TSTP Solution File: HAL002+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n010.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 01:53:48 EDT 2023
% Result : Theorem 13.88s 2.64s
% Output : Proof 27.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 02:21:04 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.44/1.12 Prover 1: Preprocessing ...
% 2.44/1.12 Prover 4: Preprocessing ...
% 3.22/1.16 Prover 2: Preprocessing ...
% 3.22/1.16 Prover 0: Preprocessing ...
% 3.22/1.16 Prover 5: Preprocessing ...
% 3.22/1.16 Prover 3: Preprocessing ...
% 3.22/1.16 Prover 6: Preprocessing ...
% 6.39/1.68 Prover 6: Proving ...
% 6.39/1.69 Prover 1: Constructing countermodel ...
% 6.39/1.69 Prover 5: Proving ...
% 6.39/1.71 Prover 2: Proving ...
% 6.39/1.71 Prover 3: Constructing countermodel ...
% 8.51/1.92 Prover 3: gave up
% 8.89/1.93 Prover 4: Constructing countermodel ...
% 8.89/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.02/1.96 Prover 0: Proving ...
% 9.02/1.97 Prover 1: gave up
% 9.02/1.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.41/2.05 Prover 7: Preprocessing ...
% 9.76/2.07 Prover 8: Preprocessing ...
% 10.53/2.19 Prover 7: Constructing countermodel ...
% 10.53/2.20 Prover 8: Warning: ignoring some quantifiers
% 10.53/2.21 Prover 8: Constructing countermodel ...
% 11.03/2.25 Prover 7: gave up
% 11.03/2.25 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 11.03/2.33 Prover 9: Preprocessing ...
% 11.03/2.38 Prover 8: gave up
% 11.03/2.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.98/2.46 Prover 10: Preprocessing ...
% 12.71/2.54 Prover 10: Constructing countermodel ...
% 13.49/2.60 Prover 10: gave up
% 13.49/2.61 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.88/2.64 Prover 11: Preprocessing ...
% 13.88/2.64 Prover 0: proved (1989ms)
% 13.88/2.64
% 13.88/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.88/2.64
% 13.88/2.64 Prover 6: stopped
% 13.88/2.64 Prover 2: stopped
% 13.88/2.64 Prover 5: stopped
% 13.88/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.88/2.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 13.88/2.64 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 13.88/2.70 Prover 16: Preprocessing ...
% 13.88/2.70 Prover 19: Preprocessing ...
% 14.44/2.72 Prover 13: Preprocessing ...
% 14.44/2.74 Prover 9: Constructing countermodel ...
% 14.44/2.74 Prover 9: stopped
% 14.44/2.75 Prover 16: Warning: ignoring some quantifiers
% 14.44/2.75 Prover 16: Constructing countermodel ...
% 14.94/2.82 Prover 19: Warning: ignoring some quantifiers
% 14.94/2.83 Prover 19: Constructing countermodel ...
% 14.94/2.83 Prover 13: Warning: ignoring some quantifiers
% 14.94/2.84 Prover 13: Constructing countermodel ...
% 15.73/2.89 Prover 11: Constructing countermodel ...
% 16.63/3.06 Prover 19: gave up
% 26.23/4.39 Prover 13: Found proof (size 396)
% 26.23/4.39 Prover 13: proved (1751ms)
% 26.23/4.39 Prover 16: stopped
% 26.23/4.40 Prover 4: stopped
% 26.23/4.40 Prover 11: stopped
% 26.23/4.40
% 26.23/4.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.23/4.40
% 27.21/4.55 % SZS output start Proof for theBenchmark
% 27.21/4.55 Assumptions after simplification:
% 27.21/4.55 ---------------------------------
% 27.21/4.55
% 27.21/4.55 (injection_properties)
% 27.33/4.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.33/4.58 $i] : (v3 = v2 | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~
% 27.33/4.58 $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ injection(v0) |
% 27.33/4.58 ~ element(v3, v1) | ~ element(v2, v1) | ~ morphism(v0, v1, v5)) & ! [v0:
% 27.33/4.58 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v2 | ~
% 27.33/4.58 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ injection(v0) |
% 27.33/4.58 ~ element(v3, v1) | ~ element(v2, v1) | ~ morphism(v0, v1, v4) | ? [v5:
% 27.33/4.58 $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v3) = v6 & apply(v0, v2) =
% 27.33/4.58 v5 & $i(v6) & $i(v5)))
% 27.33/4.58
% 27.33/4.58 (injection_properties_2)
% 27.33/4.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.33/4.58 $i] : (v5 = v4 | ~ (zero(v2) = v3) | ~ (zero(v1) = v4) | ~ (apply(v0, v5)
% 27.33/4.58 = v3) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ injection_2(v0)
% 27.33/4.58 | ~ element(v5, v1) | ~ morphism(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i]
% 27.33/4.58 : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ injection_2(v0) | ~
% 27.33/4.58 morphism(v0, v1, v2) | ? [v3: $i] : ? [v4: $i] : (zero(v2) = v3 & zero(v1)
% 27.33/4.58 = v4 & $i(v4) & $i(v3) & ! [v5: $i] : (v5 = v4 | ~ $i(v5) | ~
% 27.33/4.58 element(v5, v1) | ? [v6: $i] : ( ~ (v6 = v3) & apply(v0, v5) = v6 &
% 27.33/4.58 $i(v6)))))
% 27.33/4.58
% 27.33/4.58 (morphism)
% 27.33/4.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.33/4.58 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (zero(v2) = v5) | ~ (zero(v1) = v3) |
% 27.33/4.58 ~ (apply(v0, v6) = v7) | ~ (apply(v0, v3) = v4) | ~ $i(v6) | ~ $i(v2) |
% 27.33/4.58 ~ $i(v1) | ~ $i(v0) | ~ element(v6, v1) | ~ morphism(v0, v1, v2) |
% 27.33/4.58 element(v7, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 27.33/4.58 ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (zero(v2) = v5) | ~ (zero(v1) = v3)
% 27.33/4.58 | ~ (apply(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.33/4.58 morphism(v0, v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 27.33/4.58 $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v3, v1) |
% 27.33/4.58 ~ morphism(v0, v1, v2) | ? [v4: $i] : (apply(v0, v3) = v4 & $i(v4) &
% 27.33/4.58 element(v4, v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) |
% 27.33/4.58 ~ $i(v1) | ~ $i(v0) | ~ morphism(v0, v1, v2) | ? [v3: $i] : ? [v4: $i]
% 27.33/4.58 : (zero(v2) = v4 & zero(v1) = v3 & apply(v0, v3) = v4 & $i(v4) & $i(v3)))
% 27.33/4.58
% 27.33/4.58 (my)
% 27.33/4.58 $i(x) & ((injection_2(x) & ~ injection(x)) | (injection(x) & ~
% 27.33/4.58 injection_2(x)))
% 27.33/4.58
% 27.33/4.58 (properties_for_injection)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.33/4.59 ~ morphism(v0, v1, v2) | injection(v0) | ? [v3: $i] : ? [v4: $i] : ?
% 27.33/4.59 [v5: $i] : ( ~ (v4 = v3) & apply(v0, v4) = v5 & apply(v0, v3) = v5 & $i(v5)
% 27.33/4.59 & $i(v4) & $i(v3) & element(v4, v1) & element(v3, v1)))
% 27.33/4.59
% 27.33/4.59 (properties_for_injection_2)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 27.33/4.59 (zero(v2) = v3) | ~ (zero(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.33/4.59 ~ morphism(v0, v1, v2) | injection_2(v0) | ? [v5: $i] : ( ~ (v5 = v4) &
% 27.33/4.59 apply(v0, v5) = v3 & $i(v5) & $i(v3) & element(v5, v1))) & ! [v0: $i] :
% 27.33/4.59 ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.33/4.59 morphism(v0, v1, v2) | injection_2(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 27.33/4.59 $i] : ( ~ (v5 = v4) & zero(v2) = v3 & zero(v1) = v4 & apply(v0, v5) = v3 &
% 27.33/4.59 $i(v5) & $i(v4) & $i(v3) & element(v5, v1)))
% 27.33/4.59
% 27.33/4.59 (subtract_cancellation)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v2
% 27.33/4.59 | ~ (subtract(v0, v1, v3) = v4) | ~ (subtract(v0, v1, v2) = v3) | ~
% 27.33/4.59 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v2, v0) | ~ element(v1, v0)) &
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.33/4.59 ~ element(v2, v0) | ~ element(v1, v0) | ? [v3: $i] : (subtract(v0, v1, v3)
% 27.33/4.59 = v2 & subtract(v0, v1, v2) = v3 & $i(v3)))
% 27.33/4.59
% 27.33/4.59 (subtract_distribution)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.33/4.59 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (subtract(v2, v5, v6) = v7) | ~
% 27.33/4.59 (apply(v0, v4) = v6) | ~ (apply(v0, v3) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 27.33/4.59 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v4, v1) | ~ element(v3, v1) |
% 27.33/4.59 ~ morphism(v0, v1, v2) | ? [v8: $i] : (subtract(v1, v3, v4) = v8 &
% 27.33/4.59 apply(v0, v8) = v7 & $i(v8) & $i(v7))) & ! [v0: $i] : ! [v1: $i] : !
% 27.33/4.59 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 27.33/4.59 $i(v1) | ~ $i(v0) | ~ element(v4, v1) | ~ element(v3, v1) | ~
% 27.33/4.59 morphism(v0, v1, v2) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 27.33/4.59 : (subtract(v2, v7, v8) = v6 & subtract(v1, v3, v4) = v5 & apply(v0, v5) =
% 27.33/4.59 v6 & apply(v0, v4) = v8 & apply(v0, v3) = v7 & $i(v8) & $i(v7) & $i(v6) &
% 27.33/4.59 $i(v5)))
% 27.33/4.59
% 27.33/4.59 (subtract_in_domain)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (subtract(v0, v1,
% 27.33/4.59 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v2, v0) | ~
% 27.33/4.59 element(v1, v0) | element(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 27.33/4.59 : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v2, v0) | ~ element(v1, v0)
% 27.33/4.59 | ? [v3: $i] : (subtract(v0, v1, v2) = v3 & $i(v3) & element(v3, v0)))
% 27.33/4.59
% 27.33/4.59 (subtract_to_0)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subtract(v0, v1, v1) = v2) | ~
% 27.33/4.59 $i(v1) | ~ $i(v0) | ~ element(v1, v0) | (zero(v0) = v2 & $i(v2))) & !
