TSTP Solution File: RNG114+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : RNG114+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 : n006.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 51.78s 7.60s
% Output : Proof 62.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG114+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 02:22:37 EDT 2023
% 0.12/0.34 % 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
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 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 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 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 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.65/1.24 Prover 1: Preprocessing ...
% 4.04/1.27 Prover 4: Preprocessing ...
% 4.04/1.29 Prover 3: Preprocessing ...
% 4.04/1.29 Prover 0: Preprocessing ...
% 4.04/1.29 Prover 2: Preprocessing ...
% 4.04/1.29 Prover 6: Preprocessing ...
% 4.04/1.31 Prover 5: Preprocessing ...
% 10.12/2.19 Prover 1: Constructing countermodel ...
% 10.12/2.19 Prover 3: Constructing countermodel ...
% 10.12/2.22 Prover 6: Proving ...
% 10.12/2.23 Prover 5: Proving ...
% 11.03/2.31 Prover 2: Proving ...
% 13.07/2.53 Prover 4: Constructing countermodel ...
% 13.83/2.67 Prover 0: Proving ...
% 51.78/7.59 Prover 3: proved (6969ms)
% 51.78/7.59
% 51.78/7.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.78/7.60
% 51.78/7.60 Prover 6: stopped
% 51.78/7.60 Prover 5: stopped
% 51.78/7.62 Prover 2: stopped
% 51.78/7.63 Prover 0: stopped
% 51.78/7.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 51.78/7.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 51.78/7.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 51.78/7.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 51.78/7.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 52.64/7.72 Prover 7: Preprocessing ...
% 52.64/7.73 Prover 10: Preprocessing ...
% 52.93/7.80 Prover 13: Preprocessing ...
% 52.93/7.80 Prover 11: Preprocessing ...
% 52.93/7.82 Prover 8: Preprocessing ...
% 54.56/7.95 Prover 7: Constructing countermodel ...
% 54.64/7.98 Prover 10: Constructing countermodel ...
% 54.94/8.09 Prover 8: Warning: ignoring some quantifiers
% 54.94/8.09 Prover 8: Constructing countermodel ...
% 54.94/8.16 Prover 13: Warning: ignoring some quantifiers
% 54.94/8.19 Prover 13: Constructing countermodel ...
% 57.01/8.30 Prover 11: Constructing countermodel ...
% 60.38/8.89 Prover 10: Found proof (size 51)
% 60.38/8.89 Prover 10: proved (1261ms)
% 60.38/8.89 Prover 11: stopped
% 60.38/8.89 Prover 13: stopped
% 60.38/8.89 Prover 7: stopped
% 60.38/8.89 Prover 1: stopped
% 61.41/8.89 Prover 4: stopped
% 61.41/8.90 Prover 8: stopped
% 61.41/8.90
% 61.41/8.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.41/8.90
% 61.41/8.90 % SZS output start Proof for theBenchmark
% 61.41/8.90 Assumptions after simplification:
% 61.41/8.90 ---------------------------------
% 61.41/8.90
% 61.41/8.91 (mDefPrIdeal)
% 61.41/8.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (slsdtgt0(v0) =
% 61.41/8.93 v1) | ~ (sdtasdt0(v0, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 61.41/8.93 $i(v0) | ~ aElement0(v3) | ~ aElement0(v0) | aElementOf0(v2, v1)) & !
% 61.41/8.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slsdtgt0(v0) = v1) | ~
% 61.41/8.93 $i(v2) | ~ $i(v0) | ~ aSet0(v2) | ~ aElement0(v0) | ? [v3: $i] : ? [v4:
% 61.41/8.94 $i] : ? [v5: $i] : ($i(v4) & $i(v3) & ( ~ aElementOf0(v3, v2) | ! [v6:
% 61.41/8.94 $i] : ( ~ (sdtasdt0(v0, v6) = v3) | ~ $i(v6) | ~ aElement0(v6))) &
% 61.41/8.94 (aElementOf0(v3, v2) | (v5 = v3 & sdtasdt0(v0, v4) = v3 &
% 61.41/8.94 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 61.41/8.94 (slsdtgt0(v0) = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2,
% 61.41/8.94 v1) | ~ aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 61.41/8.94 aElement0(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 61.41/8.94 $i(v1) | ~ $i(v0) | ~ aElement0(v0) | aSet0(v1))
% 61.41/8.94
% 61.41/8.94 (mMulComm)
% 61.41/8.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 61.41/8.94 $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aElement0(v0) | (sdtasdt0(v1, v0)
% 61.41/8.94 = v2 & $i(v2)))
% 61.41/8.94
% 61.41/8.94 (m__)
% 61.41/8.94 $i(xu) & $i(xb) & $i(xa) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 61.41/8.94 $i] : ( ~ (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~
% 61.41/8.94 (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~
% 61.41/8.94 aElement0(v0))
% 61.41/8.94
% 61.41/8.94 (m__2091)
% 61.41/8.94 $i(xb) & $i(xa) & aElement0(xb) & aElement0(xa)
% 61.41/8.94
% 61.41/8.94 (m__2129)
% 61.41/8.95 $i(xc) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = xa
% 61.41/8.95 & sdtasdt0(xc, v0) = xb & $i(v1) & $i(v0) & aGcdOfAnd0(xc, xa, xb) &
% 61.41/8.95 aDivisorOf0(xc, xb) & aDivisorOf0(xc, xa) & doDivides0(xc, xb) &
% 61.41/8.95 doDivides0(xc, xa) & aElement0(v1) & aElement0(v0) & aElement0(xc) & ! [v2:
% 61.41/8.95 $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v2, v4) = xa) | ~
% 61.41/8.95 (sdtasdt0(v2, v3) = xb) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2, xc))
% 61.41/8.95 & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v2, v4) = xa) | ~
% 61.41/8.95 (sdtasdt0(v2, v3) = xb) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v5: $i] :
% 61.41/8.95 (sdtasdt0(v2, v5) = xc & $i(v5) & aElement0(v5))) & ! [v2: $i] : ! [v3:
% 61.41/8.95 $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 aDivisorOf0(v2, xa) | ~ aElement0(v3) | doDivides0(v2, xc)) & ! [v2: $i]
% 61.41/8.95 : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 aDivisorOf0(v2, xa) | ~ aElement0(v3) | ? [v4: $i] : (sdtasdt0(v2, v4) =
% 61.41/8.95 xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 61.41/8.95 (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xa) |
% 61.41/8.95 ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] :
% 61.41/8.95 ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 doDivides0(v2, xa) | ~ aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] :
% 61.41/8.95 (sdtasdt0(v2, v4) = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3:
% 61.41/8.95 $i] : ( ~ (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 aDivisorOf0(v2, xb) | ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2,
% 61.41/8.95 xc)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xa) | ~
% 61.41/8.95 $i(v3) | ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ aElement0(v3) | ~
% 61.41/8.95 aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4) = xc & $i(v4) &
% 61.41/8.95 aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) =
% 61.41/8.95 xa) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xb) | ~ aElement0(v3) |
% 61.41/8.95 ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ( ~
% 61.41/8.95 (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xb) |
% 61.41/8.95 ~ aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4) = xc
% 61.41/8.95 & $i(v4) & aElement0(v4))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 61.41/8.95 aDivisorOf0(v2, xb) | ~ aDivisorOf0(v2, xa) | doDivides0(v2, xc)) & !
