TSTP Solution File: NUM401+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM401+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 : n031.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 11:47:35 EDT 2023
% Result : Theorem 59.73s 8.63s
% Output : Proof 60.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n031.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 : Fri Aug 25 15:54:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.97/1.10 Prover 4: Preprocessing ...
% 2.97/1.11 Prover 1: Preprocessing ...
% 3.39/1.14 Prover 6: Preprocessing ...
% 3.39/1.15 Prover 2: Preprocessing ...
% 3.39/1.15 Prover 0: Preprocessing ...
% 3.39/1.15 Prover 5: Preprocessing ...
% 3.53/1.16 Prover 3: Preprocessing ...
% 7.03/1.71 Prover 1: Warning: ignoring some quantifiers
% 7.03/1.71 Prover 5: Proving ...
% 7.74/1.76 Prover 1: Constructing countermodel ...
% 7.74/1.78 Prover 2: Proving ...
% 7.74/1.79 Prover 3: Warning: ignoring some quantifiers
% 7.74/1.80 Prover 6: Proving ...
% 7.74/1.82 Prover 3: Constructing countermodel ...
% 7.74/1.83 Prover 4: Warning: ignoring some quantifiers
% 8.65/1.90 Prover 4: Constructing countermodel ...
% 8.65/1.92 Prover 0: Proving ...
% 15.03/2.76 Prover 3: gave up
% 15.03/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.03/2.81 Prover 7: Preprocessing ...
% 16.45/2.95 Prover 7: Warning: ignoring some quantifiers
% 16.45/2.96 Prover 7: Constructing countermodel ...
% 27.00/4.33 Prover 1: gave up
% 27.13/4.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.13/4.41 Prover 8: Preprocessing ...
% 28.11/4.59 Prover 8: Warning: ignoring some quantifiers
% 28.11/4.60 Prover 8: Constructing countermodel ...
% 35.42/5.50 Prover 8: gave up
% 36.08/5.51 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 36.08/5.56 Prover 9: Preprocessing ...
% 37.80/5.77 Prover 9: Warning: ignoring some quantifiers
% 37.80/5.77 Prover 9: Constructing countermodel ...
% 58.53/8.55 Prover 7: Found proof (size 154)
% 58.53/8.55 Prover 7: proved (5780ms)
% 58.53/8.56 Prover 2: stopped
% 58.53/8.56 Prover 6: stopped
% 58.53/8.56 Prover 4: stopped
% 58.53/8.57 Prover 0: stopped
% 58.53/8.57 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 58.53/8.57 Prover 5: stopped
% 59.73/8.60 Prover 10: Preprocessing ...
% 59.73/8.61 Prover 10: stopped
% 59.73/8.63 Prover 9: stopped
% 59.73/8.63
% 59.73/8.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.73/8.63
% 59.73/8.64 % SZS output start Proof for theBenchmark
% 59.73/8.65 Assumptions after simplification:
% 59.73/8.65 ---------------------------------
% 59.73/8.65
% 59.73/8.65 (cc1_ordinal1)
% 59.73/8.65 ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0:
% 59.73/8.65 $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 59.73/8.65
% 59.73/8.65 (commutativity_k2_xboole_0)
% 60.15/8.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~
% 60.15/8.67 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 60.15/8.67 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 60.15/8.67 | (set_union2(v1, v0) = v2 & $i(v2)))
% 60.15/8.67
% 60.15/8.68 (connectedness_r1_ordinal1)
% 60.15/8.68 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal(v1) | ~
% 60.15/8.68 ordinal(v0) | ordinal_subset(v1, v0) | ordinal_subset(v0, v1))
% 60.15/8.68
% 60.15/8.68 (d10_xboole_0)
% 60.15/8.68 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v1,
% 60.15/8.68 v0) | ~ subset(v0, v1)) & ? [v0: $i] : ( ~ $i(v0) | subset(v0, v0))
% 60.15/8.68
% 60.15/8.68 (d1_ordinal1)
% 60.15/8.68 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 60.15/8.68 (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) & $i(v1))) & ! [v0:
% 60.15/8.68 $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 60.15/8.68 (succ(v0) = v2 & set_union2(v0, v1) = v2 & $i(v2)))
% 60.15/8.68
% 60.15/8.68 (d1_tarski)
% 60.15/8.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) |
% 60.15/8.68 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1)) & ? [v0: $i] : ! [v1:
% 60.15/8.68 $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~
% 60.15/8.68 $i(v0) | ? [v3: $i] : ($i(v3) & ( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 |
% 60.15/8.68 in(v3, v0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) |
