TSTP Solution File: NUM620+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM620+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 11:49:01 EDT 2023
% Result : Theorem 51.29s 7.60s
% Output : Proof 77.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM620+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 16:34:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 6.66/1.68 Prover 4: Preprocessing ...
% 6.66/1.72 Prover 0: Preprocessing ...
% 6.66/1.72 Prover 6: Preprocessing ...
% 6.66/1.73 Prover 2: Preprocessing ...
% 6.66/1.73 Prover 3: Preprocessing ...
% 7.21/1.73 Prover 1: Preprocessing ...
% 7.21/1.74 Prover 5: Preprocessing ...
% 18.85/3.34 Prover 1: Constructing countermodel ...
% 19.93/3.46 Prover 6: Proving ...
% 19.93/3.46 Prover 3: Constructing countermodel ...
% 23.97/4.03 Prover 5: Proving ...
% 47.72/7.11 Prover 4: Constructing countermodel ...
% 51.29/7.60 Prover 6: proved (6949ms)
% 51.29/7.60
% 51.29/7.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.29/7.60
% 51.29/7.61 Prover 3: stopped
% 51.29/7.63 Prover 5: stopped
% 51.77/7.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 51.77/7.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 51.77/7.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 52.82/7.84 Prover 7: Preprocessing ...
% 52.82/7.89 Prover 8: Preprocessing ...
% 52.82/7.89 Prover 10: Preprocessing ...
% 52.82/7.93 Prover 2: Proving ...
% 52.82/7.96 Prover 2: stopped
% 52.82/7.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 55.72/8.20 Prover 11: Preprocessing ...
% 57.01/8.35 Prover 8: Warning: ignoring some quantifiers
% 57.21/8.37 Prover 8: Constructing countermodel ...
% 58.61/8.54 Prover 0: Proving ...
% 58.61/8.62 Prover 0: stopped
% 58.61/8.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 58.61/8.75 Prover 13: Preprocessing ...
% 59.16/8.78 Prover 10: Constructing countermodel ...
% 59.16/8.81 Prover 7: Constructing countermodel ...
% 68.28/9.80 Prover 13: Warning: ignoring some quantifiers
% 68.72/9.86 Prover 13: Constructing countermodel ...
% 74.70/10.65 Prover 10: Found proof (size 55)
% 74.70/10.65 Prover 10: proved (3013ms)
% 74.70/10.65 Prover 4: stopped
% 74.70/10.65 Prover 13: stopped
% 74.70/10.65 Prover 7: stopped
% 74.70/10.66 Prover 8: stopped
% 74.70/10.66 Prover 1: stopped
% 76.30/11.06 Prover 11: Constructing countermodel ...
% 76.50/11.09 Prover 11: stopped
% 76.50/11.09
% 76.50/11.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 76.50/11.09
% 76.50/11.10 % SZS output start Proof for theBenchmark
% 76.50/11.11 Assumptions after simplification:
% 76.50/11.11 ---------------------------------
% 76.50/11.11
% 76.50/11.11 (mCountNFin_01)
% 76.50/11.12 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 76.50/11.12
% 76.50/11.12 (mDefEmp)
% 76.50/11.12 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 76.50/11.12 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 76.50/11.12 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 76.50/11.12
% 76.50/11.12 (mDefSub)
% 76.50/11.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 76.50/11.13 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 76.50/11.13 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 76.50/11.13 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 76.50/11.13 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 76.50/11.13 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 76.50/11.13
% 76.50/11.13 (mSuccNum)
% 76.88/11.17 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 76.88/11.17 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 76.88/11.17 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 76.88/11.17 aElementOf0(v0, szNzAzT0))
% 76.88/11.17
% 76.88/11.17 (m__)
% 76.88/11.17 $i(xm) & $i(xx) & $i(xn) & $i(xN) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 76.88/11.17 (sdtlpdtrp0(xN, v1) = v2 & sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 &
% 76.88/11.17 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v2) & ~ aElementOf0(xx, v2) & !
