TSTP Solution File: SYN980+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SYN980+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 : n007.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 03:29:27 EDT 2023

% Result   : Theorem 3.48s 1.16s
% Output   : Proof 4.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN980+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n007.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 : Sat Aug 26 17:11:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.60  ________       _____
% 0.20/0.60  ___  __ \_________(_)________________________________
% 0.20/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60  (2023-06-19)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2023
% 0.20/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60                Amanda Stjerna.
% 0.20/0.60  Free software under BSD-3-Clause.
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61  Running up to 7 provers in parallel.
% 0.20/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62  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 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.83/0.93  Prover 1: Preprocessing ...
% 1.83/0.93  Prover 4: Preprocessing ...
% 2.12/0.97  Prover 3: Preprocessing ...
% 2.12/0.97  Prover 0: Preprocessing ...
% 2.12/0.97  Prover 2: Preprocessing ...
% 2.12/0.97  Prover 5: Preprocessing ...
% 2.12/0.97  Prover 6: Preprocessing ...
% 2.76/1.05  Prover 2: Proving ...
% 2.76/1.05  Prover 6: Proving ...
% 2.76/1.05  Prover 1: Constructing countermodel ...
% 2.76/1.06  Prover 5: Proving ...
% 2.76/1.06  Prover 3: Constructing countermodel ...
% 2.76/1.08  Prover 4: Constructing countermodel ...
% 3.07/1.09  Prover 0: Proving ...
% 3.48/1.15  Prover 5: proved (530ms)
% 3.48/1.15  Prover 3: proved (530ms)
% 3.48/1.15  
% 3.48/1.16  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.16  
% 3.48/1.16  
% 3.48/1.16  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.16  
% 3.48/1.16  Prover 0: stopped
% 3.48/1.16  Prover 6: stopped
% 3.48/1.17  Prover 2: stopped
% 3.48/1.17  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.48/1.17  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.48/1.17  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.48/1.17  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.48/1.17  Prover 7: Preprocessing ...
% 3.48/1.17  Prover 8: Preprocessing ...
% 3.48/1.18  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.48/1.18  Prover 11: Preprocessing ...
% 3.48/1.18  Prover 10: Preprocessing ...
% 3.48/1.18  Prover 13: Preprocessing ...
% 3.48/1.19  Prover 1: Found proof (size 17)
% 3.48/1.19  Prover 1: proved (580ms)
% 3.48/1.20  Prover 4: stopped
% 3.48/1.20  Prover 10: Constructing countermodel ...
% 3.48/1.20  Prover 11: stopped
% 3.48/1.20  Prover 10: stopped
% 3.48/1.20  Prover 7: Constructing countermodel ...
% 3.48/1.20  Prover 7: stopped
% 3.48/1.21  Prover 8: Warning: ignoring some quantifiers
% 3.48/1.21  Prover 8: Constructing countermodel ...
% 3.48/1.21  Prover 13: Warning: ignoring some quantifiers
% 3.48/1.21  Prover 8: stopped
% 3.48/1.22  Prover 13: Constructing countermodel ...
% 3.48/1.22  Prover 13: stopped
% 3.48/1.22  
% 3.48/1.22  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/1.22  
% 3.48/1.22  % SZS output start Proof for theBenchmark
% 3.48/1.22  Assumptions after simplification:
% 3.48/1.22  ---------------------------------
% 3.48/1.22  
% 3.48/1.22    (prove_this)
% 3.48/1.26     ? [v0: $i] :  ? [v1: any] :  ? [v2: $i] :  ? [v3: any] : (q(v2, v0) = v3 &
% 3.48/1.26      f(v0) = v2 & r(v0) = v1 & $i(v2) & $i(v0) &  ! [v4: $i] :  ! [v5: $i] :  !
% 3.48/1.26      [v6: int] : (v6 = 0 |  ~ (f(v4) = v5) |  ~ (p(v5, v4) = v6) |  ~ $i(v4) |
% 3.48/1.26        (v1 = 0 &  ? [v7: int] : ( ~ (v7 = 0) & r(v4) = v7))) &  ! [v4: $i] :  !
