TSTP Solution File: KRS110+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KRS110+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n020.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 05:51:17 EDT 2023

% Result   : Unsatisfiable 6.72s 1.61s
% Output   : Proof 8.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KRS110+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34  % Computer : n020.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Mon Aug 28 01:10:29 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62  Running up to 7 provers in parallel.
% 0.20/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.58/1.05  Prover 1: Preprocessing ...
% 2.58/1.05  Prover 4: Preprocessing ...
% 2.58/1.09  Prover 6: Preprocessing ...
% 2.58/1.09  Prover 5: Preprocessing ...
% 2.58/1.09  Prover 2: Preprocessing ...
% 2.58/1.09  Prover 3: Preprocessing ...
% 2.58/1.09  Prover 0: Preprocessing ...
% 4.71/1.38  Prover 5: Proving ...
% 4.71/1.39  Prover 2: Proving ...
% 5.39/1.44  Prover 6: Proving ...
% 5.39/1.48  Prover 3: Constructing countermodel ...
% 5.39/1.48  Prover 1: Constructing countermodel ...
% 5.39/1.55  Prover 4: Constructing countermodel ...
% 5.39/1.56  Prover 0: Proving ...
% 6.64/1.61  Prover 2: proved (981ms)
% 6.72/1.61  
% 6.72/1.61  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/1.61  
% 6.72/1.61  Prover 3: stopped
% 6.72/1.61  Prover 6: stopped
% 6.72/1.61  Prover 0: stopped
% 6.72/1.61  Prover 5: stopped
% 6.72/1.63  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.72/1.64  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.72/1.64  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.72/1.64  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.72/1.64  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.72/1.68  Prover 1: gave up
% 6.72/1.69  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.72/1.70  Prover 7: Preprocessing ...
% 7.44/1.72  Prover 13: Preprocessing ...
% 7.44/1.72  Prover 10: Preprocessing ...
% 7.44/1.72  Prover 8: Preprocessing ...
% 7.44/1.74  Prover 11: Preprocessing ...
% 7.44/1.77  Prover 16: Preprocessing ...
% 7.44/1.77  Prover 7: Warning: ignoring some quantifiers
% 7.44/1.78  Prover 7: Constructing countermodel ...
% 7.44/1.79  Prover 10: Warning: ignoring some quantifiers
% 8.10/1.80  Prover 10: Constructing countermodel ...
% 8.10/1.81  Prover 4: Found proof (size 16)
% 8.10/1.81  Prover 4: proved (1185ms)
% 8.10/1.82  Prover 7: stopped
% 8.10/1.82  Prover 10: stopped
% 8.10/1.82  Prover 11: stopped
% 8.10/1.82  Prover 13: Warning: ignoring some quantifiers
% 8.10/1.83  Prover 13: Constructing countermodel ...
% 8.10/1.83  Prover 16: Warning: ignoring some quantifiers
% 8.10/1.84  Prover 13: stopped
% 8.10/1.84  Prover 16: Constructing countermodel ...
% 8.10/1.85  Prover 16: stopped
% 8.10/1.86  Prover 8: Warning: ignoring some quantifiers
% 8.10/1.87  Prover 8: Constructing countermodel ...
