TSTP Solution File: NUM583+3 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM583+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 : n031.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 11:48:46 EDT 2023
% Result : Theorem 109.54s 15.20s
% Output : Proof 110.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM583+3 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n031.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 : Fri Aug 25 09:19:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.28/1.45 Prover 4: Preprocessing ...
% 5.28/1.45 Prover 1: Preprocessing ...
% 5.60/1.49 Prover 2: Preprocessing ...
% 5.60/1.49 Prover 5: Preprocessing ...
% 5.60/1.49 Prover 6: Preprocessing ...
% 5.60/1.49 Prover 0: Preprocessing ...
% 5.60/1.49 Prover 3: Preprocessing ...
% 15.48/2.84 Prover 3: Constructing countermodel ...
% 15.48/2.86 Prover 1: Constructing countermodel ...
% 15.97/2.93 Prover 6: Proving ...
% 16.58/2.98 Prover 5: Proving ...
% 19.57/3.38 Prover 2: Proving ...
% 26.50/4.32 Prover 4: Constructing countermodel ...
% 28.92/4.68 Prover 0: Proving ...
% 74.88/10.69 Prover 2: stopped
% 75.48/10.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 76.67/10.89 Prover 7: Preprocessing ...
% 78.81/11.21 Prover 7: Constructing countermodel ...
% 99.32/13.95 Prover 5: stopped
% 99.32/13.97 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 100.54/14.09 Prover 8: Preprocessing ...
% 102.88/14.33 Prover 8: Warning: ignoring some quantifiers
% 102.88/14.34 Prover 8: Constructing countermodel ...
% 108.59/15.17 Prover 7: Found proof (size 74)
% 108.59/15.17 Prover 7: proved (4454ms)
% 108.59/15.17 Prover 8: stopped
% 108.59/15.18 Prover 4: stopped
% 108.59/15.18 Prover 3: stopped
% 108.59/15.18 Prover 6: stopped
% 108.59/15.18 Prover 1: stopped
% 109.54/15.20 Prover 0: stopped
% 109.54/15.20
% 109.54/15.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 109.54/15.20
% 109.54/15.21 % SZS output start Proof for theBenchmark
% 109.54/15.22 Assumptions after simplification:
% 109.54/15.22 ---------------------------------
% 109.54/15.22
% 109.54/15.22 (mDefSub)
% 109.54/15.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 109.54/15.23 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 109.54/15.23 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 109.54/15.23 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 109.54/15.23 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 109.54/15.23 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 109.54/15.23
% 109.54/15.23 (mZeroLess)
% 109.54/15.23 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 109.54/15.23 szNzAzT0) | sdtlseqdt0(sz00, v0))
% 109.54/15.23
% 109.54/15.23 (mZeroNum)
% 109.54/15.23 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 109.54/15.23
% 109.54/15.23 (m__)
% 109.54/15.25 $i(xQ) & $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 109.54/15.25 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1)
% 109.54/15.25 = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2) &
% 109.54/15.25 aElementOf0(v1, v0) & aSet0(v2) & ~ aSubsetOf0(v2, xS) & ~ aElementOf0(v3,
% 109.54/15.25 xS) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v2) |
% 109.54/15.25 aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2) |
% 109.54/15.25 aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 109.54/15.25 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) |
% 109.54/15.25 ~ aElement0(v4) | aElementOf0(v4, v2)) & ( ~ aElement0(v1) |
% 109.54/15.25 aElementOf0(v1, v2)))
% 109.54/15.25
% 109.54/15.25 (m__3435)
% 109.54/15.26 $i(xS) & $i(szNzAzT0) & aSubsetOf0(xS, szNzAzT0) & isCountable0(xS) &
% 109.54/15.26 aSet0(xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xS) |
% 109.54/15.26 aElementOf0(v0, szNzAzT0))
% 109.54/15.26
% 109.54/15.26 (m__3623)
% 109.54/15.27 sdtlpdtrp0(xN, sz00) = xS & szDzozmdt0(xN) = szNzAzT0 & $i(xN) & $i(xS) &
% 109.54/15.27 $i(sz00) & $i(szNzAzT0) & aFunction0(xN) & ! [v0: $i] : ! [v1: $i] : ( ~
% 109.54/15.27 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ aSubsetOf0(v1, szNzAzT0) | ~
% 109.54/15.27 isCountable0(v1) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 109.54/15.27 : ? [v4: $i] : ? [v5: $i] : (sdtlpdtrp0(xN, v4) = v5 & szmzizndt0(v1) = v2
% 109.54/15.27 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 & $i(v5) & $i(v4) & $i(v3)
% 109.54/15.27 & $i(v2) & aSubsetOf0(v5, v3) & isCountable0(v5) & aElementOf0(v2, v1) &
% 109.54/15.27 aSet0(v5) & aSet0(v3) & ~ aElementOf0(v2, v3) & ! [v6: $i] : (v6 = v2 |
% 109.54/15.27 ~ $i(v6) | ~ aElementOf0(v6, v1) | ~ aElement0(v6) | aElementOf0(v6,
% 109.54/15.27 v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v5) |
% 109.54/15.27 aElementOf0(v6, v3)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6, v3)
% 109.54/15.27 | aElementOf0(v6, v1)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6,
% 109.54/15.27 v3) | aElement0(v6)) & ! [v6: $i] : ( ~ $i(v6) | ~ aElementOf0(v6,
% 109.54/15.27 v1) | sdtlseqdt0(v2, v6)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 109.54/15.27 (sdtlpdtrp0(xN, v0) = v1) | ~ $i(v0) | ~ isCountable0(v1) | ~
% 109.54/15.27 aElementOf0(v0, szNzAzT0) | ~ aSet0(v1) | ? [v2: $i] : ? [v3: $i] : ?
