TSTP Solution File: NUM590+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM590+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 : n022.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 11:48:48 EDT 2023
% Result : Theorem 45.86s 6.84s
% Output : Proof 67.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM590+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 12:46:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 5.93/1.61 Prover 1: Preprocessing ...
% 5.93/1.62 Prover 4: Preprocessing ...
% 6.32/1.64 Prover 5: Preprocessing ...
% 6.32/1.64 Prover 2: Preprocessing ...
% 6.32/1.64 Prover 6: Preprocessing ...
% 6.32/1.64 Prover 0: Preprocessing ...
% 6.32/1.64 Prover 3: Preprocessing ...
% 18.90/3.33 Prover 1: Constructing countermodel ...
% 19.26/3.36 Prover 3: Constructing countermodel ...
% 19.26/3.37 Prover 6: Proving ...
% 20.94/3.65 Prover 5: Proving ...
% 42.45/6.40 Prover 4: Constructing countermodel ...
% 45.13/6.84 Prover 3: proved (6205ms)
% 45.13/6.84
% 45.86/6.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.86/6.84
% 45.86/6.84 Prover 6: stopped
% 45.86/6.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 45.86/6.86 Prover 5: stopped
% 45.86/6.87 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 45.86/6.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 47.44/7.09 Prover 7: Preprocessing ...
% 47.44/7.10 Prover 8: Preprocessing ...
% 47.44/7.11 Prover 10: Preprocessing ...
% 47.44/7.21 Prover 2: Proving ...
% 47.44/7.24 Prover 2: stopped
% 47.44/7.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 50.15/7.44 Prover 11: Preprocessing ...
% 51.39/7.61 Prover 8: Warning: ignoring some quantifiers
% 51.39/7.62 Prover 8: Constructing countermodel ...
% 52.73/7.80 Prover 0: Proving ...
% 53.37/7.86 Prover 0: stopped
% 53.37/7.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 53.37/7.96 Prover 10: Constructing countermodel ...
% 54.03/8.06 Prover 7: Constructing countermodel ...
% 55.36/8.09 Prover 13: Preprocessing ...
% 61.71/8.98 Prover 10: Found proof (size 21)
% 61.71/8.98 Prover 10: proved (2112ms)
% 61.71/8.98 Prover 7: stopped
% 62.24/8.99 Prover 8: stopped
% 62.24/8.99 Prover 1: stopped
% 62.24/8.99 Prover 4: stopped
% 62.24/9.06 Prover 13: Warning: ignoring some quantifiers
% 62.96/9.13 Prover 13: Constructing countermodel ...
% 62.96/9.15 Prover 13: stopped
% 66.85/10.08 Prover 11: Constructing countermodel ...
% 66.85/10.11 Prover 11: stopped
% 66.85/10.11
% 66.85/10.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.85/10.11
% 66.85/10.12 % SZS output start Proof for theBenchmark
% 66.85/10.13 Assumptions after simplification:
% 66.85/10.13 ---------------------------------
% 66.85/10.13
% 66.85/10.13 (mCountNFin_01)
% 66.85/10.14 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 66.85/10.14
% 66.85/10.14 (mDefEmp)
% 66.85/10.14 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 66.85/10.14 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 66.85/10.14 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 66.85/10.14
% 66.85/10.14 (mDefSub)
% 66.85/10.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 66.85/10.15 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 66.85/10.15 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 66.85/10.15 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 66.85/10.15 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 66.85/10.15 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 66.85/10.15
% 66.85/10.15 (mNATSet)
% 66.85/10.15 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 66.85/10.15
% 66.85/10.15 (m__)
% 66.85/10.15 $i(xY) & $i(szNzAzT0) & ? [v0: $i] : ($i(v0) & aElementOf0(v0, xY) & ~
% 66.85/10.15 aSubsetOf0(xY, szNzAzT0) & ~ aElementOf0(v0, szNzAzT0))
% 66.85/10.15
% 66.85/10.15 (m__3671)
% 67.49/10.19 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 67.49/10.19 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v2, v1) |
% 67.49/10.19 ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 67.49/10.19 [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 67.49/10.19 szNzAzT0) | aSubsetOf0(v1, szNzAzT0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 67.49/10.19 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 67.49/10.19 isCountable0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) =
% 67.49/10.19 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aSet0(v1))
% 67.49/10.19
% 67.49/10.19 (m__4151)
% 67.66/10.21 szDzozmdt0(xC) = szNzAzT0 & $i(xC) & $i(xN) & $i(xk) & $i(xc) & $i(szNzAzT0) &
% 67.66/10.21 aFunction0(xC) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 67.66/10.21 [v4: $i] : (v4 = v2 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2)
% 67.66/10.21 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4,
% 67.66/10.21 v1) | ~ aElementOf0(v0, szNzAzT0) | ~ aElement0(v4) | aElementOf0(v4,
% 67.66/10.21 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 67.66/10.21 : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1,
% 67.66/10.21 v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, v3) | ~
% 67.66/10.21 aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1)) & ! [v0: $i] : ! [v1: $i]
% 67.66/10.21 : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 67.66/10.21 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) |
% 67.66/10.21 ~ aElementOf0(v4, v3) | ~ aElementOf0(v0, szNzAzT0) | aElement0(v4)) & !
