TSTP Solution File: SEU382+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n018.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 17:44:24 EDT 2023
% Result : Theorem 57.38s 8.38s
% Output : Proof 62.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n018.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 : Wed Aug 23 12:54:26 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 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 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 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 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 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
% 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
% 4.25/1.35 Prover 1: Preprocessing ...
% 4.25/1.35 Prover 4: Preprocessing ...
% 4.25/1.39 Prover 3: Preprocessing ...
% 4.25/1.39 Prover 5: Preprocessing ...
% 4.25/1.39 Prover 2: Preprocessing ...
% 4.25/1.39 Prover 0: Preprocessing ...
% 4.25/1.41 Prover 6: Preprocessing ...
% 10.03/2.18 Prover 1: Warning: ignoring some quantifiers
% 10.76/2.21 Prover 5: Proving ...
% 10.76/2.26 Prover 1: Constructing countermodel ...
% 10.76/2.29 Prover 2: Proving ...
% 10.76/2.30 Prover 6: Proving ...
% 10.76/2.33 Prover 3: Warning: ignoring some quantifiers
% 10.76/2.40 Prover 3: Constructing countermodel ...
% 13.34/2.65 Prover 4: Warning: ignoring some quantifiers
% 14.31/2.71 Prover 4: Constructing countermodel ...
% 17.09/3.12 Prover 0: Proving ...
% 57.38/8.38 Prover 0: proved (7680ms)
% 57.38/8.38
% 57.38/8.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.38/8.38
% 57.38/8.38 Prover 3: stopped
% 57.38/8.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 57.38/8.38 Prover 6: stopped
% 57.38/8.40 Prover 5: stopped
% 57.38/8.41 Prover 2: stopped
% 57.38/8.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 57.38/8.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 57.38/8.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 57.38/8.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 58.44/8.54 Prover 10: Preprocessing ...
% 58.44/8.56 Prover 7: Preprocessing ...
% 59.10/8.58 Prover 8: Preprocessing ...
% 59.10/8.59 Prover 11: Preprocessing ...
% 59.26/8.60 Prover 13: Preprocessing ...
% 59.45/8.65 Prover 7: Warning: ignoring some quantifiers
% 59.45/8.66 Prover 10: Warning: ignoring some quantifiers
% 59.45/8.67 Prover 7: Constructing countermodel ...
% 59.45/8.69 Prover 10: Constructing countermodel ...
% 60.07/8.77 Prover 13: Warning: ignoring some quantifiers
% 60.67/8.80 Prover 13: Constructing countermodel ...
% 60.67/8.85 Prover 8: Warning: ignoring some quantifiers
% 60.67/8.86 Prover 8: Constructing countermodel ...
% 61.73/8.99 Prover 7: Found proof (size 50)
% 61.73/8.99 Prover 7: proved (606ms)
% 61.73/8.99 Prover 13: stopped
% 61.73/8.99 Prover 8: stopped
% 61.73/8.99 Prover 10: stopped
% 61.73/9.00 Prover 4: stopped
% 61.73/9.00 Prover 11: Warning: ignoring some quantifiers
% 61.73/9.00 Prover 1: stopped
% 61.73/9.01 Prover 11: Constructing countermodel ...
