TSTP Solution File: SEU360+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU360+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 : n020.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 17:44:17 EDT 2023
% Result : Theorem 9.84s 2.23s
% Output : Proof 15.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU360+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 01:31:31 EDT 2023
% 0.14/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 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 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.88/1.10 Prover 1: Preprocessing ...
% 2.88/1.10 Prover 4: Preprocessing ...
% 3.09/1.14 Prover 5: Preprocessing ...
% 3.09/1.14 Prover 3: Preprocessing ...
% 3.09/1.14 Prover 0: Preprocessing ...
% 3.09/1.14 Prover 2: Preprocessing ...
% 3.09/1.14 Prover 6: Preprocessing ...
% 4.76/1.51 Prover 2: Proving ...
% 6.00/1.56 Prover 5: Proving ...
% 6.00/1.56 Prover 1: Warning: ignoring some quantifiers
% 6.00/1.58 Prover 1: Constructing countermodel ...
% 6.39/1.61 Prover 6: Proving ...
% 6.39/1.62 Prover 3: Warning: ignoring some quantifiers
% 6.39/1.63 Prover 3: Constructing countermodel ...
% 8.28/1.91 Prover 0: Proving ...
% 8.28/1.94 Prover 4: Warning: ignoring some quantifiers
% 9.06/1.96 Prover 4: Constructing countermodel ...
% 9.84/2.23 Prover 2: proved (1595ms)
% 9.84/2.23
% 9.84/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.84/2.23
% 9.84/2.24 Prover 3: stopped
% 9.84/2.24 Prover 6: stopped
% 9.84/2.26 Prover 5: stopped
% 10.71/2.27 Prover 0: stopped
% 10.71/2.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.71/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.71/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.71/2.28 Prover 7: Preprocessing ...
% 10.71/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.71/2.28 Prover 8: Preprocessing ...
% 10.71/2.29 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.71/2.31 Prover 11: Preprocessing ...
% 11.71/2.32 Prover 10: Preprocessing ...
% 11.71/2.33 Prover 13: Preprocessing ...
% 12.11/2.36 Prover 7: Warning: ignoring some quantifiers
% 12.11/2.37 Prover 7: Constructing countermodel ...
% 12.11/2.39 Prover 10: Warning: ignoring some quantifiers
% 12.11/2.39 Prover 8: Warning: ignoring some quantifiers
% 12.11/2.42 Prover 8: Constructing countermodel ...
% 12.11/2.42 Prover 10: Constructing countermodel ...
% 12.11/2.43 Prover 7: gave up
% 12.11/2.43 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.11/2.44 Prover 13: Warning: ignoring some quantifiers
% 12.72/2.45 Prover 13: Constructing countermodel ...
% 12.72/2.45 Prover 16: Preprocessing ...
% 12.72/2.47 Prover 10: gave up
% 12.99/2.49 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.99/2.50 Prover 16: Warning: ignoring some quantifiers
% 12.99/2.51 Prover 16: Constructing countermodel ...
% 12.99/2.51 Prover 19: Preprocessing ...
% 13.47/2.60 Prover 11: Warning: ignoring some quantifiers
% 13.94/2.63 Prover 11: Constructing countermodel ...
% 14.31/2.69 Prover 19: Warning: ignoring some quantifiers
% 14.31/2.71 Prover 19: Constructing countermodel ...
% 14.31/2.73 Prover 13: Found proof (size 84)
% 14.31/2.73 Prover 13: proved (440ms)
% 14.31/2.73 Prover 16: stopped
% 14.31/2.73 Prover 1: stopped
% 14.31/2.73 Prover 4: stopped
% 14.31/2.73 Prover 8: stopped
% 14.31/2.73 Prover 19: stopped
% 14.31/2.73 Prover 11: stopped
% 14.31/2.73
% 14.31/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.31/2.73
% 14.31/2.74 % SZS output start Proof for theBenchmark
% 14.31/2.74 Assumptions after simplification:
% 14.31/2.74 ---------------------------------
% 14.31/2.74
% 14.31/2.74 (d4_yellow_0)
% 14.93/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v1) | ~
% 14.93/2.77 $i(v2) | ~ $i(v0) | ~ relstr_element_smaller(v0, v1, v2) | ~ element(v2,
% 14.93/2.77 v1) | ~ rel_str(v0) | lower_bounded_relstr(v0)) & ! [v0: $i] : ! [v1:
% 14.93/2.77 $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~ lower_bounded_relstr(v0) |
% 14.93/2.77 ~ rel_str(v0) | ? [v2: $i] : ($i(v2) & relstr_element_smaller(v0, v1, v2)
% 14.93/2.77 & element(v2, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ rel_str(v0) | ? [v1:
% 14.93/2.77 $i] : ? [v2: $i] : (the_carrier(v0) = v1 & $i(v2) & $i(v1) & ( ~
% 14.93/2.77 lower_bounded_relstr(v0) | (relstr_element_smaller(v0, v1, v2) &
% 14.93/2.77 element(v2, v1))) & (lower_bounded_relstr(v0) | ! [v3: $i] : ( ~
% 14.93/2.77 $i(v3) | ~ relstr_element_smaller(v0, v1, v3) | ~ element(v3,
% 14.93/2.77 v1)))))
% 14.93/2.77
% 14.93/2.77 (d8_lattice3)
% 14.93/2.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 14.93/2.77 (the_carrier(v0) = v1) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 14.93/2.77 relstr_element_smaller(v0, v2, v3) | ~ element(v4, v1) | ~ element(v3, v1)
% 14.93/2.77 | ~ rel_str(v0) | ~ in(v4, v2) | related(v0, v3, v4)) & ? [v0: $i] : !
