TSTP Solution File: RNG115+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG115+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 13:57:58 EDT 2023
% Result : Theorem 16.27s 2.96s
% Output : Proof 32.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG115+4 : 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 : n014.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 : Sun Aug 27 01:24:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 3.31/1.22 Prover 4: Preprocessing ...
% 3.31/1.22 Prover 1: Preprocessing ...
% 3.83/1.26 Prover 3: Preprocessing ...
% 3.83/1.26 Prover 2: Preprocessing ...
% 3.83/1.27 Prover 5: Preprocessing ...
% 3.83/1.27 Prover 6: Preprocessing ...
% 3.83/1.27 Prover 0: Preprocessing ...
% 11.44/2.29 Prover 6: Proving ...
% 11.44/2.29 Prover 3: Constructing countermodel ...
% 11.44/2.32 Prover 1: Constructing countermodel ...
% 11.44/2.33 Prover 5: Proving ...
% 12.63/2.49 Prover 2: Proving ...
% 13.66/2.65 Prover 4: Constructing countermodel ...
% 13.66/2.66 Prover 0: Proving ...
% 16.27/2.95 Prover 3: proved (2307ms)
% 16.27/2.95
% 16.27/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.27/2.96
% 16.27/2.96 Prover 0: stopped
% 16.27/2.96 Prover 5: stopped
% 16.27/2.96 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.27/2.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.27/2.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.27/2.96 Prover 6: stopped
% 16.27/2.97 Prover 2: stopped
% 16.64/2.98 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.64/2.98 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.86/3.19 Prover 13: Preprocessing ...
% 17.86/3.19 Prover 10: Preprocessing ...
% 17.86/3.19 Prover 11: Preprocessing ...
% 17.86/3.21 Prover 8: Preprocessing ...
% 18.40/3.22 Prover 7: Preprocessing ...
% 19.47/3.45 Prover 7: Constructing countermodel ...
% 19.47/3.45 Prover 10: Constructing countermodel ...
% 19.47/3.46 Prover 8: Warning: ignoring some quantifiers
% 19.47/3.51 Prover 13: Warning: ignoring some quantifiers
% 19.47/3.51 Prover 8: Constructing countermodel ...
% 19.47/3.53 Prover 13: Constructing countermodel ...
% 19.47/3.54 Prover 11: Constructing countermodel ...
% 30.60/4.99 Prover 10: Found proof (size 68)
% 30.60/5.00 Prover 10: proved (2038ms)
% 30.60/5.00 Prover 7: stopped
% 30.60/5.00 Prover 11: stopped
% 30.60/5.00 Prover 8: stopped
% 30.60/5.00 Prover 1: stopped
% 30.60/5.00 Prover 13: stopped
% 30.60/5.00 Prover 4: stopped
% 30.60/5.00
% 30.60/5.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.60/5.00
% 30.60/5.01 % SZS output start Proof for theBenchmark
% 30.60/5.01 Assumptions after simplification:
% 30.60/5.01 ---------------------------------
% 30.60/5.01
% 30.60/5.01 (mDefPrIdeal)
% 30.60/5.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 30.60/5.05 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 30.60/5.05 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 30.60/5.05 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 30.60/5.05 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 30.60/5.05 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 30.60/5.05 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 30.60/5.05 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 30.60/5.05 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 30.60/5.05 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 30.60/5.05 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 30.60/5.05 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 30.60/5.05 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 30.60/5.05
% 30.60/5.05 (mMulAsso)
% 31.94/5.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 31.94/5.05 (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 31.94/5.05 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ?
% 31.94/5.05 [v5: $i] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4 & $i(v5) &
% 31.94/5.05 $i(v4)))
% 31.94/5.05
% 31.94/5.05 (mMulComm)
% 31.94/5.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 31.94/5.05 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0)
% 31.94/5.05 = v2 & $i(v2)))
% 31.94/5.05
% 31.94/5.05 (m__)
% 31.94/5.06 $i(xu) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 31.94/5.06 slsdtgt0(xa) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 31.94/5.06 $i] : ! [v5: $i] : ( ~ (sdtasdt0(xb, v4) = v3) | ~ (sdtasdt0(xa, v5) =
% 31.94/5.06 v2) | ~ (sdtpldt0(v2, v3) = xu) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 31.94/5.06 ~ $i(v2) | ~ aElement0(v5) | ~ aElement0(v4)) & ! [v2: $i] : ! [v3:
% 31.94/5.06 $i] : ! [v4: $i] : ( ~ (sdtasdt0(xb, v4) = v3) | ~ (sdtpldt0(v2, v3) =
% 31.94/5.06 xu) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, v0) | ~
% 31.94/5.06 aElement0(v4)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 31.94/5.06 (sdtasdt0(xa, v4) = v2) | ~ (sdtpldt0(v2, v3) = xu) | ~ $i(v4) | ~
% 31.94/5.06 $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, v1) | ~ aElement0(v4)) & ! [v2:
% 31.94/5.06 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v2, v3) = xu) | ~ $i(v3) | ~ $i(v2) |
% 31.94/5.06 ~ aElementOf0(v3, v1) | ~ aElementOf0(v2, v0)))
% 31.94/5.06
% 31.94/5.06 (m__2091)
% 31.94/5.06 $i(xb) & $i(xa) & aElement0(xb) & aElement0(xa)
% 31.94/5.06
% 31.94/5.06 (m__2129)
% 31.94/5.07 $i(xc) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = xa
% 31.94/5.07 & sdtasdt0(xc, v0) = xb & $i(v1) & $i(v0) & aGcdOfAnd0(xc, xa, xb) &
% 31.94/5.07 aDivisorOf0(xc, xb) & aDivisorOf0(xc, xa) & doDivides0(xc, xb) &
% 31.94/5.07 doDivides0(xc, xa) & aElement0(v1) & aElement0(v0) & aElement0(xc) & ! [v2:
% 31.94/5.07 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v2, v4) = xa) | ~
% 31.94/5.07 (sdtasdt0(v2, v3) = xb) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2, xc))
% 31.94/5.07 & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v2, v4) = xa) | ~
% 31.94/5.07 (sdtasdt0(v2, v3) = xb) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v5: $i] :
% 31.94/5.07 (sdtasdt0(v2, v5) = xc & $i(v5) & aElement0(v5))) & ! [v2: $i] : ! [v3:
% 31.94/5.07 $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 aDivisorOf0(v2, xa) | ~ aElement0(v3) | doDivides0(v2, xc)) & ! [v2: $i]
% 31.94/5.07 : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 aDivisorOf0(v2, xa) | ~ aElement0(v3) | ? [v4: $i] : (sdtasdt0(v2, v4) =
% 31.94/5.07 xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 31.94/5.07 (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xa) |
% 31.94/5.07 ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] :
% 31.94/5.07 ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 doDivides0(v2, xa) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] :
% 31.94/5.07 (sdtasdt0(v2, v4) = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3:
% 31.94/5.07 $i] : ( ~ (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 aDivisorOf0(v2, xb) | ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2,
% 31.94/5.07 xc)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xa) | ~
% 31.94/5.07 $i(v3) | ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ aElement0(v3) | ~
% 31.94/5.07 aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4) = xc & $i(v4) &
% 31.94/5.07 aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) =
% 31.94/5.07 xa) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xb) | ~ aElement0(v3) |
% 31.94/5.07 ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 31.94/5.07 (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xb) |
% 31.94/5.07 ~ aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4) = xc
% 31.94/5.07 & $i(v4) & aElement0(v4))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 31.94/5.07 aDivisorOf0(v2, xb) | ~ aDivisorOf0(v2, xa) | doDivides0(v2, xc)) & !
