TSTP Solution File: SET991+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SET991+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 : n016.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 15:27:18 EDT 2023

% Result   : Theorem 7.76s 1.87s
% Output   : Proof 12.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET991+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34  % Computer : n016.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 16:00:57 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.18/0.61  ________       _____
% 0.18/0.61  ___  __ \_________(_)________________________________
% 0.18/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.61  
% 0.18/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.61  (2023-06-19)
% 0.18/0.61  
% 0.18/0.61  (c) Philipp Rümmer, 2009-2023
% 0.18/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.61                Amanda Stjerna.
% 0.18/0.61  Free software under BSD-3-Clause.
% 0.18/0.61  
% 0.18/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.61  
% 0.18/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.62  Running up to 7 provers in parallel.
% 0.18/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.45/1.07  Prover 4: Preprocessing ...
% 2.45/1.07  Prover 1: Preprocessing ...
% 2.45/1.11  Prover 2: Preprocessing ...
% 2.45/1.11  Prover 6: Preprocessing ...
% 2.45/1.11  Prover 5: Preprocessing ...
% 2.45/1.11  Prover 0: Preprocessing ...
% 2.45/1.12  Prover 3: Preprocessing ...
% 5.62/1.54  Prover 1: Warning: ignoring some quantifiers
% 5.62/1.55  Prover 3: Warning: ignoring some quantifiers
% 5.62/1.57  Prover 6: Proving ...
% 5.62/1.57  Prover 1: Constructing countermodel ...
% 5.62/1.58  Prover 3: Constructing countermodel ...
% 5.62/1.58  Prover 2: Proving ...
% 5.62/1.58  Prover 5: Proving ...
% 6.97/1.69  Prover 4: Warning: ignoring some quantifiers
% 7.08/1.74  Prover 0: Proving ...
% 7.08/1.77  Prover 4: Constructing countermodel ...
% 7.76/1.87  Prover 3: proved (1233ms)
% 7.76/1.87  
% 7.76/1.87  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.76/1.87  
% 7.76/1.87  Prover 0: stopped
% 7.76/1.87  Prover 6: stopped
% 7.76/1.87  Prover 5: stopped
% 7.76/1.88  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.76/1.88  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.76/1.88  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.76/1.88  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.76/1.88  Prover 2: stopped
% 8.37/1.91  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.37/1.93  Prover 10: Preprocessing ...
% 8.37/1.95  Prover 8: Preprocessing ...
% 8.37/1.99  Prover 7: Preprocessing ...
% 8.98/1.99  Prover 13: Preprocessing ...
% 8.98/1.99  Prover 11: Preprocessing ...
% 9.00/2.14  Prover 7: Warning: ignoring some quantifiers
% 9.00/2.14  Prover 10: Warning: ignoring some quantifiers
% 9.00/2.15  Prover 10: Constructing countermodel ...
% 9.15/2.16  Prover 7: Constructing countermodel ...
% 10.05/2.19  Prover 8: Warning: ignoring some quantifiers
% 10.05/2.21  Prover 8: Constructing countermodel ...
% 10.05/2.22  Prover 13: Warning: ignoring some quantifiers
% 10.05/2.25  Prover 13: Constructing countermodel ...
% 11.48/2.36  Prover 10: Found proof (size 12)
% 11.48/2.36  Prover 10: proved (482ms)
% 11.48/2.36  Prover 8: stopped
% 11.48/2.36  Prover 1: stopped
% 11.48/2.36  Prover 13: stopped
% 11.48/2.36  Prover 7: stopped
% 11.48/2.36  Prover 4: stopped
% 11.79/2.41  Prover 11: Warning: ignoring some quantifiers
% 11.79/2.42  Prover 11: Constructing countermodel ...
