TSTP Solution File: NUM606+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM606+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.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 11:48:55 EDT 2023
% Result : Theorem 37.84s 5.77s
% Output : Proof 52.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM606+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.09 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.08/0.28 % Computer : n005.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Fri Aug 25 11:05:53 EDT 2023
% 0.08/0.28 % CPUTime :
% 0.13/0.53 ________ _____
% 0.13/0.53 ___ __ \_________(_)________________________________
% 0.13/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.13/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.13/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.13/0.53
% 0.13/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.13/0.53 (2023-06-19)
% 0.13/0.53
% 0.13/0.53 (c) Philipp Rümmer, 2009-2023
% 0.13/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.13/0.53 Amanda Stjerna.
% 0.13/0.53 Free software under BSD-3-Clause.
% 0.13/0.53
% 0.13/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.13/0.53
% 0.13/0.53 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.13/0.54 Running up to 7 provers in parallel.
% 0.13/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.13/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.13/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.13/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.13/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.13/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.13/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.72/1.34 Prover 4: Preprocessing ...
% 4.72/1.34 Prover 1: Preprocessing ...
% 5.23/1.39 Prover 6: Preprocessing ...
% 5.23/1.39 Prover 0: Preprocessing ...
% 5.23/1.39 Prover 5: Preprocessing ...
% 5.23/1.39 Prover 3: Preprocessing ...
% 5.23/1.39 Prover 2: Preprocessing ...
% 17.24/3.03 Prover 3: Constructing countermodel ...
% 17.24/3.05 Prover 1: Constructing countermodel ...
% 17.24/3.06 Prover 6: Proving ...
% 18.61/3.30 Prover 5: Proving ...
% 22.45/3.73 Prover 2: Proving ...
% 28.26/4.58 Prover 4: Constructing countermodel ...
% 29.92/4.74 Prover 0: Proving ...
% 37.84/5.77 Prover 3: proved (5213ms)
% 37.84/5.77
% 37.84/5.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.84/5.77
% 37.84/5.79 Prover 5: stopped
% 37.84/5.80 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 37.84/5.80 Prover 6: stopped
% 37.84/5.80 Prover 0: stopped
% 37.84/5.81 Prover 2: stopped
% 37.84/5.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 37.84/5.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 37.84/5.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 37.84/5.83 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 40.82/6.19 Prover 10: Preprocessing ...
% 40.82/6.20 Prover 11: Preprocessing ...
% 40.82/6.20 Prover 7: Preprocessing ...
% 40.82/6.20 Prover 8: Preprocessing ...
% 40.82/6.21 Prover 13: Preprocessing ...
% 43.15/6.60 Prover 7: Constructing countermodel ...
% 43.15/6.68 Prover 10: Constructing countermodel ...
% 45.12/6.75 Prover 8: Warning: ignoring some quantifiers
% 45.49/6.77 Prover 8: Constructing countermodel ...
% 46.88/6.96 Prover 13: Warning: ignoring some quantifiers
% 46.88/7.00 Prover 13: Constructing countermodel ...
% 50.82/7.48 Prover 10: Found proof (size 62)
% 50.82/7.48 Prover 10: proved (1652ms)
% 50.82/7.48 Prover 7: stopped
% 50.82/7.48 Prover 8: stopped
% 50.82/7.48 Prover 13: stopped
% 50.82/7.48 Prover 4: stopped
% 51.03/7.51 Prover 1: stopped
% 51.79/7.72 Prover 11: Constructing countermodel ...
% 51.79/7.76 Prover 11: stopped
% 51.79/7.76
% 51.79/7.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.79/7.76
% 52.08/7.77 % SZS output start Proof for theBenchmark
% 52.11/7.77 Assumptions after simplification:
% 52.11/7.77 ---------------------------------
% 52.11/7.77
% 52.11/7.77 (mDefPtt)
% 52.25/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 52.25/7.81 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 52.25/7.81 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 52.25/7.81 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4,
% 52.25/7.81 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 52.25/7.81 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & !
% 52.25/7.81 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i]
% 52.25/7.81 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 =
% 52.25/7.81 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4)
% 52.25/7.81 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & !
% 52.25/7.81 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 52.25/7.81 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2))))
% 52.25/7.81
% 52.25/7.81 (mDefSub)
% 52.25/7.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 52.25/7.81 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 52.25/7.81 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 52.25/7.81 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 52.25/7.81 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 52.25/7.81 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 52.25/7.81
% 52.25/7.81 (mEOfElem)
% 52.25/7.81 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 52.25/7.81 ~ aSet0(v0) | aElement0(v1))
% 52.25/7.81
% 52.25/7.81 (mNATSet)
% 52.25/7.81 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 52.25/7.81
% 52.25/7.81 (mNatExtra)
% 52.25/7.82 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 52.25/7.82 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 52.25/7.82 aElementOf0(v1, szNzAzT0)))
% 52.25/7.82
% 52.25/7.82 (mPttSet)
% 52.25/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 52.25/7.82 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 52.25/7.82 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3)))
% 52.25/7.82
% 52.25/7.82 (mSubTrans)
% 52.25/7.82 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 52.25/7.82 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1)
% 52.25/7.82 | ~ aSet0(v0) | aSubsetOf0(v0, v2))
% 52.25/7.82
% 52.25/7.82 (m__)
% 52.25/7.82 $i(xQ) & $i(szNzAzT0) & ~ aSubsetOf0(xQ, szNzAzT0)
% 52.25/7.82
% 52.25/7.82 (m__3291)
% 52.25/7.82 $i(xT) & isFinite0(xT) & aSet0(xT)
% 52.25/7.82
% 52.25/7.82 (m__3418)
% 52.25/7.82 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 52.25/7.82
% 52.25/7.82 (m__3435)
% 52.25/7.82 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)
% 52.25/7.82
% 52.25/7.82 (m__3462)
% 52.25/7.82 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 52.25/7.82
% 52.25/7.82 (m__3520)
% 52.25/7.82 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 52.25/7.82
% 52.25/7.82 (m__4730)
% 52.25/7.82 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 52.25/7.82 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 52.25/7.82 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 52.25/7.82 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 52.25/7.82 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 52.25/7.82 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 52.25/7.82 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~
% 52.25/7.82 aSet0(v6))))
% 52.25/7.82
% 52.25/7.82 (m__4758)
% 52.25/7.82 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 52.25/7.82 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT))
% 52.25/7.82
% 52.25/7.82 (m__4854)
% 52.25/7.82 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 52.25/7.82 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) &
% 52.25/7.82 aElementOf0(v0, xT))
% 52.25/7.82
% 52.25/7.82 (m__4891)
% 52.25/7.82 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 52.25/7.82 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 52.25/7.82 aSet0(xO))
% 52.25/7.82
% 52.25/7.82 (m__4982)
% 52.25/7.83 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 52.25/7.83 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 52.25/7.83 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) =
% 52.25/7.83 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 52.25/7.83
% 52.25/7.83 (m__4998)
% 52.25/7.83 $i(xO) & $i(xS) & aSubsetOf0(xO, xS)
% 52.25/7.83
% 52.25/7.83 (m__5078)
% 52.25/7.83 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) &
% 52.25/7.83 aElementOf0(xQ, v0))
% 52.25/7.83
