34/20.27 | ~ $i(v1) | ~ aElementOf0(v1, xQ) | sdtlseqdt0(v0, v1)))
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5309) implies:
% 146.34/20.27 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 &
% 146.34/20.27 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe,
% 146.34/20.27 | xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 146.34/20.27 | aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn,
% 146.34/20.27 | szNzAzT0))
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5348) implies:
% 146.34/20.27 | (16) $i(xQ)
% 146.34/20.27 | (17) ? [v0: $i] : ( ~ (v0 = xx) & szmzizndt0(xQ) = v0 & $i(v0) &
% 146.34/20.27 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx))
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5389) implies:
% 146.34/20.27 | (18) aElementOf0(xm, szNzAzT0)
% 146.34/20.27 | (19) sdtlpdtrp0(xe, xm) = xx
% 146.34/20.27 |
% 146.34/20.27 | ALPHA: (m__5401) implies:
% 146.34/20.27 | (20) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 146.34/20.27 | $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (m__5442) implies:
% 146.34/20.28 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 146.34/20.28 | (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn)
% 146.34/20.28 | = v1 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v0) & ~
% 146.34/20.28 | aSubsetOf0(v0, v2) & ~ aElementOf0(v3, v2))
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (m__) implies:
% 146.34/20.28 | (22) $i(xn)
% 146.34/20.28 | (23) $i(xm)
% 146.34/20.28 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 146.34/20.28 | (sdtlpdtrp0(xN, v2) = v3 & sdtlpdtrp0(xN, xm) = v1 & sdtlpdtrp0(xN,
% 146.34/20.28 | xn) = v0 & szszuzczcdt0(xn) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 146.34/20.28 | $i(v0) & aSubsetOf0(v0, v1) & ~ aElementOf0(xx, v3) & ! [v4: $i] :
% 146.34/20.28 | ( ~ $i(v4) | ~ aElementOf0(v4, v0) | aElementOf0(v4, v1)))
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (function-axioms) implies:
% 146.34/20.28 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 146.34/20.28 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 146.34/20.28 | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 146.34/20.28 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 146.34/20.28 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 146.34/20.28 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 146.34/20.28 |
% 146.34/20.28 | DELTA: instantiating (20) with fresh symbol all_86_0 gives:
% 146.34/20.28 | (28) sdtlpdtrp0(xN, xm) = all_86_0 & $i(all_86_0) & ! [v0: $i] : ( ~
% 146.34/20.28 | $i(v0) | ~ aElementOf0(v0, all_86_0) | sdtlseqdt0(xx, v0))
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (28) implies:
% 146.34/20.28 | (29) sdtlpdtrp0(xN, xm) = all_86_0
% 146.34/20.28 |
% 146.34/20.28 | DELTA: instantiating (11) with fresh symbol all_89_0 gives:
% 146.34/20.28 | (30) ~ (xQ = slcrc0) & $i(all_89_0) & aElementOf0(all_89_0, xQ) & ! [v0:
% 146.34/20.28 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xO))
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (30) implies:
% 146.34/20.28 | (31) ~ (xQ = slcrc0)
% 146.34/20.28 |
% 146.34/20.28 | DELTA: instantiating (17) with fresh symbol all_92_0 gives:
% 146.34/20.28 | (32) ~ (all_92_0 = xx) & szmzizndt0(xQ) = all_92_0 & $i(all_92_0) &
% 146.34/20.28 | aElementOf0(xx, xP) & aElementOf0(xx, xQ) & aElement0(xx)