% 76.88/11.17 [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElementOf0(v3, v2)))
% 76.88/11.17
% 76.88/11.17 (m__3671)
% 76.88/11.17 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 76.88/11.17 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 76.88/11.17 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 76.88/11.17 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 76.88/11.17 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 76.88/11.17 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 76.88/11.17 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 76.88/11.17 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 76.88/11.17
% 76.88/11.17 (m__4660)
% 76.88/11.18 szDzozmdt0(xe) = szNzAzT0 & $i(xe) & $i(xN) & $i(szNzAzT0) & aFunction0(xe) &
% 76.88/11.18 ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) | ~
% 76.88/11.18 aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 76.88/11.18 szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & ! [v3: $i]
% 76.88/11.18 : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1, v3))))
% 76.88/11.18
% 76.88/11.18 (m__4730)
% 77.04/11.18 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 77.04/11.18 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 77.04/11.18 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 77.04/11.18 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 77.04/11.18 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 77.04/11.18 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 77.04/11.18 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSubsetOf0(v6, v3) | ~
% 77.04/11.18 aSet0(v6) | ? [v8: $i] : ( ~ (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8))) &
% 77.04/11.18 ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~
% 77.04/11.18 $i(v6) | ~ aElementOf0(v6, v4) | ~ aSet0(v6)) & ! [v6: $i] : ! [v7:
% 77.04/11.18 $i] : (v7 = v5 | ~ (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aSet0(v6)
% 77.04/11.18 | ? [v8: $i] : ? [v9: $i] : ($i(v9) & (( ~ (v8 = xk) & sbrdtbr0(v6) =
% 77.04/11.18 v8 & $i(v8)) | (aElementOf0(v9, v6) & ~ aElementOf0(v9, v3)))))))
% 77.04/11.18
% 77.04/11.18 (m__4758)
% 77.04/11.19 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 77.04/11.19 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & !
% 77.04/11.19 [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~
% 77.04/11.19 $i(v2) | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 77.04/11.19 $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2: $i] : ( ~
% 77.04/11.19 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtlpdtrp0(xd, v3) = v2 &
% 77.04/11.19 $i(v3) & aElementOf0(v3, v0))))
% 77.04/11.19
% 77.04/11.19 (m__4854)
% 77.04/11.19 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) =
% 77.04/11.19 v0 & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 77.04/11.19 $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i] : (v4 =
% 77.04/11.19 v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1)) &
% 77.04/11.19 ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 77.04/11.19 aElementOf0(v3, v1) | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~
% 77.04/11.19 (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 77.04/11.19 aElementOf0(v3, v1)))
% 77.04/11.19
% 77.04/11.19 (m__4891)
% 77.04/11.20 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 77.04/11.20 (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 &
% 77.04/11.20 szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & !
% 77.04/11.20 [v3: $i] : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 77.04/11.20 | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 77.04/11.20 (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 77.04/11.20 aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xe, v4)
% 77.04/11.20 = v3) | ~ $i(v4) | ~ $i(v3) | ~ aElementOf0(v4, v1) | aElementOf0(v3,
% 77.04/11.20 xO)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~
% 77.04/11.20 aElementOf0(v3, v2) | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 77.04/11.20 aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 & $i(v4) &
