TSTP Solution File: SEU148+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : Thu Aug 31 17:42:47 EDT 2023

% Result   : Theorem 4.57s 1.42s
% Output   : Proof 6.52s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 16:25:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.66  ________       _____
% 0.20/0.66  ___  __ \_________(_)________________________________
% 0.20/0.66  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.66  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.66  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.66  
% 0.20/0.66  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.66  (2023-06-19)
% 0.20/0.66  
% 0.20/0.66  (c) Philipp Rümmer, 2009-2023
% 0.20/0.66  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.66                Amanda Stjerna.
% 0.20/0.66  Free software under BSD-3-Clause.
% 0.20/0.66  
% 0.20/0.66  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.66  
% 0.20/0.66  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.67  Running up to 7 provers in parallel.
% 0.20/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.82/1.00  Prover 4: Preprocessing ...
% 1.82/1.00  Prover 1: Preprocessing ...
% 1.82/1.05  Prover 3: Preprocessing ...
% 1.82/1.05  Prover 2: Preprocessing ...
% 1.82/1.05  Prover 6: Preprocessing ...
% 1.82/1.05  Prover 0: Preprocessing ...
% 1.82/1.05  Prover 5: Preprocessing ...
% 3.50/1.20  Prover 1: Warning: ignoring some quantifiers
% 3.50/1.22  Prover 4: Warning: ignoring some quantifiers
% 3.50/1.22  Prover 5: Proving ...
% 3.50/1.22  Prover 6: Proving ...
% 3.50/1.22  Prover 0: Proving ...
% 3.50/1.22  Prover 3: Warning: ignoring some quantifiers
% 3.50/1.23  Prover 2: Proving ...
% 3.50/1.23  Prover 4: Constructing countermodel ...
% 3.50/1.23  Prover 3: Constructing countermodel ...
% 3.50/1.23  Prover 1: Constructing countermodel ...
% 4.57/1.42  Prover 5: proved (730ms)
% 4.57/1.42  Prover 2: proved (738ms)
% 4.57/1.42  
% 4.57/1.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.42  
% 4.57/1.42  
% 4.57/1.42  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.42  
% 4.57/1.42  Prover 3: stopped
% 4.57/1.42  Prover 6: stopped
% 4.57/1.42  Prover 0: stopped
% 4.57/1.43  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.57/1.43  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.57/1.43  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.57/1.43  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.57/1.43  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.57/1.45  Prover 1: gave up
% 4.57/1.46  Prover 8: Preprocessing ...
% 4.57/1.46  Prover 11: Preprocessing ...
% 4.57/1.46  Prover 13: Preprocessing ...
% 4.57/1.46  Prover 7: Preprocessing ...
% 4.57/1.46  Prover 10: Preprocessing ...
% 4.57/1.46  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 4.57/1.49  Prover 13: Warning: ignoring some quantifiers
% 4.57/1.49  Prover 13: Constructing countermodel ...
% 4.57/1.50  Prover 16: Preprocessing ...
% 4.57/1.50  Prover 10: Warning: ignoring some quantifiers
% 4.57/1.50  Prover 10: Constructing countermodel ...
% 5.04/1.51  Prover 7: Warning: ignoring some quantifiers
% 5.04/1.51  Prover 7: Constructing countermodel ...
% 5.04/1.53  Prover 11: Warning: ignoring some quantifiers
% 5.04/1.53  Prover 4: gave up
% 5.04/1.53  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 5.04/1.53  Prover 8: Warning: ignoring some quantifiers
% 5.04/1.53  Prover 11: Constructing countermodel ...
% 5.04/1.54  Prover 19: Preprocessing ...
% 5.04/1.55  Prover 8: Constructing countermodel ...
% 6.02/1.57  Prover 16: Warning: ignoring some quantifiers
% 6.02/1.57  Prover 16: Constructing countermodel ...