% 109.54/15.27 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ($i(v6) & ((sdtlpdtrp0(xN, v4) = v5 &
% 109.54/15.27 szmzizndt0(v1) = v2 & szszuzczcdt0(v0) = v4 & sdtmndt0(v1, v2) = v3 &
% 109.54/15.27 $i(v5) & $i(v4) & $i(v3) & $i(v2) & aSubsetOf0(v5, v3) &
% 109.54/15.27 isCountable0(v5) & aElementOf0(v2, v1) & aSet0(v5) & aSet0(v3) & ~
% 109.54/15.27 aElementOf0(v2, v3) & ! [v7: $i] : (v7 = v2 | ~ $i(v7) | ~
% 109.54/15.27 aElementOf0(v7, v1) | ~ aElement0(v7) | aElementOf0(v7, v3)) & !
% 109.54/15.27 [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v5) | aElementOf0(v7, v3))
% 109.54/15.27 & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) | aElementOf0(v7,
% 109.54/15.27 v1)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v3) |
% 109.54/15.27 aElement0(v7)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7, v1) |
% 109.54/15.27 sdtlseqdt0(v2, v7))) | (aElementOf0(v6, v1) & ~ aElementOf0(v6,
% 109.54/15.27 szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 109.54/15.27 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ? [v2: $i] : ? [v3: $i]
% 109.54/15.27 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (sdtlpdtrp0(xN, v0) = v2 &
% 109.54/15.27 $i(v6) & $i(v2) & ( ~ isCountable0(v2) | (sdtlpdtrp0(xN, v1) = v5 &
% 109.54/15.27 szmzizndt0(v2) = v3 & sdtmndt0(v2, v3) = v4 & $i(v5) & $i(v4) & $i(v3)
% 109.54/15.27 & aSubsetOf0(v5, v4) & isCountable0(v5) & aElementOf0(v3, v2) &
% 109.54/15.27 aSet0(v5) & aSet0(v4) & ~ aElementOf0(v3, v4) & ! [v7: $i] : (v7 =
% 109.54/15.27 v3 | ~ $i(v7) | ~ aElementOf0(v7, v2) | ~ aElement0(v7) |
% 109.54/15.27 aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~ aElementOf0(v7,
% 109.54/15.27 v5) | aElementOf0(v7, v4)) & ! [v7: $i] : ( ~ $i(v7) | ~
% 109.54/15.27 aElementOf0(v7, v4) | aElementOf0(v7, v2)) & ! [v7: $i] : ( ~
% 109.54/15.27 $i(v7) | ~ aElementOf0(v7, v4) | aElement0(v7)) & ! [v7: $i] : ( ~
% 109.54/15.27 $i(v7) | ~ aElementOf0(v7, v2) | sdtlseqdt0(v3, v7))) | ( ~
% 109.54/15.27 aSubsetOf0(v2, szNzAzT0) & ( ~ aSet0(v2) | (aElementOf0(v6, v2) & ~
% 109.54/15.27 aElementOf0(v6, szNzAzT0)))))))
% 109.54/15.27
% 109.54/15.27 (m__3754)
% 109.54/15.27 $i(xN) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 109.54/15.27 : ! [v4: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 109.54/15.27 ~ $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 109.54/15.27 aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 109.54/15.27 szNzAzT0) | aElementOf0(v4, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 109.54/15.27 : ! [v3: $i] : ( ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) |
% 109.54/15.27 ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~ aElementOf0(v1, szNzAzT0)
% 109.54/15.27 | ~ aElementOf0(v0, szNzAzT0) | aSubsetOf0(v2, v3))
% 109.54/15.27
% 109.54/15.27 (m__3989)
% 109.54/15.27 $i(xi) & $i(szNzAzT0) & aElementOf0(xi, szNzAzT0)
% 109.54/15.27
% 109.54/15.27 (m__3989_02)
% 109.54/15.27 $i(xQ) & $i(xi) & $i(xN) & $i(xk) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 109.54/15.27 ? [v3: $i] : (sdtlpdtrp0(xN, xi) = v0 & slbdtsldtrb0(v2, xk) = v3 &
% 109.54/15.27 szmzizndt0(v0) = v1 & sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) &
% 109.54/15.27 $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) &
% 109.54/15.27 aElementOf0(xQ, v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & !
% 109.54/15.27 [v4: $i] : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4)
% 109.54/15.27 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 109.54/15.27 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v2)
% 109.54/15.27 | aElement0(v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) |
% 109.54/15.27 sdtlseqdt0(v1, v4)) & ! [v4: $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) |
% 109.54/15.27 aElementOf0(v4, v2)))
% 109.54/15.27
% 109.54/15.27 (m__4007)
% 109.95/15.27 $i(xQ) & $i(xi) & $i(xN) & $i(xK) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 109.95/15.27 (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK &
% 109.95/15.27 sdtpldt0(xQ, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) &
% 109.95/15.27 aSet0(v2) & ! [v3: $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 109.95/15.27 aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 109.95/15.27 aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, v0) |
% 109.95/15.27 sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~ $i(v3) | ~ aElementOf0(v3, xQ) |
% 109.95/15.27 ~ aElement0(v3) | aElementOf0(v3, v2)) & ( ~ aElement0(v1) |
% 109.95/15.27 aElementOf0(v1, v2)))
% 109.95/15.27
% 109.95/15.27 (m__4037)
% 109.95/15.28 $i(xi) & $i(xN) & $i(xS) & ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) &
% 109.95/15.28 aSubsetOf0(v0, xS) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) |
% 109.95/15.28 aElementOf0(v1, xS)))
% 109.95/15.28
% 109.95/15.28 (function-axioms)
% 109.95/15.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 109.95/15.28 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 109.95/15.28 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 109.95/15.28 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 109.95/15.28 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 109.95/15.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 109.95/15.28 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 109.95/15.28 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 109.95/15.28 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 109.95/15.28 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~
% 109.95/15.28 (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 109.95/15.28 $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) &
% 109.95/15.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 109.95/15.28 ~ (szDzizrdt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 109.95/15.28 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 109.95/15.28 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 109.95/15.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 109.95/15.28 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 109.95/15.28 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 109.95/15.28 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 109.95/15.28 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 109.95/15.28 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 109.95/15.28 v0))
% 109.95/15.28
% 109.95/15.28 Further assumptions not needed in the proof:
% 109.95/15.28 --------------------------------------------
% 109.95/15.28 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 109.95/15.28 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 109.95/15.28 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg,
% 109.95/15.28 mDefSeg, mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin,
% 109.95/15.28 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount,
% 109.95/15.28 mImgElm, mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal,
