TSTP Solution File: ALG070+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG070+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n026.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 : Wed Aug 30 16:36:12 EDT 2023
% Result : Theorem 8.60s 2.01s
% Output : Proof 15.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG070+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 02:55:04 EDT 2023
% 0.14/0.35 % 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 2.16/1.03 Prover 4: Preprocessing ...
% 2.16/1.03 Prover 1: Preprocessing ...
% 2.53/1.07 Prover 5: Preprocessing ...
% 2.53/1.07 Prover 0: Preprocessing ...
% 2.53/1.07 Prover 2: Preprocessing ...
% 2.53/1.07 Prover 3: Preprocessing ...
% 2.53/1.07 Prover 6: Preprocessing ...
% 4.78/1.46 Prover 3: Constructing countermodel ...
% 4.78/1.46 Prover 6: Proving ...
% 4.78/1.47 Prover 1: Constructing countermodel ...
% 4.78/1.48 Prover 5: Constructing countermodel ...
% 4.78/1.50 Prover 2: Proving ...
% 5.49/1.60 Prover 4: Constructing countermodel ...
% 5.49/1.61 Prover 0: Proving ...
% 5.49/1.63 Prover 3: gave up
% 5.49/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.49/1.66 Prover 1: gave up
% 5.49/1.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.49/1.68 Prover 7: Preprocessing ...
% 5.49/1.69 Prover 8: Preprocessing ...
% 6.26/1.79 Prover 8: Warning: ignoring some quantifiers
% 6.26/1.79 Prover 8: Constructing countermodel ...
% 7.14/1.82 Prover 7: Constructing countermodel ...
% 7.14/1.85 Prover 7: gave up
% 7.14/1.85 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.14/1.88 Prover 9: Preprocessing ...
% 8.60/2.01 Prover 5: proved (1357ms)
% 8.60/2.01
% 8.60/2.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.60/2.01
% 8.60/2.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.60/2.01 Prover 0: stopped
% 8.60/2.01 Prover 2: stopped
% 8.60/2.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.60/2.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.60/2.01 Prover 6: stopped
% 8.60/2.03 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.60/2.05 Prover 11: Preprocessing ...
% 8.60/2.05 Prover 10: Preprocessing ...
% 8.60/2.05 Prover 16: Preprocessing ...
% 8.60/2.05 Prover 13: Preprocessing ...
% 8.60/2.06 Prover 9: Constructing countermodel ...
% 8.60/2.06 Prover 9: stopped
% 8.60/2.07 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.60/2.09 Prover 19: Preprocessing ...
% 9.31/2.10 Prover 16: Constructing countermodel ...
% 9.31/2.10 Prover 10: Constructing countermodel ...
% 9.31/2.12 Prover 10: gave up
% 9.31/2.14 Prover 13: Constructing countermodel ...
% 9.31/2.17 Prover 11: Constructing countermodel ...
% 9.31/2.19 Prover 19: Warning: ignoring some quantifiers
% 10.00/2.19 Prover 19: Constructing countermodel ...
% 14.22/2.80 Prover 19: gave up
% 14.22/2.84 Prover 13: Found proof (size 103)
% 14.22/2.84 Prover 13: proved (828ms)
% 14.22/2.84 Prover 16: stopped
% 14.22/2.84 Prover 11: stopped
% 14.22/2.84 Prover 8: stopped
% 14.22/2.84 Prover 4: stopped
% 14.22/2.84
% 14.22/2.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.22/2.84
% 14.90/2.86 % SZS output start Proof for theBenchmark
% 14.90/2.86 Assumptions after simplification:
% 14.90/2.86 ---------------------------------
% 14.90/2.86
% 14.90/2.86 (ax2)
% 15.06/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (op2(v0, v1) = v2) | ~ $i(v1) |
% 15.06/2.89 ~ $i(v0) | ~ sorti2(v1) | ~ sorti2(v0) | sorti2(v2)) & ! [v0: $i] : !