% 60.15/8.68 ~ $i(v1) | ~ $i(v0) | in(v0, v1))
% 60.15/8.68
% 60.15/8.68 (d2_ordinal1)
% 60.15/8.68 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0)
% 60.15/8.68 | ~ in(v1, v0) | subset(v1, v0)) & ? [v0: $i] : ( ~ $i(v0) |
% 60.15/8.68 epsilon_transitive(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0) & ~ subset(v1,
% 60.15/8.68 v0)))
% 60.15/8.68
% 60.15/8.68 (d2_xboole_0)
% 60.15/8.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0,
% 60.15/8.69 v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3,
% 60.15/8.69 v2) | in(v3, v1) | in(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 60.15/8.69 ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 60.15/8.69 $i(v1) | ~ $i(v0) | ~ in(v3, v1) | in(v3, v2)) & ! [v0: $i] : ! [v1: $i]
% 60.15/8.69 : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v3) | ~
% 60.15/8.69 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v3, v0) | in(v3, v2)) & ? [v0: $i] :
% 60.15/8.69 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_union2(v1, v2) =
% 60.15/8.69 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 60.15/8.69 in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1)
% 60.15/8.69 | in(v4, v0))))
% 60.15/8.69
% 60.15/8.69 (fc2_ordinal1)
% 60.15/8.69 $i(empty_set) & relation_empty_yielding(empty_set) & one_to_one(empty_set) &
% 60.15/8.69 relation(empty_set) & epsilon_connected(empty_set) &
% 60.15/8.69 epsilon_transitive(empty_set) & ordinal(empty_set) & function(empty_set) &
% 60.15/8.69 empty(empty_set)
% 60.15/8.69
% 60.15/8.69 (rc1_ordinal1)
% 60.15/8.69 ? [v0: $i] : ($i(v0) & epsilon_connected(v0) & epsilon_transitive(v0) &
% 60.15/8.69 ordinal(v0))
% 60.15/8.69
% 60.15/8.69 (rc1_relat_1)
% 60.15/8.69 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0))
% 60.15/8.69
% 60.15/8.69 (rc1_xboole_0)
% 60.15/8.69 ? [v0: $i] : ($i(v0) & empty(v0))
% 60.15/8.69
% 60.15/8.69 (rc2_funct_1)
% 60.15/8.69 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0) & empty(v0))
% 60.15/8.69
% 60.15/8.69 (rc2_ordinal1)
% 60.15/8.69 ? [v0: $i] : ($i(v0) & one_to_one(v0) & relation(v0) & epsilon_connected(v0)
% 60.15/8.69 & epsilon_transitive(v0) & ordinal(v0) & function(v0) & empty(v0))
% 60.15/8.69
% 60.15/8.69 (rc3_ordinal1)
% 60.15/8.69 ? [v0: $i] : ($i(v0) & epsilon_connected(v0) & epsilon_transitive(v0) &
% 60.15/8.69 ordinal(v0) & ~ empty(v0))
% 60.15/8.69
% 60.15/8.69 (redefinition_r1_ordinal1)
% 60.15/8.69 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) | ~
% 60.15/8.69 ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1)) & ! [v0: $i] : !
% 60.15/8.69 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal_subset(v0, v1) | ~ ordinal(v1)
% 60.15/8.69 | ~ ordinal(v0) | subset(v0, v1))
% 60.15/8.69
% 60.15/8.69 (reflexivity_r1_ordinal1)
% 60.15/8.69 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ ordinal(v1) | ~
% 60.15/8.69 ordinal(v0) | ordinal_subset(v0, v0))
% 60.15/8.69
% 60.15/8.69 (t10_ordinal1)
% 60.15/8.69 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | in(v0, v1))
% 60.15/8.69
% 60.15/8.69 (t24_ordinal1)
% 60.15/8.69 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ ordinal(v1)
% 60.15/8.69 | ~ ordinal(v0) | in(v1, v0) | in(v0, v1))
% 60.15/8.69
% 60.27/8.70 (t34_ordinal1)
% 60.27/8.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v1) = v2 & $i(v2) & $i(v1) &
% 60.27/8.70 $i(v0) & ordinal(v1) & ordinal(v0) & ((ordinal_subset(v0, v1) & ~ in(v0,
% 60.27/8.70 v2)) | (in(v0, v2) & ~ ordinal_subset(v0, v1))))
% 60.27/8.70
% 60.27/8.70 (t6_boole)
% 60.27/8.70 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 60.27/8.70
% 60.27/8.70 (t7_boole)
% 60.27/8.70 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | ~ in(v0,
% 60.27/8.70 v1))
% 60.27/8.70
% 60.27/8.70 (t8_boole)
% 60.27/8.70 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) |
% 60.27/8.70 ~ empty(v0))
% 60.27/8.70
% 60.27/8.70 Further assumptions not needed in the proof:
% 60.27/8.70 --------------------------------------------
% 60.27/8.70 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, cc2_ordinal1,
% 60.27/8.70 cc3_ordinal1, existence_m1_subset_1, fc12_relat_1, fc1_ordinal1, fc1_xboole_0,
% 60.27/8.70 fc2_relat_1, fc2_xboole_0, fc3_ordinal1, fc3_xboole_0, fc4_relat_1,
