TSTP Solution File: SEU094+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU094+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 : n023.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 17:42:30 EDT 2023

% Result   : Theorem 13.42s 2.67s
% Output   : Proof 18.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 23 19:27:27 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.67/0.65  ________       _____
% 0.67/0.65  ___  __ \_________(_)________________________________
% 0.67/0.65  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.67/0.65  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.67/0.65  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.67/0.65  
% 0.67/0.65  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.67/0.65  (2023-06-19)
% 0.67/0.65  
% 0.67/0.65  (c) Philipp Rümmer, 2009-2023
% 0.67/0.65  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.67/0.65                Amanda Stjerna.
% 0.67/0.65  Free software under BSD-3-Clause.
% 0.67/0.65  
% 0.67/0.65  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.67/0.65  
% 0.67/0.65  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67  Running up to 7 provers in parallel.
% 0.67/0.69  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.67/0.69  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.67/0.69  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.67/0.69  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.67/0.69  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.67/0.69  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.67/0.69  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.32/1.20  Prover 1: Preprocessing ...
% 3.32/1.20  Prover 4: Preprocessing ...
% 3.51/1.24  Prover 5: Preprocessing ...
% 3.51/1.24  Prover 3: Preprocessing ...
% 3.51/1.24  Prover 6: Preprocessing ...
% 3.51/1.24  Prover 0: Preprocessing ...
% 3.51/1.24  Prover 2: Preprocessing ...
% 6.82/1.77  Prover 2: Proving ...
% 6.82/1.77  Prover 5: Proving ...
% 7.48/1.81  Prover 1: Warning: ignoring some quantifiers
% 7.61/1.86  Prover 1: Constructing countermodel ...
% 7.61/1.89  Prover 6: Proving ...
% 8.27/1.92  Prover 3: Warning: ignoring some quantifiers
% 8.27/1.93  Prover 3: Constructing countermodel ...
% 8.27/1.97  Prover 4: Warning: ignoring some quantifiers
% 8.85/2.01  Prover 4: Constructing countermodel ...
% 9.68/2.19  Prover 0: Proving ...
% 13.42/2.67  Prover 5: proved (1978ms)
% 13.42/2.67  
% 13.42/2.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.42/2.67  
% 13.42/2.67  Prover 0: stopped
% 13.42/2.67  Prover 6: stopped
% 13.42/2.67  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.42/2.67  Prover 2: stopped
% 13.42/2.69  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.42/2.69  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.42/2.69  Prover 3: stopped
% 14.08/2.70  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.08/2.70  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.08/2.76  Prover 11: Preprocessing ...
% 14.08/2.77  Prover 10: Preprocessing ...
% 14.08/2.78  Prover 7: Preprocessing ...
% 14.88/2.79  Prover 8: Preprocessing ...
% 14.88/2.80  Prover 13: Preprocessing ...
% 15.21/2.88  Prover 10: Warning: ignoring some quantifiers
% 15.21/2.89  Prover 10: Constructing countermodel ...
% 15.21/2.90  Prover 7: Warning: ignoring some quantifiers
% 15.21/2.90  Prover 7: Constructing countermodel ...
% 15.86/2.96  Prover 13: Warning: ignoring some quantifiers
% 15.86/2.98  Prover 13: Constructing countermodel ...
% 16.30/3.00  Prover 8: Warning: ignoring some quantifiers
% 16.30/3.02  Prover 8: Constructing countermodel ...
% 16.92/3.09  Prover 11: Warning: ignoring some quantifiers
% 17.23/3.13  Prover 11: Constructing countermodel ...
