TSTP Solution File: KLE006+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KLE006+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n018.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 05:34:09 EDT 2023

% Result   : Theorem 7.14s 1.72s
% Output   : Proof 8.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : KLE006+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Tue Aug 29 11:40:33 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.62  ________       _____
% 0.21/0.62  ___  __ \_________(_)________________________________
% 0.21/0.62  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.62  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.62  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62  
% 0.21/0.62  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62  (2023-06-19)
% 0.21/0.62  
% 0.21/0.62  (c) Philipp Rümmer, 2009-2023
% 0.21/0.62  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62                Amanda Stjerna.
% 0.21/0.62  Free software under BSD-3-Clause.
% 0.21/0.62  
% 0.21/0.62  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62  
% 0.21/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63  Running up to 7 provers in parallel.
% 0.21/0.65  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.65  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 2.11/1.06  Prover 4: Preprocessing ...
% 2.11/1.06  Prover 1: Preprocessing ...
% 2.83/1.10  Prover 5: Preprocessing ...
% 2.83/1.10  Prover 3: Preprocessing ...
% 2.90/1.11  Prover 0: Preprocessing ...
% 2.90/1.11  Prover 6: Preprocessing ...
% 2.90/1.11  Prover 2: Preprocessing ...
% 4.21/1.41  Prover 6: Proving ...
% 4.21/1.42  Prover 3: Constructing countermodel ...
% 4.21/1.44  Prover 1: Constructing countermodel ...
% 5.55/1.47  Prover 5: Proving ...
% 5.74/1.50  Prover 0: Proving ...
% 5.87/1.53  Prover 4: Constructing countermodel ...
% 5.87/1.54  Prover 2: Proving ...
% 6.61/1.65  Prover 3: gave up
% 6.61/1.65  Prover 1: gave up
% 6.61/1.66  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.61/1.68  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.61/1.68  Prover 7: Preprocessing ...
% 7.14/1.71  Prover 8: Preprocessing ...
% 7.14/1.71  Prover 0: proved (1074ms)
% 7.14/1.71  
% 7.14/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.14/1.72  
% 7.14/1.72  Prover 6: stopped
% 7.14/1.72  Prover 5: stopped
% 7.14/1.72  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.14/1.72  Prover 2: stopped
% 7.14/1.74  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.14/1.74  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.14/1.74  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 7.14/1.76  Prover 10: Preprocessing ...
% 7.14/1.77  Prover 16: Preprocessing ...
% 7.14/1.77  Prover 11: Preprocessing ...
% 7.14/1.77  Prover 13: Preprocessing ...
% 7.81/1.79  Prover 7: Constructing countermodel ...
% 7.81/1.80  Prover 8: Warning: ignoring some quantifiers
% 8.00/1.82  Prover 8: Constructing countermodel ...
% 8.15/1.83  Prover 10: Constructing countermodel ...
% 8.15/1.86  Prover 7: Found proof (size 12)
% 8.15/1.86  Prover 7: proved (202ms)
% 8.15/1.86  Prover 16: Warning: ignoring some quantifiers
% 8.15/1.86  Prover 10: stopped
% 8.15/1.87  Prover 4: stopped
% 8.15/1.87  Prover 8: stopped
% 8.15/1.87  Prover 16: Constructing countermodel ...
% 8.15/1.87  Prover 16: stopped
% 8.15/1.88  Prover 13: Warning: ignoring some quantifiers
% 8.15/1.89  Prover 13: Constructing countermodel ...
% 8.15/1.89  Prover 13: stopped
% 8.15/1.92  Prover 11: Constructing countermodel ...
% 8.15/1.93  Prover 11: stopped
% 8.15/1.93  
% 8.15/1.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.15/1.93  
% 8.15/1.93  % SZS output start Proof for theBenchmark
% 8.15/1.93  Assumptions after simplification:
% 8.15/1.93  ---------------------------------
% 8.15/1.93  
% 8.15/1.93    (additive_commutativity)
% 8.15/1.96     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |  ~
% 8.15/1.96      $i(v1) |  ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2))) &  ! [v0: $i] :  !