% 14.93/2.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v1) = v2) | ~ $i(v3)
% 14.93/2.77 | ~ $i(v1) | ~ $i(v0) | ~ element(v3, v2) | ~ rel_str(v1) |
% 14.93/2.77 relstr_element_smaller(v1, v0, v3) | ? [v4: $i] : ($i(v4) & element(v4, v2)
% 14.93/2.77 & in(v4, v0) & ~ related(v1, v3, v4))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 14.93/2.77 rel_str(v0) | ? [v1: $i] : (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] :
% 14.93/2.77 ! [v3: $i] : ! [v4: $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 14.93/2.77 relstr_element_smaller(v0, v2, v3) | ~ element(v4, v1) | ~ element(v3,
% 14.93/2.77 v1) | ~ in(v4, v2) | related(v0, v3, v4)) & ? [v2: $i] : ! [v3: $i]
% 14.93/2.77 : ( ~ $i(v3) | ~ $i(v2) | ~ element(v3, v1) | relstr_element_smaller(v0,
% 14.93/2.77 v2, v3) | ? [v4: $i] : ($i(v4) & element(v4, v1) & in(v4, v2) & ~
% 14.93/2.77 related(v0, v3, v4)))))
% 14.93/2.77
% 14.93/2.77 (dt_l1_orders_2)
% 14.93/2.77 ! [v0: $i] : ( ~ $i(v0) | ~ rel_str(v0) | one_sorted_str(v0))
% 14.93/2.77
% 14.93/2.77 (fc1_struct_0)
% 14.93/2.77 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 14.93/2.77 one_sorted_str(v0) | ~ empty(v1) | empty_carrier(v0)) & ! [v0: $i] : ( ~
% 14.93/2.77 $i(v0) | ~ one_sorted_str(v0) | empty_carrier(v0) | ? [v1: $i] :
% 14.93/2.77 (the_carrier(v0) = v1 & $i(v1) & ~ empty(v1)))
% 14.93/2.77
% 14.93/2.77 (rc1_xboole_0)
% 14.93/2.78 ? [v0: $i] : ($i(v0) & empty(v0))
% 14.93/2.78
% 14.93/2.78 (t15_yellow_0)
% 14.93/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) =
% 14.93/2.78 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ relstr_set_smaller(v0, v2,
% 14.93/2.78 v3) | ~ antisymmetric_relstr(v0) | ~ element(v3, v1) | ~ rel_str(v0) |
% 14.93/2.78 ex_sup_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) &
% 14.93/2.78 relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v3,
% 14.93/2.78 v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) =
% 14.93/2.78 v1) | ~ $i(v2) | ~ $i(v0) | ~ ex_sup_of_relstr_set(v0, v2) | ~
% 14.93/2.78 antisymmetric_relstr(v0) | ~ rel_str(v0) | ? [v3: $i] : ($i(v3) &
% 14.93/2.78 relstr_set_smaller(v0, v2, v3) & element(v3, v1) & ! [v4: $i] : ( ~
% 14.93/2.78 $i(v4) | ~ relstr_set_smaller(v0, v2, v4) | ~ element(v4, v1) |
% 14.93/2.78 related(v0, v3, v4)))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 14.93/2.78 antisymmetric_relstr(v0) | ~ rel_str(v0) | ? [v1: $i] : (the_carrier(v0) =
% 14.93/2.78 v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 14.93/2.78 relstr_set_smaller(v0, v2, v3) | ~ element(v3, v1) |
% 14.93/2.78 ex_sup_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) &
% 14.93/2.78 relstr_set_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v3,
% 14.93/2.78 v4))) & ! [v2: $i] : ( ~ $i(v2) | ~ ex_sup_of_relstr_set(v0, v2) |
% 14.93/2.78 ? [v3: $i] : ($i(v3) & relstr_set_smaller(v0, v2, v3) & element(v3, v1)
% 14.93/2.78 & ! [v4: $i] : ( ~ $i(v4) | ~ relstr_set_smaller(v0, v2, v4) | ~
% 14.93/2.78 element(v4, v1) | related(v0, v3, v4))))))
% 14.93/2.78
% 14.93/2.78 (t16_yellow_0)
% 15.08/2.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) =
% 15.08/2.78 v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ antisymmetric_relstr(v0) | ~
% 15.08/2.78 relstr_element_smaller(v0, v2, v3) | ~ element(v3, v1) | ~ rel_str(v0) |
% 15.08/2.78 ex_inf_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) &
% 15.08/2.78 relstr_element_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0, v4,
% 15.08/2.78 v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) =
% 15.08/2.78 v1) | ~ $i(v2) | ~ $i(v0) | ~ ex_inf_of_relstr_set(v0, v2) | ~
% 15.08/2.78 antisymmetric_relstr(v0) | ~ rel_str(v0) | ? [v3: $i] : ($i(v3) &
% 15.08/2.78 relstr_element_smaller(v0, v2, v3) & element(v3, v1) & ! [v4: $i] : ( ~
% 15.08/2.78 $i(v4) | ~ relstr_element_smaller(v0, v2, v4) | ~ element(v4, v1) |
% 15.08/2.78 related(v0, v4, v3)))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.08/2.78 antisymmetric_relstr(v0) | ~ rel_str(v0) | ? [v1: $i] : (the_carrier(v0) =
% 15.08/2.78 v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~
% 15.08/2.78 relstr_element_smaller(v0, v2, v3) | ~ element(v3, v1) |
% 15.08/2.78 ex_inf_of_relstr_set(v0, v2) | ? [v4: $i] : ($i(v4) &
% 15.08/2.78 relstr_element_smaller(v0, v2, v4) & element(v4, v1) & ~ related(v0,
% 15.08/2.78 v4, v3))) & ! [v2: $i] : ( ~ $i(v2) | ~ ex_inf_of_relstr_set(v0,
% 15.08/2.78 v2) | ? [v3: $i] : ($i(v3) & relstr_element_smaller(v0, v2, v3) &
% 15.08/2.78 element(v3, v1) & ! [v4: $i] : ( ~ $i(v4) | ~
% 15.08/2.78 relstr_element_smaller(v0, v2, v4) | ~ element(v4, v1) |
% 15.08/2.78 related(v0, v4, v3))))))
% 15.08/2.78
% 15.08/2.78 (t2_subset)
% 15.08/2.78 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) |
% 15.08/2.78 empty(v1) | in(v0, v1))
% 15.08/2.78
% 15.08/2.78 (t42_yellow_0)
% 15.08/2.78 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : (the_carrier(v0) = v1 & $i(v1) &
% 15.08/2.78 $i(v0) & antisymmetric_relstr(v0) & lower_bounded_relstr(v0) & rel_str(v0) &
% 15.08/2.78 ~ empty_carrier(v0) & ( ~ ex_inf_of_relstr_set(v0, v1) | ~
% 15.08/2.78 ex_sup_of_relstr_set(v0, empty_set)))
% 15.08/2.78
% 15.08/2.78 (t6_boole)
% 15.08/2.78 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 15.08/2.78
% 15.08/2.78 (t6_yellow_0)
% 15.08/2.79 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0)
% 15.08/2.79 = v1) | ~ $i(v2) | ~ $i(v0) | ~ element(v2, v1) | ~ rel_str(v0) |
% 15.08/2.79 relstr_set_smaller(v0, empty_set, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.08/2.79 $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ element(v2,
% 15.08/2.79 v1) | ~ rel_str(v0) | relstr_element_smaller(v0, empty_set, v2)) & !