% 15.06/2.89 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sorti2(v1) | ~ sorti2(v0) | ? [v2:
% 15.06/2.89 $i] : (op2(v0, v1) = v2 & $i(v2) & sorti2(v2)))
% 15.06/2.89
% 15.06/2.89 (ax3)
% 15.06/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (op1(v0, v1) = v2) |
% 15.06/2.89 ~ (op1(v0, v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ sorti1(v1) | ~
% 15.06/2.89 sorti1(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] :
% 15.06/2.89 (op1(v0, v0) = v1 & $i(v1) & ( ~ sorti1(v1) | op1(v0, v1) = v0)))
% 15.06/2.89
% 15.06/2.89 (ax4)
% 15.06/2.90 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & op2(v0, v1) = v2 &
% 15.06/2.90 op2(v0, v0) = v1 & $i(v2) & $i(v1) & $i(v0) & sorti2(v1) & sorti2(v0))
% 15.06/2.90
% 15.06/2.90 (co1)
% 15.06/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 15.06/2.90 (j(v2) = v3) | ~ (j(v0) = v1) | ~ (op1(v1, v3) = v4) | ~ $i(v2) | ~
% 15.06/2.90 $i(v0) | ~ sorti2(v2) | ~ sorti2(v0) | ? [v5: $i] : (j(v5) = v4 & op2(v0,
% 15.06/2.90 v2) = v5 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.06/2.90 ! [v3: $i] : ! [v4: $i] : ( ~ (h(v2) = v3) | ~ (h(v0) = v1) | ~ (op2(v1,
% 15.06/2.90 v3) = v4) | ~ $i(v2) | ~ $i(v0) | ~ sorti1(v2) | ~ sorti1(v0) | ?
% 15.06/2.90 [v5: $i] : (h(v5) = v4 & op1(v0, v2) = v5 & $i(v5) & $i(v4))) & ! [v0: $i]
% 15.06/2.90 : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ~ sorti2(v0) | h(v1) = v0) &
% 15.06/2.90 ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ~ sorti2(v0) |
% 15.06/2.91 sorti1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~ $i(v0) | ~
% 15.06/2.91 sorti1(v0) | j(v1) = v0) & ! [v0: $i] : ! [v1: $i] : ( ~ (h(v0) = v1) | ~
% 15.06/2.91 $i(v0) | ~ sorti1(v0) | sorti2(v1)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.06/2.91 sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & h(v1) = v0 & $i(v1))) & ! [v0: $i]
% 15.06/2.91 : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 & $i(v1) &
% 15.06/2.91 sorti1(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] :
% 15.06/2.91 (j(v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti2(v2) | ? [v3:
% 15.06/2.91 $i] : ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0,
% 15.06/2.91 v2) = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3))))) & ! [v0:
% 15.06/2.91 $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : (j(v1) = v0 & h(v0) = v1 &
% 15.06/2.91 $i(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : (h(v0)
% 15.06/2.91 = v1 & $i(v1) & sorti2(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) |
% 15.06/2.91 ? [v1: $i] : (h(v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti1(v2)
% 15.06/2.91 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (h(v3) = v4 & h(v2) = v5 &
% 15.06/2.91 op2(v1, v5) = v4 & op1(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v3)))))
% 15.06/2.91
% 15.06/2.91 (function-axioms)
% 15.06/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op2(v3,
% 15.06/2.91 v2) = v1) | ~ (op2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.06/2.91 $i] : ! [v3: $i] : (v1 = v0 | ~ (op1(v3, v2) = v1) | ~ (op1(v3, v2) =
% 15.06/2.91 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) =
% 15.06/2.91 v1) | ~ (j(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 15.06/2.91 v0 | ~ (h(v2) = v1) | ~ (h(v2) = v0))
% 15.06/2.91
% 15.06/2.91 Further assumptions not needed in the proof:
% 15.06/2.91 --------------------------------------------
% 15.06/2.91 ax1
% 15.06/2.91
% 15.06/2.91 Those formulas are unsatisfiable:
% 15.06/2.91 ---------------------------------
% 15.06/2.91
% 15.06/2.91 Begin of proof