% 61.41/8.95 [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ aDivisorOf0(v2, xa) | ?
% 61.41/8.95 [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & ! [v2: $i]
% 61.41/8.95 : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ doDivides0(v2, xa) | ~
% 61.41/8.95 aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 61.41/8.95 aDivisorOf0(v2, xb) | ~ doDivides0(v2, xa) | ~ aElement0(v2) | ? [v3:
% 61.41/8.95 $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & ! [v2: $i] :
% 61.41/8.95 ( ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~ doDivides0(v2, xb) | doDivides0(v2,
% 61.41/8.95 xc)) & ! [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~
% 61.41/8.95 doDivides0(v2, xb) | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) &
% 61.41/8.95 aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ doDivides0(v2, xb) | ~
% 61.41/8.95 doDivides0(v2, xa) | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i]
% 61.41/8.95 : ( ~ $i(v2) | ~ doDivides0(v2, xb) | ~ doDivides0(v2, xa) | ~
% 61.41/8.95 aElement0(v2) | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) &
% 61.41/8.95 aElement0(v3))))
% 61.41/8.95
% 61.41/8.95 (m__2174)
% 61.41/8.95 $i(xI) & $i(xb) & $i(xa) & ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 &
% 61.41/8.95 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI) &
% 61.41/8.95 aSet0(xI) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v2)
% 61.41/8.95 = v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ~
% 61.41/8.95 aElement0(v3) | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 61.41/8.95 $i] : ( ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.95 aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | aElementOf0(v2, xI)) & !
% 61.41/8.95 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v2, v3) = v4) | ~
% 61.41/8.95 $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xI) | ~ aElementOf0(v2, xI) |
% 61.41/8.95 aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(xb, v3) =
% 61.41/8.95 v2) | ~ $i(v3) | ~ $i(v2) | ~ aElement0(v3) | aElementOf0(v2, v1)) &
% 61.41/8.95 ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(xa, v3) = v2) | ~ $i(v3) | ~
% 61.41/8.95 $i(v2) | ~ aElement0(v3) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~
% 61.41/8.95 $i(v2) | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 &
% 61.41/8.95 $i(v3) & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 61.41/8.95 v0) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & $i(v3) & aElement0(v3))) &
% 61.41/8.95 ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2, xI) | ? [v3: $i] : ? [v4: $i]
% 61.41/8.95 : (sdtpldt0(v3, v4) = v2 & $i(v4) & $i(v3) & aElementOf0(v4, v1) &
% 61.41/8.95 aElementOf0(v3, v0))))
% 61.41/8.95
% 61.41/8.95 (m__2203)
% 61.41/8.95 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 61.41/8.95 $i] : ? [v4: $i] : ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 61.41/8.95 sdtasdt0(xb, v3) = sz00 & sdtasdt0(xb, v2) = xb & sdtasdt0(xa, v5) = sz00 &
% 61.41/8.95 sdtasdt0(xa, v4) = xa & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 61.41/8.95 & aElementOf0(xb, v1) & aElementOf0(xa, v0) & aElementOf0(sz00, v1) &
% 61.41/8.95 aElementOf0(sz00, v0) & aElement0(v5) & aElement0(v4) & aElement0(v3) &
% 61.41/8.95 aElement0(v2))
% 61.41/8.95
% 61.41/8.95 (m__2228)
% 61.41/8.96 $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 61.41/8.96 $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 &
% 61.41/8.96 slsdtgt0(xa) = v0 & sdtpldt1(v0, v1) = v2 & sdtpldt0(v4, v5) = v3 & $i(v5) &
% 61.41/8.96 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v1) &
% 61.41/8.96 aElementOf0(v4, v0) & aElementOf0(v3, v2) & ! [v6: $i] : ! [v7: $i] : ( ~
% 61.41/8.96 (sdtasdt0(xb, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) |
% 61.41/8.96 aElementOf0(v6, v1)) & ! [v6: $i] : ! [v7: $i] : ( ~ (sdtasdt0(xa, v7) =
% 61.41/8.96 v6) | ~ $i(v7) | ~ $i(v6) | ~ aElement0(v7) | aElementOf0(v6, v0)) &
% 61.41/8.96 ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v1) | ? [v7: $i] :
% 61.41/8.96 (sdtasdt0(xb, v7) = v6 & $i(v7) & aElement0(v7))) & ! [v6: $i] : ( ~
% 61.41/8.96 $i(v6) | ~ aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 &
% 61.41/8.96 $i(v7) & aElement0(v7))))
% 61.41/8.96
% 61.41/8.96 (m__2273)
% 61.41/8.96 $i(xu) & $i(xI) & $i(xb) & $i(xa) & $i(sz00) & ? [v0: $i] : ? [v1: $i] : ?