% 15.08/2.79 [v0: $i] : ( ~ $i(v0) | ~ rel_str(v0) | ? [v1: $i] : (the_carrier(v0) = v1 &
% 15.08/2.79 $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~ element(v2, v1) |
% 15.08/2.79 relstr_set_smaller(v0, empty_set, v2)) & ! [v2: $i] : ( ~ $i(v2) | ~
% 15.08/2.79 element(v2, v1) | relstr_element_smaller(v0, empty_set, v2))))
% 15.08/2.79
% 15.08/2.79 (function-axioms)
% 15.08/2.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (the_carrier(v2) = v1)
% 15.08/2.79 | ~ (the_carrier(v2) = v0))
% 15.08/2.79
% 15.08/2.79 Further assumptions not needed in the proof:
% 15.08/2.79 --------------------------------------------
% 15.08/2.79 antisymmetry_r2_hidden, cc1_finset_1, dt_k1_xboole_0, dt_l1_struct_0,
% 15.08/2.79 dt_m1_subset_1, dt_u1_struct_0, existence_l1_orders_2, existence_l1_struct_0,
% 15.08/2.79 existence_m1_subset_1, fc1_xboole_0, rc1_finset_1, rc2_xboole_0, rc3_struct_0,
% 15.08/2.79 t1_subset, t7_boole, t8_boole
% 15.08/2.79
% 15.08/2.79 Those formulas are unsatisfiable:
% 15.08/2.79 ---------------------------------
% 15.08/2.79
% 15.08/2.79 Begin of proof
% 15.08/2.79 |
% 15.08/2.79 | ALPHA: (d4_yellow_0) implies:
% 15.08/2.79 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ rel_str(v0) | ? [v1: $i] : ? [v2: $i] :
% 15.08/2.79 | (the_carrier(v0) = v1 & $i(v2) & $i(v1) & ( ~
% 15.08/2.79 | lower_bounded_relstr(v0) | (relstr_element_smaller(v0, v1, v2) &
% 15.08/2.79 | element(v2, v1))) & (lower_bounded_relstr(v0) | ! [v3: $i] : (
% 15.08/2.79 | ~ $i(v3) | ~ relstr_element_smaller(v0, v1, v3) | ~
% 15.08/2.79 | element(v3, v1)))))
% 15.08/2.79 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ~
% 15.08/2.79 | lower_bounded_relstr(v0) | ~ rel_str(v0) | ? [v2: $i] : ($i(v2) &
% 15.08/2.79 | relstr_element_smaller(v0, v1, v2) & element(v2, v1)))
% 15.08/2.79 |
% 15.08/2.79 | ALPHA: (d8_lattice3) implies:
% 15.08/2.79 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ rel_str(v0) | ? [v1: $i] :
% 15.08/2.79 | (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ! [v4:
% 15.08/2.79 | $i] : ( ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 15.08/2.79 | relstr_element_smaller(v0, v2, v3) | ~ element(v4, v1) | ~
% 15.08/2.79 | element(v3, v1) | ~ in(v4, v2) | related(v0, v3, v4)) & ? [v2:
% 15.08/2.79 | $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ element(v3, v1) |
% 15.08/2.79 | relstr_element_smaller(v0, v2, v3) | ? [v4: $i] : ($i(v4) &
% 15.08/2.79 | element(v4, v1) & in(v4, v2) & ~ related(v0, v3, v4)))))
% 15.08/2.80 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 15.08/2.80 | ~ (the_carrier(v0) = v1) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 15.08/2.80 | $i(v0) | ~ relstr_element_smaller(v0, v2, v3) | ~ element(v4, v1) |
% 15.08/2.80 | ~ element(v3, v1) | ~ rel_str(v0) | ~ in(v4, v2) | related(v0, v3,
% 15.08/2.80 | v4))
% 15.08/2.80 |
% 15.08/2.80 | ALPHA: (fc1_struct_0) implies:
% 15.08/2.80 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ one_sorted_str(v0) | empty_carrier(v0) |
% 15.08/2.80 | ? [v1: $i] : (the_carrier(v0) = v1 & $i(v1) & ~ empty(v1)))
% 15.08/2.80 |
% 15.08/2.80 | ALPHA: (t15_yellow_0) implies:
% 15.08/2.80 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0)
% 15.08/2.80 | | ? [v1: $i] : (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : !
% 15.08/2.80 | [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ relstr_set_smaller(v0, v2,
% 15.08/2.80 | v3) | ~ element(v3, v1) | ex_sup_of_relstr_set(v0, v2) | ?
% 15.08/2.80 | [v4: $i] : ($i(v4) & relstr_set_smaller(v0, v2, v4) & element(v4,
% 15.08/2.80 | v1) & ~ related(v0, v3, v4))) & ! [v2: $i] : ( ~ $i(v2) |
% 15.08/2.80 | ~ ex_sup_of_relstr_set(v0, v2) | ? [v3: $i] : ($i(v3) &
% 15.08/2.80 | relstr_set_smaller(v0, v2, v3) & element(v3, v1) & ! [v4: $i]
% 15.08/2.80 | : ( ~ $i(v4) | ~ relstr_set_smaller(v0, v2, v4) | ~
% 15.08/2.80 | element(v4, v1) | related(v0, v3, v4))))))
% 15.08/2.80 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.08/2.80 | (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 15.08/2.80 | relstr_set_smaller(v0, v2, v3) | ~ antisymmetric_relstr(v0) | ~
% 15.08/2.80 | element(v3, v1) | ~ rel_str(v0) | ex_sup_of_relstr_set(v0, v2) | ?
