TSTP Solution File: SET877+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET877+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 : n017.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 15:26:52 EDT 2023

% Result   : Theorem 4.75s 1.38s
% Output   : Proof 5.66s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n017.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 13:07:56 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.61  ________       _____
% 0.20/0.61  ___  __ \_________(_)________________________________
% 0.20/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61  
% 0.20/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61  (2023-06-19)
% 0.20/0.61  
% 0.20/0.61  (c) Philipp Rümmer, 2009-2023
% 0.20/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61                Amanda Stjerna.
% 0.20/0.61  Free software under BSD-3-Clause.
% 0.20/0.61  
% 0.20/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61  
% 0.20/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62  Running up to 7 provers in parallel.
% 0.20/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.16/1.02  Prover 4: Preprocessing ...
% 2.16/1.02  Prover 1: Preprocessing ...
% 2.55/1.07  Prover 5: Preprocessing ...
% 2.55/1.07  Prover 6: Preprocessing ...
% 2.55/1.07  Prover 3: Preprocessing ...
% 2.55/1.07  Prover 2: Preprocessing ...
% 2.55/1.07  Prover 0: Preprocessing ...
% 3.47/1.21  Prover 1: Warning: ignoring some quantifiers
% 3.47/1.23  Prover 6: Proving ...
% 3.47/1.23  Prover 3: Warning: ignoring some quantifiers
% 3.47/1.23  Prover 0: Proving ...
% 3.47/1.23  Prover 1: Constructing countermodel ...
% 3.47/1.23  Prover 4: Warning: ignoring some quantifiers
% 3.47/1.24  Prover 3: Constructing countermodel ...
% 3.47/1.24  Prover 5: Proving ...
% 3.47/1.24  Prover 4: Constructing countermodel ...
% 3.47/1.28  Prover 2: Proving ...
% 4.75/1.38  Prover 3: proved (748ms)
% 4.75/1.38  
% 4.75/1.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.38  
% 4.75/1.38  Prover 0: stopped
% 4.75/1.38  Prover 6: stopped
% 4.75/1.40  Prover 2: stopped
% 4.75/1.40  Prover 5: stopped
% 4.75/1.40  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.75/1.40  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.75/1.40  Prover 7: Preprocessing ...
% 4.75/1.40  Prover 4: Found proof (size 10)
% 4.75/1.40  Prover 4: proved (768ms)
% 4.75/1.40  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.75/1.40  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.75/1.40  Prover 8: Preprocessing ...
% 4.75/1.40  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.75/1.40  Prover 1: stopped
% 4.75/1.41  Prover 7: stopped
% 4.75/1.42  Prover 11: Preprocessing ...
% 4.75/1.42  Prover 10: Preprocessing ...
% 4.75/1.42  Prover 13: Preprocessing ...
% 4.75/1.43  Prover 10: stopped
% 4.75/1.43  Prover 11: stopped
% 4.75/1.44  Prover 13: stopped
% 4.75/1.45  Prover 8: Warning: ignoring some quantifiers
% 4.75/1.45  Prover 8: Constructing countermodel ...
% 4.75/1.46  Prover 8: stopped
% 4.75/1.46  
% 4.75/1.46  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/1.46  
% 4.75/1.46  % SZS output start Proof for theBenchmark
% 5.37/1.46  Assumptions after simplification:
% 5.37/1.46  ---------------------------------
% 5.37/1.46  
% 5.37/1.46    (commutativity_k3_xboole_0)
% 5.49/1.50     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2)
% 5.49/1.50      |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) &  !
% 5.49/1.50    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | 
% 5.49/1.50      ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2)))
% 5.49/1.50  
% 5.49/1.50    (d1_tarski)
% 5.49/1.50     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v0) = v1) |
% 5.49/1.50       ~ (in(v2, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0)) &  ! [v0: $i] :  !
% 5.49/1.50    [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (in(v0, v1) =
% 5.49/1.50        v2) |  ~ $i(v1) |  ~ $i(v0)) &  ? [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :
% 5.49/1.50    (v2 = v0 |  ~ (singleton(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ?
