TSTP Solution File: SEU096+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : SEU096+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 : n008.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 15.26s 2.85s
% Output   : Proof 17.12s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34  % Computer : n008.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
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 18:07:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.59  ________       _____
% 0.21/0.59  ___  __ \_________(_)________________________________
% 0.21/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.59  
% 0.21/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.59  (2023-06-19)
% 0.21/0.59  
% 0.21/0.59  (c) Philipp Rümmer, 2009-2023
% 0.21/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.59                Amanda Stjerna.
% 0.21/0.59  Free software under BSD-3-Clause.
% 0.21/0.59  
% 0.21/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.59  
% 0.21/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.61  Running up to 7 provers in parallel.
% 0.21/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.39/1.17  Prover 1: Preprocessing ...
% 3.39/1.17  Prover 4: Preprocessing ...
% 3.39/1.21  Prover 0: Preprocessing ...
% 3.39/1.21  Prover 2: Preprocessing ...
% 3.39/1.21  Prover 6: Preprocessing ...
% 3.39/1.21  Prover 3: Preprocessing ...
% 3.39/1.21  Prover 5: Preprocessing ...
% 6.82/1.67  Prover 2: Proving ...
% 6.82/1.68  Prover 5: Proving ...
% 7.01/1.72  Prover 1: Warning: ignoring some quantifiers
% 7.41/1.76  Prover 1: Constructing countermodel ...
% 7.41/1.79  Prover 3: Warning: ignoring some quantifiers
% 7.96/1.82  Prover 3: Constructing countermodel ...
% 7.96/1.84  Prover 6: Proving ...
% 8.39/1.95  Prover 4: Warning: ignoring some quantifiers
% 9.23/1.99  Prover 4: Constructing countermodel ...
% 9.23/2.02  Prover 0: Proving ...
% 12.43/2.42  Prover 3: gave up
% 12.43/2.43  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.95/2.49  Prover 7: Preprocessing ...
% 13.93/2.61  Prover 7: Warning: ignoring some quantifiers
% 13.93/2.62  Prover 7: Constructing countermodel ...
% 15.26/2.85  Prover 2: proved (2233ms)
% 15.26/2.85  
% 15.26/2.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.26/2.85  
% 15.26/2.85  Prover 5: stopped
% 15.26/2.85  Prover 6: stopped
% 15.82/2.86  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.82/2.86  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.82/2.86  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.82/2.86  Prover 0: stopped
% 15.82/2.87  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.82/2.95  Prover 11: Preprocessing ...
% 15.82/2.95  Prover 8: Preprocessing ...
% 15.82/2.96  Prover 13: Preprocessing ...
% 15.82/2.96  Prover 10: Preprocessing ...
% 15.82/2.96  Prover 7: Found proof (size 14)
% 15.82/2.96  Prover 7: proved (533ms)
% 15.82/2.96  Prover 1: stopped
% 15.82/2.96  Prover 4: stopped
% 15.82/2.98  Prover 10: stopped
% 15.82/3.00  Prover 13: stopped
% 15.82/3.01  Prover 11: stopped
% 16.28/3.04  Prover 8: Warning: ignoring some quantifiers
% 17.03/3.05  Prover 8: Constructing countermodel ...
% 17.03/3.06  Prover 8: stopped
% 17.03/3.06  
% 17.03/3.06  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.03/3.06  
% 17.03/3.06  % SZS output start Proof for theBenchmark
% 17.12/3.07  Assumptions after simplification:
% 17.12/3.07  ---------------------------------
% 17.12/3.07  
% 17.12/3.07    (t147_funct_1)
% 17.12/3.09     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (relation_inverse_image(v1, v0)
% 17.12/3.09        = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ relation(v1) |  ~ function(v1) |  ?