% 15.08/2.80 | [v4: $i] : ($i(v4) & relstr_set_smaller(v0, v2, v4) & element(v4, v1)
% 15.08/2.80 | & ~ related(v0, v3, v4)))
% 15.08/2.80 |
% 15.08/2.80 | ALPHA: (t16_yellow_0) implies:
% 15.08/2.80 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ antisymmetric_relstr(v0) | ~ rel_str(v0)
% 15.08/2.80 | | ? [v1: $i] : (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : !
% 15.08/2.80 | [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ relstr_element_smaller(v0,
% 15.08/2.80 | v2, v3) | ~ element(v3, v1) | ex_inf_of_relstr_set(v0, v2) |
% 15.08/2.80 | ? [v4: $i] : ($i(v4) & relstr_element_smaller(v0, v2, v4) &
% 15.08/2.80 | element(v4, v1) & ~ related(v0, v4, v3))) & ! [v2: $i] : ( ~
% 15.08/2.80 | $i(v2) | ~ ex_inf_of_relstr_set(v0, v2) | ? [v3: $i] : ($i(v3)
% 15.08/2.80 | & relstr_element_smaller(v0, v2, v3) & element(v3, v1) & !
% 15.08/2.80 | [v4: $i] : ( ~ $i(v4) | ~ relstr_element_smaller(v0, v2, v4) |
% 15.08/2.80 | ~ element(v4, v1) | related(v0, v4, v3))))))
% 15.08/2.80 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 15.08/2.80 | (the_carrier(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 15.08/2.80 | antisymmetric_relstr(v0) | ~ relstr_element_smaller(v0, v2, v3) | ~
% 15.08/2.80 | element(v3, v1) | ~ rel_str(v0) | ex_inf_of_relstr_set(v0, v2) | ?
% 15.08/2.80 | [v4: $i] : ($i(v4) & relstr_element_smaller(v0, v2, v4) & element(v4,
% 15.08/2.80 | v1) & ~ related(v0, v4, v3)))
% 15.08/2.80 |
% 15.08/2.80 | ALPHA: (t6_boole) implies:
% 15.08/2.80 | (10) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 15.08/2.80 |
% 15.08/2.80 | ALPHA: (t6_yellow_0) implies:
% 15.08/2.80 | (11) ! [v0: $i] : ( ~ $i(v0) | ~ rel_str(v0) | ? [v1: $i] :
% 15.08/2.80 | (the_carrier(v0) = v1 & $i(v1) & ! [v2: $i] : ( ~ $i(v2) | ~
% 15.08/2.80 | element(v2, v1) | relstr_set_smaller(v0, empty_set, v2)) & !
% 15.08/2.80 | [v2: $i] : ( ~ $i(v2) | ~ element(v2, v1) |
% 15.08/2.80 | relstr_element_smaller(v0, empty_set, v2))))
% 15.08/2.81 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (the_carrier(v0) = v1) |
% 15.08/2.81 | ~ $i(v2) | ~ $i(v0) | ~ element(v2, v1) | ~ rel_str(v0) |
% 15.08/2.81 | relstr_set_smaller(v0, empty_set, v2))
% 15.08/2.81 |
% 15.08/2.81 | ALPHA: (t42_yellow_0) implies:
% 15.08/2.81 | (13) ? [v0: $i] : ? [v1: $i] : (the_carrier(v0) = v1 & $i(v1) & $i(v0) &
% 15.08/2.81 | antisymmetric_relstr(v0) & lower_bounded_relstr(v0) & rel_str(v0) &
% 15.08/2.81 | ~ empty_carrier(v0) & ( ~ ex_inf_of_relstr_set(v0, v1) | ~
% 15.08/2.81 | ex_sup_of_relstr_set(v0, empty_set)))
% 15.08/2.81 |
% 15.08/2.81 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_20_0 gives:
% 15.08/2.81 | (14) $i(all_20_0) & empty(all_20_0)
% 15.08/2.81 |
% 15.08/2.81 | ALPHA: (14) implies:
% 15.08/2.81 | (15) empty(all_20_0)
% 15.08/2.81 | (16) $i(all_20_0)
% 15.08/2.81 |
% 15.08/2.81 | DELTA: instantiating (13) with fresh symbols all_31_0, all_31_1 gives:
% 15.08/2.81 | (17) the_carrier(all_31_1) = all_31_0 & $i(all_31_0) & $i(all_31_1) &
% 15.08/2.81 | antisymmetric_relstr(all_31_1) & lower_bounded_relstr(all_31_1) &
% 15.08/2.81 | rel_str(all_31_1) & ~ empty_carrier(all_31_1) & ( ~
% 15.08/2.81 | ex_inf_of_relstr_set(all_31_1, all_31_0) | ~
% 15.08/2.81 | ex_sup_of_relstr_set(all_31_1, empty_set))
% 15.08/2.81 |
% 15.08/2.81 | ALPHA: (17) implies:
% 15.08/2.81 | (18) ~ empty_carrier(all_31_1)
% 15.08/2.81 | (19) rel_str(all_31_1)
% 15.08/2.81 | (20) lower_bounded_relstr(all_31_1)
% 15.08/2.81 | (21) antisymmetric_relstr(all_31_1)
% 15.08/2.81 | (22) $i(all_31_1)
% 15.08/2.81 | (23) the_carrier(all_31_1) = all_31_0
% 15.08/2.81 | (24) ~ ex_inf_of_relstr_set(all_31_1, all_31_0) | ~
% 15.08/2.81 | ex_sup_of_relstr_set(all_31_1, empty_set)
% 15.08/2.81 |
% 15.08/2.81 | GROUND_INST: instantiating (10) with all_20_0, simplifying with (15), (16)
% 15.08/2.81 | gives:
% 15.08/2.81 | (25) all_20_0 = empty_set
% 15.08/2.81 |
% 15.08/2.81 | GROUND_INST: instantiating (dt_l1_orders_2) with all_31_1, simplifying with
% 15.08/2.81 | (19), (22) gives:
% 15.08/2.81 | (26) one_sorted_str(all_31_1)
% 15.08/2.81 |
% 15.08/2.81 | GROUND_INST: instantiating (1) with all_31_1, simplifying with (19), (22)
% 15.08/2.81 | gives:
% 15.08/2.81 | (27) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_31_1) = v0 & $i(v1) &
% 15.08/2.81 | $i(v0) & ( ~ lower_bounded_relstr(all_31_1) |
% 15.08/2.81 | (relstr_element_smaller(all_31_1, v0, v1) & element(v1, v0))) &
% 15.08/2.81 | (lower_bounded_relstr(all_31_1) | ! [v2: $i] : ( ~ $i(v2) | ~
% 15.08/2.81 | relstr_element_smaller(all_31_1, v0, v2) | ~ element(v2, v0))))
% 15.08/2.81 |
% 15.08/2.81 | GROUND_INST: instantiating (3) with all_31_1, simplifying with (19), (22)
% 15.08/2.81 | gives:
% 15.08/2.81 | (28) ? [v0: $i] : (the_carrier(all_31_1) = v0 & $i(v0) & ! [v1: $i] : !