% 27.33/4.59 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v1, v0) | ? [v2:
% 27.33/4.59 $i] : (subtract(v0, v1, v1) = v2 & zero(v0) = v2 & $i(v2)))
% 27.33/4.59
% 27.33/4.59 (x_morphism)
% 27.33/4.59 $i(any2) & $i(any1) & $i(x) & morphism(x, any1, any2)
% 27.33/4.59
% 27.33/4.59 (function-axioms)
% 27.33/4.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 27.33/4.59 | ~ (subtract(v4, v3, v2) = v1) | ~ (subtract(v4, v3, v2) = v0)) & ! [v0:
% 27.33/4.59 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 27.33/4.59 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 27.33/4.59 : (v1 = v0 | ~ (zero(v2) = v1) | ~ (zero(v2) = v0))
% 27.33/4.59
% 27.33/4.59 Further assumptions not needed in the proof:
% 27.33/4.59 --------------------------------------------
% 27.33/4.59 commute_properties, exact_properties, properties_for_commute,
% 27.33/4.59 properties_for_exact, properties_for_surjection, surjection_properties
% 27.33/4.59
% 27.33/4.59 Those formulas are unsatisfiable:
% 27.33/4.59 ---------------------------------
% 27.33/4.59
% 27.33/4.59 Begin of proof
% 27.33/4.59 |
% 27.33/4.60 | ALPHA: (morphism) implies:
% 27.33/4.60 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 27.33/4.60 | $i(v0) | ~ morphism(v0, v1, v2) | ? [v3: $i] : ? [v4: $i] :
% 27.33/4.60 | (zero(v2) = v4 & zero(v1) = v3 & apply(v0, v3) = v4 & $i(v4) &
% 27.33/4.60 | $i(v3)))
% 27.33/4.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~
% 27.33/4.60 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v3, v1) | ~ morphism(v0,
% 27.33/4.60 | v1, v2) | ? [v4: $i] : (apply(v0, v3) = v4 & $i(v4) & element(v4,
% 27.33/4.60 | v2)))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (injection_properties) implies:
% 27.33/4.60 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.33/4.60 | ! [v5: $i] : (v3 = v2 | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) =
% 27.33/4.60 | v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.33/4.60 | ~ injection(v0) | ~ element(v3, v1) | ~ element(v2, v1) | ~
% 27.33/4.60 | morphism(v0, v1, v5))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (subtract_in_domain) implies:
% 27.33/4.60 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 27.33/4.60 | $i(v0) | ~ element(v2, v0) | ~ element(v1, v0) | ? [v3: $i] :
% 27.33/4.60 | (subtract(v0, v1, v2) = v3 & $i(v3) & element(v3, v0)))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (subtract_to_0) implies:
% 27.33/4.60 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v1, v0)
% 27.33/4.60 | | ? [v2: $i] : (subtract(v0, v1, v1) = v2 & zero(v0) = v2 & $i(v2)))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (subtract_cancellation) implies:
% 27.33/4.60 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 27.33/4.60 | $i(v0) | ~ element(v2, v0) | ~ element(v1, v0) | ? [v3: $i] :
% 27.33/4.60 | (subtract(v0, v1, v3) = v2 & subtract(v0, v1, v2) = v3 & $i(v3)))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (subtract_distribution) implies:
% 27.33/4.60 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 27.33/4.60 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.33/4.60 | element(v4, v1) | ~ element(v3, v1) | ~ morphism(v0, v1, v2) | ?
% 27.33/4.60 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (subtract(v2,
% 27.33/4.60 | v7, v8) = v6 & subtract(v1, v3, v4) = v5 & apply(v0, v5) = v6 &
% 27.33/4.60 | apply(v0, v4) = v8 & apply(v0, v3) = v7 & $i(v8) & $i(v7) & $i(v6)
% 27.33/4.60 | & $i(v5)))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (injection_properties_2) implies:
% 27.33/4.60 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 27.33/4.60 | $i(v0) | ~ injection_2(v0) | ~ morphism(v0, v1, v2) | ? [v3: $i] :
% 27.33/4.60 | ? [v4: $i] : (zero(v2) = v3 & zero(v1) = v4 & $i(v4) & $i(v3) & !
% 27.33/4.60 | [v5: $i] : (v5 = v4 | ~ $i(v5) | ~ element(v5, v1) | ? [v6: $i]
% 27.33/4.60 | : ( ~ (v6 = v3) & apply(v0, v5) = v6 & $i(v6)))))
% 27.33/4.60 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.33/4.60 | ! [v5: $i] : (v5 = v4 | ~ (zero(v2) = v3) | ~ (zero(v1) = v4) | ~
% 27.33/4.60 | (apply(v0, v5) = v3) | ~ $i(v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 27.33/4.60 | | ~ injection_2(v0) | ~ element(v5, v1) | ~ morphism(v0, v1, v2))
% 27.33/4.60 |
% 27.33/4.60 | ALPHA: (properties_for_injection_2) implies:
% 27.33/4.60 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 27.33/4.60 | $i(v0) | ~ morphism(v0, v1, v2) | injection_2(v0) | ? [v3: $i] :
% 27.33/4.60 | ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v4) & zero(v2) = v3 & zero(v1)
% 27.33/4.60 | = v4 & apply(v0, v5) = v3 & $i(v5) & $i(v4) & $i(v3) & element(v5,
% 27.33/4.61 | v1)))
% 27.33/4.61 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.33/4.61 | ( ~ (zero(v2) = v3) | ~ (zero(v1) = v4) | ~ $i(v2) | ~ $i(v1) | ~
% 27.33/4.61 | $i(v0) | ~ morphism(v0, v1, v2) | injection_2(v0) | ? [v5: $i] : (
% 27.33/4.61 | ~ (v5 = v4) & apply(v0, v5) = v3 & $i(v5) & $i(v3) & element(v5,
% 27.33/4.61 | v1)))
% 27.33/4.61 |
% 27.33/4.61 | ALPHA: (x_morphism) implies:
% 27.33/4.61 | (12) morphism(x, any1, any2)
% 27.33/4.61 | (13) $i(any1)
% 27.33/4.61 | (14) $i(any2)
% 27.33/4.61 |
% 27.33/4.61 | ALPHA: (my) implies:
% 27.33/4.61 | (15) $i(x)
% 27.33/4.61 | (16) (injection_2(x) & ~ injection(x)) | (injection(x) & ~
% 27.33/4.61 | injection_2(x))
% 27.33/4.61 |
% 27.33/4.61 | ALPHA: (function-axioms) implies:
% 27.33/4.61 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (zero(v2) =
% 27.33/4.61 | v1) | ~ (zero(v2) = v0))
% 27.33/4.61 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.33/4.61 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 27.33/4.61 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 27.33/4.61 | (v1 = v0 | ~ (subtract(v4, v3, v2) = v1) | ~ (subtract(v4, v3, v2) =
% 27.33/4.61 | v0))
% 27.33/4.61 |
% 27.33/4.61 | GROUND_INST: instantiating (10) with x, any1, any2, simplifying with (12),
% 27.33/4.61 | (13), (14), (15) gives:
% 27.33/4.61 | (20) injection_2(x) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 =
% 27.33/4.61 | v1) & zero(any2) = v0 & zero(any1) = v1 & apply(x, v2) = v0 &
% 27.33/4.61 | $i(v2) & $i(v1) & $i(v0) & element(v2, any1))
% 27.33/4.61 |
% 27.33/4.61 | GROUND_INST: instantiating (properties_for_injection) with x, any1, any2,
% 27.33/4.61 | simplifying with (12), (13), (14), (15) gives:
% 27.33/4.61 | (21) injection(x) | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0)
% 27.33/4.61 | & apply(x, v1) = v2 & apply(x, v0) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 27.33/4.61 | element(v1, any1) & element(v0, any1))
% 27.33/4.61 |
% 27.33/4.61 | GROUND_INST: instantiating (1) with x, any1, any2, simplifying with (12),
% 27.33/4.61 | (13), (14), (15) gives:
% 27.33/4.61 | (22) ? [v0: $i] : ? [v1: $i] : (zero(any2) = v1 & zero(any1) = v0 &
% 27.33/4.61 | apply(x, v0) = v1 & $i(v1) & $i(v0))
% 27.33/4.61 |
% 27.33/4.61 | DELTA: instantiating (22) with fresh symbols all_24_0, all_24_1 gives:
% 27.33/4.61 | (23) zero(any2) = all_24_0 & zero(any1) = all_24_1 & apply(x, all_24_1) =
% 27.33/4.61 | all_24_0 & $i(all_24_0) & $i(all_24_1)
% 27.33/4.61 |
% 27.33/4.61 | ALPHA: (23) implies:
% 27.33/4.61 | (24) apply(x, all_24_1) = all_24_0
% 27.33/4.61 | (25) zero(any1) = all_24_1
% 27.33/4.61 | (26) zero(any2) = all_24_0
% 27.33/4.61 |
% 27.33/4.61 | GROUND_INST: instantiating (11) with x, any1, any2, all_24_0, all_24_1,
% 27.33/4.61 | simplifying with (12), (13), (14), (15), (25), (26) gives:
% 27.33/4.62 | (27) injection_2(x) | ? [v0: any] : ( ~ (v0 = all_24_1) & apply(x, v0) =
% 27.33/4.62 | all_24_0 & $i(v0) & $i(all_24_0) & element(v0, any1))
% 27.33/4.62 |
% 27.33/4.62 | BETA: splitting (16) gives:
% 27.33/4.62 |
% 27.33/4.62 | Case 1:
% 27.33/4.62 | |
% 27.33/4.62 | | (28) injection_2(x) & ~ injection(x)
% 27.33/4.62 | |
% 27.33/4.62 | | ALPHA: (28) implies:
% 27.33/4.62 | | (29) ~ injection(x)
% 27.33/4.62 | | (30) injection_2(x)
% 27.33/4.62 | |
% 27.33/4.62 | | BETA: splitting (21) gives:
% 27.33/4.62 | |
% 27.33/4.62 | | Case 1:
% 27.33/4.62 | | |
% 27.33/4.62 | | | (31) injection(x)
% 27.33/4.62 | | |
% 27.33/4.62 | | | PRED_UNIFY: (29), (31) imply:
% 27.33/4.62 | | | (32) $false
% 27.33/4.62 | | |
% 27.33/4.62 | | | CLOSE: (32) is inconsistent.
