TSTP Solution File: SYN056+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SYN056+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 : n019.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 03:26:22 EDT 2023

% Result   : Theorem 3.87s 1.22s
% Output   : Proof 4.88s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN056+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 19:18:58 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.63  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.94/0.95  Prover 4: Preprocessing ...
% 1.94/0.95  Prover 1: Preprocessing ...
% 1.94/0.99  Prover 0: Preprocessing ...
% 1.94/0.99  Prover 2: Preprocessing ...
% 1.94/0.99  Prover 6: Preprocessing ...
% 1.94/0.99  Prover 3: Preprocessing ...
% 1.94/0.99  Prover 5: Preprocessing ...
% 2.85/1.09  Prover 5: Constructing countermodel ...
% 2.85/1.09  Prover 2: Constructing countermodel ...
% 2.85/1.11  Prover 3: Constructing countermodel ...
% 2.85/1.11  Prover 6: Proving ...
% 2.85/1.11  Prover 1: Constructing countermodel ...
% 2.85/1.16  Prover 4: Constructing countermodel ...
% 3.51/1.18  Prover 0: Proving ...
% 3.68/1.22  Prover 2: proved (594ms)
% 3.87/1.22  
% 3.87/1.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.87/1.22  
% 3.87/1.22  Prover 3: gave up
% 3.87/1.22  Prover 5: stopped
% 3.87/1.22  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.87/1.22  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.87/1.22  Prover 6: stopped
% 3.87/1.23  Prover 0: stopped
% 3.92/1.23  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.92/1.23  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.92/1.23  Prover 1: gave up
% 3.92/1.25  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.92/1.25  Prover 7: Preprocessing ...
% 3.92/1.25  Prover 8: Preprocessing ...
% 3.92/1.25  Prover 10: Preprocessing ...
% 3.92/1.25  Prover 11: Preprocessing ...
% 3.92/1.25  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 3.92/1.25  Prover 13: Preprocessing ...
% 3.92/1.26  Prover 10: Constructing countermodel ...
% 3.92/1.26  Prover 7: Constructing countermodel ...
% 3.92/1.27  Prover 16: Preprocessing ...
% 3.92/1.28  Prover 13: Constructing countermodel ...
% 3.92/1.29  Prover 8: Warning: ignoring some quantifiers
% 3.92/1.29  Prover 8: Constructing countermodel ...
% 3.92/1.30  Prover 16: Constructing countermodel ...
% 3.92/1.34  Prover 10: Found proof (size 24)
% 3.92/1.34  Prover 10: proved (117ms)
% 3.92/1.34  Prover 4: stopped
% 3.92/1.34  Prover 13: stopped
% 3.92/1.34  Prover 16: stopped
% 3.92/1.34  Prover 8: stopped
% 3.92/1.34  Prover 7: stopped
% 3.92/1.38  Prover 11: Constructing countermodel ...
% 3.92/1.38  Prover 11: stopped
% 3.92/1.38  
% 3.92/1.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.92/1.38  
% 3.92/1.39  % SZS output start Proof for theBenchmark
% 3.92/1.39  Assumptions after simplification:
% 3.92/1.39  ---------------------------------
% 3.92/1.39  
% 3.92/1.39    (pel26)
% 3.92/1.40     ? [v0: $i] : ($i(v0) & ((big_q(v0) &  ~ big_s(v0) &  ! [v1: $i] : ( ~ $i(v1)
% 3.92/1.40            |  ~ big_p(v1) | big_r(v1))) | (big_p(v0) &  ~ big_r(v0) &  ! [v1: $i]
% 3.92/1.40          : ( ~ $i(v1) |  ~ big_q(v1) | big_s(v1)))))
% 3.92/1.40  
% 3.92/1.40    (pel26_1)
% 3.92/1.40     ? [v0: $i] :  ? [v1: $i] : ($i(v1) & $i(v0) & ((big_q(v0) & big_p(v1)) | ( !