% 5.49/1.50      [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) |  ~ (v3 = v1)) & (v4 =
% 5.49/1.50          0 | v3 = v1)))
% 5.49/1.50  
% 5.49/1.50    (l30_zfmisc_1)
% 5.49/1.51     ! [v0: $i] :  ! [v1: $i] :  ! [v2: int] : (v2 = 0 |  ~ (in(v1, v0) = v2) |  ~
% 5.49/1.51      $i(v1) |  ~ $i(v0) |  ? [v3: $i] :  ? [v4: $i] : ( ~ (v4 = v3) &
% 5.49/1.51        singleton(v1) = v3 & set_intersection2(v0, v3) = v4 & $i(v4) & $i(v3))) & 
% 5.49/1.51    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (singleton(v1) = v2) |  ~
% 5.49/1.51      (set_intersection2(v0, v2) = v2) |  ~ $i(v1) |  ~ $i(v0) | in(v1, v0) = 0)
% 5.49/1.51  
% 5.49/1.51    (t18_zfmisc_1)
% 5.49/1.51     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (v1 = v0) &
% 5.49/1.51      singleton(v1) = v3 & singleton(v0) = v2 & set_intersection2(v2, v3) = v2 &
% 5.49/1.51      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 5.49/1.51  
% 5.49/1.51  Further assumptions not needed in the proof:
% 5.49/1.51  --------------------------------------------
% 5.49/1.51  antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc1_xboole_0, rc2_xboole_0
% 5.49/1.51  
% 5.49/1.51  Those formulas are unsatisfiable:
% 5.49/1.51  ---------------------------------
% 5.49/1.51  
% 5.49/1.51  Begin of proof
% 5.49/1.51  | 
% 5.49/1.51  | ALPHA: (commutativity_k3_xboole_0) implies:
% 5.49/1.51  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (set_intersection2(v1,
% 5.49/1.51  |              v0) = v2) |  ~ $i(v1) |  ~ $i(v0) | (set_intersection2(v0, v1) =
% 5.49/1.51  |            v2 & $i(v2)))
% 5.49/1.51  | 
% 5.49/1.51  | ALPHA: (d1_tarski) implies:
% 5.49/1.51  |   (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = v0 |  ~ (singleton(v0)
% 5.49/1.51  |            = v1) |  ~ (in(v2, v1) = 0) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0))
% 5.49/1.51  | 
% 5.49/1.51  | ALPHA: (l30_zfmisc_1) implies:
% 5.49/1.52  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (singleton(v1) = v2) |  ~
% 5.49/1.52  |          (set_intersection2(v0, v2) = v2) |  ~ $i(v1) |  ~ $i(v0) | in(v1, v0)
% 5.49/1.52  |          = 0)
% 5.49/1.52  | 
% 5.49/1.52  | DELTA: instantiating (t18_zfmisc_1) with fresh symbols all_12_0, all_12_1,
% 5.49/1.52  |        all_12_2, all_12_3 gives:
% 5.49/1.52  |   (4)   ~ (all_12_2 = all_12_3) & singleton(all_12_2) = all_12_0 &
% 5.49/1.52  |        singleton(all_12_3) = all_12_1 & set_intersection2(all_12_1, all_12_0)
% 5.49/1.52  |        = all_12_1 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & $i(all_12_3)
% 5.49/1.52  | 
% 5.49/1.52  | ALPHA: (4) implies:
% 5.49/1.52  |   (5)   ~ (all_12_2 = all_12_3)
% 5.49/1.52  |   (6)  $i(all_12_3)
% 5.49/1.52  |   (7)  $i(all_12_2)
% 5.49/1.52  |   (8)  $i(all_12_1)
% 5.49/1.52  |   (9)  $i(all_12_0)
% 5.49/1.52  |   (10)  set_intersection2(all_12_1, all_12_0) = all_12_1
% 5.49/1.52  |   (11)  singleton(all_12_3) = all_12_1
% 5.49/1.52  |   (12)  singleton(all_12_2) = all_12_0
% 5.49/1.52  | 
% 5.49/1.52  | GROUND_INST: instantiating (1) with all_12_0, all_12_1, all_12_1, simplifying
% 5.49/1.52  |              with (8), (9), (10) gives:
% 5.49/1.52  |   (13)  set_intersection2(all_12_0, all_12_1) = all_12_1
% 5.49/1.52  | 
% 5.66/1.52  | GROUND_INST: instantiating (3) with all_12_0, all_12_3, all_12_1, simplifying
% 5.66/1.52  |              with (6), (9), (11), (13) gives:
% 5.66/1.52  |   (14)  in(all_12_3, all_12_0) = 0
% 5.66/1.52  | 
% 5.66/1.53  | GROUND_INST: instantiating (2) with all_12_2, all_12_0, all_12_3, simplifying
% 5.66/1.53  |              with (6), (7), (9), (12), (14) gives:
% 5.66/1.53  |   (15)  all_12_2 = all_12_3
% 5.66/1.53  | 
% 5.66/1.53  | REDUCE: (5), (15) imply:
% 5.66/1.53  |   (16)  $false
% 5.66/1.53  | 
% 5.66/1.53  | CLOSE: (16) is inconsistent.
% 5.66/1.53  | 
% 5.66/1.53  End of proof
% 5.66/1.53  % SZS output end Proof for theBenchmark
% 5.66/1.53  
% 5.66/1.53  917ms
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