% 27.33/4.62 | | |
% 27.33/4.62 | | Case 2:
% 27.33/4.62 | | |
% 27.33/4.62 | | | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & apply(x,
% 27.33/4.62 | | | v1) = v2 & apply(x, v0) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 27.33/4.62 | | | element(v1, any1) & element(v0, any1))
% 27.33/4.62 | | |
% 27.33/4.62 | | | DELTA: instantiating (33) with fresh symbols all_37_0, all_37_1, all_37_2
% 27.33/4.62 | | | gives:
% 27.33/4.62 | | | (34) ~ (all_37_1 = all_37_2) & apply(x, all_37_1) = all_37_0 &
% 27.33/4.62 | | | apply(x, all_37_2) = all_37_0 & $i(all_37_0) & $i(all_37_1) &
% 27.33/4.62 | | | $i(all_37_2) & element(all_37_1, any1) & element(all_37_2, any1)
% 27.33/4.62 | | |
% 27.33/4.62 | | | ALPHA: (34) implies:
% 27.33/4.62 | | | (35) ~ (all_37_1 = all_37_2)
% 27.33/4.62 | | | (36) element(all_37_2, any1)
% 27.33/4.62 | | | (37) element(all_37_1, any1)
% 27.33/4.62 | | | (38) $i(all_37_2)
% 27.33/4.62 | | | (39) $i(all_37_1)
% 27.33/4.62 | | | (40) apply(x, all_37_2) = all_37_0
% 27.33/4.62 | | | (41) apply(x, all_37_1) = all_37_0
% 27.33/4.62 | | |
% 27.33/4.62 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_2, all_37_2,
% 27.33/4.62 | | | simplifying with (12), (13), (14), (15), (36), (38) gives:
% 27.33/4.62 | | | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.33/4.62 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_2, all_37_2)
% 27.33/4.62 | | | = v0 & apply(x, v0) = v1 & apply(x, all_37_2) = v3 & apply(x,
% 27.33/4.62 | | | all_37_2) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.33/4.62 | | |
% 27.33/4.62 | | | GROUND_INST: instantiating (4) with any1, all_37_2, all_37_2, simplifying
% 27.33/4.62 | | | with (13), (36), (38) gives:
% 27.33/4.62 | | | (43) ? [v0: $i] : (subtract(any1, all_37_2, all_37_2) = v0 & $i(v0) &
% 27.33/4.62 | | | element(v0, any1))
% 27.33/4.62 | | |
% 27.33/4.62 | | | GROUND_INST: instantiating (2) with x, any1, any2, all_37_2, simplifying
% 27.33/4.62 | | | with (12), (13), (14), (15), (36), (38) gives:
% 27.33/4.62 | | | (44) ? [v0: $i] : (apply(x, all_37_2) = v0 & $i(v0) & element(v0,
% 27.33/4.62 | | | any2))
% 27.33/4.62 | | |
% 27.33/4.62 | | | GROUND_INST: instantiating (5) with any1, all_37_2, simplifying with (13),
% 27.33/4.62 | | | (36), (38) gives:
% 27.33/4.63 | | | (45) ? [v0: $i] : (subtract(any1, all_37_2, all_37_2) = v0 &
% 27.33/4.63 | | | zero(any1) = v0 & $i(v0))
% 27.33/4.63 | | |
% 27.33/4.63 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_1, all_37_1,
% 27.33/4.63 | | | simplifying with (12), (13), (14), (15), (37), (39) gives:
% 27.64/4.63 | | | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.64/4.63 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_1, all_37_1)
% 27.64/4.63 | | | = v0 & apply(x, v0) = v1 & apply(x, all_37_1) = v3 & apply(x,
% 27.64/4.63 | | | all_37_1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (6) with any1, all_37_1, all_37_1, simplifying
% 27.64/4.63 | | | with (13), (37), (39) gives:
% 27.64/4.63 | | | (47) ? [v0: $i] : (subtract(any1, all_37_1, v0) = all_37_1 &
% 27.64/4.63 | | | subtract(any1, all_37_1, all_37_1) = v0 & $i(v0))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (4) with any1, all_37_1, all_37_1, simplifying
% 27.64/4.63 | | | with (13), (37), (39) gives:
% 27.64/4.63 | | | (48) ? [v0: $i] : (subtract(any1, all_37_1, all_37_1) = v0 & $i(v0) &
% 27.64/4.63 | | | element(v0, any1))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_2, all_37_1,
% 27.64/4.63 | | | simplifying with (12), (13), (14), (15), (36), (37), (38),
% 27.64/4.63 | | | (39) gives:
% 27.64/4.63 | | | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.64/4.63 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_2, all_37_1)
% 27.64/4.63 | | | = v0 & apply(x, v0) = v1 & apply(x, all_37_1) = v3 & apply(x,
% 27.64/4.63 | | | all_37_2) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_1, all_37_2,
% 27.64/4.63 | | | simplifying with (12), (13), (14), (15), (36), (37), (38),
% 27.64/4.63 | | | (39) gives:
% 27.64/4.63 | | | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.64/4.63 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_1, all_37_2)
% 27.64/4.63 | | | = v0 & apply(x, v0) = v1 & apply(x, all_37_1) = v2 & apply(x,
% 27.64/4.63 | | | all_37_2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (6) with any1, all_37_2, all_37_1, simplifying
% 27.64/4.63 | | | with (13), (36), (37), (38), (39) gives:
% 27.64/4.63 | | | (51) ? [v0: $i] : (subtract(any1, all_37_2, v0) = all_37_1 &
% 27.64/4.63 | | | subtract(any1, all_37_2, all_37_1) = v0 & $i(v0))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (6) with any1, all_37_1, all_37_2, simplifying
% 27.64/4.63 | | | with (13), (36), (37), (38), (39) gives:
% 27.64/4.63 | | | (52) ? [v0: $i] : (subtract(any1, all_37_1, v0) = all_37_2 &
% 27.64/4.63 | | | subtract(any1, all_37_1, all_37_2) = v0 & $i(v0))
% 27.64/4.63 | | |
% 27.64/4.63 | | | GROUND_INST: instantiating (4) with any1, all_37_2, all_37_1, simplifying
% 27.64/4.63 | | | with (13), (36), (37), (38), (39) gives:
% 27.64/4.63 | | | (53) ? [v0: $i] : (subtract(any1, all_37_2, all_37_1) = v0 & $i(v0) &
% 27.64/4.63 | | | element(v0, any1))
% 27.64/4.63 | | |
% 27.64/4.64 | | | GROUND_INST: instantiating (4) with any1, all_37_1, all_37_2, simplifying
% 27.64/4.64 | | | with (13), (36), (37), (38), (39) gives:
% 27.64/4.64 | | | (54) ? [v0: $i] : (subtract(any1, all_37_1, all_37_2) = v0 & $i(v0) &
% 27.64/4.64 | | | element(v0, any1))
% 27.64/4.64 | | |
% 27.64/4.64 | | | GROUND_INST: instantiating (2) with x, any1, any2, all_37_1, simplifying
% 27.64/4.64 | | | with (12), (13), (14), (15), (37), (39) gives:
% 27.64/4.64 | | | (55) ? [v0: $i] : (apply(x, all_37_1) = v0 & $i(v0) & element(v0,
% 27.64/4.64 | | | any2))
% 27.64/4.64 | | |
% 27.64/4.64 | | | GROUND_INST: instantiating (5) with any1, all_37_1, simplifying with (13),
% 27.64/4.64 | | | (37), (39) gives:
% 27.64/4.64 | | | (56) ? [v0: $i] : (subtract(any1, all_37_1, all_37_1) = v0 &
% 27.64/4.64 | | | zero(any1) = v0 & $i(v0))
% 27.64/4.64 | | |
% 27.64/4.64 | | | GROUND_INST: instantiating (8) with x, any1, any2, simplifying with (12),
% 27.64/4.64 | | | (13), (14), (15), (30) gives:
% 27.64/4.64 | | | (57) ? [v0: $i] : ? [v1: $i] : (zero(any2) = v0 & zero(any1) = v1 &
% 27.64/4.64 | | | $i(v1) & $i(v0) & ! [v2: $i] : (v2 = v1 | ~ $i(v2) | ~
% 27.64/4.64 | | | element(v2, any1) | ? [v3: $i] : ( ~ (v3 = v0) & apply(x, v2)
% 27.64/4.64 | | | = v3 & $i(v3))))
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (54) with fresh symbol all_45_0 gives:
% 27.64/4.64 | | | (58) subtract(any1, all_37_1, all_37_2) = all_45_0 & $i(all_45_0) &
% 27.64/4.64 | | | element(all_45_0, any1)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (58) implies:
% 27.64/4.64 | | | (59) element(all_45_0, any1)
% 27.64/4.64 | | | (60) subtract(any1, all_37_1, all_37_2) = all_45_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (53) with fresh symbol all_47_0 gives:
% 27.64/4.64 | | | (61) subtract(any1, all_37_2, all_37_1) = all_47_0 & $i(all_47_0) &
% 27.64/4.64 | | | element(all_47_0, any1)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (61) implies:
% 27.64/4.64 | | | (62) element(all_47_0, any1)
% 27.64/4.64 | | | (63) subtract(any1, all_37_2, all_37_1) = all_47_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (52) with fresh symbol all_49_0 gives:
% 27.64/4.64 | | | (64) subtract(any1, all_37_1, all_49_0) = all_37_2 & subtract(any1,
% 27.64/4.64 | | | all_37_1, all_37_2) = all_49_0 & $i(all_49_0)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (64) implies:
% 27.64/4.64 | | | (65) $i(all_49_0)
% 27.64/4.64 | | | (66) subtract(any1, all_37_1, all_37_2) = all_49_0
% 27.64/4.64 | | | (67) subtract(any1, all_37_1, all_49_0) = all_37_2
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (45) with fresh symbol all_51_0 gives:
% 27.64/4.64 | | | (68) subtract(any1, all_37_2, all_37_2) = all_51_0 & zero(any1) =
% 27.64/4.64 | | | all_51_0 & $i(all_51_0)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (68) implies:
% 27.64/4.64 | | | (69) $i(all_51_0)
% 27.64/4.64 | | | (70) zero(any1) = all_51_0
% 27.64/4.64 | | | (71) subtract(any1, all_37_2, all_37_2) = all_51_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (44) with fresh symbol all_55_0 gives:
% 27.64/4.64 | | | (72) apply(x, all_37_2) = all_55_0 & $i(all_55_0) & element(all_55_0,
% 27.64/4.64 | | | any2)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (72) implies:
% 27.64/4.64 | | | (73) apply(x, all_37_2) = all_55_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (43) with fresh symbol all_57_0 gives:
% 27.64/4.64 | | | (74) subtract(any1, all_37_2, all_37_2) = all_57_0 & $i(all_57_0) &
% 27.64/4.64 | | | element(all_57_0, any1)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (74) implies:
% 27.64/4.64 | | | (75) element(all_57_0, any1)
% 27.64/4.64 | | | (76) subtract(any1, all_37_2, all_37_2) = all_57_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (48) with fresh symbol all_59_0 gives:
% 27.64/4.64 | | | (77) subtract(any1, all_37_1, all_37_1) = all_59_0 & $i(all_59_0) &
% 27.64/4.64 | | | element(all_59_0, any1)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (77) implies:
% 27.64/4.64 | | | (78) subtract(any1, all_37_1, all_37_1) = all_59_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (51) with fresh symbol all_61_0 gives:
% 27.64/4.64 | | | (79) subtract(any1, all_37_2, all_61_0) = all_37_1 & subtract(any1,
% 27.64/4.64 | | | all_37_2, all_37_1) = all_61_0 & $i(all_61_0)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (79) implies:
% 27.64/4.64 | | | (80) $i(all_61_0)
% 27.64/4.64 | | | (81) subtract(any1, all_37_2, all_37_1) = all_61_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (56) with fresh symbol all_63_0 gives:
% 27.64/4.64 | | | (82) subtract(any1, all_37_1, all_37_1) = all_63_0 & zero(any1) =
% 27.64/4.64 | | | all_63_0 & $i(all_63_0)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (82) implies:
% 27.64/4.64 | | | (83) zero(any1) = all_63_0
% 27.64/4.64 | | | (84) subtract(any1, all_37_1, all_37_1) = all_63_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (55) with fresh symbol all_65_0 gives:
% 27.64/4.64 | | | (85) apply(x, all_37_1) = all_65_0 & $i(all_65_0) & element(all_65_0,
% 27.64/4.64 | | | any2)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (85) implies:
% 27.64/4.64 | | | (86) apply(x, all_37_1) = all_65_0
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (47) with fresh symbol all_67_0 gives:
% 27.64/4.64 | | | (87) subtract(any1, all_37_1, all_67_0) = all_37_1 & subtract(any1,
% 27.64/4.64 | | | all_37_1, all_37_1) = all_67_0 & $i(all_67_0)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (87) implies:
% 27.64/4.64 | | | (88) subtract(any1, all_37_1, all_37_1) = all_67_0
% 27.64/4.64 | | | (89) subtract(any1, all_37_1, all_67_0) = all_37_1
% 27.64/4.64 | | |
% 27.64/4.64 | | | DELTA: instantiating (50) with fresh symbols all_69_0, all_69_1, all_69_2,
% 27.64/4.64 | | | all_69_3 gives:
% 27.64/4.64 | | | (90) subtract(any2, all_69_1, all_69_0) = all_69_2 & subtract(any1,
% 27.64/4.64 | | | all_37_1, all_37_2) = all_69_3 & apply(x, all_69_3) = all_69_2 &
% 27.64/4.64 | | | apply(x, all_37_1) = all_69_1 & apply(x, all_37_2) = all_69_0 &
% 27.64/4.64 | | | $i(all_69_0) & $i(all_69_1) & $i(all_69_2) & $i(all_69_3)
% 27.64/4.64 | | |
% 27.64/4.64 | | | ALPHA: (90) implies:
% 27.64/4.64 | | | (91) apply(x, all_37_2) = all_69_0
% 27.64/4.64 | | | (92) apply(x, all_37_1) = all_69_1
% 27.64/4.64 | | | (93) apply(x, all_69_3) = all_69_2
% 27.64/4.64 | | | (94) subtract(any1, all_37_1, all_37_2) = all_69_3
% 27.64/4.65 | | | (95) subtract(any2, all_69_1, all_69_0) = all_69_2