% 77.04/11.20 aElementOf0(v4, v1))))
% 77.04/11.20
% 77.04/11.20 (m__5309)
% 77.04/11.20 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 77.04/11.20 ? [v2: $i] : (szDzizrdt0(xd) = v1 & sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd,
% 77.04/11.20 xn) = v1 & sdtlpdtrp0(xe, xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1)
% 77.04/11.20 & $i(v0) & aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn,
% 77.04/11.20 szNzAzT0))
% 77.04/11.20
% 77.04/11.20 (m__5389)
% 77.04/11.20 sdtlpdtrp0(xe, xm) = xx & $i(xm) & $i(xx) & $i(xe) & $i(szNzAzT0) &
% 77.04/11.20 aElementOf0(xm, szNzAzT0)
% 77.04/11.20
% 77.04/11.20 (m__5401)
% 77.04/11.20 $i(xm) & $i(xx) & $i(xN) & ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) &
% 77.04/11.20 ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 77.04/11.20
% 77.04/11.20 (function-axioms)
% 77.04/11.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.04/11.21 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 77.04/11.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 77.04/11.21 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 77.04/11.21 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 77.04/11.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 77.04/11.21 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 77.04/11.21 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 77.04/11.21 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 77.04/11.21 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 77.04/11.21 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 77.04/11.21 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 77.04/11.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 77.04/11.21 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 77.04/11.21 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 77.04/11.21 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 77.04/11.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.04/11.21 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 77.04/11.21 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 77.04/11.21 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.04/11.21 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 77.04/11.21 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 77.04/11.21 v0))
% 77.04/11.21
% 77.04/11.21 Further assumptions not needed in the proof:
% 77.04/11.21 --------------------------------------------
% 77.04/11.21 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 77.04/11.21 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 77.04/11.21 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 77.04/11.21 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 77.04/11.21 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 77.04/11.21 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 77.04/11.21 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 77.04/11.21 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 77.04/11.21 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mZeroLess,
% 77.04/11.21 mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520,
% 77.04/11.21 m__3533, m__3623, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331, m__4411,
% 77.04/11.21 m__4618, m__4908, m__4982, m__4998, m__5078, m__5093, m__5106, m__5116, m__5147,
% 77.04/11.21 m__5164, m__5173, m__5182, m__5195, m__5208, m__5217, m__5270, m__5321, m__5348,
% 77.04/11.21 m__5365
% 77.04/11.21
% 77.04/11.21 Those formulas are unsatisfiable:
% 77.04/11.21 ---------------------------------
% 77.04/11.21
% 77.04/11.21 Begin of proof
% 77.04/11.21 |
% 77.04/11.21 | ALPHA: (mDefEmp) implies:
% 77.04/11.21 | (1) aSet0(slcrc0)
% 77.04/11.21 |
% 77.04/11.21 | ALPHA: (mCountNFin_01) implies:
% 77.04/11.21 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 77.04/11.21 |
% 77.04/11.21 | ALPHA: (mDefSub) implies:
% 77.04/11.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 77.04/11.21 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 77.04/11.21 | aSet0(v0) | aElementOf0(v2, v0))