% 31.94/5.07 [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ aDivisorOf0(v2, xa) | ?
% 31.94/5.07 [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & ! [v2: $i]
% 31.94/5.07 : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ doDivides0(v2, xa) | ~
% 31.94/5.07 aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 31.94/5.07 aDivisorOf0(v2, xb) | ~ doDivides0(v2, xa) | ~ aElement0(v2) | ? [v3:
% 31.94/5.07 $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & ! [v2: $i] :
% 31.94/5.07 ( ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~ doDivides0(v2, xb) | doDivides0(v2,
% 31.94/5.07 xc)) & ! [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~
% 31.94/5.07 doDivides0(v2, xb) | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) &
% 31.94/5.07 aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ doDivides0(v2, xb) | ~
% 31.94/5.07 doDivides0(v2, xa) | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i]
% 31.94/5.07 : ( ~ $i(v2) | ~ doDivides0(v2, xb) | ~ doDivides0(v2, xa) | ~
% 31.94/5.07 aElement0(v2) | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) &
% 31.94/5.07 aElement0(v3))))
% 31.94/5.07
% 31.94/5.07 (m__2174)
% 31.94/5.07 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 31.94/5.07 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI) &
% 31.94/5.07 aSet0(xI) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v2)
% 31.94/5.07 = v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ~
% 31.94/5.07 aElement0(v3) | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 31.94/5.07 $i] : ( ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.07 aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | aElementOf0(v2, xI)) & !
% 31.94/5.07 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v2, v3) = v4) | ~
% 31.94/5.07 $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xI) | ~ aElementOf0(v2, xI) |
% 31.94/5.07 aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(xb, v3) =
% 31.94/5.07 v2) | ~ $i(v3) | ~ $i(v2) | ~ aElement0(v3) | aElementOf0(v2, v1)) &
% 31.94/5.07 ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(xa, v3) = v2) | ~ $i(v3) | ~
% 31.94/5.07 $i(v2) | ~ aElement0(v3) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~
% 31.94/5.07 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 &
% 31.94/5.07 $i(v3) & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 31.94/5.07 v0) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & $i(v3) & aElement0(v3))) &
% 31.94/5.07 ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xI) | ? [v3: $i] : ? [v4: $i]
% 31.94/5.07 : (sdtpldt0(v3, v4) = v2 & $i(v4) & $i(v3) & aElementOf0(v4, v1) &
% 31.94/5.07 aElementOf0(v3, v0))))
% 31.94/5.07
% 31.94/5.07 (m__2203)
% 31.94/5.08 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 31.94/5.08 $i] : ? [v4: $i] : ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 31.94/5.08 sdtasdt0(xb, v3) = sz00 & sdtasdt0(xb, v2) = xb & sdtasdt0(xa, v5) = sz00 &
% 31.94/5.08 sdtasdt0(xa, v4) = xa & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 31.94/5.08 & aElementOf0(xb, v1) & aElementOf0(xa, v0) & aElementOf0(sz00, v1) &
% 31.94/5.08 aElementOf0(sz00, v0) & aElement0(v5) & aElement0(v4) & aElement0(v3) &
% 31.94/5.08 aElement0(v2))
% 31.94/5.08
% 31.94/5.08 (m__2228)
% 31.94/5.08 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 31.94/5.08 $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 &
% 31.94/5.08 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & sdtpldt0(v4, v5) = v3 & $i(v5) &
% 31.94/5.08 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v1) &
% 31.94/5.08 aElementOf0(v4, v0) & aElementOf0(v3, v2) & ! [v6: $i] : ! [v7: $i] : ( ~
% 31.94/5.08 (sdtasdt0(xb, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) |
% 31.94/5.08 aElementOf0(v6, v1)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtasdt0(xa, v7) =
% 31.94/5.08 v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) | aElementOf0(v6, v0)) &
% 31.94/5.08 ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v1) | ? [v7: $i] :
% 31.94/5.08 (sdtasdt0(xb, v7) = v6 & $i(v7) & aElement0(v7))) & ! [v6: $i] : ( ~
% 31.94/5.08 $i(v6) | ~ aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 &
% 31.94/5.08 $i(v7) & aElement0(v7))))
% 31.94/5.08
% 31.94/5.08 (m__2273)
% 31.94/5.08 $i(xu) & $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ?
