TSTP Solution File: NUM617+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM617+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 : n012.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 11:49:00 EDT 2023
% Result : Theorem 32.22s 5.06s
% Output : Proof 44.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM617+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 08:32:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.33/1.44 Prover 1: Preprocessing ...
% 4.33/1.46 Prover 4: Preprocessing ...
% 4.33/1.48 Prover 2: Preprocessing ...
% 4.33/1.48 Prover 3: Preprocessing ...
% 4.33/1.48 Prover 5: Preprocessing ...
% 4.33/1.48 Prover 0: Preprocessing ...
% 4.33/1.48 Prover 6: Preprocessing ...
% 13.87/2.60 Prover 3: Constructing countermodel ...
% 13.87/2.64 Prover 1: Constructing countermodel ...
% 14.26/2.65 Prover 6: Proving ...
% 14.61/2.79 Prover 5: Proving ...
% 15.09/2.89 Prover 2: Proving ...
% 19.48/3.35 Prover 4: Constructing countermodel ...
% 19.48/3.40 Prover 0: Proving ...
% 32.22/5.06 Prover 0: proved (4401ms)
% 32.22/5.06
% 32.22/5.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.22/5.06
% 32.22/5.06 Prover 3: stopped
% 32.22/5.06 Prover 5: stopped
% 32.22/5.06 Prover 2: stopped
% 32.22/5.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 32.22/5.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 32.22/5.07 Prover 6: stopped
% 32.22/5.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 32.22/5.08 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 32.22/5.08 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.91/5.30 Prover 13: Preprocessing ...
% 34.52/5.33 Prover 11: Preprocessing ...
% 34.52/5.33 Prover 8: Preprocessing ...
% 34.52/5.35 Prover 7: Preprocessing ...
% 34.52/5.35 Prover 10: Preprocessing ...
% 36.88/5.65 Prover 10: Constructing countermodel ...
% 36.88/5.65 Prover 8: Warning: ignoring some quantifiers
% 37.09/5.67 Prover 8: Constructing countermodel ...
% 37.09/5.69 Prover 13: Warning: ignoring some quantifiers
% 37.09/5.71 Prover 7: Constructing countermodel ...
% 37.09/5.71 Prover 13: Constructing countermodel ...
% 42.10/6.36 Prover 11: Constructing countermodel ...
% 43.83/6.61 Prover 10: Found proof (size 83)
% 43.83/6.61 Prover 10: proved (1532ms)
% 43.83/6.61 Prover 11: stopped
% 43.83/6.61 Prover 7: stopped
% 43.83/6.61 Prover 1: stopped
% 44.48/6.61 Prover 13: stopped
% 44.48/6.61 Prover 8: stopped
% 44.48/6.61 Prover 4: stopped
% 44.48/6.61
% 44.48/6.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.48/6.62
% 44.48/6.63 % SZS output start Proof for theBenchmark
% 44.48/6.63 Assumptions after simplification:
% 44.48/6.63 ---------------------------------
% 44.48/6.63
% 44.48/6.63 (mDefPtt)
% 44.48/6.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 44.48/6.65 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 44.48/6.65 (szDzozmdt0(v0) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v5 = v1 | ~
% 44.48/6.65 (sdtlpdtrp0(v0, v4) = v5) | ~ $i(v4) | ~ $i(v2) | ~ aElementOf0(v4,
% 44.48/6.65 v2)) & ! [v4: $i] : ! [v5: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v5) | ~
% 44.48/6.65 $i(v4) | ~ $i(v2) | ~ aElementOf0(v4, v2) | aElementOf0(v4, v3)) & !
% 44.48/6.65 [v4: $i] : (v4 = v2 | ~ $i(v4) | ~ aSet0(v4) | ? [v5: $i] : ? [v6: $i]
% 44.48/6.65 : ($i(v5) & ( ~ aElementOf0(v5, v4) | ~ aElementOf0(v5, v3) | ( ~ (v6 =
% 44.48/6.65 v1) & sdtlpdtrp0(v0, v5) = v6 & $i(v6))) & (aElementOf0(v5, v4)
% 44.48/6.65 | (v6 = v1 & sdtlpdtrp0(v0, v5) = v1 & aElementOf0(v5, v3))))) & !