% 27.64/4.65 | | |
% 27.64/4.65 | | | DELTA: instantiating (46) with fresh symbols all_71_0, all_71_1, all_71_2,
% 27.64/4.65 | | | all_71_3 gives:
% 27.64/4.65 | | | (96) subtract(any2, all_71_1, all_71_0) = all_71_2 & subtract(any1,
% 27.64/4.65 | | | all_37_1, all_37_1) = all_71_3 & apply(x, all_71_3) = all_71_2 &
% 27.64/4.65 | | | apply(x, all_37_1) = all_71_0 & apply(x, all_37_1) = all_71_1 &
% 27.64/4.65 | | | $i(all_71_0) & $i(all_71_1) & $i(all_71_2) & $i(all_71_3)
% 27.64/4.65 | | |
% 27.64/4.65 | | | ALPHA: (96) implies:
% 27.64/4.65 | | | (97) apply(x, all_37_1) = all_71_1
% 27.64/4.65 | | | (98) apply(x, all_37_1) = all_71_0
% 27.64/4.65 | | | (99) apply(x, all_71_3) = all_71_2
% 27.64/4.65 | | | (100) subtract(any1, all_37_1, all_37_1) = all_71_3
% 27.64/4.65 | | | (101) subtract(any2, all_71_1, all_71_0) = all_71_2
% 27.64/4.65 | | |
% 27.64/4.65 | | | DELTA: instantiating (42) with fresh symbols all_73_0, all_73_1, all_73_2,
% 27.64/4.65 | | | all_73_3 gives:
% 27.64/4.65 | | | (102) subtract(any2, all_73_1, all_73_0) = all_73_2 & subtract(any1,
% 27.64/4.65 | | | all_37_2, all_37_2) = all_73_3 & apply(x, all_73_3) = all_73_2
% 27.64/4.65 | | | & apply(x, all_37_2) = all_73_0 & apply(x, all_37_2) = all_73_1 &
% 27.64/4.65 | | | $i(all_73_0) & $i(all_73_1) & $i(all_73_2) & $i(all_73_3)
% 27.64/4.65 | | |
% 27.64/4.65 | | | ALPHA: (102) implies:
% 27.64/4.65 | | | (103) apply(x, all_37_2) = all_73_1
% 27.64/4.65 | | | (104) apply(x, all_37_2) = all_73_0
% 27.64/4.65 | | | (105) subtract(any2, all_73_1, all_73_0) = all_73_2
% 27.64/4.65 | | |
% 27.64/4.65 | | | DELTA: instantiating (49) with fresh symbols all_75_0, all_75_1, all_75_2,
% 27.64/4.65 | | | all_75_3 gives:
% 27.64/4.65 | | | (106) subtract(any2, all_75_1, all_75_0) = all_75_2 & subtract(any1,
% 27.64/4.65 | | | all_37_2, all_37_1) = all_75_3 & apply(x, all_75_3) = all_75_2
% 27.64/4.65 | | | & apply(x, all_37_1) = all_75_0 & apply(x, all_37_2) = all_75_1 &
% 27.64/4.65 | | | $i(all_75_0) & $i(all_75_1) & $i(all_75_2) & $i(all_75_3)
% 27.64/4.65 | | |
% 27.64/4.65 | | | ALPHA: (106) implies:
% 27.64/4.65 | | | (107) apply(x, all_37_2) = all_75_1
% 27.64/4.65 | | | (108) apply(x, all_37_1) = all_75_0
% 27.64/4.65 | | | (109) apply(x, all_75_3) = all_75_2
% 27.64/4.65 | | | (110) subtract(any1, all_37_2, all_37_1) = all_75_3
% 27.64/4.65 | | | (111) subtract(any2, all_75_1, all_75_0) = all_75_2
% 27.64/4.65 | | |
% 27.64/4.65 | | | DELTA: instantiating (57) with fresh symbols all_77_0, all_77_1 gives:
% 27.64/4.65 | | | (112) zero(any2) = all_77_1 & zero(any1) = all_77_0 & $i(all_77_0) &
% 27.64/4.65 | | | $i(all_77_1) & ! [v0: any] : (v0 = all_77_0 | ~ $i(v0) | ~
% 27.64/4.65 | | | element(v0, any1) | ? [v1: any] : ( ~ (v1 = all_77_1) &
% 27.64/4.65 | | | apply(x, v0) = v1 & $i(v1)))
% 27.64/4.65 | | |
% 27.64/4.65 | | | ALPHA: (112) implies:
% 27.64/4.65 | | | (113) zero(any1) = all_77_0
% 27.64/4.65 | | | (114) zero(any2) = all_77_1
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_55_0, all_73_1, all_37_2, x,
% 27.64/4.65 | | | simplifying with (73), (103) gives:
% 27.64/4.65 | | | (115) all_73_1 = all_55_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_73_1, all_73_0, all_37_2, x,
% 27.64/4.65 | | | simplifying with (103), (104) gives:
% 27.64/4.65 | | | (116) all_73_0 = all_73_1
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_69_0, all_73_0, all_37_2, x,
% 27.64/4.65 | | | simplifying with (91), (104) gives:
% 27.64/4.65 | | | (117) all_73_0 = all_69_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_37_0, all_75_1, all_37_2, x,
% 27.64/4.65 | | | simplifying with (40), (107) gives:
% 27.64/4.65 | | | (118) all_75_1 = all_37_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_73_0, all_75_1, all_37_2, x,
% 27.64/4.65 | | | simplifying with (104), (107) gives:
% 27.64/4.65 | | | (119) all_75_1 = all_73_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_37_0, all_69_1, all_37_1, x,
% 27.64/4.65 | | | simplifying with (41), (92) gives:
% 27.64/4.65 | | | (120) all_69_1 = all_37_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_71_1, all_71_0, all_37_1, x,
% 27.64/4.65 | | | simplifying with (97), (98) gives:
% 27.64/4.65 | | | (121) all_71_0 = all_71_1
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_69_1, all_71_0, all_37_1, x,
% 27.64/4.65 | | | simplifying with (92), (98) gives:
% 27.64/4.65 | | | (122) all_71_0 = all_69_1
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_71_0, all_75_0, all_37_1, x,
% 27.64/4.65 | | | simplifying with (98), (108) gives:
% 27.64/4.65 | | | (123) all_75_0 = all_71_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (18) with all_65_0, all_75_0, all_37_1, x,
% 27.64/4.65 | | | simplifying with (86), (108) gives:
% 27.64/4.65 | | | (124) all_75_0 = all_65_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (17) with all_24_1, all_63_0, any1, simplifying
% 27.64/4.65 | | | with (25), (83) gives:
% 27.64/4.65 | | | (125) all_63_0 = all_24_1
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (17) with all_63_0, all_77_0, any1, simplifying
% 27.64/4.65 | | | with (83), (113) gives:
% 27.64/4.65 | | | (126) all_77_0 = all_63_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (17) with all_51_0, all_77_0, any1, simplifying
% 27.64/4.65 | | | with (70), (113) gives:
% 27.64/4.65 | | | (127) all_77_0 = all_51_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (17) with all_24_0, all_77_1, any2, simplifying
% 27.64/4.65 | | | with (26), (114) gives:
% 27.64/4.65 | | | (128) all_77_1 = all_24_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_51_0, all_57_0, all_37_2,
% 27.64/4.65 | | | all_37_2, any1, simplifying with (71), (76) gives:
% 27.64/4.65 | | | (129) all_57_0 = all_51_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_61_0, all_75_3, all_37_1,
% 27.64/4.65 | | | all_37_2, any1, simplifying with (81), (110) gives:
% 27.64/4.65 | | | (130) all_75_3 = all_61_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_47_0, all_75_3, all_37_1,
% 27.64/4.65 | | | all_37_2, any1, simplifying with (63), (110) gives:
% 27.64/4.65 | | | (131) all_75_3 = all_47_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_49_0, all_69_3, all_37_2,
% 27.64/4.65 | | | all_37_1, any1, simplifying with (66), (94) gives:
% 27.64/4.65 | | | (132) all_69_3 = all_49_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_45_0, all_69_3, all_37_2,
% 27.64/4.65 | | | all_37_1, any1, simplifying with (60), (94) gives:
% 27.64/4.65 | | | (133) all_69_3 = all_45_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_59_0, all_67_0, all_37_1,
% 27.64/4.65 | | | all_37_1, any1, simplifying with (78), (88) gives:
% 27.64/4.65 | | | (134) all_67_0 = all_59_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_67_0, all_71_3, all_37_1,
% 27.64/4.65 | | | all_37_1, any1, simplifying with (88), (100) gives:
% 27.64/4.65 | | | (135) all_71_3 = all_67_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | GROUND_INST: instantiating (19) with all_63_0, all_71_3, all_37_1,
% 27.64/4.65 | | | all_37_1, any1, simplifying with (84), (100) gives:
% 27.64/4.65 | | | (136) all_71_3 = all_63_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | COMBINE_EQS: (126), (127) imply:
% 27.64/4.65 | | | (137) all_63_0 = all_51_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | SIMP: (137) implies:
% 27.64/4.65 | | | (138) all_63_0 = all_51_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | COMBINE_EQS: (123), (124) imply:
% 27.64/4.65 | | | (139) all_71_0 = all_65_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | SIMP: (139) implies:
% 27.64/4.65 | | | (140) all_71_0 = all_65_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | COMBINE_EQS: (118), (119) imply:
% 27.64/4.65 | | | (141) all_73_0 = all_37_0
% 27.64/4.65 | | |
% 27.64/4.65 | | | SIMP: (141) implies:
% 27.64/4.65 | | | (142) all_73_0 = all_37_0
% 27.64/4.65 | | |
% 27.64/4.66 | | | COMBINE_EQS: (130), (131) imply:
% 27.64/4.66 | | | (143) all_61_0 = all_47_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | SIMP: (143) implies:
% 27.64/4.66 | | | (144) all_61_0 = all_47_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (116), (117) imply:
% 27.64/4.66 | | | (145) all_73_1 = all_69_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | SIMP: (145) implies:
% 27.64/4.66 | | | (146) all_73_1 = all_69_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (117), (142) imply:
% 27.64/4.66 | | | (147) all_69_0 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (115), (146) imply:
% 27.64/4.66 | | | (148) all_69_0 = all_55_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | SIMP: (148) implies:
% 27.64/4.66 | | | (149) all_69_0 = all_55_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (121), (122) imply:
% 27.64/4.66 | | | (150) all_71_1 = all_69_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (121), (140) imply:
% 27.64/4.66 | | | (151) all_71_1 = all_65_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (150), (151) imply:
% 27.64/4.66 | | | (152) all_69_1 = all_65_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | SIMP: (152) implies:
% 27.64/4.66 | | | (153) all_69_1 = all_65_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (135), (136) imply:
% 27.64/4.66 | | | (154) all_67_0 = all_63_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | SIMP: (154) implies:
% 27.64/4.66 | | | (155) all_67_0 = all_63_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (147), (149) imply:
% 27.64/4.66 | | | (156) all_55_0 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (120), (153) imply:
% 27.64/4.66 | | | (157) all_65_0 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (132), (133) imply:
% 27.64/4.66 | | | (158) all_49_0 = all_45_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (134), (155) imply:
% 27.64/4.66 | | | (159) all_63_0 = all_59_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (138), (159) imply:
% 27.64/4.66 | | | (160) all_59_0 = all_51_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (125), (159) imply:
% 27.64/4.66 | | | (161) all_59_0 = all_24_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (160), (161) imply:
% 27.64/4.66 | | | (162) all_51_0 = all_24_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (129), (162) imply:
% 27.64/4.66 | | | (163) all_57_0 = all_24_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (125), (155) imply:
% 27.64/4.66 | | | (164) all_67_0 = all_24_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (125), (136) imply:
% 27.64/4.66 | | | (165) all_71_3 = all_24_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (151), (157) imply:
% 27.64/4.66 | | | (166) all_71_1 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (121), (166) imply:
% 27.64/4.66 | | | (167) all_71_0 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (115), (156) imply:
% 27.64/4.66 | | | (168) all_73_1 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | COMBINE_EQS: (124), (157) imply:
% 27.64/4.66 | | | (169) all_75_0 = all_37_0
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (111), (118), (169) imply:
% 27.64/4.66 | | | (170) subtract(any2, all_37_0, all_37_0) = all_75_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (105), (142), (168) imply:
% 27.64/4.66 | | | (171) subtract(any2, all_37_0, all_37_0) = all_73_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (101), (166), (167) imply:
% 27.64/4.66 | | | (172) subtract(any2, all_37_0, all_37_0) = all_71_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (95), (120), (147) imply:
% 27.64/4.66 | | | (173) subtract(any2, all_37_0, all_37_0) = all_69_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (89), (164) imply:
% 27.64/4.66 | | | (174) subtract(any1, all_37_1, all_24_1) = all_37_1
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (67), (158) imply:
% 27.64/4.66 | | | (175) subtract(any1, all_37_1, all_45_0) = all_37_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (109), (131) imply:
% 27.64/4.66 | | | (176) apply(x, all_47_0) = all_75_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (99), (165) imply:
% 27.64/4.66 | | | (177) apply(x, all_24_1) = all_71_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (93), (133) imply:
% 27.64/4.66 | | | (178) apply(x, all_45_0) = all_69_2
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (80), (144) imply:
% 27.64/4.66 | | | (179) $i(all_47_0)
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (69), (162) imply:
% 27.64/4.66 | | | (180) $i(all_24_1)
% 27.64/4.66 | | |
% 27.64/4.66 | | | REDUCE: (65), (158) imply:
% 27.80/4.66 | | | (181) $i(all_45_0)
% 27.80/4.66 | | |
% 27.80/4.66 | | | REDUCE: (75), (163) imply:
% 27.80/4.66 | | | (182) element(all_24_1, any1)
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (18) with all_24_0, all_71_2, all_24_1, x,
% 27.80/4.66 | | | simplifying with (24), (177) gives:
% 27.80/4.66 | | | (183) all_71_2 = all_24_0
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (19) with all_71_2, all_73_2, all_37_0,
% 27.80/4.66 | | | all_37_0, any2, simplifying with (171), (172) gives:
% 27.80/4.66 | | | (184) all_73_2 = all_71_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (19) with all_73_2, all_75_2, all_37_0,
% 27.80/4.66 | | | all_37_0, any2, simplifying with (170), (171) gives:
% 27.80/4.66 | | | (185) all_75_2 = all_73_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (19) with all_69_2, all_75_2, all_37_0,
% 27.80/4.66 | | | all_37_0, any2, simplifying with (170), (173) gives:
% 27.80/4.66 | | | (186) all_75_2 = all_69_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | COMBINE_EQS: (185), (186) imply:
% 27.80/4.66 | | | (187) all_73_2 = all_69_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | SIMP: (187) implies:
% 27.80/4.66 | | | (188) all_73_2 = all_69_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | COMBINE_EQS: (184), (188) imply:
% 27.80/4.66 | | | (189) all_71_2 = all_69_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | SIMP: (189) implies:
% 27.80/4.66 | | | (190) all_71_2 = all_69_2
% 27.80/4.66 | | |
% 27.80/4.66 | | | COMBINE_EQS: (183), (190) imply:
% 27.80/4.66 | | | (191) all_69_2 = all_24_0
% 27.80/4.66 | | |
% 27.80/4.66 | | | SIMP: (191) implies:
% 27.80/4.66 | | | (192) all_69_2 = all_24_0
% 27.80/4.66 | | |
% 27.80/4.66 | | | COMBINE_EQS: (186), (192) imply:
% 27.80/4.66 | | | (193) all_75_2 = all_24_0
% 27.80/4.66 | | |
% 27.80/4.66 | | | REDUCE: (176), (193) imply:
% 27.80/4.66 | | | (194) apply(x, all_47_0) = all_24_0
% 27.80/4.66 | | |
% 27.80/4.66 | | | REDUCE: (178), (192) imply:
% 27.80/4.66 | | | (195) apply(x, all_45_0) = all_24_0
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_1, all_24_1,
% 27.80/4.66 | | | simplifying with (12), (13), (14), (15), (37), (39), (180),
% 27.80/4.66 | | | (182) gives:
% 27.80/4.66 | | | (196) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.66 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_1, all_24_1)
% 27.80/4.66 | | | = v0 & apply(x, v0) = v1 & apply(x, all_37_1) = v2 & apply(x,
% 27.80/4.66 | | | all_24_1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_1, all_45_0,
% 27.80/4.66 | | | simplifying with (12), (13), (14), (15), (37), (39), (59),
% 27.80/4.66 | | | (181) gives:
% 27.80/4.66 | | | (197) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.66 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_1, all_45_0)
% 27.80/4.66 | | | = v0 & apply(x, v0) = v1 & apply(x, all_45_0) = v3 & apply(x,
% 27.80/4.66 | | | all_37_1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.80/4.66 | | |
% 27.80/4.66 | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_1, all_47_0,
% 27.80/4.66 | | | simplifying with (12), (13), (14), (15), (37), (39), (62),
% 27.80/4.66 | | | (179) gives:
% 27.80/4.67 | | | (198) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.67 | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_1, all_47_0)
% 27.80/4.67 | | | = v0 & apply(x, v0) = v1 & apply(x, all_47_0) = v3 & apply(x,
% 27.80/4.67 | | | all_37_1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (6) with any1, all_37_1, all_47_0, simplifying
% 27.80/4.67 | | | with (13), (37), (39), (62), (179) gives:
% 27.80/4.67 | | | (199) ? [v0: $i] : (subtract(any1, all_37_1, v0) = all_47_0 &
% 27.80/4.67 | | | subtract(any1, all_37_1, all_47_0) = v0 & $i(v0))
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (4) with any1, all_37_1, all_47_0, simplifying
% 27.80/4.67 | | | with (13), (37), (39), (62), (179) gives:
% 27.80/4.67 | | | (200) ? [v0: $i] : (subtract(any1, all_37_1, all_47_0) = v0 & $i(v0) &
% 27.80/4.67 | | | element(v0, any1))
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (9) with x, any1, any2, all_24_0, all_24_1,
% 27.80/4.67 | | | all_45_0, simplifying with (12), (13), (14), (15), (25),
% 27.80/4.67 | | | (26), (30), (59), (181), (195) gives:
% 27.80/4.67 | | | (201) all_45_0 = all_24_1
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (9) with x, any1, any2, all_24_0, all_24_1,
% 27.80/4.67 | | | all_47_0, simplifying with (12), (13), (14), (15), (25),
% 27.80/4.67 | | | (26), (30), (62), (179), (194) gives:
% 27.80/4.67 | | | (202) all_47_0 = all_24_1
% 27.80/4.67 | | |
% 27.80/4.67 | | | DELTA: instantiating (200) with fresh symbol all_132_0 gives:
% 27.80/4.67 | | | (203) subtract(any1, all_37_1, all_47_0) = all_132_0 & $i(all_132_0) &
% 27.80/4.67 | | | element(all_132_0, any1)
% 27.80/4.67 | | |
% 27.80/4.67 | | | ALPHA: (203) implies:
% 27.80/4.67 | | | (204) subtract(any1, all_37_1, all_47_0) = all_132_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | DELTA: instantiating (199) with fresh symbol all_146_0 gives:
% 27.80/4.67 | | | (205) subtract(any1, all_37_1, all_146_0) = all_47_0 & subtract(any1,
% 27.80/4.67 | | | all_37_1, all_47_0) = all_146_0 & $i(all_146_0)
% 27.80/4.67 | | |
% 27.80/4.67 | | | ALPHA: (205) implies:
% 27.80/4.67 | | | (206) subtract(any1, all_37_1, all_47_0) = all_146_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | DELTA: instantiating (198) with fresh symbols all_204_0, all_204_1,
% 27.80/4.67 | | | all_204_2, all_204_3 gives:
% 27.80/4.67 | | | (207) subtract(any2, all_204_1, all_204_0) = all_204_2 & subtract(any1,
% 27.80/4.67 | | | all_37_1, all_47_0) = all_204_3 & apply(x, all_204_3) =
% 27.80/4.67 | | | all_204_2 & apply(x, all_47_0) = all_204_0 & apply(x, all_37_1) =
% 27.80/4.67 | | | all_204_1 & $i(all_204_0) & $i(all_204_1) & $i(all_204_2) &
% 27.80/4.67 | | | $i(all_204_3)
% 27.80/4.67 | | |
% 27.80/4.67 | | | ALPHA: (207) implies:
% 27.80/4.67 | | | (208) subtract(any1, all_37_1, all_47_0) = all_204_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | DELTA: instantiating (196) with fresh symbols all_208_0, all_208_1,
% 27.80/4.67 | | | all_208_2, all_208_3 gives:
% 27.80/4.67 | | | (209) subtract(any2, all_208_1, all_208_0) = all_208_2 & subtract(any1,
% 27.80/4.67 | | | all_37_1, all_24_1) = all_208_3 & apply(x, all_208_3) =
% 27.80/4.67 | | | all_208_2 & apply(x, all_37_1) = all_208_1 & apply(x, all_24_1) =
% 27.80/4.67 | | | all_208_0 & $i(all_208_0) & $i(all_208_1) & $i(all_208_2) &
% 27.80/4.67 | | | $i(all_208_3)
% 27.80/4.67 | | |
% 27.80/4.67 | | | ALPHA: (209) implies:
% 27.80/4.67 | | | (210) subtract(any1, all_37_1, all_24_1) = all_208_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | DELTA: instantiating (197) with fresh symbols all_214_0, all_214_1,
% 27.80/4.67 | | | all_214_2, all_214_3 gives:
% 27.80/4.67 | | | (211) subtract(any2, all_214_1, all_214_0) = all_214_2 & subtract(any1,
% 27.80/4.67 | | | all_37_1, all_45_0) = all_214_3 & apply(x, all_214_3) =
% 27.80/4.67 | | | all_214_2 & apply(x, all_45_0) = all_214_0 & apply(x, all_37_1) =
% 27.80/4.67 | | | all_214_1 & $i(all_214_0) & $i(all_214_1) & $i(all_214_2) &
% 27.80/4.67 | | | $i(all_214_3)
% 27.80/4.67 | | |
% 27.80/4.67 | | | ALPHA: (211) implies:
% 27.80/4.67 | | | (212) subtract(any1, all_37_1, all_45_0) = all_214_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | REDUCE: (202), (208) imply:
% 27.80/4.67 | | | (213) subtract(any1, all_37_1, all_24_1) = all_204_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | REDUCE: (202), (206) imply:
% 27.80/4.67 | | | (214) subtract(any1, all_37_1, all_24_1) = all_146_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | REDUCE: (202), (204) imply:
% 27.80/4.67 | | | (215) subtract(any1, all_37_1, all_24_1) = all_132_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | REDUCE: (201), (212) imply:
% 27.80/4.67 | | | (216) subtract(any1, all_37_1, all_24_1) = all_214_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | REDUCE: (175), (201) imply:
% 27.80/4.67 | | | (217) subtract(any1, all_37_1, all_24_1) = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (19) with all_37_1, all_132_0, all_24_1,
% 27.80/4.67 | | | all_37_1, any1, simplifying with (174), (215) gives:
% 27.80/4.67 | | | (218) all_132_0 = all_37_1
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (19) with all_204_3, all_208_3, all_24_1,
% 27.80/4.67 | | | all_37_1, any1, simplifying with (210), (213) gives:
% 27.80/4.67 | | | (219) all_208_3 = all_204_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (19) with all_146_0, all_208_3, all_24_1,
% 27.80/4.67 | | | all_37_1, any1, simplifying with (210), (214) gives:
% 27.80/4.67 | | | (220) all_208_3 = all_146_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (19) with all_132_0, all_208_3, all_24_1,
% 27.80/4.67 | | | all_37_1, any1, simplifying with (210), (215) gives:
% 27.80/4.67 | | | (221) all_208_3 = all_132_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (19) with all_204_3, all_214_3, all_24_1,
% 27.80/4.67 | | | all_37_1, any1, simplifying with (213), (216) gives:
% 27.80/4.67 | | | (222) all_214_3 = all_204_3
% 27.80/4.67 | | |
% 27.80/4.67 | | | GROUND_INST: instantiating (19) with all_37_2, all_214_3, all_24_1,
% 27.80/4.67 | | | all_37_1, any1, simplifying with (216), (217) gives:
% 27.80/4.67 | | | (223) all_214_3 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | COMBINE_EQS: (222), (223) imply:
% 27.80/4.67 | | | (224) all_204_3 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | SIMP: (224) implies:
% 27.80/4.67 | | | (225) all_204_3 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | COMBINE_EQS: (220), (221) imply:
% 27.80/4.67 | | | (226) all_146_0 = all_132_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | COMBINE_EQS: (219), (220) imply:
% 27.80/4.67 | | | (227) all_204_3 = all_146_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | SIMP: (227) implies:
% 27.80/4.67 | | | (228) all_204_3 = all_146_0
% 27.80/4.67 | | |
% 27.80/4.67 | | | COMBINE_EQS: (225), (228) imply:
% 27.80/4.67 | | | (229) all_146_0 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | SIMP: (229) implies:
% 27.80/4.67 | | | (230) all_146_0 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | COMBINE_EQS: (226), (230) imply:
% 27.80/4.67 | | | (231) all_132_0 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | SIMP: (231) implies:
% 27.80/4.67 | | | (232) all_132_0 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | COMBINE_EQS: (218), (232) imply:
% 27.80/4.67 | | | (233) all_37_1 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | SIMP: (233) implies:
% 27.80/4.67 | | | (234) all_37_1 = all_37_2
% 27.80/4.67 | | |
% 27.80/4.67 | | | REDUCE: (35), (234) imply:
% 27.80/4.67 | | | (235) $false
% 27.80/4.67 | | |
% 27.80/4.67 | | | CLOSE: (235) is inconsistent.