% 67.66/10.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 67.66/10.21 (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2)
% 67.66/10.21 = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4, v1) | ~
% 67.66/10.21 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v4)) & ! [v0: $i] : ! [v1: $i]
% 67.66/10.21 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 67.66/10.21 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v2) | ~ $i(v0) |
% 67.66/10.21 ~ aElementOf0(v2, v3) | ~ aElementOf0(v0, szNzAzT0)) & ! [v0: $i] : !
% 67.66/10.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 67.66/10.21 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 67.66/10.21 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 67.66/10.21 : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~
% 67.66/10.21 (szmzizndt0(v1) = v2) | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~
% 67.66/10.21 aElementOf0(v0, szNzAzT0) | aSet0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 67.66/10.21 $i] : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2)
% 67.66/10.21 | ~ (sdtmndt0(v1, v2) = v3) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ?
% 67.66/10.21 [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xC, v0) = v4 & szDzozmdt0(v4) = v5 &
% 67.66/10.21 slbdtsldtrb0(v3, xk) = v5 & $i(v5) & $i(v4) & aFunction0(v4) & ! [v6: $i]
% 67.66/10.21 : ! [v7: $i] : ! [v8: $i] : ( ~ (sbrdtbr0(v6) = v7) | ~ $i(v8) | ~
% 67.66/10.21 $i(v6) | ~ aElementOf0(v8, v6) | ~ aElementOf0(v6, v5) |
% 67.66/10.21 aElementOf0(v8, v3)) & ! [v6: $i] : ! [v7: $i] : (v7 = xk | ~
% 67.66/10.21 (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5)) & ! [v6: $i]
% 67.66/10.21 : ! [v7: $i] : ( ~ (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6,
% 67.66/10.21 v5) | aSubsetOf0(v6, v3)) & ! [v6: $i] : ! [v7: $i] : ( ~
% 67.66/10.21 (sbrdtbr0(v6) = v7) | ~ $i(v6) | ~ aElementOf0(v6, v5) | aSet0(v6)) &
% 67.66/10.21 ! [v6: $i] : ! [v7: $i] : ( ~ (sdtpldt0(v6, v2) = v7) | ~ $i(v6) | ~
% 67.66/10.21 aSet0(v6) | ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] :
% 67.66/10.21 ($i(v11) & aElementOf0(v2, v1) & ! [v12: $i] : ( ~ $i(v12) | ~
% 67.66/10.21 aElementOf0(v12, v1) | sdtlseqdt0(v2, v12)) & ((v10 = v9 &
% 67.66/10.21 sdtlpdtrp0(v4, v6) = v9 & sdtlpdtrp0(xc, v7) = v9 & $i(v9) & !
% 67.66/10.21 [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ aElementOf0(v12, v7) |
% 67.66/10.21 aElementOf0(v12, v6)) & ! [v12: $i] : ( ~ $i(v12) | ~
% 67.66/10.21 aElementOf0(v12, v7) | aElement0(v12)) & ! [v12: $i] : ( ~
% 67.66/10.21 $i(v12) | ~ aElementOf0(v12, v6) | ~ aElement0(v12) |
% 67.66/10.21 aElementOf0(v12, v7)) & ( ~ $i(v2) | ~ aElement0(v2) |
% 67.66/10.21 aElementOf0(v2, v7))) | (aSet0(v3) & ~ aElementOf0(v6, v5) & !
% 67.66/10.21 [v12: $i] : (v12 = v2 | ~ $i(v12) | ~ aElementOf0(v12, v1) | ~
% 67.66/10.21 aElement0(v12) | aElementOf0(v12, v3)) & ! [v12: $i] : ( ~
% 67.66/10.21 $i(v12) | ~ aElementOf0(v12, v3) | aElementOf0(v12, v1)) & !