% 31.94/5.08 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (xu = sz00) & slsdtgt0(xb) = v1 &
% 31.94/5.08 slsdtgt0(xa) = v0 & sbrdtbr0(xu) = v2 & sdtpldt0(v3, v4) = xu & $i(v4) &
% 31.94/5.08 $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v4, v1) & aElementOf0(v3,
% 31.94/5.08 v0) & aElementOf0(xu, xI) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 31.94/5.08 [v8: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ (sdtpldt0(v7, v8) = v5)
% 31.94/5.08 | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ iLess0(v6, v2) | ~
% 31.94/5.08 aElementOf0(v8, v1) | ~ aElementOf0(v7, v0)) & ! [v5: $i] : ! [v6: $i]
% 31.94/5.08 : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ~ iLess0(v6, v2) | ~
% 31.94/5.08 aElementOf0(v5, xI)))
% 31.94/5.08
% 31.94/5.08 (function-axioms)
% 31.94/5.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.94/5.08 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.94/5.08 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 31.94/5.08 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 31.94/5.08 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 31.94/5.08 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 31.94/5.08 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 31.94/5.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 31.94/5.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.94/5.08 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 31.94/5.08 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 31.94/5.08
% 31.94/5.09 Further assumptions not needed in the proof:
% 31.94/5.09 --------------------------------------------
% 31.94/5.09 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 31.94/5.09 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum,
% 31.94/5.09 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulMnOne, mMulUnit,
% 31.94/5.09 mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsB, mSortsB_02,
% 31.94/5.09 mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2110, m__2383
% 31.94/5.09
% 31.94/5.09 Those formulas are unsatisfiable:
% 31.94/5.09 ---------------------------------
% 31.94/5.09
% 31.94/5.09 Begin of proof
% 31.94/5.09 |
% 31.94/5.09 | ALPHA: (mDefPrIdeal) implies:
% 31.94/5.09 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 31.94/5.09 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 31.94/5.09 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 31.94/5.09 | aElement0(v3)))
% 31.94/5.09 |
% 31.94/5.09 | ALPHA: (m__2091) implies:
% 31.94/5.09 | (2) aElement0(xa)
% 31.94/5.09 | (3) aElement0(xb)
% 31.94/5.09 |
% 31.94/5.09 | ALPHA: (m__2129) implies:
% 31.94/5.09 | (4) $i(xc)
% 31.94/5.10 | (5) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = xa & sdtasdt0(xc, v0) =
% 31.94/5.10 | xb & $i(v1) & $i(v0) & aGcdOfAnd0(xc, xa, xb) & aDivisorOf0(xc, xb) &
% 31.94/5.10 | aDivisorOf0(xc, xa) & doDivides0(xc, xb) & doDivides0(xc, xa) &
% 31.94/5.10 | aElement0(v1) & aElement0(v0) & aElement0(xc) & ! [v2: $i] : ! [v3:
% 31.94/5.10 | $i] : ! [v4: $i] : ( ~ (sdtasdt0(v2, v4) = xa) | ~ (sdtasdt0(v2,
% 31.94/5.10 | v3) = xb) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) |
% 31.94/5.10 | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 31.94/5.10 | (sdtasdt0(v2, v4) = xa) | ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v4) |
% 31.94/5.10 | ~ $i(v3) | ~ $i(v2) | ~ aElement0(v4) | ~ aElement0(v3) | ~
% 31.94/5.10 | aElement0(v2) | ? [v5: $i] : (sdtasdt0(v2, v5) = xc & $i(v5) &
% 31.94/5.10 | aElement0(v5))) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2,
% 31.94/5.10 | v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~
% 31.94/5.10 | aElement0(v3) | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : (
% 31.94/5.10 | ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | aDivisorOf0(v2, xa) | ~ aElement0(v3) | ? [v4: $i] :
% 31.94/5.10 | (sdtasdt0(v2, v4) = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] :
% 31.94/5.10 | ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | doDivides0(v2, xa) | ~ aElement0(v3) | ~ aElement0(v2) |
% 31.94/5.10 | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2,
% 31.94/5.10 | v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xa) | ~
% 31.94/5.10 | aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4)
% 31.94/5.10 | = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 31.94/5.10 | (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | aDivisorOf0(v2, xb) | ~ aElement0(v3) | ~ aElement0(v2) |
% 31.94/5.10 | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2,
% 31.94/5.10 | v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~
% 31.94/5.10 | aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4)
% 31.94/5.10 | = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 31.94/5.10 | (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2,
% 31.94/5.10 | xb) | ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2, xc)) &
% 31.94/5.10 | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xa) | ~ $i(v3) |
% 31.94/5.10 | ~ $i(v2) | ~ doDivides0(v2, xb) | ~ aElement0(v3) | ~
% 31.94/5.10 | aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4) = xc & $i(v4) &
% 31.94/5.10 | aElement0(v4))) & ! [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2,
% 31.94/5.10 | xb) | ~ aDivisorOf0(v2, xa) | doDivides0(v2, xc)) & ! [v2: $i]
% 31.94/5.10 | : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ aDivisorOf0(v2, xa) | ?
% 31.94/5.10 | [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & !
% 31.94/5.10 | [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ doDivides0(v2,
% 31.94/5.10 | xa) | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ( ~
% 31.94/5.10 | $i(v2) | ~ aDivisorOf0(v2, xb) | ~ doDivides0(v2, xa) | ~
% 31.94/5.10 | aElement0(v2) | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) &
% 31.94/5.10 | aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2,
% 31.94/5.10 | xa) | ~ doDivides0(v2, xb) | doDivides0(v2, xc)) & ! [v2: $i] :
% 31.94/5.10 | ( ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~ doDivides0(v2, xb) | ? [v3:
% 31.94/5.10 | $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & ! [v2:
% 31.94/5.10 | $i] : ( ~ $i(v2) | ~ doDivides0(v2, xb) | ~ doDivides0(v2, xa) |
% 31.94/5.10 | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ( ~ $i(v2) |
% 31.94/5.10 | ~ doDivides0(v2, xb) | ~ doDivides0(v2, xa) | ~ aElement0(v2) |
% 31.94/5.10 | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))))
% 31.94/5.10 |
% 31.94/5.10 | ALPHA: (m__2174) implies:
% 31.94/5.10 | (6) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 31.94/5.10 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI) & aSet0(xI) &
% 31.94/5.10 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v2) = v4)
% 31.94/5.10 | | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ~ aElement0(v3)
% 31.94/5.10 | | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 31.94/5.10 | ( ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | aElementOf0(v2, xI))
% 31.94/5.10 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v2, v3) =
% 31.94/5.10 | v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xI) | ~
% 31.94/5.10 | aElementOf0(v2, xI) | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3:
% 31.94/5.10 | $i] : ( ~ (sdtasdt0(xb, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | aElement0(v3) | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] :
% 31.94/5.10 | ( ~ (sdtasdt0(xa, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.10 | aElement0(v3) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) |
% 31.94/5.10 | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 &
% 31.94/5.10 | $i(v3) & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 31.94/5.10 | aElementOf0(v2, v0) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & $i(v3)
% 31.94/5.10 | & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 31.94/5.10 | xI) | ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v3, v4) = v2 & $i(v4)
% 31.94/5.10 | & $i(v3) & aElementOf0(v4, v1) & aElementOf0(v3, v0))))
% 31.94/5.10 |
% 31.94/5.10 | ALPHA: (m__2203) implies:
% 31.94/5.11 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 31.94/5.11 | ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtasdt0(xb, v3)
% 31.94/5.11 | = sz00 & sdtasdt0(xb, v2) = xb & sdtasdt0(xa, v5) = sz00 &
% 31.94/5.11 | sdtasdt0(xa, v4) = xa & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 31.94/5.11 | $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, v0) &
% 31.94/5.11 | aElementOf0(sz00, v1) & aElementOf0(sz00, v0) & aElement0(v5) &
% 31.94/5.11 | aElement0(v4) & aElement0(v3) & aElement0(v2))
% 31.94/5.11 |
% 31.94/5.11 | ALPHA: (m__2228) implies:
% 31.94/5.11 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 31.94/5.11 | ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 31.94/5.11 | sdtpldt1(v0, v1) = v2 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 31.94/5.11 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v1) &
% 31.94/5.11 | aElementOf0(v4, v0) & aElementOf0(v3, v2) & ! [v6: $i] : ! [v7: $i]
% 31.94/5.11 | : ( ~ (sdtasdt0(xb, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~
% 31.94/5.11 | aElement0(v7) | aElementOf0(v6, v1)) & ! [v6: $i] : ! [v7: $i] :
% 31.94/5.11 | ( ~ (sdtasdt0(xa, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~
% 31.94/5.11 | aElement0(v7) | aElementOf0(v6, v0)) & ! [v6: $i] : ( ~ $i(v6) |
% 31.94/5.11 | ~ aElementOf0(v6, v1) | ? [v7: $i] : (sdtasdt0(xb, v7) = v6 &
% 31.94/5.11 | $i(v7) & aElement0(v7))) & ! [v6: $i] : ( ~ $i(v6) | ~
% 31.94/5.11 | aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 & $i(v7)
% 31.94/5.11 | & aElement0(v7))))
% 31.94/5.11 |
% 31.94/5.11 | ALPHA: (m__2273) implies:
% 31.94/5.11 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 31.94/5.11 | ~ (xu = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sbrdtbr0(xu)
% 31.94/5.11 | = v2 & sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 31.94/5.11 | $i(v0) & aElementOf0(v4, v1) & aElementOf0(v3, v0) & aElementOf0(xu,
% 31.94/5.11 | xI) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v5 =
% 31.94/5.11 | sz00 | ~ (sbrdtbr0(v5) = v6) | ~ (sdtpldt0(v7, v8) = v5) | ~
% 31.94/5.11 | $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ iLess0(v6, v2) | ~
% 31.94/5.11 | aElementOf0(v8, v1) | ~ aElementOf0(v7, v0)) & ! [v5: $i] : !
% 31.94/5.11 | [v6: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ~
% 31.94/5.11 | iLess0(v6, v2) | ~ aElementOf0(v5, xI)))
% 31.94/5.11 |
% 31.94/5.11 | ALPHA: (m__) implies:
% 31.94/5.11 | (10) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 31.94/5.11 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 31.94/5.11 | $i] : ( ~ (sdtasdt0(xb, v4) = v3) | ~ (sdtasdt0(xa, v5) = v2) |
% 31.94/5.11 | ~ (sdtpldt0(v2, v3) = xu) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~
% 31.94/5.11 | $i(v2) | ~ aElement0(v5) | ~ aElement0(v4)) & ! [v2: $i] : !