% 44.48/6.65 [v4: $i] : ( ~ (sdtlpdtrp0(v0, v4) = v1) | ~ $i(v4) | ~ $i(v2) | ~
% 44.48/6.66 aElementOf0(v4, v3) | aElementOf0(v4, v2)) & ( ~ $i(v2) | aSet0(v2))))
% 44.48/6.66
% 44.48/6.66 (mDefSub)
% 44.48/6.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 44.48/6.66 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 44.48/6.66 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 44.48/6.66 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 44.48/6.66 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 44.48/6.66 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 44.48/6.66
% 44.48/6.66 (mImgElm)
% 44.48/6.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(v0,
% 44.48/6.66 v2) = v3) | ~ (szDzozmdt0(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 44.48/6.66 aFunction0(v0) | ~ aElementOf0(v2, v1) | aElement0(v3))
% 44.48/6.66
% 44.48/6.66 (mNATSet)
% 44.48/6.66 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 44.48/6.66
% 44.48/6.66 (mNatExtra)
% 44.48/6.66 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~
% 44.48/6.66 aElementOf0(v0, szNzAzT0) | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) &
% 44.48/6.66 aElementOf0(v1, szNzAzT0)))
% 44.48/6.66
% 44.48/6.66 (mPttSet)
% 44.48/6.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtlbdtrb0(v0, v1) = v2) | ~
% 44.48/6.66 $i(v1) | ~ $i(v0) | ~ aFunction0(v0) | ~ aElement0(v1) | ? [v3: $i] :
% 44.48/6.66 (szDzozmdt0(v0) = v3 & $i(v3) & aSubsetOf0(v2, v3)))
% 44.48/6.66
% 44.48/6.66 (mSubTrans)
% 44.48/6.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 44.48/6.66 ~ aSubsetOf0(v1, v2) | ~ aSubsetOf0(v0, v1) | ~ aSet0(v2) | ~ aSet0(v1)
% 44.48/6.66 | ~ aSet0(v0) | aSubsetOf0(v0, v2))
% 44.48/6.66
% 44.48/6.66 (m__)
% 44.48/6.66 $i(xx) & $i(szNzAzT0) & ~ aElementOf0(xx, szNzAzT0)
% 44.48/6.66
% 44.48/6.66 (m__3418)
% 44.48/6.66 $i(xK) & $i(szNzAzT0) & aElementOf0(xK, szNzAzT0)
% 44.48/6.66
% 44.48/6.66 (m__3462)
% 44.48/6.66 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 44.48/6.66
% 44.48/6.66 (m__3520)
% 44.48/6.66 ~ (xK = sz00) & $i(xK) & $i(sz00)
% 44.48/6.66
% 44.48/6.66 (m__4730)
% 44.48/6.66 szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) & $i(xk) & $i(szNzAzT0) &
% 44.48/6.66 aFunction0(xd) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) = v1) |
% 44.48/6.66 ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i] : ?
% 44.48/6.66 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xd, v0) = v5 & sdtlpdtrp0(xN, v2) = v3
% 44.48/6.66 & slbdtsldtrb0(v3, xk) = v4 & szszuzczcdt0(v0) = v2 & $i(v5) & $i(v4) &
% 44.48/6.66 $i(v3) & $i(v2) & ! [v6: $i] : ! [v7: $i] : (v7 = v5 | ~
% 44.48/6.66 (sdtlpdtrp0(v1, v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v4) | ~
% 44.48/6.66 aSet0(v6))))
% 44.48/6.66
% 44.48/6.66 (m__4758)
% 44.48/6.66 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 44.48/6.66 szDzozmdt0(xd) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT))
% 44.48/6.66
% 44.48/6.66 (m__4854)
% 44.48/6.67 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 44.48/6.67 sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & isCountable0(v1) &
% 44.48/6.67 aElementOf0(v0, xT))
% 44.48/6.67
% 44.48/6.67 (m__4891)
% 44.48/6.67 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 44.48/6.67 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) &
% 44.48/6.67 aSet0(xO))
% 44.48/6.67
% 44.48/6.67 (m__4982)
% 44.48/6.67 $i(xO) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 44.48/6.67 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i]
