TSTP Solution File: NUN088+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUN088+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n004.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 12:51:06 EDT 2023

% Result   : Theorem 6.57s 1.63s
% Output   : Proof 7.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : NUN088+1 : TPTP v8.1.2. Released v7.3.0.
% 0.12/0.14  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.35  % Computer : n004.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun Aug 27 09:00:53 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.21/0.66  ________       _____
% 0.21/0.66  ___  __ \_________(_)________________________________
% 0.21/0.66  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.66  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.66  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.66  
% 0.21/0.66  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.66  (2023-06-19)
% 0.21/0.66  
% 0.21/0.66  (c) Philipp Rümmer, 2009-2023
% 0.21/0.66  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.66                Amanda Stjerna.
% 0.21/0.66  Free software under BSD-3-Clause.
% 0.21/0.66  
% 0.21/0.66  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.66  
% 0.21/0.66  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.67  Running up to 7 provers in parallel.
% 0.21/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.04/1.17  Prover 4: Preprocessing ...
% 3.04/1.17  Prover 1: Preprocessing ...
% 3.04/1.20  Prover 3: Preprocessing ...
% 3.04/1.20  Prover 5: Preprocessing ...
% 3.04/1.20  Prover 6: Preprocessing ...
% 3.04/1.20  Prover 0: Preprocessing ...
% 3.04/1.22  Prover 2: Preprocessing ...
% 4.77/1.46  Prover 2: Proving ...
% 5.34/1.46  Prover 5: Proving ...
% 5.92/1.54  Prover 6: Proving ...
% 5.92/1.55  Prover 1: Warning: ignoring some quantifiers
% 5.92/1.55  Prover 3: Warning: ignoring some quantifiers
% 5.92/1.57  Prover 1: Constructing countermodel ...
% 5.92/1.57  Prover 3: Constructing countermodel ...
% 5.92/1.62  Prover 4: Warning: ignoring some quantifiers
% 5.92/1.63  Prover 2: proved (950ms)
% 6.57/1.63  
% 6.57/1.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.57/1.63  
% 6.57/1.63  Prover 5: proved (942ms)
% 6.57/1.63  
% 6.57/1.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.57/1.63  
% 6.57/1.63  Prover 3: stopped
% 6.57/1.64  Prover 6: stopped
% 6.57/1.64  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.57/1.64  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.57/1.64  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 6.57/1.64  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 6.57/1.66  Prover 0: Proving ...
% 6.57/1.68  Prover 0: stopped
% 6.97/1.70  Prover 4: Constructing countermodel ...
% 6.97/1.70  Prover 8: Preprocessing ...
% 6.97/1.70  Prover 11: Preprocessing ...
% 6.97/1.70  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 6.97/1.70  Prover 7: Preprocessing ...
% 6.97/1.73  Prover 10: Preprocessing ...
% 6.97/1.74  Prover 13: Preprocessing ...
% 6.97/1.75  Prover 1: Found proof (size 14)
% 6.97/1.75  Prover 1: proved (1068ms)
% 6.97/1.75  Prover 10: stopped
% 6.97/1.75  Prover 4: stopped
% 7.45/1.76  Prover 11: stopped
% 7.52/1.76  Prover 13: stopped
% 7.52/1.78  Prover 7: Warning: ignoring some quantifiers
% 7.52/1.79  Prover 7: Constructing countermodel ...
% 7.52/1.80  Prover 7: stopped
% 7.79/1.83  Prover 8: Warning: ignoring some quantifiers
% 7.79/1.84  Prover 8: Constructing countermodel ...
% 7.97/1.84  Prover 8: stopped
% 7.97/1.84  
% 7.97/1.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.97/1.85  
% 7.97/1.85  % SZS output start Proof for theBenchmark
% 7.97/1.85  Assumptions after simplification:
% 7.97/1.85  ---------------------------------
% 7.97/1.85  
% 7.97/1.85    (axiom_7a)
% 7.97/1.88     ! [v0: $i] :  ! [v1: $i] : ( ~ (r2(v0, v1) = 0) |  ~ $i(v1) |  ~ $i(v0) |  !