% 31.94/5.11 | [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(xb, v4) = v3) | ~
% 31.94/5.11 | (sdtpldt0(v2, v3) = xu) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.11 | aElementOf0(v2, v0) | ~ aElement0(v4)) & ! [v2: $i] : ! [v3:
% 31.94/5.11 | $i] : ! [v4: $i] : ( ~ (sdtasdt0(xa, v4) = v2) | ~ (sdtpldt0(v2,
% 31.94/5.11 | v3) = xu) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.11 | aElementOf0(v3, v1) | ~ aElement0(v4)) & ! [v2: $i] : ! [v3:
% 31.94/5.11 | $i] : ( ~ (sdtpldt0(v2, v3) = xu) | ~ $i(v3) | ~ $i(v2) | ~
% 31.94/5.11 | aElementOf0(v3, v1) | ~ aElementOf0(v2, v0)))
% 31.94/5.11 |
% 31.94/5.11 | ALPHA: (function-axioms) implies:
% 31.94/5.11 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2)
% 31.94/5.11 | = v1) | ~ (slsdtgt0(v2) = v0))
% 31.94/5.11 |
% 31.94/5.11 | DELTA: instantiating (7) with fresh symbols all_37_0, all_37_1, all_37_2,
% 31.94/5.11 | all_37_3, all_37_4, all_37_5 gives:
% 31.94/5.12 | (12) slsdtgt0(xb) = all_37_4 & slsdtgt0(xa) = all_37_5 & sdtasdt0(xb,
% 31.94/5.12 | all_37_2) = sz00 & sdtasdt0(xb, all_37_3) = xb & sdtasdt0(xa,
% 31.94/5.12 | all_37_0) = sz00 & sdtasdt0(xa, all_37_1) = xa & $i(all_37_0) &
% 31.94/5.12 | $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & $i(all_37_4) &
% 31.94/5.12 | $i(all_37_5) & aElementOf0(xb, all_37_4) & aElementOf0(xa, all_37_5) &
% 31.94/5.12 | aElementOf0(sz00, all_37_4) & aElementOf0(sz00, all_37_5) &
% 31.94/5.12 | aElement0(all_37_0) & aElement0(all_37_1) & aElement0(all_37_2) &
% 31.94/5.12 | aElement0(all_37_3)
% 31.94/5.12 |
% 31.94/5.12 | ALPHA: (12) implies:
% 31.94/5.12 | (13) aElement0(all_37_3)
% 31.94/5.12 | (14) aElement0(all_37_1)
% 31.94/5.12 | (15) $i(all_37_3)
% 31.94/5.12 | (16) $i(all_37_1)
% 31.94/5.12 | (17) sdtasdt0(xa, all_37_1) = xa
% 31.94/5.12 | (18) sdtasdt0(xb, all_37_3) = xb
% 31.94/5.12 | (19) slsdtgt0(xa) = all_37_5
% 31.94/5.12 | (20) slsdtgt0(xb) = all_37_4
% 31.94/5.12 |
% 31.94/5.12 | DELTA: instantiating (9) with fresh symbols all_39_0, all_39_1, all_39_2,
% 31.94/5.12 | all_39_3, all_39_4 gives:
% 31.94/5.12 | (21) ~ (xu = sz00) & slsdtgt0(xb) = all_39_3 & slsdtgt0(xa) = all_39_4 &
% 31.94/5.12 | sbrdtbr0(xu) = all_39_2 & sdtpldt0(all_39_1, all_39_0) = xu &
% 31.94/5.12 | $i(all_39_0) & $i(all_39_1) & $i(all_39_2) & $i(all_39_3) &
% 31.94/5.12 | $i(all_39_4) & aElementOf0(all_39_0, all_39_3) & aElementOf0(all_39_1,
% 31.94/5.12 | all_39_4) & aElementOf0(xu, xI) & ! [v0: $i] : ! [v1: $i] : !
% 31.94/5.12 | [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~
% 31.94/5.12 | (sdtpldt0(v2, v3) = v0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 31.94/5.12 | iLess0(v1, all_39_2) | ~ aElementOf0(v3, all_39_3) | ~
% 31.94/5.12 | aElementOf0(v2, all_39_4)) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00
% 31.94/5.12 | | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ iLess0(v1, all_39_2) | ~
% 31.94/5.12 | aElementOf0(v0, xI))
% 31.94/5.12 |
% 31.94/5.12 | ALPHA: (21) implies:
% 31.94/5.12 | (22) aElementOf0(all_39_1, all_39_4)
% 31.94/5.12 | (23) aElementOf0(all_39_0, all_39_3)
% 31.94/5.12 | (24) $i(all_39_4)
% 31.94/5.12 | (25) $i(all_39_3)
% 31.94/5.12 | (26) $i(all_39_1)
% 31.94/5.12 | (27) $i(all_39_0)
% 31.94/5.12 | (28) sdtpldt0(all_39_1, all_39_0) = xu
% 31.94/5.12 | (29) slsdtgt0(xa) = all_39_4
% 31.94/5.12 | (30) slsdtgt0(xb) = all_39_3
% 31.94/5.12 |
% 31.94/5.12 | DELTA: instantiating (10) with fresh symbols all_42_0, all_42_1 gives:
% 31.94/5.12 | (31) slsdtgt0(xb) = all_42_0 & slsdtgt0(xa) = all_42_1 & $i(all_42_0) &
% 31.94/5.12 | $i(all_42_1) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 31.94/5.12 | ( ~ (sdtasdt0(xb, v2) = v1) | ~ (sdtasdt0(xa, v3) = v0) | ~
% 31.94/5.12 | (sdtpldt0(v0, v1) = xu) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 31.94/5.12 | $i(v0) | ~ aElement0(v3) | ~ aElement0(v2)) & ! [v0: $i] : !
% 31.94/5.12 | [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(xb, v2) = v1) | ~
% 31.94/5.12 | (sdtpldt0(v0, v1) = xu) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 31.94/5.12 | aElementOf0(v0, all_42_1) | ~ aElement0(v2)) & ! [v0: $i] : !
% 31.94/5.12 | [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(xa, v2) = v0) | ~
% 31.94/5.12 | (sdtpldt0(v0, v1) = xu) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 31.94/5.12 | aElementOf0(v1, all_42_0) | ~ aElement0(v2)) & ! [v0: $i] : !