% 52.25/7.83 (m__5093)
% 52.25/7.83 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO)
% 52.25/7.83
% 52.25/7.83 (function-axioms)
% 52.25/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.25/7.83 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 52.25/7.83 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 52.25/7.83 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 52.25/7.83 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 52.25/7.83 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 52.25/7.83 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 52.25/7.83 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 52.25/7.83 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 52.25/7.83 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 52.25/7.83 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 52.25/7.83 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 52.25/7.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 52.25/7.83 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 52.25/7.83 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 52.25/7.83 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 52.25/7.83 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 52.25/7.83 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 52.25/7.83 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 52.25/7.83 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 52.25/7.83 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 52.25/7.83 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 52.25/7.83 v0))
% 52.25/7.83
% 52.25/7.83 Further assumptions not needed in the proof:
% 52.25/7.83 --------------------------------------------
% 52.25/7.83 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 52.25/7.83 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 52.25/7.83 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg,
% 52.25/7.83 mDefSel, mDiffCons, mDirichlet, mDomSet, mElmSort, mEmpFin, mFConsSet,
% 52.25/7.83 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 52.25/7.83 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 52.25/7.83 mMinMin, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero,
% 52.25/7.83 mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet,
% 52.25/7.83 mSubRefl, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3398,
% 52.25/7.83 m__3453, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182,
% 52.25/7.83 m__4331, m__4411, m__4618, m__4660, m__4908
% 52.25/7.83
% 52.25/7.83 Those formulas are unsatisfiable:
% 52.25/7.83 ---------------------------------
% 52.25/7.83
% 52.25/7.83 Begin of proof
% 52.25/7.83 |
% 52.25/7.83 | ALPHA: (mDefSub) implies:
% 52.25/7.84 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 52.25/7.84 | v0) | ~ aSet0(v0) | aSet0(v1))
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (mNATSet) implies:
% 52.25/7.84 | (2) aSet0(szNzAzT0)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (mNatExtra) implies:
% 52.25/7.84 | (3) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 52.25/7.84 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 52.25/7.84 | szNzAzT0)))
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__3291) implies:
% 52.25/7.84 | (4) aSet0(xT)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__3418) implies:
% 52.25/7.84 | (5) aElementOf0(xK, szNzAzT0)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__3435) implies:
% 52.25/7.84 | (6) aSubsetOf0(xS, szNzAzT0)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__3520) implies:
% 52.25/7.84 | (7) ~ (xK = sz00)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__4730) implies:
% 52.25/7.84 | (8) aFunction0(xd)