% 109.95/15.28 mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet,
% 109.95/15.28 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet,
% 109.95/15.28 mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc,
% 109.95/15.28 mSuccLess, mSuccNum, m__3291, m__3398, m__3418, m__3453, m__3462, m__3520,
% 109.95/15.28 m__3533, m__3671, m__3821
% 109.95/15.28
% 109.95/15.28 Those formulas are unsatisfiable:
% 109.95/15.28 ---------------------------------
% 109.95/15.28
% 109.95/15.28 Begin of proof
% 109.95/15.28 |
% 109.95/15.28 | ALPHA: (mDefSub) implies:
% 109.95/15.28 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 109.95/15.28 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 109.95/15.28 | aSet0(v0) | aElementOf0(v2, v0))
% 109.95/15.28 |
% 109.95/15.28 | ALPHA: (mZeroNum) implies:
% 109.95/15.28 | (2) aElementOf0(sz00, szNzAzT0)
% 109.95/15.29 |
% 109.95/15.29 | ALPHA: (mZeroLess) implies:
% 109.95/15.29 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 109.95/15.29 | sdtlseqdt0(sz00, v0))
% 109.95/15.29 |
% 109.95/15.29 | ALPHA: (m__3435) implies:
% 109.95/15.29 | (4) aSet0(xS)
% 109.95/15.29 |
% 109.95/15.29 | ALPHA: (m__3623) implies:
% 109.95/15.29 | (5) $i(sz00)
% 109.95/15.29 | (6) sdtlpdtrp0(xN, sz00) = xS
% 109.95/15.29 |
% 109.95/15.29 | ALPHA: (m__3754) implies:
% 110.02/15.29 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 110.02/15.29 | ~ (sdtlpdtrp0(xN, v1) = v3) | ~ (sdtlpdtrp0(xN, v0) = v2) | ~
% 110.02/15.29 | $i(v4) | ~ $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v0) | ~
% 110.02/15.29 | aElementOf0(v4, v2) | ~ aElementOf0(v1, szNzAzT0) | ~
% 110.02/15.29 | aElementOf0(v0, szNzAzT0) | aElementOf0(v4, v3))
% 110.02/15.29 |
% 110.02/15.29 | ALPHA: (m__3989) implies:
% 110.02/15.29 | (8) aElementOf0(xi, szNzAzT0)
% 110.02/15.29 |
% 110.02/15.29 | ALPHA: (m__3989_02) implies:
% 110.02/15.29 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (sdtlpdtrp0(xN,
% 110.02/15.29 | xi) = v0 & slbdtsldtrb0(v2, xk) = v3 & szmzizndt0(v0) = v1 &
% 110.02/15.29 | sbrdtbr0(xQ) = xk & sdtmndt0(v0, v1) = v2 & $i(v3) & $i(v2) & $i(v1)
% 110.02/15.29 | & $i(v0) & aSubsetOf0(xQ, v2) & aElementOf0(v1, v0) & aElementOf0(xQ,
% 110.02/15.29 | v3) & aSet0(v2) & aSet0(xQ) & ~ aElementOf0(v1, v2) & ! [v4: $i]
% 110.02/15.29 | : (v4 = v1 | ~ $i(v4) | ~ aElementOf0(v4, v0) | ~ aElement0(v4) |
% 110.02/15.29 | aElementOf0(v4, v2)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 110.02/15.29 | aElementOf0(v4, v2) | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~
% 110.02/15.29 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : (
% 110.02/15.29 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 110.02/15.29 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | aElementOf0(v4, v2)))
% 110.02/15.29 |
% 110.02/15.29 | ALPHA: (m__4007) implies:
% 110.02/15.29 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlpdtrp0(xN, xi) = v0 &
% 110.02/15.29 | szmzizndt0(v0) = v1 & sbrdtbr0(v2) = xK & sdtpldt0(xQ, v1) = v2 &
% 110.02/15.29 | $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) & aSet0(v2) & ! [v3:
% 110.02/15.29 | $i] : (v3 = v1 | ~ $i(v3) | ~ aElementOf0(v3, v2) |
% 110.02/15.29 | aElementOf0(v3, xQ)) & ! [v3: $i] : ( ~ $i(v3) | ~
% 110.02/15.29 | aElementOf0(v3, v2) | aElement0(v3)) & ! [v3: $i] : ( ~ $i(v3) |
% 110.02/15.29 | ~ aElementOf0(v3, v0) | sdtlseqdt0(v1, v3)) & ! [v3: $i] : ( ~
% 110.02/15.29 | $i(v3) | ~ aElementOf0(v3, xQ) | ~ aElement0(v3) |
% 110.02/15.29 | aElementOf0(v3, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 110.02/15.29 |
% 110.02/15.29 | ALPHA: (m__4037) implies:
% 110.02/15.29 | (11) ? [v0: $i] : (sdtlpdtrp0(xN, xi) = v0 & $i(v0) & aSubsetOf0(v0, xS) &
% 110.02/15.29 | ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0) | aElementOf0(v1,
% 110.02/15.29 | xS)))
% 110.02/15.29 |
% 110.02/15.29 | ALPHA: (m__) implies:
% 110.02/15.29 | (12) $i(xS)
% 110.02/15.29 | (13) $i(xi)
% 110.02/15.29 | (14) $i(xQ)
% 110.02/15.30 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 110.02/15.30 | (sdtlpdtrp0(xN, xi) = v0 & szmzizndt0(v0) = v1 & sdtpldt0(xQ, v1) = v2
% 110.02/15.30 | & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v3, v2) &
% 110.02/15.30 | aElementOf0(v1, v0) & aSet0(v2) & ~ aSubsetOf0(v2, xS) & ~
% 110.02/15.30 | aElementOf0(v3, xS) & ! [v4: $i] : (v4 = v1 | ~ $i(v4) | ~
% 110.02/15.30 | aElementOf0(v4, v2) | aElementOf0(v4, xQ)) & ! [v4: $i] : ( ~
% 110.02/15.30 | $i(v4) | ~ aElementOf0(v4, v2) | aElement0(v4)) & ! [v4: $i] : (
% 110.02/15.30 | ~ $i(v4) | ~ aElementOf0(v4, v0) | sdtlseqdt0(v1, v4)) & ! [v4:
% 110.02/15.30 | $i] : ( ~ $i(v4) | ~ aElementOf0(v4, xQ) | ~ aElement0(v4) |
% 110.02/15.30 | aElementOf0(v4, v2)) & ( ~ aElement0(v1) | aElementOf0(v1, v2)))
% 110.02/15.30 |
% 110.02/15.30 | ALPHA: (function-axioms) implies:
% 110.02/15.30 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 110.02/15.30 | (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2) = v0))
% 110.02/15.30 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.02/15.30 | (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 110.02/15.30 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 110.02/15.30 | (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0))
% 110.02/15.30 |
% 110.02/15.30 | DELTA: instantiating (11) with fresh symbol all_70_0 gives:
% 110.02/15.30 | (19) sdtlpdtrp0(xN, xi) = all_70_0 & $i(all_70_0) & aSubsetOf0(all_70_0,
% 110.02/15.30 | xS) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_70_0) |
% 110.02/15.30 | aElementOf0(v0, xS))
% 110.02/15.30 |
% 110.02/15.30 | ALPHA: (19) implies:
% 110.02/15.30 | (20) aSubsetOf0(all_70_0, xS)
% 110.02/15.30 | (21) sdtlpdtrp0(xN, xi) = all_70_0
% 110.02/15.30 |
% 110.02/15.30 | DELTA: instantiating (10) with fresh symbols all_73_0, all_73_1, all_73_2
% 110.02/15.30 | gives:
% 110.02/15.30 | (22) sdtlpdtrp0(xN, xi) = all_73_2 & szmzizndt0(all_73_2) = all_73_1 &
% 110.02/15.30 | sbrdtbr0(all_73_0) = xK & sdtpldt0(xQ, all_73_1) = all_73_0 &
% 110.02/15.30 | $i(all_73_0) & $i(all_73_1) & $i(all_73_2) & aElementOf0(all_73_1,
% 110.02/15.30 | all_73_2) & aSet0(all_73_0) & ! [v0: any] : (v0 = all_73_1 | ~
% 110.02/15.30 | $i(v0) | ~ aElementOf0(v0, all_73_0) | aElementOf0(v0, xQ)) & !
% 110.02/15.30 | [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_73_0) | aElement0(v0))
% 110.02/15.30 | & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_73_2) |
% 110.02/15.30 | sdtlseqdt0(all_73_1, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 110.02/15.30 | aElementOf0(v0, xQ) | ~ aElement0(v0) | aElementOf0(v0, all_73_0))
% 110.02/15.30 | & ( ~ aElement0(all_73_1) | aElementOf0(all_73_1, all_73_0))
% 110.02/15.30 |
% 110.02/15.30 | ALPHA: (22) implies:
% 110.02/15.30 | (23) $i(all_73_2)
% 110.02/15.30 | (24) sdtpldt0(xQ, all_73_1) = all_73_0
% 110.02/15.30 | (25) szmzizndt0(all_73_2) = all_73_1
% 110.02/15.30 | (26) sdtlpdtrp0(xN, xi) = all_73_2
% 110.02/15.30 | (27) ! [v0: any] : (v0 = all_73_1 | ~ $i(v0) | ~ aElementOf0(v0,
% 110.02/15.30 | all_73_0) | aElementOf0(v0, xQ))
% 110.02/15.30 |
% 110.02/15.30 | DELTA: instantiating (15) with fresh symbols all_76_0, all_76_1, all_76_2,
% 110.02/15.30 | all_76_3 gives:
% 110.02/15.31 | (28) sdtlpdtrp0(xN, xi) = all_76_3 & szmzizndt0(all_76_3) = all_76_2 &
% 110.02/15.31 | sdtpldt0(xQ, all_76_2) = all_76_1 & $i(all_76_0) & $i(all_76_1) &
% 110.02/15.31 | $i(all_76_2) & $i(all_76_3) & aElementOf0(all_76_0, all_76_1) &
% 110.02/15.31 | aElementOf0(all_76_2, all_76_3) & aSet0(all_76_1) & ~
% 110.02/15.31 | aSubsetOf0(all_76_1, xS) & ~ aElementOf0(all_76_0, xS) & ! [v0: any]
% 110.02/15.31 | : (v0 = all_76_2 | ~ $i(v0) | ~ aElementOf0(v0, all_76_1) |
% 110.02/15.31 | aElementOf0(v0, xQ)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 110.02/15.31 | all_76_1) | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 110.02/15.31 | aElementOf0(v0, all_76_3) | sdtlseqdt0(all_76_2, v0)) & ! [v0: $i]
% 110.02/15.31 | : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0) |
% 110.02/15.31 | aElementOf0(v0, all_76_1)) & ( ~ aElement0(all_76_2) |
% 110.02/15.31 | aElementOf0(all_76_2, all_76_1))
% 110.02/15.31 |
% 110.02/15.31 | ALPHA: (28) implies:
% 110.02/15.31 | (29) ~ aElementOf0(all_76_0, xS)
% 110.02/15.31 | (30) aElementOf0(all_76_2, all_76_3)
% 110.02/15.31 | (31) aElementOf0(all_76_0, all_76_1)
% 110.02/15.31 | (32) $i(all_76_2)
% 110.02/15.31 | (33) $i(all_76_0)
% 110.02/15.31 | (34) sdtpldt0(xQ, all_76_2) = all_76_1
% 110.02/15.31 | (35) szmzizndt0(all_76_3) = all_76_2
% 110.02/15.31 | (36) sdtlpdtrp0(xN, xi) = all_76_3
% 110.02/15.31 |
% 110.02/15.31 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2,
% 110.02/15.31 | all_79_3 gives:
% 110.13/15.31 | (37) sdtlpdtrp0(xN, xi) = all_79_3 & slbdtsldtrb0(all_79_1, xk) = all_79_0
% 110.13/15.31 | & szmzizndt0(all_79_3) = all_79_2 & sbrdtbr0(xQ) = xk &
% 110.13/15.31 | sdtmndt0(all_79_3, all_79_2) = all_79_1 & $i(all_79_0) & $i(all_79_1)
% 110.13/15.31 | & $i(all_79_2) & $i(all_79_3) & aSubsetOf0(xQ, all_79_1) &
% 110.13/15.31 | aElementOf0(all_79_2, all_79_3) & aElementOf0(xQ, all_79_0) &
% 110.13/15.31 | aSet0(all_79_1) & aSet0(xQ) & ~ aElementOf0(all_79_2, all_79_1) & !
% 110.13/15.31 | [v0: any] : (v0 = all_79_2 | ~ $i(v0) | ~ aElementOf0(v0, all_79_3)
% 110.13/15.31 | | ~ aElement0(v0) | aElementOf0(v0, all_79_1)) & ! [v0: $i] : ( ~
% 110.13/15.31 | $i(v0) | ~ aElementOf0(v0, all_79_1) | aElementOf0(v0, all_79_3)) &
% 110.13/15.31 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_79_1) |
% 110.13/15.31 | aElement0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0,
% 110.13/15.31 | all_79_3) | sdtlseqdt0(all_79_2, v0)) & ! [v0: $i] : ( ~ $i(v0) |
% 110.13/15.31 | ~ aElementOf0(v0, xQ) | aElementOf0(v0, all_79_1))
% 110.13/15.31 |
% 110.13/15.31 | ALPHA: (37) implies:
% 110.13/15.31 | (38) aSet0(all_79_1)
% 110.13/15.31 | (39) aSubsetOf0(xQ, all_79_1)
% 110.13/15.31 | (40) $i(all_79_1)
% 110.13/15.31 | (41) szmzizndt0(all_79_3) = all_79_2
% 110.13/15.31 | (42) sdtlpdtrp0(xN, xi) = all_79_3
% 110.13/15.31 | (43) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_79_1) |
% 110.13/15.31 | aElementOf0(v0, all_79_3))
% 110.13/15.31 |
% 110.13/15.31 | GROUND_INST: instantiating (17) with all_73_0, all_76_1, all_73_1, xQ,
% 110.13/15.31 | simplifying with (24) gives:
% 110.13/15.31 | (44) all_76_1 = all_73_0 | ~ (sdtpldt0(xQ, all_73_1) = all_76_1)
% 110.13/15.31 |
% 110.13/15.31 | GROUND_INST: instantiating (16) with all_76_2, all_79_2, all_76_3, simplifying
% 110.13/15.31 | with (35) gives:
% 110.13/15.31 | (45) all_79_2 = all_76_2 | ~ (szmzizndt0(all_76_3) = all_79_2)
% 110.13/15.31 |
% 110.13/15.31 | GROUND_INST: instantiating (16) with all_73_1, all_79_2, all_73_2, simplifying
% 110.13/15.31 | with (25) gives:
% 110.13/15.31 | (46) all_79_2 = all_73_1 | ~ (szmzizndt0(all_73_2) = all_79_2)
% 110.13/15.31 |
% 110.13/15.31 | GROUND_INST: instantiating (18) with all_73_2, all_76_3, xi, xN, simplifying
% 110.13/15.31 | with (26), (36) gives:
% 110.13/15.31 | (47) all_76_3 = all_73_2
% 110.13/15.31 |
% 110.13/15.31 | GROUND_INST: instantiating (18) with all_76_3, all_79_3, xi, xN, simplifying
% 110.13/15.31 | with (36), (42) gives:
% 110.13/15.31 | (48) all_79_3 = all_76_3
% 110.13/15.31 |
% 110.13/15.32 | GROUND_INST: instantiating (18) with all_70_0, all_79_3, xi, xN, simplifying
% 110.13/15.32 | with (21), (42) gives:
% 110.13/15.32 | (49) all_79_3 = all_70_0
% 110.13/15.32 |
% 110.13/15.32 | COMBINE_EQS: (48), (49) imply:
% 110.13/15.32 | (50) all_76_3 = all_70_0
% 110.13/15.32 |
% 110.13/15.32 | SIMP: (50) implies:
% 110.13/15.32 | (51) all_76_3 = all_70_0
% 110.13/15.32 |
% 110.13/15.32 | COMBINE_EQS: (47), (51) imply:
% 110.13/15.32 | (52) all_73_2 = all_70_0
% 110.13/15.32 |
% 110.13/15.32 | REDUCE: (41), (49) imply:
% 110.13/15.32 | (53) szmzizndt0(all_70_0) = all_79_2
% 110.13/15.32 |
% 110.13/15.32 | REDUCE: (23), (52) imply:
% 110.13/15.32 | (54) $i(all_70_0)
% 110.13/15.32 |
% 110.13/15.32 | REDUCE: (30), (51) imply:
% 110.13/15.32 | (55) aElementOf0(all_76_2, all_70_0)
% 110.13/15.32 |
% 110.13/15.32 | BETA: splitting (46) gives:
% 110.13/15.32 |
% 110.13/15.32 | Case 1:
% 110.13/15.32 | |
% 110.13/15.32 | | (56) ~ (szmzizndt0(all_73_2) = all_79_2)
% 110.13/15.32 | |
% 110.13/15.32 | | REDUCE: (52), (56) imply:
% 110.13/15.32 | | (57) ~ (szmzizndt0(all_70_0) = all_79_2)
% 110.13/15.32 | |
% 110.13/15.32 | | PRED_UNIFY: (53), (57) imply:
% 110.17/15.32 | | (58) $false
% 110.17/15.32 | |
% 110.17/15.32 | | CLOSE: (58) is inconsistent.
% 110.17/15.32 | |
% 110.17/15.32 | Case 2:
% 110.17/15.32 | |
% 110.17/15.32 | | (59) all_79_2 = all_73_1
% 110.17/15.32 | |
% 110.17/15.32 | | REDUCE: (53), (59) imply:
% 110.17/15.32 | | (60) szmzizndt0(all_70_0) = all_73_1
% 110.17/15.32 | |
% 110.17/15.32 | | BETA: splitting (45) gives:
% 110.17/15.32 | |
% 110.17/15.32 | | Case 1:
% 110.17/15.32 | | |
% 110.17/15.32 | | | (61) ~ (szmzizndt0(all_76_3) = all_79_2)
% 110.17/15.32 | | |
% 110.17/15.32 | | | REDUCE: (51), (59), (61) imply:
% 110.17/15.32 | | | (62) ~ (szmzizndt0(all_70_0) = all_73_1)
% 110.17/15.32 | | |
% 110.17/15.32 | | | PRED_UNIFY: (60), (62) imply:
% 110.17/15.32 | | | (63) $false
% 110.17/15.32 | | |
% 110.17/15.32 | | | CLOSE: (63) is inconsistent.
% 110.17/15.32 | | |
% 110.17/15.32 | | Case 2:
% 110.17/15.32 | | |
% 110.17/15.32 | | | (64) all_79_2 = all_76_2
% 110.17/15.32 | | |
% 110.17/15.32 | | | COMBINE_EQS: (59), (64) imply:
% 110.17/15.32 | | | (65) all_76_2 = all_73_1
% 110.17/15.32 | | |
% 110.17/15.32 | | | SIMP: (65) implies:
% 110.17/15.32 | | | (66) all_76_2 = all_73_1
% 110.17/15.32 | | |
% 110.17/15.32 | | | REDUCE: (34), (66) imply:
% 110.17/15.32 | | | (67) sdtpldt0(xQ, all_73_1) = all_76_1
% 110.17/15.32 | | |
% 110.17/15.32 | | | REDUCE: (32), (66) imply:
% 110.17/15.32 | | | (68) $i(all_73_1)
% 110.17/15.32 | | |
% 110.17/15.32 | | | REDUCE: (55), (66) imply:
% 110.17/15.32 | | | (69) aElementOf0(all_73_1, all_70_0)
% 110.17/15.32 | | |
% 110.17/15.32 | | | BETA: splitting (44) gives:
% 110.17/15.32 | | |
% 110.17/15.32 | | | Case 1:
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | (70) ~ (sdtpldt0(xQ, all_73_1) = all_76_1)
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | PRED_UNIFY: (67), (70) imply:
% 110.17/15.32 | | | | (71) $false
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | CLOSE: (71) is inconsistent.