% 31.94/5.12 | [v1: $i] : ( ~ (sdtpldt0(v0, v1) = xu) | ~ $i(v1) | ~ $i(v0) | ~
% 31.94/5.12 | aElementOf0(v1, all_42_0) | ~ aElementOf0(v0, all_42_1))
% 31.94/5.12 |
% 31.94/5.12 | ALPHA: (31) implies:
% 31.94/5.12 | (32) slsdtgt0(xa) = all_42_1
% 31.94/5.12 | (33) slsdtgt0(xb) = all_42_0
% 31.94/5.12 | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 31.94/5.12 | (sdtasdt0(xb, v2) = v1) | ~ (sdtasdt0(xa, v3) = v0) | ~
% 31.94/5.12 | (sdtpldt0(v0, v1) = xu) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 31.94/5.12 | $i(v0) | ~ aElement0(v3) | ~ aElement0(v2))
% 31.94/5.12 |
% 31.94/5.12 | DELTA: instantiating (8) with fresh symbols all_45_0, all_45_1, all_45_2,
% 31.94/5.12 | all_45_3, all_45_4, all_45_5 gives:
% 32.46/5.13 | (35) ~ (all_45_2 = sz00) & slsdtgt0(xb) = all_45_4 & slsdtgt0(xa) =
% 32.46/5.13 | all_45_5 & sdtpldt1(all_45_5, all_45_4) = all_45_3 &
% 32.46/5.13 | sdtpldt0(all_45_1, all_45_0) = all_45_2 & $i(all_45_0) & $i(all_45_1)
% 32.46/5.13 | & $i(all_45_2) & $i(all_45_3) & $i(all_45_4) & $i(all_45_5) &
% 32.46/5.13 | aElementOf0(all_45_0, all_45_4) & aElementOf0(all_45_1, all_45_5) &
% 32.46/5.13 | aElementOf0(all_45_2, all_45_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 32.46/5.13 | (sdtasdt0(xb, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 32.46/5.13 | aElementOf0(v0, all_45_4)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 32.46/5.13 | (sdtasdt0(xa, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 32.46/5.13 | aElementOf0(v0, all_45_5)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.13 | aElementOf0(v0, all_45_4) | ? [v1: $i] : (sdtasdt0(xb, v1) = v0 &
% 32.46/5.13 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.13 | aElementOf0(v0, all_45_5) | ? [v1: $i] : (sdtasdt0(xa, v1) = v0 &
% 32.46/5.13 | $i(v1) & aElement0(v1)))
% 32.46/5.13 |
% 32.46/5.13 | ALPHA: (35) implies:
% 32.46/5.13 | (36) slsdtgt0(xa) = all_45_5
% 32.46/5.13 | (37) slsdtgt0(xb) = all_45_4
% 32.46/5.13 |
% 32.46/5.13 | DELTA: instantiating (6) with fresh symbols all_48_0, all_48_1 gives:
% 32.46/5.13 | (38) slsdtgt0(xb) = all_48_0 & slsdtgt0(xa) = all_48_1 & sdtpldt1(all_48_1,
% 32.46/5.13 | all_48_0) = xI & $i(all_48_0) & $i(all_48_1) & aIdeal0(xI) &
% 32.46/5.13 | aSet0(xI) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 32.46/5.13 | (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 32.46/5.13 | xI) | ~ aElement0(v1) | aElementOf0(v2, xI)) & ! [v0: $i] : !
% 32.46/5.13 | [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v2) = v0) | ~ $i(v2) | ~
% 32.46/5.13 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, all_48_0) | ~
% 32.46/5.13 | aElementOf0(v1, all_48_1) | aElementOf0(v0, xI)) & ! [v0: $i] : !
% 32.46/5.13 | [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~
% 32.46/5.13 | $i(v0) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) |
% 32.46/5.13 | aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(xb,
% 32.46/5.13 | v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 32.46/5.13 | aElementOf0(v0, all_48_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 32.46/5.13 | (sdtasdt0(xa, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 32.46/5.13 | aElementOf0(v0, all_48_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.13 | aElementOf0(v0, all_48_0) | ? [v1: $i] : (sdtasdt0(xb, v1) = v0 &
% 32.46/5.13 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.13 | aElementOf0(v0, all_48_1) | ? [v1: $i] : (sdtasdt0(xa, v1) = v0 &
% 32.46/5.13 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.13 | aElementOf0(v0, xI) | ? [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v2)
% 32.46/5.13 | = v0 & $i(v2) & $i(v1) & aElementOf0(v2, all_48_0) &
% 32.46/5.13 | aElementOf0(v1, all_48_1)))
% 32.46/5.13 |
% 32.46/5.13 | ALPHA: (38) implies:
% 32.46/5.13 | (39) slsdtgt0(xa) = all_48_1
% 32.46/5.13 | (40) slsdtgt0(xb) = all_48_0
% 32.46/5.13 |
% 32.46/5.13 | DELTA: instantiating (5) with fresh symbols all_51_0, all_51_1 gives:
% 32.46/5.13 | (41) sdtasdt0(xc, all_51_0) = xa & sdtasdt0(xc, all_51_1) = xb &
% 32.46/5.13 | $i(all_51_0) & $i(all_51_1) & aGcdOfAnd0(xc, xa, xb) & aDivisorOf0(xc,
% 32.46/5.13 | xb) & aDivisorOf0(xc, xa) & doDivides0(xc, xb) & doDivides0(xc, xa)
% 32.46/5.13 | & aElement0(all_51_0) & aElement0(all_51_1) & aElement0(xc) & ! [v0:
% 32.46/5.13 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = xa) | ~
% 32.46/5.13 | (sdtasdt0(v0, v1) = xb) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 32.46/5.13 | aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | doDivides0(v0,
% 32.46/5.13 | xc)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0,
% 32.46/5.13 | v2) = xa) | ~ (sdtasdt0(v0, v1) = xb) | ~ $i(v2) | ~ $i(v1) |
% 32.46/5.13 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) |
% 32.46/5.13 | ? [v3: $i] : (sdtasdt0(v0, v3) = xc & $i(v3) & aElement0(v3))) & !
% 32.46/5.13 | [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xb) | ~ $i(v1) | ~
% 32.46/5.13 | $i(v0) | ~ aDivisorOf0(v0, xa) | ~ aElement0(v1) | doDivides0(v0,
% 32.46/5.13 | xc)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xb) |
% 32.46/5.13 | ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v0, xa) | ~ aElement0(v1) |
% 32.46/5.13 | ? [v2: $i] : (sdtasdt0(v0, v2) = xc & $i(v2) & aElement0(v2))) & !
% 32.46/5.14 | [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xb) | ~ $i(v1) | ~
% 32.46/5.14 | $i(v0) | ~ doDivides0(v0, xa) | ~ aElement0(v1) | ~ aElement0(v0)
% 32.46/5.14 | | doDivides0(v0, xc)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 32.46/5.14 | (sdtasdt0(v0, v1) = xb) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 32.46/5.14 | xa) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] :
% 32.46/5.14 | (sdtasdt0(v0, v2) = xc & $i(v2) & aElement0(v2))) & ! [v0: $i] : !
