TSTP Solution File: SET917+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET917+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n027.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 15:27:02 EDT 2023

% Result   : Theorem 3.85s 1.39s
% Output   : Proof 5.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET917+1 : 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 : n027.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 : Sat Aug 26 12:36:19 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.67  ________       _____
% 0.21/0.67  ___  __ \_________(_)________________________________
% 0.21/0.67  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.67  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.67  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.67  
% 0.21/0.67  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.67  (2023-06-19)
% 0.21/0.67  
% 0.21/0.67  (c) Philipp Rümmer, 2009-2023
% 0.21/0.67  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.67                Amanda Stjerna.
% 0.21/0.67  Free software under BSD-3-Clause.
% 0.21/0.67  
% 0.21/0.67  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.67  
% 0.21/0.67  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.69  Running up to 7 provers in parallel.
% 0.21/0.70  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.70  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.70  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.70  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.70  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.70  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.70  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.94/1.08  Prover 1: Preprocessing ...
% 1.94/1.08  Prover 4: Preprocessing ...
% 2.51/1.12  Prover 3: Preprocessing ...
% 2.51/1.12  Prover 0: Preprocessing ...
% 2.51/1.12  Prover 5: Preprocessing ...
% 2.51/1.12  Prover 2: Preprocessing ...
% 2.51/1.12  Prover 6: Preprocessing ...
% 3.02/1.25  Prover 1: Warning: ignoring some quantifiers
% 3.02/1.26  Prover 6: Proving ...
% 3.02/1.26  Prover 1: Constructing countermodel ...
% 3.02/1.27  Prover 5: Proving ...
% 3.02/1.27  Prover 3: Warning: ignoring some quantifiers
% 3.02/1.27  Prover 2: Proving ...
% 3.72/1.28  Prover 3: Constructing countermodel ...
% 3.85/1.30  Prover 4: Constructing countermodel ...
% 3.85/1.30  Prover 0: Proving ...
% 3.85/1.39  Prover 3: proved (690ms)
% 3.85/1.39  
% 3.85/1.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.85/1.39  
% 3.85/1.40  Prover 2: stopped
% 3.85/1.40  Prover 0: stopped
% 3.85/1.40  Prover 6: stopped
% 3.85/1.42  Prover 5: stopped
% 3.85/1.44  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.85/1.44  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.85/1.44  Prover 8: Preprocessing ...
% 3.85/1.44  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.85/1.44  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.85/1.44  Prover 10: Preprocessing ...
% 4.75/1.44  Prover 1: Found proof (size 18)
% 4.75/1.44  Prover 11: Preprocessing ...
% 4.75/1.44  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.75/1.44  Prover 7: Preprocessing ...
% 4.75/1.45  Prover 1: proved (754ms)
% 4.75/1.45  Prover 13: Preprocessing ...
% 4.75/1.45  Prover 4: stopped
% 4.92/1.45  Prover 11: stopped
% 4.92/1.46  Prover 10: Warning: ignoring some quantifiers
% 4.92/1.46  Prover 13: stopped
% 4.92/1.47  Prover 10: Constructing countermodel ...
% 4.92/1.47  Prover 7: Warning: ignoring some quantifiers
% 4.92/1.47  Prover 10: stopped
% 4.92/1.47  Prover 7: Constructing countermodel ...
% 4.92/1.47  Prover 7: stopped
% 4.92/1.47  Prover 8: Warning: ignoring some quantifiers
% 4.92/1.48  Prover 8: Constructing countermodel ...