% 61.41/8.96 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (xu = sz00) & slsdtgt0(xb) = v1 &
% 61.41/8.96 slsdtgt0(xa) = v0 & sbrdtbr0(xu) = v2 & sdtpldt0(v3, v4) = xu & $i(v4) &
% 61.41/8.96 $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v4, v1) & aElementOf0(v3,
% 61.41/8.96 v0) & aElementOf0(xu, xI) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : !
% 61.41/8.96 [v8: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ (sdtpldt0(v7, v8) = v5)
% 61.41/8.96 | ~ $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ iLess0(v6, v2) | ~
% 61.41/8.96 aElementOf0(v8, v1) | ~ aElementOf0(v7, v0)) & ! [v5: $i] : ! [v6: $i]
% 61.41/8.96 : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ~ iLess0(v6, v2) | ~
% 61.41/8.96 aElementOf0(v5, xI)))
% 61.41/8.96
% 61.41/8.96 (function-axioms)
% 61.41/8.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 61.41/8.96 (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 61.41/8.96 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) |
% 61.41/8.96 ~ (sdtpldt1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 61.41/8.96 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 61.41/8.96 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 61.41/8.96 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 61.41/8.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2) = v1) | ~ (slsdtgt0(v2)
% 61.41/8.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 61.41/8.96 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 61.41/8.96 ! [v2: $i] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 61.41/8.96
% 61.41/8.96 Further assumptions not needed in the proof:
% 61.41/8.96 --------------------------------------------
% 61.41/8.96 mAMDistr, mAddAsso, mAddComm, mAddInvr, mAddZero, mCancel, mChineseRemainder,
% 61.41/8.96 mDefDiv, mDefDvs, mDefGCD, mDefIdeal, mDefMod, mDefRel, mDefSInt, mDefSSum,
% 61.41/8.96 mDivision, mEOfElem, mElmSort, mEucSort, mIdeInt, mIdeSum, mMulAsso, mMulMnOne,
% 61.41/8.96 mMulUnit, mMulZero, mNatLess, mNatSort, mPrIdeal, mSetEq, mSetSort, mSortsB,
% 61.41/8.96 mSortsB_02, mSortsC, mSortsC_01, mSortsU, mUnNeZr, m__2110, m__2383
% 61.41/8.96
% 61.41/8.96 Those formulas are unsatisfiable:
% 61.41/8.96 ---------------------------------
% 61.41/8.96
% 61.41/8.96 Begin of proof
% 61.41/8.96 |
% 61.41/8.96 | ALPHA: (mDefPrIdeal) implies:
% 61.41/8.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slsdtgt0(v0) = v1) | ~
% 61.41/8.96 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 61.41/8.96 | aElement0(v0) | ? [v3: $i] : (sdtasdt0(v0, v3) = v2 & $i(v3) &
% 61.41/8.96 | aElement0(v3)))
% 61.41/8.96 |
% 61.41/8.96 | ALPHA: (m__2091) implies:
% 61.41/8.96 | (2) aElement0(xa)
% 61.41/8.96 | (3) aElement0(xb)
% 61.41/8.96 |
% 61.41/8.96 | ALPHA: (m__2129) implies:
% 61.41/8.97 | (4) $i(xc)
% 61.41/8.97 | (5) ? [v0: $i] : ? [v1: $i] : (sdtasdt0(xc, v1) = xa & sdtasdt0(xc, v0) =
% 61.41/8.97 | xb & $i(v1) & $i(v0) & aGcdOfAnd0(xc, xa, xb) & aDivisorOf0(xc, xb) &
% 61.41/8.97 | aDivisorOf0(xc, xa) & doDivides0(xc, xb) & doDivides0(xc, xa) &
% 61.41/8.97 | aElement0(v1) & aElement0(v0) & aElement0(xc) & ! [v2: $i] : ! [v3:
% 61.41/8.97 | $i] : ! [v4: $i] : ( ~ (sdtasdt0(v2, v4) = xa) | ~ (sdtasdt0(v2,
% 61.41/8.97 | v3) = xb) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.97 | aElement0(v4) | ~ aElement0(v3) | ~ aElement0(v2) |
% 61.41/8.97 | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 61.41/8.97 | (sdtasdt0(v2, v4) = xa) | ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v4) |
% 61.41/8.97 | ~ $i(v3) | ~ $i(v2) | ~ aElement0(v4) | ~ aElement0(v3) | ~
% 61.41/8.97 | aElement0(v2) | ? [v5: $i] : (sdtasdt0(v2, v5) = xc & $i(v5) &
% 61.41/8.97 | aElement0(v5))) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2,
% 61.41/8.97 | v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~
% 61.41/8.97 | aElement0(v3) | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : (
% 61.41/8.97 | ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.97 | aDivisorOf0(v2, xa) | ~ aElement0(v3) | ? [v4: $i] :
% 61.41/8.97 | (sdtasdt0(v2, v4) = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] :
% 61.41/8.97 | ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.97 | doDivides0(v2, xa) | ~ aElement0(v3) | ~ aElement0(v2) |
% 61.41/8.97 | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2,
% 61.41/8.97 | v3) = xb) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2, xa) | ~
% 61.41/8.97 | aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4)
% 61.41/8.97 | = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 61.41/8.97 | (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.97 | aDivisorOf0(v2, xb) | ~ aElement0(v3) | ~ aElement0(v2) |
% 61.41/8.97 | doDivides0(v2, xc)) & ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2,
% 61.41/8.97 | v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~
% 61.41/8.97 | aElement0(v3) | ~ aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4)
% 61.41/8.97 | = xc & $i(v4) & aElement0(v4))) & ! [v2: $i] : ! [v3: $i] : ( ~
% 61.41/8.97 | (sdtasdt0(v2, v3) = xa) | ~ $i(v3) | ~ $i(v2) | ~ doDivides0(v2,
% 61.41/8.97 | xb) | ~ aElement0(v3) | ~ aElement0(v2) | doDivides0(v2, xc)) &
% 61.41/8.97 | ! [v2: $i] : ! [v3: $i] : ( ~ (sdtasdt0(v2, v3) = xa) | ~ $i(v3) |
% 61.41/8.97 | ~ $i(v2) | ~ doDivides0(v2, xb) | ~ aElement0(v3) | ~
% 61.41/8.97 | aElement0(v2) | ? [v4: $i] : (sdtasdt0(v2, v4) = xc & $i(v4) &
% 61.41/8.97 | aElement0(v4))) & ! [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2,
% 61.41/8.97 | xb) | ~ aDivisorOf0(v2, xa) | doDivides0(v2, xc)) & ! [v2: $i]
% 61.41/8.97 | : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ aDivisorOf0(v2, xa) | ?