% 15.08/2.81 | [v2: $i] : ! [v3: $i] : ( ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 15.08/2.81 | relstr_element_smaller(all_31_1, v1, v2) | ~ element(v3, v0) | ~
% 15.08/2.81 | element(v2, v0) | ~ in(v3, v1) | related(all_31_1, v2, v3)) & ?
% 15.08/2.81 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ element(v2, v0)
% 15.08/2.81 | | relstr_element_smaller(all_31_1, v1, v2) | ? [v3: $i] : ($i(v3)
% 15.08/2.81 | & element(v3, v0) & in(v3, v1) & ~ related(all_31_1, v2, v3))))
% 15.08/2.81 |
% 15.08/2.81 | GROUND_INST: instantiating (11) with all_31_1, simplifying with (19), (22)
% 15.08/2.81 | gives:
% 15.08/2.82 | (29) ? [v0: $i] : (the_carrier(all_31_1) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 15.08/2.82 | $i(v1) | ~ element(v1, v0) | relstr_set_smaller(all_31_1,
% 15.08/2.82 | empty_set, v1)) & ! [v1: $i] : ( ~ $i(v1) | ~ element(v1, v0)
% 15.08/2.82 | | relstr_element_smaller(all_31_1, empty_set, v1)))
% 15.08/2.82 |
% 15.08/2.82 | GROUND_INST: instantiating (6) with all_31_1, simplifying with (19), (21),
% 15.08/2.82 | (22) gives:
% 15.08/2.82 | (30) ? [v0: $i] : (the_carrier(all_31_1) = v0 & $i(v0) & ! [v1: $i] : !
% 15.08/2.82 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ relstr_set_smaller(all_31_1,
% 15.08/2.82 | v1, v2) | ~ element(v2, v0) | ex_sup_of_relstr_set(all_31_1,
% 15.08/2.82 | v1) | ? [v3: $i] : ($i(v3) & relstr_set_smaller(all_31_1, v1,
% 15.08/2.82 | v3) & element(v3, v0) & ~ related(all_31_1, v2, v3))) & !
% 15.08/2.82 | [v1: $i] : ( ~ $i(v1) | ~ ex_sup_of_relstr_set(all_31_1, v1) | ?
% 15.08/2.82 | [v2: $i] : ($i(v2) & relstr_set_smaller(all_31_1, v1, v2) &
% 15.08/2.82 | element(v2, v0) & ! [v3: $i] : ( ~ $i(v3) | ~
% 15.08/2.82 | relstr_set_smaller(all_31_1, v1, v3) | ~ element(v3, v0) |
% 15.08/2.82 | related(all_31_1, v2, v3)))))
% 15.08/2.82 |
% 15.08/2.82 | GROUND_INST: instantiating (8) with all_31_1, simplifying with (19), (21),
% 15.08/2.82 | (22) gives:
% 15.08/2.82 | (31) ? [v0: $i] : (the_carrier(all_31_1) = v0 & $i(v0) & ! [v1: $i] : !
% 15.08/2.82 | [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 15.08/2.82 | relstr_element_smaller(all_31_1, v1, v2) | ~ element(v2, v0) |
% 15.08/2.82 | ex_inf_of_relstr_set(all_31_1, v1) | ? [v3: $i] : ($i(v3) &
% 15.08/2.82 | relstr_element_smaller(all_31_1, v1, v3) & element(v3, v0) & ~
% 15.08/2.82 | related(all_31_1, v3, v2))) & ! [v1: $i] : ( ~ $i(v1) | ~
% 15.08/2.82 | ex_inf_of_relstr_set(all_31_1, v1) | ? [v2: $i] : ($i(v2) &
% 15.08/2.82 | relstr_element_smaller(all_31_1, v1, v2) & element(v2, v0) & !