% 61.73/9.03 Prover 11: stopped
% 61.73/9.03
% 61.73/9.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.73/9.03
% 61.73/9.03 % SZS output start Proof for theBenchmark
% 61.73/9.04 Assumptions after simplification:
% 61.73/9.04 ---------------------------------
% 61.73/9.04
% 61.73/9.04 (abstractness_v1_orders_2)
% 61.73/9.07 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ~
% 61.73/9.07 strict_rel_str(v0) | ~ rel_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 &
% 61.73/9.07 rel_str_of(v2, v1) = v0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 61.73/9.07 (the_carrier(v0) = v1) | ~ $i(v0) | ~ strict_rel_str(v0) | ~ rel_str(v0)
% 61.73/9.07 | ? [v2: $i] : (the_InternalRel(v0) = v2 & rel_str_of(v1, v2) = v0 &
% 61.73/9.07 $i(v2)))
% 61.73/9.07
% 61.73/9.07 (d1_yellow_1)
% 61.73/9.07 ! [v0: $i] : ! [v1: $i] : ( ~ (incl_POSet(v0) = v1) | ~ $i(v0) | ? [v2:
% 61.73/9.07 $i] : (inclusion_order(v0) = v2 & rel_str_of(v0, v2) = v1 & $i(v2) &
% 61.73/9.07 $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ (inclusion_order(v0) = v1) | ~
% 61.73/9.07 $i(v0) | ? [v2: $i] : (incl_POSet(v0) = v2 & rel_str_of(v0, v1) = v2 &
% 61.73/9.07 $i(v2)))
% 61.73/9.07
% 61.73/9.07 (dt_k3_yellow_1)
% 61.73/9.07 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.07 strict_rel_str(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1)
% 61.73/9.07 | ~ $i(v0) | rel_str(v1))
% 61.73/9.07
% 61.73/9.07 (dt_u1_orders_2)
% 61.73/9.07 ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0) | ~
% 61.73/9.07 rel_str(v0) | ? [v2: $i] : (the_carrier(v0) = v2 & $i(v2) &
% 61.73/9.07 relation_of2_as_subset(v1, v2, v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 61.73/9.07 (the_carrier(v0) = v1) | ~ $i(v0) | ~ rel_str(v0) | ? [v2: $i] :
% 61.73/9.07 (the_InternalRel(v0) = v2 & $i(v2) & relation_of2_as_subset(v2, v1, v1)))
% 61.73/9.07
% 61.73/9.07 (fc9_waybel_1)
% 61.73/9.08 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | ~
% 61.73/9.08 empty_carrier(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1)
% 61.73/9.08 | ~ $i(v0) | complemented_relstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 61.73/9.08 (boole_POSet(v0) = v1) | ~ $i(v0) | bounded_relstr(v1)) & ! [v0: $i] : !
% 61.73/9.08 [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | lower_bounded_relstr(v1))
% 61.73/9.08 & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.08 distributive_relstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0)
% 61.73/9.08 = v1) | ~ $i(v0) | upper_bounded_relstr(v1)) & ! [v0: $i] : ! [v1: $i]
% 61.73/9.08 : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | with_infima_relstr(v1)) & ! [v0:
% 61.73/9.08 $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.08 with_suprema_relstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0)
% 61.73/9.08 = v1) | ~ $i(v0) | antisymmetric_relstr(v1)) & ! [v0: $i] : ! [v1: $i]
% 61.73/9.08 : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | transitive_relstr(v1)) & ! [v0:
% 61.73/9.08 $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.08 join_complete_relstr(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0)
% 61.73/9.08 = v1) | ~ $i(v0) | up_complete_relstr(v1)) & ! [v0: $i] : ! [v1: $i] :
% 61.73/9.08 ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | complete_relstr(v1)) & ! [v0: $i] :
% 61.73/9.08 ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | reflexive_relstr(v1)) &
% 61.73/9.08 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.08 strict_rel_str(v1))
% 61.73/9.08
% 61.73/9.08 (free_g1_orders_2)
% 61.73/9.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v1
% 61.73/9.08 | ~ (rel_str_of(v3, v4) = v2) | ~ (rel_str_of(v0, v1) = v2) | ~ $i(v4) |
% 61.73/9.08 ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation_of2(v1, v0, v0)) & ! [v0:
% 61.73/9.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v3 = v0 | ~
% 61.73/9.08 (rel_str_of(v3, v4) = v2) | ~ (rel_str_of(v0, v1) = v2) | ~ $i(v4) | ~
% 61.73/9.08 $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation_of2(v1, v0, v0))
% 61.73/9.08
% 61.73/9.08 (redefinition_m2_relset_1)
% 61.73/9.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 61.73/9.08 ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0, v1)) & ! [v0:
% 61.73/9.08 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 61.73/9.08 relation_of2(v2, v0, v1) | relation_of2_as_subset(v2, v0, v1))
% 61.73/9.08
% 61.73/9.08 (t4_waybel_7)
% 61.73/9.08 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 61.73/9.08 boole_POSet(v0) = v1 & powerset(v0) = v3 & the_carrier(v1) = v2 & $i(v3) &
% 61.73/9.08 $i(v2) & $i(v1) & $i(v0))
% 61.73/9.08
% 61.73/9.08 (t4_yellow_1)
% 61.73/9.08 ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) | ? [v2:
% 61.73/9.08 $i] : (incl_POSet(v2) = v1 & powerset(v0) = v2 & $i(v2) & $i(v1))) & !