% 61.41/8.97 | [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & !
% 61.41/8.97 | [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2, xb) | ~ doDivides0(v2,
% 61.41/8.97 | xa) | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ( ~
% 61.41/8.97 | $i(v2) | ~ aDivisorOf0(v2, xb) | ~ doDivides0(v2, xa) | ~
% 61.41/8.97 | aElement0(v2) | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) &
% 61.41/8.97 | aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aDivisorOf0(v2,
% 61.41/8.97 | xa) | ~ doDivides0(v2, xb) | doDivides0(v2, xc)) & ! [v2: $i] :
% 61.41/8.97 | ( ~ $i(v2) | ~ aDivisorOf0(v2, xa) | ~ doDivides0(v2, xb) | ? [v3:
% 61.41/8.97 | $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))) & ! [v2:
% 61.41/8.97 | $i] : ( ~ $i(v2) | ~ doDivides0(v2, xb) | ~ doDivides0(v2, xa) |
% 61.41/8.97 | ~ aElement0(v2) | doDivides0(v2, xc)) & ! [v2: $i] : ( ~ $i(v2) |
% 61.41/8.97 | ~ doDivides0(v2, xb) | ~ doDivides0(v2, xa) | ~ aElement0(v2) |
% 61.41/8.97 | ? [v3: $i] : (sdtasdt0(v2, v3) = xc & $i(v3) & aElement0(v3))))
% 61.41/8.97 |
% 61.41/8.97 | ALPHA: (m__2174) implies:
% 61.41/8.98 | (6) ? [v0: $i] : ? [v1: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 61.41/8.98 | sdtpldt1(v0, v1) = xI & $i(v1) & $i(v0) & aIdeal0(xI) & aSet0(xI) &
% 61.41/8.98 | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtasdt0(v3, v2) = v4)
% 61.41/8.98 | | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v2, xI) | ~ aElement0(v3)
% 61.41/8.98 | | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 61.41/8.98 | ( ~ (sdtpldt0(v3, v4) = v2) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.98 | aElementOf0(v4, v1) | ~ aElementOf0(v3, v0) | aElementOf0(v2, xI))
% 61.41/8.98 | & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v2, v3) =
% 61.41/8.98 | v4) | ~ $i(v3) | ~ $i(v2) | ~ aElementOf0(v3, xI) | ~
% 61.41/8.98 | aElementOf0(v2, xI) | aElementOf0(v4, xI)) & ! [v2: $i] : ! [v3:
% 61.41/8.98 | $i] : ( ~ (sdtasdt0(xb, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.98 | aElement0(v3) | aElementOf0(v2, v1)) & ! [v2: $i] : ! [v3: $i] :
% 61.41/8.98 | ( ~ (sdtasdt0(xa, v3) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 61.41/8.98 | aElement0(v3) | aElementOf0(v2, v0)) & ! [v2: $i] : ( ~ $i(v2) |
% 61.41/8.98 | ~ aElementOf0(v2, v1) | ? [v3: $i] : (sdtasdt0(xb, v3) = v2 &
% 61.41/8.98 | $i(v3) & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~
% 61.41/8.98 | aElementOf0(v2, v0) | ? [v3: $i] : (sdtasdt0(xa, v3) = v2 & $i(v3)
% 61.41/8.98 | & aElement0(v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ aElementOf0(v2,
% 61.41/8.98 | xI) | ? [v3: $i] : ? [v4: $i] : (sdtpldt0(v3, v4) = v2 & $i(v4)
% 61.41/8.98 | & $i(v3) & aElementOf0(v4, v1) & aElementOf0(v3, v0))))
% 61.41/8.98 |
% 61.41/8.98 | ALPHA: (m__2203) implies:
% 61.41/8.98 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 61.41/8.98 | ? [v5: $i] : (slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sdtasdt0(xb, v3)
% 61.41/8.98 | = sz00 & sdtasdt0(xb, v2) = xb & sdtasdt0(xa, v5) = sz00 &
% 61.41/8.98 | sdtasdt0(xa, v4) = xa & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 61.41/8.98 | $i(v0) & aElementOf0(xb, v1) & aElementOf0(xa, v0) &
% 61.41/8.98 | aElementOf0(sz00, v1) & aElementOf0(sz00, v0) & aElement0(v5) &
% 61.41/8.98 | aElement0(v4) & aElement0(v3) & aElement0(v2))
% 61.41/8.98 |
% 61.41/8.98 | ALPHA: (m__2228) implies:
% 62.12/8.98 | (8) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 62.12/8.98 | ? [v5: $i] : ( ~ (v3 = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 &
% 62.12/8.98 | sdtpldt1(v0, v1) = v2 & sdtpldt0(v4, v5) = v3 & $i(v5) & $i(v4) &
% 62.12/8.98 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v1) &
% 62.12/8.98 | aElementOf0(v4, v0) & aElementOf0(v3, v2) & ! [v6: $i] : ! [v7: $i]
% 62.12/8.98 | : ( ~ (sdtasdt0(xb, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~
% 62.12/8.98 | aElement0(v7) | aElementOf0(v6, v1)) & ! [v6: $i] : ! [v7: $i] :
% 62.12/8.98 | ( ~ (sdtasdt0(xa, v7) = v6) | ~ $i(v7) | ~ $i(v6) | ~
% 62.12/8.98 | aElement0(v7) | aElementOf0(v6, v0)) & ! [v6: $i] : ( ~ $i(v6) |
% 62.12/8.98 | ~ aElementOf0(v6, v1) | ? [v7: $i] : (sdtasdt0(xb, v7) = v6 &
% 62.12/8.98 | $i(v7) & aElement0(v7))) & ! [v6: $i] : ( ~ $i(v6) | ~
% 62.12/8.98 | aElementOf0(v6, v0) | ? [v7: $i] : (sdtasdt0(xa, v7) = v6 & $i(v7)
% 62.12/8.98 | & aElement0(v7))))
% 62.12/8.98 |
% 62.12/8.98 | ALPHA: (m__2273) implies:
% 62.12/8.98 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (
% 62.12/8.98 | ~ (xu = sz00) & slsdtgt0(xb) = v1 & slsdtgt0(xa) = v0 & sbrdtbr0(xu)
% 62.12/8.98 | = v2 & sdtpldt0(v3, v4) = xu & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 62.12/8.98 | $i(v0) & aElementOf0(v4, v1) & aElementOf0(v3, v0) & aElementOf0(xu,
% 62.12/8.98 | xI) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: $i] : (v5 =
% 62.12/8.98 | sz00 | ~ (sbrdtbr0(v5) = v6) | ~ (sdtpldt0(v7, v8) = v5) | ~
% 62.12/8.98 | $i(v8) | ~ $i(v7) | ~ $i(v5) | ~ iLess0(v6, v2) | ~
% 62.12/8.98 | aElementOf0(v8, v1) | ~ aElementOf0(v7, v0)) & ! [v5: $i] : !