% 4.92/1.49  Prover 8: stopped
% 4.92/1.49  
% 4.92/1.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.49  
% 4.92/1.49  % SZS output start Proof for theBenchmark
% 4.92/1.49  Assumptions after simplification:
% 4.92/1.49  ---------------------------------
% 4.92/1.49  
% 4.92/1.49    (commutativity_k3_xboole_0)
% 4.92/1.52     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 4.92/1.52      |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 4.92/1.52  
% 4.92/1.52    (l28_zfmisc_1)
% 4.92/1.52     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: int] : (v3 = 0 |  ~
% 4.92/1.52      (singleton(v0) = v2) |  ~ (disjoint(v2, v1) = v3) |  ~ $i(v1) |  ~ $i(v0) |
% 4.92/1.52      in(v0, v1) = 0)
% 4.92/1.52  
% 4.92/1.52    (l32_zfmisc_1)
% 4.92/1.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v2 |  ~
% 4.92/1.53      (singleton(v0) = v2) |  ~ (set_intersection2(v1, v2) = v3) |  ~ $i(v1) |  ~
% 4.92/1.53      $i(v0) |  ? [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 4.92/1.53  
% 4.92/1.53    (t58_zfmisc_1)
% 5.38/1.53     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: int] :  ? [v4: $i] : ( ~ (v4
% 5.38/1.53        = v2) &  ~ (v3 = 0) & singleton(v0) = v2 & disjoint(v2, v1) = v3 &
% 5.38/1.53      set_intersection2(v2, v1) = v4 & $i(v4) & $i(v2) & $i(v1) & $i(v0))
% 5.38/1.53  
% 5.38/1.53    (function-axioms)
% 5.38/1.53     ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  !
% 5.38/1.53    [v3: $i] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 5.38/1.53    &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 5.38/1.53      (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  !
% 5.38/1.53    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 5.38/1.53      $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0:
% 5.38/1.53      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] : (v1 = v0 | 
% 5.38/1.53      ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 5.38/1.54    [v2: $i] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 5.38/1.54  
% 5.38/1.54  Further assumptions not needed in the proof:
% 5.38/1.54  --------------------------------------------
% 5.38/1.54  antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0,
% 5.38/1.54  symmetry_r1_xboole_0
% 5.38/1.54  
% 5.38/1.54  Those formulas are unsatisfiable:
% 5.38/1.54  ---------------------------------
% 5.38/1.54  
% 5.38/1.54  Begin of proof
% 5.38/1.54  | 
% 5.38/1.54  | ALPHA: (function-axioms) implies:
% 5.38/1.54  |   (1)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 5.38/1.54  |         ! [v3: $i] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 5.38/1.54  | 
% 5.38/1.54  | DELTA: instantiating (t58_zfmisc_1) with fresh symbols all_14_0, all_14_1,
% 5.38/1.54  |        all_14_2, all_14_3, all_14_4 gives:
% 5.38/1.54  |   (2)   ~ (all_14_0 = all_14_2) &  ~ (all_14_1 = 0) & singleton(all_14_4) =
% 5.38/1.54  |        all_14_2 & disjoint(all_14_2, all_14_3) = all_14_1 &
% 5.38/1.54  |        set_intersection2(all_14_2, all_14_3) = all_14_0 & $i(all_14_0) &
% 5.38/1.54  |        $i(all_14_2) & $i(all_14_3) & $i(all_14_4)
% 5.38/1.54  | 
% 5.38/1.54  | ALPHA: (2) implies:
% 5.38/1.54  |   (3)   ~ (all_14_1 = 0)
% 5.38/1.54  |   (4)   ~ (all_14_0 = all_14_2)
