TSTP Solution File: SEU012+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n007.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 17:42:17 EDT 2023

% Result   : Theorem 12.87s 2.69s
% Output   : Proof 18.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.33  % Computer : n007.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Wed Aug 23 18:09:24 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.16/0.59  ________       _____
% 0.16/0.59  ___  __ \_________(_)________________________________
% 0.16/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.16/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.16/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.16/0.59  
% 0.16/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.59  (2023-06-19)
% 0.16/0.59  
% 0.16/0.59  (c) Philipp Rümmer, 2009-2023
% 0.16/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.59                Amanda Stjerna.
% 0.16/0.59  Free software under BSD-3-Clause.
% 0.16/0.59  
% 0.16/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.60  
% 0.16/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.61  Running up to 7 provers in parallel.
% 0.16/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.02/1.18  Prover 1: Preprocessing ...
% 3.02/1.18  Prover 4: Preprocessing ...
% 3.49/1.24  Prover 2: Preprocessing ...
% 3.49/1.24  Prover 5: Preprocessing ...
% 3.49/1.24  Prover 3: Preprocessing ...
% 3.49/1.24  Prover 6: Preprocessing ...
% 3.49/1.25  Prover 0: Preprocessing ...
% 8.02/1.91  Prover 1: Warning: ignoring some quantifiers
% 8.55/2.00  Prover 1: Constructing countermodel ...
% 8.55/2.09  Prover 3: Warning: ignoring some quantifiers
% 8.55/2.10  Prover 3: Constructing countermodel ...
% 8.55/2.13  Prover 5: Proving ...
% 8.55/2.13  Prover 6: Proving ...
% 9.32/2.18  Prover 2: Proving ...
% 10.86/2.32  Prover 4: Warning: ignoring some quantifiers
% 10.86/2.38  Prover 4: Constructing countermodel ...
% 12.24/2.50  Prover 0: Proving ...
% 12.87/2.67  Prover 3: proved (2041ms)
% 12.87/2.67  
% 12.87/2.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.87/2.69  
% 12.87/2.69  Prover 2: stopped
% 12.87/2.69  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.87/2.69  Prover 0: stopped
% 12.87/2.70  Prover 5: stopped
% 12.87/2.71  Prover 6: stopped
% 12.87/2.71  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.87/2.71  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.87/2.71  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.87/2.71  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.87/2.77  Prover 10: Preprocessing ...
% 12.87/2.79  Prover 7: Preprocessing ...
% 13.46/2.81  Prover 13: Preprocessing ...
% 13.46/2.82  Prover 11: Preprocessing ...
% 13.46/2.82  Prover 8: Preprocessing ...
% 13.46/2.88  Prover 10: Warning: ignoring some quantifiers
% 14.92/2.90  Prover 10: Constructing countermodel ...
% 14.92/2.92  Prover 7: Warning: ignoring some quantifiers
% 14.92/2.95  Prover 7: Constructing countermodel ...
% 14.92/2.98  Prover 13: Warning: ignoring some quantifiers
% 14.92/2.98  Prover 8: Warning: ignoring some quantifiers
% 15.68/3.00  Prover 8: Constructing countermodel ...
% 15.89/3.02  Prover 13: Constructing countermodel ...
% 17.25/3.20  Prover 1: Found proof (size 117)
% 17.25/3.20  Prover 1: proved (2579ms)
% 17.25/3.20  Prover 13: stopped
% 17.25/3.20  Prover 4: stopped
% 17.25/3.20  Prover 10: stopped
% 17.25/3.20  Prover 7: stopped
% 17.25/3.20  Prover 8: stopped
% 17.25/3.27  Prover 11: Warning: ignoring some quantifiers
% 17.73/3.29  Prover 11: Constructing countermodel ...
% 17.77/3.30  Prover 11: stopped
% 17.77/3.30  
% 17.77/3.30  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.77/3.30  
% 17.86/3.34  % SZS output start Proof for theBenchmark
% 17.86/3.34  Assumptions after simplification:
% 17.86/3.34  ---------------------------------
% 17.86/3.34  
% 17.86/3.34    (d5_funct_1)
% 17.86/3.39     ! [v0: $i] :  ! [v1: $i] : ( ~ (relation_rng(v0) = v1) |  ~ $i(v0) |  ? [v2:
% 17.86/3.40        any] :  ? [v3: any] :  ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0)
% 17.86/3.40        = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) |  ~ (v2 = 0) | ( ? [v5:
% 17.86/3.40              $i] : (v5 = v1 |  ~ $i(v5) |  ? [v6: $i] :  ? [v7: any] : (in(v6,
% 17.86/3.40                  v5) = v7 & $i(v6) & ( ~ (v7 = 0) |  ! [v8: $i] : ( ~ (in(v8, v4)
% 17.86/3.40                      = 0) |  ~ $i(v8) |  ? [v9: $i] : ( ~ (v9 = v6) & apply(v0,
% 17.86/3.40                        v8) = v9 & $i(v9)))) & (v7 = 0 |  ? [v8: $i] : (apply(v0,
% 17.86/3.40                      v8) = v6 & in(v8, v4) = 0 & $i(v8))))) & ( ~ $i(v1) | ( !
% 17.86/3.40                [v5: $i] :  ! [v6: int] : (v6 = 0 |  ~ (in(v5, v1) = v6) |  ~
% 17.86/3.40                  $i(v5) |  ! [v7: $i] : ( ~ (in(v7, v4) = 0) |  ~ $i(v7) |  ?
% 17.86/3.40                    [v8: $i] : ( ~ (v8 = v5) & apply(v0, v7) = v8 & $i(v8)))) &  !
% 17.86/3.40                [v5: $i] : ( ~ (in(v5, v1) = 0) |  ~ $i(v5) |  ? [v6: $i] :
% 17.86/3.40                  (apply(v0, v6) = v5 & in(v6, v4) = 0 & $i(v6)))))))))
% 17.86/3.40  
% 17.86/3.40    (fc10_relat_1)
% 17.86/3.40     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (relation_composition(v1, v0) =
% 17.86/3.40        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 17.86/3.40       ? [v6: any] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 &
% 17.86/3.40        empty(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 17.86/3.40  
% 17.86/3.40    (fc5_relat_1)
% 17.86/3.41     ! [v0: $i] :  ! [v1: $i] : ( ~ (relation_dom(v0) = v1) |  ~ $i(v0) |  ? [v2:
% 17.86/3.41        any] :  ? [v3: any] :  ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 17.86/3.41        empty(v0) = v2 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v2 = 0)))
% 17.86/3.41  
% 17.86/3.41    (fc6_relat_1)
% 17.86/3.41     ! [v0: $i] :  ! [v1: $i] : ( ~ (relation_rng(v0) = v1) |  ~ $i(v0) |  ? [v2:
% 17.86/3.41        any] :  ? [v3: any] :  ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 17.86/3.41        empty(v0) = v2 & ( ~ (v4 = 0) |  ~ (v3 = 0) | v2 = 0)))
% 17.86/3.41  
% 17.86/3.41    (fc9_relat_1)
% 17.86/3.41     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 17.86/3.41        v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: any] :  ? [v4: any] :  ? [v5: any] :
% 17.86/3.41       ? [v6: any] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 &
% 17.86/3.41        empty(v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 17.86/3.41  
% 17.86/3.41    (t23_funct_1)
% 17.86/3.42     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: any] : ( ~ (relation_dom(v1)
% 17.86/3.42        = v2) |  ~ (in(v0, v2) = v3) |  ~ $i(v1) |  ~ $i(v0) |  ? [v4: any] :  ?
% 17.86/3.42      [v5: any] :  ? [v6: $i] : (apply(v1, v0) = v6 & relation(v1) = v4 &
% 17.86/3.42        function(v1) = v5 & $i(v6) & ( ~ (v5 = 0) |  ~ (v4 = 0) |  ! [v7: $i] :  !