% 17.48/3.18  Prover 10: Found proof (size 24)
% 17.48/3.19  Prover 10: proved (510ms)
% 17.48/3.19  Prover 13: stopped
% 17.48/3.19  Prover 7: stopped
% 17.48/3.19  Prover 1: stopped
% 17.48/3.19  Prover 8: stopped
% 17.48/3.19  Prover 11: stopped
% 17.48/3.19  Prover 4: stopped
% 17.48/3.19  
% 17.48/3.19  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.48/3.19  
% 17.48/3.20  % SZS output start Proof for theBenchmark
% 17.48/3.20  Assumptions after simplification:
% 17.48/3.20  ---------------------------------
% 17.48/3.20  
% 17.48/3.20    (l22_finset_1)
% 17.48/3.23     ! [v0: $i] :  ! [v1: $i] : ( ~ (union(v0) = v1) |  ~ $i(v0) |  ~ finite(v0) |
% 17.48/3.23      finite(v1) |  ? [v2: $i] : ($i(v2) & in(v2, v0) &  ~ finite(v2)))
% 18.06/3.23  
% 18.06/3.23    (t100_zfmisc_1)
% 18.06/3.23     ! [v0: $i] :  ! [v1: $i] : ( ~ (union(v0) = v1) |  ~ $i(v0) |  ? [v2: $i] :
% 18.06/3.23      (powerset(v1) = v2 & $i(v2) & subset(v0, v2)))
% 18.06/3.23  
% 18.06/3.23    (t13_finset_1)
% 18.06/3.23     ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ subset(v0, v1) |  ~
% 18.06/3.23      finite(v1) | finite(v0))
% 18.06/3.23  
% 18.06/3.23    (t24_finset_1)
% 18.06/3.23     ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v0) |  ~
% 18.06/3.23      finite(v1) | finite(v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) =
% 18.06/3.23        v1) |  ~ $i(v0) |  ~ finite(v0) | finite(v1))
% 18.06/3.23  
% 18.06/3.23    (t25_finset_1)
% 18.06/3.23     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (union(v0) = v1 & $i(v2) & $i(v1) &
% 18.06/3.23      $i(v0) & ((finite(v1) & ( ~ finite(v0) | (in(v2, v0) &  ~ finite(v2)))) |
% 18.06/3.23        (finite(v0) &  ~ finite(v1) &  ! [v3: $i] : ( ~ $i(v3) |  ~ in(v3, v0) |
% 18.06/3.23            finite(v3)))))
% 18.06/3.23  
% 18.06/3.23    (t92_zfmisc_1)
% 18.06/3.23     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (union(v1) = v2) |  ~ $i(v1) | 
% 18.06/3.23      ~ $i(v0) |  ~ in(v0, v1) | subset(v0, v2))
% 18.06/3.23  
% 18.06/3.23  Further assumptions not needed in the proof:
% 18.06/3.23  --------------------------------------------
% 18.06/3.23  antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 18.06/3.23  cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 18.06/3.23  cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0,
% 18.06/3.23  fc2_ordinal1, fc4_ordinal1, fc4_relat_1, fc8_arytm_3, rc1_arytm_3, rc1_finset_1,
% 18.06/3.23  rc1_funcop_1, rc1_funct_1, rc1_ordinal1, rc1_ordinal2, rc1_relat_1,
% 18.06/3.23  rc1_subset_1, rc1_xboole_0, rc2_arytm_3, rc2_finset_1, rc2_funct_1,
% 18.06/3.23  rc2_ordinal1, rc2_ordinal2, rc2_relat_1, rc2_subset_1, rc2_xboole_0,
% 18.06/3.24  rc3_arytm_3, rc3_finset_1, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1,
% 18.06/3.24  rc4_ordinal1, rc5_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 18.06/3.24  t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 18.06/3.24  
% 18.06/3.24  Those formulas are unsatisfiable:
% 18.06/3.24  ---------------------------------
% 18.06/3.24  
% 18.06/3.24  Begin of proof
% 18.06/3.24  | 
