TSTP Solution File: COM002_2 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : COM002_2 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 18:44:11 EDT 2023

% Result   : Theorem 6.79s 1.72s
% Output   : Proof 10.48s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM002_2 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue Aug 29 13:24:10 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.52/0.59  ________       _____
% 0.52/0.59  ___  __ \_________(_)________________________________
% 0.52/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.52/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.52/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.52/0.59  
% 0.52/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.59  (2023-06-19)
% 0.52/0.59  
% 0.52/0.59  (c) Philipp Rümmer, 2009-2023
% 0.52/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.59                Amanda Stjerna.
% 0.52/0.59  Free software under BSD-3-Clause.
% 0.52/0.59  
% 0.52/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.59  
% 0.52/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.60  Running up to 7 provers in parallel.
% 0.52/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.52/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.70/1.12  Prover 1: Preprocessing ...
% 2.70/1.12  Prover 4: Preprocessing ...
% 2.70/1.15  Prover 3: Preprocessing ...
% 2.70/1.15  Prover 6: Preprocessing ...
% 2.70/1.16  Prover 5: Preprocessing ...
% 2.70/1.16  Prover 2: Preprocessing ...
% 2.70/1.16  Prover 0: Preprocessing ...
% 4.58/1.36  Prover 6: Constructing countermodel ...
% 4.58/1.36  Prover 1: Constructing countermodel ...
% 4.58/1.37  Prover 3: Constructing countermodel ...
% 4.58/1.37  Prover 5: Proving ...
% 4.58/1.37  Prover 2: Proving ...
% 4.58/1.41  Prover 4: Constructing countermodel ...
% 4.58/1.42  Prover 0: Proving ...
% 6.79/1.72  Prover 3: proved (1105ms)
% 6.79/1.72  
% 6.79/1.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.79/1.72  
% 6.79/1.72  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.79/1.73  Prover 6: stopped
% 6.79/1.73  Prover 2: stopped
% 6.79/1.73  Prover 5: stopped
% 6.79/1.73  Prover 0: stopped
% 6.79/1.73  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.79/1.74  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.79/1.74  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.79/1.74  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.48/1.77  Prover 8: Preprocessing ...
% 7.48/1.78  Prover 7: Preprocessing ...
% 7.48/1.78  Prover 13: Preprocessing ...
% 7.48/1.78  Prover 10: Preprocessing ...
% 7.48/1.79  Prover 11: Preprocessing ...
% 7.86/1.84  Prover 10: Warning: ignoring some quantifiers
% 7.86/1.84  Prover 10: Constructing countermodel ...
% 7.86/1.86  Prover 7: Warning: ignoring some quantifiers
% 7.86/1.87  Prover 7: Constructing countermodel ...
% 7.86/1.87  Prover 13: Warning: ignoring some quantifiers
% 7.86/1.87  Prover 13: Constructing countermodel ...
% 8.38/1.89  Prover 8: Warning: ignoring some quantifiers
% 8.38/1.90  Prover 8: Constructing countermodel ...
% 8.38/1.91  Prover 10: gave up
% 8.38/1.92  Prover 11: Constructing countermodel ...
% 8.38/1.93  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.38/1.96  Prover 16: Preprocessing ...
% 9.06/1.98  Prover 13: gave up
% 9.06/1.98  Prover 7: gave up
% 9.06/1.98  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.40/2.02  Prover 19: Preprocessing ...
% 9.40/2.04  Prover 16: Warning: ignoring some quantifiers
% 9.40/2.05  Prover 16: Constructing countermodel ...
% 9.40/2.09  Prover 19: Warning: ignoring some quantifiers
% 9.40/2.09  Prover 19: Constructing countermodel ...