% 17.86/3.42          [v8: $i] :  ! [v9: $i] : ( ~ (v3 = 0) |  ~ (relation_composition(v1, v7)
% 17.86/3.42              = v8) |  ~ (apply(v8, v0) = v9) |  ~ $i(v7) |  ? [v10: any] :  ?
% 17.86/3.42            [v11: any] :  ? [v12: $i] : (apply(v7, v6) = v12 & relation(v7) = v10
% 17.86/3.42              & function(v7) = v11 & $i(v12) & ( ~ (v11 = 0) |  ~ (v10 = 0) | v12
% 17.86/3.42                = v9))))))
% 17.86/3.42  
% 17.86/3.42    (t34_funct_1)
% 18.15/3.43     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : ( ~
% 18.15/3.43      (identity_relation(v0) = v2) |  ~ (relation_dom(v1) = v3) |  ~ $i(v1) |  ~
% 18.15/3.43      $i(v0) |  ? [v4: any] :  ? [v5: any] : (relation(v1) = v4 & function(v1) =
% 18.15/3.43        v5 & ( ~ (v5 = 0) |  ~ (v4 = 0))) | (( ~ (v3 = v0) | v2 = v1 |  ? [v4: $i]
% 18.15/3.43          :  ? [v5: $i] : ( ~ (v5 = v4) & apply(v1, v4) = v5 & in(v4, v0) = 0 &
% 18.15/3.43            $i(v5) & $i(v4))) & ( ~ (v2 = v1) | (v3 = v0 &  ! [v4: $i] :  ! [v5:
% 18.15/3.43              $i] : (v5 = v4 |  ~ (apply(v1, v4) = v5) |  ~ $i(v4) |  ? [v6: int]
% 18.15/3.43              : ( ~ (v6 = 0) & in(v4, v0) = v6))))))
% 18.15/3.43  
% 18.15/3.43    (t44_funct_1)
% 18.15/3.43     ? [v0: $i] :  ? [v1: $i] : (relation_rng(v0) = v1 & relation(v0) = 0 &
% 18.15/3.43      function(v0) = 0 & $i(v1) & $i(v0) &  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 =
% 18.15/3.43          v2) & identity_relation(v1) = v3 & relation_composition(v0, v2) = v0 &
% 18.15/3.43        relation_dom(v2) = v1 & relation(v2) = 0 & function(v2) = 0 & $i(v3) &
% 18.15/3.43        $i(v2)))
% 18.15/3.43  
% 18.15/3.43    (function-axioms)
% 18.15/3.44     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 18.15/3.44    [v3: $i] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) & 
% 18.15/3.44    ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 18.15/3.44      $i] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0)) &  !
% 18.15/3.44    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 18.15/3.44      (relation_composition(v3, v2) = v1) |  ~ (relation_composition(v3, v2) =
% 18.15/3.44        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 18.15/3.44      ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0:
% 18.15/3.44      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 18.15/3.44    : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0: $i] :  !
% 18.15/3.44    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2)
% 18.15/3.44        = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 18.15/3.44      $i] : (v1 = v0 |  ~ (relation_empty_yielding(v2) = v1) |  ~
% 18.15/3.44      (relation_empty_yielding(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 18.15/3.44      $i] : (v1 = v0 |  ~ (identity_relation(v2) = v1) |  ~ (identity_relation(v2)
% 18.15/3.44        = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 18.15/3.44      (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0)) &  ! [v0: $i] :  !
% 18.15/3.44    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (relation_dom(v2) = v1) |  ~
% 18.15/3.44      (relation_dom(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 18.15/3.44      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (relation(v2) = v1) |  ~
% 18.15/3.44      (relation(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 18.15/3.44      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (function(v2) = v1) |  ~
% 18.15/3.44      (function(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 18.15/3.44      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~
% 18.15/3.44      (empty(v2) = v0))
% 18.15/3.44  
% 18.15/3.44  Further assumptions not needed in the proof:
% 18.15/3.44  --------------------------------------------
% 18.15/3.44  antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, dt_k5_relat_1, dt_k6_relat_1,
% 18.15/3.44  existence_m1_subset_1, fc12_relat_1, fc1_funct_1, fc1_subset_1, fc1_xboole_0,
% 18.15/3.44  fc2_funct_1, fc4_relat_1, fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1,
% 18.15/3.44  rc1_subset_1, rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0,
% 18.15/3.44  rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset,
% 18.15/3.44  t5_subset, t6_boole, t7_boole, t8_boole
% 18.15/3.44  
% 18.15/3.44  Those formulas are unsatisfiable:
% 18.15/3.44  ---------------------------------
% 18.15/3.44  
% 18.15/3.44  Begin of proof
% 18.15/3.45  | 
% 18.15/3.45  | ALPHA: (function-axioms) implies:
% 18.15/3.45  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 18.15/3.45  |        (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0))
% 18.15/3.45  |   (2)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 18.15/3.45  |        (v1 = v0 |  ~ (relation(v2) = v1) |  ~ (relation(v2) = v0))
% 18.15/3.45  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 18.15/3.45  |          (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 18.15/3.45  | 
% 18.15/3.45  | DELTA: instantiating (t44_funct_1) with fresh symbols all_46_0, all_46_1
% 18.15/3.45  |        gives:
% 18.15/3.45  |   (4)  relation_rng(all_46_1) = all_46_0 & relation(all_46_1) = 0 &
% 18.15/3.45  |        function(all_46_1) = 0 & $i(all_46_0) & $i(all_46_1) &  ? [v0: $i] :  ?
% 18.15/3.45  |        [v1: $i] : ( ~ (v1 = v0) & identity_relation(all_46_0) = v1 &
% 18.15/3.45  |          relation_composition(all_46_1, v0) = all_46_1 & relation_dom(v0) =
% 18.15/3.45  |          all_46_0 & relation(v0) = 0 & function(v0) = 0 & $i(v1) & $i(v0))
% 18.15/3.45  | 
% 18.15/3.45  | ALPHA: (4) implies:
% 18.15/3.45  |   (5)  $i(all_46_1)
% 18.15/3.45  |   (6)  $i(all_46_0)
% 18.15/3.45  |   (7)  function(all_46_1) = 0
% 18.15/3.45  |   (8)  relation(all_46_1) = 0
% 18.15/3.45  |   (9)  relation_rng(all_46_1) = all_46_0
% 18.15/3.45  |   (10)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) &
% 18.15/3.45  |           identity_relation(all_46_0) = v1 & relation_composition(all_46_1,
% 18.15/3.45  |             v0) = all_46_1 & relation_dom(v0) = all_46_0 & relation(v0) = 0 &
% 18.15/3.45  |           function(v0) = 0 & $i(v1) & $i(v0))
% 18.15/3.45  | 
% 18.15/3.46  | DELTA: instantiating (10) with fresh symbols all_48_0, all_48_1 gives:
% 18.15/3.46  |   (11)   ~ (all_48_0 = all_48_1) & identity_relation(all_46_0) = all_48_0 &
% 18.15/3.46  |         relation_composition(all_46_1, all_48_1) = all_46_1 &
% 18.15/3.46  |         relation_dom(all_48_1) = all_46_0 & relation(all_48_1) = 0 &
% 18.15/3.46  |         function(all_48_1) = 0 & $i(all_48_0) & $i(all_48_1)
% 18.15/3.46  | 
% 18.15/3.46  | ALPHA: (11) implies:
% 18.15/3.46  |   (12)   ~ (all_48_0 = all_48_1)
% 18.15/3.46  |   (13)  $i(all_48_1)
% 18.15/3.46  |   (14)  function(all_48_1) = 0
% 18.15/3.46  |   (15)  relation(all_48_1) = 0
% 18.15/3.46  |   (16)  relation_dom(all_48_1) = all_46_0
% 18.15/3.46  |   (17)  relation_composition(all_46_1, all_48_1) = all_46_1
% 18.15/3.46  |   (18)  identity_relation(all_46_0) = all_48_0
% 18.15/3.46  | 
% 18.15/3.46  | GROUND_INST: instantiating (fc5_relat_1) with all_48_1, all_46_0, simplifying
% 18.15/3.46  |              with (13), (16) gives:
% 18.15/3.46  |   (19)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (relation(all_48_1) = v1
% 18.15/3.46  |           & empty(all_48_1) = v0 & empty(all_46_0) = v2 & ( ~ (v2 = 0) |  ~
% 18.15/3.46  |             (v1 = 0) | v0 = 0))
% 18.15/3.46  | 
% 18.15/3.46  | GROUND_INST: instantiating (d5_funct_1) with all_46_1, all_46_0, simplifying
% 18.15/3.46  |              with (5), (9) gives:
% 18.15/3.46  |   (20)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (relation_dom(all_46_1) =
% 18.15/3.46  |           v2 & relation(all_46_1) = v0 & function(all_46_1) = v1 & $i(v2) & (
% 18.15/3.46  |             ~ (v1 = 0) |  ~ (v0 = 0) | ( ? [v3: any] : (v3 = all_46_0 |  ~
% 18.15/3.46  |                 $i(v3) |  ? [v4: $i] :  ? [v5: any] : (in(v4, v3) = v5 &
% 18.15/3.46  |                   $i(v4) & ( ~ (v5 = 0) |  ! [v6: $i] : ( ~ (in(v6, v2) = 0) |
% 18.15/3.46  |                        ~ $i(v6) |  ? [v7: $i] : ( ~ (v7 = v4) &
% 18.15/3.46  |                         apply(all_46_1, v6) = v7 & $i(v7)))) & (v5 = 0 |  ?