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (32) implies:
% 146.34/20.28 | (33) ~ (all_92_0 = xx)
% 146.34/20.28 | (34) aElementOf0(xx, xQ)
% 146.34/20.28 | (35) szmzizndt0(xQ) = all_92_0
% 146.34/20.28 |
% 146.34/20.28 | DELTA: instantiating (21) with fresh symbols all_104_0, all_104_1, all_104_2,
% 146.34/20.28 | all_104_3 gives:
% 146.34/20.28 | (36) sdtlpdtrp0(xN, all_104_2) = all_104_1 & sdtlpdtrp0(xN, xm) = all_104_3
% 146.34/20.28 | & szszuzczcdt0(xn) = all_104_2 & $i(all_104_0) & $i(all_104_1) &
% 146.34/20.28 | $i(all_104_2) & $i(all_104_3) & aElementOf0(all_104_0, all_104_3) & ~
% 146.34/20.28 | aSubsetOf0(all_104_3, all_104_1) & ~ aElementOf0(all_104_0,
% 146.34/20.28 | all_104_1)
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (36) implies:
% 146.34/20.28 | (37) sdtlpdtrp0(xN, xm) = all_104_3
% 146.34/20.28 |
% 146.34/20.28 | DELTA: instantiating (15) with fresh symbols all_106_0, all_106_1, all_106_2
% 146.34/20.28 | gives:
% 146.34/20.28 | (38) szDzizrdt0(xd) = all_106_1 & sdtlbdtrb0(xd, all_106_1) = all_106_0 &
% 146.34/20.28 | sdtlpdtrp0(xd, xn) = all_106_1 & sdtlpdtrp0(xe, xn) = xp &
% 146.34/20.28 | szDzozmdt0(xd) = all_106_2 & $i(all_106_0) & $i(all_106_1) &
% 146.34/20.28 | $i(all_106_2) & aElementOf0(xn, all_106_0) & aElementOf0(xn,
% 146.34/20.28 | all_106_2) & aElementOf0(xn, szNzAzT0)
% 146.34/20.28 |
% 146.34/20.28 | ALPHA: (38) implies:
% 146.34/20.28 | (39) aElementOf0(xn, all_106_2)
% 146.34/20.28 | (40) szDzozmdt0(xd) = all_106_2
% 146.34/20.28 | (41) sdtlpdtrp0(xe, xn) = xp
% 146.34/20.28 |
% 146.34/20.28 | DELTA: instantiating (24) with fresh symbols all_108_0, all_108_1, all_108_2,
% 146.34/20.28 | all_108_3 gives:
% 146.34/20.29 | (42) sdtlpdtrp0(xN, all_108_1) = all_108_0 & sdtlpdtrp0(xN, xm) = all_108_2
% 146.34/20.29 | & sdtlpdtrp0(xN, xn) = all_108_3 & szszuzczcdt0(xn) = all_108_1 &
% 146.34/20.29 | $i(all_108_0) & $i(all_108_1) & $i(all_108_2) & $i(all_108_3) &
% 146.34/20.29 | aSubsetOf0(all_108_3, all_108_2) & ~ aElementOf0(xx, all_108_0) & !
% 146.34/20.29 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_108_3) |
% 146.34/20.29 | aElementOf0(v0, all_108_2))
% 146.34/20.29 |
% 146.34/20.29 | ALPHA: (42) implies:
% 146.34/20.29 | (43) sdtlpdtrp0(xN, xn) = all_108_3
% 146.34/20.29 | (44) sdtlpdtrp0(xN, xm) = all_108_2
% 146.34/20.29 | (45) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_108_3) |
% 146.34/20.29 | aElementOf0(v0, all_108_2))
% 146.34/20.29 |
% 146.34/20.29 | DELTA: instantiating (8) with fresh symbols all_111_0, all_111_1 gives:
% 146.34/20.29 | (46) sdtlcdtrc0(xd, all_111_1) = all_111_0 & szDzozmdt0(xd) = all_111_1 &
% 146.34/20.29 | $i(all_111_0) & $i(all_111_1) & aSubsetOf0(all_111_0, xT) &
% 146.34/20.29 | aSet0(all_111_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1)
% 146.34/20.29 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_111_1) |
% 146.34/20.29 | aElementOf0(v0, all_111_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 146.34/20.29 | aElementOf0(v0, all_111_0) | aElementOf0(v0, xT)) & ! [v0: $i] : (
% 146.34/20.29 | ~ $i(v0) | ~ aElementOf0(v0, all_111_0) | ? [v1: $i] :
% 146.34/20.29 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_111_1)))
% 146.34/20.29 |
% 146.34/20.29 | ALPHA: (46) implies:
% 146.34/20.29 | (47) szDzozmdt0(xd) = all_111_1
% 146.34/20.29 |
% 146.34/20.29 | DELTA: instantiating (14) with fresh symbol all_114_0 gives:
% 146.34/20.29 | (48) szmzizndt0(xQ) = all_114_0 & sdtmndt0(xQ, all_114_0) = xP &
% 146.34/20.29 | $i(all_114_0) & aSet0(xP) & ~ aElementOf0(all_114_0, xP) & ! [v0:
% 146.34/20.29 | any] : (v0 = all_114_0 | ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~
% 146.34/20.29 | aElement0(v0) | aElementOf0(v0, xP)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 146.34/20.29 | aElementOf0(v0, xP) | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~
% 146.34/20.29 | $i(v0) | ~ aElementOf0(v0, xP) | aElement0(v0)) & ! [v0: $i] : ( ~
% 146.34/20.29 | $i(v0) | ~ aElementOf0(v0, xQ) | sdtlseqdt0(all_114_0, v0))
% 146.34/20.29 |
% 146.34/20.29 | ALPHA: (48) implies:
% 146.34/20.29 | (49) szmzizndt0(xQ) = all_114_0
% 146.34/20.29 |
% 146.34/20.29 | DELTA: instantiating (9) with fresh symbols all_120_0, all_120_1, all_120_2
% 146.34/20.29 | gives:
% 146.34/20.29 | (50) szDzizrdt0(xd) = all_120_2 & sdtlbdtrb0(xd, all_120_2) = all_120_1 &
% 146.34/20.29 | szDzozmdt0(xd) = all_120_0 & $i(all_120_0) & $i(all_120_1) &
% 146.34/20.29 | $i(all_120_2) & aElementOf0(all_120_2, xT) & aSet0(all_120_1) & !
% 146.34/20.29 | [v0: $i] : ! [v1: int] : (v1 = all_120_2 | ~ (sdtlpdtrp0(xd, v0) =
% 146.34/20.29 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_120_1)) & ! [v0: $i] :
% 146.34/20.29 | ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 146.34/20.29 | aElementOf0(v0, all_120_1) | aElementOf0(v0, all_120_0)) & ! [v0:
% 146.34/20.29 | $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_120_2) | ~ $i(v0) | ~
% 146.34/20.29 | aElementOf0(v0, all_120_0) | aElementOf0(v0, all_120_1))
% 146.34/20.29 |
% 146.34/20.29 | ALPHA: (50) implies:
% 146.34/20.29 | (51) szDzozmdt0(xd) = all_120_0
% 146.34/20.29 |
% 146.34/20.29 | DELTA: instantiating (10) with fresh symbols all_123_0, all_123_1, all_123_2
% 146.34/20.29 | gives:
% 146.34/20.29 | (52) szDzizrdt0(xd) = all_123_2 & sdtlcdtrc0(xe, all_123_1) = xO &
% 146.34/20.29 | sdtlbdtrb0(xd, all_123_2) = all_123_1 & szDzozmdt0(xd) = all_123_0 &
% 146.34/20.29 | $i(all_123_0) & $i(all_123_1) & $i(all_123_2) & aSet0(all_123_1) &
% 146.34/20.29 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_123_2 | ~
% 146.34/20.29 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 146.34/20.29 | all_123_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 146.34/20.29 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_123_1) |
% 146.34/20.29 | aElementOf0(v0, all_123_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 146.34/20.29 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 146.34/20.29 | aElementOf0(v1, all_123_1) | aElementOf0(v0, xO)) & ! [v0: $i] : (
% 146.34/20.29 | ~ (sdtlpdtrp0(xd, v0) = all_123_2) | ~ $i(v0) | ~ aElementOf0(v0,
% 146.34/20.29 | all_123_0) | aElementOf0(v0, all_123_1)) & ! [v0: $i] : ( ~
% 146.34/20.29 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1)
% 146.34/20.29 | = v0 & $i(v1) & aElementOf0(v1, all_123_1)))
% 146.34/20.29 |
% 146.34/20.29 | ALPHA: (52) implies:
% 146.34/20.29 | (53) szDzozmdt0(xd) = all_123_0
% 146.34/20.29 |
% 146.34/20.29 | BETA: splitting (2) gives:
% 146.34/20.29 |
% 146.34/20.30 | Case 1:
% 146.34/20.30 | |
% 146.34/20.30 | | (54) ~ aSet0(slcrc0)
% 146.34/20.30 | |
% 146.34/20.30 | | PRED_UNIFY: (1), (54) imply:
% 146.34/20.30 | | (55) $false
% 146.34/20.30 | |
% 146.34/20.30 | | CLOSE: (55) is inconsistent.