% 61.73/9.08 [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 61.73/9.08 (boole_POSet(v0) = v2 & incl_POSet(v1) = v2 & $i(v2)))
% 61.73/9.08
% 61.73/9.08 (function-axioms)
% 61.73/9.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 61.73/9.09 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 61.73/9.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 61.73/9.09 (rel_str_of(v3, v2) = v1) | ~ (rel_str_of(v3, v2) = v0)) & ! [v0: $i] : !
% 61.73/9.09 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (boole_POSet(v2) = v1) | ~
% 61.73/9.09 (boole_POSet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 61.73/9.09 | ~ (inclusion_relation(v2) = v1) | ~ (inclusion_relation(v2) = v0)) & !
% 61.73/9.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (incl_POSet(v2) = v1) |
% 61.73/9.09 ~ (incl_POSet(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 61.73/9.09 v0 | ~ (inclusion_order(v2) = v1) | ~ (inclusion_order(v2) = v0)) & !
% 61.73/9.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 61.73/9.09 (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 61.73/9.09 ~ (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0)) & ! [v0: $i]
% 61.73/9.09 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1) | ~
% 61.73/9.09 (the_carrier(v2) = v0))
% 61.73/9.09
% 61.73/9.09 Further assumptions not needed in the proof:
% 61.73/9.09 --------------------------------------------
% 61.73/9.09 antisymmetry_r2_hidden, cc10_waybel_0, cc10_waybel_1, cc11_waybel_0,
% 61.73/9.09 cc12_waybel_0, cc13_waybel_0, cc14_waybel_0, cc1_finset_1, cc1_lattice3,
% 61.73/9.09 cc1_yellow_0, cc1_yellow_2, cc1_yellow_3, cc2_finset_1, cc2_lattice3,
% 61.73/9.09 cc2_yellow_3, cc3_yellow_0, cc3_yellow_3, cc4_yellow_0, cc5_waybel_1,
% 61.73/9.09 cc5_yellow_0, cc6_waybel_1, cc7_waybel_1, cc8_waybel_1, cc9_waybel_0,
% 61.73/9.09 cc9_waybel_1, dt_g1_orders_2, dt_k1_wellord2, dt_k1_xboole_0, dt_k1_yellow_1,
% 61.73/9.09 dt_k1_zfmisc_1, dt_k2_yellow_1, dt_k2_zfmisc_1, dt_l1_orders_2, dt_l1_struct_0,
% 61.73/9.09 dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_struct_0,
% 61.73/9.09 existence_l1_orders_2, existence_l1_struct_0, existence_m1_relset_1,
% 61.73/9.09 existence_m1_subset_1, existence_m2_relset_1, fc13_yellow_3, fc14_finset_1,
% 61.73/9.09 fc1_struct_0, fc1_subset_1, fc1_waybel_1, fc1_xboole_0, fc4_subset_1,
% 61.73/9.09 fc5_yellow_1, fc6_yellow_1, fc7_yellow_1, fc8_yellow_1, rc13_waybel_0,
% 61.73/9.09 rc1_finset_1, rc1_lattice3, rc1_subset_1, rc1_xboole_0, rc1_yellow_3,
% 61.73/9.09 rc2_lattice3, rc2_subset_1, rc2_xboole_0, rc2_yellow_0, rc3_finset_1,
