TSTP Solution File: SYN355+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SYN355+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.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 : Fri Sep  1 03:27:20 EDT 2023

% Result   : Theorem 3.17s 1.20s
% Output   : Proof 4.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN355+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.11  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.32  % Computer : n009.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Sat Aug 26 21:30:35 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.46/0.59  ________       _____
% 0.46/0.59  ___  __ \_________(_)________________________________
% 0.46/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.46/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.46/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.46/0.59  
% 0.46/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.46/0.59  (2023-06-19)
% 0.46/0.59  
% 0.46/0.59  (c) Philipp Rümmer, 2009-2023
% 0.46/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.46/0.59                Amanda Stjerna.
% 0.46/0.59  Free software under BSD-3-Clause.
% 0.46/0.59  
% 0.46/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.46/0.59  
% 0.46/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.46/0.61  Running up to 7 provers in parallel.
% 0.46/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.46/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.46/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.46/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.46/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.46/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.67/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.78/0.95  Prover 4: Preprocessing ...
% 1.78/0.95  Prover 1: Preprocessing ...
% 2.19/1.01  Prover 5: Preprocessing ...
% 2.19/1.01  Prover 6: Preprocessing ...
% 2.19/1.01  Prover 0: Preprocessing ...
% 2.19/1.01  Prover 3: Preprocessing ...
% 2.19/1.01  Prover 2: Preprocessing ...
% 2.73/1.08  Prover 2: Proving ...
% 2.73/1.08  Prover 5: Proving ...
% 2.73/1.10  Prover 6: Proving ...
% 2.73/1.10  Prover 4: Constructing countermodel ...
% 2.73/1.10  Prover 1: Constructing countermodel ...
% 2.73/1.10  Prover 3: Constructing countermodel ...
% 2.73/1.11  Prover 0: Proving ...
% 3.17/1.19  Prover 1: gave up
% 3.17/1.19  Prover 3: gave up
% 3.17/1.19  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.17/1.19  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.17/1.20  Prover 0: proved (576ms)
% 3.17/1.20  
% 3.17/1.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.17/1.20  
% 3.17/1.20  Prover 2: stopped
% 3.17/1.21  Prover 5: stopped
% 3.17/1.21  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.17/1.21  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.17/1.21  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.17/1.21  Prover 7: Preprocessing ...
% 3.17/1.21  Prover 8: Preprocessing ...
% 3.17/1.22  Prover 10: Preprocessing ...
% 3.17/1.22  Prover 6: stopped
% 3.17/1.22  Prover 13: Preprocessing ...
% 3.17/1.22  Prover 11: Preprocessing ...
% 3.17/1.23  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.73/1.23  Prover 7: Warning: ignoring some quantifiers
% 3.73/1.23  Prover 7: Constructing countermodel ...
% 3.73/1.24  Prover 16: Preprocessing ...
% 3.73/1.24  Prover 13: Warning: ignoring some quantifiers
% 3.73/1.24  Prover 10: Warning: ignoring some quantifiers
% 3.73/1.24  Prover 13: Constructing countermodel ...
% 3.73/1.24  Prover 10: Constructing countermodel ...
% 3.73/1.24  Prover 8: Warning: ignoring some quantifiers
% 3.73/1.25  Prover 8: Constructing countermodel ...
% 3.73/1.25  Prover 7: gave up
% 3.73/1.25  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 3.73/1.25  Prover 16: Warning: ignoring some quantifiers
% 3.73/1.25  Prover 16: Constructing countermodel ...
% 3.73/1.25  Prover 13: gave up
% 3.73/1.26  Prover 19: Preprocessing ...
% 3.73/1.26  Prover 10: gave up
% 3.73/1.27  Prover 16: gave up
% 4.13/1.28  Prover 8: gave up
% 4.13/1.29  Prover 4: Found proof (size 16)
% 4.13/1.29  Prover 4: proved (669ms)
% 4.13/1.30  Prover 11: Constructing countermodel ...
% 4.13/1.30  Prover 19: Warning: ignoring some quantifiers
% 4.13/1.30  Prover 11: stopped
% 4.13/1.31  Prover 19: Constructing countermodel ...