% 62.12/8.98 | [v6: $i] : (v5 = sz00 | ~ (sbrdtbr0(v5) = v6) | ~ $i(v5) | ~
% 62.12/8.98 | iLess0(v6, v2) | ~ aElementOf0(v5, xI)))
% 62.12/8.98 |
% 62.12/8.98 | ALPHA: (m__) implies:
% 62.12/8.98 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 62.12/8.98 | (sdtasdt0(xb, v1) = v3) | ~ (sdtasdt0(xa, v0) = v2) | ~
% 62.12/8.98 | (sdtpldt0(v2, v3) = xu) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 62.12/8.98 | ~ aElement0(v0))
% 62.12/8.98 |
% 62.12/8.98 | ALPHA: (function-axioms) implies:
% 62.12/8.99 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slsdtgt0(v2)
% 62.12/8.99 | = v1) | ~ (slsdtgt0(v2) = v0))
% 62.12/8.99 |
% 62.12/8.99 | DELTA: instantiating (7) with fresh symbols all_38_0, all_38_1, all_38_2,
% 62.12/8.99 | all_38_3, all_38_4, all_38_5 gives:
% 62.12/8.99 | (12) slsdtgt0(xb) = all_38_4 & slsdtgt0(xa) = all_38_5 & sdtasdt0(xb,
% 62.12/8.99 | all_38_2) = sz00 & sdtasdt0(xb, all_38_3) = xb & sdtasdt0(xa,
% 62.12/8.99 | all_38_0) = sz00 & sdtasdt0(xa, all_38_1) = xa & $i(all_38_0) &
% 62.12/8.99 | $i(all_38_1) & $i(all_38_2) & $i(all_38_3) & $i(all_38_4) &
% 62.12/8.99 | $i(all_38_5) & aElementOf0(xb, all_38_4) & aElementOf0(xa, all_38_5) &
% 62.12/8.99 | aElementOf0(sz00, all_38_4) & aElementOf0(sz00, all_38_5) &
% 62.12/8.99 | aElement0(all_38_0) & aElement0(all_38_1) & aElement0(all_38_2) &
% 62.12/8.99 | aElement0(all_38_3)
% 62.12/8.99 |
% 62.12/8.99 | ALPHA: (12) implies:
% 62.12/8.99 | (13) slsdtgt0(xa) = all_38_5
% 62.12/8.99 | (14) slsdtgt0(xb) = all_38_4
% 62.12/8.99 |
% 62.12/8.99 | DELTA: instantiating (9) with fresh symbols all_40_0, all_40_1, all_40_2,
% 62.12/8.99 | all_40_3, all_40_4 gives:
% 62.12/8.99 | (15) ~ (xu = sz00) & slsdtgt0(xb) = all_40_3 & slsdtgt0(xa) = all_40_4 &
% 62.12/8.99 | sbrdtbr0(xu) = all_40_2 & sdtpldt0(all_40_1, all_40_0) = xu &
% 62.12/8.99 | $i(all_40_0) & $i(all_40_1) & $i(all_40_2) & $i(all_40_3) &
% 62.12/8.99 | $i(all_40_4) & aElementOf0(all_40_0, all_40_3) & aElementOf0(all_40_1,
% 62.12/8.99 | all_40_4) & aElementOf0(xu, xI) & ! [v0: $i] : ! [v1: $i] : !