% 60.27/8.70 idempotence_k2_xboole_0, rc1_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1,
% 60.27/8.70 rc3_relat_1, rc4_funct_1, rc5_funct_1, reflexivity_r1_tarski, t14_ordinal1,
% 60.27/8.70 t1_boole, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset
% 60.27/8.70
% 60.27/8.70 Those formulas are unsatisfiable:
% 60.27/8.70 ---------------------------------
% 60.27/8.70
% 60.27/8.70 Begin of proof
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (cc1_ordinal1) implies:
% 60.27/8.70 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0))
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (commutativity_k2_xboole_0) implies:
% 60.27/8.70 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2)
% 60.27/8.70 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2)))
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (d10_xboole_0) implies:
% 60.27/8.70 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 60.27/8.70 | subset(v1, v0) | ~ subset(v0, v1))
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (d1_ordinal1) implies:
% 60.27/8.70 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | ? [v2:
% 60.27/8.70 | $i] : (singleton(v0) = v2 & set_union2(v0, v2) = v1 & $i(v2) &
% 60.27/8.70 | $i(v1)))
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (d1_tarski) implies:
% 60.27/8.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0)
% 60.27/8.70 | = v1) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v2, v1))
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (d2_ordinal1) implies:
% 60.27/8.70 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 60.27/8.70 | epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0))
% 60.27/8.70 |
% 60.27/8.70 | ALPHA: (d2_xboole_0) implies:
% 60.27/8.71 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 60.27/8.71 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 60.27/8.71 | $i(v0) | ~ in(v3, v0) | in(v3, v2))
% 60.27/8.71 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 60.27/8.71 | (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 60.27/8.71 | $i(v0) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (fc2_ordinal1) implies:
% 60.27/8.71 | (9) ordinal(empty_set)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (redefinition_r1_ordinal1) implies:
% 60.27/8.71 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 60.27/8.71 | ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) |
% 60.27/8.71 | subset(v0, v1))
% 60.27/8.71 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1)
% 60.27/8.71 | | ~ ordinal(v1) | ~ ordinal(v0) | ordinal_subset(v0, v1))
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (t6_boole) implies:
% 60.27/8.71 | (12) $i(empty_set)
% 60.27/8.71 | (13) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_38_0 gives:
% 60.27/8.71 | (14) $i(all_38_0) & empty(all_38_0)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (14) implies:
% 60.27/8.71 | (15) empty(all_38_0)
% 60.27/8.71 | (16) $i(all_38_0)
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_44_0 gives:
% 60.27/8.71 | (17) $i(all_44_0) & relation(all_44_0) & empty(all_44_0)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (17) implies:
% 60.27/8.71 | (18) empty(all_44_0)
% 60.27/8.71 | (19) $i(all_44_0)
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_53_0 gives:
% 60.27/8.71 | (20) $i(all_53_0) & relation(all_53_0) & function(all_53_0) &
% 60.27/8.71 | empty(all_53_0)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (20) implies:
% 60.27/8.71 | (21) empty(all_53_0)
% 60.27/8.71 | (22) $i(all_53_0)
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (rc1_ordinal1) with fresh symbol all_57_0 gives:
% 60.27/8.71 | (23) $i(all_57_0) & epsilon_connected(all_57_0) &
% 60.27/8.71 | epsilon_transitive(all_57_0) & ordinal(all_57_0)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (23) implies:
% 60.27/8.71 | (24) ordinal(all_57_0)
% 60.27/8.71 | (25) $i(all_57_0)
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (rc3_ordinal1) with fresh symbol all_63_0 gives:
% 60.27/8.71 | (26) $i(all_63_0) & epsilon_connected(all_63_0) &
% 60.27/8.71 | epsilon_transitive(all_63_0) & ordinal(all_63_0) & ~ empty(all_63_0)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (26) implies:
% 60.27/8.71 | (27) ordinal(all_63_0)
% 60.27/8.71 | (28) epsilon_transitive(all_63_0)
% 60.27/8.71 | (29) $i(all_63_0)
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (rc2_ordinal1) with fresh symbol all_66_0 gives:
% 60.27/8.71 | (30) $i(all_66_0) & one_to_one(all_66_0) & relation(all_66_0) &
% 60.27/8.71 | epsilon_connected(all_66_0) & epsilon_transitive(all_66_0) &
% 60.27/8.71 | ordinal(all_66_0) & function(all_66_0) & empty(all_66_0)
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (30) implies:
% 60.27/8.71 | (31) empty(all_66_0)
% 60.27/8.71 | (32) $i(all_66_0)
% 60.27/8.71 |
% 60.27/8.71 | DELTA: instantiating (t34_ordinal1) with fresh symbols all_70_0, all_70_1,
% 60.27/8.71 | all_70_2 gives:
% 60.27/8.71 | (33) succ(all_70_1) = all_70_0 & $i(all_70_0) & $i(all_70_1) & $i(all_70_2)
% 60.27/8.71 | & ordinal(all_70_1) & ordinal(all_70_2) & ((ordinal_subset(all_70_2,
% 60.27/8.71 | all_70_1) & ~ in(all_70_2, all_70_0)) | (in(all_70_2, all_70_0)
% 60.27/8.71 | & ~ ordinal_subset(all_70_2, all_70_1)))
% 60.27/8.71 |
% 60.27/8.71 | ALPHA: (33) implies:
% 60.27/8.71 | (34) ordinal(all_70_2)
% 60.27/8.71 | (35) ordinal(all_70_1)
% 60.27/8.71 | (36) $i(all_70_2)
% 60.27/8.71 | (37) $i(all_70_1)
% 60.27/8.71 | (38) succ(all_70_1) = all_70_0
% 60.27/8.71 | (39) (ordinal_subset(all_70_2, all_70_1) & ~ in(all_70_2, all_70_0)) |
% 60.27/8.71 | (in(all_70_2, all_70_0) & ~ ordinal_subset(all_70_2, all_70_1))
% 60.27/8.71 |
% 60.27/8.72 | GROUND_INST: instantiating (t8_boole) with all_44_0, all_53_0, simplifying
% 60.27/8.72 | with (18), (19), (21), (22) gives:
% 60.27/8.72 | (40) all_53_0 = all_44_0
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (t8_boole) with all_38_0, all_53_0, simplifying
% 60.27/8.72 | with (15), (16), (21), (22) gives:
% 60.27/8.72 | (41) all_53_0 = all_38_0
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (t8_boole) with all_53_0, all_66_0, simplifying
% 60.27/8.72 | with (21), (22), (31), (32) gives:
% 60.27/8.72 | (42) all_66_0 = all_53_0
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (13) with all_66_0, simplifying with (31), (32)
% 60.27/8.72 | gives:
% 60.27/8.72 | (43) all_66_0 = empty_set
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (t24_ordinal1) with empty_set, all_57_0,
% 60.27/8.72 | simplifying with (9), (12), (24), (25) gives:
% 60.27/8.72 | (44) all_57_0 = empty_set | in(all_57_0, empty_set) | in(empty_set,
% 60.27/8.72 | all_57_0)
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (1) with all_70_2, simplifying with (34), (36)
% 60.27/8.72 | gives:
% 60.27/8.72 | (45) epsilon_transitive(all_70_2)
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (t24_ordinal1) with all_70_2, all_70_1, simplifying
% 60.27/8.72 | with (34), (35), (36), (37) gives:
% 60.27/8.72 | (46) all_70_1 = all_70_2 | in(all_70_1, all_70_2) | in(all_70_2, all_70_1)
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (connectedness_r1_ordinal1) with all_70_2,
% 60.27/8.72 | all_70_1, simplifying with (34), (35), (36), (37) gives:
% 60.27/8.72 | (47) ordinal_subset(all_70_1, all_70_2) | ordinal_subset(all_70_2,
% 60.27/8.72 | all_70_1)
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (t24_ordinal1) with all_63_0, all_70_1, simplifying
% 60.27/8.72 | with (27), (29), (35), (37) gives:
% 60.27/8.72 | (48) all_70_1 = all_63_0 | in(all_70_1, all_63_0) | in(all_63_0, all_70_1)
% 60.27/8.72 |
% 60.27/8.72 | GROUND_INST: instantiating (connectedness_r1_ordinal1) with all_63_0,
% 60.40/8.72 | all_70_1, simplifying with (27), (29), (35), (37) gives:
% 60.40/8.72 | (49) ordinal_subset(all_70_1, all_63_0) | ordinal_subset(all_63_0,
% 60.40/8.72 | all_70_1)
% 60.40/8.72 |
% 60.40/8.72 | GROUND_INST: instantiating (reflexivity_r1_ordinal1) with all_70_1, empty_set,
% 60.40/8.72 | simplifying with (9), (12), (35), (37) gives:
% 60.40/8.72 | (50) ordinal_subset(all_70_1, all_70_1)
% 60.40/8.72 |
% 60.40/8.72 | GROUND_INST: instantiating (1) with all_70_1, simplifying with (35), (37)
% 60.40/8.72 | gives:
% 60.40/8.72 | (51) epsilon_transitive(all_70_1)
% 60.40/8.72 |
% 60.40/8.72 | GROUND_INST: instantiating (t10_ordinal1) with all_70_1, all_70_0, simplifying
% 60.40/8.72 | with (37), (38) gives:
% 60.40/8.72 | (52) in(all_70_1, all_70_0)
% 60.40/8.72 |
% 60.40/8.72 | GROUND_INST: instantiating (4) with all_70_1, all_70_0, simplifying with (37),
% 60.40/8.72 | (38) gives:
% 60.40/8.72 | (53) ? [v0: $i] : (singleton(all_70_1) = v0 & set_union2(all_70_1, v0) =
% 60.40/8.72 | all_70_0 & $i(v0) & $i(all_70_0))
% 60.40/8.72 |
% 60.40/8.72 | COMBINE_EQS: (42), (43) imply:
% 60.40/8.72 | (54) all_53_0 = empty_set
% 60.40/8.72 |
% 60.40/8.72 | SIMP: (54) implies:
% 60.40/8.72 | (55) all_53_0 = empty_set
% 60.40/8.72 |
% 60.40/8.72 | COMBINE_EQS: (40), (55) imply:
% 60.40/8.72 | (56) all_44_0 = empty_set
% 60.40/8.72 |
% 60.40/8.72 | COMBINE_EQS: (40), (41) imply:
% 60.40/8.72 | (57) all_44_0 = all_38_0
% 60.40/8.72 |
% 60.40/8.72 | COMBINE_EQS: (56), (57) imply:
% 60.40/8.72 | (58) all_38_0 = empty_set
% 60.40/8.72 |
% 60.40/8.72 | SIMP: (58) implies:
% 60.40/8.72 | (59) all_38_0 = empty_set
% 60.40/8.72 |
% 60.40/8.72 | DELTA: instantiating (53) with fresh symbol all_84_0 gives:
% 60.40/8.72 | (60) singleton(all_70_1) = all_84_0 & set_union2(all_70_1, all_84_0) =
% 60.40/8.72 | all_70_0 & $i(all_84_0) & $i(all_70_0)
% 60.40/8.72 |
% 60.40/8.72 | ALPHA: (60) implies:
% 60.40/8.72 | (61) $i(all_84_0)
% 60.40/8.73 | (62) set_union2(all_70_1, all_84_0) = all_70_0
% 60.40/8.73 | (63) singleton(all_70_1) = all_84_0
% 60.40/8.73 |
% 60.40/8.73 | REDUCE: (15), (59) imply:
% 60.40/8.73 | (64) empty(empty_set)
% 60.40/8.73 |
% 60.40/8.73 | GROUND_INST: instantiating (6) with all_63_0, all_70_1, simplifying with (28),
% 60.40/8.73 | (29), (37) gives:
% 60.40/8.73 | (65) ~ in(all_70_1, all_63_0) | subset(all_70_1, all_63_0)
% 60.40/8.73 |
% 60.40/8.73 | GROUND_INST: instantiating (6) with all_70_2, all_70_1, simplifying with (36),
% 60.40/8.73 | (37), (45) gives:
% 60.40/8.73 | (66) ~ in(all_70_1, all_70_2) | subset(all_70_1, all_70_2)
% 60.40/8.73 |
% 60.40/8.73 | GROUND_INST: instantiating (2) with all_84_0, all_70_1, all_70_0, simplifying
% 60.40/8.73 | with (37), (61), (62) gives:
% 60.40/8.73 | (67) set_union2(all_84_0, all_70_1) = all_70_0 & $i(all_70_0)
% 60.40/8.73 |
% 60.40/8.73 | ALPHA: (67) implies:
% 60.40/8.73 | (68) $i(all_70_0)
% 60.40/8.73 |
% 60.40/8.73 | GROUND_INST: instantiating (11) with all_70_1, all_63_0, simplifying with
% 60.40/8.73 | (27), (29), (35), (37) gives:
% 60.40/8.73 | (69) ~ subset(all_70_1, all_63_0) | ordinal_subset(all_70_1, all_63_0)
% 60.40/8.73 |
% 60.40/8.73 | GROUND_INST: instantiating (10) with all_70_1, all_70_2, simplifying with
% 60.40/8.73 | (34), (35), (36), (37) gives:
% 60.40/8.73 | (70) ~ ordinal_subset(all_70_1, all_70_2) | subset(all_70_1, all_70_2)
% 60.40/8.73 |
% 60.40/8.73 | GROUND_INST: instantiating (10) with all_70_1, all_63_0, simplifying with
% 60.40/8.73 | (27), (29), (35), (37) gives:
% 60.40/8.73 | (71) ~ ordinal_subset(all_70_1, all_63_0) | subset(all_70_1, all_63_0)
% 60.40/8.73 |
% 60.40/8.73 | BETA: splitting (39) gives:
% 60.40/8.73 |
% 60.40/8.73 | Case 1:
% 60.40/8.73 | |
% 60.40/8.73 | | (72) ordinal_subset(all_70_2, all_70_1) & ~ in(all_70_2, all_70_0)
% 60.40/8.73 | |
% 60.40/8.73 | | ALPHA: (72) implies:
% 60.40/8.73 | | (73) ~ in(all_70_2, all_70_0)
% 60.40/8.73 | | (74) ordinal_subset(all_70_2, all_70_1)
% 60.40/8.73 | |
% 60.40/8.73 | | PRED_UNIFY: (52), (73) imply:
% 60.40/8.73 | | (75) ~ (all_70_1 = all_70_2)
% 60.40/8.73 | |
% 60.40/8.73 | | BETA: splitting (49) gives:
% 60.40/8.73 | |
% 60.40/8.73 | | Case 1:
% 60.40/8.73 | | |
% 60.40/8.73 | | | (76) ordinal_subset(all_70_1, all_63_0)
% 60.40/8.73 | | |
% 60.40/8.73 | | | BETA: splitting (71) gives:
% 60.40/8.73 | | |
% 60.40/8.73 | | | Case 1:
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | (77) ~ ordinal_subset(all_70_1, all_63_0)
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | PRED_UNIFY: (76), (77) imply:
% 60.40/8.73 | | | | (78) $false
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | CLOSE: (78) is inconsistent.
% 60.40/8.73 | | | |
% 60.40/8.73 | | | Case 2:
% 60.40/8.73 | | | |
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | REF_CLOSE: (3), (7), (10), (34), (35), (36), (37), (46), (61), (62),
% 60.40/8.73 | | | | (66), (68), (73), (74), (75) are inconsistent by sub-proof
% 60.40/8.73 | | | | #1.
