TSTP Solution File: KLE076+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : KLE076+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 : n014.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 05:34:28 EDT 2023

% Result   : Theorem 5.30s 1.53s
% Output   : Proof 6.53s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : KLE076+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue Aug 29 11:30:45 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.61  ________       _____
% 0.19/0.61  ___  __ \_________(_)________________________________
% 0.19/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61  
% 0.19/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61  (2023-06-19)
% 0.19/0.61  
% 0.19/0.61  (c) Philipp Rümmer, 2009-2023
% 0.19/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61                Amanda Stjerna.
% 0.19/0.61  Free software under BSD-3-Clause.
% 0.19/0.61  
% 0.19/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61  
% 0.19/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/1.04  Prover 4: Preprocessing ...
% 2.26/1.04  Prover 1: Preprocessing ...
% 2.26/1.08  Prover 2: Preprocessing ...
% 2.26/1.08  Prover 0: Preprocessing ...
% 2.26/1.08  Prover 6: Preprocessing ...
% 2.26/1.08  Prover 5: Preprocessing ...
% 2.26/1.08  Prover 3: Preprocessing ...
% 4.44/1.37  Prover 1: Constructing countermodel ...
% 4.44/1.37  Prover 3: Constructing countermodel ...
% 4.44/1.37  Prover 6: Constructing countermodel ...
% 4.44/1.41  Prover 4: Constructing countermodel ...
% 4.44/1.45  Prover 5: Proving ...
% 4.44/1.45  Prover 0: Proving ...
% 5.30/1.52  Prover 3: proved (890ms)
% 5.30/1.53  
% 5.30/1.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.30/1.53  
% 5.30/1.53  Prover 6: stopped
% 5.30/1.53  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.30/1.53  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.30/1.53  Prover 0: stopped
% 5.30/1.53  Prover 5: stopped
% 5.30/1.55  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.30/1.55  Prover 2: Proving ...
% 5.30/1.55  Prover 2: stopped
% 5.30/1.55  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.30/1.55  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.30/1.55  Prover 8: Preprocessing ...
% 5.30/1.58  Prover 4: Found proof (size 14)
% 5.30/1.58  Prover 4: proved (941ms)
% 5.30/1.58  Prover 1: Found proof (size 16)
% 5.30/1.58  Prover 1: proved (944ms)
% 6.33/1.58  Prover 11: Preprocessing ...
% 6.33/1.59  Prover 10: Preprocessing ...
% 6.33/1.59  Prover 7: Preprocessing ...
% 6.33/1.59  Prover 13: Preprocessing ...
% 6.42/1.60  Prover 11: stopped
% 6.42/1.61  Prover 10: stopped
% 6.53/1.62  Prover 7: stopped
% 6.53/1.62  Prover 8: Warning: ignoring some quantifiers
% 6.53/1.62  Prover 13: stopped
% 6.53/1.63  Prover 8: Constructing countermodel ...
% 6.53/1.64  Prover 8: stopped
% 6.53/1.64  
% 6.53/1.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.53/1.64  
% 6.53/1.64  % SZS output start Proof for theBenchmark
% 6.53/1.64  Assumptions after simplification:
% 6.53/1.64  ---------------------------------
% 6.53/1.64  
% 6.53/1.64    (domain4)
% 6.53/1.67    domain(zero) = zero & $i(zero)
% 6.53/1.67  
% 6.53/1.67    (goals)
% 6.53/1.67    $i(zero) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 =
% 6.53/1.67        zero) & domain(v2) = v3 & domain(zero) = v0 & multiplication(v1, v0) = v2
% 6.53/1.67      & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.67  
% 6.53/1.67    (right_annihilation)
% 6.53/1.67    $i(zero) &  ! [v0: $i] :  ! [v1: $i] : (v1 = zero |  ~ (multiplication(v0,
% 6.53/1.67          zero) = v1) |  ~ $i(v0))
% 6.53/1.67  
% 6.53/1.67    (function-axioms)