% 18.15/3.47  |                     [v6: $i] : (apply(all_46_1, v6) = v4 & in(v6, v2) = 0 &
% 18.15/3.47  |                       $i(v6))))) & ( ~ $i(all_46_0) | ( ! [v3: $i] :  ! [v4:
% 18.15/3.47  |                     int] : (v4 = 0 |  ~ (in(v3, all_46_0) = v4) |  ~ $i(v3) | 
% 18.15/3.47  |                     ! [v5: $i] : ( ~ (in(v5, v2) = 0) |  ~ $i(v5) |  ? [v6:
% 18.15/3.47  |                         $i] : ( ~ (v6 = v3) & apply(all_46_1, v5) = v6 &
% 18.15/3.47  |                         $i(v6)))) &  ! [v3: $i] : ( ~ (in(v3, all_46_0) = 0) |
% 18.15/3.47  |                      ~ $i(v3) |  ? [v4: $i] : (apply(all_46_1, v4) = v3 &
% 18.15/3.47  |                       in(v4, v2) = 0 & $i(v4))))))))
% 18.15/3.47  | 
% 18.15/3.47  | GROUND_INST: instantiating (fc6_relat_1) with all_46_1, all_46_0, simplifying
% 18.15/3.47  |              with (5), (9) gives:
% 18.15/3.47  |   (21)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] : (relation(all_46_1) = v1
% 18.15/3.47  |           & empty(all_46_0) = v2 & empty(all_46_1) = v0 & ( ~ (v2 = 0) |  ~
% 18.15/3.47  |             (v1 = 0) | v0 = 0))
% 18.15/3.47  | 
% 18.15/3.47  | GROUND_INST: instantiating (fc10_relat_1) with all_48_1, all_46_1, all_46_1,
% 18.15/3.47  |              simplifying with (5), (13), (17) gives:
% 18.15/3.47  |   (22)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 18.15/3.47  |         (relation(all_46_1) = v3 & relation(all_46_1) = v1 & empty(all_48_1) =
% 18.15/3.47  |           v0 & empty(all_46_1) = v2 & ( ~ (v1 = 0) |  ~ (v0 = 0) | (v3 = 0 &
% 18.15/3.47  |               v2 = 0)))
% 18.15/3.47  | 
% 18.15/3.47  | GROUND_INST: instantiating (fc9_relat_1) with all_46_1, all_48_1, all_46_1,
% 18.15/3.47  |              simplifying with (5), (13), (17) gives:
% 18.15/3.47  |   (23)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :  ? [v3: any] :
% 18.15/3.47  |         (relation(all_48_1) = v1 & relation(all_46_1) = v3 & empty(all_46_1) =
% 18.15/3.47  |           v2 & empty(all_46_1) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0) | (v3 = 0 &
% 18.15/3.47  |               v2 = 0)))
% 18.15/3.47  | 
% 18.15/3.47  | GROUND_INST: instantiating (t34_funct_1) with all_46_0, all_48_1, all_48_0,
% 18.15/3.47  |              all_46_0, simplifying with (6), (13), (16), (18) gives:
% 18.15/3.47  |   (24)   ? [v0: any] :  ? [v1: any] : (relation(all_48_1) = v0 &
% 18.15/3.47  |           function(all_48_1) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0))) | (( ~
% 18.15/3.47  |             (all_48_0 = all_48_1) |  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~
% 18.15/3.47  |               (apply(all_48_1, v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2
% 18.15/3.47  |                   = 0) & in(v0, all_46_0) = v2))) & (all_48_0 = all_48_1 |  ?
% 18.15/3.47  |             [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) & apply(all_48_1, v0) = v1
% 18.15/3.47  |               & in(v0, all_46_0) = 0 & $i(v1) & $i(v0))))
% 18.15/3.47  | 
% 18.15/3.47  | DELTA: instantiating (21) with fresh symbols all_56_0, all_56_1, all_56_2
% 18.15/3.47  |        gives:
% 18.15/3.47  |   (25)  relation(all_46_1) = all_56_1 & empty(all_46_0) = all_56_0 &
% 18.15/3.47  |         empty(all_46_1) = all_56_2 & ( ~ (all_56_0 = 0) |  ~ (all_56_1 = 0) |
% 18.15/3.47  |           all_56_2 = 0)
% 18.15/3.47  | 
% 18.15/3.47  | ALPHA: (25) implies:
% 18.15/3.47  |   (26)  relation(all_46_1) = all_56_1
% 18.15/3.47  | 
% 18.15/3.47  | DELTA: instantiating (19) with fresh symbols all_60_0, all_60_1, all_60_2
% 18.15/3.47  |        gives:
% 18.15/3.48  |   (27)  relation(all_48_1) = all_60_1 & empty(all_48_1) = all_60_2 &
% 18.15/3.48  |         empty(all_46_0) = all_60_0 & ( ~ (all_60_0 = 0) |  ~ (all_60_1 = 0) |
% 18.15/3.48  |           all_60_2 = 0)
% 18.15/3.48  | 
% 18.15/3.48  | ALPHA: (27) implies:
% 18.15/3.48  |   (28)  relation(all_48_1) = all_60_1
% 18.15/3.48  | 
% 18.15/3.48  | DELTA: instantiating (23) with fresh symbols all_64_0, all_64_1, all_64_2,
% 18.15/3.48  |        all_64_3 gives:
% 18.15/3.48  |   (29)  relation(all_48_1) = all_64_2 & relation(all_46_1) = all_64_0 &
% 18.15/3.48  |         empty(all_46_1) = all_64_1 & empty(all_46_1) = all_64_3 & ( ~
% 18.15/3.48  |           (all_64_2 = 0) |  ~ (all_64_3 = 0) | (all_64_0 = 0 & all_64_1 = 0))
% 18.15/3.48  | 
% 18.15/3.48  | ALPHA: (29) implies:
% 18.15/3.48  |   (30)  relation(all_46_1) = all_64_0
% 18.15/3.48  |   (31)  relation(all_48_1) = all_64_2
% 18.15/3.48  | 
% 18.15/3.48  | DELTA: instantiating (22) with fresh symbols all_66_0, all_66_1, all_66_2,
% 18.15/3.48  |        all_66_3 gives:
% 18.15/3.48  |   (32)  relation(all_46_1) = all_66_0 & relation(all_46_1) = all_66_2 &
% 18.15/3.48  |         empty(all_48_1) = all_66_3 & empty(all_46_1) = all_66_1 & ( ~
% 18.15/3.48  |           (all_66_2 = 0) |  ~ (all_66_3 = 0) | (all_66_0 = 0 & all_66_1 = 0))
% 18.15/3.48  | 
% 18.15/3.48  | ALPHA: (32) implies:
% 18.15/3.48  |   (33)  relation(all_46_1) = all_66_2
% 18.15/3.48  |   (34)  relation(all_46_1) = all_66_0
% 18.15/3.48  | 
% 18.15/3.48  | DELTA: instantiating (20) with fresh symbols all_68_0, all_68_1, all_68_2
% 18.15/3.48  |        gives:
% 18.15/3.48  |   (35)  relation_dom(all_46_1) = all_68_0 & relation(all_46_1) = all_68_2 &
% 18.15/3.48  |         function(all_46_1) = all_68_1 & $i(all_68_0) & ( ~ (all_68_1 = 0) |  ~
% 18.15/3.48  |           (all_68_2 = 0) | ( ? [v0: any] : (v0 = all_46_0 |  ~ $i(v0) |  ?