% 44.48/6.67 : ( ~ $i(v2) | ~ aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) =
% 44.48/6.67 v2 & $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 44.48/6.67
% 44.48/6.67 (m__5078)
% 44.48/6.67 $i(xQ) & $i(xO) & $i(xK) & ? [v0: $i] : (slbdtsldtrb0(xO, xK) = v0 & $i(v0) &
% 44.48/6.67 aElementOf0(xQ, v0))
% 44.48/6.67
% 44.48/6.67 (m__5093)
% 44.48/6.67 ~ (xQ = slcrc0) & $i(xQ) & $i(xO) & $i(slcrc0) & aSubsetOf0(xQ, xO)
% 44.48/6.67
% 44.48/6.67 (m__5106)
% 44.48/6.67 $i(xQ) & $i(szNzAzT0) & aSubsetOf0(xQ, szNzAzT0)
% 44.48/6.67
% 44.48/6.67 (m__5164)
% 44.48/6.67 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 44.48/6.67 $i(v0) & aSet0(xP))
% 44.48/6.67
% 44.48/6.67 (m__5195)
% 44.48/6.67 $i(xP) & $i(xQ) & aSubsetOf0(xP, xQ)
% 44.48/6.67
% 44.48/6.67 (m__5270)
% 44.48/6.67 $i(xP) & $i(xO) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xO, xk) = v0 & $i(v0) &
% 44.48/6.67 aElementOf0(xP, v0))
% 44.48/6.67
% 44.48/6.67 (m__5309)
% 44.48/6.67 $i(xn) & $i(xp) & $i(xd) & $i(xe) & $i(szNzAzT0) & ? [v0: $i] : ? [v1: $i] :
% 44.48/6.67 (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0) = v1 & sdtlpdtrp0(xe, xn) = xp &
% 44.48/6.67 $i(v1) & $i(v0) & aElementOf0(xn, v1) & aElementOf0(xn, szNzAzT0))
% 44.48/6.67
% 44.48/6.67 (m__5321)
% 44.48/6.67 $i(xn) & $i(xd) & ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0
% 44.48/6.67 & $i(v0))
% 44.48/6.67
% 44.48/6.67 (m__5348)
% 44.48/6.67 $i(xx) & $i(xP) & aElementOf0(xx, xP)
% 44.48/6.67
% 44.48/6.67 (function-axioms)
% 44.48/6.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.48/6.67 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 44.48/6.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 44.48/6.67 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 44.48/6.67 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 44.48/6.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 44.48/6.67 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 44.48/6.67 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 44.48/6.67 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 44.48/6.67 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 44.48/6.67 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 44.48/6.67 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 44.48/6.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 44.48/6.67 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 44.48/6.67 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 44.48/6.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 44.48/6.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.48/6.67 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 44.48/6.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 44.48/6.67 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.48/6.67 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 44.48/6.67 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 44.48/6.67 v0))
% 44.48/6.67
% 44.48/6.67 Further assumptions not needed in the proof:
% 44.48/6.67 --------------------------------------------
% 44.48/6.67 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 44.48/6.67 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 44.48/6.67 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefRst, mDefSImg, mDefSeg,
% 44.48/6.67 mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 44.48/6.67 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgRng,
% 44.48/6.67 mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin,