% 4.13/1.31  Prover 19: stopped
% 4.13/1.31  
% 4.13/1.31  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.13/1.31  
% 4.13/1.32  % SZS output start Proof for theBenchmark
% 4.13/1.32  Assumptions after simplification:
% 4.13/1.32  ---------------------------------
% 4.13/1.32  
% 4.13/1.32    (x2106)
% 4.47/1.36     ? [v0: $i] :  ? [v1: int] :  ? [v2: int] : ( ~ (v2 = 0) &  ~ (v1 = 0) &
% 4.47/1.36      big_q(v0) = v2 & big_p(v0) = v1 & $i(v0) &  ! [v3: $i] :  ! [v4: int] : (v4
% 4.47/1.36        = 0 |  ~ (big_q(v3) = v4) |  ~ $i(v3) | big_r(v3) = 0) &  ! [v3: $i] :  !
% 4.47/1.36      [v4: int] : (v4 = 0 |  ~ (big_p(v3) = v4) |  ~ $i(v3) |  ? [v5: int] : ( ~
% 4.47/1.36          (v5 = 0) & big_r(v3) = v5)) &  ! [v3: $i] :  ! [v4: int] : (v4 = 0 |  ~
% 4.47/1.36        (big_r(v3) = v4) |  ~ $i(v3) | big_q(v3) = 0) &  ! [v3: $i] : ( ~
% 4.47/1.36        (big_r(v3) = 0) |  ~ $i(v3) | big_p(v3) = 0))
% 4.47/1.36  
% 4.47/1.36    (function-axioms)
% 4.47/1.36     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 =
% 4.47/1.36      v0 |  ~ (big_q(v2) = v1) |  ~ (big_q(v2) = v0)) &  ! [v0: MultipleValueBool]
% 4.47/1.36    :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (big_p(v2) = v1) | 
% 4.47/1.37      ~ (big_p(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 4.47/1.37      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (big_r(v2) = v1) |  ~
% 4.47/1.37      (big_r(v2) = v0))
% 4.47/1.37  
% 4.47/1.37  Those formulas are unsatisfiable:
% 4.47/1.37  ---------------------------------
% 4.47/1.37  
% 4.47/1.37  Begin of proof
% 4.47/1.37  | 
% 4.47/1.37  | ALPHA: (function-axioms) implies:
% 4.55/1.37  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.55/1.37  |        (v1 = v0 |  ~ (big_r(v2) = v1) |  ~ (big_r(v2) = v0))
% 4.55/1.37  | 
% 4.55/1.37  | DELTA: instantiating (x2106) with fresh symbols all_3_0, all_3_1, all_3_2
% 4.55/1.37  |        gives:
% 4.55/1.37  |   (2)   ~ (all_3_0 = 0) &  ~ (all_3_1 = 0) & big_q(all_3_2) = all_3_0 &
% 4.55/1.37  |        big_p(all_3_2) = all_3_1 & $i(all_3_2) &  ! [v0: $i] :  ! [v1: int] :
% 4.55/1.37  |        (v1 = 0 |  ~ (big_q(v0) = v1) |  ~ $i(v0) | big_r(v0) = 0) &  ! [v0:
% 4.55/1.37  |          $i] :  ! [v1: int] : (v1 = 0 |  ~ (big_p(v0) = v1) |  ~ $i(v0) |  ?
