TSTP Solution File: SEU161+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU161+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n032.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 17:42:55 EDT 2023

% Result   : Theorem 3.08s 1.07s
% Output   : Proof 4.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : SEU161+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Wed Aug 23 16:38:11 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.15/0.51  ________       _____
% 0.15/0.51  ___  __ \_________(_)________________________________
% 0.15/0.51  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.15/0.51  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.15/0.51  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.15/0.51  
% 0.15/0.51  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.51  (2023-06-19)
% 0.15/0.51  
% 0.15/0.51  (c) Philipp Rümmer, 2009-2023
% 0.15/0.51  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.51                Amanda Stjerna.
% 0.15/0.51  Free software under BSD-3-Clause.
% 0.15/0.51  
% 0.15/0.51  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.51  
% 0.15/0.51  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.15/0.52  Running up to 7 provers in parallel.
% 0.15/0.54  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.54  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.54  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.54  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.54  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.54  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.87/0.81  Prover 4: Preprocessing ...
% 0.87/0.81  Prover 1: Preprocessing ...
% 1.65/0.86  Prover 3: Preprocessing ...
% 1.65/0.86  Prover 0: Preprocessing ...
% 1.65/0.86  Prover 5: Preprocessing ...
% 1.65/0.86  Prover 6: Preprocessing ...
% 1.65/0.86  Prover 2: Preprocessing ...
% 2.51/0.96  Prover 1: Warning: ignoring some quantifiers
% 2.51/0.96  Prover 3: Warning: ignoring some quantifiers
% 2.65/0.98  Prover 1: Constructing countermodel ...
% 2.65/0.98  Prover 6: Proving ...
% 2.65/0.98  Prover 5: Proving ...
% 2.65/0.98  Prover 4: Constructing countermodel ...
% 2.65/0.99  Prover 3: Constructing countermodel ...
% 2.65/0.99  Prover 2: Proving ...
% 2.65/0.99  Prover 0: Proving ...
% 3.08/1.07  Prover 3: proved (533ms)
% 3.08/1.07  
% 3.08/1.07  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/1.07  
% 3.08/1.07  Prover 5: stopped
% 3.08/1.07  Prover 0: stopped
% 3.08/1.08  Prover 2: stopped
% 3.08/1.08  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.08/1.08  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.08/1.08  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.08/1.09  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.08/1.09  Prover 6: proved (549ms)
% 3.08/1.09  
% 3.08/1.09  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/1.09  
% 3.08/1.09  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.08/1.09  Prover 7: Preprocessing ...
% 3.08/1.09  Prover 8: Preprocessing ...
% 3.08/1.11  Prover 10: Preprocessing ...
% 3.08/1.11  Prover 11: Preprocessing ...
% 3.08/1.11  Prover 13: Preprocessing ...
% 3.66/1.13  Prover 8: Warning: ignoring some quantifiers
% 3.66/1.14  Prover 10: Constructing countermodel ...
% 3.66/1.15  Prover 8: Constructing countermodel ...
% 3.66/1.16  Prover 1: Found proof (size 12)
% 3.66/1.16  Prover 1: proved (625ms)
% 3.66/1.16  Prover 7: Constructing countermodel ...
% 3.66/1.16  Prover 8: stopped
% 3.66/1.16  Prover 11: Constructing countermodel ...
% 3.66/1.16  Prover 4: stopped
% 3.66/1.16  Prover 13: Warning: ignoring some quantifiers
% 3.66/1.16  Prover 7: stopped
% 3.66/1.16  Prover 11: stopped
% 3.66/1.16  Prover 10: stopped
% 3.66/1.16  Prover 13: Constructing countermodel ...
% 3.66/1.17  Prover 13: stopped
% 3.66/1.17  
% 3.66/1.17  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.66/1.17  
% 3.66/1.17  % SZS output start Proof for theBenchmark
% 3.66/1.17  Assumptions after simplification:
% 3.66/1.17  ---------------------------------
% 3.66/1.17  
% 3.66/1.17    (l23_zfmisc_1)
% 4.06/1.20     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v1 |  ~
% 4.06/1.20      (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ~ $i(v1) |  ~ $i(v0)
% 4.06/1.20      |  ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.06/1.20  
% 4.06/1.20    (t46_zfmisc_1)
% 4.06/1.21     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v3 = v1) &
% 4.06/1.21      singleton(v0) = v2 & in(v0, v1) = 0 & set_union2(v2, v1) = v3 & $i(v3) &
% 4.06/1.21      $i(v2) & $i(v1) & $i(v0))
% 4.06/1.21  
% 4.06/1.21    (function-axioms)
% 4.06/1.21     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 4.06/1.21    [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 4.06/1.21      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 4.06/1.21      (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0: $i] :  !