% 146.34/20.30 | |
% 146.34/20.30 | Case 2:
% 146.34/20.30 | |
% 146.34/20.30 | | (56) ~ isCountable0(slcrc0)
% 146.34/20.30 | |
% 146.34/20.30 | | GROUND_INST: instantiating (25) with all_92_0, all_114_0, xQ, simplifying
% 146.34/20.30 | | with (35), (49) gives:
% 146.34/20.30 | | (57) all_114_0 = all_92_0
% 146.34/20.30 | |
% 146.34/20.30 | | GROUND_INST: instantiating (25) with xp, all_114_0, xQ, simplifying with
% 146.34/20.30 | | (13), (49) gives:
% 146.34/20.30 | | (58) all_114_0 = xp
% 146.34/20.30 | |
% 146.34/20.30 | | GROUND_INST: instantiating (26) with szNzAzT0, all_111_1, xd, simplifying
% 146.34/20.30 | | with (7), (47) gives:
% 146.84/20.30 | | (59) all_111_1 = szNzAzT0
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (26) with all_120_0, all_123_0, xd, simplifying
% 146.84/20.30 | | with (51), (53) gives:
% 146.84/20.30 | | (60) all_123_0 = all_120_0
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (26) with all_111_1, all_123_0, xd, simplifying
% 146.84/20.30 | | with (47), (53) gives:
% 146.84/20.30 | | (61) all_123_0 = all_111_1
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (26) with all_106_2, all_123_0, xd, simplifying
% 146.84/20.30 | | with (40), (53) gives:
% 146.84/20.30 | | (62) all_123_0 = all_106_2
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (27) with all_104_3, all_108_2, xm, xN,
% 146.84/20.30 | | simplifying with (37), (44) gives:
% 146.84/20.30 | | (63) all_108_2 = all_104_3
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (27) with all_86_0, all_108_2, xm, xN,
% 146.84/20.30 | | simplifying with (29), (44) gives:
% 146.84/20.30 | | (64) all_108_2 = all_86_0
% 146.84/20.30 | |
% 146.84/20.30 | | COMBINE_EQS: (60), (62) imply:
% 146.84/20.30 | | (65) all_120_0 = all_106_2
% 146.84/20.30 | |
% 146.84/20.30 | | COMBINE_EQS: (60), (61) imply:
% 146.84/20.30 | | (66) all_120_0 = all_111_1
% 146.84/20.30 | |
% 146.84/20.30 | | COMBINE_EQS: (65), (66) imply:
% 146.84/20.30 | | (67) all_111_1 = all_106_2
% 146.84/20.30 | |
% 146.84/20.30 | | SIMP: (67) implies:
% 146.84/20.30 | | (68) all_111_1 = all_106_2
% 146.84/20.30 | |
% 146.84/20.30 | | COMBINE_EQS: (57), (58) imply:
% 146.84/20.30 | | (69) all_92_0 = xp
% 146.84/20.30 | |
% 146.84/20.30 | | SIMP: (69) implies:
% 146.84/20.30 | | (70) all_92_0 = xp
% 146.84/20.30 | |
% 146.84/20.30 | | COMBINE_EQS: (59), (68) imply:
% 146.84/20.30 | | (71) all_106_2 = szNzAzT0
% 146.84/20.30 | |
% 146.84/20.30 | | COMBINE_EQS: (63), (64) imply:
% 146.84/20.30 | | (72) all_104_3 = all_86_0
% 146.84/20.30 | |
% 146.84/20.30 | | REDUCE: (33), (70) imply:
% 146.84/20.30 | | (73) ~ (xx = xp)
% 146.84/20.30 | |