% 62.12/8.99 | [v2: $i] : ! [v3: $i] : (v0 = sz00 | ~ (sbrdtbr0(v0) = v1) | ~
% 62.12/8.99 | (sdtpldt0(v2, v3) = v0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 62.12/8.99 | iLess0(v1, all_40_2) | ~ aElementOf0(v3, all_40_3) | ~
% 62.12/8.99 | aElementOf0(v2, all_40_4)) & ! [v0: $i] : ! [v1: $i] : (v0 = sz00
% 62.12/8.99 | | ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ iLess0(v1, all_40_2) | ~
% 62.12/8.99 | aElementOf0(v0, xI))
% 62.12/8.99 |
% 62.12/8.99 | ALPHA: (15) implies:
% 62.12/8.99 | (16) aElementOf0(all_40_1, all_40_4)
% 62.12/8.99 | (17) aElementOf0(all_40_0, all_40_3)
% 62.12/8.99 | (18) $i(all_40_4)
% 62.12/8.99 | (19) $i(all_40_3)
% 62.12/8.99 | (20) $i(all_40_1)
% 62.12/8.99 | (21) $i(all_40_0)
% 62.12/8.99 | (22) sdtpldt0(all_40_1, all_40_0) = xu
% 62.12/8.99 | (23) slsdtgt0(xa) = all_40_4
% 62.12/8.99 | (24) slsdtgt0(xb) = all_40_3
% 62.12/8.99 |
% 62.12/8.99 | DELTA: instantiating (8) with fresh symbols all_43_0, all_43_1, all_43_2,
% 62.12/8.99 | all_43_3, all_43_4, all_43_5 gives:
% 62.12/8.99 | (25) ~ (all_43_2 = sz00) & slsdtgt0(xb) = all_43_4 & slsdtgt0(xa) =
% 62.12/8.99 | all_43_5 & sdtpldt1(all_43_5, all_43_4) = all_43_3 &
% 62.12/8.99 | sdtpldt0(all_43_1, all_43_0) = all_43_2 & $i(all_43_0) & $i(all_43_1)
% 62.12/8.99 | & $i(all_43_2) & $i(all_43_3) & $i(all_43_4) & $i(all_43_5) &
% 62.12/8.99 | aElementOf0(all_43_0, all_43_4) & aElementOf0(all_43_1, all_43_5) &
% 62.12/8.99 | aElementOf0(all_43_2, all_43_3) & ! [v0: $i] : ! [v1: $i] : ( ~
% 62.12/8.99 | (sdtasdt0(xb, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 62.12/8.99 | aElementOf0(v0, all_43_4)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 62.12/8.99 | (sdtasdt0(xa, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 62.12/8.99 | aElementOf0(v0, all_43_5)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/8.99 | aElementOf0(v0, all_43_4) | ? [v1: $i] : (sdtasdt0(xb, v1) = v0 &
% 62.12/8.99 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/8.99 | aElementOf0(v0, all_43_5) | ? [v1: $i] : (sdtasdt0(xa, v1) = v0 &
% 62.12/8.99 | $i(v1) & aElement0(v1)))
% 62.12/8.99 |
% 62.12/8.99 | ALPHA: (25) implies:
% 62.12/8.99 | (26) slsdtgt0(xa) = all_43_5
% 62.12/8.99 | (27) slsdtgt0(xb) = all_43_4
% 62.12/8.99 |
% 62.12/8.99 | DELTA: instantiating (6) with fresh symbols all_46_0, all_46_1 gives:
% 62.12/9.00 | (28) slsdtgt0(xb) = all_46_0 & slsdtgt0(xa) = all_46_1 & sdtpldt1(all_46_1,
% 62.12/9.00 | all_46_0) = xI & $i(all_46_0) & $i(all_46_1) & aIdeal0(xI) &
% 62.12/9.00 | aSet0(xI) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 62.12/9.00 | (sdtasdt0(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0,
% 62.12/9.00 | xI) | ~ aElement0(v1) | aElementOf0(v2, xI)) & ! [v0: $i] : !
% 62.12/9.00 | [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v1, v2) = v0) | ~ $i(v2) | ~
% 62.12/9.00 | $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, all_46_0) | ~
% 62.12/9.00 | aElementOf0(v1, all_46_1) | aElementOf0(v0, xI)) & ! [v0: $i] : !
% 62.12/9.00 | [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v1) | ~
% 62.12/9.00 | $i(v0) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) |
% 62.12/9.00 | aElementOf0(v2, xI)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(xb,
% 62.12/9.00 | v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 62.12/9.00 | aElementOf0(v0, all_46_0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 62.12/9.00 | (sdtasdt0(xa, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) |
% 62.12/9.00 | aElementOf0(v0, all_46_1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/9.00 | aElementOf0(v0, all_46_0) | ? [v1: $i] : (sdtasdt0(xb, v1) = v0 &
% 62.12/9.00 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/9.00 | aElementOf0(v0, all_46_1) | ? [v1: $i] : (sdtasdt0(xa, v1) = v0 &
% 62.12/9.00 | $i(v1) & aElement0(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/9.00 | aElementOf0(v0, xI) | ? [v1: $i] : ? [v2: $i] : (sdtpldt0(v1, v2)
% 62.12/9.00 | = v0 & $i(v2) & $i(v1) & aElementOf0(v2, all_46_0) &
% 62.12/9.00 | aElementOf0(v1, all_46_1)))
% 62.12/9.00 |
% 62.12/9.00 | ALPHA: (28) implies:
% 62.12/9.00 | (29) slsdtgt0(xa) = all_46_1
% 62.12/9.00 | (30) slsdtgt0(xb) = all_46_0
% 62.12/9.00 |
% 62.12/9.00 | DELTA: instantiating (5) with fresh symbols all_49_0, all_49_1 gives:
% 62.12/9.00 | (31) sdtasdt0(xc, all_49_0) = xa & sdtasdt0(xc, all_49_1) = xb &
% 62.12/9.00 | $i(all_49_0) & $i(all_49_1) & aGcdOfAnd0(xc, xa, xb) & aDivisorOf0(xc,
% 62.12/9.00 | xb) & aDivisorOf0(xc, xa) & doDivides0(xc, xb) & doDivides0(xc, xa)
% 62.12/9.00 | & aElement0(all_49_0) & aElement0(all_49_1) & aElement0(xc) & ! [v0:
% 62.12/9.00 | $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = xa) | ~
% 62.12/9.00 | (sdtasdt0(v0, v1) = xb) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 62.12/9.00 | aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | doDivides0(v0,
% 62.12/9.00 | xc)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0,
% 62.12/9.00 | v2) = xa) | ~ (sdtasdt0(v0, v1) = xb) | ~ $i(v2) | ~ $i(v1) |
% 62.12/9.00 | ~ $i(v0) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) |
% 62.12/9.00 | ? [v3: $i] : (sdtasdt0(v0, v3) = xc & $i(v3) & aElement0(v3))) & !