% 10.06/2.13  Prover 1: Found proof (size 74)
% 10.06/2.13  Prover 1: proved (1520ms)
% 10.06/2.13  Prover 19: stopped
% 10.06/2.13  Prover 16: stopped
% 10.06/2.13  Prover 4: stopped
% 10.06/2.13  Prover 8: stopped
% 10.06/2.13  Prover 11: stopped
% 10.06/2.13  
% 10.06/2.13  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.06/2.13  
% 10.06/2.15  % SZS output start Proof for theBenchmark
% 10.06/2.15  Assumptions after simplification:
% 10.06/2.15  ---------------------------------
% 10.06/2.15  
% 10.06/2.15    (conditional_success)
% 10.06/2.18     ! [v0: boolean] :  ! [v1: state] :  ! [v2: state] :  ! [v3: statement] : ( ~
% 10.06/2.18      (ifthen(v0, v2) = v3) |  ~ (has(v1, v3) = 0) |  ~ boolean(v0) |  ~ state(v2)
% 10.06/2.18      |  ~ state(v1) |  ? [v4: int] : ( ~ (v4 = 0) & fails(v2, v1) = v4))
% 10.06/2.18  
% 10.06/2.18    (direct_success)
% 10.06/2.18     ! [v0: state] :  ! [v1: state] : ( ~ (follows(v1, v0) = 0) |  ~ state(v1) | 
% 10.06/2.18      ~ state(v0) |  ? [v2: int] : ( ~ (v2 = 0) & fails(v1, v0) = v2))
% 10.06/2.18  
% 10.06/2.18    (goto_success)
% 10.48/2.18     ! [v0: label] :  ! [v1: state] :  ! [v2: state] :  ! [v3: statement] : ( ~
% 10.48/2.18      (goto(v0) = v3) |  ~ (has(v1, v3) = 0) |  ~ (labels(v0, v2) = 0) |  ~
% 10.48/2.18      label(v0) |  ~ state(v2) |  ~ state(v1) |  ? [v4: int] : ( ~ (v4 = 0) &
% 10.48/2.18        fails(v2, v1) = v4))
% 10.48/2.18  
% 10.48/2.18    (label_state_3)
% 10.48/2.18    labels(loop, p3) = 0 & label(loop) & state(p3)
% 10.48/2.18  
% 10.48/2.18    (prove_there_is_a_loop_through_p3)
% 10.48/2.18    fails(p3, p3) = 0 & state(p3)
% 10.48/2.18  
% 10.48/2.18    (state_3)
% 10.48/2.18    number(n) & register(register_j) & state(p4) & state(p3) &  ? [v0: boolean] : 
% 10.48/2.18    ? [v1: statement] : (equal_function(register_j, n) = v0 & ifthen(v0, p4) = v1
% 10.48/2.18      & has(p3, v1) = 0 & boolean(v0) & statement(v1))
% 10.48/2.18  
% 10.48/2.18    (state_8)
% 10.48/2.19    label(loop) & state(p8) &  ? [v0: statement] : (goto(loop) = v0 & has(p8, v0)
% 10.48/2.19      = 0 & statement(v0))
% 10.48/2.19  
% 10.48/2.19    (transition_2_to_3)
% 10.48/2.19    follows(p3, p2) = 0 & state(p3) & state(p2)
% 10.48/2.19  
% 10.48/2.19    (transition_3_to_6)
% 10.48/2.19    follows(p6, p3) = 0 & state(p6) & state(p3)
% 10.48/2.19  
% 10.48/2.19    (transition_4_to_5)
% 10.48/2.19    follows(p5, p4) = 0 & state(p5) & state(p4)
% 10.48/2.19  
% 10.48/2.19    (transition_6_to_7)
% 10.48/2.19    follows(p7, p6) = 0 & state(p7) & state(p6)
% 10.48/2.19  
% 10.48/2.19    (transition_7_to_8)
% 10.48/2.19    follows(p8, p7) = 0 & state(p8) & state(p7)
% 10.48/2.19  
% 10.48/2.19    (transitivity_of_success)
% 10.48/2.19     ! [v0: state] :  ! [v1: state] :  ! [v2: state] :  ! [v3: int] :  ! [v4: int]
% 10.48/2.19    : (v4 = 0 | v3 = 0 |  ~ (fails(v2, v0) = v3) |  ~ (fails(v0, v1) = v4) |  ~
% 10.48/2.19      state(v2) |  ~ state(v1) |  ~ state(v0) |  ? [v5: int] : ( ~ (v5 = 0) &
% 10.48/2.19        fails(v2, v1) = v5))
% 10.48/2.19  
% 10.48/2.19    (function-axioms)
% 10.48/2.20     ! [v0: number] :  ! [v1: number] :  ! [v2: number] :  ! [v3: register] : (v1