% 4.06/1.21    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~
% 4.06/1.21      (singleton(v2) = v0))
% 4.06/1.21  
% 4.06/1.21  Further assumptions not needed in the proof:
% 4.06/1.21  --------------------------------------------
% 4.06/1.21  antisymmetry_r2_hidden, commutativity_k2_xboole_0, dt_k1_tarski, dt_k2_xboole_0,
% 4.06/1.21  idempotence_k2_xboole_0
% 4.06/1.21  
% 4.06/1.21  Those formulas are unsatisfiable:
% 4.06/1.21  ---------------------------------
% 4.06/1.21  
% 4.06/1.21  Begin of proof
% 4.06/1.21  | 
% 4.06/1.21  | ALPHA: (function-axioms) implies:
% 4.06/1.21  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 4.06/1.21  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 4.06/1.22  | 
% 4.06/1.22  | DELTA: instantiating (t46_zfmisc_1) with fresh symbols all_8_0, all_8_1,
% 4.06/1.22  |        all_8_2, all_8_3 gives:
% 4.06/1.22  |   (2)   ~ (all_8_0 = all_8_2) & singleton(all_8_3) = all_8_1 & in(all_8_3,
% 4.06/1.22  |          all_8_2) = 0 & set_union2(all_8_1, all_8_2) = all_8_0 & $i(all_8_0) &
% 4.06/1.22  |        $i(all_8_1) & $i(all_8_2) & $i(all_8_3)
% 4.06/1.22  | 
% 4.06/1.22  | ALPHA: (2) implies:
% 4.06/1.22  |   (3)   ~ (all_8_0 = all_8_2)
% 4.06/1.22  |   (4)  $i(all_8_3)
% 4.06/1.22  |   (5)  $i(all_8_2)
% 4.06/1.22  |   (6)  set_union2(all_8_1, all_8_2) = all_8_0
% 4.06/1.22  |   (7)  in(all_8_3, all_8_2) = 0
% 4.06/1.22  |   (8)  singleton(all_8_3) = all_8_1
% 4.06/1.22  | 
% 4.06/1.22  | GROUND_INST: instantiating (l23_zfmisc_1) with all_8_3, all_8_2, all_8_1,
% 4.06/1.22  |              all_8_0, simplifying with (4), (5), (6), (8) gives:
% 4.06/1.22  |   (9)  all_8_0 = all_8_2 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_8_3, all_8_2)
% 4.06/1.22  |          = v0)
% 4.06/1.22  | 
% 4.06/1.22  | BETA: splitting (9) gives:
% 4.06/1.22  | 
% 4.06/1.22  | Case 1:
% 4.06/1.22  | | 
% 4.06/1.22  | |   (10)  all_8_0 = all_8_2
% 4.06/1.22  | | 
% 4.06/1.22  | | REDUCE: (3), (10) imply:
% 4.06/1.22  | |   (11)  $false
% 4.06/1.23  | | 
% 4.06/1.23  | | CLOSE: (11) is inconsistent.
% 4.06/1.23  | | 
% 4.06/1.23  | Case 2:
% 4.06/1.23  | | 
% 4.06/1.23  | |   (12)   ? [v0: int] : ( ~ (v0 = 0) & in(all_8_3, all_8_2) = v0)
% 4.06/1.23  | | 
% 4.06/1.23  | | DELTA: instantiating (12) with fresh symbol all_22_0 gives:
% 4.06/1.23  | |   (13)   ~ (all_22_0 = 0) & in(all_8_3, all_8_2) = all_22_0
% 4.06/1.23  | | 
% 4.06/1.23  | | ALPHA: (13) implies:
% 4.06/1.23  | |   (14)   ~ (all_22_0 = 0)
% 4.06/1.23  | |   (15)  in(all_8_3, all_8_2) = all_22_0
% 4.06/1.23  | | 
% 4.06/1.23  | | GROUND_INST: instantiating (1) with 0, all_22_0, all_8_2, all_8_3,
% 4.06/1.23  | |              simplifying with (7), (15) gives:
% 4.06/1.23  | |   (16)  all_22_0 = 0
% 4.06/1.23  | | 
% 4.06/1.23  | | REDUCE: (14), (16) imply:
% 4.06/1.23  | |   (17)  $false
% 4.06/1.23  | | 
% 4.06/1.23  | | CLOSE: (17) is inconsistent.
% 4.06/1.23  | | 
% 4.06/1.23  | End of split
% 4.06/1.23  | 
% 4.06/1.23  End of proof
% 4.06/1.23  % SZS output end Proof for theBenchmark
% 4.06/1.23  
% 4.06/1.23  716ms
%------------------------------------------------------------------------------