% 15.08/2.82 | [v3: $i] : ( ~ $i(v3) | ~ relstr_element_smaller(all_31_1, v1,
% 15.08/2.82 | v3) | ~ element(v3, v0) | related(all_31_1, v3, v2)))))
% 15.08/2.82 |
% 15.08/2.82 | GROUND_INST: instantiating (2) with all_31_1, all_31_0, simplifying with (19),
% 15.08/2.82 | (20), (22), (23) gives:
% 15.08/2.82 | (32) ? [v0: $i] : ($i(v0) & relstr_element_smaller(all_31_1, all_31_0, v0)
% 15.08/2.82 | & element(v0, all_31_0))
% 15.08/2.82 |
% 15.08/2.82 | DELTA: instantiating (32) with fresh symbol all_41_0 gives:
% 15.08/2.82 | (33) $i(all_41_0) & relstr_element_smaller(all_31_1, all_31_0, all_41_0) &
% 15.08/2.82 | element(all_41_0, all_31_0)
% 15.08/2.82 |
% 15.08/2.82 | ALPHA: (33) implies:
% 15.08/2.82 | (34) element(all_41_0, all_31_0)
% 15.08/2.82 | (35) relstr_element_smaller(all_31_1, all_31_0, all_41_0)
% 15.08/2.82 | (36) $i(all_41_0)
% 15.08/2.82 |
% 15.08/2.82 | DELTA: instantiating (29) with fresh symbol all_48_0 gives:
% 15.08/2.82 | (37) the_carrier(all_31_1) = all_48_0 & $i(all_48_0) & ! [v0: $i] : ( ~
% 15.08/2.82 | $i(v0) | ~ element(v0, all_48_0) | relstr_set_smaller(all_31_1,
% 15.08/2.82 | empty_set, v0)) & ! [v0: $i] : ( ~ $i(v0) | ~ element(v0,
% 15.08/2.82 | all_48_0) | relstr_element_smaller(all_31_1, empty_set, v0))
% 15.08/2.82 |
% 15.08/2.82 | ALPHA: (37) implies:
% 15.08/2.82 | (38) $i(all_48_0)
% 15.08/2.82 | (39) the_carrier(all_31_1) = all_48_0
% 15.08/2.82 |
% 15.08/2.82 | DELTA: instantiating (27) with fresh symbols all_51_0, all_51_1 gives:
% 15.08/2.82 | (40) the_carrier(all_31_1) = all_51_1 & $i(all_51_0) & $i(all_51_1) & ( ~
% 15.08/2.82 | lower_bounded_relstr(all_31_1) | (relstr_element_smaller(all_31_1,
% 15.08/2.82 | all_51_1, all_51_0) & element(all_51_0, all_51_1))) &
% 15.08/2.82 | (lower_bounded_relstr(all_31_1) | ! [v0: $i] : ( ~ $i(v0) | ~
% 15.08/2.82 | relstr_element_smaller(all_31_1, all_51_1, v0) | ~ element(v0,
% 15.08/2.82 | all_51_1)))
% 15.08/2.82 |
% 15.08/2.82 | ALPHA: (40) implies:
% 15.08/2.82 | (41) the_carrier(all_31_1) = all_51_1
% 15.08/2.82 | (42) ~ lower_bounded_relstr(all_31_1) | (relstr_element_smaller(all_31_1,
% 15.08/2.82 | all_51_1, all_51_0) & element(all_51_0, all_51_1))
% 15.08/2.82 |
% 15.08/2.82 | DELTA: instantiating (28) with fresh symbol all_55_0 gives:
% 15.08/2.83 | (43) the_carrier(all_31_1) = all_55_0 & $i(all_55_0) & ! [v0: $i] : !
% 15.08/2.83 | [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 15.08/2.83 | relstr_element_smaller(all_31_1, v0, v1) | ~ element(v2, all_55_0)
% 15.08/2.83 | | ~ element(v1, all_55_0) | ~ in(v2, v0) | related(all_31_1, v1,
% 15.08/2.83 | v2)) & ? [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 15.08/2.83 | element(v1, all_55_0) | relstr_element_smaller(all_31_1, v0, v1) |
% 15.08/2.83 | ? [v2: $i] : ($i(v2) & element(v2, all_55_0) & in(v2, v0) & ~
% 15.08/2.83 | related(all_31_1, v1, v2)))
% 15.08/2.83 |
% 15.08/2.83 | ALPHA: (43) implies:
% 15.08/2.83 | (44) the_carrier(all_31_1) = all_55_0
% 15.08/2.83 |
% 15.08/2.83 | DELTA: instantiating (31) with fresh symbol all_61_0 gives:
% 15.08/2.83 | (45) the_carrier(all_31_1) = all_61_0 & $i(all_61_0) & ! [v0: $i] : !
% 15.08/2.83 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 15.08/2.83 | relstr_element_smaller(all_31_1, v0, v1) | ~ element(v1, all_61_0)
% 15.08/2.83 | | ex_inf_of_relstr_set(all_31_1, v0) | ? [v2: $i] : ($i(v2) &
% 15.08/2.83 | relstr_element_smaller(all_31_1, v0, v2) & element(v2, all_61_0) &
% 15.08/2.83 | ~ related(all_31_1, v2, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.08/2.83 | ex_inf_of_relstr_set(all_31_1, v0) | ? [v1: $i] : ($i(v1) &
% 15.08/2.83 | relstr_element_smaller(all_31_1, v0, v1) & element(v1, all_61_0) &
% 15.08/2.83 | ! [v2: $i] : ( ~ $i(v2) | ~ relstr_element_smaller(all_31_1, v0,
% 15.08/2.83 | v2) | ~ element(v2, all_61_0) | related(all_31_1, v2, v1))))
% 15.08/2.83 |
% 15.08/2.83 | ALPHA: (45) implies:
% 15.08/2.83 | (46) the_carrier(all_31_1) = all_61_0
% 15.08/2.83 |
% 15.08/2.83 | DELTA: instantiating (30) with fresh symbol all_64_0 gives:
% 15.08/2.83 | (47) the_carrier(all_31_1) = all_64_0 & $i(all_64_0) & ! [v0: $i] : !
% 15.08/2.83 | [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relstr_set_smaller(all_31_1,
% 15.08/2.83 | v0, v1) | ~ element(v1, all_64_0) |
% 15.08/2.83 | ex_sup_of_relstr_set(all_31_1, v0) | ? [v2: $i] : ($i(v2) &
% 15.08/2.83 | relstr_set_smaller(all_31_1, v0, v2) & element(v2, all_64_0) & ~
% 15.08/2.83 | related(all_31_1, v1, v2))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 15.08/2.83 | ex_sup_of_relstr_set(all_31_1, v0) | ? [v1: $i] : ($i(v1) &
% 15.08/2.83 | relstr_set_smaller(all_31_1, v0, v1) & element(v1, all_64_0) & !
% 15.08/2.83 | [v2: $i] : ( ~ $i(v2) | ~ relstr_set_smaller(all_31_1, v0, v2) |
% 15.08/2.83 | ~ element(v2, all_64_0) | related(all_31_1, v1, v2))))
% 15.08/2.83 |
% 15.08/2.83 | ALPHA: (47) implies:
% 15.08/2.83 | (48) the_carrier(all_31_1) = all_64_0
% 15.08/2.83 |
% 15.08/2.83 | REDUCE: (16), (25) imply:
% 15.08/2.83 | (49) $i(empty_set)
% 15.08/2.83 |
% 15.08/2.83 | BETA: splitting (42) gives:
% 15.08/2.83 |
% 15.08/2.83 | Case 1:
% 15.08/2.83 | |
% 15.08/2.83 | | (50) ~ lower_bounded_relstr(all_31_1)
% 15.08/2.83 | |
% 15.08/2.83 | | PRED_UNIFY: (20), (50) imply:
% 15.08/2.83 | | (51) $false
% 15.08/2.83 | |
% 15.08/2.83 | | CLOSE: (51) is inconsistent.