% 52.25/7.84 | (9) szDzozmdt0(xd) = szNzAzT0
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__4758) implies:
% 52.25/7.84 | (10) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd)
% 52.25/7.84 | = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT))
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__4854) implies:
% 52.25/7.84 | (11) $i(xT)
% 52.25/7.84 | (12) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 52.25/7.84 | = v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT))
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__4891) implies:
% 52.25/7.84 | (13) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1)
% 52.25/7.84 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__4982) implies:
% 52.25/7.84 | (14) $i(xd)
% 52.25/7.84 | (15) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 52.25/7.84 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~
% 52.25/7.84 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 &
% 52.25/7.84 | $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__4998) implies:
% 52.25/7.84 | (16) aSubsetOf0(xO, xS)
% 52.25/7.84 | (17) $i(xS)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__5078) implies:
% 52.25/7.84 | (18) $i(xK)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__5093) implies:
% 52.25/7.84 | (19) aSubsetOf0(xQ, xO)
% 52.25/7.84 | (20) $i(xO)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (m__) implies:
% 52.25/7.84 | (21) ~ aSubsetOf0(xQ, szNzAzT0)
% 52.25/7.84 | (22) $i(xQ)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (function-axioms) implies:
% 52.25/7.84 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 52.25/7.84 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 52.25/7.84 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 52.25/7.84 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 52.25/7.84 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 52.25/7.84 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 52.25/7.84 |
% 52.25/7.84 | DELTA: instantiating (10) with fresh symbols all_78_0, all_78_1 gives:
% 52.25/7.84 | (26) sdtlcdtrc0(xd, all_78_1) = all_78_0 & szDzozmdt0(xd) = all_78_1 &
% 52.25/7.84 | $i(all_78_0) & $i(all_78_1) & aSubsetOf0(all_78_0, xT)
% 52.25/7.84 |
% 52.25/7.84 | ALPHA: (26) implies:
% 52.25/7.84 | (27) $i(all_78_1)
% 52.25/7.84 | (28) szDzozmdt0(xd) = all_78_1
% 52.25/7.84 |
% 52.25/7.84 | DELTA: instantiating (13) with fresh symbols all_80_0, all_80_1 gives:
% 52.25/7.86 | (29) szDzizrdt0(xd) = all_80_1 & sdtlcdtrc0(xe, all_80_0) = xO &
% 52.25/7.86 | sdtlbdtrb0(xd, all_80_1) = all_80_0 & $i(all_80_0) & $i(all_80_1) &
% 52.25/7.86 | aSet0(xO)
% 52.25/7.86 |
% 52.25/7.86 | ALPHA: (29) implies:
% 52.25/7.86 | (30) aSet0(xO)
% 52.25/7.86 | (31) sdtlbdtrb0(xd, all_80_1) = all_80_0
% 52.25/7.86 | (32) szDzizrdt0(xd) = all_80_1
% 52.25/7.86 |
% 52.25/7.86 | DELTA: instantiating (12) with fresh symbols all_82_0, all_82_1 gives:
% 52.25/7.86 | (33) szDzizrdt0(xd) = all_82_1 & sdtlbdtrb0(xd, all_82_1) = all_82_0 &
% 52.25/7.86 | $i(all_82_0) & $i(all_82_1) & isCountable0(all_82_0) &
% 52.25/7.86 | aElementOf0(all_82_1, xT)
% 52.25/7.86 |
% 52.25/7.86 | ALPHA: (33) implies:
% 52.25/7.86 | (34) aElementOf0(all_82_1, xT)
% 52.25/7.86 | (35) $i(all_82_1)
% 52.25/7.86 | (36) sdtlbdtrb0(xd, all_82_1) = all_82_0
% 52.25/7.86 | (37) szDzizrdt0(xd) = all_82_1
% 52.25/7.86 |
% 52.25/7.86 | DELTA: instantiating (15) with fresh symbols all_86_0, all_86_1 gives:
% 52.25/7.86 | (38) szDzizrdt0(xd) = all_86_1 & sdtlbdtrb0(xd, all_86_1) = all_86_0 &
% 52.25/7.86 | $i(all_86_0) & $i(all_86_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 52.25/7.86 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 52.25/7.86 | $i(v1) & aElementOf0(v1, all_86_0) & aElementOf0(v1, szNzAzT0)))