% 18.15/3.48  |               [v1: $i] :  ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 =
% 18.15/3.48  |                     0) |  ! [v3: $i] : ( ~ (in(v3, all_68_0) = 0) |  ~ $i(v3)
% 18.15/3.48  |                     |  ? [v4: $i] : ( ~ (v4 = v1) & apply(all_46_1, v3) = v4 &
% 18.15/3.48  |                       $i(v4)))) & (v2 = 0 |  ? [v3: $i] : (apply(all_46_1, v3)
% 18.15/3.48  |                     = v1 & in(v3, all_68_0) = 0 & $i(v3))))) & ( ~
% 18.15/3.48  |               $i(all_46_0) | ( ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 18.15/3.48  |                   (in(v0, all_46_0) = v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~
% 18.15/3.48  |                     (in(v2, all_68_0) = 0) |  ~ $i(v2) |  ? [v3: $i] : ( ~ (v3
% 18.15/3.48  |                         = v0) & apply(all_46_1, v2) = v3 & $i(v3)))) &  ! [v0:
% 18.15/3.48  |                   $i] : ( ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 18.15/3.48  |                   (apply(all_46_1, v1) = v0 & in(v1, all_68_0) = 0 &
% 18.15/3.48  |                     $i(v1)))))))
% 18.15/3.48  | 
% 18.15/3.48  | ALPHA: (35) implies:
% 18.15/3.48  |   (36)  function(all_46_1) = all_68_1
% 18.15/3.48  |   (37)  relation(all_46_1) = all_68_2
% 18.15/3.48  |   (38)  relation_dom(all_46_1) = all_68_0
% 18.15/3.49  |   (39)   ~ (all_68_1 = 0) |  ~ (all_68_2 = 0) | ( ? [v0: any] : (v0 = all_46_0
% 18.15/3.49  |             |  ~ $i(v0) |  ? [v1: $i] :  ? [v2: any] : (in(v1, v0) = v2 &
% 18.15/3.49  |               $i(v1) & ( ~ (v2 = 0) |  ! [v3: $i] : ( ~ (in(v3, all_68_0) = 0)
% 18.15/3.49  |                   |  ~ $i(v3) |  ? [v4: $i] : ( ~ (v4 = v1) & apply(all_46_1,
% 18.15/3.49  |                       v3) = v4 & $i(v4)))) & (v2 = 0 |  ? [v3: $i] :
% 18.15/3.49  |                 (apply(all_46_1, v3) = v1 & in(v3, all_68_0) = 0 & $i(v3)))))
% 18.15/3.49  |           & ( ~ $i(all_46_0) | ( ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 18.15/3.49  |                 (in(v0, all_46_0) = v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~
% 18.15/3.49  |                   (in(v2, all_68_0) = 0) |  ~ $i(v2) |  ? [v3: $i] : ( ~ (v3 =
% 18.15/3.49  |                       v0) & apply(all_46_1, v2) = v3 & $i(v3)))) &  ! [v0: $i]
% 18.15/3.49  |               : ( ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 18.15/3.49  |                 (apply(all_46_1, v1) = v0 & in(v1, all_68_0) = 0 & $i(v1))))))
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (1) with 0, all_68_1, all_46_1, simplifying with
% 18.15/3.49  |              (7), (36) gives:
% 18.15/3.49  |   (40)  all_68_1 = 0
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with all_66_2, all_66_0, all_46_1, simplifying
% 18.15/3.49  |              with (33), (34) gives:
% 18.15/3.49  |   (41)  all_66_0 = all_66_2
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with all_64_0, all_66_0, all_46_1, simplifying
% 18.15/3.49  |              with (30), (34) gives:
% 18.15/3.49  |   (42)  all_66_0 = all_64_0
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with all_56_1, all_66_0, all_46_1, simplifying
% 18.15/3.49  |              with (26), (34) gives:
% 18.15/3.49  |   (43)  all_66_0 = all_56_1
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with 0, all_68_2, all_46_1, simplifying with
% 18.15/3.49  |              (8), (37) gives:
% 18.15/3.49  |   (44)  all_68_2 = 0
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with all_66_2, all_68_2, all_46_1, simplifying
% 18.15/3.49  |              with (33), (37) gives:
% 18.15/3.49  |   (45)  all_68_2 = all_66_2
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with 0, all_64_2, all_48_1, simplifying with
% 18.15/3.49  |              (15), (31) gives:
% 18.15/3.49  |   (46)  all_64_2 = 0
% 18.15/3.49  | 
% 18.15/3.49  | GROUND_INST: instantiating (2) with all_60_1, all_64_2, all_48_1, simplifying
% 18.15/3.49  |              with (28), (31) gives:
% 18.15/3.49  |   (47)  all_64_2 = all_60_1
% 18.15/3.49  | 
% 18.15/3.49  | COMBINE_EQS: (44), (45) imply:
% 18.15/3.49  |   (48)  all_66_2 = 0
% 18.15/3.49  | 
% 18.15/3.49  | SIMP: (48) implies:
% 18.15/3.49  |   (49)  all_66_2 = 0
% 18.15/3.49  | 
% 18.15/3.49  | COMBINE_EQS: (41), (42) imply:
% 18.15/3.49  |   (50)  all_66_2 = all_64_0
% 18.15/3.49  | 
% 18.15/3.49  | SIMP: (50) implies:
% 18.15/3.49  |   (51)  all_66_2 = all_64_0
% 18.15/3.49  | 
% 18.15/3.49  | COMBINE_EQS: (42), (43) imply:
% 18.15/3.49  |   (52)  all_64_0 = all_56_1
% 18.15/3.49  | 
% 18.15/3.50  | COMBINE_EQS: (49), (51) imply:
% 18.15/3.50  |   (53)  all_64_0 = 0
% 18.15/3.50  | 
% 18.15/3.50  | SIMP: (53) implies:
% 18.15/3.50  |   (54)  all_64_0 = 0
% 18.15/3.50  | 
% 18.15/3.50  | COMBINE_EQS: (52), (54) imply:
% 18.15/3.50  |   (55)  all_56_1 = 0
% 18.15/3.50  | 
% 18.15/3.50  | SIMP: (55) implies:
% 18.15/3.50  |   (56)  all_56_1 = 0
% 18.15/3.50  | 
% 18.15/3.50  | COMBINE_EQS: (46), (47) imply:
% 18.15/3.50  |   (57)  all_60_1 = 0
% 18.15/3.50  | 
% 18.15/3.50  | BETA: splitting (39) gives:
% 18.15/3.50  | 
% 18.15/3.50  | Case 1:
% 18.15/3.50  | | 
% 18.15/3.50  | |   (58)   ~ (all_68_1 = 0)
% 18.15/3.50  | | 
% 18.15/3.50  | | REDUCE: (40), (58) imply:
% 18.15/3.50  | |   (59)  $false
% 18.15/3.50  | | 
% 18.15/3.50  | | CLOSE: (59) is inconsistent.