% 62.12/9.00 | [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xb) | ~ $i(v1) | ~
% 62.12/9.00 | $i(v0) | ~ aDivisorOf0(v0, xa) | ~ aElement0(v1) | doDivides0(v0,
% 62.12/9.00 | xc)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xb) |
% 62.12/9.00 | ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v0, xa) | ~ aElement0(v1) |
% 62.12/9.00 | ? [v2: $i] : (sdtasdt0(v0, v2) = xc & $i(v2) & aElement0(v2))) & !
% 62.12/9.00 | [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xb) | ~ $i(v1) | ~
% 62.12/9.00 | $i(v0) | ~ doDivides0(v0, xa) | ~ aElement0(v1) | ~ aElement0(v0)
% 62.12/9.00 | | doDivides0(v0, xc)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 62.12/9.00 | (sdtasdt0(v0, v1) = xb) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 62.12/9.00 | xa) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] :
% 62.12/9.00 | (sdtasdt0(v0, v2) = xc & $i(v2) & aElement0(v2))) & ! [v0: $i] : !
% 62.12/9.00 | [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xa) | ~ $i(v1) | ~ $i(v0) | ~
% 62.12/9.00 | aDivisorOf0(v0, xb) | ~ aElement0(v1) | ~ aElement0(v0) |
% 62.12/9.00 | doDivides0(v0, xc)) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0,
% 62.12/9.00 | v1) = xa) | ~ $i(v1) | ~ $i(v0) | ~ aDivisorOf0(v0, xb) | ~
% 62.12/9.00 | aElement0(v1) | ~ aElement0(v0) | ? [v2: $i] : (sdtasdt0(v0, v2) =
% 62.12/9.00 | xc & $i(v2) & aElement0(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 62.12/9.00 | (sdtasdt0(v0, v1) = xa) | ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0,
% 62.12/9.00 | xb) | ~ aElement0(v1) | ~ aElement0(v0) | doDivides0(v0, xc)) &
% 62.12/9.00 | ! [v0: $i] : ! [v1: $i] : ( ~ (sdtasdt0(v0, v1) = xa) | ~ $i(v1) |
% 62.12/9.00 | ~ $i(v0) | ~ doDivides0(v0, xb) | ~ aElement0(v1) | ~
% 62.12/9.00 | aElement0(v0) | ? [v2: $i] : (sdtasdt0(v0, v2) = xc & $i(v2) &
% 62.12/9.00 | aElement0(v2))) & ! [v0: $i] : ( ~ $i(v0) | ~ aDivisorOf0(v0,
% 62.12/9.00 | xb) | ~ aDivisorOf0(v0, xa) | doDivides0(v0, xc)) & ! [v0: $i] :
% 62.12/9.00 | ( ~ $i(v0) | ~ aDivisorOf0(v0, xb) | ~ aDivisorOf0(v0, xa) | ? [v1:
% 62.12/9.00 | $i] : (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1))) & ! [v0:
% 62.12/9.00 | $i] : ( ~ $i(v0) | ~ aDivisorOf0(v0, xb) | ~ doDivides0(v0, xa) |
% 62.12/9.00 | ~ aElement0(v0) | doDivides0(v0, xc)) & ! [v0: $i] : ( ~ $i(v0) |
% 62.12/9.00 | ~ aDivisorOf0(v0, xb) | ~ doDivides0(v0, xa) | ~ aElement0(v0) |
% 62.12/9.00 | ? [v1: $i] : (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1))) & !
% 62.12/9.00 | [v0: $i] : ( ~ $i(v0) | ~ aDivisorOf0(v0, xa) | ~ doDivides0(v0, xb)
% 62.12/9.00 | | doDivides0(v0, xc)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/9.00 | aDivisorOf0(v0, xa) | ~ doDivides0(v0, xb) | ? [v1: $i] :
% 62.12/9.00 | (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1))) & ! [v0: $i] : (
% 62.12/9.00 | ~ $i(v0) | ~ doDivides0(v0, xb) | ~ doDivides0(v0, xa) | ~
% 62.12/9.00 | aElement0(v0) | doDivides0(v0, xc)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 62.12/9.00 | doDivides0(v0, xb) | ~ doDivides0(v0, xa) | ~ aElement0(v0) | ?
% 62.12/9.00 | [v1: $i] : (sdtasdt0(v0, v1) = xc & $i(v1) & aElement0(v1)))
% 62.12/9.00 |
% 62.12/9.00 | ALPHA: (31) implies:
% 62.12/9.00 | (32) aElement0(xc)
% 62.12/9.00 | (33) aElement0(all_49_1)
% 62.12/9.00 | (34) aElement0(all_49_0)
% 62.12/9.00 | (35) $i(all_49_1)
% 62.12/9.00 | (36) $i(all_49_0)
% 62.12/9.00 | (37) sdtasdt0(xc, all_49_1) = xb
% 62.12/9.00 | (38) sdtasdt0(xc, all_49_0) = xa
% 62.12/9.00 |
% 62.12/9.00 | GROUND_INST: instantiating (11) with all_40_4, all_43_5, xa, simplifying with
% 62.12/9.00 | (23), (26) gives:
% 62.12/9.00 | (39) all_43_5 = all_40_4
% 62.12/9.00 |
% 62.12/9.00 | GROUND_INST: instantiating (11) with all_43_5, all_46_1, xa, simplifying with
% 62.12/9.00 | (26), (29) gives:
% 62.12/9.00 | (40) all_46_1 = all_43_5
% 62.12/9.00 |
% 62.12/9.00 | GROUND_INST: instantiating (11) with all_38_5, all_46_1, xa, simplifying with
% 62.12/9.00 | (13), (29) gives:
% 62.12/9.00 | (41) all_46_1 = all_38_5
% 62.12/9.00 |
% 62.12/9.00 | GROUND_INST: instantiating (11) with all_40_3, all_43_4, xb, simplifying with
% 62.12/9.00 | (24), (27) gives:
% 62.12/9.00 | (42) all_43_4 = all_40_3
% 62.12/9.00 |
% 62.12/9.00 | GROUND_INST: instantiating (11) with all_43_4, all_46_0, xb, simplifying with
% 62.12/9.00 | (27), (30) gives:
% 62.12/9.00 | (43) all_46_0 = all_43_4
% 62.12/9.00 |
% 62.12/9.01 | GROUND_INST: instantiating (11) with all_38_4, all_46_0, xb, simplifying with
% 62.12/9.01 | (14), (30) gives:
% 62.12/9.01 | (44) all_46_0 = all_38_4
% 62.12/9.01 |
% 62.12/9.01 | COMBINE_EQS: (43), (44) imply:
% 62.12/9.01 | (45) all_43_4 = all_38_4
% 62.12/9.01 |
% 62.12/9.01 | SIMP: (45) implies:
% 62.12/9.01 | (46) all_43_4 = all_38_4
% 62.12/9.01 |
% 62.12/9.01 | COMBINE_EQS: (40), (41) imply:
% 62.12/9.01 | (47) all_43_5 = all_38_5
% 62.12/9.01 |
% 62.12/9.01 | SIMP: (47) implies:
% 62.12/9.01 | (48) all_43_5 = all_38_5
% 62.12/9.01 |
% 62.12/9.01 | COMBINE_EQS: (42), (46) imply:
% 62.12/9.01 | (49) all_40_3 = all_38_4
% 62.12/9.01 |
% 62.12/9.01 | SIMP: (49) implies:
% 62.12/9.01 | (50) all_40_3 = all_38_4
% 62.12/9.01 |
% 62.12/9.01 | COMBINE_EQS: (39), (48) imply:
% 62.12/9.01 | (51) all_40_4 = all_38_5
% 62.12/9.01 |
% 62.12/9.01 | SIMP: (51) implies:
% 62.12/9.01 | (52) all_40_4 = all_38_5
% 62.12/9.01 |
% 62.12/9.01 | REDUCE: (19), (50) imply:
% 62.12/9.01 | (53) $i(all_38_4)
% 62.12/9.01 |
% 62.12/9.01 | REDUCE: (18), (52) imply:
% 62.12/9.01 | (54) $i(all_38_5)
% 62.12/9.01 |
% 62.12/9.01 | REDUCE: (17), (50) imply:
% 62.12/9.01 | (55) aElementOf0(all_40_0, all_38_4)
% 62.12/9.01 |
% 62.12/9.01 | REDUCE: (16), (52) imply:
% 62.12/9.01 | (56) aElementOf0(all_40_1, all_38_5)
% 62.12/9.01 |
% 62.12/9.01 | GROUND_INST: instantiating (mMulComm) with xc, all_49_1, xb, simplifying with
% 62.12/9.01 | (4), (32), (33), (35), (37) gives:
% 62.12/9.01 | (57) sdtasdt0(all_49_1, xc) = xb & $i(xb)
% 62.12/9.01 |
% 62.12/9.01 | ALPHA: (57) implies:
% 62.12/9.01 | (58) $i(xb)
% 62.12/9.01 |
% 62.12/9.01 | GROUND_INST: instantiating (mMulComm) with xc, all_49_0, xa, simplifying with
% 62.12/9.01 | (4), (32), (34), (36), (38) gives:
% 62.12/9.01 | (59) sdtasdt0(all_49_0, xc) = xa & $i(xa)
% 62.12/9.01 |
% 62.12/9.01 | ALPHA: (59) implies:
% 62.12/9.01 | (60) $i(xa)
% 62.12/9.01 |
% 62.12/9.01 | GROUND_INST: instantiating (1) with xa, all_38_5, all_40_1, simplifying with
% 62.12/9.01 | (2), (13), (20), (54), (56), (60) gives:
% 62.12/9.01 | (61) ? [v0: $i] : (sdtasdt0(xa, v0) = all_40_1 & $i(v0) & aElement0(v0))
% 62.12/9.01 |
% 62.12/9.01 | GROUND_INST: instantiating (1) with xb, all_38_4, all_40_0, simplifying with
% 62.12/9.01 | (3), (14), (21), (53), (55), (58) gives:
% 62.12/9.01 | (62) ? [v0: $i] : (sdtasdt0(xb, v0) = all_40_0 & $i(v0) & aElement0(v0))
% 62.12/9.01 |
% 62.12/9.01 | DELTA: instantiating (62) with fresh symbol all_70_0 gives:
% 62.12/9.01 | (63) sdtasdt0(xb, all_70_0) = all_40_0 & $i(all_70_0) & aElement0(all_70_0)
% 62.12/9.01 |
% 62.12/9.01 | ALPHA: (63) implies:
% 62.12/9.01 | (64) aElement0(all_70_0)
% 62.12/9.01 | (65) $i(all_70_0)
% 62.12/9.01 | (66) sdtasdt0(xb, all_70_0) = all_40_0
% 62.12/9.01 |
% 62.12/9.01 | DELTA: instantiating (61) with fresh symbol all_82_0 gives:
% 62.12/9.01 | (67) sdtasdt0(xa, all_82_0) = all_40_1 & $i(all_82_0) & aElement0(all_82_0)
% 62.12/9.01 |
% 62.12/9.01 | ALPHA: (67) implies:
% 62.12/9.01 | (68) aElement0(all_82_0)
% 62.12/9.01 | (69) $i(all_82_0)
% 62.12/9.01 | (70) sdtasdt0(xa, all_82_0) = all_40_1
% 62.12/9.01 |
% 62.12/9.01 | GROUND_INST: instantiating (10) with all_82_0, all_70_0, all_40_1, all_40_0,
% 62.12/9.01 | simplifying with (22), (64), (65), (66), (68), (69), (70) gives:
% 62.12/9.01 | (71) $false
% 62.12/9.01 |
% 62.12/9.01 | CLOSE: (71) is inconsistent.
% 62.12/9.01 |
% 62.12/9.01 End of proof
% 62.12/9.01 % SZS output end Proof for theBenchmark
% 62.12/9.01
% 62.12/9.01 8410ms
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