% 8.15/1.96    [v1: $i] :  ! [v2: $i] : ( ~ (addition(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 8.15/1.96      (addition(v1, v0) = v2 & $i(v2)))
% 8.15/1.96  
% 8.15/1.96    (goals)
% 8.15/1.96    $i(one) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = one) & c(v0) =
% 8.15/1.96      v1 & addition(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & test(v0))
% 8.15/1.96  
% 8.15/1.96    (test_2)
% 8.15/1.97    $i(one) & $i(zero) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = one |  ~
% 8.15/1.97      (addition(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ complement(v1, v0)) & 
% 8.15/1.97    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = zero |  ~ (multiplication(v1,
% 8.15/1.97          v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ complement(v1, v0)) &  ! [v0: $i]
% 8.15/1.97    :  ! [v1: $i] :  ! [v2: $i] : (v2 = zero |  ~ (multiplication(v0, v1) = v2) | 
% 8.15/1.97      ~ $i(v1) |  ~ $i(v0) |  ~ complement(v1, v0)) &  ! [v0: $i] :  ! [v1: $i] : 
% 8.15/1.97    ! [v2: $i] : ( ~ (multiplication(v1, v0) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 8.15/1.97      complement(v1, v0) | (multiplication(v0, v1) = zero & addition(v0, v1) =
% 8.15/1.97        one)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (multiplication(v0,
% 8.15/1.97          v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ complement(v1, v0) |
% 8.15/1.97      (multiplication(v1, v0) = zero & addition(v0, v1) = one)) &  ! [v0: $i] :  !
% 8.15/1.97    [v1: $i] :  ! [v2: $i] : ( ~ (addition(v0, v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |
% 8.15/1.97       ~ complement(v1, v0) | (multiplication(v1, v0) = zero & multiplication(v0,
% 8.15/1.97          v1) = zero)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (multiplication(v1, v0) =
% 8.15/1.97        zero) |  ~ $i(v1) |  ~ $i(v0) | complement(v1, v0) |  ? [v2: $i] :  ? [v3:
% 8.15/1.97        $i] : (( ~ (v3 = one) & addition(v0, v1) = v3 & $i(v3)) | ( ~ (v2 = zero)
% 8.15/1.97          & multiplication(v0, v1) = v2 & $i(v2)))) &  ! [v0: $i] :  ! [v1: $i] :
% 8.15/1.97    ( ~ (multiplication(v0, v1) = zero) |  ~ $i(v1) |  ~ $i(v0) | complement(v1,
% 8.15/1.97        v0) |  ? [v2: $i] :  ? [v3: $i] : (( ~ (v3 = one) & addition(v0, v1) = v3
% 8.15/1.97          & $i(v3)) | ( ~ (v2 = zero) & multiplication(v1, v0) = v2 & $i(v2)))) & 
% 8.15/1.97    ! [v0: $i] :  ! [v1: $i] : ( ~ (addition(v0, v1) = one) |  ~ $i(v1) |  ~
% 8.15/1.97      $i(v0) | complement(v1, v0) |  ? [v2: $i] :  ? [v3: $i] : (( ~ (v3 = zero) &
% 8.15/1.97          multiplication(v1, v0) = v3 & $i(v3)) | ( ~ (v2 = zero) &
% 8.15/1.97          multiplication(v0, v1) = v2 & $i(v2))))
% 8.15/1.97  
% 8.15/1.97    (test_3)
% 8.85/1.98     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v1 |  ~ (c(v0) = v2) |  ~
% 8.85/1.98      $i(v1) |  ~ $i(v0) |  ~ complement(v0, v1) |  ~ test(v0)) &  ! [v0: $i] :  !