% 7.97/1.88      [v2: $i] : ( ~ (r1(v2) = 0) |  ~ $i(v2) |  ? [v3: int] : ( ~ (v3 = 0) &
% 7.97/1.88          id(v2, v1) = v3)))
% 7.97/1.88  
% 7.97/1.88    (zerounidone)
% 7.97/1.88     ? [v0: $i] : ($i(v0) &  ? [v1: $i] : (r2(v1, v0) = 0 & r1(v1) = 0 & $i(v1)) &
% 7.97/1.88       ? [v1: $i] : (r1(v1) = 0 & id(v1, v0) = 0 & $i(v1)))
% 7.97/1.88  
% 7.97/1.88    (function-axioms)
% 7.97/1.89     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 7.97/1.89    [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (r4(v4, v3, v2) = v1) |  ~ (r4(v4, v3,
% 7.97/1.89          v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] : 
% 7.97/1.89    ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v1 = v0 |  ~ (r3(v4, v3, v2) = v1) |
% 7.97/1.89       ~ (r3(v4, v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.97/1.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (r2(v3, v2) =
% 7.97/1.89        v1) |  ~ (r2(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.97/1.89      MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (id(v3, v2) =
% 7.97/1.89        v1) |  ~ (id(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 7.97/1.89      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (r1(v2) = v1) |  ~ (r1(v2)
% 7.97/1.89        = v0))
% 7.97/1.89  
% 7.97/1.89  Further assumptions not needed in the proof:
% 7.97/1.89  --------------------------------------------
% 7.97/1.89  axiom_1, axiom_10, axiom_11, axiom_1a, axiom_2, axiom_2a, axiom_3, axiom_3a,
% 7.97/1.89  axiom_4, axiom_4a, axiom_5, axiom_5a, axiom_6, axiom_6a, axiom_7, axiom_8,
% 7.97/1.89  axiom_9
% 7.97/1.89  
% 7.97/1.89  Those formulas are unsatisfiable:
% 7.97/1.89  ---------------------------------
% 7.97/1.89  
% 7.97/1.89  Begin of proof
% 7.97/1.89  | 
% 7.97/1.89  | ALPHA: (function-axioms) implies:
% 7.97/1.89  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 7.97/1.89  |         ! [v3: $i] : (v1 = v0 |  ~ (id(v3, v2) = v1) |  ~ (id(v3, v2) = v0))
% 7.97/1.89  | 
% 7.97/1.89  | DELTA: instantiating (zerounidone) with fresh symbol all_13_0 gives:
% 7.97/1.90  |   (2)  $i(all_13_0) &  ? [v0: $i] : (r2(v0, all_13_0) = 0 & r1(v0) = 0 &
% 7.97/1.90  |          $i(v0)) &  ? [v0: $i] : (r1(v0) = 0 & id(v0, all_13_0) = 0 & $i(v0))
% 7.97/1.90  | 
% 7.97/1.90  | ALPHA: (2) implies:
% 7.97/1.90  |   (3)  $i(all_13_0)
% 7.97/1.90  |   (4)   ? [v0: $i] : (r1(v0) = 0 & id(v0, all_13_0) = 0 & $i(v0))
% 7.97/1.90  |   (5)   ? [v0: $i] : (r2(v0, all_13_0) = 0 & r1(v0) = 0 & $i(v0))
% 7.97/1.90  | 
% 7.97/1.90  | DELTA: instantiating (4) with fresh symbol all_25_0 gives:
% 7.97/1.90  |   (6)  r1(all_25_0) = 0 & id(all_25_0, all_13_0) = 0 & $i(all_25_0)
% 7.97/1.90  | 
% 7.97/1.90  | ALPHA: (6) implies:
% 7.97/1.90  |   (7)  $i(all_25_0)
% 7.97/1.90  |   (8)  id(all_25_0, all_13_0) = 0
% 7.97/1.90  |   (9)  r1(all_25_0) = 0
% 7.97/1.90  | 
% 7.97/1.90  | DELTA: instantiating (5) with fresh symbol all_27_0 gives:
% 7.97/1.90  |   (10)  r2(all_27_0, all_13_0) = 0 & r1(all_27_0) = 0 & $i(all_27_0)
% 7.97/1.90  | 
% 7.97/1.90  | ALPHA: (10) implies:
% 7.97/1.90  |   (11)  $i(all_27_0)
% 7.97/1.90  |   (12)  r2(all_27_0, all_13_0) = 0
% 7.97/1.90  | 
% 7.97/1.90  | GROUND_INST: instantiating (axiom_7a) with all_27_0, all_13_0, simplifying
% 7.97/1.90  |              with (3), (11), (12) gives:
% 7.97/1.91  |   (13)   ! [v0: $i] : ( ~ (r1(v0) = 0) |  ~ $i(v0) |  ? [v1: int] : ( ~ (v1 =
% 7.97/1.91  |               0) & id(v0, all_13_0) = v1))
% 7.97/1.91  | 
% 7.97/1.91  | GROUND_INST: instantiating (13) with all_25_0, simplifying with (7), (9)
% 7.97/1.91  |              gives:
% 7.97/1.91  |   (14)   ? [v0: int] : ( ~ (v0 = 0) & id(all_25_0, all_13_0) = v0)
% 7.97/1.91  | 
% 7.97/1.91  | DELTA: instantiating (14) with fresh symbol all_38_0 gives:
% 7.97/1.91  |   (15)   ~ (all_38_0 = 0) & id(all_25_0, all_13_0) = all_38_0
% 7.97/1.91  | 
% 7.97/1.91  | ALPHA: (15) implies:
% 7.97/1.91  |   (16)   ~ (all_38_0 = 0)
% 7.97/1.91  |   (17)  id(all_25_0, all_13_0) = all_38_0
% 7.97/1.91  | 
% 7.97/1.91  | GROUND_INST: instantiating (1) with 0, all_38_0, all_13_0, all_25_0,
% 7.97/1.91  |              simplifying with (8), (17) gives:
% 7.97/1.91  |   (18)  all_38_0 = 0
% 7.97/1.91  | 
% 7.97/1.91  | REDUCE: (16), (18) imply:
% 7.97/1.91  |   (19)  $false
% 7.97/1.91  | 
% 7.97/1.91  | CLOSE: (19) is inconsistent.
% 7.97/1.91  | 
% 7.97/1.91  End of proof
% 7.97/1.91  % SZS output end Proof for theBenchmark
% 7.97/1.91  
% 7.97/1.91  1252ms
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