% 32.46/5.14 | [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xa) | ~ $i(v1) | ~ $i(v0) | ~
% 32.46/5.14 | aDivisorOf0(v0, xb) | ~ aElement0(v1) | ~ aElement0(v0) |
% 32.46/5.14 | doDivides0(v0, xc)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0,
% 32.46/5.14 | v1) = xa) | ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v0, xb) | ~
% 32.46/5.14 | aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] : (sdtasdt0(v0, v2) =
% 32.46/5.14 | xc & $i(v2) & aElement0(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 32.46/5.14 | (sdtasdt0(v0, v1) = xa) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 32.46/5.14 | xb) | ~ aElement0(v1) | ~ aElement0(v0) | doDivides0(v0, xc)) &
% 32.46/5.14 | ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xa) | ~ $i(v1) |
% 32.46/5.14 | ~ $i(v0) | ~ doDivides0(v0, xb) | ~ aElement0(v1) | ~
% 32.46/5.14 | aElement0(v0) | ? [v2: $i] : (sdtasdt0(v0, v2) = xc & $i(v2) &
% 32.46/5.14 | aElement0(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ aDivisorOf0(v0,
% 32.46/5.14 | xb) | ~ aDivisorOf0(v0, xa) | doDivides0(v0, xc)) & ! [v0: $i] :
% 32.46/5.14 | ( ~ $i(v0) | ~ aDivisorOf0(v0, xb) | ~ aDivisorOf0(v0, xa) | ? [v1:
% 32.46/5.14 | $i] : (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1))) & ! [v0:
% 32.46/5.14 | $i] : ( ~ $i(v0) | ~ aDivisorOf0(v0, xb) | ~ doDivides0(v0, xa) |
% 32.46/5.14 | ~ aElement0(v0) | doDivides0(v0, xc)) & ! [v0: $i] : ( ~ $i(v0) |
% 32.46/5.14 | ~ aDivisorOf0(v0, xb) | ~ doDivides0(v0, xa) | ~ aElement0(v0) |
% 32.46/5.14 | ? [v1: $i] : (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1))) & !
% 32.46/5.14 | [v0: $i] : ( ~ $i(v0) | ~ aDivisorOf0(v0, xa) | ~ doDivides0(v0, xb)
% 32.46/5.14 | | doDivides0(v0, xc)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.14 | aDivisorOf0(v0, xa) | ~ doDivides0(v0, xb) | ? [v1: $i] :
% 32.46/5.14 | (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1))) & ! [v0: $i] : (
% 32.46/5.14 | ~ $i(v0) | ~ doDivides0(v0, xb) | ~ doDivides0(v0, xa) | ~
% 32.46/5.14 | aElement0(v0) | doDivides0(v0, xc)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 32.46/5.14 | doDivides0(v0, xb) | ~ doDivides0(v0, xa) | ~ aElement0(v0) | ?
% 32.46/5.14 | [v1: $i] : (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1)))
% 32.46/5.14 |
% 32.46/5.14 | ALPHA: (41) implies:
% 32.46/5.14 | (42) aElement0(xc)
% 32.46/5.14 | (43) aElement0(all_51_1)
% 32.46/5.14 | (44) aElement0(all_51_0)
% 32.46/5.14 | (45) $i(all_51_1)
% 32.46/5.14 | (46) $i(all_51_0)
% 32.46/5.14 | (47) sdtasdt0(xc, all_51_1) = xb
% 32.46/5.14 | (48) sdtasdt0(xc, all_51_0) = xa
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_39_4, all_45_5, xa, simplifying with
% 32.46/5.14 | (29), (36) gives:
% 32.46/5.14 | (49) all_45_5 = all_39_4
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_37_5, all_45_5, xa, simplifying with
% 32.46/5.14 | (19), (36) gives:
% 32.46/5.14 | (50) all_45_5 = all_37_5
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_45_5, all_48_1, xa, simplifying with
% 32.46/5.14 | (36), (39) gives:
% 32.46/5.14 | (51) all_48_1 = all_45_5
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_42_1, all_48_1, xa, simplifying with
% 32.46/5.14 | (32), (39) gives:
% 32.46/5.14 | (52) all_48_1 = all_42_1
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_42_0, all_45_4, xb, simplifying with
% 32.46/5.14 | (33), (37) gives:
% 32.46/5.14 | (53) all_45_4 = all_42_0
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_39_3, all_45_4, xb, simplifying with
% 32.46/5.14 | (30), (37) gives:
% 32.46/5.14 | (54) all_45_4 = all_39_3
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_45_4, all_48_0, xb, simplifying with
% 32.46/5.14 | (37), (40) gives:
% 32.46/5.14 | (55) all_48_0 = all_45_4
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (11) with all_37_4, all_48_0, xb, simplifying with
% 32.46/5.14 | (20), (40) gives:
% 32.46/5.14 | (56) all_48_0 = all_37_4
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (55), (56) imply:
% 32.46/5.14 | (57) all_45_4 = all_37_4
% 32.46/5.14 |
% 32.46/5.14 | SIMP: (57) implies:
% 32.46/5.14 | (58) all_45_4 = all_37_4
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (51), (52) imply:
% 32.46/5.14 | (59) all_45_5 = all_42_1
% 32.46/5.14 |
% 32.46/5.14 | SIMP: (59) implies:
% 32.46/5.14 | (60) all_45_5 = all_42_1
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (53), (54) imply:
% 32.46/5.14 | (61) all_42_0 = all_39_3
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (53), (58) imply:
% 32.46/5.14 | (62) all_42_0 = all_37_4
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (50), (60) imply:
% 32.46/5.14 | (63) all_42_1 = all_37_5