% 110.17/15.32 | | | |
% 110.17/15.32 | | | Case 2:
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | (72) all_76_1 = all_73_0
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | REDUCE: (31), (72) imply:
% 110.17/15.32 | | | | (73) aElementOf0(all_76_0, all_73_0)
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | GROUND_INST: instantiating (3) with xi, simplifying with (8), (13)
% 110.17/15.32 | | | | gives:
% 110.17/15.32 | | | | (74) sdtlseqdt0(sz00, xi)
% 110.17/15.32 | | | |
% 110.17/15.32 | | | | GROUND_INST: instantiating (27) with all_76_0, simplifying with (33),
% 110.17/15.32 | | | | (73) gives:
% 110.17/15.33 | | | | (75) all_76_0 = all_73_1 | aElementOf0(all_76_0, xQ)
% 110.17/15.33 | | | |
% 110.17/15.33 | | | | GROUND_INST: instantiating (43) with all_76_0, simplifying with (33)
% 110.17/15.33 | | | | gives:
% 110.17/15.33 | | | | (76) ~ aElementOf0(all_76_0, all_79_1) | aElementOf0(all_76_0,
% 110.17/15.33 | | | | all_79_3)
% 110.17/15.33 | | | |
% 110.17/15.33 | | | | GROUND_INST: instantiating (1) with all_79_1, xQ, all_76_0, simplifying
% 110.17/15.33 | | | | with (14), (33), (38), (39), (40) gives:
% 110.17/15.33 | | | | (77) ~ aElementOf0(all_76_0, xQ) | aElementOf0(all_76_0, all_79_1)
% 110.17/15.33 | | | |
% 110.17/15.33 | | | | GROUND_INST: instantiating (1) with xS, all_70_0, all_73_1, simplifying
% 110.17/15.33 | | | | with (4), (12), (20), (54), (68), (69) gives:
% 110.17/15.33 | | | | (78) aElementOf0(all_73_1, xS)
% 110.17/15.33 | | | |
% 110.17/15.33 | | | | PRED_UNIFY: (29), (78) imply:
% 110.17/15.33 | | | | (79) ~ (all_76_0 = all_73_1)
% 110.17/15.33 | | | |
% 110.17/15.33 | | | | BETA: splitting (75) gives:
% 110.17/15.33 | | | |
% 110.17/15.33 | | | | Case 1:
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | | (80) aElementOf0(all_76_0, xQ)
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | | BETA: splitting (77) gives:
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | | Case 1:
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | | (81) ~ aElementOf0(all_76_0, xQ)
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | | PRED_UNIFY: (80), (81) imply:
% 110.17/15.33 | | | | | | (82) $false
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | | CLOSE: (82) is inconsistent.
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | Case 2:
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | | (83) aElementOf0(all_76_0, all_79_1)
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | | BETA: splitting (76) gives:
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | | Case 1:
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | (84) ~ aElementOf0(all_76_0, all_79_1)
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | PRED_UNIFY: (83), (84) imply:
% 110.17/15.33 | | | | | | | (85) $false
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | CLOSE: (85) is inconsistent.
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | Case 2:
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | (86) aElementOf0(all_76_0, all_79_3)
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | REDUCE: (49), (86) imply:
% 110.17/15.33 | | | | | | | (87) aElementOf0(all_76_0, all_70_0)
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | GROUND_INST: instantiating (7) with xi, sz00, all_70_0, xS,
% 110.17/15.33 | | | | | | | all_76_0, simplifying with (2), (5), (6), (8), (13),
% 110.17/15.33 | | | | | | | (21), (29), (33), (74), (87) gives:
% 110.17/15.33 | | | | | | | (88) $false
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | | CLOSE: (88) is inconsistent.
% 110.17/15.33 | | | | | | |
% 110.17/15.33 | | | | | | End of split
% 110.17/15.33 | | | | | |
% 110.17/15.33 | | | | | End of split
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | Case 2:
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | | (89) all_76_0 = all_73_1
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | | REDUCE: (79), (89) imply:
% 110.17/15.33 | | | | | (90) $false
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | | CLOSE: (90) is inconsistent.
% 110.17/15.33 | | | | |
% 110.17/15.33 | | | | End of split
% 110.17/15.33 | | | |
% 110.17/15.33 | | | End of split
% 110.17/15.33 | | |
% 110.17/15.33 | | End of split
% 110.17/15.33 | |
% 110.17/15.33 | End of split
% 110.17/15.33 |
% 110.17/15.33 End of proof
% 110.17/15.33 % SZS output end Proof for theBenchmark
% 110.17/15.33
% 110.17/15.33 14737ms
%------------------------------------------------------------------------------