% 5.38/1.54  |   (5)  $i(all_14_4)
% 5.38/1.54  |   (6)  $i(all_14_3)
% 5.38/1.54  |   (7)  $i(all_14_2)
% 5.38/1.54  |   (8)  set_intersection2(all_14_2, all_14_3) = all_14_0
% 5.38/1.54  |   (9)  disjoint(all_14_2, all_14_3) = all_14_1
% 5.38/1.54  |   (10)  singleton(all_14_4) = all_14_2
% 5.38/1.54  | 
% 5.38/1.55  | GROUND_INST: instantiating (commutativity_k3_xboole_0) with all_14_2,
% 5.38/1.55  |              all_14_3, all_14_0, simplifying with (6), (7), (8) gives:
% 5.38/1.55  |   (11)  set_intersection2(all_14_3, all_14_2) = all_14_0 & $i(all_14_0)
% 5.38/1.55  | 
% 5.38/1.55  | ALPHA: (11) implies:
% 5.38/1.55  |   (12)  set_intersection2(all_14_3, all_14_2) = all_14_0
% 5.38/1.55  | 
% 5.38/1.55  | GROUND_INST: instantiating (l28_zfmisc_1) with all_14_4, all_14_3, all_14_2,
% 5.38/1.55  |              all_14_1, simplifying with (5), (6), (9), (10) gives:
% 5.38/1.55  |   (13)  all_14_1 = 0 | in(all_14_4, all_14_3) = 0
% 5.38/1.55  | 
% 5.38/1.55  | BETA: splitting (13) gives:
% 5.38/1.55  | 
% 5.38/1.55  | Case 1:
% 5.38/1.55  | | 
% 5.38/1.55  | |   (14)  in(all_14_4, all_14_3) = 0
% 5.38/1.55  | | 
% 5.38/1.55  | | GROUND_INST: instantiating (l32_zfmisc_1) with all_14_4, all_14_3, all_14_2,
% 5.38/1.55  | |              all_14_0, simplifying with (5), (6), (10), (12) gives:
% 5.38/1.55  | |   (15)  all_14_0 = all_14_2 |  ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4,
% 5.38/1.55  | |             all_14_3) = v0)
% 5.38/1.55  | | 
% 5.38/1.55  | | BETA: splitting (15) gives:
% 5.38/1.55  | | 
% 5.38/1.55  | | Case 1:
% 5.38/1.55  | | | 
% 5.38/1.55  | | |   (16)  all_14_0 = all_14_2
% 5.38/1.55  | | | 
% 5.38/1.55  | | | REDUCE: (4), (16) imply:
% 5.38/1.55  | | |   (17)  $false
% 5.38/1.55  | | | 
% 5.38/1.55  | | | CLOSE: (17) is inconsistent.
% 5.38/1.55  | | | 
% 5.38/1.55  | | Case 2:
% 5.38/1.55  | | | 
% 5.38/1.55  | | |   (18)   ? [v0: int] : ( ~ (v0 = 0) & in(all_14_4, all_14_3) = v0)
% 5.38/1.55  | | | 
% 5.38/1.55  | | | DELTA: instantiating (18) with fresh symbol all_37_0 gives:
% 5.38/1.55  | | |   (19)   ~ (all_37_0 = 0) & in(all_14_4, all_14_3) = all_37_0
% 5.38/1.55  | | | 
% 5.38/1.55  | | | ALPHA: (19) implies:
% 5.38/1.55  | | |   (20)   ~ (all_37_0 = 0)
% 5.38/1.55  | | |   (21)  in(all_14_4, all_14_3) = all_37_0
% 5.38/1.55  | | | 
% 5.38/1.55  | | | GROUND_INST: instantiating (1) with 0, all_37_0, all_14_3, all_14_4,
% 5.38/1.55  | | |              simplifying with (14), (21) gives:
% 5.38/1.55  | | |   (22)  all_37_0 = 0
% 5.38/1.55  | | | 
% 5.38/1.55  | | | REDUCE: (20), (22) imply:
% 5.38/1.55  | | |   (23)  $false
% 5.38/1.55  | | | 
% 5.38/1.55  | | | CLOSE: (23) is inconsistent.
% 5.38/1.55  | | | 
% 5.38/1.55  | | End of split
% 5.38/1.55  | | 
% 5.38/1.55  | Case 2:
% 5.38/1.55  | | 
% 5.38/1.55  | |   (24)  all_14_1 = 0
% 5.38/1.55  | | 
% 5.38/1.55  | | REDUCE: (3), (24) imply:
% 5.38/1.55  | |   (25)  $false
% 5.38/1.55  | | 
% 5.38/1.55  | | CLOSE: (25) is inconsistent.
% 5.38/1.55  | | 
% 5.38/1.55  | End of split
% 5.38/1.55  | 
% 5.38/1.55  End of proof
% 5.38/1.55  % SZS output end Proof for theBenchmark
% 5.38/1.55  
% 5.38/1.55  880ms
%------------------------------------------------------------------------------