% 8.85/1.98    [v1: $i] : ( ~ (c(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) |  ~ test(v0) |
% 8.85/1.98      complement(v0, v1))
% 8.85/1.98  
% 8.85/1.98  Further assumptions not needed in the proof:
% 8.85/1.98  --------------------------------------------
% 8.85/1.98  additive_associativity, additive_idempotence, additive_identity,
% 8.85/1.98  left_annihilation, left_distributivity, multiplicative_associativity,
% 8.85/1.98  multiplicative_left_identity, multiplicative_right_identity, order,
% 8.85/1.98  right_annihilation, right_distributivity, test_1, test_4
% 8.85/1.98  
% 8.85/1.98  Those formulas are unsatisfiable:
% 8.85/1.98  ---------------------------------
% 8.85/1.98  
% 8.85/1.98  Begin of proof
% 8.85/1.98  | 
% 8.85/1.98  | ALPHA: (additive_commutativity) implies:
% 8.85/1.98  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (addition(v1, v0) = v2) |
% 8.85/1.98  |           ~ $i(v1) |  ~ $i(v0) | (addition(v0, v1) = v2 & $i(v2)))
% 8.85/1.98  | 
% 8.85/1.98  | ALPHA: (test_2) implies:
% 8.85/1.98  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = one |  ~ (addition(v0,
% 8.85/1.98  |              v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ complement(v1, v0))
% 8.85/1.98  | 
% 8.85/1.98  | ALPHA: (test_3) implies:
% 8.85/1.98  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (c(v0) = v1) |  ~ $i(v1) |  ~ $i(v0) | 
% 8.85/1.98  |          ~ test(v0) | complement(v0, v1))
% 8.85/1.98  | 
% 8.85/1.98  | ALPHA: (goals) implies:
% 8.85/1.98  |   (4)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ( ~ (v2 = one) & c(v0) = v1 &
% 8.85/1.98  |          addition(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & test(v0))
% 8.85/1.98  | 
% 8.85/1.98  | DELTA: instantiating (4) with fresh symbols all_20_0, all_20_1, all_20_2
% 8.85/1.98  |        gives:
% 8.85/1.98  |   (5)   ~ (all_20_0 = one) & c(all_20_2) = all_20_1 & addition(all_20_2,
% 8.85/1.98  |          all_20_1) = all_20_0 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) &
% 8.85/1.98  |        test(all_20_2)
% 8.85/1.98  | 
% 8.85/1.98  | ALPHA: (5) implies:
% 8.85/1.99  |   (6)   ~ (all_20_0 = one)
% 8.85/1.99  |   (7)  test(all_20_2)
% 8.85/1.99  |   (8)  $i(all_20_2)
% 8.85/1.99  |   (9)  $i(all_20_1)
% 8.85/1.99  |   (10)  addition(all_20_2, all_20_1) = all_20_0
% 8.85/1.99  |   (11)  c(all_20_2) = all_20_1
% 8.85/1.99  | 
% 8.85/1.99  | GROUND_INST: instantiating (1) with all_20_1, all_20_2, all_20_0, simplifying
% 8.85/1.99  |              with (8), (9), (10) gives:
% 8.85/1.99  |   (12)  addition(all_20_1, all_20_2) = all_20_0 & $i(all_20_0)
% 8.85/1.99  | 
% 8.85/1.99  | ALPHA: (12) implies:
% 8.85/1.99  |   (13)  addition(all_20_1, all_20_2) = all_20_0
% 8.85/1.99  | 
% 8.85/1.99  | GROUND_INST: instantiating (3) with all_20_2, all_20_1, simplifying with (7),
% 8.85/1.99  |              (8), (9), (11) gives:
% 8.85/1.99  |   (14)  complement(all_20_2, all_20_1)
% 8.85/1.99  | 
% 8.85/1.99  | GROUND_INST: instantiating (2) with all_20_1, all_20_2, all_20_0, simplifying
% 8.85/1.99  |              with (8), (9), (13), (14) gives:
% 8.85/1.99  |   (15)  all_20_0 = one
% 8.85/1.99  | 
% 8.85/1.99  | REDUCE: (6), (15) imply:
% 8.85/1.99  |   (16)  $false
% 8.85/1.99  | 
% 8.85/1.99  | CLOSE: (16) is inconsistent.
% 8.85/1.99  | 
% 8.85/1.99  End of proof
% 8.85/1.99  % SZS output end Proof for theBenchmark
% 8.85/1.99  
% 8.85/1.99  1373ms
%------------------------------------------------------------------------------