% 77.04/11.21 |
% 77.04/11.21 | ALPHA: (mSuccNum) implies:
% 77.04/11.21 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 77.04/11.21 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 77.04/11.21 |
% 77.04/11.21 | ALPHA: (m__3671) implies:
% 77.04/11.21 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 77.04/11.21 | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 77.04/11.21 |
% 77.04/11.21 | ALPHA: (m__4660) implies:
% 77.04/11.22 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xe, v0) = v1) | ~ $i(v0) |
% 77.04/11.22 | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : (sdtlpdtrp0(xN, v0) = v2
% 77.04/11.22 | & szmzizndt0(v2) = v1 & $i(v2) & $i(v1) & aElementOf0(v1, v2) & !
% 77.04/11.22 | [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) | sdtlseqdt0(v1,
% 77.04/11.22 | v3))))
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__4730) implies:
% 77.04/11.22 | (7) szDzozmdt0(xd) = szNzAzT0
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__4758) implies:
% 77.04/11.22 | (8) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) =
% 77.04/11.22 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT) & aSet0(v1) & ! [v2: $i] :
% 77.04/11.22 | ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v2) | ~ $i(v3) | ~ $i(v2) |
% 77.04/11.22 | ~ aElementOf0(v3, v0) | aElementOf0(v2, v1)) & ! [v2: $i] : ( ~
% 77.04/11.22 | $i(v2) | ~ aElementOf0(v2, v1) | aElementOf0(v2, xT)) & ! [v2:
% 77.04/11.22 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] :
% 77.04/11.22 | (sdtlpdtrp0(xd, v3) = v2 & $i(v3) & aElementOf0(v3, v0))))
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__4854) implies:
% 77.04/11.22 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 77.04/11.22 | sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) = v2 & $i(v2) & $i(v1) &
% 77.04/11.22 | $i(v0) & aElementOf0(v0, xT) & aSet0(v1) & ! [v3: $i] : ! [v4: $i]
% 77.04/11.22 | : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~
% 77.04/11.22 | aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 77.04/11.22 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 77.04/11.22 | aElementOf0(v3, v2)) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xd, v3) = v0)
% 77.04/11.22 | | ~ $i(v3) | ~ aElementOf0(v3, v2) | aElementOf0(v3, v1)))
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__4891) implies:
% 77.04/11.22 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v0 &
% 77.04/11.22 | sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & szDzozmdt0(xd) =
% 77.04/11.22 | v2 & $i(v2) & $i(v1) & $i(v0) & aSet0(v1) & aSet0(xO) & ! [v3: $i]
% 77.04/11.22 | : ! [v4: $i] : (v4 = v0 | ~ (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3)
% 77.04/11.22 | | ~ aElementOf0(v3, v1)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 77.04/11.22 | (sdtlpdtrp0(xd, v3) = v4) | ~ $i(v3) | ~ aElementOf0(v3, v1) |
% 77.04/11.22 | aElementOf0(v3, v2)) & ! [v3: $i] : ! [v4: $i] : ( ~
% 77.04/11.22 | (sdtlpdtrp0(xe, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 77.04/11.22 | aElementOf0(v4, v1) | aElementOf0(v3, xO)) & ! [v3: $i] : ( ~
% 77.04/11.22 | (sdtlpdtrp0(xd, v3) = v0) | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 77.04/11.22 | aElementOf0(v3, v1)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 77.04/11.22 | aElementOf0(v3, xO) | ? [v4: $i] : (sdtlpdtrp0(xe, v4) = v3 &
% 77.04/11.22 | $i(v4) & aElementOf0(v4, v1))))
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__5309) implies:
% 77.04/11.22 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (szDzizrdt0(xd) = v1 &
% 77.04/11.22 | sdtlbdtrb0(xd, v1) = v2 & sdtlpdtrp0(xd, xn) = v1 & sdtlpdtrp0(xe,
% 77.04/11.22 | xn) = xp & szDzozmdt0(xd) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 77.04/11.22 | aElementOf0(xn, v2) & aElementOf0(xn, v0) & aElementOf0(xn,
% 77.04/11.22 | szNzAzT0))
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__5389) implies:
% 77.04/11.22 | (12) aElementOf0(xm, szNzAzT0)
% 77.04/11.22 | (13) sdtlpdtrp0(xe, xm) = xx
% 77.04/11.22 |
% 77.04/11.22 | ALPHA: (m__5401) implies:
% 77.04/11.23 | (14) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 77.04/11.23 | $i(v1) | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 77.04/11.23 |
% 77.04/11.23 | ALPHA: (m__) implies:
% 77.04/11.23 | (15) $i(xn)
% 77.04/11.23 | (16) $i(xm)
% 77.04/11.23 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, v1) = v2 &
% 77.04/11.23 | sdtlpdtrp0(xN, xm) = v0 & szszuzczcdt0(xn) = v1 & $i(v2) & $i(v1) &
% 77.04/11.23 | $i(v0) & aSubsetOf0(v0, v2) & ~ aElementOf0(xx, v2) & ! [v3: $i] :
% 77.04/11.23 | ( ~ $i(v3) | ~ aElementOf0(v3, v0) | aElementOf0(v3, v2)))
% 77.04/11.23 |
% 77.04/11.23 | ALPHA: (function-axioms) implies:
% 77.04/11.23 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.04/11.23 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 77.04/11.23 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.04/11.23 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 77.04/11.23 |
% 77.04/11.23 | DELTA: instantiating (14) with fresh symbol all_86_0 gives:
% 77.04/11.23 | (20) sdtlpdtrp0(xN, xm) = all_86_0 & $i(all_86_0) & ! [v0: $i] : ( ~
% 77.04/11.23 | $i(v0) | ~ aElementOf0(v0, all_86_0) | sdtlseqdt0(xx, v0))
% 77.04/11.23 |
% 77.04/11.23 | ALPHA: (20) implies:
% 77.04/11.23 | (21) sdtlpdtrp0(xN, xm) = all_86_0
% 77.04/11.23 |
% 77.04/11.23 | DELTA: instantiating (17) with fresh symbols all_104_0, all_104_1, all_104_2
% 77.04/11.23 | gives:
% 77.04/11.23 | (22) sdtlpdtrp0(xN, all_104_1) = all_104_0 & sdtlpdtrp0(xN, xm) = all_104_2
% 77.04/11.23 | & szszuzczcdt0(xn) = all_104_1 & $i(all_104_0) & $i(all_104_1) &
% 77.04/11.23 | $i(all_104_2) & aSubsetOf0(all_104_2, all_104_0) & ~ aElementOf0(xx,
% 77.04/11.23 | all_104_0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 77.04/11.23 | all_104_2) | aElementOf0(v0, all_104_0))
% 77.04/11.23 |
% 77.04/11.23 | ALPHA: (22) implies:
% 77.28/11.23 | (23) ~ aElementOf0(xx, all_104_0)
% 77.28/11.23 | (24) aSubsetOf0(all_104_2, all_104_0)
% 77.28/11.23 | (25) $i(all_104_1)
% 77.28/11.23 | (26) $i(all_104_0)
% 77.28/11.23 | (27) szszuzczcdt0(xn) = all_104_1
% 77.28/11.23 | (28) sdtlpdtrp0(xN, xm) = all_104_2
% 77.28/11.23 | (29) sdtlpdtrp0(xN, all_104_1) = all_104_0
% 77.28/11.23 |
% 77.28/11.23 | DELTA: instantiating (11) with fresh symbols all_107_0, all_107_1, all_107_2
% 77.28/11.23 | gives:
% 77.28/11.23 | (30) szDzizrdt0(xd) = all_107_1 & sdtlbdtrb0(xd, all_107_1) = all_107_0 &
% 77.28/11.23 | sdtlpdtrp0(xd, xn) = all_107_1 & sdtlpdtrp0(xe, xn) = xp &
% 77.28/11.23 | szDzozmdt0(xd) = all_107_2 & $i(all_107_0) & $i(all_107_1) &
% 77.28/11.23 | $i(all_107_2) & aElementOf0(xn, all_107_0) & aElementOf0(xn,
% 77.28/11.23 | all_107_2) & aElementOf0(xn, szNzAzT0)
% 77.28/11.23 |
% 77.28/11.23 | ALPHA: (30) implies:
% 77.28/11.23 | (31) aElementOf0(xn, all_107_2)
% 77.28/11.23 | (32) szDzozmdt0(xd) = all_107_2
% 77.28/11.23 |
% 77.28/11.23 | DELTA: instantiating (8) with fresh symbols all_112_0, all_112_1 gives:
% 77.28/11.23 | (33) sdtlcdtrc0(xd, all_112_1) = all_112_0 & szDzozmdt0(xd) = all_112_1 &
% 77.28/11.23 | $i(all_112_0) & $i(all_112_1) & aSubsetOf0(all_112_0, xT) &
% 77.28/11.23 | aSet0(all_112_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v1)
% 77.28/11.23 | = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, all_112_1) |
% 77.28/11.23 | aElementOf0(v0, all_112_0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 77.28/11.23 | aElementOf0(v0, all_112_0) | aElementOf0(v0, xT)) & ! [v0: $i] : (
% 77.28/11.23 | ~ $i(v0) | ~ aElementOf0(v0, all_112_0) | ? [v1: $i] :
% 77.28/11.23 | (sdtlpdtrp0(xd, v1) = v0 & $i(v1) & aElementOf0(v1, all_112_1)))
% 77.28/11.23 |
% 77.28/11.23 | ALPHA: (33) implies:
% 77.28/11.23 | (34) szDzozmdt0(xd) = all_112_1
% 77.28/11.23 |
% 77.28/11.23 | DELTA: instantiating (9) with fresh symbols all_118_0, all_118_1, all_118_2
% 77.28/11.23 | gives:
% 77.28/11.24 | (35) szDzizrdt0(xd) = all_118_2 & sdtlbdtrb0(xd, all_118_2) = all_118_1 &
% 77.28/11.24 | szDzozmdt0(xd) = all_118_0 & $i(all_118_0) & $i(all_118_1) &
% 77.28/11.24 | $i(all_118_2) & aElementOf0(all_118_2, xT) & aSet0(all_118_1) & !