% 15.06/2.91 |
% 15.06/2.91 | ALPHA: (ax2) implies:
% 15.06/2.91 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ sorti2(v1) | ~
% 15.06/2.91 | sorti2(v0) | ? [v2: $i] : (op2(v0, v1) = v2 & $i(v2) & sorti2(v2)))
% 15.06/2.91 |
% 15.06/2.91 | ALPHA: (ax3) implies:
% 15.06/2.91 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (op1(v0, v1) =
% 15.06/2.91 | v2) | ~ (op1(v0, v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ sorti1(v1)
% 15.06/2.91 | | ~ sorti1(v0))
% 15.06/2.91 |
% 15.06/2.91 | ALPHA: (co1) implies:
% 15.06/2.91 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : (h(v0) = v1 &
% 15.06/2.91 | $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti1(v2) | ? [v3: $i] :
% 15.06/2.91 | ? [v4: $i] : ? [v5: $i] : (h(v3) = v4 & h(v2) = v5 & op2(v1, v5)
% 15.06/2.91 | = v4 & op1(v0, v2) = v3 & $i(v5) & $i(v4) & $i(v3)))))
% 15.06/2.91 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 &
% 15.06/2.91 | $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ sorti2(v2) | ? [v3: $i] :
% 15.06/2.91 | ? [v4: $i] : ? [v5: $i] : (j(v3) = v4 & j(v2) = v5 & op2(v0, v2)
% 15.06/2.91 | = v3 & op1(v1, v5) = v4 & $i(v5) & $i(v4) & $i(v3)))))
% 15.06/2.91 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 &
% 15.06/2.91 | $i(v1) & sorti1(v1)))
% 15.06/2.91 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : (j(v0) = v1 &
% 15.06/2.91 | h(v1) = v0 & $i(v1)))
% 15.06/2.92 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (j(v0) = v1) | ~ $i(v0) | ~
% 15.06/2.92 | sorti2(v0) | h(v1) = v0)
% 15.06/2.92 |
% 15.06/2.92 | ALPHA: (function-axioms) implies:
% 15.06/2.92 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (h(v2) = v1) |
% 15.06/2.92 | ~ (h(v2) = v0))
% 15.06/2.92 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (j(v2) = v1) |
% 15.06/2.92 | ~ (j(v2) = v0))
% 15.06/2.92 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.06/2.92 | (op2(v3, v2) = v1) | ~ (op2(v3, v2) = v0))
% 15.06/2.92 |
% 15.06/2.92 | DELTA: instantiating (ax4) with fresh symbols all_7_0, all_7_1, all_7_2 gives:
% 15.06/2.92 | (11) ~ (all_7_0 = all_7_2) & op2(all_7_2, all_7_1) = all_7_0 &
% 15.06/2.92 | op2(all_7_2, all_7_2) = all_7_1 & $i(all_7_0) & $i(all_7_1) &
% 15.06/2.92 | $i(all_7_2) & sorti2(all_7_1) & sorti2(all_7_2)
% 15.06/2.92 |
% 15.06/2.92 | ALPHA: (11) implies:
% 15.06/2.92 | (12) ~ (all_7_0 = all_7_2)
% 15.06/2.92 | (13) sorti2(all_7_2)
% 15.06/2.92 | (14) sorti2(all_7_1)
% 15.06/2.92 | (15) $i(all_7_2)
% 15.06/2.92 | (16) $i(all_7_1)
% 15.06/2.92 | (17) op2(all_7_2, all_7_2) = all_7_1
% 15.06/2.92 | (18) op2(all_7_2, all_7_1) = all_7_0
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (6) with all_7_2, simplifying with (13), (15)
% 15.06/2.92 | gives:
% 15.06/2.92 | (19) ? [v0: $i] : (j(all_7_2) = v0 & h(v0) = all_7_2 & $i(v0))
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (5) with all_7_2, simplifying with (13), (15)
% 15.06/2.92 | gives:
% 15.06/2.92 | (20) ? [v0: $i] : (j(all_7_2) = v0 & $i(v0) & sorti1(v0))
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (4) with all_7_2, simplifying with (13), (15)
% 15.06/2.92 | gives:
% 15.06/2.92 | (21) ? [v0: $i] : (j(all_7_2) = v0 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) |
% 15.06/2.92 | ~ sorti2(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) =
% 15.06/2.92 | v3 & j(v1) = v4 & op2(all_7_2, v1) = v2 & op1(v0, v4) = v3 &
% 15.06/2.92 | $i(v4) & $i(v3) & $i(v2))))
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (1) with all_7_2, all_7_1, simplifying with (13),
% 15.06/2.92 | (14), (15), (16) gives:
% 15.06/2.92 | (22) ? [v0: $i] : (op2(all_7_2, all_7_1) = v0 & $i(v0) & sorti2(v0))
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (6) with all_7_1, simplifying with (14), (16)
% 15.06/2.92 | gives:
% 15.06/2.92 | (23) ? [v0: $i] : (j(all_7_1) = v0 & h(v0) = all_7_1 & $i(v0))
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (5) with all_7_1, simplifying with (14), (16)
% 15.06/2.92 | gives:
% 15.06/2.92 | (24) ? [v0: $i] : (j(all_7_1) = v0 & $i(v0) & sorti1(v0))
% 15.06/2.92 |
% 15.06/2.92 | GROUND_INST: instantiating (4) with all_7_1, simplifying with (14), (16)
% 15.06/2.92 | gives:
% 15.06/2.92 | (25) ? [v0: $i] : (j(all_7_1) = v0 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) |
% 15.06/2.92 | ~ sorti2(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (j(v2) =
% 15.06/2.92 | v3 & j(v1) = v4 & op2(all_7_1, v1) = v2 & op1(v0, v4) = v3 &
% 15.06/2.92 | $i(v4) & $i(v3) & $i(v2))))
% 15.06/2.92 |
% 15.06/2.92 | DELTA: instantiating (24) with fresh symbol all_15_0 gives:
% 15.06/2.92 | (26) j(all_7_1) = all_15_0 & $i(all_15_0) & sorti1(all_15_0)
% 15.06/2.92 |
% 15.06/2.93 | ALPHA: (26) implies:
% 15.06/2.93 | (27) sorti1(all_15_0)
% 15.06/2.93 | (28) j(all_7_1) = all_15_0
% 15.06/2.93 |
% 15.06/2.93 | DELTA: instantiating (23) with fresh symbol all_17_0 gives:
% 15.06/2.93 | (29) j(all_7_1) = all_17_0 & h(all_17_0) = all_7_1 & $i(all_17_0)
% 15.06/2.93 |
% 15.06/2.93 | ALPHA: (29) implies:
% 15.06/2.93 | (30) j(all_7_1) = all_17_0
% 15.06/2.93 |
% 15.06/2.93 | DELTA: instantiating (20) with fresh symbol all_23_0 gives:
% 15.06/2.93 | (31) j(all_7_2) = all_23_0 & $i(all_23_0) & sorti1(all_23_0)
% 15.06/2.93 |
% 15.06/2.93 | ALPHA: (31) implies:
% 15.06/2.93 | (32) sorti1(all_23_0)
% 15.06/2.93 | (33) j(all_7_2) = all_23_0
% 15.06/2.93 |
% 15.06/2.93 | DELTA: instantiating (19) with fresh symbol all_25_0 gives:
% 15.06/2.93 | (34) j(all_7_2) = all_25_0 & h(all_25_0) = all_7_2 & $i(all_25_0)
% 15.06/2.93 |
% 15.06/2.93 | ALPHA: (34) implies:
% 15.06/2.93 | (35) $i(all_25_0)
% 15.06/2.93 | (36) h(all_25_0) = all_7_2
% 15.06/2.93 | (37) j(all_7_2) = all_25_0
% 15.06/2.93 |
% 15.06/2.93 | DELTA: instantiating (22) with fresh symbol all_27_0 gives:
% 15.06/2.93 | (38) op2(all_7_2, all_7_1) = all_27_0 & $i(all_27_0) & sorti2(all_27_0)
% 15.06/2.93 |
% 15.06/2.93 | ALPHA: (38) implies:
% 15.06/2.93 | (39) sorti2(all_27_0)
% 15.06/2.93 | (40) $i(all_27_0)
% 15.06/2.93 | (41) op2(all_7_2, all_7_1) = all_27_0
% 15.06/2.93 |
% 15.06/2.93 | DELTA: instantiating (25) with fresh symbol all_29_0 gives:
% 15.06/2.93 | (42) j(all_7_1) = all_29_0 & $i(all_29_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.06/2.93 | sorti2(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 &
% 15.06/2.93 | j(v0) = v3 & op2(all_7_1, v0) = v1 & op1(all_29_0, v3) = v2 &
% 15.06/2.93 | $i(v3) & $i(v2) & $i(v1)))
% 15.25/2.93 |
% 15.25/2.93 | ALPHA: (42) implies:
% 15.25/2.93 | (43) j(all_7_1) = all_29_0
% 15.25/2.93 | (44) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : ? [v2: $i] :
% 15.25/2.93 | ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_7_1, v0) = v1 &
% 15.25/2.93 | op1(all_29_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1)))
% 15.25/2.93 |
% 15.25/2.93 | GROUND_INST: instantiating (44) with all_7_2, simplifying with (13), (15)
% 15.25/2.93 | gives:
% 15.25/2.93 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_2) =
% 15.25/2.93 | v2 & op2(all_7_1, all_7_2) = v0 & op1(all_29_0, v2) = v1 & $i(v2) &
% 15.25/2.93 | $i(v1) & $i(v0))
% 15.25/2.93 |
% 15.25/2.93 | GROUND_INST: instantiating (44) with all_7_1, simplifying with (14), (16)