% 17.12/3.09      [v3: $i] :  ? [v4: $i] : ((v4 = v0 & relation_image(v1, v2) = v0) |
% 17.12/3.09        (relation_rng(v1) = v3 & $i(v3) &  ~ subset(v0, v3))))
% 17.12/3.09  
% 17.12/3.09    (t17_finset_1)
% 17.12/3.09     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (relation_image(v1, v0) = v2) | 
% 17.12/3.09      ~ $i(v1) |  ~ $i(v0) |  ~ relation(v1) |  ~ function(v1) |  ~ finite(v0) |
% 17.12/3.09      finite(v2))
% 17.12/3.09  
% 17.12/3.09    (t27_finset_1)
% 17.12/3.09     ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :
% 17.12/3.09    (relation_inverse_image(v1, v0) = v3 & relation_rng(v1) = v2 & $i(v3) & $i(v2)
% 17.12/3.09      & $i(v1) & $i(v0) & subset(v0, v2) & relation(v1) & function(v1) &
% 17.12/3.09      finite(v3) &  ~ finite(v0))
% 17.12/3.09  
% 17.12/3.09    (function-axioms)
% 17.12/3.10     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 17.12/3.10      (relation_inverse_image(v3, v2) = v1) |  ~ (relation_inverse_image(v3, v2) =
% 17.12/3.10        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 17.12/3.10      ~ (relation_image(v3, v2) = v1) |  ~ (relation_image(v3, v2) = v0)) &  !
% 17.12/3.10    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (relation_rng(v2) = v1) |
% 17.12/3.10       ~ (relation_rng(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1
% 17.12/3.10      = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 17.12/3.10  
% 17.12/3.10  Further assumptions not needed in the proof:
% 17.12/3.10  --------------------------------------------
% 17.12/3.10  antisymmetry_r2_hidden, cc1_arytm_3, cc1_finset_1, cc1_funct_1, cc1_ordinal1,
% 17.12/3.10  cc1_relat_1, cc2_arytm_3, cc2_finset_1, cc2_funct_1, cc2_ordinal1, cc3_ordinal1,
% 17.12/3.10  cc4_arytm_3, existence_m1_subset_1, fc12_relat_1, fc13_finset_1, fc1_subset_1,
% 17.12/3.10  fc1_xboole_0, fc2_ordinal1, fc4_relat_1, fc6_funct_1, fc6_relat_1, fc8_arytm_3,
% 17.12/3.10  fc8_relat_1, rc1_arytm_3, rc1_finset_1, rc1_funcop_1, rc1_funct_1, rc1_ordinal1,
% 17.12/3.10  rc1_ordinal2, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_arytm_3,
% 17.12/3.10  rc2_finset_1, rc2_funct_1, rc2_ordinal1, rc2_ordinal2, rc2_relat_1,
% 17.12/3.10  rc2_subset_1, rc2_xboole_0, rc3_arytm_3, rc3_finset_1, rc3_funct_1,
% 17.12/3.10  rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, rc5_funct_1,
% 17.12/3.10  reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 17.12/3.10  t6_boole, t7_boole, t8_boole
% 17.12/3.10  
% 17.12/3.10  Those formulas are unsatisfiable:
% 17.12/3.10  ---------------------------------
% 17.12/3.10  
% 17.12/3.10  Begin of proof
% 17.12/3.10  | 
% 17.12/3.10  | ALPHA: (function-axioms) implies:
% 17.12/3.10  |   (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 17.12/3.10  |          (relation_rng(v2) = v1) |  ~ (relation_rng(v2) = v0))
% 17.12/3.10  | 
% 17.12/3.10  | DELTA: instantiating (t27_finset_1) with fresh symbols all_79_0, all_79_1,
% 17.12/3.10  |        all_79_2, all_79_3 gives:
% 17.12/3.10  |   (2)  relation_inverse_image(all_79_2, all_79_3) = all_79_0 &
% 17.12/3.10  |        relation_rng(all_79_2) = all_79_1 & $i(all_79_0) & $i(all_79_1) &
% 17.12/3.10  |        $i(all_79_2) & $i(all_79_3) & subset(all_79_3, all_79_1) &