% 18.06/3.24  | ALPHA: (t24_finset_1) implies:
% 18.06/3.24  |   (1)   ! [v0: $i] :  ! [v1: $i] : ( ~ (powerset(v0) = v1) |  ~ $i(v0) |  ~
% 18.06/3.24  |          finite(v0) | finite(v1))
% 18.06/3.24  | 
% 18.06/3.24  | DELTA: instantiating (t25_finset_1) with fresh symbols all_79_0, all_79_1,
% 18.06/3.24  |        all_79_2 gives:
% 18.06/3.24  |   (2)  union(all_79_2) = all_79_1 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2)
% 18.06/3.24  |        & ((finite(all_79_1) & ( ~ finite(all_79_2) | (in(all_79_0, all_79_2) &
% 18.06/3.24  |                 ~ finite(all_79_0)))) | (finite(all_79_2) &  ~
% 18.06/3.24  |            finite(all_79_1) &  ! [v0: $i] : ( ~ $i(v0) |  ~ in(v0, all_79_2) |
% 18.06/3.24  |              finite(v0))))
% 18.06/3.24  | 
% 18.06/3.24  | ALPHA: (2) implies:
% 18.06/3.24  |   (3)  $i(all_79_2)
% 18.06/3.24  |   (4)  $i(all_79_1)
% 18.06/3.24  |   (5)  $i(all_79_0)
% 18.06/3.24  |   (6)  union(all_79_2) = all_79_1
% 18.06/3.24  |   (7)  (finite(all_79_1) & ( ~ finite(all_79_2) | (in(all_79_0, all_79_2) &  ~
% 18.06/3.24  |              finite(all_79_0)))) | (finite(all_79_2) &  ~ finite(all_79_1) & 
% 18.06/3.24  |          ! [v0: $i] : ( ~ $i(v0) |  ~ in(v0, all_79_2) | finite(v0)))
% 18.06/3.24  | 
% 18.06/3.24  | GROUND_INST: instantiating (t100_zfmisc_1) with all_79_2, all_79_1,
% 18.06/3.24  |              simplifying with (3), (6) gives:
% 18.06/3.24  |   (8)   ? [v0: $i] : (powerset(all_79_1) = v0 & $i(v0) & subset(all_79_2, v0))
% 18.06/3.24  | 
% 18.06/3.24  | DELTA: instantiating (8) with fresh symbol all_87_0 gives:
% 18.06/3.24  |   (9)  powerset(all_79_1) = all_87_0 & $i(all_87_0) & subset(all_79_2,
% 18.06/3.24  |          all_87_0)
% 18.06/3.24  | 
% 18.06/3.24  | ALPHA: (9) implies:
% 18.06/3.24  |   (10)  subset(all_79_2, all_87_0)
% 18.06/3.24  |   (11)  $i(all_87_0)
% 18.06/3.24  |   (12)  powerset(all_79_1) = all_87_0
% 18.06/3.25  | 
% 18.06/3.25  | BETA: splitting (7) gives:
% 18.06/3.25  | 
% 18.06/3.25  | Case 1:
% 18.06/3.25  | | 
% 18.06/3.25  | |   (13)  finite(all_79_1) & ( ~ finite(all_79_2) | (in(all_79_0, all_79_2) & 
% 18.06/3.25  | |             ~ finite(all_79_0)))
% 18.06/3.25  | | 
% 18.06/3.25  | | ALPHA: (13) implies:
% 18.06/3.25  | |   (14)  finite(all_79_1)
% 18.06/3.25  | |   (15)   ~ finite(all_79_2) | (in(all_79_0, all_79_2) &  ~ finite(all_79_0))
% 18.06/3.25  | | 
% 18.06/3.25  | | GROUND_INST: instantiating (1) with all_79_1, all_87_0, simplifying with
% 18.06/3.25  | |              (4), (12), (14) gives:
% 18.06/3.25  | |   (16)  finite(all_87_0)
% 18.06/3.25  | | 
% 18.06/3.25  | | GROUND_INST: instantiating (t13_finset_1) with all_79_2, all_87_0,
% 18.06/3.25  | |              simplifying with (3), (10), (11), (16) gives:
% 18.06/3.25  | |   (17)  finite(all_79_2)
% 18.06/3.25  | | 
% 18.06/3.25  | | BETA: splitting (15) gives:
% 18.06/3.25  | | 
% 18.06/3.25  | | Case 1:
% 18.06/3.25  | | | 
% 18.06/3.25  | | |   (18)   ~ finite(all_79_2)
% 18.06/3.25  | | | 
% 18.06/3.25  | | | PRED_UNIFY: (17), (18) imply:
% 18.06/3.25  | | |   (19)  $false
% 18.06/3.25  | | | 
% 18.06/3.25  | | | CLOSE: (19) is inconsistent.