% 10.48/2.20      = v0 |  ~ (plus(v3, v2) = v1) |  ~ (plus(v3, v2) = v0)) &  ! [v0: number] : 
% 10.48/2.20    ! [v1: number] :  ! [v2: register] :  ! [v3: number] : (v1 = v0 |  ~
% 10.48/2.20      (times(v3, v2) = v1) |  ~ (times(v3, v2) = v0)) &  ! [v0: boolean] :  ! [v1:
% 10.48/2.20      boolean] :  ! [v2: number] :  ! [v3: register] : (v1 = v0 |  ~
% 10.48/2.20      (equal_function(v3, v2) = v1) |  ~ (equal_function(v3, v2) = v0)) &  ! [v0:
% 10.48/2.20      statement] :  ! [v1: statement] :  ! [v2: number] :  ! [v3: register] : (v1
% 10.48/2.20      = v0 |  ~ (assign(v3, v2) = v1) |  ~ (assign(v3, v2) = v0)) &  ! [v0:
% 10.48/2.20      statement] :  ! [v1: statement] :  ! [v2: state] :  ! [v3: boolean] : (v1 =
% 10.48/2.20      v0 |  ~ (ifthen(v3, v2) = v1) |  ~ (ifthen(v3, v2) = v0)) &  ! [v0:
% 10.48/2.20      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: statement] :  !
% 10.48/2.20    [v3: state] : (v1 = v0 |  ~ (has(v3, v2) = v1) |  ~ (has(v3, v2) = v0)) &  !
% 10.48/2.20    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: state] :  !
% 10.48/2.20    [v3: label] : (v1 = v0 |  ~ (labels(v3, v2) = v1) |  ~ (labels(v3, v2) = v0))
% 10.48/2.20    &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: state] : 
% 10.48/2.20    ! [v3: state] : (v1 = v0 |  ~ (follows(v3, v2) = v1) |  ~ (follows(v3, v2) =
% 10.48/2.20        v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 10.48/2.20      state] :  ! [v3: state] : (v1 = v0 |  ~ (fails(v3, v2) = v1) |  ~ (fails(v3,
% 10.48/2.20          v2) = v0)) &  ! [v0: statement] :  ! [v1: statement] :  ! [v2: label] :
% 10.48/2.20    (v1 = v0 |  ~ (goto(v2) = v1) |  ~ (goto(v2) = v0))
% 10.48/2.20  
% 10.48/2.20  Further assumptions not needed in the proof:
% 10.48/2.20  --------------------------------------------
% 10.48/2.20  state_1, state_2, state_4, state_6, state_7, transition_1_to_2
% 10.48/2.20  
% 10.48/2.20  Those formulas are unsatisfiable:
% 10.48/2.20  ---------------------------------
% 10.48/2.20  
% 10.48/2.20  Begin of proof
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (label_state_3) implies:
% 10.48/2.20  |   (1)  labels(loop, p3) = 0
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (transition_2_to_3) implies:
% 10.48/2.20  |   (2)  state(p2)
% 10.48/2.20  |   (3)  follows(p3, p2) = 0
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (state_3) implies:
% 10.48/2.20  |   (4)   ? [v0: boolean] :  ? [v1: statement] : (equal_function(register_j, n)
% 10.48/2.20  |          = v0 & ifthen(v0, p4) = v1 & has(p3, v1) = 0 & boolean(v0) &
% 10.48/2.20  |          statement(v1))
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (transition_4_to_5) implies:
% 10.48/2.20  |   (5)  state(p4)
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (transition_3_to_6) implies:
% 10.48/2.20  |   (6)  follows(p6, p3) = 0
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (transition_6_to_7) implies:
% 10.48/2.20  |   (7)  state(p6)
% 10.48/2.20  |   (8)  follows(p7, p6) = 0
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (transition_7_to_8) implies:
% 10.48/2.20  |   (9)  state(p7)
% 10.48/2.20  |   (10)  follows(p8, p7) = 0