% 11.79/2.43  Prover 11: stopped
% 11.79/2.43  
% 11.79/2.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.79/2.43  
% 11.79/2.43  % SZS output start Proof for theBenchmark
% 11.79/2.44  Assumptions after simplification:
% 11.79/2.44  ---------------------------------
% 11.79/2.44  
% 11.79/2.44    (d5_funct_1)
% 12.07/2.47     ! [v0: $i] :  ! [v1: $i] : ( ~ (relation_rng(v0) = v1) |  ~ $i(v0) |  ~
% 12.07/2.47      function(v0) |  ~ relation(v0) |  ? [v2: $i] : (relation_dom(v0) = v2 &
% 12.07/2.47        $i(v2) &  ! [v3: $i] :  ! [v4: $i] : ( ~ (apply(v0, v4) = v3) |  ~ $i(v4)
% 12.07/2.47          |  ~ $i(v3) |  ~ $i(v1) |  ~ in(v4, v2) | in(v3, v1)) &  ! [v3: $i] : (
% 12.07/2.47          ~ $i(v3) |  ~ $i(v1) |  ~ in(v3, v1) |  ? [v4: $i] : (apply(v0, v4) = v3
% 12.07/2.47            & $i(v4) & in(v4, v2))) &  ? [v3: $i] : (v3 = v1 |  ~ $i(v3) |  ? [v4:
% 12.07/2.47            $i] :  ? [v5: $i] :  ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) | 
% 12.07/2.47              ! [v7: $i] : ( ~ (apply(v0, v7) = v4) |  ~ $i(v7) |  ~ in(v7, v2)))
% 12.07/2.47            & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 12.07/2.47  
% 12.07/2.47    (t12_funct_1)
% 12.07/2.47     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] :
% 12.07/2.47    (apply(v1, v0) = v3 & relation_rng(v1) = v4 & relation_dom(v1) = v2 & $i(v4) &
% 12.07/2.47      $i(v3) & $i(v2) & $i(v1) & $i(v0) & in(v0, v2) & function(v1) & relation(v1)
% 12.07/2.47      &  ~ in(v3, v4))
% 12.07/2.47  
% 12.07/2.47    (function-axioms)
% 12.07/2.47     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.07/2.47      (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i]
% 12.07/2.47    :  ! [v2: $i] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |  ~ (relation_rng(v2) =
% 12.07/2.47        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 12.07/2.47      (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0)) &  ! [v0: $i] :  !
% 12.07/2.47    [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2)
% 12.07/2.47        = v0))
% 12.07/2.47  
% 12.07/2.47  Further assumptions not needed in the proof:
% 12.07/2.47  --------------------------------------------
% 12.07/2.47  antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, existence_m1_subset_1,
% 12.07/2.47  fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc5_relat_1, fc6_relat_1,
% 12.07/2.47  fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 12.07/2.47  rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski,
% 12.07/2.47  t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 12.07/2.47  t8_boole
% 12.07/2.47  
% 12.07/2.47  Those formulas are unsatisfiable:
% 12.07/2.47  ---------------------------------
% 12.07/2.47  
% 12.07/2.47  Begin of proof
% 12.07/2.48  | 
% 12.07/2.48  | ALPHA: (function-axioms) implies:
% 12.07/2.48  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 12.07/2.48  |          (relation_dom(v2) = v1) |  ~ (relation_dom(v2) = v0))
% 12.07/2.48  | 
% 12.07/2.48  | DELTA: instantiating (t12_funct_1) with fresh symbols all_37_0, all_37_1,
% 12.07/2.48  |        all_37_2, all_37_3, all_37_4 gives:
% 12.07/2.48  |   (2)  apply(all_37_3, all_37_4) = all_37_1 & relation_rng(all_37_3) =
% 12.07/2.48  |        all_37_0 & relation_dom(all_37_3) = all_37_2 & $i(all_37_0) &
% 12.07/2.48  |        $i(all_37_1) & $i(all_37_2) & $i(all_37_3) & $i(all_37_4) &
% 12.07/2.48  |        in(all_37_4, all_37_2) & function(all_37_3) & relation(all_37_3) &  ~
% 12.07/2.48  |        in(all_37_1, all_37_0)
% 12.07/2.48  | 
% 12.07/2.48  | ALPHA: (2) implies:
% 12.07/2.48  |   (3)   ~ in(all_37_1, all_37_0)
% 12.07/2.48  |   (4)  relation(all_37_3)
% 12.07/2.48  |   (5)  function(all_37_3)
% 12.07/2.48  |   (6)  in(all_37_4, all_37_2)
% 12.07/2.48  |   (7)  $i(all_37_4)
% 12.07/2.48  |   (8)  $i(all_37_3)
% 12.07/2.48  |   (9)  $i(all_37_1)
% 12.07/2.48  |   (10)  $i(all_37_0)
% 12.07/2.48  |   (11)  relation_dom(all_37_3) = all_37_2
% 12.07/2.48  |   (12)  relation_rng(all_37_3) = all_37_0
% 12.07/2.48  |   (13)  apply(all_37_3, all_37_4) = all_37_1
% 12.07/2.48  | 
% 12.07/2.48  | GROUND_INST: instantiating (d5_funct_1) with all_37_3, all_37_0, simplifying
% 12.07/2.48  |              with (4), (5), (8), (12) gives:
% 12.07/2.49  |   (14)   ? [v0: $i] : (relation_dom(all_37_3) = v0 & $i(v0) &  ! [v1: $i] :  !