% 18.06/3.25  | | | 
% 18.06/3.25  | | Case 2:
% 18.06/3.25  | | | 
% 18.06/3.25  | | |   (20)  in(all_79_0, all_79_2) &  ~ finite(all_79_0)
% 18.06/3.25  | | | 
% 18.06/3.25  | | | ALPHA: (20) implies:
% 18.06/3.25  | | |   (21)   ~ finite(all_79_0)
% 18.06/3.25  | | |   (22)  in(all_79_0, all_79_2)
% 18.06/3.25  | | | 
% 18.06/3.25  | | | GROUND_INST: instantiating (t92_zfmisc_1) with all_79_0, all_79_2,
% 18.06/3.25  | | |              all_79_1, simplifying with (3), (5), (6), (22) gives:
% 18.06/3.25  | | |   (23)  subset(all_79_0, all_79_1)
% 18.06/3.25  | | | 
% 18.06/3.25  | | | GROUND_INST: instantiating (t13_finset_1) with all_79_0, all_79_1,
% 18.06/3.25  | | |              simplifying with (4), (5), (14), (21), (23) gives:
% 18.06/3.25  | | |   (24)  $false
% 18.06/3.25  | | | 
% 18.06/3.25  | | | CLOSE: (24) is inconsistent.
% 18.06/3.25  | | | 
% 18.06/3.25  | | End of split
% 18.06/3.25  | | 
% 18.06/3.25  | Case 2:
% 18.06/3.25  | | 
% 18.06/3.25  | |   (25)  finite(all_79_2) &  ~ finite(all_79_1) &  ! [v0: $i] : ( ~ $i(v0) | 
% 18.06/3.25  | |           ~ in(v0, all_79_2) | finite(v0))
% 18.06/3.25  | | 
% 18.06/3.25  | | ALPHA: (25) implies:
% 18.06/3.25  | |   (26)   ~ finite(all_79_1)
% 18.06/3.25  | |   (27)  finite(all_79_2)
% 18.06/3.25  | |   (28)   ! [v0: $i] : ( ~ $i(v0) |  ~ in(v0, all_79_2) | finite(v0))
% 18.06/3.25  | | 
% 18.06/3.25  | | GROUND_INST: instantiating (l22_finset_1) with all_79_2, all_79_1,
% 18.06/3.25  | |              simplifying with (3), (6), (26), (27) gives:
% 18.06/3.25  | |   (29)   ? [v0: $i] : ($i(v0) & in(v0, all_79_2) &  ~ finite(v0))
% 18.06/3.25  | | 
% 18.06/3.25  | | DELTA: instantiating (29) with fresh symbol all_131_0 gives:
% 18.06/3.25  | |   (30)  $i(all_131_0) & in(all_131_0, all_79_2) &  ~ finite(all_131_0)
% 18.06/3.25  | | 
% 18.06/3.25  | | ALPHA: (30) implies:
% 18.06/3.25  | |   (31)   ~ finite(all_131_0)
% 18.06/3.25  | |   (32)  in(all_131_0, all_79_2)
% 18.06/3.25  | |   (33)  $i(all_131_0)
% 18.06/3.25  | | 
% 18.06/3.25  | | GROUND_INST: instantiating (28) with all_131_0, simplifying with (31), (32),
% 18.06/3.25  | |              (33) gives:
% 18.06/3.25  | |   (34)  $false
% 18.06/3.25  | | 
% 18.06/3.25  | | CLOSE: (34) is inconsistent.
% 18.06/3.25  | | 
% 18.06/3.25  | End of split
% 18.06/3.25  | 
% 18.06/3.25  End of proof
% 18.06/3.26  % SZS output end Proof for theBenchmark
% 18.06/3.26  
% 18.06/3.26  2601ms
%------------------------------------------------------------------------------