% 6.53/1.68     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 6.53/1.68    [v3: $i] : (v1 = v0 |  ~ (leq(v3, v2) = v1) |  ~ (leq(v3, v2) = v0)) &  ! [v0:
% 6.53/1.68      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 6.53/1.68      (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0)) &  ! [v0:
% 6.53/1.68      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (addition(v3,
% 6.53/1.68          v2) = v1) |  ~ (addition(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 6.53/1.68    [v2: $i] : (v1 = v0 |  ~ (domain(v2) = v1) |  ~ (domain(v2) = v0))
% 6.53/1.68  
% 6.53/1.68  Further assumptions not needed in the proof:
% 6.53/1.68  --------------------------------------------
% 6.53/1.68  additive_associativity, additive_commutativity, additive_idempotence,
% 6.53/1.68  additive_identity, domain1, domain2, domain3, domain5, left_annihilation,
% 6.53/1.68  left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 6.53/1.68  multiplicative_right_identity, order, right_distributivity
% 6.53/1.68  
% 6.53/1.68  Those formulas are unsatisfiable:
% 6.53/1.68  ---------------------------------
% 6.53/1.68  
% 6.53/1.68  Begin of proof
% 6.53/1.68  | 
% 6.53/1.68  | ALPHA: (right_annihilation) implies:
% 6.53/1.68  |   (1)   ! [v0: $i] :  ! [v1: $i] : (v1 = zero |  ~ (multiplication(v0, zero) =
% 6.53/1.68  |            v1) |  ~ $i(v0))
% 6.53/1.68  | 
% 6.53/1.68  | ALPHA: (domain4) implies:
% 6.53/1.68  |   (2)  domain(zero) = zero
% 6.53/1.68  | 
% 6.53/1.68  | ALPHA: (goals) implies:
% 6.53/1.68  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = zero)
% 6.53/1.68  |          & domain(v2) = v3 & domain(zero) = v0 & multiplication(v1, v0) = v2 &
% 6.53/1.68  |          $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 6.53/1.68  | 
% 6.53/1.68  | ALPHA: (function-axioms) implies:
% 6.53/1.69  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (domain(v2) =
% 6.53/1.69  |            v1) |  ~ (domain(v2) = v0))
% 6.53/1.69  | 
% 6.53/1.69  | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1, all_20_2,
% 6.53/1.69  |        all_20_3 gives:
% 6.53/1.69  |   (5)   ~ (all_20_0 = zero) & domain(all_20_1) = all_20_0 & domain(zero) =
% 6.53/1.69  |        all_20_3 & multiplication(all_20_2, all_20_3) = all_20_1 & $i(all_20_0)
% 6.53/1.69  |        & $i(all_20_1) & $i(all_20_2) & $i(all_20_3)
% 6.53/1.69  | 
% 6.53/1.69  | ALPHA: (5) implies:
% 6.53/1.69  |   (6)   ~ (all_20_0 = zero)
% 6.53/1.69  |   (7)  $i(all_20_2)
% 6.53/1.69  |   (8)  multiplication(all_20_2, all_20_3) = all_20_1
% 6.53/1.69  |   (9)  domain(zero) = all_20_3
% 6.53/1.69  |   (10)  domain(all_20_1) = all_20_0
% 6.53/1.69  | 
% 6.53/1.69  | GROUND_INST: instantiating (4) with zero, all_20_3, zero, simplifying with
% 6.53/1.69  |              (2), (9) gives:
% 6.53/1.69  |   (11)  all_20_3 = zero
% 6.53/1.69  | 
% 6.53/1.69  | REDUCE: (8), (11) imply:
% 6.53/1.69  |   (12)  multiplication(all_20_2, zero) = all_20_1
% 6.53/1.69  | 
% 6.53/1.69  | GROUND_INST: instantiating (1) with all_20_2, all_20_1, simplifying with (7),
% 6.53/1.69  |              (12) gives:
% 6.53/1.69  |   (13)  all_20_1 = zero
% 6.53/1.69  | 
% 6.53/1.69  | REDUCE: (10), (13) imply:
% 6.53/1.69  |   (14)  domain(zero) = all_20_0
% 6.53/1.69  | 
% 6.53/1.69  | GROUND_INST: instantiating (4) with zero, all_20_0, zero, simplifying with
% 6.53/1.69  |              (2), (14) gives:
% 6.53/1.69  |   (15)  all_20_0 = zero
% 6.53/1.69  | 
% 6.53/1.69  | REDUCE: (6), (15) imply:
% 6.53/1.69  |   (16)  $false
% 6.53/1.70  | 
% 6.53/1.70  | CLOSE: (16) is inconsistent.
% 6.53/1.70  | 
% 6.53/1.70  End of proof
% 6.53/1.70  % SZS output end Proof for theBenchmark
% 6.53/1.70  
% 6.53/1.70  1084ms
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