% 8.10/1.88  Prover 8: stopped
% 8.10/1.88  
% 8.10/1.88  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.10/1.88  
% 8.10/1.88  % SZS output start Proof for theBenchmark
% 8.10/1.88  Assumptions after simplification:
% 8.10/1.88  ---------------------------------
% 8.10/1.88  
% 8.10/1.88    (axiom_12)
% 8.73/1.90    cUnsatisfiable(i2003_11_14_17_21_12565) = 0 & $i(i2003_11_14_17_21_12565)
% 8.73/1.90  
% 8.73/1.90    (axiom_2)
% 8.77/1.91     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (cpxcomp(v1) = v2) | 
% 8.77/1.91      ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3
% 8.77/1.91          = 0) & rs(v0, v1) = v3)) &  ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] :
% 8.77/1.91    (v1 = 0 |  ~ (rs(v0, v2) = 0) |  ~ (cUnsatisfiable(v0) = v1) |  ~ $i(v2) |  ~
% 8.77/1.91      $i(v0) |  ? [v3: $i] :  ? [v4: int] :  ? [v5: int] :  ? [v6: int] : ($i(v3)
% 8.77/1.91        & ((v4 = 0 &  ~ (v5 = 0) & rs(v0, v3) = 0 & cpxcomp(v3) = v5) | ( ~ (v6 =
% 8.77/1.91              0) & ca_Ax2(v2) = v6)))) &  ! [v0: $i] :  ! [v1: int] :  ! [v2: $i]
% 8.77/1.91    : (v1 = 0 |  ~ (ca_Ax2(v2) = 0) |  ~ (cUnsatisfiable(v0) = v1) |  ~ $i(v2) | 
% 8.77/1.91      ~ $i(v0) |  ? [v3: $i] :  ? [v4: int] :  ? [v5: int] :  ? [v6: int] :
% 8.77/1.91      ($i(v3) & ((v4 = 0 &  ~ (v5 = 0) & rs(v0, v3) = 0 & cpxcomp(v3) = v5) | ( ~
% 8.77/1.91            (v6 = 0) & rs(v0, v2) = v6)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 8.77/1.91      (rs(v0, v1) = 0) |  ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |
% 8.77/1.91      cpxcomp(v1) = 0) &  ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) | 
% 8.77/1.91      ? [v1: $i] : (rs(v0, v1) = 0 & ca_Ax2(v1) = 0 & $i(v1)))
% 8.77/1.91  
% 8.77/1.91    (axiom_3)
% 8.77/1.91     ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (cp(v0) = v1) |  ~ $i(v0) |  ? [v2:
% 8.77/1.91        $i] : (ra_Px1(v0, v2) = 0 & $i(v2))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 8.77/1.91      (ra_Px1(v0, v1) = 0) |  ~ (cp(v0) = 0) |  ~ $i(v1) |  ~ $i(v0))
% 8.77/1.91  
% 8.77/1.91    (axiom_4)
% 8.77/1.92     ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] : (v1 = 0 |  ~ (ra_Px1(v0, v2) = 0) |
% 8.77/1.92       ~ (cpxcomp(v0) = v1) |  ~ $i(v2) |  ~ $i(v0)) &  ! [v0: $i] : ( ~
% 8.77/1.92      (cpxcomp(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] : (ra_Px1(v0, v1) = 0 & $i(v1)))
% 8.77/1.92  
% 8.77/1.92    (axiom_5)
% 8.77/1.92     ! [v0: $i] :  ! [v1: int] :  ! [v2: $i] : (v1 = 0 |  ~ (rinvS(v0, v2) = 0) | 
% 8.77/1.92      ~ (ca_Ax2(v0) = v1) |  ~ $i(v2) |  ~ $i(v0) |  ? [v3: int] : (( ~ (v3 = 0) &
% 8.77/1.92          cp(v2) = v3) | ( ~ (v3 = 0) & cp(v0) = v3))) &  ! [v0: $i] :  ! [v1:
% 8.77/1.92      int] :  ! [v2: $i] : (v1 = 0 |  ~ (cp(v2) = 0) |  ~ (ca_Ax2(v0) = v1) |  ~
% 8.77/1.92      $i(v2) |  ~ $i(v0) |  ? [v3: int] : (( ~ (v3 = 0) & rinvS(v0, v2) = v3) | (
% 8.77/1.92          ~ (v3 = 0) & cp(v0) = v3))) &  ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~
% 8.77/1.92      (cp(v0) = v1) |  ~ $i(v0) |  ? [v2: int] : ( ~ (v2 = 0) & ca_Ax2(v0) = v2))
% 8.77/1.92    &  ! [v0: $i] :  ! [v1: $i] : ( ~ (rinvS(v0, v1) = 0) |  ~ (cp(v0) = 0) |  ~
% 8.77/1.92      $i(v1) |  ~ $i(v0) |  ? [v2: int] : ((v2 = 0 & ca_Ax2(v0) = 0) | ( ~ (v2 =
% 8.77/1.92            0) & cp(v1) = v2))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (cp(v1) = 0) | 
% 8.77/1.92      ~ (cp(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) |  ? [v2: int] : ((v2 = 0 &
% 8.77/1.92          ca_Ax2(v0) = 0) | ( ~ (v2 = 0) & rinvS(v0, v1) = v2))) &  ! [v0: $i] : 
% 8.77/1.92    ! [v1: MultipleValueBool] : ( ~ (cp(v0) = v1) |  ~ $i(v0) |  ? [v2: int] :  ?