% 3.92/1.40          [v2: $i] : ( ~ $i(v2) |  ~ big_q(v2)) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 3.92/1.40            big_p(v2)))))
% 3.92/1.40  
% 3.92/1.40    (pel26_2)
% 3.92/1.40     ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ big_s(v1) |  ~
% 3.92/1.40      big_q(v1) |  ~ big_p(v0) | big_r(v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 3.92/1.40      $i(v1) |  ~ $i(v0) |  ~ big_r(v0) |  ~ big_q(v1) |  ~ big_p(v0) | big_s(v1))
% 3.92/1.40  
% 3.92/1.40  Those formulas are unsatisfiable:
% 3.92/1.40  ---------------------------------
% 3.92/1.40  
% 3.92/1.40  Begin of proof
% 3.92/1.40  | 
% 3.92/1.40  | ALPHA: (pel26_2) implies:
% 3.92/1.41  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ big_r(v0) |  ~
% 3.92/1.41  |          big_q(v1) |  ~ big_p(v0) | big_s(v1))
% 3.92/1.41  |   (2)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ big_s(v1) |  ~
% 3.92/1.41  |          big_q(v1) |  ~ big_p(v0) | big_r(v0))
% 3.92/1.41  | 
% 3.92/1.41  | DELTA: instantiating (pel26_1) with fresh symbols all_3_0, all_3_1 gives:
% 3.92/1.41  |   (3)  $i(all_3_0) & $i(all_3_1) & ((big_q(all_3_1) & big_p(all_3_0)) | ( !
% 3.92/1.41  |            [v0: $i] : ( ~ $i(v0) |  ~ big_q(v0)) &  ! [v0: $i] : ( ~ $i(v0) | 
% 3.92/1.41  |              ~ big_p(v0))))
% 3.92/1.41  | 
% 3.92/1.41  | ALPHA: (3) implies:
% 4.88/1.41  |   (4)  $i(all_3_1)
% 4.88/1.41  |   (5)  $i(all_3_0)
% 4.88/1.41  |   (6)  (big_q(all_3_1) & big_p(all_3_0)) | ( ! [v0: $i] : ( ~ $i(v0) |  ~
% 4.88/1.41  |            big_q(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ big_p(v0)))
% 4.88/1.41  | 
% 4.88/1.41  | DELTA: instantiating (pel26) with fresh symbol all_5_0 gives:
% 4.88/1.41  |   (7)  $i(all_5_0) & ((big_q(all_5_0) &  ~ big_s(all_5_0) &  ! [v0: $i] : ( ~
% 4.88/1.41  |              $i(v0) |  ~ big_p(v0) | big_r(v0))) | (big_p(all_5_0) &  ~
% 4.88/1.41  |            big_r(all_5_0) &  ! [v0: $i] : ( ~ $i(v0) |  ~ big_q(v0) |
% 4.88/1.41  |              big_s(v0))))
% 4.88/1.41  | 
% 4.88/1.41  | ALPHA: (7) implies:
% 4.88/1.41  |   (8)  $i(all_5_0)
% 4.88/1.41  |   (9)  (big_q(all_5_0) &  ~ big_s(all_5_0) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 4.88/1.42  |            big_p(v0) | big_r(v0))) | (big_p(all_5_0) &  ~ big_r(all_5_0) &  !
% 4.88/1.42  |          [v0: $i] : ( ~ $i(v0) |  ~ big_q(v0) | big_s(v0)))
% 4.88/1.42  | 
% 4.88/1.42  | BETA: splitting (6) gives:
% 4.88/1.42  | 
% 4.88/1.42  | Case 1:
% 4.88/1.42  | | 
% 4.88/1.42  | |   (10)  big_q(all_3_1) & big_p(all_3_0)
% 4.88/1.42  | | 
% 4.88/1.42  | | ALPHA: (10) implies:
% 4.88/1.42  | |   (11)  big_p(all_3_0)
% 4.88/1.42  | |   (12)  big_q(all_3_1)
% 4.88/1.42  | | 
% 4.88/1.42  | | BETA: splitting (9) gives:
% 4.88/1.42  | | 
% 4.88/1.42  | | Case 1:
% 4.88/1.42  | | | 
% 4.88/1.42  | | |   (13)  big_q(all_5_0) &  ~ big_s(all_5_0) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 4.88/1.42  | | |           big_p(v0) | big_r(v0))
% 4.88/1.42  | | | 
% 4.88/1.42  | | | ALPHA: (13) implies:
% 4.88/1.42  | | |   (14)   ~ big_s(all_5_0)
% 4.88/1.42  | | |   (15)  big_q(all_5_0)
% 4.88/1.42  | | |   (16)   ! [v0: $i] : ( ~ $i(v0) |  ~ big_p(v0) | big_r(v0))
% 4.88/1.42  | | | 
% 4.88/1.42  | | | GROUND_INST: instantiating (16) with all_3_0, simplifying with (5), (11)
% 4.88/1.42  | | |              gives:
% 4.88/1.42  | | |   (17)  big_r(all_3_0)
% 4.88/1.42  | | | 
% 4.88/1.42  | | | GROUND_INST: instantiating (1) with all_3_0, all_5_0, simplifying with
% 4.88/1.42  | | |              (5), (8), (11), (14), (15), (17) gives:
% 4.88/1.42  | | |   (18)  $false
% 4.88/1.42  | | | 
% 4.88/1.42  | | | CLOSE: (18) is inconsistent.