% 61.73/9.09 rc3_struct_0, rc4_finset_1, rc4_waybel_1, rc5_struct_0, rc5_waybel_1,
% 61.73/9.09 redefinition_k1_yellow_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 61.73/9.09 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 61.73/9.09
% 61.73/9.09 Those formulas are unsatisfiable:
% 61.73/9.09 ---------------------------------
% 61.73/9.09
% 61.73/9.09 Begin of proof
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (abstractness_v1_orders_2) implies:
% 61.73/9.09 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 61.73/9.09 | strict_rel_str(v0) | ~ rel_str(v0) | ? [v2: $i] :
% 61.73/9.09 | (the_InternalRel(v0) = v2 & rel_str_of(v1, v2) = v0 & $i(v2)))
% 61.73/9.09 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_InternalRel(v0) = v1) | ~ $i(v0)
% 61.73/9.09 | | ~ strict_rel_str(v0) | ~ rel_str(v0) | ? [v2: $i] :
% 61.73/9.09 | (the_carrier(v0) = v2 & rel_str_of(v2, v1) = v0 & $i(v2)))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (d1_yellow_1) implies:
% 61.73/9.09 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (incl_POSet(v0) = v1) | ~ $i(v0) | ?
% 61.73/9.09 | [v2: $i] : (inclusion_order(v0) = v2 & rel_str_of(v0, v2) = v1 &
% 61.73/9.09 | $i(v2) & $i(v1)))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (dt_k3_yellow_1) implies:
% 61.73/9.09 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.09 | rel_str(v1))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (dt_u1_orders_2) implies:
% 61.73/9.09 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 61.73/9.09 | rel_str(v0) | ? [v2: $i] : (the_InternalRel(v0) = v2 & $i(v2) &
% 61.73/9.09 | relation_of2_as_subset(v2, v1, v1)))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (fc9_waybel_1) implies:
% 61.73/9.09 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.09 | strict_rel_str(v1))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (free_g1_orders_2) implies:
% 61.73/9.09 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 61.73/9.09 | (v3 = v0 | ~ (rel_str_of(v3, v4) = v2) | ~ (rel_str_of(v0, v1) = v2)
% 61.73/9.09 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ relation_of2(v1,
% 61.73/9.09 | v0, v0))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (redefinition_m2_relset_1) implies:
% 61.73/9.09 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 61.73/9.09 | $i(v0) | ~ relation_of2_as_subset(v2, v0, v1) | relation_of2(v2, v0,
% 61.73/9.09 | v1))
% 61.73/9.09 |
% 61.73/9.09 | ALPHA: (t4_yellow_1) implies:
% 61.73/9.09 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ?