% 60.40/8.73 | | | |
% 60.40/8.73 | | | End of split
% 60.40/8.73 | | |
% 60.40/8.73 | | Case 2:
% 60.40/8.73 | | |
% 60.40/8.73 | | | (79) ~ ordinal_subset(all_70_1, all_63_0)
% 60.40/8.73 | | |
% 60.40/8.73 | | | BETA: splitting (69) gives:
% 60.40/8.73 | | |
% 60.40/8.73 | | | Case 1:
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | (80) ~ subset(all_70_1, all_63_0)
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | BETA: splitting (65) gives:
% 60.40/8.73 | | | |
% 60.40/8.73 | | | | Case 1:
% 60.40/8.73 | | | | |
% 60.40/8.73 | | | | | (81) ~ in(all_70_1, all_63_0)
% 60.40/8.73 | | | | |
% 60.40/8.73 | | | | | BETA: splitting (48) gives:
% 60.40/8.73 | | | | |
% 60.40/8.73 | | | | | Case 1:
% 60.40/8.73 | | | | | |
% 60.40/8.73 | | | | | | (82) in(all_70_1, all_63_0)
% 60.40/8.73 | | | | | |
% 60.40/8.73 | | | | | | PRED_UNIFY: (81), (82) imply:
% 60.40/8.73 | | | | | | (83) $false
% 60.40/8.73 | | | | | |
% 60.40/8.73 | | | | | | CLOSE: (83) is inconsistent.
% 60.40/8.73 | | | | | |
% 60.40/8.73 | | | | | Case 2:
% 60.40/8.73 | | | | | |
% 60.40/8.73 | | | | | |
% 60.40/8.74 | | | | | | REF_CLOSE: (3), (7), (10), (34), (35), (36), (37), (46), (61), (62),
% 60.40/8.74 | | | | | | (66), (68), (73), (74), (75) are inconsistent by
% 60.40/8.74 | | | | | | sub-proof #1.
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | End of split
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | Case 2:
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | (84) subset(all_70_1, all_63_0)
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | PRED_UNIFY: (80), (84) imply:
% 60.40/8.74 | | | | | (85) $false
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | CLOSE: (85) is inconsistent.
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | End of split
% 60.40/8.74 | | | |
% 60.40/8.74 | | | Case 2:
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | (86) ordinal_subset(all_70_1, all_63_0)
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | PRED_UNIFY: (79), (86) imply:
% 60.40/8.74 | | | | (87) $false
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | CLOSE: (87) is inconsistent.
% 60.40/8.74 | | | |
% 60.40/8.74 | | | End of split
% 60.40/8.74 | | |
% 60.40/8.74 | | End of split
% 60.40/8.74 | |
% 60.40/8.74 | Case 2:
% 60.40/8.74 | |
% 60.40/8.74 | | (88) in(all_70_2, all_70_0) & ~ ordinal_subset(all_70_2, all_70_1)
% 60.40/8.74 | |
% 60.40/8.74 | | ALPHA: (88) implies:
% 60.40/8.74 | | (89) ~ ordinal_subset(all_70_2, all_70_1)
% 60.40/8.74 | | (90) in(all_70_2, all_70_0)
% 60.40/8.74 | |
% 60.40/8.74 | | BETA: splitting (47) gives:
% 60.40/8.74 | |
% 60.40/8.74 | | Case 1:
% 60.40/8.74 | | |
% 60.40/8.74 | | | (91) ordinal_subset(all_70_1, all_70_2)
% 60.40/8.74 | | |
% 60.40/8.74 | | | BETA: splitting (70) gives:
% 60.40/8.74 | | |
% 60.40/8.74 | | | Case 1:
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | (92) ~ ordinal_subset(all_70_1, all_70_2)
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | PRED_UNIFY: (91), (92) imply:
% 60.40/8.74 | | | | (93) $false
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | CLOSE: (93) is inconsistent.
% 60.40/8.74 | | | |
% 60.40/8.74 | | | Case 2:
% 60.40/8.74 | | | |
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | PRED_UNIFY: (50), (89) imply:
% 60.40/8.74 | | | | (94) ~ (all_70_1 = all_70_2)
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | BETA: splitting (44) gives:
% 60.40/8.74 | | | |
% 60.40/8.74 | | | | Case 1:
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | (95) in(all_57_0, empty_set)
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | GROUND_INST: instantiating (t7_boole) with all_57_0, empty_set,
% 60.40/8.74 | | | | | simplifying with (12), (25), (64), (95) gives:
% 60.40/8.74 | | | | | (96) $false
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | CLOSE: (96) is inconsistent.