% 44.48/6.67 mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet,
% 44.48/6.67 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl,
% 44.48/6.67 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__3291, m__3398,
% 44.48/6.67 m__3435, m__3453, m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151,
% 44.48/6.67 m__4182, m__4331, m__4411, m__4618, m__4660, m__4908, m__4998, m__5116, m__5147,
% 44.48/6.67 m__5173, m__5182, m__5208, m__5217
% 44.48/6.67
% 44.48/6.67 Those formulas are unsatisfiable:
% 44.48/6.67 ---------------------------------
% 44.48/6.67
% 44.48/6.67 Begin of proof
% 44.48/6.68 |
% 44.48/6.68 | ALPHA: (mDefSub) implies:
% 44.48/6.68 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v1,
% 44.48/6.68 | v0) | ~ aSet0(v0) | aSet0(v1))
% 44.48/6.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 44.48/6.68 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 44.80/6.68 | aSet0(v0) | aElementOf0(v2, v0))
% 44.80/6.68 |
% 44.80/6.68 | ALPHA: (mNATSet) implies:
% 44.80/6.68 | (3) aSet0(szNzAzT0)
% 44.80/6.68 |
% 44.80/6.68 | ALPHA: (mNatExtra) implies:
% 44.80/6.69 | (4) ! [v0: $i] : (v0 = sz00 | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 44.80/6.69 | ? [v1: $i] : (szszuzczcdt0(v1) = v0 & $i(v1) & aElementOf0(v1,
% 44.80/6.69 | szNzAzT0)))
% 44.80/6.69 |
% 44.80/6.69 | ALPHA: (m__3418) implies:
% 44.80/6.69 | (5) aElementOf0(xK, szNzAzT0)
% 44.80/6.69 |
% 44.80/6.69 | ALPHA: (m__3520) implies:
% 44.80/6.69 | (6) ~ (xK = sz00)
% 44.80/6.69 |
% 44.80/6.69 | ALPHA: (m__4730) implies:
% 44.80/6.69 | (7) aFunction0(xd)
% 44.80/6.69 | (8) szDzozmdt0(xd) = szNzAzT0
% 44.80/6.69 |
% 44.80/6.69 | ALPHA: (m__4758) implies:
% 44.80/6.69 | (9) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) =
% 44.80/6.69 | v0 & $i(v1) & $i(v0) & aSubsetOf0(v1, xT))
% 44.80/6.69 |
% 44.80/6.69 | ALPHA: (m__4854) implies:
% 44.80/6.70 | (10) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 44.80/6.70 | = v1 & $i(v1) & $i(v0) & isCountable0(v1) & aElementOf0(v0, xT))
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__4891) implies:
% 44.80/6.70 | (11) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1)
% 44.80/6.70 | = xO & sdtlbdtrb0(xd, v0) = v1 & $i(v1) & $i(v0) & aSet0(xO))
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__4982) implies:
% 44.80/6.70 | (12) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 44.80/6.70 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~
% 44.80/6.70 | aElementOf0(v2, xO) | ? [v3: $i] : (sdtlpdtrp0(xe, v3) = v2 &
% 44.80/6.70 | $i(v3) & aElementOf0(v3, v1) & aElementOf0(v3, szNzAzT0))))
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5078) implies:
% 44.80/6.70 | (13) $i(xK)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5093) implies:
% 44.80/6.70 | (14) aSubsetOf0(xQ, xO)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5106) implies:
% 44.80/6.70 | (15) aSubsetOf0(xQ, szNzAzT0)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5164) implies:
% 44.80/6.70 | (16) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & $i(v0) &
% 44.80/6.70 | aSet0(xP))
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5195) implies:
% 44.80/6.70 | (17) aSubsetOf0(xP, xQ)
% 44.80/6.70 | (18) $i(xQ)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5270) implies:
% 44.80/6.70 | (19) $i(xO)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5309) implies:
% 44.80/6.70 | (20) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlbdtrb0(xd, v0)
% 44.80/6.70 | = v1 & sdtlpdtrp0(xe, xn) = xp & $i(v1) & $i(v0) & aElementOf0(xn,