% 8.77/1.92      [v3: $i] :  ? [v4: int] :  ? [v5: int] : ($i(v3) & ((v5 = 0 & v4 = 0 &
% 8.77/1.92            rinvS(v0, v3) = 0 & cp(v3) = 0) | ( ~ (v2 = 0) & ca_Ax2(v0) = v2)))) &
% 8.77/1.92     ! [v0: $i] : ( ~ (ca_Ax2(v0) = 0) |  ~ $i(v0) | cp(v0) = 0) &  ! [v0: $i] : (
% 8.77/1.92      ~ (ca_Ax2(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] : (rinvS(v0, v1) = 0 & cp(v1) =
% 8.77/1.92        0 & $i(v1)))
% 8.77/1.92  
% 8.77/1.92  Further assumptions not needed in the proof:
% 8.77/1.92  --------------------------------------------
% 8.77/1.92  axiom_0, axiom_1, axiom_10, axiom_11, axiom_13, axiom_14, axiom_6, axiom_7,
% 8.77/1.92  axiom_8, axiom_9, cUnsatisfiable_substitution_1, ca_Ax2_substitution_1,
% 8.77/1.92  cowlNothing_substitution_1, cowlThing_substitution_1, cp_substitution_1,
% 8.77/1.92  cpxcomp_substitution_1, ra_Px1_substitution_1, ra_Px1_substitution_2,
% 8.77/1.92  rf1_substitution_1, rf1_substitution_2, rf_substitution_1, rf_substitution_2,
% 8.77/1.92  rinvF1_substitution_1, rinvF1_substitution_2, rinvF_substitution_1,
% 8.77/1.92  rinvF_substitution_2, rinvS_substitution_1, rinvS_substitution_2,
% 8.77/1.92  rs_substitution_1, rs_substitution_2, xsd_integer_substitution_1,
% 8.77/1.92  xsd_string_substitution_1
% 8.77/1.92  
% 8.77/1.92  Those formulas are unsatisfiable:
% 8.77/1.92  ---------------------------------
% 8.77/1.92  
% 8.77/1.92  Begin of proof
% 8.77/1.93  | 
% 8.77/1.93  | ALPHA: (axiom_2) implies:
% 8.77/1.93  |   (1)   ! [v0: $i] : ( ~ (cUnsatisfiable(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 8.77/1.93  |          (rs(v0, v1) = 0 & ca_Ax2(v1) = 0 & $i(v1)))
% 8.77/1.93  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ (rs(v0, v1) = 0) |  ~
% 8.77/1.93  |          (cUnsatisfiable(v0) = 0) |  ~ $i(v1) |  ~ $i(v0) | cpxcomp(v1) = 0)
% 8.77/1.93  | 
% 8.77/1.93  | ALPHA: (axiom_3) implies:
% 8.77/1.93  |   (3)   ! [v0: $i] :  ! [v1: $i] : ( ~ (ra_Px1(v0, v1) = 0) |  ~ (cp(v0) = 0)
% 8.77/1.93  |          |  ~ $i(v1) |  ~ $i(v0))
% 8.77/1.93  | 
% 8.77/1.93  | ALPHA: (axiom_4) implies:
% 8.77/1.93  |   (4)   ! [v0: $i] : ( ~ (cpxcomp(v0) = 0) |  ~ $i(v0) |  ? [v1: $i] :
% 8.77/1.93  |          (ra_Px1(v0, v1) = 0 & $i(v1)))
% 8.77/1.93  | 
% 8.77/1.93  | ALPHA: (axiom_5) implies:
% 8.77/1.93  |   (5)   ! [v0: $i] : ( ~ (ca_Ax2(v0) = 0) |  ~ $i(v0) | cp(v0) = 0)
% 8.77/1.93  | 
% 8.77/1.93  | ALPHA: (axiom_12) implies:
% 8.77/1.93  |   (6)  $i(i2003_11_14_17_21_12565)
% 8.77/1.93  |   (7)  cUnsatisfiable(i2003_11_14_17_21_12565) = 0
% 8.77/1.93  | 
% 8.77/1.93  | GROUND_INST: instantiating (1) with i2003_11_14_17_21_12565, simplifying with
% 8.77/1.93  |              (6), (7) gives:
% 8.77/1.93  |   (8)   ? [v0: $i] : (rs(i2003_11_14_17_21_12565, v0) = 0 & ca_Ax2(v0) = 0 &
% 8.77/1.93  |          $i(v0))
% 8.77/1.93  | 
% 8.77/1.93  | DELTA: instantiating (8) with fresh symbol all_23_0 gives:
% 8.77/1.93  |   (9)  rs(i2003_11_14_17_21_12565, all_23_0) = 0 & ca_Ax2(all_23_0) = 0 &
% 8.77/1.93  |        $i(all_23_0)
% 8.77/1.93  | 
% 8.77/1.93  | ALPHA: (9) implies:
% 8.77/1.93  |   (10)  $i(all_23_0)
% 8.77/1.93  |   (11)  ca_Ax2(all_23_0) = 0
% 8.77/1.93  |   (12)  rs(i2003_11_14_17_21_12565, all_23_0) = 0
% 8.77/1.93  | 
% 8.77/1.93  | GROUND_INST: instantiating (5) with all_23_0, simplifying with (10), (11)
% 8.77/1.93  |              gives:
% 8.77/1.93  |   (13)  cp(all_23_0) = 0
% 8.77/1.93  | 
% 8.77/1.94  | GROUND_INST: instantiating (2) with i2003_11_14_17_21_12565, all_23_0,
% 8.77/1.94  |              simplifying with (6), (7), (10), (12) gives:
% 8.77/1.94  |   (14)  cpxcomp(all_23_0) = 0
% 8.77/1.94  | 
% 8.77/1.94  | GROUND_INST: instantiating (4) with all_23_0, simplifying with (10), (14)
% 8.77/1.94  |              gives:
% 8.77/1.94  |   (15)   ? [v0: $i] : (ra_Px1(all_23_0, v0) = 0 & $i(v0))
% 8.77/1.94  | 
% 8.77/1.94  | DELTA: instantiating (15) with fresh symbol all_39_0 gives:
% 8.77/1.94  |   (16)  ra_Px1(all_23_0, all_39_0) = 0 & $i(all_39_0)
% 8.77/1.94  | 
% 8.77/1.94  | ALPHA: (16) implies:
% 8.77/1.94  |   (17)  $i(all_39_0)
% 8.77/1.94  |   (18)  ra_Px1(all_23_0, all_39_0) = 0
% 8.77/1.94  | 
% 8.77/1.94  | GROUND_INST: instantiating (3) with all_23_0, all_39_0, simplifying with (10),
% 8.77/1.94  |              (13), (17), (18) gives:
% 8.77/1.94  |   (19)  $false
% 8.77/1.94  | 
% 8.77/1.94  | CLOSE: (19) is inconsistent.
% 8.77/1.94  | 
% 8.77/1.94  End of proof
% 8.77/1.94  % SZS output end Proof for theBenchmark
% 8.77/1.94  
% 8.77/1.94  1330ms
%------------------------------------------------------------------------------