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | Case 2:
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | GROUND_INST: instantiating (8) with all_70_1, all_84_0, all_70_0,
% 60.40/8.74 | | | | | all_70_2, simplifying with (36), (37), (61), (62), (68),
% 60.40/8.74 | | | | | (90) gives:
% 60.40/8.74 | | | | | (97) in(all_70_2, all_84_0) | in(all_70_2, all_70_1)
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | BETA: splitting (46) gives:
% 60.40/8.74 | | | | |
% 60.40/8.74 | | | | | Case 1:
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | | (98) in(all_70_1, all_70_2)
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | | BETA: splitting (97) gives:
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | | Case 1:
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | (99) in(all_70_2, all_84_0)
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | GROUND_INST: instantiating (5) with all_70_1, all_84_0, all_70_2,
% 60.40/8.74 | | | | | | | simplifying with (36), (37), (61), (63), (99) gives:
% 60.40/8.74 | | | | | | | (100) all_70_1 = all_70_2
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | REDUCE: (94), (100) imply:
% 60.40/8.74 | | | | | | | (101) $false
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | CLOSE: (101) is inconsistent.
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | Case 2:
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | (102) in(all_70_2, all_70_1)
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | GROUND_INST: instantiating (6) with all_70_1, all_70_2,
% 60.40/8.74 | | | | | | | simplifying with (36), (37), (51), (102) gives:
% 60.40/8.74 | | | | | | | (103) subset(all_70_2, all_70_1)
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | REF_CLOSE: (3), (36), (37), (66), (94), (98), (103) are
% 60.40/8.74 | | | | | | | inconsistent by sub-proof #2.
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | End of split
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | Case 2:
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | | (104) all_70_1 = all_70_2 | in(all_70_2, all_70_1)
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | | BETA: splitting (104) gives:
% 60.40/8.74 | | | | | |
% 60.40/8.74 | | | | | | Case 1:
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | (105) in(all_70_2, all_70_1)
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | GROUND_INST: instantiating (6) with all_70_1, all_70_2,
% 60.40/8.74 | | | | | | | simplifying with (36), (37), (51), (105) gives:
% 60.40/8.74 | | | | | | | (106) subset(all_70_2, all_70_1)
% 60.40/8.74 | | | | | | |
% 60.40/8.74 | | | | | | | GROUND_INST: instantiating (11) with all_70_2, all_70_1,
% 60.40/8.75 | | | | | | | simplifying with (34), (35), (36), (37), (89), (106)
% 60.40/8.75 | | | | | | | gives:
% 60.40/8.75 | | | | | | | (107) $false
% 60.40/8.75 | | | | | | |
% 60.40/8.75 | | | | | | | CLOSE: (107) is inconsistent.
% 60.40/8.75 | | | | | | |
% 60.40/8.75 | | | | | | Case 2:
% 60.40/8.75 | | | | | | |
% 60.40/8.75 | | | | | | | (108) all_70_1 = all_70_2
% 60.40/8.75 | | | | | | |
% 60.40/8.75 | | | | | | | REDUCE: (94), (108) imply:
% 60.40/8.75 | | | | | | | (109) $false
% 60.40/8.75 | | | | | | |
% 60.40/8.75 | | | | | | | CLOSE: (109) is inconsistent.
% 60.40/8.75 | | | | | | |
% 60.40/8.75 | | | | | | End of split
% 60.40/8.75 | | | | | |
% 60.40/8.75 | | | | | End of split
% 60.40/8.75 | | | | |
% 60.40/8.75 | | | | End of split
% 60.40/8.75 | | | |
% 60.40/8.75 | | | End of split
% 60.40/8.75 | | |
% 60.40/8.75 | | Case 2:
% 60.40/8.75 | | |
% 60.40/8.75 | | | (110) ordinal_subset(all_70_2, all_70_1)
% 60.40/8.75 | | |
% 60.40/8.75 | | | PRED_UNIFY: (89), (110) imply:
% 60.40/8.75 | | | (111) $false
% 60.40/8.75 | | |
% 60.40/8.75 | | | CLOSE: (111) is inconsistent.
% 60.40/8.75 | | |
% 60.40/8.75 | | End of split
% 60.40/8.75 | |
% 60.40/8.75 | End of split
% 60.40/8.75 |
% 60.40/8.75 End of proof
% 60.40/8.75
% 60.40/8.75 Sub-proof #1 shows that the following formulas are inconsistent:
% 60.40/8.75 ----------------------------------------------------------------
% 60.40/8.75 (1) ordinal(all_70_1)
% 60.40/8.75 (2) ~ in(all_70_2, all_70_0)
% 60.40/8.75 (3) $i(all_70_2)
% 60.40/8.75 (4) $i(all_70_0)
% 60.40/8.75 (5) ~ in(all_70_1, all_70_2) | subset(all_70_1, all_70_2)
% 60.40/8.75 (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 60.40/8.75 ordinal_subset(v0, v1) | ~ ordinal(v1) | ~ ordinal(v0) | subset(v0,
% 60.40/8.75 v1))
% 60.40/8.75 (7) all_70_1 = all_70_2 | in(all_70_1, all_70_2) | in(all_70_2, all_70_1)
% 60.40/8.75 (8) ordinal(all_70_2)
% 60.40/8.75 (9) set_union2(all_70_1, all_84_0) = all_70_0
% 60.40/8.75 (10) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 60.40/8.75 subset(v1, v0) | ~ subset(v0, v1))
% 60.40/8.75 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 60.40/8.75 (set_union2(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 60.40/8.75 $i(v0) | ~ in(v3, v0) | in(v3, v2))
% 60.40/8.75 (12) ordinal_subset(all_70_2, all_70_1)
% 60.40/8.75 (13) $i(all_84_0)
% 60.40/8.75 (14) $i(all_70_1)
% 60.40/8.75 (15) ~ (all_70_1 = all_70_2)
% 60.40/8.75
% 60.40/8.75 Begin of proof
% 60.40/8.75 |
% 60.40/8.75 | GROUND_INST: instantiating (6) with all_70_2, all_70_1, simplifying with (1),
% 60.40/8.75 | (3), (8), (12), (14) gives:
% 60.40/8.75 | (16) subset(all_70_2, all_70_1)
% 60.40/8.75 |
% 60.40/8.75 | BETA: splitting (7) gives:
% 60.40/8.75 |
% 60.40/8.75 | Case 1:
% 60.40/8.75 | |
% 60.40/8.75 | | (17) in(all_70_1, all_70_2)
% 60.40/8.75 | |
% 60.40/8.75 | | REF_CLOSE: (3), (5), (10), (14), (15), (16), (17) are inconsistent by
% 60.40/8.75 | | sub-proof #2.