% 61.73/9.09 | [v2: $i] : (boole_POSet(v0) = v2 & incl_POSet(v1) = v2 & $i(v2)))
% 61.73/9.10 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (boole_POSet(v0) = v1) | ~ $i(v0) |
% 61.73/9.10 | ? [v2: $i] : (incl_POSet(v2) = v1 & powerset(v0) = v2 & $i(v2) &
% 61.73/9.10 | $i(v1)))
% 61.73/9.10 |
% 61.73/9.10 | ALPHA: (function-axioms) implies:
% 61.73/9.10 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 61.73/9.10 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 61.73/9.10 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 61.73/9.10 | (the_InternalRel(v2) = v1) | ~ (the_InternalRel(v2) = v0))
% 61.73/9.10 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2)
% 61.73/9.10 | = v1) | ~ (powerset(v2) = v0))
% 62.66/9.10 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 62.66/9.10 | (boole_POSet(v2) = v1) | ~ (boole_POSet(v2) = v0))
% 62.66/9.10 |
% 62.66/9.10 | DELTA: instantiating (t4_waybel_7) with fresh symbols all_83_0, all_83_1,
% 62.66/9.10 | all_83_2, all_83_3 gives:
% 62.66/9.10 | (15) ~ (all_83_0 = all_83_1) & boole_POSet(all_83_3) = all_83_2 &
% 62.66/9.10 | powerset(all_83_3) = all_83_0 & the_carrier(all_83_2) = all_83_1 &
% 62.66/9.10 | $i(all_83_0) & $i(all_83_1) & $i(all_83_2) & $i(all_83_3)
% 62.66/9.10 |
% 62.66/9.10 | ALPHA: (15) implies:
% 62.66/9.10 | (16) ~ (all_83_0 = all_83_1)
% 62.66/9.10 | (17) $i(all_83_3)
% 62.66/9.10 | (18) $i(all_83_2)
% 62.66/9.10 | (19) $i(all_83_1)
% 62.66/9.10 | (20) the_carrier(all_83_2) = all_83_1
% 62.66/9.10 | (21) powerset(all_83_3) = all_83_0
% 62.66/9.10 | (22) boole_POSet(all_83_3) = all_83_2
% 62.66/9.10 |
% 62.66/9.10 | GROUND_INST: instantiating (5) with all_83_2, all_83_1, simplifying with (18),
% 62.66/9.10 | (20) gives:
% 62.66/9.10 | (23) ~ rel_str(all_83_2) | ? [v0: $i] : (the_InternalRel(all_83_2) = v0 &
% 62.66/9.10 | $i(v0) & relation_of2_as_subset(v0, all_83_1, all_83_1))
% 62.66/9.10 |
% 62.66/9.10 | GROUND_INST: instantiating (9) with all_83_3, all_83_0, simplifying with (17),
% 62.66/9.10 | (21) gives:
% 62.66/9.10 | (24) ? [v0: $i] : (boole_POSet(all_83_3) = v0 & incl_POSet(all_83_0) = v0
% 62.66/9.10 | & $i(v0))
% 62.66/9.10 |
% 62.66/9.10 | GROUND_INST: instantiating (6) with all_83_3, all_83_2, simplifying with (17),
% 62.66/9.10 | (22) gives:
% 62.66/9.10 | (25) strict_rel_str(all_83_2)
% 62.66/9.10 |
% 62.66/9.10 | GROUND_INST: instantiating (4) with all_83_3, all_83_2, simplifying with (17),
% 62.66/9.10 | (22) gives:
% 62.66/9.10 | (26) rel_str(all_83_2)
% 62.66/9.10 |
% 62.66/9.10 | GROUND_INST: instantiating (10) with all_83_3, all_83_2, simplifying with
% 62.66/9.10 | (17), (22) gives:
% 62.66/9.10 | (27) ? [v0: $i] : (incl_POSet(v0) = all_83_2 & powerset(all_83_3) = v0 &
% 62.66/9.10 | $i(v0) & $i(all_83_2))
% 62.66/9.10 |
% 62.66/9.10 | DELTA: instantiating (24) with fresh symbol all_111_0 gives:
% 62.66/9.10 | (28) boole_POSet(all_83_3) = all_111_0 & incl_POSet(all_83_0) = all_111_0 &
% 62.66/9.10 | $i(all_111_0)
% 62.66/9.10 |
% 62.66/9.10 | ALPHA: (28) implies:
% 62.66/9.10 | (29) $i(all_111_0)
% 62.66/9.10 | (30) incl_POSet(all_83_0) = all_111_0
% 62.66/9.10 | (31) boole_POSet(all_83_3) = all_111_0
% 62.66/9.10 |
% 62.66/9.10 | DELTA: instantiating (27) with fresh symbol all_113_0 gives:
% 62.66/9.10 | (32) incl_POSet(all_113_0) = all_83_2 & powerset(all_83_3) = all_113_0 &
% 62.66/9.10 | $i(all_113_0) & $i(all_83_2)
% 62.66/9.10 |
% 62.66/9.10 | ALPHA: (32) implies:
% 62.66/9.10 | (33) $i(all_113_0)
% 62.66/9.10 | (34) powerset(all_83_3) = all_113_0
% 62.66/9.10 |
% 62.66/9.10 | BETA: splitting (23) gives:
% 62.66/9.10 |
% 62.66/9.10 | Case 1:
% 62.66/9.10 | |
% 62.66/9.10 | | (35) ~ rel_str(all_83_2)
% 62.66/9.10 | |
% 62.66/9.10 | | PRED_UNIFY: (26), (35) imply:
% 62.66/9.10 | | (36) $false
% 62.66/9.11 | |
% 62.66/9.11 | | CLOSE: (36) is inconsistent.