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (49), (60) imply:
% 32.46/5.14 | (64) all_42_1 = all_39_4
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (61), (62) imply:
% 32.46/5.14 | (65) all_39_3 = all_37_4
% 32.46/5.14 |
% 32.46/5.14 | COMBINE_EQS: (63), (64) imply:
% 32.46/5.14 | (66) all_39_4 = all_37_5
% 32.46/5.14 |
% 32.46/5.14 | SIMP: (66) implies:
% 32.46/5.14 | (67) all_39_4 = all_37_5
% 32.46/5.14 |
% 32.46/5.14 | REDUCE: (25), (65) imply:
% 32.46/5.14 | (68) $i(all_37_4)
% 32.46/5.14 |
% 32.46/5.14 | REDUCE: (24), (67) imply:
% 32.46/5.14 | (69) $i(all_37_5)
% 32.46/5.14 |
% 32.46/5.14 | REDUCE: (23), (65) imply:
% 32.46/5.14 | (70) aElementOf0(all_39_0, all_37_4)
% 32.46/5.14 |
% 32.46/5.14 | REDUCE: (22), (67) imply:
% 32.46/5.14 | (71) aElementOf0(all_39_1, all_37_5)
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (mMulAsso) with xc, all_51_1, all_37_3, xb, xb,
% 32.46/5.14 | simplifying with (4), (13), (15), (18), (42), (43), (45), (47)
% 32.46/5.14 | gives:
% 32.46/5.14 | (72) ? [v0: $i] : (sdtasdt0(all_51_1, all_37_3) = v0 & sdtasdt0(xc, v0) =
% 32.46/5.14 | xb & $i(v0) & $i(xb))
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (mMulComm) with xc, all_51_1, xb, simplifying with
% 32.46/5.14 | (4), (42), (43), (45), (47) gives:
% 32.46/5.14 | (73) sdtasdt0(all_51_1, xc) = xb & $i(xb)
% 32.46/5.14 |
% 32.46/5.14 | ALPHA: (73) implies:
% 32.46/5.14 | (74) $i(xb)
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (mMulAsso) with xc, all_51_0, all_37_1, xa, xa,
% 32.46/5.14 | simplifying with (4), (14), (16), (17), (42), (44), (46), (48)
% 32.46/5.14 | gives:
% 32.46/5.14 | (75) ? [v0: $i] : (sdtasdt0(all_51_0, all_37_1) = v0 & sdtasdt0(xc, v0) =
% 32.46/5.14 | xa & $i(v0) & $i(xa))
% 32.46/5.14 |
% 32.46/5.14 | GROUND_INST: instantiating (mMulComm) with xc, all_51_0, xa, simplifying with
% 32.46/5.14 | (4), (42), (44), (46), (48) gives:
% 32.46/5.14 | (76) sdtasdt0(all_51_0, xc) = xa & $i(xa)
% 32.46/5.14 |
% 32.46/5.14 | ALPHA: (76) implies:
% 32.46/5.14 | (77) $i(xa)
% 32.46/5.14 |
% 32.46/5.15 | GROUND_INST: instantiating (1) with xa, all_37_5, all_39_1, simplifying with
% 32.46/5.15 | (2), (19), (26), (69), (71), (77) gives:
% 32.46/5.15 | (78) ? [v0: $i] : (sdtasdt0(xa, v0) = all_39_1 & $i(v0) & aElement0(v0))
% 32.46/5.15 |
% 32.46/5.15 | GROUND_INST: instantiating (1) with xb, all_37_4, all_39_0, simplifying with
% 32.46/5.15 | (3), (20), (27), (68), (70), (74) gives:
% 32.46/5.15 | (79) ? [v0: $i] : (sdtasdt0(xb, v0) = all_39_0 & $i(v0) & aElement0(v0))
% 32.46/5.15 |
% 32.46/5.15 | DELTA: instantiating (79) with fresh symbol all_72_0 gives:
% 32.46/5.15 | (80) sdtasdt0(xb, all_72_0) = all_39_0 & $i(all_72_0) & aElement0(all_72_0)
% 32.46/5.15 |
% 32.46/5.15 | ALPHA: (80) implies:
% 32.46/5.15 | (81) aElement0(all_72_0)
% 32.46/5.15 | (82) $i(all_72_0)
% 32.46/5.15 | (83) sdtasdt0(xb, all_72_0) = all_39_0
% 32.46/5.15 |
% 32.46/5.15 | DELTA: instantiating (78) with fresh symbol all_84_0 gives:
% 32.46/5.15 | (84) sdtasdt0(xa, all_84_0) = all_39_1 & $i(all_84_0) & aElement0(all_84_0)
% 32.46/5.15 |
% 32.46/5.15 | ALPHA: (84) implies:
% 32.46/5.15 | (85) aElement0(all_84_0)
% 32.46/5.15 | (86) $i(all_84_0)
% 32.46/5.15 | (87) sdtasdt0(xa, all_84_0) = all_39_1
% 32.46/5.15 |
% 32.46/5.15 | DELTA: instantiating (75) with fresh symbol all_96_0 gives:
% 32.46/5.15 | (88) sdtasdt0(all_51_0, all_37_1) = all_96_0 & sdtasdt0(xc, all_96_0) = xa
% 32.46/5.15 | & $i(all_96_0) & $i(xa)
% 32.46/5.15 |
% 32.46/5.15 | DELTA: instantiating (72) with fresh symbol all_102_0 gives:
% 32.46/5.15 | (89) sdtasdt0(all_51_1, all_37_3) = all_102_0 & sdtasdt0(xc, all_102_0) =
% 32.46/5.15 | xb & $i(all_102_0) & $i(xb)
% 32.46/5.15 |
% 32.46/5.15 | GROUND_INST: instantiating (mMulComm) with xa, all_84_0, all_39_1, simplifying
% 32.46/5.15 | with (2), (77), (85), (86), (87) gives:
% 32.46/5.15 | (90) sdtasdt0(all_84_0, xa) = all_39_1 & $i(all_39_1)
% 32.46/5.15 |
% 32.46/5.15 | GROUND_INST: instantiating (mMulComm) with xb, all_72_0, all_39_0, simplifying
% 32.46/5.15 | with (3), (74), (81), (82), (83) gives:
% 32.46/5.15 | (91) sdtasdt0(all_72_0, xb) = all_39_0 & $i(all_39_0)
% 32.46/5.15 |
% 32.46/5.15 | GROUND_INST: instantiating (34) with all_39_1, all_39_0, all_72_0, all_84_0,
% 32.46/5.15 | simplifying with (26), (27), (28), (81), (82), (83), (85), (86),
% 32.46/5.15 | (87) gives:
% 32.46/5.15 | (92) $false
% 32.46/5.15 |
% 32.46/5.15 | CLOSE: (92) is inconsistent.
% 32.46/5.15 |
% 32.46/5.15 End of proof
% 32.46/5.15 % SZS output end Proof for theBenchmark
% 32.46/5.15
% 32.46/5.15 4529ms
%------------------------------------------------------------------------------