% 15.08/2.83 | |
% 15.08/2.83 | Case 2:
% 15.08/2.83 | |
% 15.08/2.83 | |
% 15.08/2.83 | | GROUND_INST: instantiating (function-axioms) with all_31_0, all_51_1,
% 15.08/2.83 | | all_31_1, simplifying with (23), (41) gives:
% 15.08/2.83 | | (52) all_51_1 = all_31_0
% 15.08/2.83 | |
% 15.08/2.83 | | GROUND_INST: instantiating (function-axioms) with all_51_1, all_55_0,
% 15.08/2.83 | | all_31_1, simplifying with (41), (44) gives:
% 15.08/2.83 | | (53) all_55_0 = all_51_1
% 15.08/2.83 | |
% 15.08/2.83 | | GROUND_INST: instantiating (function-axioms) with all_55_0, all_61_0,
% 15.08/2.83 | | all_31_1, simplifying with (44), (46) gives:
% 15.08/2.83 | | (54) all_61_0 = all_55_0
% 15.08/2.83 | |
% 15.08/2.83 | | GROUND_INST: instantiating (function-axioms) with all_61_0, all_64_0,
% 15.08/2.83 | | all_31_1, simplifying with (46), (48) gives:
% 15.08/2.83 | | (55) all_64_0 = all_61_0
% 15.08/2.83 | |
% 15.08/2.83 | | GROUND_INST: instantiating (function-axioms) with all_48_0, all_64_0,
% 15.08/2.83 | | all_31_1, simplifying with (39), (48) gives:
% 15.08/2.83 | | (56) all_64_0 = all_48_0
% 15.08/2.83 | |
% 15.08/2.83 | | COMBINE_EQS: (55), (56) imply:
% 15.08/2.83 | | (57) all_61_0 = all_48_0
% 15.08/2.83 | |
% 15.08/2.83 | | SIMP: (57) implies:
% 15.08/2.83 | | (58) all_61_0 = all_48_0
% 15.08/2.83 | |
% 15.08/2.84 | | COMBINE_EQS: (54), (58) imply:
% 15.08/2.84 | | (59) all_55_0 = all_48_0
% 15.08/2.84 | |
% 15.08/2.84 | | SIMP: (59) implies:
% 15.08/2.84 | | (60) all_55_0 = all_48_0
% 15.08/2.84 | |
% 15.08/2.84 | | COMBINE_EQS: (53), (60) imply:
% 15.08/2.84 | | (61) all_51_1 = all_48_0
% 15.08/2.84 | |
% 15.08/2.84 | | SIMP: (61) implies:
% 15.08/2.84 | | (62) all_51_1 = all_48_0
% 15.08/2.84 | |
% 15.08/2.84 | | COMBINE_EQS: (52), (62) imply:
% 15.08/2.84 | | (63) all_48_0 = all_31_0
% 15.08/2.84 | |
% 15.08/2.84 | | REDUCE: (38), (63) imply:
% 15.08/2.84 | | (64) $i(all_31_0)
% 15.08/2.84 | |
% 15.08/2.84 | | GROUND_INST: instantiating (12) with all_31_1, all_31_0, all_41_0,
% 15.08/2.84 | | simplifying with (19), (22), (23), (34), (36) gives:
% 15.08/2.84 | | (65) relstr_set_smaller(all_31_1, empty_set, all_41_0)
% 15.08/2.84 | |
% 15.08/2.84 | | GROUND_INST: instantiating (t2_subset) with all_41_0, all_31_0, simplifying
% 15.08/2.84 | | with (34), (36), (64) gives:
% 15.08/2.84 | | (66) empty(all_31_0) | in(all_41_0, all_31_0)
% 15.08/2.84 | |
% 15.08/2.84 | | GROUND_INST: instantiating (9) with all_31_1, all_31_0, all_31_0, all_41_0,
% 15.08/2.84 | | simplifying with (19), (21), (22), (23), (34), (35), (36), (64)
% 15.08/2.84 | | gives:
% 15.08/2.84 | | (67) ex_inf_of_relstr_set(all_31_1, all_31_0) | ? [v0: $i] : ($i(v0) &
% 15.08/2.84 | | relstr_element_smaller(all_31_1, all_31_0, v0) & element(v0,
% 15.08/2.84 | | all_31_0) & ~ related(all_31_1, v0, all_41_0))
% 15.08/2.84 | |
% 15.08/2.84 | | GROUND_INST: instantiating (5) with all_31_1, simplifying with (18), (22),
% 15.08/2.84 | | (26) gives:
% 15.08/2.84 | | (68) ? [v0: $i] : (the_carrier(all_31_1) = v0 & $i(v0) & ~ empty(v0))
% 15.08/2.84 | |
% 15.08/2.84 | | DELTA: instantiating (68) with fresh symbol all_85_0 gives:
% 15.08/2.84 | | (69) the_carrier(all_31_1) = all_85_0 & $i(all_85_0) & ~ empty(all_85_0)
% 15.08/2.84 | |
% 15.08/2.84 | | ALPHA: (69) implies:
% 15.08/2.84 | | (70) ~ empty(all_85_0)
% 15.08/2.84 | | (71) $i(all_85_0)
% 15.08/2.84 | | (72) the_carrier(all_31_1) = all_85_0
% 15.08/2.84 | |
% 15.08/2.84 | | GROUND_INST: instantiating (function-axioms) with all_31_0, all_85_0,
% 15.08/2.84 | | all_31_1, simplifying with (23), (72) gives:
% 15.08/2.84 | | (73) all_85_0 = all_31_0
% 15.08/2.84 | |
% 15.08/2.84 | | REDUCE: (70), (73) imply:
% 15.08/2.84 | | (74) ~ empty(all_31_0)
% 15.08/2.84 | |
% 15.08/2.84 | | BETA: splitting (66) gives:
% 15.08/2.84 | |
% 15.08/2.84 | | Case 1:
% 15.08/2.84 | | |
% 15.08/2.84 | | | (75) empty(all_31_0)
% 15.08/2.84 | | |
% 15.08/2.84 | | | PRED_UNIFY: (74), (75) imply:
% 15.08/2.84 | | | (76) $false
% 15.08/2.84 | | |
% 15.08/2.84 | | | CLOSE: (76) is inconsistent.