% 18.15/3.50  | | 
% 18.15/3.50  | Case 2:
% 18.15/3.50  | | 
% 18.15/3.50  | |   (60)   ~ (all_68_2 = 0) | ( ? [v0: any] : (v0 = all_46_0 |  ~ $i(v0) |  ?
% 18.15/3.50  | |             [v1: $i] :  ? [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 =
% 18.15/3.50  | |                   0) |  ! [v3: $i] : ( ~ (in(v3, all_68_0) = 0) |  ~ $i(v3)
% 18.15/3.50  | |                   |  ? [v4: $i] : ( ~ (v4 = v1) & apply(all_46_1, v3) = v4 &
% 18.15/3.50  | |                     $i(v4)))) & (v2 = 0 |  ? [v3: $i] : (apply(all_46_1, v3)
% 18.15/3.50  | |                   = v1 & in(v3, all_68_0) = 0 & $i(v3))))) & ( ~
% 18.15/3.50  | |             $i(all_46_0) | ( ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 18.15/3.50  | |                 (in(v0, all_46_0) = v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~
% 18.15/3.50  | |                   (in(v2, all_68_0) = 0) |  ~ $i(v2) |  ? [v3: $i] : ( ~ (v3
% 18.15/3.50  | |                       = v0) & apply(all_46_1, v2) = v3 & $i(v3)))) &  ! [v0:
% 18.15/3.50  | |                 $i] : ( ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 18.15/3.50  | |                 (apply(all_46_1, v1) = v0 & in(v1, all_68_0) = 0 &
% 18.15/3.50  | |                   $i(v1))))))
% 18.15/3.50  | | 
% 18.15/3.50  | | BETA: splitting (24) gives:
% 18.15/3.50  | | 
% 18.15/3.50  | | Case 1:
% 18.15/3.50  | | | 
% 18.15/3.51  | | |   (61)   ? [v0: any] :  ? [v1: any] : (relation(all_48_1) = v0 &
% 18.15/3.51  | | |           function(all_48_1) = v1 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 18.15/3.51  | | | 
% 18.15/3.51  | | | DELTA: instantiating (61) with fresh symbols all_80_0, all_80_1 gives:
% 18.15/3.51  | | |   (62)  relation(all_48_1) = all_80_1 & function(all_48_1) = all_80_0 & (
% 18.15/3.51  | | |           ~ (all_80_0 = 0) |  ~ (all_80_1 = 0))
% 18.15/3.51  | | | 
% 18.15/3.51  | | | ALPHA: (62) implies:
% 18.15/3.51  | | |   (63)  function(all_48_1) = all_80_0
% 18.15/3.51  | | |   (64)  relation(all_48_1) = all_80_1
% 18.15/3.51  | | |   (65)   ~ (all_80_0 = 0) |  ~ (all_80_1 = 0)
% 18.15/3.51  | | | 
% 18.15/3.51  | | | GROUND_INST: instantiating (1) with 0, all_80_0, all_48_1, simplifying
% 18.15/3.51  | | |              with (14), (63) gives:
% 18.15/3.51  | | |   (66)  all_80_0 = 0
% 18.15/3.51  | | | 
% 18.15/3.51  | | | GROUND_INST: instantiating (2) with 0, all_80_1, all_48_1, simplifying
% 18.15/3.51  | | |              with (15), (64) gives:
% 18.15/3.51  | | |   (67)  all_80_1 = 0
% 18.15/3.51  | | | 
% 18.15/3.51  | | | BETA: splitting (65) gives:
% 18.15/3.51  | | | 
% 18.15/3.51  | | | Case 1:
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | |   (68)   ~ (all_80_0 = 0)
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | | REDUCE: (66), (68) imply:
% 18.15/3.51  | | | |   (69)  $false
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | | CLOSE: (69) is inconsistent.
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | Case 2:
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | |   (70)   ~ (all_80_1 = 0)
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | | REDUCE: (67), (70) imply:
% 18.15/3.51  | | | |   (71)  $false
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | | CLOSE: (71) is inconsistent.
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | End of split
% 18.15/3.51  | | | 
% 18.15/3.51  | | Case 2:
% 18.15/3.51  | | | 
% 18.15/3.51  | | |   (72)  ( ~ (all_48_0 = all_48_1) |  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |
% 18.15/3.51  | | |              ~ (apply(all_48_1, v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~
% 18.15/3.51  | | |               (v2 = 0) & in(v0, all_46_0) = v2))) & (all_48_0 = all_48_1 |
% 18.15/3.51  | | |            ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) & apply(all_48_1, v0)
% 18.15/3.51  | | |             = v1 & in(v0, all_46_0) = 0 & $i(v1) & $i(v0)))
% 18.15/3.51  | | | 
% 18.15/3.51  | | | ALPHA: (72) implies:
% 18.15/3.51  | | |   (73)  all_48_0 = all_48_1 |  ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) &
% 18.15/3.51  | | |           apply(all_48_1, v0) = v1 & in(v0, all_46_0) = 0 & $i(v1) &
% 18.15/3.51  | | |           $i(v0))
% 18.15/3.51  | | | 
% 18.15/3.51  | | | BETA: splitting (60) gives:
% 18.15/3.51  | | | 
% 18.15/3.51  | | | Case 1:
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | |   (74)   ~ (all_68_2 = 0)
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | | REDUCE: (44), (74) imply:
% 18.15/3.51  | | | |   (75)  $false
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | | CLOSE: (75) is inconsistent.
% 18.15/3.51  | | | | 
% 18.15/3.51  | | | Case 2:
% 18.15/3.51  | | | | 
% 18.15/3.52  | | | |   (76)   ? [v0: any] : (v0 = all_46_0 |  ~ $i(v0) |  ? [v1: $i] :  ?
% 18.90/3.52  | | | |           [v2: any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) |  ! [v3:
% 18.90/3.52  | | | |                 $i] : ( ~ (in(v3, all_68_0) = 0) |  ~ $i(v3) |  ? [v4:
% 18.90/3.52  | | | |                   $i] : ( ~ (v4 = v1) & apply(all_46_1, v3) = v4 &
% 18.90/3.52  | | | |                   $i(v4)))) & (v2 = 0 |  ? [v3: $i] : (apply(all_46_1,
% 18.90/3.52  | | | |                   v3) = v1 & in(v3, all_68_0) = 0 & $i(v3))))) & ( ~
% 18.90/3.52  | | | |           $i(all_46_0) | ( ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 18.90/3.52  | | | |               (in(v0, all_46_0) = v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~
% 18.90/3.52  | | | |                 (in(v2, all_68_0) = 0) |  ~ $i(v2) |  ? [v3: $i] : ( ~
% 18.90/3.52  | | | |                   (v3 = v0) & apply(all_46_1, v2) = v3 & $i(v3)))) &  !