% 44.80/6.70 | v1) & aElementOf0(xn, szNzAzT0))
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5321) implies:
% 44.80/6.70 | (21) $i(xd)
% 44.80/6.70 | (22) $i(xn)
% 44.80/6.70 | (23) ? [v0: $i] : (szDzizrdt0(xd) = v0 & sdtlpdtrp0(xd, xn) = v0 & $i(v0))
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__5348) implies:
% 44.80/6.70 | (24) aElementOf0(xx, xP)
% 44.80/6.70 | (25) $i(xP)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (m__) implies:
% 44.80/6.70 | (26) ~ aElementOf0(xx, szNzAzT0)
% 44.80/6.70 | (27) $i(xx)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (function-axioms) implies:
% 44.80/6.70 | (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.80/6.70 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 44.80/6.70 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 44.80/6.70 | (szDzizrdt0(v2) = v1) | ~ (szDzizrdt0(v2) = v0))
% 44.80/6.70 | (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 44.80/6.70 | (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0))
% 44.80/6.70 |
% 44.80/6.70 | DELTA: instantiating (23) with fresh symbol all_80_0 gives:
% 44.80/6.70 | (31) szDzizrdt0(xd) = all_80_0 & sdtlpdtrp0(xd, xn) = all_80_0 &
% 44.80/6.70 | $i(all_80_0)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (31) implies:
% 44.80/6.70 | (32) sdtlpdtrp0(xd, xn) = all_80_0
% 44.80/6.70 | (33) szDzizrdt0(xd) = all_80_0
% 44.80/6.70 |
% 44.80/6.70 | DELTA: instantiating (16) with fresh symbol all_84_0 gives:
% 44.80/6.70 | (34) szmzizndt0(xQ) = all_84_0 & sdtmndt0(xQ, all_84_0) = xP & $i(all_84_0)
% 44.80/6.70 | & aSet0(xP)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (34) implies:
% 44.80/6.70 | (35) aSet0(xP)
% 44.80/6.70 |
% 44.80/6.70 | DELTA: instantiating (9) with fresh symbols all_86_0, all_86_1 gives:
% 44.80/6.70 | (36) sdtlcdtrc0(xd, all_86_1) = all_86_0 & szDzozmdt0(xd) = all_86_1 &
% 44.80/6.70 | $i(all_86_0) & $i(all_86_1) & aSubsetOf0(all_86_0, xT)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (36) implies:
% 44.80/6.70 | (37) $i(all_86_1)
% 44.80/6.70 | (38) szDzozmdt0(xd) = all_86_1
% 44.80/6.70 |
% 44.80/6.70 | DELTA: instantiating (11) with fresh symbols all_88_0, all_88_1 gives:
% 44.80/6.70 | (39) szDzizrdt0(xd) = all_88_1 & sdtlcdtrc0(xe, all_88_0) = xO &
% 44.80/6.70 | sdtlbdtrb0(xd, all_88_1) = all_88_0 & $i(all_88_0) & $i(all_88_1) &
% 44.80/6.70 | aSet0(xO)
% 44.80/6.70 |
% 44.80/6.70 | ALPHA: (39) implies:
% 44.80/6.70 | (40) aSet0(xO)
% 44.80/6.70 | (41) $i(all_88_1)
% 44.80/6.70 | (42) sdtlbdtrb0(xd, all_88_1) = all_88_0
% 44.80/6.70 | (43) szDzizrdt0(xd) = all_88_1
% 44.80/6.70 |
% 44.80/6.70 | DELTA: instantiating (10) with fresh symbols all_90_0, all_90_1 gives:
% 44.80/6.71 | (44) szDzizrdt0(xd) = all_90_1 & sdtlbdtrb0(xd, all_90_1) = all_90_0 &
% 44.80/6.71 | $i(all_90_0) & $i(all_90_1) & isCountable0(all_90_0) &
% 44.80/6.71 | aElementOf0(all_90_1, xT)
% 44.80/6.71 |
% 44.80/6.71 | ALPHA: (44) implies:
% 44.80/6.71 | (45) sdtlbdtrb0(xd, all_90_1) = all_90_0
% 44.80/6.71 | (46) szDzizrdt0(xd) = all_90_1
% 44.80/6.71 |
% 44.80/6.71 | DELTA: instantiating (20) with fresh symbols all_94_0, all_94_1 gives:
% 44.80/6.71 | (47) szDzizrdt0(xd) = all_94_1 & sdtlbdtrb0(xd, all_94_1) = all_94_0 &
% 44.80/6.71 | sdtlpdtrp0(xe, xn) = xp & $i(all_94_0) & $i(all_94_1) &
% 44.80/6.71 | aElementOf0(xn, all_94_0) & aElementOf0(xn, szNzAzT0)
% 44.80/6.71 |
% 44.80/6.71 | ALPHA: (47) implies:
% 44.80/6.71 | (48) aElementOf0(xn, szNzAzT0)
% 44.80/6.71 | (49) sdtlbdtrb0(xd, all_94_1) = all_94_0