% 15.25/2.93 | gives:
% 15.25/2.93 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_1) =
% 15.25/2.93 | v2 & op2(all_7_1, all_7_1) = v0 & op1(all_29_0, v2) = v1 & $i(v2) &
% 15.25/2.93 | $i(v1) & $i(v0))
% 15.25/2.93 |
% 15.25/2.93 | DELTA: instantiating (21) with fresh symbol all_32_0 gives:
% 15.25/2.93 | (47) j(all_7_2) = all_32_0 & $i(all_32_0) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.25/2.93 | sorti2(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (j(v1) = v2 &
% 15.25/2.93 | j(v0) = v3 & op2(all_7_2, v0) = v1 & op1(all_32_0, v3) = v2 &
% 15.25/2.93 | $i(v3) & $i(v2) & $i(v1)))
% 15.25/2.93 |
% 15.25/2.93 | ALPHA: (47) implies:
% 15.25/2.93 | (48) j(all_7_2) = all_32_0
% 15.25/2.93 | (49) ! [v0: $i] : ( ~ $i(v0) | ~ sorti2(v0) | ? [v1: $i] : ? [v2: $i] :
% 15.25/2.93 | ? [v3: $i] : (j(v1) = v2 & j(v0) = v3 & op2(all_7_2, v0) = v1 &
% 15.25/2.93 | op1(all_32_0, v3) = v2 & $i(v3) & $i(v2) & $i(v1)))
% 15.25/2.93 |
% 15.25/2.93 | GROUND_INST: instantiating (49) with all_7_2, simplifying with (13), (15)
% 15.25/2.93 | gives:
% 15.28/2.93 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_2) =
% 15.28/2.93 | v2 & op2(all_7_2, all_7_2) = v0 & op1(all_32_0, v2) = v1 & $i(v2) &
% 15.28/2.93 | $i(v1) & $i(v0))
% 15.28/2.93 |
% 15.28/2.93 | GROUND_INST: instantiating (49) with all_7_1, simplifying with (14), (16)
% 15.28/2.93 | gives:
% 15.28/2.94 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (j(v0) = v1 & j(all_7_1) =
% 15.28/2.94 | v2 & op2(all_7_2, all_7_1) = v0 & op1(all_32_0, v2) = v1 & $i(v2) &
% 15.28/2.94 | $i(v1) & $i(v0))
% 15.28/2.94 |
% 15.28/2.94 | DELTA: instantiating (46) with fresh symbols all_35_0, all_35_1, all_35_2
% 15.28/2.94 | gives:
% 15.28/2.94 | (52) j(all_35_2) = all_35_1 & j(all_7_1) = all_35_0 & op2(all_7_1, all_7_1)
% 15.28/2.94 | = all_35_2 & op1(all_29_0, all_35_0) = all_35_1 & $i(all_35_0) &
% 15.28/2.94 | $i(all_35_1) & $i(all_35_2)
% 15.28/2.94 |
% 15.28/2.94 | ALPHA: (52) implies:
% 15.28/2.94 | (53) j(all_7_1) = all_35_0
% 15.28/2.94 |
% 15.28/2.94 | DELTA: instantiating (45) with fresh symbols all_37_0, all_37_1, all_37_2
% 15.28/2.94 | gives:
% 15.28/2.94 | (54) j(all_37_2) = all_37_1 & j(all_7_2) = all_37_0 & op2(all_7_1, all_7_2)
% 15.28/2.94 | = all_37_2 & op1(all_29_0, all_37_0) = all_37_1 & $i(all_37_0) &
% 15.28/2.94 | $i(all_37_1) & $i(all_37_2)
% 15.28/2.94 |
% 15.28/2.94 | ALPHA: (54) implies:
% 15.28/2.94 | (55) j(all_7_2) = all_37_0
% 15.28/2.94 |
% 15.28/2.94 | DELTA: instantiating (51) with fresh symbols all_39_0, all_39_1, all_39_2
% 15.28/2.94 | gives:
% 15.28/2.94 | (56) j(all_39_2) = all_39_1 & j(all_7_1) = all_39_0 & op2(all_7_2, all_7_1)
% 15.28/2.94 | = all_39_2 & op1(all_32_0, all_39_0) = all_39_1 & $i(all_39_0) &
% 15.28/2.94 | $i(all_39_1) & $i(all_39_2)
% 15.28/2.94 |
% 15.28/2.94 | ALPHA: (56) implies:
% 15.28/2.94 | (57) op1(all_32_0, all_39_0) = all_39_1
% 15.28/2.94 | (58) op2(all_7_2, all_7_1) = all_39_2
% 15.28/2.94 | (59) j(all_7_1) = all_39_0
% 15.28/2.94 | (60) j(all_39_2) = all_39_1
% 15.28/2.94 |
% 15.28/2.94 | DELTA: instantiating (50) with fresh symbols all_41_0, all_41_1, all_41_2
% 15.28/2.94 | gives:
% 15.28/2.94 | (61) j(all_41_2) = all_41_1 & j(all_7_2) = all_41_0 & op2(all_7_2, all_7_2)
% 15.28/2.94 | = all_41_2 & op1(all_32_0, all_41_0) = all_41_1 & $i(all_41_0) &
% 15.28/2.94 | $i(all_41_1) & $i(all_41_2)
% 15.28/2.94 |
% 15.28/2.94 | ALPHA: (61) implies:
% 15.28/2.94 | (62) $i(all_41_1)
% 15.28/2.94 | (63) op1(all_32_0, all_41_0) = all_41_1
% 15.28/2.94 | (64) op2(all_7_2, all_7_2) = all_41_2