% 52.25/7.86 |
% 52.25/7.86 | ALPHA: (38) implies:
% 52.25/7.86 | (39) sdtlbdtrb0(xd, all_86_1) = all_86_0
% 52.25/7.86 | (40) szDzizrdt0(xd) = all_86_1
% 52.25/7.86 |
% 52.25/7.86 | GROUND_INST: instantiating (23) with szNzAzT0, all_78_1, xd, simplifying with
% 52.25/7.86 | (9), (28) gives:
% 52.25/7.86 | (41) all_78_1 = szNzAzT0
% 52.25/7.86 |
% 52.25/7.86 | GROUND_INST: instantiating (24) with all_82_1, all_86_1, xd, simplifying with
% 52.25/7.86 | (37), (40) gives:
% 52.25/7.86 | (42) all_86_1 = all_82_1
% 52.25/7.86 |
% 52.25/7.86 | GROUND_INST: instantiating (24) with all_80_1, all_86_1, xd, simplifying with
% 52.25/7.86 | (32), (40) gives:
% 52.25/7.86 | (43) all_86_1 = all_80_1
% 52.25/7.86 |
% 52.25/7.86 | COMBINE_EQS: (42), (43) imply:
% 52.25/7.86 | (44) all_82_1 = all_80_1
% 52.25/7.86 |
% 52.25/7.86 | REDUCE: (39), (43) imply:
% 52.25/7.86 | (45) sdtlbdtrb0(xd, all_80_1) = all_86_0
% 52.25/7.86 |
% 52.25/7.86 | REDUCE: (36), (44) imply:
% 52.25/7.86 | (46) sdtlbdtrb0(xd, all_80_1) = all_82_0
% 52.25/7.86 |
% 52.25/7.86 | REDUCE: (35), (44) imply:
% 52.25/7.86 | (47) $i(all_80_1)
% 52.25/7.86 |
% 52.25/7.86 | REDUCE: (27), (41) imply:
% 52.25/7.86 | (48) $i(szNzAzT0)
% 52.25/7.86 |
% 52.25/7.86 | REDUCE: (34), (44) imply:
% 52.25/7.86 | (49) aElementOf0(all_80_1, xT)
% 52.25/7.86 |
% 52.25/7.86 | GROUND_INST: instantiating (25) with all_80_0, all_86_0, all_80_1, xd,
% 52.25/7.87 | simplifying with (31), (45) gives:
% 52.25/7.87 | (50) all_86_0 = all_80_0
% 52.25/7.87 |
% 52.25/7.87 | GROUND_INST: instantiating (25) with all_82_0, all_86_0, all_80_1, xd,
% 52.25/7.87 | simplifying with (45), (46) gives:
% 52.25/7.87 | (51) all_86_0 = all_82_0
% 52.25/7.87 |
% 52.25/7.87 | COMBINE_EQS: (50), (51) imply:
% 52.25/7.87 | (52) all_82_0 = all_80_0
% 52.25/7.87 |
% 52.25/7.87 | GROUND_INST: instantiating (3) with xK, simplifying with (5), (18) gives:
% 52.25/7.87 | (53) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 52.25/7.87 | aElementOf0(v0, szNzAzT0))
% 52.25/7.87 |
% 52.25/7.87 | GROUND_INST: instantiating (mEOfElem) with xT, all_80_1, simplifying with (4),
% 52.25/7.87 | (11), (47), (49) gives:
% 52.25/7.87 | (54) aElement0(all_80_1)
% 52.25/7.87 |
% 52.25/7.87 | GROUND_INST: instantiating (1) with szNzAzT0, xS, simplifying with (2), (6),
% 52.25/7.87 | (17), (48) gives:
% 52.25/7.87 | (55) aSet0(xS)
% 52.25/7.87 |
% 52.25/7.87 | GROUND_INST: instantiating (1) with xO, xQ, simplifying with (19), (20), (22),
% 52.25/7.87 | (30) gives:
% 52.25/7.87 | (56) aSet0(xQ)
% 52.25/7.87 |
% 52.25/7.87 | BETA: splitting (53) gives:
% 52.25/7.87 |
% 52.25/7.87 | Case 1:
% 52.25/7.87 | |
% 52.25/7.87 | | (57) xK = sz00
% 52.25/7.87 | |
% 52.25/7.87 | | REDUCE: (7), (57) imply:
% 52.25/7.87 | | (58) $false
% 52.25/7.87 | |
% 52.25/7.87 | | CLOSE: (58) is inconsistent.
% 52.25/7.87 | |
% 52.25/7.87 | Case 2:
% 52.25/7.87 | |
% 52.25/7.87 | |
% 52.25/7.88 | | GROUND_INST: instantiating (mSubTrans) with xQ, xO, xS, simplifying with
% 52.25/7.90 | | (16), (17), (19), (20), (22), (30), (55), (56) gives:
% 52.25/7.90 | | (59) aSubsetOf0(xQ, xS)
% 52.25/7.90 | |
% 52.25/7.90 | | GROUND_INST: instantiating (mPttSet) with xd, all_80_1, all_80_0,
% 52.25/7.90 | | simplifying with (8), (14), (31), (47), (54) gives:
% 52.25/7.90 | | (60) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_80_0,
% 52.25/7.90 | | v0))
% 52.25/7.90 | |
% 52.25/7.90 | | GROUND_INST: instantiating (mDefPtt) with xd, all_80_1, all_80_0,
% 52.25/7.90 | | simplifying with (8), (14), (31), (47), (54) gives:
% 52.25/7.90 | | (61) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 52.25/7.90 | | int] : (v2 = all_80_1 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1)
% 52.25/7.90 | | | ~ $i(all_80_0) | ~ aElementOf0(v1, all_80_0)) & ! [v1: $i]
% 52.25/7.90 | | : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~
% 52.25/7.90 | | $i(all_80_0) | ~ aElementOf0(v1, all_80_0) | aElementOf0(v1,
% 52.25/7.90 | | v0)) & ! [v1: any] : (v1 = all_80_0 | ~ $i(v1) | ~
% 52.25/7.90 | | aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) & ( ~
% 52.25/7.90 | | aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 =
% 52.25/7.90 | | all_80_1) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) &
% 52.25/7.90 | | (aElementOf0(v2, v1) | (v3 = all_80_1 & sdtlpdtrp0(xd, v2) =
% 52.25/7.90 | | all_80_1 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~
% 52.25/7.90 | | (sdtlpdtrp0(xd, v1) = all_80_1) | ~ $i(v1) | ~ $i(all_80_0) |
% 52.25/7.90 | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_80_0)) & ( ~
% 52.25/7.90 | | $i(all_80_0) | aSet0(all_80_0)))
% 52.25/7.90 | |
% 52.25/7.90 | | DELTA: instantiating (60) with fresh symbol all_133_0 gives:
% 52.25/7.90 | | (62) szDzozmdt0(xd) = all_133_0 & $i(all_133_0) & aSubsetOf0(all_80_0,
% 52.25/7.90 | | all_133_0)
% 52.25/7.90 | |
% 52.25/7.90 | | ALPHA: (62) implies:
% 52.25/7.90 | | (63) $i(all_133_0)
% 52.25/7.90 | | (64) szDzozmdt0(xd) = all_133_0
% 52.25/7.90 | |
% 52.25/7.90 | | DELTA: instantiating (61) with fresh symbol all_139_0 gives:
% 52.25/7.90 | | (65) szDzozmdt0(xd) = all_139_0 & $i(all_139_0) & ! [v0: $i] : ! [v1:
% 52.25/7.90 | | int] : (v1 = all_80_1 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 52.25/7.90 | | ~ $i(all_80_0) | ~ aElementOf0(v0, all_80_0)) & ! [v0: $i] : !
% 52.25/7.90 | | [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 52.25/7.90 | | $i(all_80_0) | ~ aElementOf0(v0, all_80_0) | aElementOf0(v0,
% 52.25/7.90 | | all_139_0)) & ! [v0: any] : (v0 = all_80_0 | ~ $i(v0) | ~
% 52.25/7.90 | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~
% 52.25/7.90 | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_139_0) | ( ~ (v2
% 52.25/7.90 | | = all_80_1) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) &
% 52.25/7.90 | | (aElementOf0(v1, v0) | (v2 = all_80_1 & sdtlpdtrp0(xd, v1) =
% 52.25/7.90 | | all_80_1 & aElementOf0(v1, all_139_0))))) & ! [v0: $i] : (
% 52.25/7.90 | | ~ (sdtlpdtrp0(xd, v0) = all_80_1) | ~ $i(v0) | ~ $i(all_80_0) |
% 52.25/7.90 | | ~ aElementOf0(v0, all_139_0) | aElementOf0(v0, all_80_0)) & ( ~
% 52.25/7.90 | | $i(all_80_0) | aSet0(all_80_0))
% 52.25/7.90 | |
% 52.25/7.90 | | ALPHA: (65) implies:
% 52.25/7.90 | | (66) szDzozmdt0(xd) = all_139_0
% 52.25/7.90 | |
% 52.25/7.90 | | GROUND_INST: instantiating (23) with szNzAzT0, all_139_0, xd, simplifying
% 52.25/7.90 | | with (9), (66) gives:
% 52.25/7.90 | | (67) all_139_0 = szNzAzT0
% 52.25/7.90 | |
% 52.25/7.90 | | GROUND_INST: instantiating (23) with all_133_0, all_139_0, xd, simplifying
% 52.25/7.90 | | with (64), (66) gives:
% 52.25/7.90 | | (68) all_139_0 = all_133_0
% 52.25/7.90 | |
% 52.25/7.90 | | COMBINE_EQS: (67), (68) imply:
% 52.25/7.90 | | (69) all_133_0 = szNzAzT0
% 52.25/7.90 | |
% 52.25/7.90 | | GROUND_INST: instantiating (mSubTrans) with xQ, xS, szNzAzT0, simplifying
% 52.25/7.90 | | with (2), (6), (17), (21), (22), (48), (55), (56), (59) gives:
% 52.25/7.90 | | (70) $false
% 52.25/7.90 | |
% 52.25/7.90 | | CLOSE: (70) is inconsistent.
% 52.25/7.90 | |
% 52.25/7.90 | End of split
% 52.25/7.90 |
% 52.25/7.90 End of proof
% 52.25/7.90 % SZS output end Proof for theBenchmark
% 52.25/7.90
% 52.25/7.90 7373ms
%------------------------------------------------------------------------------