% 146.84/20.30 | | SIMP: (73) implies:
% 146.84/20.30 | | (74) ~ (xx = xp)
% 146.84/20.30 | |
% 146.84/20.30 | | REDUCE: (39), (71) imply:
% 146.84/20.30 | | (75) aElementOf0(xn, szNzAzT0)
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (5) with xm, all_86_0, simplifying with (18),
% 146.84/20.30 | | (23), (29) gives:
% 146.84/20.30 | | (76) aSubsetOf0(all_86_0, szNzAzT0)
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (4) with xm, all_86_0, simplifying with (18),
% 146.84/20.30 | | (23), (29) gives:
% 146.84/20.30 | | (77) isCountable0(all_86_0)
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (6) with xn, xp, simplifying with (22), (41),
% 146.84/20.30 | | (75) gives:
% 146.84/20.30 | | (78) ? [v0: $i] : (sdtlpdtrp0(xN, xn) = v0 & szmzizndt0(v0) = xp &
% 146.84/20.30 | | $i(v0) & $i(xp) & aElementOf0(xp, v0) & ! [v1: $i] : ( ~ $i(v1) |
% 146.84/20.30 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xp, v1)))
% 146.84/20.30 | |
% 146.84/20.30 | | GROUND_INST: instantiating (6) with xm, xx, simplifying with (18), (19),
% 146.84/20.30 | | (23) gives:
% 146.84/20.30 | | (79) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx &
% 146.84/20.30 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) |
% 146.84/20.30 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 146.84/20.30 | |
% 146.84/20.30 | | DELTA: instantiating (79) with fresh symbol all_152_0 gives:
% 146.84/20.30 | | (80) sdtlpdtrp0(xN, xm) = all_152_0 & szmzizndt0(all_152_0) = xx &
% 146.84/20.30 | | $i(all_152_0) & $i(xx) & aElementOf0(xx, all_152_0) & ! [v0: $i] :
% 146.84/20.30 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_152_0) | sdtlseqdt0(xx, v0))
% 146.84/20.30 | |
% 146.84/20.30 | | ALPHA: (80) implies:
% 146.84/20.30 | | (81) $i(all_152_0)
% 146.84/20.30 | | (82) szmzizndt0(all_152_0) = xx
% 146.84/20.30 | | (83) sdtlpdtrp0(xN, xm) = all_152_0
% 146.84/20.30 | |
% 146.84/20.30 | | DELTA: instantiating (78) with fresh symbol all_155_0 gives:
% 146.84/20.31 | | (84) sdtlpdtrp0(xN, xn) = all_155_0 & szmzizndt0(all_155_0) = xp &
% 146.84/20.31 | | $i(all_155_0) & $i(xp) & aElementOf0(xp, all_155_0) & ! [v0: $i] :
% 146.84/20.31 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_155_0) | sdtlseqdt0(xp, v0))
% 146.84/20.31 | |
% 146.84/20.31 | | ALPHA: (84) implies:
% 146.84/20.31 | | (85) aElementOf0(xp, all_155_0)
% 146.84/20.31 | | (86) $i(xp)
% 146.84/20.31 | | (87) sdtlpdtrp0(xN, xn) = all_155_0
% 146.84/20.31 | |
% 146.84/20.31 | | GROUND_INST: instantiating (27) with all_108_3, all_155_0, xn, xN,
% 146.84/20.31 | | simplifying with (43), (87) gives:
% 146.84/20.31 | | (88) all_155_0 = all_108_3
% 146.84/20.31 | |