% 27.80/4.67 | | |
% 27.80/4.67 | | End of split
% 27.80/4.67 | |
% 27.80/4.67 | Case 2:
% 27.80/4.67 | |
% 27.80/4.67 | | (236) injection(x) & ~ injection_2(x)
% 27.80/4.67 | |
% 27.80/4.67 | | ALPHA: (236) implies:
% 27.80/4.67 | | (237) ~ injection_2(x)
% 27.80/4.67 | | (238) injection(x)
% 27.80/4.67 | |
% 27.80/4.67 | | BETA: splitting (20) gives:
% 27.80/4.67 | |
% 27.80/4.67 | | Case 1:
% 27.80/4.67 | | |
% 27.80/4.67 | | | (239) injection_2(x)
% 27.80/4.67 | | |
% 27.80/4.67 | | | PRED_UNIFY: (237), (239) imply:
% 27.80/4.67 | | | (240) $false
% 27.80/4.67 | | |
% 27.80/4.67 | | | CLOSE: (240) is inconsistent.
% 27.80/4.67 | | |
% 27.80/4.67 | | Case 2:
% 27.80/4.67 | | |
% 27.80/4.67 | | | (241) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 27.80/4.67 | | | zero(any2) = v0 & zero(any1) = v1 & apply(x, v2) = v0 & $i(v2)
% 27.80/4.67 | | | & $i(v1) & $i(v0) & element(v2, any1))
% 27.80/4.67 | | |
% 27.80/4.67 | | | DELTA: instantiating (241) with fresh symbols all_37_0, all_37_1, all_37_2
% 27.80/4.67 | | | gives:
% 27.80/4.67 | | | (242) ~ (all_37_0 = all_37_1) & zero(any2) = all_37_2 & zero(any1) =
% 27.80/4.67 | | | all_37_1 & apply(x, all_37_0) = all_37_2 & $i(all_37_0) &
% 27.80/4.67 | | | $i(all_37_1) & $i(all_37_2) & element(all_37_0, any1)
% 27.80/4.67 | | |
% 27.80/4.67 | | | ALPHA: (242) implies:
% 27.80/4.68 | | | (243) element(all_37_0, any1)
% 27.80/4.68 | | | (244) $i(all_37_0)
% 27.80/4.68 | | | (245) apply(x, all_37_0) = all_37_2
% 27.80/4.68 | | | (246) zero(any1) = all_37_1
% 27.80/4.68 | | | (247) zero(any2) = all_37_2
% 27.80/4.68 | | |
% 27.80/4.68 | | | BETA: splitting (27) gives:
% 27.80/4.68 | | |
% 27.80/4.68 | | | Case 1:
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | (248) injection_2(x)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | PRED_UNIFY: (237), (248) imply:
% 27.80/4.68 | | | | (249) $false
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | CLOSE: (249) is inconsistent.
% 27.80/4.68 | | | |
% 27.80/4.68 | | | Case 2:
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | (250) ? [v0: any] : ( ~ (v0 = all_24_1) & apply(x, v0) = all_24_0 &
% 27.80/4.68 | | | | $i(v0) & $i(all_24_0) & element(v0, any1))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | DELTA: instantiating (250) with fresh symbol all_42_0 gives:
% 27.80/4.68 | | | | (251) ~ (all_42_0 = all_24_1) & apply(x, all_42_0) = all_24_0 &
% 27.80/4.68 | | | | $i(all_42_0) & $i(all_24_0) & element(all_42_0, any1)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | ALPHA: (251) implies:
% 27.80/4.68 | | | | (252) ~ (all_42_0 = all_24_1)
% 27.80/4.68 | | | | (253) element(all_42_0, any1)
% 27.80/4.68 | | | | (254) $i(all_42_0)
% 27.80/4.68 | | | | (255) apply(x, all_42_0) = all_24_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (17) with all_24_1, all_37_1, any1,
% 27.80/4.68 | | | | simplifying with (25), (246) gives:
% 27.80/4.68 | | | | (256) all_37_1 = all_24_1
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (17) with all_24_0, all_37_2, any2,
% 27.80/4.68 | | | | simplifying with (26), (247) gives:
% 27.80/4.68 | | | | (257) all_37_2 = all_24_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | REDUCE: (245), (257) imply:
% 27.80/4.68 | | | | (258) apply(x, all_37_0) = all_24_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_0, all_37_0,
% 27.80/4.68 | | | | simplifying with (12), (13), (14), (15), (243), (244)
% 27.80/4.68 | | | | gives:
% 27.80/4.68 | | | | (259) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.68 | | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_0,
% 27.80/4.68 | | | | all_37_0) = v0 & apply(x, v0) = v1 & apply(x, all_37_0) =
% 27.80/4.68 | | | | v3 & apply(x, all_37_0) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 27.80/4.68 | | | | $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (6) with any1, all_37_0, all_37_0,
% 27.80/4.68 | | | | simplifying with (13), (243), (244) gives:
% 27.80/4.68 | | | | (260) ? [v0: $i] : (subtract(any1, all_37_0, v0) = all_37_0 &
% 27.80/4.68 | | | | subtract(any1, all_37_0, all_37_0) = v0 & $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (4) with any1, all_37_0, all_37_0,
% 27.80/4.68 | | | | simplifying with (13), (243), (244) gives:
% 27.80/4.68 | | | | (261) ? [v0: $i] : (subtract(any1, all_37_0, all_37_0) = v0 & $i(v0)
% 27.80/4.68 | | | | & element(v0, any1))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (2) with x, any1, any2, all_37_0, simplifying
% 27.80/4.68 | | | | with (12), (13), (14), (15), (243), (244) gives:
% 27.80/4.68 | | | | (262) ? [v0: $i] : (apply(x, all_37_0) = v0 & $i(v0) & element(v0,
% 27.80/4.68 | | | | any2))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (5) with any1, all_37_0, simplifying with
% 27.80/4.68 | | | | (13), (243), (244) gives:
% 27.80/4.68 | | | | (263) ? [v0: $i] : (subtract(any1, all_37_0, all_37_0) = v0 &
% 27.80/4.68 | | | | zero(any1) = v0 & $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (7) with x, any1, any2, all_42_0, all_42_0,
% 27.80/4.68 | | | | simplifying with (12), (13), (14), (15), (253), (254)
% 27.80/4.68 | | | | gives:
% 27.80/4.68 | | | | (264) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.68 | | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_42_0,
% 27.80/4.68 | | | | all_42_0) = v0 & apply(x, v0) = v1 & apply(x, all_42_0) =
% 27.80/4.68 | | | | v3 & apply(x, all_42_0) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 27.80/4.68 | | | | $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (6) with any1, all_42_0, all_42_0,
% 27.80/4.68 | | | | simplifying with (13), (253), (254) gives:
% 27.80/4.68 | | | | (265) ? [v0: $i] : (subtract(any1, all_42_0, v0) = all_42_0 &
% 27.80/4.68 | | | | subtract(any1, all_42_0, all_42_0) = v0 & $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (4) with any1, all_42_0, all_42_0,
% 27.80/4.68 | | | | simplifying with (13), (253), (254) gives:
% 27.80/4.68 | | | | (266) ? [v0: $i] : (subtract(any1, all_42_0, all_42_0) = v0 & $i(v0)
% 27.80/4.68 | | | | & element(v0, any1))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (7) with x, any1, any2, all_37_0, all_42_0,
% 27.80/4.68 | | | | simplifying with (12), (13), (14), (15), (243), (244),
% 27.80/4.68 | | | | (253), (254) gives:
% 27.80/4.68 | | | | (267) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.68 | | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_37_0,
% 27.80/4.68 | | | | all_42_0) = v0 & apply(x, v0) = v1 & apply(x, all_42_0) =
% 27.80/4.68 | | | | v3 & apply(x, all_37_0) = v2 & $i(v3) & $i(v2) & $i(v1) &
% 27.80/4.68 | | | | $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (7) with x, any1, any2, all_42_0, all_37_0,
% 27.80/4.68 | | | | simplifying with (12), (13), (14), (15), (243), (244),
% 27.80/4.68 | | | | (253), (254) gives:
% 27.80/4.68 | | | | (268) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 27.80/4.68 | | | | (subtract(any2, v2, v3) = v1 & subtract(any1, all_42_0,
% 27.80/4.68 | | | | all_37_0) = v0 & apply(x, v0) = v1 & apply(x, all_42_0) =
% 27.80/4.68 | | | | v2 & apply(x, all_37_0) = v3 & $i(v3) & $i(v2) & $i(v1) &
% 27.80/4.68 | | | | $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (6) with any1, all_37_0, all_42_0,
% 27.80/4.68 | | | | simplifying with (13), (243), (244), (253), (254) gives:
% 27.80/4.68 | | | | (269) ? [v0: $i] : (subtract(any1, all_37_0, v0) = all_42_0 &
% 27.80/4.68 | | | | subtract(any1, all_37_0, all_42_0) = v0 & $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (6) with any1, all_42_0, all_37_0,
% 27.80/4.68 | | | | simplifying with (13), (243), (244), (253), (254) gives:
% 27.80/4.68 | | | | (270) ? [v0: $i] : (subtract(any1, all_42_0, v0) = all_37_0 &
% 27.80/4.68 | | | | subtract(any1, all_42_0, all_37_0) = v0 & $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (4) with any1, all_37_0, all_42_0,
% 27.80/4.68 | | | | simplifying with (13), (243), (244), (253), (254) gives:
% 27.80/4.68 | | | | (271) ? [v0: $i] : (subtract(any1, all_37_0, all_42_0) = v0 & $i(v0)
% 27.80/4.68 | | | | & element(v0, any1))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (4) with any1, all_42_0, all_37_0,
% 27.80/4.68 | | | | simplifying with (13), (243), (244), (253), (254) gives:
% 27.80/4.68 | | | | (272) ? [v0: $i] : (subtract(any1, all_42_0, all_37_0) = v0 & $i(v0)
% 27.80/4.68 | | | | & element(v0, any1))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (2) with x, any1, any2, all_42_0, simplifying
% 27.80/4.68 | | | | with (12), (13), (14), (15), (253), (254) gives:
% 27.80/4.68 | | | | (273) ? [v0: $i] : (apply(x, all_42_0) = v0 & $i(v0) & element(v0,
% 27.80/4.68 | | | | any2))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (5) with any1, all_42_0, simplifying with
% 27.80/4.68 | | | | (13), (253), (254) gives:
% 27.80/4.68 | | | | (274) ? [v0: $i] : (subtract(any1, all_42_0, all_42_0) = v0 &
% 27.80/4.68 | | | | zero(any1) = v0 & $i(v0))
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | GROUND_INST: instantiating (3) with x, any1, all_37_0, all_42_0,
% 27.80/4.68 | | | | all_24_0, any2, simplifying with (12), (13), (14), (15),
% 27.80/4.68 | | | | (238), (243), (244), (253), (254), (255), (258) gives:
% 27.80/4.68 | | | | (275) all_42_0 = all_37_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | DELTA: instantiating (274) with fresh symbol all_54_0 gives:
% 27.80/4.68 | | | | (276) subtract(any1, all_42_0, all_42_0) = all_54_0 & zero(any1) =
% 27.80/4.68 | | | | all_54_0 & $i(all_54_0)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | ALPHA: (276) implies:
% 27.80/4.68 | | | | (277) $i(all_54_0)
% 27.80/4.68 | | | | (278) subtract(any1, all_42_0, all_42_0) = all_54_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | DELTA: instantiating (273) with fresh symbol all_56_0 gives:
% 27.80/4.68 | | | | (279) apply(x, all_42_0) = all_56_0 & $i(all_56_0) &
% 27.80/4.68 | | | | element(all_56_0, any2)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | ALPHA: (279) implies:
% 27.80/4.68 | | | | (280) apply(x, all_42_0) = all_56_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | DELTA: instantiating (272) with fresh symbol all_58_0 gives:
% 27.80/4.68 | | | | (281) subtract(any1, all_42_0, all_37_0) = all_58_0 & $i(all_58_0) &
% 27.80/4.68 | | | | element(all_58_0, any1)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | ALPHA: (281) implies:
% 27.80/4.68 | | | | (282) element(all_58_0, any1)
% 27.80/4.68 | | | | (283) subtract(any1, all_42_0, all_37_0) = all_58_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | DELTA: instantiating (271) with fresh symbol all_60_0 gives:
% 27.80/4.68 | | | | (284) subtract(any1, all_37_0, all_42_0) = all_60_0 & $i(all_60_0) &
% 27.80/4.68 | | | | element(all_60_0, any1)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | ALPHA: (284) implies:
% 27.80/4.68 | | | | (285) subtract(any1, all_37_0, all_42_0) = all_60_0
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | DELTA: instantiating (270) with fresh symbol all_62_0 gives:
% 27.80/4.68 | | | | (286) subtract(any1, all_42_0, all_62_0) = all_37_0 & subtract(any1,
% 27.80/4.68 | | | | all_42_0, all_37_0) = all_62_0 & $i(all_62_0)
% 27.80/4.68 | | | |
% 27.80/4.68 | | | | ALPHA: (286) implies:
% 27.80/4.69 | | | | (287) subtract(any1, all_42_0, all_37_0) = all_62_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (269) with fresh symbol all_64_0 gives:
% 27.80/4.69 | | | | (288) subtract(any1, all_37_0, all_64_0) = all_42_0 & subtract(any1,
% 27.80/4.69 | | | | all_37_0, all_42_0) = all_64_0 & $i(all_64_0)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (288) implies:
% 27.80/4.69 | | | | (289) subtract(any1, all_37_0, all_42_0) = all_64_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (263) with fresh symbol all_66_0 gives:
% 27.80/4.69 | | | | (290) subtract(any1, all_37_0, all_37_0) = all_66_0 & zero(any1) =
% 27.80/4.69 | | | | all_66_0 & $i(all_66_0)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (290) implies:
% 27.80/4.69 | | | | (291) zero(any1) = all_66_0
% 27.80/4.69 | | | | (292) subtract(any1, all_37_0, all_37_0) = all_66_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (260) with fresh symbol all_68_0 gives:
% 27.80/4.69 | | | | (293) subtract(any1, all_37_0, all_68_0) = all_37_0 & subtract(any1,
% 27.80/4.69 | | | | all_37_0, all_37_0) = all_68_0 & $i(all_68_0)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (293) implies:
% 27.80/4.69 | | | | (294) subtract(any1, all_37_0, all_37_0) = all_68_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (262) with fresh symbol all_70_0 gives:
% 27.80/4.69 | | | | (295) apply(x, all_37_0) = all_70_0 & $i(all_70_0) &
% 27.80/4.69 | | | | element(all_70_0, any2)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (295) implies:
% 27.80/4.69 | | | | (296) apply(x, all_37_0) = all_70_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (266) with fresh symbol all_72_0 gives:
% 27.80/4.69 | | | | (297) subtract(any1, all_42_0, all_42_0) = all_72_0 & $i(all_72_0) &
% 27.80/4.69 | | | | element(all_72_0, any1)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (297) implies:
% 27.80/4.69 | | | | (298) subtract(any1, all_42_0, all_42_0) = all_72_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (265) with fresh symbol all_74_0 gives:
% 27.80/4.69 | | | | (299) subtract(any1, all_42_0, all_74_0) = all_42_0 & subtract(any1,
% 27.80/4.69 | | | | all_42_0, all_42_0) = all_74_0 & $i(all_74_0)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (299) implies:
% 27.80/4.69 | | | | (300) subtract(any1, all_42_0, all_42_0) = all_74_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (261) with fresh symbol all_76_0 gives:
% 27.80/4.69 | | | | (301) subtract(any1, all_37_0, all_37_0) = all_76_0 & $i(all_76_0) &
% 27.80/4.69 | | | | element(all_76_0, any1)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (301) implies:
% 27.80/4.69 | | | | (302) subtract(any1, all_37_0, all_37_0) = all_76_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (268) with fresh symbols all_78_0, all_78_1,
% 27.80/4.69 | | | | all_78_2, all_78_3 gives:
% 27.80/4.69 | | | | (303) subtract(any2, all_78_1, all_78_0) = all_78_2 & subtract(any1,
% 27.80/4.69 | | | | all_42_0, all_37_0) = all_78_3 & apply(x, all_78_3) =
% 27.80/4.69 | | | | all_78_2 & apply(x, all_42_0) = all_78_1 & apply(x, all_37_0) =
% 27.80/4.69 | | | | all_78_0 & $i(all_78_0) & $i(all_78_1) & $i(all_78_2) &
% 27.80/4.69 | | | | $i(all_78_3)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (303) implies:
% 27.80/4.69 | | | | (304) apply(x, all_37_0) = all_78_0
% 27.80/4.69 | | | | (305) apply(x, all_42_0) = all_78_1
% 27.80/4.69 | | | | (306) apply(x, all_78_3) = all_78_2
% 27.80/4.69 | | | | (307) subtract(any1, all_42_0, all_37_0) = all_78_3
% 27.80/4.69 | | | | (308) subtract(any2, all_78_1, all_78_0) = all_78_2
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (264) with fresh symbols all_80_0, all_80_1,
% 27.80/4.69 | | | | all_80_2, all_80_3 gives:
% 27.80/4.69 | | | | (309) subtract(any2, all_80_1, all_80_0) = all_80_2 & subtract(any1,
% 27.80/4.69 | | | | all_42_0, all_42_0) = all_80_3 & apply(x, all_80_3) =
% 27.80/4.69 | | | | all_80_2 & apply(x, all_42_0) = all_80_0 & apply(x, all_42_0) =
% 27.80/4.69 | | | | all_80_1 & $i(all_80_0) & $i(all_80_1) & $i(all_80_2) &
% 27.80/4.69 | | | | $i(all_80_3)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (309) implies:
% 27.80/4.69 | | | | (310) apply(x, all_42_0) = all_80_1
% 27.80/4.69 | | | | (311) apply(x, all_42_0) = all_80_0
% 27.80/4.69 | | | | (312) subtract(any1, all_42_0, all_42_0) = all_80_3
% 27.80/4.69 | | | | (313) subtract(any2, all_80_1, all_80_0) = all_80_2
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (259) with fresh symbols all_82_0, all_82_1,
% 27.80/4.69 | | | | all_82_2, all_82_3 gives:
% 27.80/4.69 | | | | (314) subtract(any2, all_82_1, all_82_0) = all_82_2 & subtract(any1,
% 27.80/4.69 | | | | all_37_0, all_37_0) = all_82_3 & apply(x, all_82_3) =
% 27.80/4.69 | | | | all_82_2 & apply(x, all_37_0) = all_82_0 & apply(x, all_37_0) =
% 27.80/4.69 | | | | all_82_1 & $i(all_82_0) & $i(all_82_1) & $i(all_82_2) &
% 27.80/4.69 | | | | $i(all_82_3)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (314) implies:
% 27.80/4.69 | | | | (315) apply(x, all_37_0) = all_82_1
% 27.80/4.69 | | | | (316) apply(x, all_37_0) = all_82_0
% 27.80/4.69 | | | | (317) apply(x, all_82_3) = all_82_2
% 27.80/4.69 | | | | (318) subtract(any1, all_37_0, all_37_0) = all_82_3
% 27.80/4.69 | | | | (319) subtract(any2, all_82_1, all_82_0) = all_82_2
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | DELTA: instantiating (267) with fresh symbols all_84_0, all_84_1,
% 27.80/4.69 | | | | all_84_2, all_84_3 gives:
% 27.80/4.69 | | | | (320) subtract(any2, all_84_1, all_84_0) = all_84_2 & subtract(any1,
% 27.80/4.69 | | | | all_37_0, all_42_0) = all_84_3 & apply(x, all_84_3) =
% 27.80/4.69 | | | | all_84_2 & apply(x, all_42_0) = all_84_0 & apply(x, all_37_0) =
% 27.80/4.69 | | | | all_84_1 & $i(all_84_0) & $i(all_84_1) & $i(all_84_2) &
% 27.80/4.69 | | | | $i(all_84_3)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | ALPHA: (320) implies:
% 27.80/4.69 | | | | (321) apply(x, all_37_0) = all_84_1
% 27.80/4.69 | | | | (322) apply(x, all_42_0) = all_84_0
% 27.80/4.69 | | | | (323) subtract(any1, all_37_0, all_42_0) = all_84_3
% 27.80/4.69 | | | | (324) subtract(any2, all_84_1, all_84_0) = all_84_2
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (252), (275) imply:
% 27.80/4.69 | | | | (325) ~ (all_37_0 = all_24_1)
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (312) imply:
% 27.80/4.69 | | | | (326) subtract(any1, all_37_0, all_37_0) = all_80_3
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (300) imply:
% 27.80/4.69 | | | | (327) subtract(any1, all_37_0, all_37_0) = all_74_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (298) imply:
% 27.80/4.69 | | | | (328) subtract(any1, all_37_0, all_37_0) = all_72_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (278) imply:
% 27.80/4.69 | | | | (329) subtract(any1, all_37_0, all_37_0) = all_54_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (307) imply:
% 27.80/4.69 | | | | (330) subtract(any1, all_37_0, all_37_0) = all_78_3
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (287) imply:
% 27.80/4.69 | | | | (331) subtract(any1, all_37_0, all_37_0) = all_62_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (283) imply:
% 27.80/4.69 | | | | (332) subtract(any1, all_37_0, all_37_0) = all_58_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (323) imply:
% 27.80/4.69 | | | | (333) subtract(any1, all_37_0, all_37_0) = all_84_3
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (289) imply:
% 27.80/4.69 | | | | (334) subtract(any1, all_37_0, all_37_0) = all_64_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (285) imply:
% 27.80/4.69 | | | | (335) subtract(any1, all_37_0, all_37_0) = all_60_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (322) imply:
% 27.80/4.69 | | | | (336) apply(x, all_37_0) = all_84_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (311) imply:
% 27.80/4.69 | | | | (337) apply(x, all_37_0) = all_80_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (310) imply:
% 27.80/4.69 | | | | (338) apply(x, all_37_0) = all_80_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (305) imply:
% 27.80/4.69 | | | | (339) apply(x, all_37_0) = all_78_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | REDUCE: (275), (280) imply:
% 27.80/4.69 | | | | (340) apply(x, all_37_0) = all_56_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_70_0, all_80_1, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (296), (338) gives:
% 27.80/4.69 | | | | (341) all_80_1 = all_70_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_24_0, all_80_0, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (258), (337) gives:
% 27.80/4.69 | | | | (342) all_80_0 = all_24_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_80_1, all_80_0, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (337), (338) gives:
% 27.80/4.69 | | | | (343) all_80_0 = all_80_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_78_1, all_80_0, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (337), (339) gives:
% 27.80/4.69 | | | | (344) all_80_0 = all_78_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_80_0, all_82_1, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (315), (337) gives:
% 27.80/4.69 | | | | (345) all_82_1 = all_80_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_82_1, all_82_0, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (315), (316) gives:
% 27.80/4.69 | | | | (346) all_82_0 = all_82_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_78_1, all_84_1, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (321), (339) gives:
% 27.80/4.69 | | | | (347) all_84_1 = all_78_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_56_0, all_84_1, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (321), (340) gives:
% 27.80/4.69 | | | | (348) all_84_1 = all_56_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_82_0, all_84_0, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (316), (336) gives:
% 27.80/4.69 | | | | (349) all_84_0 = all_82_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (18) with all_78_0, all_84_0, all_37_0, x,
% 27.80/4.69 | | | | simplifying with (304), (336) gives:
% 27.80/4.69 | | | | (350) all_84_0 = all_78_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (17) with all_24_1, all_66_0, any1,
% 27.80/4.69 | | | | simplifying with (25), (291) gives:
% 27.80/4.69 | | | | (351) all_66_0 = all_24_1
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_54_0, all_60_0, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (329), (335) gives:
% 27.80/4.69 | | | | (352) all_60_0 = all_54_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_58_0, all_66_0, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (292), (332) gives:
% 27.80/4.69 | | | | (353) all_66_0 = all_58_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_68_0, all_72_0, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (294), (328) gives:
% 27.80/4.69 | | | | (354) all_72_0 = all_68_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_72_0, all_74_0, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (327), (328) gives:
% 27.80/4.69 | | | | (355) all_74_0 = all_72_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_74_0, all_76_0, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (302), (327) gives:
% 27.80/4.69 | | | | (356) all_76_0 = all_74_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_76_0, all_78_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (302), (330) gives:
% 27.80/4.69 | | | | (357) all_78_3 = all_76_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_78_3, all_80_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (326), (330) gives:
% 27.80/4.69 | | | | (358) all_80_3 = all_78_3
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_62_0, all_80_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (326), (331) gives:
% 27.80/4.69 | | | | (359) all_80_3 = all_62_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_68_0, all_82_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (294), (318) gives:
% 27.80/4.69 | | | | (360) all_82_3 = all_68_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_66_0, all_82_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (292), (318) gives:
% 27.80/4.69 | | | | (361) all_82_3 = all_66_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_60_0, all_82_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (318), (335) gives:
% 27.80/4.69 | | | | (362) all_82_3 = all_60_0
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_82_3, all_84_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (318), (333) gives:
% 27.80/4.69 | | | | (363) all_84_3 = all_82_3
% 27.80/4.69 | | | |
% 27.80/4.69 | | | | GROUND_INST: instantiating (19) with all_64_0, all_84_3, all_37_0,
% 27.80/4.69 | | | | all_37_0, any1, simplifying with (333), (334) gives:
% 27.80/4.70 | | | | (364) all_84_3 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (349), (350) imply:
% 27.80/4.70 | | | | (365) all_82_0 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (365) implies:
% 27.80/4.70 | | | | (366) all_82_0 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (347), (348) imply:
% 27.80/4.70 | | | | (367) all_78_1 = all_56_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (367) implies:
% 27.80/4.70 | | | | (368) all_78_1 = all_56_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (363), (364) imply:
% 27.80/4.70 | | | | (369) all_82_3 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (369) implies:
% 27.80/4.70 | | | | (370) all_82_3 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (346), (366) imply:
% 27.80/4.70 | | | | (371) all_82_1 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (371) implies:
% 27.80/4.70 | | | | (372) all_82_1 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (345), (372) imply:
% 27.80/4.70 | | | | (373) all_80_0 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (373) implies:
% 27.80/4.70 | | | | (374) all_80_0 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (361), (370) imply:
% 27.80/4.70 | | | | (375) all_66_0 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (375) implies:
% 27.80/4.70 | | | | (376) all_66_0 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (360), (370) imply:
% 27.80/4.70 | | | | (377) all_68_0 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (377) implies:
% 27.80/4.70 | | | | (378) all_68_0 = all_64_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (362), (370) imply:
% 27.80/4.70 | | | | (379) all_64_0 = all_60_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (343), (374) imply:
% 27.80/4.70 | | | | (380) all_80_1 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (380) implies:
% 27.80/4.70 | | | | (381) all_80_1 = all_78_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (342), (374) imply:
% 27.80/4.70 | | | | (382) all_78_0 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (344), (374) imply:
% 27.80/4.70 | | | | (383) all_78_0 = all_78_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (341), (381) imply:
% 27.80/4.70 | | | | (384) all_78_0 = all_70_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (384) implies:
% 27.80/4.70 | | | | (385) all_78_0 = all_70_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (358), (359) imply:
% 27.80/4.70 | | | | (386) all_78_3 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (386) implies:
% 27.80/4.70 | | | | (387) all_78_3 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (382), (385) imply:
% 27.80/4.70 | | | | (388) all_70_0 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (383), (385) imply:
% 27.80/4.70 | | | | (389) all_78_1 = all_70_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (389) implies:
% 27.80/4.70 | | | | (390) all_78_1 = all_70_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (368), (390) imply:
% 27.80/4.70 | | | | (391) all_70_0 = all_56_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (391) implies:
% 27.80/4.70 | | | | (392) all_70_0 = all_56_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (357), (387) imply:
% 27.80/4.70 | | | | (393) all_76_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (393) implies:
% 27.80/4.70 | | | | (394) all_76_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (356), (394) imply:
% 27.80/4.70 | | | | (395) all_74_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (395) implies:
% 27.80/4.70 | | | | (396) all_74_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (355), (396) imply:
% 27.80/4.70 | | | | (397) all_72_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (397) implies:
% 27.80/4.70 | | | | (398) all_72_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (354), (398) imply:
% 27.80/4.70 | | | | (399) all_68_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (399) implies:
% 27.80/4.70 | | | | (400) all_68_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (388), (392) imply:
% 27.80/4.70 | | | | (401) all_56_0 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (378), (400) imply:
% 27.80/4.70 | | | | (402) all_64_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (402) implies:
% 27.80/4.70 | | | | (403) all_64_0 = all_62_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (353), (376) imply:
% 27.80/4.70 | | | | (404) all_64_0 = all_58_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (404) implies:
% 27.80/4.70 | | | | (405) all_64_0 = all_58_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (351), (353) imply:
% 27.80/4.70 | | | | (406) all_58_0 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (403), (405) imply:
% 27.80/4.70 | | | | (407) all_62_0 = all_58_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (379), (403) imply:
% 27.80/4.70 | | | | (408) all_62_0 = all_60_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (407), (408) imply:
% 27.80/4.70 | | | | (409) all_60_0 = all_58_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (409) implies:
% 27.80/4.70 | | | | (410) all_60_0 = all_58_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (352), (410) imply:
% 27.80/4.70 | | | | (411) all_58_0 = all_54_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (411) implies:
% 27.80/4.70 | | | | (412) all_58_0 = all_54_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (406), (412) imply:
% 27.80/4.70 | | | | (413) all_54_0 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (406), (407) imply:
% 27.80/4.70 | | | | (414) all_62_0 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (403), (414) imply:
% 27.80/4.70 | | | | (415) all_64_0 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (387), (414) imply:
% 27.80/4.70 | | | | (416) all_78_3 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (368), (401) imply:
% 27.80/4.70 | | | | (417) all_78_1 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (341), (388) imply:
% 27.80/4.70 | | | | (418) all_80_1 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (370), (415) imply:
% 27.80/4.70 | | | | (419) all_82_3 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (372), (382) imply:
% 27.80/4.70 | | | | (420) all_82_1 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (366), (382) imply:
% 27.80/4.70 | | | | (421) all_82_0 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (348), (401) imply:
% 27.80/4.70 | | | | (422) all_84_1 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (350), (382) imply:
% 27.80/4.70 | | | | (423) all_84_0 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (324), (422), (423) imply:
% 27.80/4.70 | | | | (424) subtract(any2, all_24_0, all_24_0) = all_84_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (319), (420), (421) imply:
% 27.80/4.70 | | | | (425) subtract(any2, all_24_0, all_24_0) = all_82_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (313), (342), (418) imply:
% 27.80/4.70 | | | | (426) subtract(any2, all_24_0, all_24_0) = all_80_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (308), (382), (417) imply:
% 27.80/4.70 | | | | (427) subtract(any2, all_24_0, all_24_0) = all_78_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (317), (419) imply:
% 27.80/4.70 | | | | (428) apply(x, all_24_1) = all_82_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (306), (416) imply:
% 27.80/4.70 | | | | (429) apply(x, all_24_1) = all_78_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (277), (413) imply:
% 27.80/4.70 | | | | (430) $i(all_24_1)
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (282), (406) imply:
% 27.80/4.70 | | | | (431) element(all_24_1, any1)
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | GROUND_INST: instantiating (18) with all_24_0, all_82_2, all_24_1, x,
% 27.80/4.70 | | | | simplifying with (24), (428) gives:
% 27.80/4.70 | | | | (432) all_82_2 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | GROUND_INST: instantiating (19) with all_80_2, all_82_2, all_24_0,
% 27.80/4.70 | | | | all_24_0, any2, simplifying with (425), (426) gives:
% 27.80/4.70 | | | | (433) all_82_2 = all_80_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | GROUND_INST: instantiating (19) with all_82_2, all_84_2, all_24_0,
% 27.80/4.70 | | | | all_24_0, any2, simplifying with (424), (425) gives:
% 27.80/4.70 | | | | (434) all_84_2 = all_82_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | GROUND_INST: instantiating (19) with all_78_2, all_84_2, all_24_0,
% 27.80/4.70 | | | | all_24_0, any2, simplifying with (424), (427) gives:
% 27.80/4.70 | | | | (435) all_84_2 = all_78_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (434), (435) imply:
% 27.80/4.70 | | | | (436) all_82_2 = all_78_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (436) implies:
% 27.80/4.70 | | | | (437) all_82_2 = all_78_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (432), (433) imply:
% 27.80/4.70 | | | | (438) all_80_2 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (433), (437) imply:
% 27.80/4.70 | | | | (439) all_80_2 = all_78_2
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | COMBINE_EQS: (438), (439) imply:
% 27.80/4.70 | | | | (440) all_78_2 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | SIMP: (440) implies:
% 27.80/4.70 | | | | (441) all_78_2 = all_24_0
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | GROUND_INST: instantiating (3) with x, any1, all_24_1, all_37_0,
% 27.80/4.70 | | | | all_24_0, any2, simplifying with (12), (13), (14), (15),
% 27.80/4.70 | | | | (24), (238), (243), (244), (258), (430), (431) gives:
% 27.80/4.70 | | | | (442) all_37_0 = all_24_1
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | REDUCE: (325), (442) imply:
% 27.80/4.70 | | | | (443) $false
% 27.80/4.70 | | | |
% 27.80/4.70 | | | | CLOSE: (443) is inconsistent.
% 27.80/4.70 | | | |
% 27.80/4.70 | | | End of split
% 27.80/4.70 | | |
% 27.80/4.70 | | End of split
% 27.80/4.70 | |
% 27.80/4.70 | End of split
% 27.80/4.70 |
% 27.80/4.70 End of proof
% 27.80/4.70 % SZS output end Proof for theBenchmark
% 27.80/4.70
% 27.80/4.70 4074ms
%------------------------------------------------------------------------------