% 3.48/1.26      [v5: $i] :  ! [v6: any] : ( ~ (q(v4, v5) = v6) |  ~ $i(v5) |  ~ $i(v4) |  ?
% 3.48/1.26        [v7: int] : ( ~ (v7 = 0) & p(v4, v5) = v7) | (v3 = 0 &  ~ (v6 = 0))))
% 3.48/1.26  
% 3.48/1.26    (function-axioms)
% 3.48/1.27     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 3.48/1.27    [v3: $i] : (v1 = v0 |  ~ (q(v3, v2) = v1) |  ~ (q(v3, v2) = v0)) &  ! [v0:
% 3.48/1.27      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 3.48/1.27    : (v1 = v0 |  ~ (p(v3, v2) = v1) |  ~ (p(v3, v2) = v0)) &  ! [v0: $i] :  !
% 3.48/1.27    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (f(v2) = v1) |  ~ (f(v2) = v0)) &  !
% 3.48/1.27    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0
% 3.48/1.27      |  ~ (r(v2) = v1) |  ~ (r(v2) = v0))
% 3.48/1.27  
% 3.48/1.27  Those formulas are unsatisfiable:
% 3.48/1.27  ---------------------------------
% 3.48/1.27  
% 3.48/1.27  Begin of proof
% 3.48/1.27  | 
% 4.17/1.27  | ALPHA: (function-axioms) implies:
% 4.17/1.27  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.17/1.27  |        (v1 = v0 |  ~ (r(v2) = v1) |  ~ (r(v2) = v0))
% 4.17/1.27  | 
% 4.17/1.27  | DELTA: instantiating (prove_this) with fresh symbols all_3_0, all_3_1,
% 4.17/1.27  |        all_3_2, all_3_3 gives:
% 4.17/1.28  |   (2)  q(all_3_1, all_3_3) = all_3_0 & f(all_3_3) = all_3_1 & r(all_3_3) =
% 4.17/1.28  |        all_3_2 & $i(all_3_1) & $i(all_3_3) &  ! [v0: $i] :  ! [v1: $i] :  !
% 4.17/1.28  |        [v2: int] : (v2 = 0 |  ~ (f(v0) = v1) |  ~ (p(v1, v0) = v2) |  ~ $i(v0)
% 4.17/1.28  |          | (all_3_2 = 0 &  ? [v3: int] : ( ~ (v3 = 0) & r(v0) = v3))) &  !
% 4.17/1.28  |        [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (q(v0, v1) = v2) |  ~
% 4.17/1.28  |          $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & p(v0, v1) = v3) |
% 4.17/1.28  |          (all_3_0 = 0 &  ~ (v2 = 0)))
% 4.17/1.28  | 
% 4.17/1.28  | ALPHA: (2) implies:
% 4.17/1.28  |   (3)  $i(all_3_3)
% 4.17/1.28  |   (4)  $i(all_3_1)
% 4.17/1.28  |   (5)  r(all_3_3) = all_3_2
% 4.17/1.28  |   (6)  f(all_3_3) = all_3_1
% 4.17/1.28  |   (7)  q(all_3_1, all_3_3) = all_3_0
% 4.17/1.28  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: any] : ( ~ (q(v0, v1) = v2) |  ~
% 4.17/1.28  |          $i(v1) |  ~ $i(v0) |  ? [v3: int] : ( ~ (v3 = 0) & p(v0, v1) = v3) |
% 4.17/1.28  |          (all_3_0 = 0 &  ~ (v2 = 0)))
% 4.17/1.28  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (f(v0) = v1) | 
% 4.17/1.28  |          ~ (p(v1, v0) = v2) |  ~ $i(v0) | (all_3_2 = 0 &  ? [v3: int] : ( ~