% 146.84/20.31 | | GROUND_INST: instantiating (27) with all_86_0, all_152_0, xm, xN,
% 146.84/20.31 | | simplifying with (29), (83) gives:
% 146.84/20.31 | | (89) all_152_0 = all_86_0
% 146.84/20.31 | |
% 146.84/20.31 | | REDUCE: (82), (89) imply:
% 146.84/20.31 | | (90) szmzizndt0(all_86_0) = xx
% 146.84/20.31 | |
% 146.84/20.31 | | REDUCE: (81), (89) imply:
% 146.84/20.31 | | (91) $i(all_86_0)
% 146.84/20.31 | |
% 146.84/20.31 | | REDUCE: (85), (88) imply:
% 146.84/20.31 | | (92) aElementOf0(xp, all_108_3)
% 146.84/20.31 | |
% 146.84/20.31 | | GROUND_INST: instantiating (45) with xp, simplifying with (86), (92) gives:
% 146.84/20.31 | | (93) aElementOf0(xp, all_108_2)
% 146.84/20.31 | |
% 146.84/20.31 | | REDUCE: (64), (93) imply:
% 146.84/20.31 | | (94) aElementOf0(xp, all_86_0)
% 146.84/20.31 | |
% 146.84/20.31 | | GROUND_INST: instantiating (3) with xQ, all_86_0, xp, xx, simplifying with
% 146.84/20.31 | | (12), (13), (16), (34), (76), (90), (91), (94) gives:
% 146.84/20.31 | | (95) all_86_0 = slcrc0 | xx = xp | xQ = slcrc0
% 146.84/20.31 | |
% 146.84/20.31 | | BETA: splitting (95) gives:
% 146.84/20.31 | |
% 146.84/20.31 | | Case 1:
% 146.84/20.31 | | |
% 146.84/20.31 | | | (96) all_86_0 = slcrc0
% 146.84/20.31 | | |
% 146.84/20.31 | | | REDUCE: (77), (96) imply:
% 146.84/20.31 | | | (97) isCountable0(slcrc0)
% 146.84/20.31 | | |
% 146.84/20.31 | | | PRED_UNIFY: (56), (97) imply:
% 146.84/20.31 | | | (98) $false
% 146.84/20.31 | | |
% 146.84/20.31 | | | CLOSE: (98) is inconsistent.
% 146.84/20.31 | | |
% 146.84/20.31 | | Case 2:
% 146.84/20.31 | | |
% 146.84/20.31 | | | (99) xx = xp | xQ = slcrc0
% 146.84/20.31 | | |
% 146.84/20.31 | | | BETA: splitting (99) gives:
% 146.84/20.31 | | |
% 146.84/20.31 | | | Case 1:
% 146.84/20.31 | | | |
% 146.84/20.31 | | | | (100) xQ = slcrc0
% 146.84/20.31 | | | |
% 146.84/20.31 | | | | REDUCE: (31), (100) imply:
% 146.84/20.31 | | | | (101) $false
% 146.84/20.31 | | | |
% 146.84/20.31 | | | | CLOSE: (101) is inconsistent.
% 146.84/20.31 | | | |
% 146.84/20.31 | | | Case 2:
% 146.84/20.31 | | | |
% 146.84/20.31 | | | | (102) xx = xp
% 146.84/20.31 | | | |
% 146.84/20.31 | | | | REDUCE: (74), (102) imply:
% 146.84/20.31 | | | | (103) $false
% 146.84/20.31 | | | |
% 146.84/20.31 | | | | CLOSE: (103) is inconsistent.
% 146.84/20.31 | | | |
% 146.84/20.31 | | | End of split
% 146.84/20.31 | | |
% 146.84/20.31 | | End of split
% 146.84/20.31 | |
% 146.84/20.31 | End of split
% 146.84/20.31 |
% 146.84/20.31 End of proof
% 146.84/20.31 % SZS output end Proof for theBenchmark
% 146.84/20.31
% 146.84/20.31 19704ms
%------------------------------------------------------------------------------