% 18.90/3.52  | | | |             [v0: $i] : ( ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ? [v1:
% 18.90/3.52  | | | |                 $i] : (apply(all_46_1, v1) = v0 & in(v1, all_68_0) = 0 &
% 18.90/3.52  | | | |                 $i(v1)))))
% 18.90/3.52  | | | | 
% 18.90/3.52  | | | | ALPHA: (76) implies:
% 18.90/3.52  | | | |   (77)   ~ $i(all_46_0) | ( ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 18.90/3.52  | | | |             (in(v0, all_46_0) = v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~
% 18.90/3.52  | | | |               (in(v2, all_68_0) = 0) |  ~ $i(v2) |  ? [v3: $i] : ( ~ (v3
% 18.90/3.52  | | | |                   = v0) & apply(all_46_1, v2) = v3 & $i(v3)))) &  ! [v0:
% 18.90/3.52  | | | |             $i] : ( ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 18.90/3.52  | | | |             (apply(all_46_1, v1) = v0 & in(v1, all_68_0) = 0 & $i(v1))))
% 18.90/3.52  | | | | 
% 18.90/3.52  | | | | BETA: splitting (73) gives:
% 18.90/3.52  | | | | 
% 18.90/3.52  | | | | Case 1:
% 18.90/3.52  | | | | | 
% 18.90/3.52  | | | | |   (78)  all_48_0 = all_48_1
% 18.90/3.52  | | | | | 
% 18.90/3.52  | | | | | REDUCE: (12), (78) imply:
% 18.90/3.52  | | | | |   (79)  $false
% 18.90/3.52  | | | | | 
% 18.90/3.52  | | | | | CLOSE: (79) is inconsistent.
% 18.90/3.52  | | | | | 
% 18.90/3.52  | | | | Case 2:
% 18.90/3.52  | | | | | 
% 18.90/3.53  | | | | |   (80)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v1 = v0) & apply(all_48_1,
% 18.90/3.53  | | | | |             v0) = v1 & in(v0, all_46_0) = 0 & $i(v1) & $i(v0))
% 18.90/3.53  | | | | | 
% 18.90/3.53  | | | | | DELTA: instantiating (80) with fresh symbols all_87_0, all_87_1 gives:
% 18.90/3.53  | | | | |   (81)   ~ (all_87_0 = all_87_1) & apply(all_48_1, all_87_1) =
% 18.90/3.53  | | | | |         all_87_0 & in(all_87_1, all_46_0) = 0 & $i(all_87_0) &
% 18.90/3.53  | | | | |         $i(all_87_1)
% 18.90/3.53  | | | | | 
% 18.90/3.53  | | | | | ALPHA: (81) implies:
% 18.90/3.53  | | | | |   (82)   ~ (all_87_0 = all_87_1)
% 18.90/3.53  | | | | |   (83)  $i(all_87_1)
% 18.90/3.53  | | | | |   (84)  in(all_87_1, all_46_0) = 0
% 18.90/3.53  | | | | |   (85)  apply(all_48_1, all_87_1) = all_87_0
% 18.90/3.53  | | | | | 
% 18.90/3.53  | | | | | BETA: splitting (77) gives:
% 18.90/3.53  | | | | | 
% 18.90/3.53  | | | | | Case 1:
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | |   (86)   ~ $i(all_46_0)
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | | PRED_UNIFY: (6), (86) imply:
% 18.90/3.53  | | | | | |   (87)  $false
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | | CLOSE: (87) is inconsistent.
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | Case 2:
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | |   (88)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (in(v0, all_46_0)
% 18.90/3.53  | | | | | |             = v1) |  ~ $i(v0) |  ! [v2: $i] : ( ~ (in(v2, all_68_0)
% 18.90/3.53  | | | | | |               = 0) |  ~ $i(v2) |  ? [v3: $i] : ( ~ (v3 = v0) &
% 18.90/3.53  | | | | | |               apply(all_46_1, v2) = v3 & $i(v3)))) &  ! [v0: $i] : (
% 18.90/3.53  | | | | | |           ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 18.90/3.53  | | | | | |           (apply(all_46_1, v1) = v0 & in(v1, all_68_0) = 0 &
% 18.90/3.53  | | | | | |             $i(v1)))
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | | ALPHA: (88) implies:
% 18.90/3.53  | | | | | |   (89)   ! [v0: $i] : ( ~ (in(v0, all_46_0) = 0) |  ~ $i(v0) |  ?
% 18.90/3.53  | | | | | |           [v1: $i] : (apply(all_46_1, v1) = v0 & in(v1, all_68_0) =
% 18.90/3.53  | | | | | |             0 & $i(v1)))
% 18.90/3.53  | | | | | | 
% 18.90/3.53  | | | | | | GROUND_INST: instantiating (t23_funct_1) with all_87_1, all_48_1,
% 18.90/3.53  | | | | | |              all_46_0, 0, simplifying with (13), (16), (83), (84)
% 18.90/3.53  | | | | | |              gives:
% 18.90/3.54  | | | | | |   (90)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] : (apply(all_48_1,
% 18.90/3.54  | | | | | |             all_87_1) = v2 & relation(all_48_1) = v0 &
% 18.90/3.54  | | | | | |           function(all_48_1) = v1 & $i(v2) & ( ~ (v1 = 0) |  ~ (v0 =
% 18.90/3.54  | | | | | |               0) |  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : ( ~
% 18.90/3.54  | | | | | |               (relation_composition(all_48_1, v3) = v4) |  ~
% 18.90/3.54  | | | | | |               (apply(v4, all_87_1) = v5) |  ~ $i(v3) |  ? [v6: any]
% 18.90/3.54  | | | | | |               :  ? [v7: any] :  ? [v8: $i] : (apply(v3, v2) = v8 &
% 18.90/3.54  | | | | | |                 relation(v3) = v6 & function(v3) = v7 & $i(v8) & ( ~
% 18.90/3.54  | | | | | |                   (v7 = 0) |  ~ (v6 = 0) | v8 = v5)))))
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | GROUND_INST: instantiating (89) with all_87_1, simplifying with
% 18.90/3.54  | | | | | |              (83), (84) gives:
% 18.90/3.54  | | | | | |   (91)   ? [v0: $i] : (apply(all_46_1, v0) = all_87_1 & in(v0,
% 18.90/3.54  | | | | | |             all_68_0) = 0 & $i(v0))
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | GROUND_INST: instantiating (fc5_relat_1) with all_46_1, all_68_0,
% 18.90/3.54  | | | | | |              simplifying with (5), (38) gives:
% 18.90/3.54  | | | | | |   (92)   ? [v0: any] :  ? [v1: any] :  ? [v2: any] :
% 18.90/3.54  | | | | | |         (relation(all_46_1) = v1 & empty(all_68_0) = v2 &
% 18.90/3.54  | | | | | |           empty(all_46_1) = v0 & ( ~ (v2 = 0) |  ~ (v1 = 0) | v0 =
% 18.90/3.54  | | | | | |             0))
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | DELTA: instantiating (91) with fresh symbol all_103_0 gives:
% 18.90/3.54  | | | | | |   (93)  apply(all_46_1, all_103_0) = all_87_1 & in(all_103_0,
% 18.90/3.54  | | | | | |           all_68_0) = 0 & $i(all_103_0)
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | ALPHA: (93) implies:
% 18.90/3.54  | | | | | |   (94)  $i(all_103_0)
% 18.90/3.54  | | | | | |   (95)  in(all_103_0, all_68_0) = 0
% 18.90/3.54  | | | | | |   (96)  apply(all_46_1, all_103_0) = all_87_1
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | DELTA: instantiating (92) with fresh symbols all_105_0, all_105_1,
% 18.90/3.54  | | | | | |        all_105_2 gives:
% 18.90/3.54  | | | | | |   (97)  relation(all_46_1) = all_105_1 & empty(all_68_0) = all_105_0
% 18.90/3.54  | | | | | |         & empty(all_46_1) = all_105_2 & ( ~ (all_105_0 = 0) |  ~
% 18.90/3.54  | | | | | |           (all_105_1 = 0) | all_105_2 = 0)
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | ALPHA: (97) implies:
% 18.90/3.54  | | | | | |   (98)  relation(all_46_1) = all_105_1
% 18.90/3.54  | | | | | | 
% 18.90/3.54  | | | | | | DELTA: instantiating (90) with fresh symbols all_109_0, all_109_1,
% 18.90/3.54  | | | | | |        all_109_2 gives:
% 18.90/3.54  | | | | | |   (99)  apply(all_48_1, all_87_1) = all_109_0 & relation(all_48_1) =
% 18.90/3.55  | | | | | |         all_109_2 & function(all_48_1) = all_109_1 & $i(all_109_0) &
% 18.90/3.55  | | | | | |         ( ~ (all_109_1 = 0) |  ~ (all_109_2 = 0) |  ! [v0: $i] :  !