% 62.66/9.11 | |
% 62.66/9.11 | Case 2:
% 62.66/9.11 | |
% 62.66/9.11 | | (37) ? [v0: $i] : (the_InternalRel(all_83_2) = v0 & $i(v0) &
% 62.66/9.11 | | relation_of2_as_subset(v0, all_83_1, all_83_1))
% 62.66/9.11 | |
% 62.66/9.11 | | DELTA: instantiating (37) with fresh symbol all_122_0 gives:
% 62.66/9.11 | | (38) the_InternalRel(all_83_2) = all_122_0 & $i(all_122_0) &
% 62.66/9.11 | | relation_of2_as_subset(all_122_0, all_83_1, all_83_1)
% 62.66/9.11 | |
% 62.66/9.11 | | ALPHA: (38) implies:
% 62.66/9.11 | | (39) relation_of2_as_subset(all_122_0, all_83_1, all_83_1)
% 62.66/9.11 | | (40) $i(all_122_0)
% 62.66/9.11 | | (41) the_InternalRel(all_83_2) = all_122_0
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (13) with all_83_0, all_113_0, all_83_3,
% 62.66/9.11 | | simplifying with (21), (34) gives:
% 62.66/9.11 | | (42) all_113_0 = all_83_0
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (14) with all_83_2, all_111_0, all_83_3,
% 62.66/9.11 | | simplifying with (22), (31) gives:
% 62.66/9.11 | | (43) all_111_0 = all_83_2
% 62.66/9.11 | |
% 62.66/9.11 | | REDUCE: (30), (43) imply:
% 62.66/9.11 | | (44) incl_POSet(all_83_0) = all_83_2
% 62.66/9.11 | |
% 62.66/9.11 | | REDUCE: (33), (42) imply:
% 62.66/9.11 | | (45) $i(all_83_0)
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (1) with all_83_2, all_83_1, simplifying with
% 62.66/9.11 | | (18), (20), (25), (26) gives:
% 62.66/9.11 | | (46) ? [v0: $i] : (the_InternalRel(all_83_2) = v0 & rel_str_of(all_83_1,
% 62.66/9.11 | | v0) = all_83_2 & $i(v0))
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (8) with all_83_1, all_83_1, all_122_0,
% 62.66/9.11 | | simplifying with (19), (39), (40) gives:
% 62.66/9.11 | | (47) relation_of2(all_122_0, all_83_1, all_83_1)
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (2) with all_83_2, all_122_0, simplifying with
% 62.66/9.11 | | (18), (25), (26), (41) gives:
% 62.66/9.11 | | (48) ? [v0: $i] : (the_carrier(all_83_2) = v0 & rel_str_of(v0,
% 62.66/9.11 | | all_122_0) = all_83_2 & $i(v0))
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (3) with all_83_0, all_83_2, simplifying with
% 62.66/9.11 | | (44), (45) gives:
% 62.66/9.11 | | (49) ? [v0: $i] : (inclusion_order(all_83_0) = v0 & rel_str_of(all_83_0,
% 62.66/9.11 | | v0) = all_83_2 & $i(v0) & $i(all_83_2))
% 62.66/9.11 | |