% 77.28/11.24 | [v0: $i] : ! [v1: int] : (v1 = all_118_2 | ~ (sdtlpdtrp0(xd, v0) =
% 77.28/11.24 | v1) | ~ $i(v0) | ~ aElementOf0(v0, all_118_1)) & ! [v0: $i] :
% 77.28/11.24 | ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 77.28/11.24 | aElementOf0(v0, all_118_1) | aElementOf0(v0, all_118_0)) & ! [v0:
% 77.28/11.24 | $i] : ( ~ (sdtlpdtrp0(xd, v0) = all_118_2) | ~ $i(v0) | ~
% 77.28/11.24 | aElementOf0(v0, all_118_0) | aElementOf0(v0, all_118_1))
% 77.28/11.24 |
% 77.28/11.24 | ALPHA: (35) implies:
% 77.28/11.24 | (36) szDzozmdt0(xd) = all_118_0
% 77.28/11.24 |
% 77.28/11.24 | DELTA: instantiating (10) with fresh symbols all_121_0, all_121_1, all_121_2
% 77.28/11.24 | gives:
% 77.28/11.24 | (37) szDzizrdt0(xd) = all_121_2 & sdtlcdtrc0(xe, all_121_1) = xO &
% 77.28/11.24 | sdtlbdtrb0(xd, all_121_2) = all_121_1 & szDzozmdt0(xd) = all_121_0 &
% 77.28/11.24 | $i(all_121_0) & $i(all_121_1) & $i(all_121_2) & aSet0(all_121_1) &
% 77.28/11.24 | aSet0(xO) & ! [v0: $i] : ! [v1: int] : (v1 = all_121_2 | ~
% 77.28/11.24 | (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 77.28/11.24 | all_121_1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0)
% 77.28/11.24 | = v1) | ~ $i(v0) | ~ aElementOf0(v0, all_121_1) |
% 77.28/11.24 | aElementOf0(v0, all_121_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 77.28/11.24 | (sdtlpdtrp0(xe, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 77.28/11.24 | aElementOf0(v1, all_121_1) | aElementOf0(v0, xO)) & ! [v0: $i] : (
% 77.28/11.24 | ~ (sdtlpdtrp0(xd, v0) = all_121_2) | ~ $i(v0) | ~ aElementOf0(v0,
% 77.28/11.24 | all_121_0) | aElementOf0(v0, all_121_1)) & ! [v0: $i] : ( ~
% 77.28/11.24 | $i(v0) | ~ aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1)
% 77.28/11.24 | = v0 & $i(v1) & aElementOf0(v1, all_121_1)))
% 77.28/11.24 |
% 77.28/11.24 | ALPHA: (37) implies:
% 77.28/11.24 | (38) szDzozmdt0(xd) = all_121_0
% 77.28/11.24 |
% 77.28/11.24 | BETA: splitting (2) gives:
% 77.28/11.24 |
% 77.28/11.24 | Case 1:
% 77.28/11.24 | |
% 77.28/11.24 | | (39) ~ aSet0(slcrc0)
% 77.28/11.24 | |
% 77.28/11.24 | | PRED_UNIFY: (1), (39) imply:
% 77.28/11.24 | | (40) $false
% 77.28/11.24 | |
% 77.28/11.24 | | CLOSE: (40) is inconsistent.
% 77.28/11.24 | |
% 77.28/11.24 | Case 2:
% 77.28/11.24 | |
% 77.28/11.24 | |
% 77.28/11.24 | | GROUND_INST: instantiating (18) with all_107_2, all_112_1, xd, simplifying
% 77.28/11.24 | | with (32), (34) gives:
% 77.28/11.24 | | (41) all_112_1 = all_107_2
% 77.28/11.24 | |
% 77.28/11.24 | | GROUND_INST: instantiating (18) with all_112_1, all_118_0, xd, simplifying
% 77.28/11.24 | | with (34), (36) gives:
% 77.28/11.24 | | (42) all_118_0 = all_112_1
% 77.28/11.24 | |
% 77.28/11.24 | | GROUND_INST: instantiating (18) with all_118_0, all_121_0, xd, simplifying
% 77.28/11.24 | | with (36), (38) gives:
% 77.28/11.24 | | (43) all_121_0 = all_118_0
% 77.28/11.24 | |
% 77.28/11.24 | | GROUND_INST: instantiating (18) with szNzAzT0, all_121_0, xd, simplifying
% 77.28/11.24 | | with (7), (38) gives:
% 77.28/11.24 | | (44) all_121_0 = szNzAzT0
% 77.28/11.24 | |
% 77.28/11.24 | | GROUND_INST: instantiating (19) with all_86_0, all_104_2, xm, xN,
% 77.28/11.24 | | simplifying with (21), (28) gives:
% 77.28/11.25 | | (45) all_104_2 = all_86_0
% 77.28/11.25 | |
% 77.28/11.25 | | COMBINE_EQS: (43), (44) imply:
% 77.28/11.25 | | (46) all_118_0 = szNzAzT0
% 77.28/11.25 | |
% 77.28/11.25 | | SIMP: (46) implies:
% 77.28/11.25 | | (47) all_118_0 = szNzAzT0
% 77.28/11.25 | |
% 77.36/11.25 | | COMBINE_EQS: (42), (47) imply:
% 77.36/11.25 | | (48) all_112_1 = szNzAzT0
% 77.36/11.25 | |
% 77.36/11.25 | | SIMP: (48) implies:
% 77.36/11.25 | | (49) all_112_1 = szNzAzT0
% 77.36/11.25 | |
% 77.36/11.25 | | COMBINE_EQS: (41), (49) imply:
% 77.36/11.25 | | (50) all_107_2 = szNzAzT0
% 77.36/11.25 | |
% 77.36/11.25 | | SIMP: (50) implies:
% 77.36/11.25 | | (51) all_107_2 = szNzAzT0
% 77.36/11.25 | |
% 77.36/11.25 | | REDUCE: (24), (45) imply:
% 77.36/11.25 | | (52) aSubsetOf0(all_86_0, all_104_0)
% 77.36/11.25 | |
% 77.36/11.25 | | REDUCE: (31), (51) imply:
% 77.36/11.25 | | (53) aElementOf0(xn, szNzAzT0)
% 77.36/11.25 | |
% 77.36/11.25 | | GROUND_INST: instantiating (4) with xn, all_104_1, simplifying with (15),
% 77.36/11.25 | | (27), (53) gives:
% 77.36/11.25 | | (54) aElementOf0(all_104_1, szNzAzT0)
% 77.36/11.25 | |
% 77.36/11.25 | | GROUND_INST: instantiating (6) with xm, xx, simplifying with (12), (13),
% 77.36/11.25 | | (16) gives:
% 77.36/11.25 | | (55) ? [v0: $i] : (sdtlpdtrp0(xN, xm) = v0 & szmzizndt0(v0) = xx &
% 77.36/11.25 | | $i(v0) & $i(xx) & aElementOf0(xx, v0) & ! [v1: $i] : ( ~ $i(v1) |
% 77.36/11.25 | | ~ aElementOf0(v1, v0) | sdtlseqdt0(xx, v1)))
% 77.36/11.25 | |
% 77.36/11.25 | | DELTA: instantiating (55) with fresh symbol all_150_0 gives:
% 77.36/11.25 | | (56) sdtlpdtrp0(xN, xm) = all_150_0 & szmzizndt0(all_150_0) = xx &
% 77.36/11.25 | | $i(all_150_0) & $i(xx) & aElementOf0(xx, all_150_0) & ! [v0: $i] :
% 77.36/11.25 | | ( ~ $i(v0) | ~ aElementOf0(v0, all_150_0) | sdtlseqdt0(xx, v0))
% 77.36/11.25 | |
% 77.36/11.25 | | ALPHA: (56) implies:
% 77.36/11.25 | | (57) aElementOf0(xx, all_150_0)
% 77.36/11.25 | | (58) $i(xx)
% 77.36/11.25 | | (59) $i(all_150_0)
% 77.36/11.25 | | (60) sdtlpdtrp0(xN, xm) = all_150_0
% 77.36/11.25 | |
% 77.36/11.25 | | GROUND_INST: instantiating (19) with all_86_0, all_150_0, xm, xN,
% 77.36/11.25 | | simplifying with (21), (60) gives:
% 77.36/11.25 | | (61) all_150_0 = all_86_0
% 77.36/11.25 | |
% 77.36/11.25 | | REDUCE: (59), (61) imply:
% 77.36/11.25 | | (62) $i(all_86_0)
% 77.36/11.25 | |
% 77.36/11.25 | | REDUCE: (57), (61) imply:
% 77.36/11.25 | | (63) aElementOf0(xx, all_86_0)
% 77.36/11.25 | |
% 77.36/11.25 | | GROUND_INST: instantiating (5) with all_104_1, all_104_0, simplifying with
% 77.36/11.25 | | (25), (29), (54) gives:
% 77.36/11.25 | | (64) aSet0(all_104_0)
% 77.36/11.25 | |
% 77.36/11.25 | | GROUND_INST: instantiating (3) with all_104_0, all_86_0, xx, simplifying
% 77.36/11.25 | | with (23), (26), (52), (58), (62), (63), (64) gives:
% 77.36/11.25 | | (65) $false
% 77.36/11.25 | |
% 77.36/11.25 | | CLOSE: (65) is inconsistent.
% 77.36/11.25 | |
% 77.36/11.25 | End of split
% 77.36/11.25 |
% 77.36/11.25 End of proof
% 77.36/11.25 % SZS output end Proof for theBenchmark
% 77.36/11.25
% 77.36/11.25 10637ms
%------------------------------------------------------------------------------