% 18.90/3.55  | | | | | |           [v1: $i] :  ! [v2: $i] : ( ~
% 18.90/3.55  | | | | | |             (relation_composition(all_48_1, v0) = v1) |  ~
% 18.90/3.55  | | | | | |             (apply(v1, all_87_1) = v2) |  ~ $i(v0) |  ? [v3: any] : 
% 18.90/3.55  | | | | | |             ? [v4: any] :  ? [v5: $i] : (apply(v0, all_109_0) = v5 &
% 18.90/3.55  | | | | | |               relation(v0) = v3 & function(v0) = v4 & $i(v5) & ( ~
% 18.90/3.55  | | | | | |                 (v4 = 0) |  ~ (v3 = 0) | v5 = v2))))
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | ALPHA: (99) implies:
% 18.90/3.55  | | | | | |   (100)  function(all_48_1) = all_109_1
% 18.90/3.55  | | | | | |   (101)  relation(all_48_1) = all_109_2
% 18.90/3.55  | | | | | |   (102)  apply(all_48_1, all_87_1) = all_109_0
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | GROUND_INST: instantiating (1) with 0, all_109_1, all_48_1,
% 18.90/3.55  | | | | | |              simplifying with (14), (100) gives:
% 18.90/3.55  | | | | | |   (103)  all_109_1 = 0
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | GROUND_INST: instantiating (2) with 0, all_105_1, all_46_1,
% 18.90/3.55  | | | | | |              simplifying with (8), (98) gives:
% 18.90/3.55  | | | | | |   (104)  all_105_1 = 0
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | GROUND_INST: instantiating (2) with 0, all_109_2, all_48_1,
% 18.90/3.55  | | | | | |              simplifying with (15), (101) gives:
% 18.90/3.55  | | | | | |   (105)  all_109_2 = 0
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | GROUND_INST: instantiating (3) with all_87_0, all_109_0, all_87_1,
% 18.90/3.55  | | | | | |              all_48_1, simplifying with (85), (102) gives:
% 18.90/3.55  | | | | | |   (106)  all_109_0 = all_87_0
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | GROUND_INST: instantiating (t23_funct_1) with all_103_0, all_46_1,
% 18.90/3.55  | | | | | |              all_68_0, 0, simplifying with (5), (38), (94), (95)
% 18.90/3.55  | | | | | |              gives:
% 18.90/3.55  | | | | | |   (107)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :
% 18.90/3.55  | | | | | |          (apply(all_46_1, all_103_0) = v2 & relation(all_46_1) = v0
% 18.90/3.55  | | | | | |            & function(all_46_1) = v1 & $i(v2) & ( ~ (v1 = 0) |  ~
% 18.90/3.55  | | | | | |              (v0 = 0) |  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] : (
% 18.90/3.55  | | | | | |                ~ (relation_composition(all_46_1, v3) = v4) |  ~
% 18.90/3.55  | | | | | |                (apply(v4, all_103_0) = v5) |  ~ $i(v3) |  ? [v6:
% 18.90/3.55  | | | | | |                  any] :  ? [v7: any] :  ? [v8: $i] : (apply(v3, v2)
% 18.90/3.55  | | | | | |                  = v8 & relation(v3) = v6 & function(v3) = v7 &
% 18.90/3.55  | | | | | |                  $i(v8) & ( ~ (v7 = 0) |  ~ (v6 = 0) | v8 = v5)))))
% 18.90/3.55  | | | | | | 
% 18.90/3.55  | | | | | | DELTA: instantiating (107) with fresh symbols all_142_0, all_142_1,
% 18.90/3.55  | | | | | |        all_142_2 gives:
% 18.90/3.56  | | | | | |   (108)  apply(all_46_1, all_103_0) = all_142_0 & relation(all_46_1)
% 18.90/3.56  | | | | | |          = all_142_2 & function(all_46_1) = all_142_1 &
% 18.90/3.56  | | | | | |          $i(all_142_0) & ( ~ (all_142_1 = 0) |  ~ (all_142_2 = 0) | 
% 18.90/3.56  | | | | | |            ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 18.90/3.56  | | | | | |              (relation_composition(all_46_1, v0) = v1) |  ~
% 18.90/3.56  | | | | | |              (apply(v1, all_103_0) = v2) |  ~ $i(v0) |  ? [v3: any]
% 18.90/3.56  | | | | | |              :  ? [v4: any] :  ? [v5: $i] : (apply(v0, all_142_0) =
% 18.90/3.56  | | | | | |                v5 & relation(v0) = v3 & function(v0) = v4 & $i(v5) &
% 18.90/3.56  | | | | | |                ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 = v2))))
% 18.90/3.56  | | | | | | 
% 18.90/3.56  | | | | | | ALPHA: (108) implies:
% 18.90/3.56  | | | | | |   (109)  function(all_46_1) = all_142_1
% 18.90/3.56  | | | | | |   (110)  relation(all_46_1) = all_142_2
% 18.90/3.56  | | | | | |   (111)  apply(all_46_1, all_103_0) = all_142_0
% 18.90/3.56  | | | | | |   (112)   ~ (all_142_1 = 0) |  ~ (all_142_2 = 0) |  ! [v0: $i] :  !
% 18.90/3.56  | | | | | |          [v1: $i] :  ! [v2: $i] : ( ~
% 18.90/3.56  | | | | | |            (relation_composition(all_46_1, v0) = v1) |  ~ (apply(v1,
% 18.90/3.56  | | | | | |                all_103_0) = v2) |  ~ $i(v0) |  ? [v3: any] :  ? [v4:
% 18.90/3.56  | | | | | |              any] :  ? [v5: $i] : (apply(v0, all_142_0) = v5 &
% 18.90/3.56  | | | | | |              relation(v0) = v3 & function(v0) = v4 & $i(v5) & ( ~
% 18.90/3.56  | | | | | |                (v4 = 0) |  ~ (v3 = 0) | v5 = v2)))
% 18.90/3.56  | | | | | | 
% 18.90/3.56  | | | | | | GROUND_INST: instantiating (1) with 0, all_142_1, all_46_1,
% 18.90/3.56  | | | | | |              simplifying with (7), (109) gives:
% 18.90/3.56  | | | | | |   (113)  all_142_1 = 0
% 18.90/3.56  | | | | | | 
% 18.90/3.56  | | | | | | GROUND_INST: instantiating (2) with 0, all_142_2, all_46_1,
% 18.90/3.56  | | | | | |              simplifying with (8), (110) gives:
% 18.90/3.56  | | | | | |   (114)  all_142_2 = 0
% 18.90/3.56  | | | | | | 
% 18.90/3.56  | | | | | | GROUND_INST: instantiating (3) with all_87_1, all_142_0, all_103_0,
% 18.90/3.56  | | | | | |              all_46_1, simplifying with (96), (111) gives:
% 18.90/3.56  | | | | | |   (115)  all_142_0 = all_87_1
% 18.90/3.56  | | | | | | 
% 18.90/3.56  | | | | | | BETA: splitting (112) gives:
% 18.90/3.56  | | | | | | 
% 18.90/3.56  | | | | | | Case 1:
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | |   (116)   ~ (all_142_1 = 0)
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | | REDUCE: (113), (116) imply:
% 18.90/3.56  | | | | | | |   (117)  $false
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | | CLOSE: (117) is inconsistent.