% 67.66/10.21 [v12: $i] : ( ~ $i(v12) | ~ aElementOf0(v12, v3) |
% 67.66/10.21 aElement0(v12)) & ( ~ $i(v2) | ~ aElementOf0(v2, v3)) & (( ~
% 67.66/10.21 (v8 = xk) & sbrdtbr0(v6) = v8 & $i(v8)) | (aElementOf0(v11,
% 67.66/10.21 v6) & ~ aSubsetOf0(v6, v3) & ~ aElementOf0(v11, v3)))))))
% 67.66/10.21 & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) | ~ $i(v6) | ~ aSubsetOf0(v6,
% 67.66/10.21 v3) | aElementOf0(v6, v5)) & ! [v6: $i] : ( ~ (sbrdtbr0(v6) = xk) |
% 67.66/10.21 ~ $i(v6) | ~ aSet0(v6) | aElementOf0(v6, v5) | ? [v7: $i] : ($i(v7) &
% 67.66/10.21 aElementOf0(v7, v6) & ~ aElementOf0(v7, v3)))))
% 67.66/10.21
% 67.66/10.21 (m__4448)
% 67.66/10.21 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0)
% 67.66/10.21
% 67.66/10.21 (m__4448_02)
% 67.66/10.22 $i(xd) & $i(xY) & $i(xi) & $i(xC) & $i(xN) & ? [v0: $i] : ? [v1: $i] :
% 67.66/10.22 (sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 &
% 67.66/10.22 sdtmndt0(v0, v1) = xY & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(xY) &
% 67.66/10.22 ~ aElementOf0(v1, xY) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~
% 67.66/10.22 aElementOf0(v2, v0) | ~ aElement0(v2) | aElementOf0(v2, xY)) & ! [v2:
% 67.66/10.22 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) & ! [v2:
% 67.66/10.22 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xY) | aElementOf0(v2, v0)) & ! [v2:
% 67.66/10.22 $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xY) | aElement0(v2)))
% 67.66/10.22
% 67.66/10.22 Further assumptions not needed in the proof:
% 67.66/10.22 --------------------------------------------
% 67.66/10.22 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 67.66/10.22 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 67.66/10.22 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 67.66/10.22 mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 67.66/10.22 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 67.66/10.22 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 67.66/10.22 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 67.66/10.22 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 67.66/10.22 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 67.66/10.22 mZeroLess, mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462,
% 67.66/10.22 m__3520, m__3533, m__3623, m__3754, m__3821, m__3965, m__4182, m__4331, m__4423
% 67.66/10.22
% 67.66/10.22 Those formulas are unsatisfiable:
% 67.66/10.22 ---------------------------------
% 67.66/10.22
% 67.66/10.22 Begin of proof
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (mDefEmp) implies:
% 67.66/10.22 | (1) aSet0(slcrc0)
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (mCountNFin_01) implies:
% 67.66/10.22 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (mDefSub) implies:
% 67.66/10.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 67.66/10.22 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 67.66/10.22 | aSet0(v0) | aElementOf0(v2, v0))
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (mNATSet) implies:
% 67.66/10.22 | (4) aSet0(szNzAzT0)
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (m__3671) implies:
% 67.66/10.22 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) |
% 67.66/10.22 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v1, szNzAzT0))
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (m__4151) implies:
% 67.66/10.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 67.66/10.22 | ~ (sdtlpdtrp0(xN, v0) = v1) | ~ (szmzizndt0(v1) = v2) | ~
% 67.66/10.22 | (sdtmndt0(v1, v2) = v3) | ~ $i(v4) | ~ $i(v0) | ~ aElementOf0(v4,
% 67.66/10.22 | v3) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v1))
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (m__4448) implies:
% 67.66/10.22 | (7) aElementOf0(xi, szNzAzT0)
% 67.66/10.22 |
% 67.66/10.22 | ALPHA: (m__4448_02) implies:
% 67.66/10.22 | (8) $i(xi)
% 67.66/10.23 | (9) ? [v0: $i] : ? [v1: $i] : (sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN,
% 67.66/10.23 | xi) = v0 & szmzizndt0(v0) = v1 & sdtmndt0(v0, v1) = xY & $i(v1) &
% 67.66/10.23 | $i(v0) & aElementOf0(v1, v0) & aSet0(xY) & ~ aElementOf0(v1, xY) &
% 67.66/10.23 | ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~ aElementOf0(v2, v0) | ~
% 67.66/10.23 | aElement0(v2) | aElementOf0(v2, xY)) & ! [v2: $i] : ( ~ $i(v2) |
% 67.66/10.23 | ~ aElementOf0(v2, v0) | sdtlseqdt0(v1, v2)) & ! [v2: $i] : ( ~
% 67.66/10.23 | $i(v2) | ~ aElementOf0(v2, xY) | aElementOf0(v2, v0)) & ! [v2:
% 67.66/10.23 | $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xY) | aElement0(v2)))
% 67.66/10.23 |
% 67.66/10.23 | ALPHA: (m__) implies:
% 67.66/10.23 | (10) $i(szNzAzT0)
% 67.66/10.23 | (11) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xY) & ~ aSubsetOf0(xY,
% 67.66/10.23 | szNzAzT0) & ~ aElementOf0(v0, szNzAzT0))
% 67.66/10.23 |
% 67.66/10.23 | DELTA: instantiating (11) with fresh symbol all_73_0 gives:
% 67.66/10.23 | (12) $i(all_73_0) & aElementOf0(all_73_0, xY) & ~ aSubsetOf0(xY, szNzAzT0)
% 67.66/10.23 | & ~ aElementOf0(all_73_0, szNzAzT0)
% 67.66/10.23 |
% 67.66/10.23 | ALPHA: (12) implies:
% 67.66/10.23 | (13) ~ aElementOf0(all_73_0, szNzAzT0)
% 67.66/10.23 | (14) aElementOf0(all_73_0, xY)
% 67.66/10.23 | (15) $i(all_73_0)
% 67.66/10.23 |
% 67.66/10.23 | DELTA: instantiating (9) with fresh symbols all_75_0, all_75_1 gives:
% 67.66/10.23 | (16) sdtlpdtrp0(xC, xi) = xd & sdtlpdtrp0(xN, xi) = all_75_1 &
% 67.66/10.23 | szmzizndt0(all_75_1) = all_75_0 & sdtmndt0(all_75_1, all_75_0) = xY &
% 67.66/10.23 | $i(all_75_0) & $i(all_75_1) & aElementOf0(all_75_0, all_75_1) &
% 67.66/10.23 | aSet0(xY) & ~ aElementOf0(all_75_0, xY) & ! [v0: any] : (v0 =
% 67.66/10.23 | all_75_0 | ~ $i(v0) | ~ aElementOf0(v0, all_75_1) | ~
% 67.66/10.23 | aElement0(v0) | aElementOf0(v0, xY)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 67.66/10.23 | aElementOf0(v0, all_75_1) | sdtlseqdt0(all_75_0, v0)) & ! [v0: $i]
% 67.66/10.23 | : ( ~ $i(v0) | ~ aElementOf0(v0, xY) | aElementOf0(v0, all_75_1)) &
% 67.66/10.23 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xY) | aElement0(v0))
% 67.66/10.23 |
% 67.66/10.23 | ALPHA: (16) implies:
% 67.66/10.23 | (17) $i(all_75_1)
% 67.66/10.23 | (18) sdtmndt0(all_75_1, all_75_0) = xY
% 67.66/10.23 | (19) szmzizndt0(all_75_1) = all_75_0
% 67.66/10.23 | (20) sdtlpdtrp0(xN, xi) = all_75_1
% 67.66/10.23 |
% 67.66/10.23 | BETA: splitting (2) gives:
% 67.66/10.23 |
% 67.66/10.23 | Case 1:
% 67.66/10.23 | |
% 67.77/10.23 | | (21) ~ aSet0(slcrc0)
% 67.77/10.23 | |
% 67.77/10.23 | | PRED_UNIFY: (1), (21) imply:
% 67.77/10.23 | | (22) $false
% 67.77/10.23 | |
% 67.77/10.23 | | CLOSE: (22) is inconsistent.
% 67.77/10.23 | |
% 67.77/10.23 | Case 2:
% 67.77/10.23 | |
% 67.77/10.23 | |
% 67.77/10.23 | | GROUND_INST: instantiating (6) with xi, all_75_1, all_75_0, xY, all_73_0,
% 67.77/10.23 | | simplifying with (7), (8), (14), (15), (18), (19), (20) gives:
% 67.77/10.23 | | (23) aElementOf0(all_73_0, all_75_1)
% 67.77/10.23 | |
% 67.77/10.23 | | GROUND_INST: instantiating (5) with xi, all_75_1, simplifying with (7), (8),
% 67.77/10.23 | | (20) gives:
% 67.77/10.23 | | (24) aSubsetOf0(all_75_1, szNzAzT0)
% 67.77/10.23 | |
% 67.77/10.24 | | GROUND_INST: instantiating (3) with szNzAzT0, all_75_1, all_73_0,
% 67.77/10.24 | | simplifying with (4), (10), (13), (15), (17), (23), (24) gives:
% 67.77/10.24 | | (25) $false
% 67.77/10.24 | |
% 67.77/10.24 | | CLOSE: (25) is inconsistent.
% 67.77/10.24 | |
% 67.77/10.24 | End of split
% 67.77/10.24 |
% 67.77/10.24 End of proof
% 67.77/10.24 % SZS output end Proof for theBenchmark
% 67.77/10.24
% 67.77/10.24 9630ms
%------------------------------------------------------------------------------