% 44.80/6.71 | (50) szDzizrdt0(xd) = all_94_1
% 44.80/6.71 |
% 44.80/6.71 | DELTA: instantiating (12) with fresh symbols all_96_0, all_96_1 gives:
% 44.80/6.71 | (51) szDzizrdt0(xd) = all_96_1 & sdtlbdtrb0(xd, all_96_1) = all_96_0 &
% 44.80/6.71 | $i(all_96_0) & $i(all_96_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 44.80/6.71 | aElementOf0(v0, xO) | ? [v1: $i] : (sdtlpdtrp0(xe, v1) = v0 &
% 44.80/6.71 | $i(v1) & aElementOf0(v1, all_96_0) & aElementOf0(v1, szNzAzT0)))
% 44.80/6.71 |
% 44.80/6.71 | ALPHA: (51) implies:
% 44.80/6.71 | (52) sdtlbdtrb0(xd, all_96_1) = all_96_0
% 44.80/6.71 | (53) szDzizrdt0(xd) = all_96_1
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (28) with szNzAzT0, all_86_1, xd, simplifying with
% 44.80/6.71 | (8), (38) gives:
% 44.80/6.71 | (54) all_86_1 = szNzAzT0
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (29) with all_90_1, all_94_1, xd, simplifying with
% 44.80/6.71 | (46), (50) gives:
% 44.80/6.71 | (55) all_94_1 = all_90_1
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (29) with all_80_0, all_94_1, xd, simplifying with
% 44.80/6.71 | (33), (50) gives:
% 44.80/6.71 | (56) all_94_1 = all_80_0
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (29) with all_94_1, all_96_1, xd, simplifying with
% 44.80/6.71 | (50), (53) gives:
% 44.80/6.71 | (57) all_96_1 = all_94_1
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (29) with all_88_1, all_96_1, xd, simplifying with
% 44.80/6.71 | (43), (53) gives:
% 44.80/6.71 | (58) all_96_1 = all_88_1
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (57), (58) imply:
% 44.80/6.71 | (59) all_94_1 = all_88_1
% 44.80/6.71 |
% 44.80/6.71 | SIMP: (59) implies:
% 44.80/6.71 | (60) all_94_1 = all_88_1
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (55), (56) imply:
% 44.80/6.71 | (61) all_90_1 = all_80_0
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (55), (60) imply:
% 44.80/6.71 | (62) all_90_1 = all_88_1
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (61), (62) imply:
% 44.80/6.71 | (63) all_88_1 = all_80_0
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (58), (63) imply:
% 44.80/6.71 | (64) all_96_1 = all_80_0
% 44.80/6.71 |
% 44.80/6.71 | REDUCE: (52), (64) imply:
% 44.80/6.71 | (65) sdtlbdtrb0(xd, all_80_0) = all_96_0
% 44.80/6.71 |
% 44.80/6.71 | REDUCE: (49), (56) imply:
% 44.80/6.71 | (66) sdtlbdtrb0(xd, all_80_0) = all_94_0
% 44.80/6.71 |
% 44.80/6.71 | REDUCE: (45), (61) imply:
% 44.80/6.71 | (67) sdtlbdtrb0(xd, all_80_0) = all_90_0
% 44.80/6.71 |
% 44.80/6.71 | REDUCE: (42), (63) imply:
% 44.80/6.71 | (68) sdtlbdtrb0(xd, all_80_0) = all_88_0
% 44.80/6.71 |
% 44.80/6.71 | REDUCE: (41), (63) imply:
% 44.80/6.71 | (69) $i(all_80_0)
% 44.80/6.71 |
% 44.80/6.71 | REDUCE: (37), (54) imply:
% 44.80/6.71 | (70) $i(szNzAzT0)
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (30) with all_90_0, all_94_0, all_80_0, xd,
% 44.80/6.71 | simplifying with (66), (67) gives:
% 44.80/6.71 | (71) all_94_0 = all_90_0
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (30) with all_94_0, all_96_0, all_80_0, xd,
% 44.80/6.71 | simplifying with (65), (66) gives:
% 44.80/6.71 | (72) all_96_0 = all_94_0
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (30) with all_88_0, all_96_0, all_80_0, xd,
% 44.80/6.71 | simplifying with (65), (68) gives:
% 44.80/6.71 | (73) all_96_0 = all_88_0
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (72), (73) imply:
% 44.80/6.71 | (74) all_94_0 = all_88_0
% 44.80/6.71 |
% 44.80/6.71 | SIMP: (74) implies:
% 44.80/6.71 | (75) all_94_0 = all_88_0
% 44.80/6.71 |
% 44.80/6.71 | COMBINE_EQS: (71), (75) imply:
% 44.80/6.71 | (76) all_90_0 = all_88_0
% 44.80/6.71 |
% 44.80/6.71 | GROUND_INST: instantiating (4) with xK, simplifying with (5), (13) gives:
% 44.80/6.72 | (77) xK = sz00 | ? [v0: $i] : (szszuzczcdt0(v0) = xK & $i(v0) &
% 44.80/6.72 | aElementOf0(v0, szNzAzT0))
% 44.80/6.72 |
% 44.80/6.72 | GROUND_INST: instantiating (1) with xO, xQ, simplifying with (14), (18), (19),
% 44.80/6.72 | (40) gives:
% 44.80/6.72 | (78) aSet0(xQ)
% 44.80/6.72 |
% 44.80/6.72 | GROUND_INST: instantiating (mImgElm) with xd, szNzAzT0, xn, all_80_0,
% 44.80/6.72 | simplifying with (7), (8), (21), (22), (32), (48) gives:
% 44.80/6.72 | (79) aElement0(all_80_0)
% 44.80/6.72 |
% 44.80/6.72 | BETA: splitting (77) gives:
% 44.80/6.72 |
% 44.80/6.72 | Case 1:
% 44.80/6.72 | |
% 44.80/6.72 | | (80) xK = sz00
% 44.80/6.72 | |
% 44.80/6.72 | | REDUCE: (6), (80) imply:
% 44.80/6.72 | | (81) $false
% 44.80/6.72 | |
% 44.80/6.72 | | CLOSE: (81) is inconsistent.
% 44.80/6.72 | |
% 44.80/6.72 | Case 2:
% 44.80/6.72 | |
% 44.80/6.72 | |
% 44.80/6.72 | | GROUND_INST: instantiating (mSubTrans) with xP, xQ, szNzAzT0, simplifying
% 44.80/6.72 | | with (3), (15), (17), (18), (25), (35), (70), (78) gives:
% 44.80/6.72 | | (82) aSubsetOf0(xP, szNzAzT0)
% 44.80/6.72 | |
% 44.80/6.72 | | GROUND_INST: instantiating (mPttSet) with xd, all_80_0, all_88_0,
% 44.80/6.72 | | simplifying with (7), (21), (68), (69), (79) gives:
% 44.80/6.72 | | (83) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & aSubsetOf0(all_88_0,
% 44.80/6.72 | | v0))
% 44.80/6.72 | |
% 44.80/6.72 | | GROUND_INST: instantiating (mDefPtt) with xd, all_80_0, all_88_0,
% 44.80/6.72 | | simplifying with (7), (21), (68), (69), (79) gives:
% 44.80/6.72 | | (84) ? [v0: $i] : (szDzozmdt0(xd) = v0 & $i(v0) & ! [v1: $i] : ! [v2:
% 44.80/6.72 | | int] : (v2 = all_80_0 | ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1)
% 44.80/6.72 | | | ~ $i(all_88_0) | ~ aElementOf0(v1, all_88_0)) & ! [v1: $i]
% 44.80/6.72 | | : ! [v2: $i] : ( ~ (sdtlpdtrp0(xd, v1) = v2) | ~ $i(v1) | ~
% 44.80/6.72 | | $i(all_88_0) | ~ aElementOf0(v1, all_88_0) | aElementOf0(v1,
% 44.80/6.72 | | v0)) & ! [v1: any] : (v1 = all_88_0 | ~ $i(v1) | ~
% 44.80/6.72 | | aSet0(v1) | ? [v2: $i] : ? [v3: any] : ($i(v2) & ( ~
% 44.80/6.72 | | aElementOf0(v2, v1) | ~ aElementOf0(v2, v0) | ( ~ (v3 =
% 44.80/6.72 | | all_80_0) & sdtlpdtrp0(xd, v2) = v3 & $i(v3))) &
% 44.80/6.72 | | (aElementOf0(v2, v1) | (v3 = all_80_0 & sdtlpdtrp0(xd, v2) =
% 44.80/6.72 | | all_80_0 & aElementOf0(v2, v0))))) & ! [v1: $i] : ( ~
% 44.80/6.72 | | (sdtlpdtrp0(xd, v1) = all_80_0) | ~ $i(v1) | ~ $i(all_88_0) |
% 44.80/6.72 | | ~ aElementOf0(v1, v0) | aElementOf0(v1, all_88_0)) & ( ~
% 44.80/6.72 | | $i(all_88_0) | aSet0(all_88_0)))
% 44.80/6.72 | |
% 44.80/6.72 | | DELTA: instantiating (83) with fresh symbol all_150_0 gives:
% 44.80/6.72 | | (85) szDzozmdt0(xd) = all_150_0 & $i(all_150_0) & aSubsetOf0(all_88_0,
% 44.80/6.72 | | all_150_0)
% 44.80/6.72 | |
% 44.80/6.72 | | ALPHA: (85) implies:
% 44.80/6.72 | | (86) $i(all_150_0)
% 44.80/6.73 | | (87) szDzozmdt0(xd) = all_150_0
% 44.80/6.73 | |
% 44.80/6.73 | | DELTA: instantiating (84) with fresh symbol all_171_0 gives:
% 44.80/6.73 | | (88) szDzozmdt0(xd) = all_171_0 & $i(all_171_0) & ! [v0: $i] : ! [v1:
% 44.80/6.73 | | int] : (v1 = all_80_0 | ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) |
% 44.80/6.73 | | ~ $i(all_88_0) | ~ aElementOf0(v0, all_88_0)) & ! [v0: $i] : !