% 60.40/8.75 | |
% 60.40/8.75 | Case 2:
% 60.40/8.75 | |
% 60.40/8.75 | | (18) all_70_1 = all_70_2 | in(all_70_2, all_70_1)
% 60.40/8.75 | |
% 60.40/8.75 | | BETA: splitting (18) gives:
% 60.40/8.75 | |
% 60.40/8.75 | | Case 1:
% 60.40/8.75 | | |
% 60.40/8.75 | | | (19) in(all_70_2, all_70_1)
% 60.40/8.75 | | |
% 60.40/8.75 | | | GROUND_INST: instantiating (11) with all_70_1, all_84_0, all_70_0,
% 60.40/8.75 | | | all_70_2, simplifying with (2), (3), (4), (9), (13), (14),
% 60.40/8.75 | | | (19) gives:
% 60.40/8.75 | | | (20) $false
% 60.40/8.75 | | |
% 60.40/8.75 | | | CLOSE: (20) is inconsistent.
% 60.40/8.75 | | |
% 60.40/8.75 | | Case 2:
% 60.40/8.75 | | |
% 60.40/8.75 | | | (21) all_70_1 = all_70_2
% 60.40/8.75 | | |
% 60.40/8.75 | | | REDUCE: (15), (21) imply:
% 60.40/8.75 | | | (22) $false
% 60.40/8.75 | | |
% 60.40/8.75 | | | CLOSE: (22) is inconsistent.
% 60.40/8.75 | | |
% 60.40/8.75 | | End of split
% 60.40/8.75 | |
% 60.40/8.75 | End of split
% 60.40/8.75 |
% 60.40/8.75 End of proof
% 60.40/8.75
% 60.40/8.75 Sub-proof #2 shows that the following formulas are inconsistent:
% 60.40/8.75 ----------------------------------------------------------------
% 60.40/8.75 (1) $i(all_70_2)
% 60.40/8.75 (2) ~ in(all_70_1, all_70_2) | subset(all_70_1, all_70_2)
% 60.40/8.75 (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 60.40/8.75 subset(v1, v0) | ~ subset(v0, v1))
% 60.40/8.75 (4) subset(all_70_2, all_70_1)
% 60.40/8.75 (5) $i(all_70_1)
% 60.40/8.75 (6) ~ (all_70_1 = all_70_2)
% 60.40/8.75 (7) in(all_70_1, all_70_2)
% 60.40/8.75
% 60.40/8.75 Begin of proof
% 60.40/8.75 |
% 60.40/8.75 | BETA: splitting (2) gives:
% 60.40/8.75 |
% 60.40/8.75 | Case 1:
% 60.40/8.75 | |
% 60.40/8.75 | | (8) ~ in(all_70_1, all_70_2)
% 60.40/8.75 | |
% 60.40/8.75 | | PRED_UNIFY: (7), (8) imply:
% 60.40/8.75 | | (9) $false
% 60.40/8.75 | |
% 60.40/8.75 | | CLOSE: (9) is inconsistent.
% 60.40/8.75 | |
% 60.40/8.75 | Case 2:
% 60.40/8.75 | |
% 60.40/8.75 | | (10) subset(all_70_1, all_70_2)
% 60.40/8.75 | |
% 60.40/8.75 | | GROUND_INST: instantiating (3) with all_70_2, all_70_1, simplifying with
% 60.40/8.75 | | (1), (4), (5), (10) gives:
% 60.40/8.76 | | (11) all_70_1 = all_70_2
% 60.40/8.76 | |
% 60.40/8.76 | | REDUCE: (6), (11) imply:
% 60.40/8.76 | | (12) $false
% 60.40/8.76 | |
% 60.40/8.76 | | CLOSE: (12) is inconsistent.
% 60.40/8.76 | |
% 60.40/8.76 | End of split
% 60.40/8.76 |
% 60.40/8.76 End of proof
% 60.40/8.76 % SZS output end Proof for theBenchmark
% 60.40/8.76
% 60.40/8.76 8140ms
%------------------------------------------------------------------------------