% 62.66/9.11 | | DELTA: instantiating (46) with fresh symbol all_146_0 gives:
% 62.66/9.11 | | (50) the_InternalRel(all_83_2) = all_146_0 & rel_str_of(all_83_1,
% 62.66/9.11 | | all_146_0) = all_83_2 & $i(all_146_0)
% 62.66/9.11 | |
% 62.66/9.11 | | ALPHA: (50) implies:
% 62.66/9.11 | | (51) $i(all_146_0)
% 62.66/9.11 | | (52) rel_str_of(all_83_1, all_146_0) = all_83_2
% 62.66/9.11 | | (53) the_InternalRel(all_83_2) = all_146_0
% 62.66/9.11 | |
% 62.66/9.11 | | DELTA: instantiating (48) with fresh symbol all_148_0 gives:
% 62.66/9.11 | | (54) the_carrier(all_83_2) = all_148_0 & rel_str_of(all_148_0, all_122_0)
% 62.66/9.11 | | = all_83_2 & $i(all_148_0)
% 62.66/9.11 | |
% 62.66/9.11 | | ALPHA: (54) implies:
% 62.66/9.11 | | (55) $i(all_148_0)
% 62.66/9.11 | | (56) the_carrier(all_83_2) = all_148_0
% 62.66/9.11 | |
% 62.66/9.11 | | DELTA: instantiating (49) with fresh symbol all_150_0 gives:
% 62.66/9.11 | | (57) inclusion_order(all_83_0) = all_150_0 & rel_str_of(all_83_0,
% 62.66/9.11 | | all_150_0) = all_83_2 & $i(all_150_0) & $i(all_83_2)
% 62.66/9.11 | |
% 62.66/9.11 | | ALPHA: (57) implies:
% 62.66/9.11 | | (58) $i(all_150_0)
% 62.66/9.11 | | (59) rel_str_of(all_83_0, all_150_0) = all_83_2
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (11) with all_83_1, all_148_0, all_83_2,
% 62.66/9.11 | | simplifying with (20), (56) gives:
% 62.66/9.11 | | (60) all_148_0 = all_83_1
% 62.66/9.11 | |
% 62.66/9.11 | | GROUND_INST: instantiating (12) with all_122_0, all_146_0, all_83_2,
% 62.66/9.11 | | simplifying with (41), (53) gives:
% 62.66/9.11 | | (61) all_146_0 = all_122_0
% 62.66/9.11 | |
% 62.66/9.11 | | REDUCE: (52), (61) imply:
% 62.66/9.11 | | (62) rel_str_of(all_83_1, all_122_0) = all_83_2
% 62.66/9.11 | |
% 62.66/9.12 | | GROUND_INST: instantiating (7) with all_83_1, all_122_0, all_83_2, all_83_0,
% 62.66/9.12 | | all_150_0, simplifying with (19), (40), (45), (47), (58), (59),
% 62.66/9.12 | | (62) gives:
% 62.66/9.12 | | (63) all_83_0 = all_83_1
% 62.66/9.12 | |
% 62.66/9.12 | | REDUCE: (16), (63) imply:
% 62.66/9.12 | | (64) $false
% 62.66/9.12 | |
% 62.66/9.12 | | CLOSE: (64) is inconsistent.
% 62.66/9.12 | |
% 62.66/9.12 | End of split
% 62.66/9.12 |
% 62.66/9.12 End of proof
% 62.66/9.12 % SZS output end Proof for theBenchmark
% 62.66/9.12
% 62.66/9.12 8503ms
%------------------------------------------------------------------------------