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (state_8) implies:
% 10.48/2.20  |   (11)  state(p8)
% 10.48/2.20  |   (12)  label(loop)
% 10.48/2.20  |   (13)   ? [v0: statement] : (goto(loop) = v0 & has(p8, v0) = 0 &
% 10.48/2.20  |           statement(v0))
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (prove_there_is_a_loop_through_p3) implies:
% 10.48/2.20  |   (14)  state(p3)
% 10.48/2.20  |   (15)  fails(p3, p3) = 0
% 10.48/2.20  | 
% 10.48/2.20  | ALPHA: (function-axioms) implies:
% 10.48/2.20  |   (16)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2:
% 10.48/2.20  |           state] :  ! [v3: state] : (v1 = v0 |  ~ (fails(v3, v2) = v1) |  ~
% 10.48/2.20  |           (fails(v3, v2) = v0))
% 10.48/2.20  | 
% 10.48/2.21  | DELTA: instantiating (13) with fresh symbol all_20_0 gives:
% 10.48/2.21  |   (17)  goto(loop) = all_20_0 & has(p8, all_20_0) = 0 & statement(all_20_0)
% 10.48/2.21  | 
% 10.48/2.21  | ALPHA: (17) implies:
% 10.48/2.21  |   (18)  has(p8, all_20_0) = 0
% 10.48/2.21  |   (19)  goto(loop) = all_20_0
% 10.48/2.21  | 
% 10.48/2.21  | DELTA: instantiating (4) with fresh symbols all_28_0, all_28_1 gives:
% 10.48/2.21  |   (20)  equal_function(register_j, n) = all_28_1 & ifthen(all_28_1, p4) =
% 10.48/2.21  |         all_28_0 & has(p3, all_28_0) = 0 & boolean(all_28_1) &
% 10.48/2.21  |         statement(all_28_0)
% 10.48/2.21  | 
% 10.48/2.21  | ALPHA: (20) implies:
% 10.48/2.21  |   (21)  boolean(all_28_1)
% 10.48/2.21  |   (22)  has(p3, all_28_0) = 0
% 10.48/2.21  |   (23)  ifthen(all_28_1, p4) = all_28_0
% 10.48/2.21  | 
% 10.48/2.21  | GROUND_INST: instantiating (direct_success) with p2, p3, simplifying with (2),
% 10.48/2.21  |              (3), (14) gives:
% 10.48/2.21  |   (24)   ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p2) = v0)
% 10.48/2.21  | 
% 10.48/2.21  | GROUND_INST: instantiating (direct_success) with p3, p6, simplifying with (6),
% 10.48/2.21  |              (7), (14) gives:
% 10.48/2.21  |   (25)   ? [v0: int] : ( ~ (v0 = 0) & fails(p6, p3) = v0)
% 10.48/2.21  | 
% 10.48/2.21  | GROUND_INST: instantiating (direct_success) with p6, p7, simplifying with (7),
% 10.48/2.21  |              (8), (9) gives:
% 10.48/2.21  |   (26)   ? [v0: int] : ( ~ (v0 = 0) & fails(p7, p6) = v0)
% 10.48/2.21  | 
% 10.48/2.21  | GROUND_INST: instantiating (direct_success) with p7, p8, simplifying with (9),
% 10.48/2.21  |              (10), (11) gives:
% 10.48/2.21  |   (27)   ? [v0: int] : ( ~ (v0 = 0) & fails(p8, p7) = v0)
% 10.48/2.21  | 
% 10.48/2.21  | GROUND_INST: instantiating (goto_success) with loop, p8, p3, all_20_0,
% 10.48/2.21  |              simplifying with (1), (11), (12), (14), (18), (19) gives:
% 10.48/2.21  |   (28)   ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p8) = v0)
% 10.48/2.21  | 
% 10.48/2.21  | GROUND_INST: instantiating (conditional_success) with all_28_1, p3, p4,
% 10.48/2.21  |              all_28_0, simplifying with (5), (14), (21), (22), (23) gives:
% 10.48/2.21  |   (29)   ? [v0: int] : ( ~ (v0 = 0) & fails(p4, p3) = v0)
% 10.48/2.21  | 
% 10.48/2.21  | DELTA: instantiating (29) with fresh symbol all_39_0 gives:
% 10.48/2.21  |   (30)   ~ (all_39_0 = 0) & fails(p4, p3) = all_39_0
% 10.48/2.21  | 
% 10.48/2.21  | ALPHA: (30) implies:
% 10.48/2.21  |   (31)   ~ (all_39_0 = 0)
% 10.48/2.21  |   (32)  fails(p4, p3) = all_39_0
% 10.48/2.21  | 
% 10.48/2.21  | DELTA: instantiating (28) with fresh symbol all_41_0 gives:
% 10.48/2.21  |   (33)   ~ (all_41_0 = 0) & fails(p3, p8) = all_41_0
% 10.48/2.21  | 
% 10.48/2.21  | ALPHA: (33) implies:
% 10.48/2.21  |   (34)   ~ (all_41_0 = 0)
% 10.48/2.21  |   (35)  fails(p3, p8) = all_41_0
% 10.48/2.21  | 
% 10.48/2.21  | DELTA: instantiating (27) with fresh symbol all_43_0 gives:
% 10.48/2.21  |   (36)   ~ (all_43_0 = 0) & fails(p8, p7) = all_43_0
% 10.48/2.21  | 
% 10.48/2.21  | ALPHA: (36) implies:
% 10.48/2.22  |   (37)   ~ (all_43_0 = 0)
% 10.48/2.22  |   (38)  fails(p8, p7) = all_43_0
% 10.48/2.22  | 
% 10.48/2.22  | DELTA: instantiating (26) with fresh symbol all_45_0 gives:
% 10.48/2.22  |   (39)   ~ (all_45_0 = 0) & fails(p7, p6) = all_45_0
% 10.48/2.22  | 
% 10.48/2.22  | ALPHA: (39) implies:
% 10.48/2.22  |   (40)   ~ (all_45_0 = 0)
% 10.48/2.22  |   (41)  fails(p7, p6) = all_45_0
% 10.48/2.22  | 
% 10.48/2.22  | DELTA: instantiating (25) with fresh symbol all_47_0 gives:
% 10.48/2.22  |   (42)   ~ (all_47_0 = 0) & fails(p6, p3) = all_47_0
% 10.48/2.22  | 
% 10.48/2.22  | ALPHA: (42) implies:
% 10.48/2.22  |   (43)   ~ (all_47_0 = 0)
% 10.48/2.22  |   (44)  fails(p6, p3) = all_47_0
% 10.48/2.22  | 
% 10.48/2.22  | DELTA: instantiating (24) with fresh symbol all_51_0 gives:
% 10.48/2.22  |   (45)   ~ (all_51_0 = 0) & fails(p3, p2) = all_51_0
% 10.48/2.22  | 
% 10.48/2.22  | ALPHA: (45) implies:
% 10.48/2.22  |   (46)   ~ (all_51_0 = 0)
% 10.48/2.22  |   (47)  fails(p3, p2) = all_51_0
% 10.48/2.22  | 
% 10.48/2.22  | GROUND_INST: instantiating (transitivity_of_success) with p3, p2, p4,
% 10.48/2.22  |              all_39_0, all_51_0, simplifying with (2), (5), (14), (32), (47)
% 10.48/2.22  |              gives:
% 10.48/2.22  |   (48)  all_51_0 = 0 | all_39_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p4,
% 10.48/2.22  |             p2) = v0)
% 10.48/2.22  | 
% 10.48/2.22  | GROUND_INST: instantiating (transitivity_of_success) with p6, p3, p7,
% 10.48/2.22  |              all_45_0, all_47_0, simplifying with (7), (9), (14), (41), (44)
% 10.48/2.22  |              gives:
% 10.48/2.22  |   (49)  all_47_0 = 0 | all_45_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p7,
% 10.48/2.22  |             p3) = v0)
% 10.48/2.22  | 
% 10.48/2.22  | GROUND_INST: instantiating (transitivity_of_success) with p8, p7, p3,
% 10.48/2.22  |              all_41_0, all_43_0, simplifying with (9), (11), (14), (35), (38)
% 10.48/2.22  |              gives:
% 10.48/2.22  |   (50)  all_43_0 = 0 | all_41_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p3,
% 10.48/2.22  |             p7) = v0)
% 10.48/2.22  | 
% 10.48/2.22  | BETA: splitting (50) gives:
% 10.48/2.22  | 
% 10.48/2.22  | Case 1:
% 10.48/2.22  | | 
% 10.48/2.22  | |   (51)  all_43_0 = 0
% 10.48/2.22  | | 
% 10.48/2.22  | | REDUCE: (37), (51) imply:
% 10.48/2.22  | |   (52)  $false
% 10.48/2.22  | | 
% 10.48/2.22  | | CLOSE: (52) is inconsistent.