% 6.02/1.58  Prover 10: Found proof (size 17)
% 6.02/1.58  Prover 10: proved (150ms)
% 6.02/1.58  Prover 16: stopped
% 6.02/1.58  Prover 8: stopped
% 6.02/1.58  Prover 7: stopped
% 6.02/1.58  Prover 11: stopped
% 6.02/1.58  Prover 13: stopped
% 6.31/1.60  Prover 19: Warning: ignoring some quantifiers
% 6.31/1.61  Prover 19: Constructing countermodel ...
% 6.31/1.61  Prover 19: stopped
% 6.31/1.61  
% 6.31/1.61  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.31/1.61  
% 6.31/1.62  % SZS output start Proof for theBenchmark
% 6.31/1.62  Assumptions after simplification:
% 6.31/1.62  ---------------------------------
% 6.31/1.62  
% 6.31/1.62    (d1_tarski)
% 6.52/1.65     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v0) = v1) |
% 6.52/1.65       ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ in(v2, v1)) &  ? [v0: $i] :  ! [v1:
% 6.52/1.65      $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ~ $i(v1) |  ~
% 6.52/1.65      $i(v0) |  ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) |  ~ in(v1, v0)) & (v3 = v1 |
% 6.52/1.65          in(v3, v0)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v0) = v1) | 
% 6.52/1.65      ~ $i(v1) |  ~ $i(v0) | in(v0, v1))
% 6.52/1.65  
% 6.52/1.65    (l1_zfmisc_1)
% 6.52/1.65    $i(empty_set) &  ! [v0: $i] : ( ~ (singleton(v0) = empty_set) |  ~ $i(v0))
% 6.52/1.65  
% 6.52/1.65    (l4_zfmisc_1)
% 6.52/1.65    $i(empty_set) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 | v0 =
% 6.52/1.66      empty_set |  ~ (singleton(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ subset(v0,
% 6.52/1.66        v2)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v1) = v0) |  ~ $i(v1) | 
% 6.52/1.66      ~ $i(v0) | subset(v0, v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v0)
% 6.52/1.66        = v1) |  ~ $i(v0) | subset(empty_set, v1))
% 6.52/1.66  
% 6.52/1.66    (t6_zfmisc_1)
% 6.52/1.66     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v1 = v0) &
% 6.52/1.66      singleton(v1) = v3 & singleton(v0) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0)
% 6.52/1.66      & subset(v2, v3))
% 6.52/1.66  
% 6.52/1.66  Further assumptions not needed in the proof:
% 6.52/1.66  --------------------------------------------
% 6.52/1.66  antisymmetry_r2_hidden, fc1_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 6.52/1.66  reflexivity_r1_tarski
% 6.52/1.66  
% 6.52/1.66  Those formulas are unsatisfiable:
% 6.52/1.66  ---------------------------------
% 6.52/1.66  
% 6.52/1.66  Begin of proof
% 6.52/1.66  | 
% 6.52/1.66  | ALPHA: (d1_tarski) implies:
% 6.52/1.66  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (singleton(v0) = v1) |  ~ $i(v1) |  ~
% 6.52/1.66  |          $i(v0) | in(v0, v1))
% 6.52/1.66  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v0)
% 6.52/1.66  |            = v1) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ in(v2, v1))
% 6.52/1.66  | 
% 6.52/1.66  | ALPHA: (l1_zfmisc_1) implies:
% 6.52/1.66  |   (3)   ! [v0: $i] : ( ~ (singleton(v0) = empty_set) |  ~ $i(v0))
% 6.52/1.66  | 
% 6.52/1.66  | ALPHA: (l4_zfmisc_1) implies:
% 6.52/1.67  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 | v0 = empty_set | 
% 6.52/1.67  |          ~ (singleton(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ subset(v0, v2))
% 6.52/1.67  | 
% 6.52/1.67  | DELTA: instantiating (t6_zfmisc_1) with fresh symbols all_13_0, all_13_1,
% 6.52/1.67  |        all_13_2, all_13_3 gives:
% 6.52/1.67  |   (5)   ~ (all_13_2 = all_13_3) & singleton(all_13_2) = all_13_0 &
% 6.52/1.67  |        singleton(all_13_3) = all_13_1 & $i(all_13_0) & $i(all_13_1) &
% 6.52/1.67  |        $i(all_13_2) & $i(all_13_3) & subset(all_13_1, all_13_0)
% 6.52/1.67  | 
% 6.52/1.67  | ALPHA: (5) implies:
% 6.52/1.67  |   (6)   ~ (all_13_2 = all_13_3)
% 6.52/1.67  |   (7)  subset(all_13_1, all_13_0)
% 6.52/1.67  |   (8)  $i(all_13_3)
% 6.52/1.67  |   (9)  $i(all_13_2)
% 6.52/1.67  |   (10)  $i(all_13_1)
% 6.52/1.67  |   (11)  $i(all_13_0)
% 6.52/1.67  |   (12)  singleton(all_13_3) = all_13_1
% 6.52/1.67  |   (13)  singleton(all_13_2) = all_13_0
% 6.52/1.67  | 
% 6.52/1.67  | GROUND_INST: instantiating (1) with all_13_3, all_13_1, simplifying with (8),
% 6.52/1.67  |              (10), (12) gives:
% 6.52/1.67  |   (14)  in(all_13_3, all_13_1)
% 6.52/1.67  | 
% 6.52/1.67  | GROUND_INST: instantiating (4) with all_13_1, all_13_2, all_13_0, simplifying
% 6.52/1.67  |              with (7), (9), (10), (13) gives:
% 6.52/1.68  |   (15)  all_13_0 = all_13_1 | all_13_1 = empty_set
% 6.52/1.68  | 
% 6.52/1.68  | BETA: splitting (15) gives:
% 6.52/1.68  | 
% 6.52/1.68  | Case 1:
% 6.52/1.68  | | 
% 6.52/1.68  | |   (16)  all_13_1 = empty_set
% 6.52/1.68  | | 
% 6.52/1.68  | | REDUCE: (12), (16) imply:
% 6.52/1.68  | |   (17)  singleton(all_13_3) = empty_set
% 6.52/1.68  | | 
% 6.52/1.68  | | GROUND_INST: instantiating (3) with all_13_3, simplifying with (8), (17)
% 6.52/1.68  | |              gives:
% 6.52/1.68  | |   (18)  $false
% 6.52/1.68  | | 
% 6.52/1.68  | | CLOSE: (18) is inconsistent.
% 6.52/1.68  | | 
% 6.52/1.68  | Case 2:
% 6.52/1.68  | | 
% 6.52/1.68  | |   (19)  all_13_0 = all_13_1
% 6.52/1.68  | | 
% 6.52/1.68  | | REDUCE: (13), (19) imply:
% 6.52/1.68  | |   (20)  singleton(all_13_2) = all_13_1
% 6.52/1.68  | | 
% 6.52/1.68  | | GROUND_INST: instantiating (2) with all_13_2, all_13_1, all_13_3,
% 6.52/1.68  | |              simplifying with (8), (9), (10), (14), (20) gives:
% 6.52/1.68  | |   (21)  all_13_2 = all_13_3
% 6.52/1.68  | | 
% 6.52/1.68  | | REDUCE: (6), (21) imply:
% 6.52/1.68  | |   (22)  $false
% 6.52/1.68  | | 
% 6.52/1.68  | | CLOSE: (22) is inconsistent.
% 6.52/1.68  | | 
% 6.52/1.68  | End of split
% 6.52/1.68  | 
% 6.52/1.68  End of proof
% 6.52/1.68  % SZS output end Proof for theBenchmark
% 6.52/1.68  
% 6.52/1.68  1018ms
%------------------------------------------------------------------------------