% 4.88/1.42  | | | 
% 4.88/1.42  | | Case 2:
% 4.88/1.42  | | | 
% 4.88/1.42  | | |   (19)  big_p(all_5_0) &  ~ big_r(all_5_0) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 4.88/1.42  | | |           big_q(v0) | big_s(v0))
% 4.88/1.42  | | | 
% 4.88/1.42  | | | ALPHA: (19) implies:
% 4.88/1.42  | | |   (20)   ~ big_r(all_5_0)
% 4.88/1.42  | | |   (21)  big_p(all_5_0)
% 4.88/1.42  | | |   (22)   ! [v0: $i] : ( ~ $i(v0) |  ~ big_q(v0) | big_s(v0))
% 4.88/1.42  | | | 
% 4.88/1.42  | | | GROUND_INST: instantiating (22) with all_3_1, simplifying with (4), (12)
% 4.88/1.42  | | |              gives:
% 4.88/1.42  | | |   (23)  big_s(all_3_1)
% 4.88/1.42  | | | 
% 4.88/1.43  | | | GROUND_INST: instantiating (2) with all_5_0, all_3_1, simplifying with
% 4.88/1.43  | | |              (4), (8), (12), (20), (21), (23) gives:
% 4.88/1.43  | | |   (24)  $false
% 4.88/1.43  | | | 
% 4.88/1.43  | | | CLOSE: (24) is inconsistent.
% 4.88/1.43  | | | 
% 4.88/1.43  | | End of split
% 4.88/1.43  | | 
% 4.88/1.43  | Case 2:
% 4.88/1.43  | | 
% 4.88/1.43  | |   (25)   ! [v0: $i] : ( ~ $i(v0) |  ~ big_q(v0)) &  ! [v0: $i] : ( ~ $i(v0)
% 4.88/1.43  | |           |  ~ big_p(v0))
% 4.88/1.43  | | 
% 4.88/1.43  | | ALPHA: (25) implies:
% 4.88/1.43  | |   (26)   ! [v0: $i] : ( ~ $i(v0) |  ~ big_p(v0))
% 4.88/1.43  | |   (27)   ! [v0: $i] : ( ~ $i(v0) |  ~ big_q(v0))
% 4.88/1.43  | | 
% 4.88/1.43  | | BETA: splitting (9) gives:
% 4.88/1.43  | | 
% 4.88/1.43  | | Case 1:
% 4.88/1.43  | | | 
% 4.88/1.43  | | |   (28)  big_q(all_5_0) &  ~ big_s(all_5_0) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 4.88/1.43  | | |           big_p(v0) | big_r(v0))
% 4.88/1.43  | | | 
% 4.88/1.43  | | | ALPHA: (28) implies:
% 4.88/1.43  | | |   (29)  big_q(all_5_0)
% 4.88/1.43  | | | 
% 4.88/1.43  | | | GROUND_INST: instantiating (27) with all_5_0, simplifying with (8), (29)
% 4.88/1.43  | | |              gives:
% 4.88/1.43  | | |   (30)  $false
% 4.88/1.43  | | | 
% 4.88/1.43  | | | CLOSE: (30) is inconsistent.
% 4.88/1.43  | | | 
% 4.88/1.43  | | Case 2:
% 4.88/1.43  | | | 
% 4.88/1.43  | | |   (31)  big_p(all_5_0) &  ~ big_r(all_5_0) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 4.88/1.43  | | |           big_q(v0) | big_s(v0))
% 4.88/1.43  | | | 
% 4.88/1.43  | | | ALPHA: (31) implies:
% 4.88/1.43  | | |   (32)  big_p(all_5_0)
% 4.88/1.43  | | | 
% 4.88/1.43  | | | GROUND_INST: instantiating (26) with all_5_0, simplifying with (8), (32)
% 4.88/1.43  | | |              gives:
% 4.88/1.43  | | |   (33)  $false
% 4.88/1.43  | | | 
% 4.88/1.43  | | | CLOSE: (33) is inconsistent.
% 4.88/1.43  | | | 
% 4.88/1.43  | | End of split
% 4.88/1.43  | | 
% 4.88/1.43  | End of split
% 4.88/1.43  | 
% 4.88/1.43  End of proof
% 4.88/1.43  % SZS output end Proof for theBenchmark
% 4.88/1.43  
% 4.88/1.43  825ms
%------------------------------------------------------------------------------