% 15.08/2.84 | | |
% 15.08/2.84 | | Case 2:
% 15.08/2.84 | | |
% 15.08/2.84 | | | (77) in(all_41_0, all_31_0)
% 15.08/2.84 | | |
% 15.08/2.84 | | | GROUND_INST: instantiating (7) with all_31_1, all_31_0, empty_set,
% 15.08/2.84 | | | all_41_0, simplifying with (19), (21), (22), (23), (34),
% 15.08/2.84 | | | (36), (49), (65) gives:
% 15.08/2.84 | | | (78) ex_sup_of_relstr_set(all_31_1, empty_set) | ? [v0: $i] : ($i(v0)
% 15.08/2.84 | | | & relstr_set_smaller(all_31_1, empty_set, v0) & element(v0,
% 15.08/2.84 | | | all_31_0) & ~ related(all_31_1, all_41_0, v0))
% 15.08/2.84 | | |
% 15.08/2.84 | | | BETA: splitting (24) gives:
% 15.08/2.84 | | |
% 15.08/2.84 | | | Case 1:
% 15.08/2.84 | | | |
% 15.08/2.84 | | | | (79) ~ ex_sup_of_relstr_set(all_31_1, empty_set)
% 15.08/2.84 | | | |
% 15.08/2.84 | | | | BETA: splitting (78) gives:
% 15.08/2.84 | | | |
% 15.08/2.84 | | | | Case 1:
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | (80) ex_sup_of_relstr_set(all_31_1, empty_set)
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | PRED_UNIFY: (79), (80) imply:
% 15.08/2.84 | | | | | (81) $false
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | CLOSE: (81) is inconsistent.
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | Case 2:
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | (82) ? [v0: $i] : ($i(v0) & relstr_set_smaller(all_31_1,
% 15.08/2.84 | | | | | empty_set, v0) & element(v0, all_31_0) & ~
% 15.08/2.84 | | | | | related(all_31_1, all_41_0, v0))
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | DELTA: instantiating (82) with fresh symbol all_121_0 gives:
% 15.08/2.84 | | | | | (83) $i(all_121_0) & relstr_set_smaller(all_31_1, empty_set,
% 15.08/2.84 | | | | | all_121_0) & element(all_121_0, all_31_0) & ~
% 15.08/2.84 | | | | | related(all_31_1, all_41_0, all_121_0)
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | ALPHA: (83) implies:
% 15.08/2.84 | | | | | (84) ~ related(all_31_1, all_41_0, all_121_0)
% 15.08/2.84 | | | | | (85) element(all_121_0, all_31_0)
% 15.08/2.84 | | | | | (86) $i(all_121_0)
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | GROUND_INST: instantiating (t2_subset) with all_121_0, all_31_0,
% 15.08/2.84 | | | | | simplifying with (64), (74), (85), (86) gives:
% 15.08/2.84 | | | | | (87) in(all_121_0, all_31_0)
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | GROUND_INST: instantiating (4) with all_31_1, all_31_0, all_31_0,
% 15.08/2.84 | | | | | all_41_0, all_121_0, simplifying with (19), (22), (23),
% 15.08/2.84 | | | | | (34), (35), (36), (64), (84), (85), (86), (87) gives:
% 15.08/2.84 | | | | | (88) $false
% 15.08/2.84 | | | | |
% 15.08/2.84 | | | | | CLOSE: (88) is inconsistent.
% 15.08/2.84 | | | | |
% 15.08/2.85 | | | | End of split
% 15.08/2.85 | | | |
% 15.08/2.85 | | | Case 2:
% 15.08/2.85 | | | |
% 15.08/2.85 | | | | (89) ~ ex_inf_of_relstr_set(all_31_1, all_31_0)
% 15.08/2.85 | | | |
% 15.08/2.85 | | | | BETA: splitting (67) gives:
% 15.08/2.85 | | | |
% 15.08/2.85 | | | | Case 1:
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | (90) ex_inf_of_relstr_set(all_31_1, all_31_0)
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | PRED_UNIFY: (89), (90) imply:
% 15.08/2.85 | | | | | (91) $false
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | CLOSE: (91) is inconsistent.
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | Case 2:
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | (92) ? [v0: $i] : ($i(v0) & relstr_element_smaller(all_31_1,
% 15.08/2.85 | | | | | all_31_0, v0) & element(v0, all_31_0) & ~
% 15.08/2.85 | | | | | related(all_31_1, v0, all_41_0))
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | DELTA: instantiating (92) with fresh symbol all_121_0 gives:
% 15.08/2.85 | | | | | (93) $i(all_121_0) & relstr_element_smaller(all_31_1, all_31_0,
% 15.08/2.85 | | | | | all_121_0) & element(all_121_0, all_31_0) & ~
% 15.08/2.85 | | | | | related(all_31_1, all_121_0, all_41_0)
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | ALPHA: (93) implies:
% 15.08/2.85 | | | | | (94) ~ related(all_31_1, all_121_0, all_41_0)
% 15.08/2.85 | | | | | (95) element(all_121_0, all_31_0)
% 15.08/2.85 | | | | | (96) relstr_element_smaller(all_31_1, all_31_0, all_121_0)
% 15.08/2.85 | | | | | (97) $i(all_121_0)
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | GROUND_INST: instantiating (4) with all_31_1, all_31_0, all_31_0,
% 15.08/2.85 | | | | | all_121_0, all_41_0, simplifying with (19), (22), (23),
% 15.08/2.85 | | | | | (34), (36), (64), (77), (94), (95), (96), (97) gives:
% 15.08/2.85 | | | | | (98) $false
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | | CLOSE: (98) is inconsistent.
% 15.08/2.85 | | | | |
% 15.08/2.85 | | | | End of split
% 15.08/2.85 | | | |
% 15.08/2.85 | | | End of split
% 15.08/2.85 | | |
% 15.08/2.85 | | End of split
% 15.08/2.85 | |
% 15.08/2.85 | End of split
% 15.08/2.85 |
% 15.08/2.85 End of proof
% 15.08/2.85 % SZS output end Proof for theBenchmark
% 15.08/2.85
% 15.08/2.85 2233ms
%------------------------------------------------------------------------------