% 4.17/1.28  |              (v3 = 0) & r(v0) = v3)))
% 4.17/1.28  | 
% 4.17/1.28  | GROUND_INST: instantiating (8) with all_3_1, all_3_3, all_3_0, simplifying
% 4.17/1.28  |              with (3), (4), (7) gives:
% 4.17/1.28  |   (10)   ? [v0: int] : ( ~ (v0 = 0) & p(all_3_1, all_3_3) = v0)
% 4.17/1.28  | 
% 4.17/1.28  | DELTA: instantiating (10) with fresh symbol all_11_0 gives:
% 4.17/1.28  |   (11)   ~ (all_11_0 = 0) & p(all_3_1, all_3_3) = all_11_0
% 4.17/1.28  | 
% 4.17/1.28  | ALPHA: (11) implies:
% 4.17/1.28  |   (12)   ~ (all_11_0 = 0)
% 4.17/1.29  |   (13)  p(all_3_1, all_3_3) = all_11_0
% 4.17/1.29  | 
% 4.17/1.29  | GROUND_INST: instantiating (9) with all_3_3, all_3_1, all_11_0, simplifying
% 4.17/1.29  |              with (3), (6), (13) gives:
% 4.17/1.29  |   (14)  all_11_0 = 0 | (all_3_2 = 0 &  ? [v0: int] : ( ~ (v0 = 0) & r(all_3_3)
% 4.17/1.29  |             = v0))
% 4.17/1.29  | 
% 4.17/1.29  | BETA: splitting (14) gives:
% 4.17/1.29  | 
% 4.17/1.29  | Case 1:
% 4.17/1.29  | | 
% 4.17/1.29  | |   (15)  all_11_0 = 0
% 4.17/1.29  | | 
% 4.17/1.29  | | REDUCE: (12), (15) imply:
% 4.17/1.29  | |   (16)  $false
% 4.17/1.29  | | 
% 4.17/1.29  | | CLOSE: (16) is inconsistent.
% 4.17/1.29  | | 
% 4.17/1.29  | Case 2:
% 4.17/1.29  | | 
% 4.17/1.29  | |   (17)  all_3_2 = 0 &  ? [v0: int] : ( ~ (v0 = 0) & r(all_3_3) = v0)
% 4.17/1.29  | | 
% 4.17/1.29  | | ALPHA: (17) implies:
% 4.17/1.29  | |   (18)  all_3_2 = 0
% 4.17/1.29  | |   (19)   ? [v0: int] : ( ~ (v0 = 0) & r(all_3_3) = v0)
% 4.17/1.29  | | 
% 4.17/1.29  | | DELTA: instantiating (19) with fresh symbol all_20_0 gives:
% 4.17/1.29  | |   (20)   ~ (all_20_0 = 0) & r(all_3_3) = all_20_0
% 4.17/1.29  | | 
% 4.17/1.29  | | ALPHA: (20) implies:
% 4.17/1.29  | |   (21)   ~ (all_20_0 = 0)
% 4.17/1.29  | |   (22)  r(all_3_3) = all_20_0
% 4.17/1.29  | | 
% 4.17/1.29  | | REDUCE: (5), (18) imply:
% 4.17/1.29  | |   (23)  r(all_3_3) = 0
% 4.17/1.29  | | 
% 4.17/1.29  | | GROUND_INST: instantiating (1) with 0, all_20_0, all_3_3, simplifying with
% 4.17/1.29  | |              (22), (23) gives:
% 4.17/1.29  | |   (24)  all_20_0 = 0
% 4.17/1.29  | | 
% 4.17/1.29  | | REDUCE: (21), (24) imply:
% 4.17/1.29  | |   (25)  $false
% 4.17/1.29  | | 
% 4.17/1.29  | | CLOSE: (25) is inconsistent.
% 4.17/1.29  | | 
% 4.17/1.29  | End of split
% 4.17/1.29  | 
% 4.17/1.29  End of proof
% 4.17/1.29  % SZS output end Proof for theBenchmark
% 4.17/1.30  
% 4.17/1.30  697ms
%------------------------------------------------------------------------------