% 15.28/2.94 | (65) j(all_7_2) = all_41_0
% 15.28/2.94 | (66) j(all_41_2) = all_41_1
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (10) with all_7_1, all_41_2, all_7_2, all_7_2,
% 15.28/2.94 | simplifying with (17), (64) gives:
% 15.28/2.94 | (67) all_41_2 = all_7_1
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (10) with all_7_0, all_39_2, all_7_1, all_7_2,
% 15.28/2.94 | simplifying with (18), (58) gives:
% 15.28/2.94 | (68) all_39_2 = all_7_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (10) with all_27_0, all_39_2, all_7_1, all_7_2,
% 15.28/2.94 | simplifying with (41), (58) gives:
% 15.28/2.94 | (69) all_39_2 = all_27_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_32_0, all_37_0, all_7_2, simplifying
% 15.28/2.94 | with (48), (55) gives:
% 15.28/2.94 | (70) all_37_0 = all_32_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_23_0, all_37_0, all_7_2, simplifying
% 15.28/2.94 | with (33), (55) gives:
% 15.28/2.94 | (71) all_37_0 = all_23_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_37_0, all_41_0, all_7_2, simplifying
% 15.28/2.94 | with (55), (65) gives:
% 15.28/2.94 | (72) all_41_0 = all_37_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_25_0, all_41_0, all_7_2, simplifying
% 15.28/2.94 | with (37), (65) gives:
% 15.28/2.94 | (73) all_41_0 = all_25_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_15_0, all_29_0, all_7_1, simplifying
% 15.28/2.94 | with (28), (43) gives:
% 15.28/2.94 | (74) all_29_0 = all_15_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_29_0, all_35_0, all_7_1, simplifying
% 15.28/2.94 | with (43), (53) gives:
% 15.28/2.94 | (75) all_35_0 = all_29_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_35_0, all_39_0, all_7_1, simplifying
% 15.28/2.94 | with (53), (59) gives:
% 15.28/2.94 | (76) all_39_0 = all_35_0
% 15.28/2.94 |
% 15.28/2.94 | GROUND_INST: instantiating (9) with all_17_0, all_39_0, all_7_1, simplifying
% 15.28/2.94 | with (30), (59) gives:
% 15.28/2.94 | (77) all_39_0 = all_17_0
% 15.28/2.94 |
% 15.28/2.94 | COMBINE_EQS: (72), (73) imply:
% 15.28/2.94 | (78) all_37_0 = all_25_0
% 15.28/2.94 |
% 15.28/2.94 | SIMP: (78) implies:
% 15.28/2.94 | (79) all_37_0 = all_25_0
% 15.28/2.94 |
% 15.28/2.94 | COMBINE_EQS: (76), (77) imply:
% 15.28/2.94 | (80) all_35_0 = all_17_0
% 15.28/2.94 |
% 15.28/2.94 | SIMP: (80) implies:
% 15.28/2.94 | (81) all_35_0 = all_17_0
% 15.28/2.94 |
% 15.28/2.94 | COMBINE_EQS: (68), (69) imply:
% 15.28/2.94 | (82) all_27_0 = all_7_0
% 15.28/2.94 |
% 15.28/2.95 | SIMP: (82) implies:
% 15.28/2.95 | (83) all_27_0 = all_7_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (70), (79) imply:
% 15.28/2.95 | (84) all_32_0 = all_25_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (70), (71) imply:
% 15.28/2.95 | (85) all_32_0 = all_23_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (75), (81) imply:
% 15.28/2.95 | (86) all_29_0 = all_17_0
% 15.28/2.95 |
% 15.28/2.95 | SIMP: (86) implies:
% 15.28/2.95 | (87) all_29_0 = all_17_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (84), (85) imply:
% 15.28/2.95 | (88) all_25_0 = all_23_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (74), (87) imply:
% 15.28/2.95 | (89) all_17_0 = all_15_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (77), (89) imply:
% 15.28/2.95 | (90) all_39_0 = all_15_0
% 15.28/2.95 |
% 15.28/2.95 | COMBINE_EQS: (73), (88) imply:
% 15.28/2.95 | (91) all_41_0 = all_23_0
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (66), (67) imply:
% 15.28/2.95 | (92) j(all_7_1) = all_41_1
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (60), (68) imply:
% 15.28/2.95 | (93) j(all_7_0) = all_39_1
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (36), (88) imply:
% 15.28/2.95 | (94) h(all_23_0) = all_7_2
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (63), (85), (91) imply:
% 15.28/2.95 | (95) op1(all_23_0, all_23_0) = all_41_1
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (57), (85), (90) imply:
% 15.28/2.95 | (96) op1(all_23_0, all_15_0) = all_39_1
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (40), (83) imply:
% 15.28/2.95 | (97) $i(all_7_0)
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (35), (88) imply:
% 15.28/2.95 | (98) $i(all_23_0)
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (39), (83) imply:
% 15.28/2.95 | (99) sorti2(all_7_0)
% 15.28/2.95 |
% 15.28/2.95 | GROUND_INST: instantiating (9) with all_15_0, all_41_1, all_7_1, simplifying
% 15.28/2.95 | with (28), (92) gives:
% 15.28/2.95 | (100) all_41_1 = all_15_0
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (95), (100) imply:
% 15.28/2.95 | (101) op1(all_23_0, all_23_0) = all_15_0
% 15.28/2.95 |
% 15.28/2.95 | REDUCE: (62), (100) imply:
% 15.28/2.95 | (102) $i(all_15_0)
% 15.28/2.95 |
% 15.28/2.95 | GROUND_INST: instantiating (3) with all_15_0, simplifying with (27), (102)
% 15.28/2.95 | gives:
% 15.28/2.95 | (103) ? [v0: $i] : (h(all_15_0) = v0 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) |
% 15.28/2.95 | ~ sorti1(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (h(v2)
% 15.28/2.95 | = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_15_0, v1) = v2 &
% 15.28/2.95 | $i(v4) & $i(v3) & $i(v2))))
% 15.28/2.95 |
% 15.28/2.95 | GROUND_INST: instantiating (3) with all_23_0, simplifying with (32), (98)
% 15.28/2.95 | gives:
% 15.28/2.95 | (104) ? [v0: $i] : (h(all_23_0) = v0 & $i(v0) & ! [v1: $i] : ( ~ $i(v1) |
% 15.28/2.95 | ~ sorti1(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (h(v2)
% 15.28/2.95 | = v3 & h(v1) = v4 & op2(v0, v4) = v3 & op1(all_23_0, v1) = v2 &
% 15.28/2.95 | $i(v4) & $i(v3) & $i(v2))))
% 15.28/2.95 |
% 15.28/2.95 | GROUND_INST: instantiating (2) with all_23_0, all_15_0, all_39_1, simplifying
% 15.28/2.95 | with (27), (32), (96), (98), (101), (102) gives:
% 15.28/2.95 | (105) all_39_1 = all_23_0
% 15.28/2.95 |
% 15.28/2.95 | GROUND_INST: instantiating (7) with all_7_0, all_39_1, simplifying with (93),
% 15.28/2.95 | (97), (99) gives:
% 15.28/2.95 | (106) h(all_39_1) = all_7_0
% 15.28/2.95 |
% 15.28/2.95 | DELTA: instantiating (103) with fresh symbol all_142_0 gives:
% 15.28/2.95 | (107) h(all_15_0) = all_142_0 & $i(all_142_0) & ! [v0: $i] : ( ~ $i(v0) |
% 15.28/2.95 | ~ sorti1(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (h(v1) =
% 15.28/2.95 | v2 & h(v0) = v3 & op2(all_142_0, v3) = v2 & op1(all_15_0, v0) =
% 15.28/2.95 | v1 & $i(v3) & $i(v2) & $i(v1)))
% 15.28/2.95 |
% 15.28/2.95 | ALPHA: (107) implies:
% 15.28/2.96 | (108) ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : ? [v2: $i]
% 15.28/2.96 | : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_142_0, v3) = v2
% 15.28/2.96 | & op1(all_15_0, v0) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 15.28/2.96 |
% 15.28/2.96 | GROUND_INST: instantiating (108) with all_23_0, simplifying with (32), (98)
% 15.28/2.96 | gives:
% 15.28/2.96 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & h(all_23_0) =
% 15.28/2.96 | v2 & op2(all_142_0, v2) = v1 & op1(all_15_0, all_23_0) = v0 &
% 15.28/2.96 | $i(v2) & $i(v1) & $i(v0))
% 15.28/2.96 |
% 15.28/2.96 | DELTA: instantiating (104) with fresh symbol all_145_0 gives:
% 15.28/2.96 | (110) h(all_23_0) = all_145_0 & $i(all_145_0) & ! [v0: $i] : ( ~ $i(v0) |
% 15.28/2.96 | ~ sorti1(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (h(v1) =
% 15.28/2.96 | v2 & h(v0) = v3 & op2(all_145_0, v3) = v2 & op1(all_23_0, v0) =
% 15.28/2.96 | v1 & $i(v3) & $i(v2) & $i(v1)))
% 15.28/2.96 |
% 15.28/2.96 | ALPHA: (110) implies:
% 15.28/2.96 | (111) h(all_23_0) = all_145_0
% 15.28/2.96 | (112) ! [v0: $i] : ( ~ $i(v0) | ~ sorti1(v0) | ? [v1: $i] : ? [v2: $i]
% 15.28/2.96 | : ? [v3: $i] : (h(v1) = v2 & h(v0) = v3 & op2(all_145_0, v3) = v2
% 15.28/2.96 | & op1(all_23_0, v0) = v1 & $i(v3) & $i(v2) & $i(v1)))
% 15.28/2.96 |
% 15.28/2.96 | GROUND_INST: instantiating (112) with all_23_0, simplifying with (32), (98)
% 15.28/2.96 | gives:
% 15.28/2.96 | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (h(v0) = v1 & h(all_23_0) =
% 15.28/2.96 | v2 & op2(all_145_0, v2) = v1 & op1(all_23_0, all_23_0) = v0 &
% 15.28/2.96 | $i(v2) & $i(v1) & $i(v0))
% 15.28/2.96 |
% 15.28/2.96 | DELTA: instantiating (109) with fresh symbols all_164_0, all_164_1, all_164_2
% 15.28/2.96 | gives:
% 15.28/2.96 | (114) h(all_164_2) = all_164_1 & h(all_23_0) = all_164_0 & op2(all_142_0,
% 15.28/2.96 | all_164_0) = all_164_1 & op1(all_15_0, all_23_0) = all_164_2 &
% 15.28/2.96 | $i(all_164_0) & $i(all_164_1) & $i(all_164_2)
% 15.28/2.96 |
% 15.28/2.96 | ALPHA: (114) implies:
% 15.28/2.96 | (115) h(all_23_0) = all_164_0
% 15.28/2.96 |
% 15.28/2.96 | DELTA: instantiating (113) with fresh symbols all_168_0, all_168_1, all_168_2
% 15.28/2.96 | gives:
% 15.28/2.96 | (116) h(all_168_2) = all_168_1 & h(all_23_0) = all_168_0 & op2(all_145_0,
% 15.28/2.96 | all_168_0) = all_168_1 & op1(all_23_0, all_23_0) = all_168_2 &
% 15.28/2.96 | $i(all_168_0) & $i(all_168_1) & $i(all_168_2)
% 15.28/2.96 |
% 15.28/2.96 | ALPHA: (116) implies:
% 15.28/2.96 | (117) h(all_23_0) = all_168_0
% 15.28/2.96 |
% 15.28/2.96 | REDUCE: (105), (106) imply:
% 15.28/2.96 | (118) h(all_23_0) = all_7_0
% 15.28/2.96 |
% 15.28/2.96 | GROUND_INST: instantiating (8) with all_7_2, all_164_0, all_23_0, simplifying
% 15.28/2.96 | with (94), (115) gives:
% 15.28/2.96 | (119) all_164_0 = all_7_2
% 15.28/2.96 |
% 15.28/2.96 | GROUND_INST: instantiating (8) with all_7_0, all_164_0, all_23_0, simplifying
% 15.28/2.96 | with (115), (118) gives:
% 15.28/2.96 | (120) all_164_0 = all_7_0
% 15.28/2.96 |
% 15.28/2.96 | GROUND_INST: instantiating (8) with all_164_0, all_168_0, all_23_0,
% 15.28/2.96 | simplifying with (115), (117) gives:
% 15.28/2.96 | (121) all_168_0 = all_164_0
% 15.28/2.96 |
% 15.28/2.96 | GROUND_INST: instantiating (8) with all_145_0, all_168_0, all_23_0,
% 15.28/2.96 | simplifying with (111), (117) gives:
% 15.28/2.96 | (122) all_168_0 = all_145_0
% 15.28/2.96 |
% 15.28/2.96 | COMBINE_EQS: (121), (122) imply:
% 15.28/2.96 | (123) all_164_0 = all_145_0
% 15.28/2.96 |
% 15.28/2.96 | SIMP: (123) implies:
% 15.28/2.96 | (124) all_164_0 = all_145_0
% 15.28/2.96 |
% 15.28/2.96 | COMBINE_EQS: (119), (124) imply:
% 15.28/2.96 | (125) all_145_0 = all_7_2
% 15.28/2.96 |
% 15.28/2.96 | COMBINE_EQS: (120), (124) imply:
% 15.28/2.96 | (126) all_145_0 = all_7_0
% 15.28/2.96 |
% 15.28/2.96 | COMBINE_EQS: (125), (126) imply:
% 15.28/2.96 | (127) all_7_0 = all_7_2
% 15.28/2.96 |
% 15.28/2.96 | REDUCE: (12), (127) imply:
% 15.28/2.96 | (128) $false
% 15.28/2.96 |
% 15.28/2.96 | CLOSE: (128) is inconsistent.
% 15.28/2.96 |
% 15.28/2.96 End of proof
% 15.28/2.96 % SZS output end Proof for theBenchmark
% 15.28/2.96
% 15.28/2.96 2344ms
%------------------------------------------------------------------------------