% 4.55/1.37  |          [v2: int] : ( ~ (v2 = 0) & big_r(v0) = v2)) &  ! [v0: $i] :  ! [v1:
% 4.55/1.37  |          int] : (v1 = 0 |  ~ (big_r(v0) = v1) |  ~ $i(v0) | big_q(v0) = 0) & 
% 4.55/1.37  |        ! [v0: $i] : ( ~ (big_r(v0) = 0) |  ~ $i(v0) | big_p(v0) = 0)
% 4.55/1.38  | 
% 4.55/1.38  | ALPHA: (2) implies:
% 4.55/1.38  |   (3)   ~ (all_3_1 = 0)
% 4.55/1.38  |   (4)   ~ (all_3_0 = 0)
% 4.55/1.38  |   (5)  $i(all_3_2)
% 4.55/1.38  |   (6)  big_p(all_3_2) = all_3_1
% 4.55/1.38  |   (7)  big_q(all_3_2) = all_3_0
% 4.55/1.38  |   (8)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (big_p(v0) = v1) |  ~ $i(v0)
% 4.55/1.38  |          |  ? [v2: int] : ( ~ (v2 = 0) & big_r(v0) = v2))
% 4.55/1.38  |   (9)   ! [v0: $i] :  ! [v1: int] : (v1 = 0 |  ~ (big_q(v0) = v1) |  ~ $i(v0)
% 4.55/1.38  |          | big_r(v0) = 0)
% 4.55/1.38  | 
% 4.55/1.38  | GROUND_INST: instantiating (8) with all_3_2, all_3_1, simplifying with (5),
% 4.55/1.38  |              (6) gives:
% 4.55/1.39  |   (10)  all_3_1 = 0 |  ? [v0: int] : ( ~ (v0 = 0) & big_r(all_3_2) = v0)
% 4.55/1.39  | 
% 4.55/1.39  | GROUND_INST: instantiating (9) with all_3_2, all_3_0, simplifying with (5),
% 4.55/1.39  |              (7) gives:
% 4.55/1.39  |   (11)  all_3_0 = 0 | big_r(all_3_2) = 0
% 4.55/1.39  | 
% 4.55/1.39  | BETA: splitting (11) gives:
% 4.55/1.39  | 
% 4.55/1.39  | Case 1:
% 4.55/1.39  | | 
% 4.55/1.39  | |   (12)  big_r(all_3_2) = 0
% 4.55/1.39  | | 
% 4.55/1.39  | | BETA: splitting (10) gives:
% 4.55/1.39  | | 
% 4.55/1.39  | | Case 1:
% 4.55/1.39  | | | 
% 4.55/1.39  | | |   (13)  all_3_1 = 0
% 4.55/1.39  | | | 
% 4.55/1.39  | | | REDUCE: (3), (13) imply:
% 4.55/1.39  | | |   (14)  $false
% 4.55/1.39  | | | 
% 4.55/1.39  | | | CLOSE: (14) is inconsistent.
% 4.55/1.39  | | | 
% 4.55/1.39  | | Case 2:
% 4.55/1.39  | | | 
% 4.55/1.39  | | |   (15)   ? [v0: int] : ( ~ (v0 = 0) & big_r(all_3_2) = v0)
% 4.55/1.39  | | | 
% 4.55/1.39  | | | DELTA: instantiating (15) with fresh symbol all_17_0 gives:
% 4.55/1.39  | | |   (16)   ~ (all_17_0 = 0) & big_r(all_3_2) = all_17_0
% 4.55/1.39  | | | 
% 4.55/1.39  | | | ALPHA: (16) implies:
% 4.55/1.39  | | |   (17)   ~ (all_17_0 = 0)
% 4.55/1.39  | | |   (18)  big_r(all_3_2) = all_17_0
% 4.55/1.39  | | | 
% 4.55/1.39  | | | GROUND_INST: instantiating (1) with 0, all_17_0, all_3_2, simplifying with
% 4.55/1.39  | | |              (12), (18) gives:
% 4.55/1.39  | | |   (19)  all_17_0 = 0
% 4.55/1.39  | | | 
% 4.55/1.39  | | | REDUCE: (17), (19) imply:
% 4.55/1.39  | | |   (20)  $false
% 4.55/1.39  | | | 
% 4.55/1.39  | | | CLOSE: (20) is inconsistent.
% 4.55/1.39  | | | 
% 4.55/1.39  | | End of split
% 4.55/1.39  | | 
% 4.55/1.39  | Case 2:
% 4.55/1.39  | | 
% 4.55/1.39  | |   (21)  all_3_0 = 0
% 4.55/1.39  | | 
% 4.55/1.39  | | REDUCE: (4), (21) imply:
% 4.55/1.40  | |   (22)  $false
% 4.55/1.40  | | 
% 4.55/1.40  | | CLOSE: (22) is inconsistent.
% 4.55/1.40  | | 
% 4.55/1.40  | End of split
% 4.55/1.40  | 
% 4.55/1.40  End of proof
% 4.55/1.40  % SZS output end Proof for theBenchmark
% 4.55/1.40  
% 4.55/1.40  803ms
%------------------------------------------------------------------------------