% 44.80/6.73 | | [v1: $i] : ( ~ (sdtlpdtrp0(xd, v0) = v1) | ~ $i(v0) | ~
% 44.80/6.73 | | $i(all_88_0) | ~ aElementOf0(v0, all_88_0) | aElementOf0(v0,
% 44.80/6.73 | | all_171_0)) & ! [v0: any] : (v0 = all_88_0 | ~ $i(v0) | ~
% 44.80/6.73 | | aSet0(v0) | ? [v1: $i] : ? [v2: any] : ($i(v1) & ( ~
% 44.80/6.73 | | aElementOf0(v1, v0) | ~ aElementOf0(v1, all_171_0) | ( ~ (v2
% 44.80/6.73 | | = all_80_0) & sdtlpdtrp0(xd, v1) = v2 & $i(v2))) &
% 44.80/6.73 | | (aElementOf0(v1, v0) | (v2 = all_80_0 & sdtlpdtrp0(xd, v1) =
% 44.80/6.73 | | all_80_0 & aElementOf0(v1, all_171_0))))) & ! [v0: $i] : (
% 44.80/6.73 | | ~ (sdtlpdtrp0(xd, v0) = all_80_0) | ~ $i(v0) | ~ $i(all_88_0) |
% 44.80/6.73 | | ~ aElementOf0(v0, all_171_0) | aElementOf0(v0, all_88_0)) & ( ~
% 44.80/6.73 | | $i(all_88_0) | aSet0(all_88_0))
% 44.80/6.73 | |
% 44.80/6.73 | | ALPHA: (88) implies:
% 44.80/6.73 | | (89) szDzozmdt0(xd) = all_171_0
% 44.80/6.73 | |
% 44.80/6.73 | | GROUND_INST: instantiating (28) with szNzAzT0, all_171_0, xd, simplifying
% 44.80/6.73 | | with (8), (89) gives:
% 44.80/6.73 | | (90) all_171_0 = szNzAzT0
% 44.80/6.73 | |
% 44.80/6.73 | | GROUND_INST: instantiating (28) with all_150_0, all_171_0, xd, simplifying
% 44.80/6.73 | | with (87), (89) gives:
% 44.80/6.73 | | (91) all_171_0 = all_150_0
% 44.80/6.73 | |
% 44.80/6.73 | | COMBINE_EQS: (90), (91) imply:
% 44.80/6.73 | | (92) all_150_0 = szNzAzT0
% 44.80/6.73 | |
% 44.80/6.73 | | GROUND_INST: instantiating (2) with szNzAzT0, xP, xx, simplifying with (3),
% 44.80/6.73 | | (24), (25), (26), (27), (70), (82) gives:
% 44.80/6.73 | | (93) $false
% 44.80/6.73 | |
% 44.80/6.73 | | CLOSE: (93) is inconsistent.
% 44.80/6.73 | |
% 44.80/6.73 | End of split
% 44.80/6.73 |
% 44.80/6.73 End of proof
% 44.80/6.73 % SZS output end Proof for theBenchmark
% 44.80/6.73
% 44.80/6.73 6103ms
%------------------------------------------------------------------------------