% 12.07/2.49  |           [v2: $i] : ( ~ (apply(all_37_3, v2) = v1) |  ~ $i(v2) |  ~ $i(v1) | 
% 12.07/2.49  |             ~ $i(all_37_0) |  ~ in(v2, v0) | in(v1, all_37_0)) &  ! [v1: $i] :
% 12.07/2.49  |           ( ~ $i(v1) |  ~ $i(all_37_0) |  ~ in(v1, all_37_0) |  ? [v2: $i] :
% 12.07/2.49  |             (apply(all_37_3, v2) = v1 & $i(v2) & in(v2, v0))) &  ? [v1: any] :
% 12.07/2.49  |           (v1 = all_37_0 |  ~ $i(v1) |  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i]
% 12.07/2.49  |             : ($i(v3) & $i(v2) & ( ~ in(v2, v1) |  ! [v5: $i] : ( ~
% 12.07/2.49  |                   (apply(all_37_3, v5) = v2) |  ~ $i(v5) |  ~ in(v5, v0))) &
% 12.07/2.49  |               (in(v2, v1) | (v4 = v2 & apply(all_37_3, v3) = v2 & in(v3,
% 12.07/2.49  |                     v0))))))
% 12.07/2.49  | 
% 12.07/2.49  | DELTA: instantiating (14) with fresh symbol all_45_0 gives:
% 12.07/2.49  |   (15)  relation_dom(all_37_3) = all_45_0 & $i(all_45_0) &  ! [v0: $i] :  !
% 12.07/2.49  |         [v1: $i] : ( ~ (apply(all_37_3, v1) = v0) |  ~ $i(v1) |  ~ $i(v0) |  ~
% 12.07/2.49  |           $i(all_37_0) |  ~ in(v1, all_45_0) | in(v0, all_37_0)) &  ! [v0: $i]
% 12.07/2.49  |         : ( ~ $i(v0) |  ~ $i(all_37_0) |  ~ in(v0, all_37_0) |  ? [v1: $i] :
% 12.07/2.49  |           (apply(all_37_3, v1) = v0 & $i(v1) & in(v1, all_45_0))) &  ? [v0:
% 12.07/2.49  |           any] : (v0 = all_37_0 |  ~ $i(v0) |  ? [v1: $i] :  ? [v2: $i] :  ?
% 12.07/2.49  |           [v3: $i] : ($i(v2) & $i(v1) & ( ~ in(v1, v0) |  ! [v4: $i] : ( ~
% 12.07/2.49  |                 (apply(all_37_3, v4) = v1) |  ~ $i(v4) |  ~ in(v4, all_45_0)))
% 12.07/2.49  |             & (in(v1, v0) | (v3 = v1 & apply(all_37_3, v2) = v1 & in(v2,
% 12.07/2.49  |                   all_45_0)))))
% 12.07/2.49  | 
% 12.07/2.49  | ALPHA: (15) implies:
% 12.07/2.49  |   (16)  relation_dom(all_37_3) = all_45_0
% 12.07/2.49  |   (17)   ! [v0: $i] :  ! [v1: $i] : ( ~ (apply(all_37_3, v1) = v0) |  ~ $i(v1)
% 12.07/2.49  |           |  ~ $i(v0) |  ~ $i(all_37_0) |  ~ in(v1, all_45_0) | in(v0,
% 12.07/2.49  |             all_37_0))
% 12.07/2.49  | 
% 12.07/2.49  | GROUND_INST: instantiating (1) with all_37_2, all_45_0, all_37_3, simplifying
% 12.07/2.49  |              with (11), (16) gives:
% 12.07/2.49  |   (18)  all_45_0 = all_37_2
% 12.07/2.49  | 
% 12.07/2.49  | GROUND_INST: instantiating (17) with all_37_1, all_37_4, simplifying with (3),
% 12.07/2.49  |              (7), (9), (10), (13) gives:
% 12.07/2.49  |   (19)   ~ in(all_37_4, all_45_0)
% 12.07/2.49  | 
% 12.07/2.49  | REDUCE: (18), (19) imply:
% 12.07/2.49  |   (20)   ~ in(all_37_4, all_37_2)
% 12.07/2.49  | 
% 12.07/2.49  | PRED_UNIFY: (6), (20) imply:
% 12.07/2.49  |   (21)  $false
% 12.07/2.49  | 
% 12.07/2.49  | CLOSE: (21) is inconsistent.
% 12.07/2.49  | 
% 12.07/2.49  End of proof
% 12.07/2.49  % SZS output end Proof for theBenchmark
% 12.07/2.49  
% 12.07/2.49  1882ms
%------------------------------------------------------------------------------