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | Case 2:
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | |   (118)   ~ (all_142_2 = 0) |  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 18.90/3.56  | | | | | | |            $i] : ( ~ (relation_composition(all_46_1, v0) = v1) | 
% 18.90/3.56  | | | | | | |            ~ (apply(v1, all_103_0) = v2) |  ~ $i(v0) |  ? [v3:
% 18.90/3.56  | | | | | | |              any] :  ? [v4: any] :  ? [v5: $i] : (apply(v0,
% 18.90/3.56  | | | | | | |                all_142_0) = v5 & relation(v0) = v3 & function(v0)
% 18.90/3.56  | | | | | | |              = v4 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3 = 0) | v5 =
% 18.90/3.56  | | | | | | |                v2)))
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | | BETA: splitting (118) gives:
% 18.90/3.56  | | | | | | | 
% 18.90/3.56  | | | | | | | Case 1:
% 18.90/3.56  | | | | | | | | 
% 18.90/3.56  | | | | | | | |   (119)   ~ (all_142_2 = 0)
% 18.90/3.56  | | | | | | | | 
% 18.90/3.56  | | | | | | | | REDUCE: (114), (119) imply:
% 18.90/3.56  | | | | | | | |   (120)  $false
% 18.90/3.56  | | | | | | | | 
% 18.90/3.56  | | | | | | | | CLOSE: (120) is inconsistent.
% 18.90/3.56  | | | | | | | | 
% 18.90/3.56  | | | | | | | Case 2:
% 18.90/3.56  | | | | | | | | 
% 18.90/3.57  | | | | | | | |   (121)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 18.90/3.57  | | | | | | | |            (relation_composition(all_46_1, v0) = v1) |  ~
% 18.90/3.57  | | | | | | | |            (apply(v1, all_103_0) = v2) |  ~ $i(v0) |  ? [v3:
% 18.90/3.57  | | | | | | | |              any] :  ? [v4: any] :  ? [v5: $i] : (apply(v0,
% 18.90/3.57  | | | | | | | |                all_142_0) = v5 & relation(v0) = v3 &
% 18.90/3.57  | | | | | | | |              function(v0) = v4 & $i(v5) & ( ~ (v4 = 0) |  ~ (v3
% 18.90/3.57  | | | | | | | |                  = 0) | v5 = v2)))
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | GROUND_INST: instantiating (121) with all_48_1, all_46_1,
% 18.90/3.57  | | | | | | | |              all_87_1, simplifying with (13), (17), (96) gives:
% 18.90/3.57  | | | | | | | |   (122)   ? [v0: any] :  ? [v1: any] :  ? [v2: $i] :
% 18.90/3.57  | | | | | | | |          (apply(all_48_1, all_142_0) = v2 & relation(all_48_1) =
% 18.90/3.57  | | | | | | | |            v0 & function(all_48_1) = v1 & $i(v2) & ( ~ (v1 = 0)
% 18.90/3.57  | | | | | | | |              |  ~ (v0 = 0) | v2 = all_87_1))
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | DELTA: instantiating (122) with fresh symbols all_157_0,
% 18.90/3.57  | | | | | | | |        all_157_1, all_157_2 gives:
% 18.90/3.57  | | | | | | | |   (123)  apply(all_48_1, all_142_0) = all_157_0 &
% 18.90/3.57  | | | | | | | |          relation(all_48_1) = all_157_2 & function(all_48_1) =
% 18.90/3.57  | | | | | | | |          all_157_1 & $i(all_157_0) & ( ~ (all_157_1 = 0) |  ~
% 18.90/3.57  | | | | | | | |            (all_157_2 = 0) | all_157_0 = all_87_1)
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | ALPHA: (123) implies:
% 18.90/3.57  | | | | | | | |   (124)  function(all_48_1) = all_157_1
% 18.90/3.57  | | | | | | | |   (125)  relation(all_48_1) = all_157_2
% 18.90/3.57  | | | | | | | |   (126)  apply(all_48_1, all_142_0) = all_157_0
% 18.90/3.57  | | | | | | | |   (127)   ~ (all_157_1 = 0) |  ~ (all_157_2 = 0) | all_157_0 =
% 18.90/3.57  | | | | | | | |          all_87_1
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | REDUCE: (115), (126) imply:
% 18.90/3.57  | | | | | | | |   (128)  apply(all_48_1, all_87_1) = all_157_0
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | GROUND_INST: instantiating (1) with 0, all_157_1, all_48_1,
% 18.90/3.57  | | | | | | | |              simplifying with (14), (124) gives:
% 18.90/3.57  | | | | | | | |   (129)  all_157_1 = 0
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | GROUND_INST: instantiating (2) with 0, all_157_2, all_48_1,
% 18.90/3.57  | | | | | | | |              simplifying with (15), (125) gives:
% 18.90/3.57  | | | | | | | |   (130)  all_157_2 = 0
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | GROUND_INST: instantiating (3) with all_87_0, all_157_0,
% 18.90/3.57  | | | | | | | |              all_87_1, all_48_1, simplifying with (85), (128)
% 18.90/3.57  | | | | | | | |              gives:
% 18.90/3.57  | | | | | | | |   (131)  all_157_0 = all_87_0
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | BETA: splitting (127) gives:
% 18.90/3.57  | | | | | | | | 
% 18.90/3.57  | | | | | | | | Case 1:
% 18.90/3.57  | | | | | | | | | 
% 18.90/3.57  | | | | | | | | |   (132)   ~ (all_157_1 = 0)
% 18.90/3.57  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | REDUCE: (129), (132) imply:
% 18.90/3.58  | | | | | | | | |   (133)  $false
% 18.90/3.58  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | CLOSE: (133) is inconsistent.
% 18.90/3.58  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | Case 2:
% 18.90/3.58  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | |   (134)   ~ (all_157_2 = 0) | all_157_0 = all_87_1
% 18.90/3.58  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | BETA: splitting (134) gives:
% 18.90/3.58  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | Case 1:
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | |   (135)   ~ (all_157_2 = 0)
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | | REDUCE: (130), (135) imply:
% 18.90/3.58  | | | | | | | | | |   (136)  $false
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | | CLOSE: (136) is inconsistent.
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | Case 2:
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | |   (137)  all_157_0 = all_87_1
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | | COMBINE_EQS: (131), (137) imply:
% 18.90/3.58  | | | | | | | | | |   (138)  all_87_0 = all_87_1
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | | REDUCE: (82), (138) imply:
% 18.90/3.58  | | | | | | | | | |   (139)  $false
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | | CLOSE: (139) is inconsistent.
% 18.90/3.58  | | | | | | | | | | 
% 18.90/3.58  | | | | | | | | | End of split
% 18.90/3.58  | | | | | | | | | 
% 18.90/3.58  | | | | | | | | End of split
% 18.90/3.58  | | | | | | | | 
% 18.90/3.58  | | | | | | | End of split
% 18.90/3.58  | | | | | | | 
% 18.90/3.58  | | | | | | End of split
% 18.90/3.58  | | | | | | 
% 18.90/3.58  | | | | | End of split
% 18.90/3.58  | | | | | 
% 18.90/3.58  | | | | End of split
% 18.90/3.58  | | | | 
% 18.90/3.58  | | | End of split
% 18.90/3.58  | | | 
% 18.90/3.58  | | End of split
% 18.90/3.58  | | 
% 18.90/3.58  | End of split
% 18.90/3.58  | 
% 18.90/3.58  End of proof
% 18.90/3.58  % SZS output end Proof for theBenchmark
% 18.90/3.58  
% 18.90/3.58  2982ms
%------------------------------------------------------------------------------