% 10.48/2.22  | | 
% 10.48/2.22  | Case 2:
% 10.48/2.22  | | 
% 10.48/2.22  | |   (53)  all_41_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p7) = v0)
% 10.48/2.22  | | 
% 10.48/2.22  | | BETA: splitting (53) gives:
% 10.48/2.22  | | 
% 10.48/2.22  | | Case 1:
% 10.48/2.22  | | | 
% 10.48/2.22  | | |   (54)  all_41_0 = 0
% 10.48/2.22  | | | 
% 10.48/2.22  | | | REDUCE: (34), (54) imply:
% 10.48/2.22  | | |   (55)  $false
% 10.48/2.22  | | | 
% 10.48/2.22  | | | CLOSE: (55) is inconsistent.
% 10.48/2.22  | | | 
% 10.48/2.22  | | Case 2:
% 10.48/2.22  | | | 
% 10.48/2.22  | | |   (56)   ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p7) = v0)
% 10.48/2.22  | | | 
% 10.48/2.22  | | | DELTA: instantiating (56) with fresh symbol all_66_0 gives:
% 10.48/2.22  | | |   (57)   ~ (all_66_0 = 0) & fails(p3, p7) = all_66_0
% 10.48/2.22  | | | 
% 10.48/2.22  | | | ALPHA: (57) implies:
% 10.48/2.22  | | |   (58)   ~ (all_66_0 = 0)
% 10.48/2.22  | | |   (59)  fails(p3, p7) = all_66_0
% 10.48/2.22  | | | 
% 10.48/2.22  | | | BETA: splitting (49) gives:
% 10.48/2.22  | | | 
% 10.48/2.22  | | | Case 1:
% 10.48/2.22  | | | | 
% 10.48/2.22  | | | |   (60)  all_47_0 = 0
% 10.48/2.22  | | | | 
% 10.48/2.22  | | | | REDUCE: (43), (60) imply:
% 10.48/2.22  | | | |   (61)  $false
% 10.48/2.22  | | | | 
% 10.48/2.22  | | | | CLOSE: (61) is inconsistent.
% 10.48/2.22  | | | | 
% 10.48/2.22  | | | Case 2:
% 10.48/2.22  | | | | 
% 10.48/2.23  | | | |   (62)  all_45_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p7, p3) = v0)
% 10.48/2.23  | | | | 
% 10.48/2.23  | | | | BETA: splitting (48) gives:
% 10.48/2.23  | | | | 
% 10.48/2.23  | | | | Case 1:
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | |   (63)  all_51_0 = 0
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | | REDUCE: (46), (63) imply:
% 10.48/2.23  | | | | |   (64)  $false
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | | CLOSE: (64) is inconsistent.
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | Case 2:
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | |   (65)  all_39_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p4, p2) =
% 10.48/2.23  | | | | |           v0)
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | | BETA: splitting (62) gives:
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | | Case 1:
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | |   (66)  all_45_0 = 0
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | | REDUCE: (40), (66) imply:
% 10.48/2.23  | | | | | |   (67)  $false
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | | CLOSE: (67) is inconsistent.