% 17.12/3.10  |        relation(all_79_2) & function(all_79_2) & finite(all_79_0) &  ~
% 17.12/3.10  |        finite(all_79_3)
% 17.12/3.10  | 
% 17.12/3.10  | ALPHA: (2) implies:
% 17.12/3.10  |   (3)   ~ finite(all_79_3)
% 17.12/3.10  |   (4)  finite(all_79_0)
% 17.12/3.10  |   (5)  function(all_79_2)
% 17.12/3.10  |   (6)  relation(all_79_2)
% 17.12/3.10  |   (7)  subset(all_79_3, all_79_1)
% 17.12/3.10  |   (8)  $i(all_79_3)
% 17.12/3.10  |   (9)  $i(all_79_2)
% 17.12/3.10  |   (10)  $i(all_79_0)
% 17.12/3.10  |   (11)  relation_rng(all_79_2) = all_79_1
% 17.12/3.10  |   (12)  relation_inverse_image(all_79_2, all_79_3) = all_79_0
% 17.12/3.10  | 
% 17.12/3.10  | GROUND_INST: instantiating (t147_funct_1) with all_79_3, all_79_2, all_79_0,
% 17.12/3.10  |              simplifying with (5), (6), (8), (9), (12) gives:
% 17.12/3.10  |   (13)   ? [v0: $i] :  ? [v1: int] : ((v1 = all_79_3 &
% 17.12/3.10  |             relation_image(all_79_2, all_79_0) = all_79_3) |
% 17.12/3.10  |           (relation_rng(all_79_2) = v0 & $i(v0) &  ~ subset(all_79_3, v0)))
% 17.12/3.10  | 
% 17.12/3.10  | DELTA: instantiating (13) with fresh symbols all_91_0, all_91_1 gives:
% 17.12/3.10  |   (14)  (all_91_0 = all_79_3 & relation_image(all_79_2, all_79_0) = all_79_3)
% 17.12/3.10  |         | (relation_rng(all_79_2) = all_91_1 & $i(all_91_1) &  ~
% 17.12/3.10  |           subset(all_79_3, all_91_1))
% 17.12/3.10  | 
% 17.12/3.10  | BETA: splitting (14) gives:
% 17.12/3.10  | 
% 17.12/3.10  | Case 1:
% 17.12/3.10  | | 
% 17.12/3.10  | |   (15)  all_91_0 = all_79_3 & relation_image(all_79_2, all_79_0) = all_79_3
% 17.12/3.10  | | 
% 17.12/3.10  | | ALPHA: (15) implies:
% 17.12/3.11  | |   (16)  relation_image(all_79_2, all_79_0) = all_79_3
% 17.12/3.11  | | 
% 17.12/3.11  | | GROUND_INST: instantiating (t17_finset_1) with all_79_0, all_79_2, all_79_3,
% 17.12/3.11  | |              simplifying with (3), (4), (5), (6), (9), (10), (16) gives:
% 17.12/3.11  | |   (17)  $false
% 17.12/3.11  | | 
% 17.12/3.11  | | CLOSE: (17) is inconsistent.
% 17.12/3.11  | | 
% 17.12/3.11  | Case 2:
% 17.12/3.11  | | 
% 17.12/3.11  | |   (18)  relation_rng(all_79_2) = all_91_1 & $i(all_91_1) &  ~
% 17.12/3.11  | |         subset(all_79_3, all_91_1)
% 17.12/3.11  | | 
% 17.12/3.11  | | ALPHA: (18) implies:
% 17.12/3.11  | |   (19)   ~ subset(all_79_3, all_91_1)
% 17.12/3.11  | |   (20)  relation_rng(all_79_2) = all_91_1
% 17.12/3.11  | | 
% 17.12/3.11  | | GROUND_INST: instantiating (1) with all_79_1, all_91_1, all_79_2,
% 17.12/3.11  | |              simplifying with (11), (20) gives:
% 17.12/3.11  | |   (21)  all_91_1 = all_79_1
% 17.12/3.11  | | 
% 17.12/3.11  | | PRED_UNIFY: (7), (19) imply:
% 17.12/3.11  | |   (22)   ~ (all_91_1 = all_79_1)
% 17.12/3.11  | | 
% 17.12/3.11  | | REDUCE: (21), (22) imply:
% 17.12/3.11  | |   (23)  $false
% 17.12/3.11  | | 
% 17.12/3.11  | | CLOSE: (23) is inconsistent.
% 17.12/3.11  | | 
% 17.12/3.11  | End of split
% 17.12/3.11  | 
% 17.12/3.11  End of proof
% 17.12/3.11  % SZS output end Proof for theBenchmark
% 17.12/3.11  
% 17.12/3.11  2514ms
%------------------------------------------------------------------------------