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | Case 2:
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | |   (68)   ? [v0: int] : ( ~ (v0 = 0) & fails(p7, p3) = v0)
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | | DELTA: instantiating (68) with fresh symbol all_96_0 gives:
% 10.48/2.23  | | | | | |   (69)   ~ (all_96_0 = 0) & fails(p7, p3) = all_96_0
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | | ALPHA: (69) implies:
% 10.48/2.23  | | | | | |   (70)   ~ (all_96_0 = 0)
% 10.48/2.23  | | | | | |   (71)  fails(p7, p3) = all_96_0
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | | BETA: splitting (65) gives:
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | | Case 1:
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | |   (72)  all_39_0 = 0
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | | REDUCE: (31), (72) imply:
% 10.48/2.23  | | | | | | |   (73)  $false
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | | CLOSE: (73) is inconsistent.
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | Case 2:
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | | GROUND_INST: instantiating (transitivity_of_success) with p7, p3,
% 10.48/2.23  | | | | | | |              p3, all_66_0, all_96_0, simplifying with (9), (14),
% 10.48/2.23  | | | | | | |              (59), (71) gives:
% 10.48/2.23  | | | | | | |   (74)  all_96_0 = 0 | all_66_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0)
% 10.48/2.23  | | | | | | |           & fails(p3, p3) = v0)
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | | BETA: splitting (74) gives:
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | | Case 1:
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | |   (75)  all_96_0 = 0
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | | REDUCE: (70), (75) imply:
% 10.48/2.23  | | | | | | | |   (76)  $false
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | | CLOSE: (76) is inconsistent.
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | Case 2:
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | |   (77)  all_66_0 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & fails(p3,
% 10.48/2.23  | | | | | | | |             p3) = v0)
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | | BETA: splitting (77) gives:
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | | Case 1:
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | |   (78)  all_66_0 = 0
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | REDUCE: (58), (78) imply:
% 10.48/2.23  | | | | | | | | |   (79)  $false
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | CLOSE: (79) is inconsistent.
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | Case 2:
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | |   (80)   ? [v0: int] : ( ~ (v0 = 0) & fails(p3, p3) = v0)
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | DELTA: instantiating (80) with fresh symbol all_204_0 gives:
% 10.48/2.23  | | | | | | | | |   (81)   ~ (all_204_0 = 0) & fails(p3, p3) = all_204_0
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | ALPHA: (81) implies:
% 10.48/2.23  | | | | | | | | |   (82)   ~ (all_204_0 = 0)
% 10.48/2.23  | | | | | | | | |   (83)  fails(p3, p3) = all_204_0
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_204_0, p3, p3,
% 10.48/2.23  | | | | | | | | |              simplifying with (15), (83) gives:
% 10.48/2.23  | | | | | | | | |   (84)  all_204_0 = 0
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | REDUCE: (82), (84) imply:
% 10.48/2.23  | | | | | | | | |   (85)  $false
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | | CLOSE: (85) is inconsistent.
% 10.48/2.23  | | | | | | | | | 
% 10.48/2.23  | | | | | | | | End of split
% 10.48/2.23  | | | | | | | | 
% 10.48/2.23  | | | | | | | End of split
% 10.48/2.23  | | | | | | | 
% 10.48/2.23  | | | | | | End of split
% 10.48/2.23  | | | | | | 
% 10.48/2.23  | | | | | End of split
% 10.48/2.23  | | | | | 
% 10.48/2.23  | | | | End of split
% 10.48/2.23  | | | | 
% 10.48/2.23  | | | End of split
% 10.48/2.23  | | | 
% 10.48/2.23  | | End of split
% 10.48/2.23  | | 
% 10.48/2.23  | End of split
% 10.48/2.23  | 
% 10.48/2.23  End of proof
% 10.48/2.23  % SZS output end Proof for theBenchmark
% 10.48/2.23  
% 10.48/2.23  1640ms
%------------------------------------------------------------------------------