TSTP Solution File: SEU243+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU243+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 : n002.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 17:43:36 EDT 2023
% Result : Theorem 8.70s 2.13s
% Output : Proof 12.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU243+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:44:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 ________ _____
% 0.19/0.63 ___ __ \_________(_)________________________________
% 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.63
% 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.63 (2023-06-19)
% 0.19/0.63
% 0.19/0.63 (c) Philipp Rümmer, 2009-2023
% 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.63 Amanda Stjerna.
% 0.19/0.63 Free software under BSD-3-Clause.
% 0.19/0.63
% 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.63
% 0.19/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.37/1.06 Prover 1: Preprocessing ...
% 2.37/1.06 Prover 4: Preprocessing ...
% 2.99/1.10 Prover 6: Preprocessing ...
% 2.99/1.10 Prover 0: Preprocessing ...
% 2.99/1.10 Prover 5: Preprocessing ...
% 2.99/1.10 Prover 3: Preprocessing ...
% 2.99/1.10 Prover 2: Preprocessing ...
% 5.57/1.55 Prover 1: Warning: ignoring some quantifiers
% 5.57/1.56 Prover 3: Warning: ignoring some quantifiers
% 5.57/1.58 Prover 3: Constructing countermodel ...
% 5.57/1.59 Prover 2: Proving ...
% 6.37/1.59 Prover 5: Proving ...
% 6.42/1.60 Prover 1: Constructing countermodel ...
% 6.55/1.66 Prover 6: Proving ...
% 6.55/1.67 Prover 4: Warning: ignoring some quantifiers
% 7.13/1.71 Prover 4: Constructing countermodel ...
% 7.80/1.82 Prover 0: Proving ...
% 8.70/2.13 Prover 3: proved (1480ms)
% 8.70/2.13
% 8.70/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.70/2.13
% 8.70/2.14 Prover 2: stopped
% 8.70/2.14 Prover 0: stopped
% 8.70/2.14 Prover 5: stopped
% 8.70/2.14 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.70/2.14 Prover 6: stopped
% 10.33/2.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.33/2.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.33/2.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.33/2.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.33/2.19 Prover 11: Preprocessing ...
% 10.33/2.20 Prover 7: Preprocessing ...
% 10.33/2.21 Prover 10: Preprocessing ...
% 10.33/2.21 Prover 8: Preprocessing ...
% 10.33/2.21 Prover 13: Preprocessing ...
% 11.03/2.29 Prover 7: Warning: ignoring some quantifiers
% 11.03/2.31 Prover 7: Constructing countermodel ...
% 11.03/2.31 Prover 10: Warning: ignoring some quantifiers
% 11.03/2.32 Prover 10: Constructing countermodel ...
% 11.69/2.36 Prover 8: Warning: ignoring some quantifiers
% 11.69/2.37 Prover 13: Warning: ignoring some quantifiers
% 11.69/2.37 Prover 8: Constructing countermodel ...
% 11.69/2.38 Prover 13: Constructing countermodel ...
% 12.17/2.39 Prover 11: Warning: ignoring some quantifiers
% 12.17/2.40 Prover 1: Found proof (size 74)
% 12.17/2.40 Prover 1: proved (1754ms)
% 12.17/2.40 Prover 8: stopped
% 12.17/2.40 Prover 13: stopped
% 12.17/2.40 Prover 7: stopped
% 12.17/2.40 Prover 4: stopped
% 12.17/2.40 Prover 10: stopped
% 12.17/2.41 Prover 11: Constructing countermodel ...
% 12.17/2.42 Prover 11: stopped
% 12.17/2.42
% 12.17/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.17/2.42
% 12.17/2.43 % SZS output start Proof for theBenchmark
% 12.17/2.44 Assumptions after simplification:
% 12.17/2.44 ---------------------------------
% 12.17/2.44
% 12.17/2.44 (d2_wellord1)
% 12.57/2.47 $i(empty_set) & ! [v0: $i] : ! [v1: any] : ( ~ (well_founded_relation(v0) =
% 12.57/2.47 v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_field(v0) = v3 &
% 12.57/2.47 relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4: $i] :
% 12.57/2.47 (v4 = empty_set | ~ (subset(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i]
% 12.57/2.47 : ? [v6: $i] : (fiber(v0, v5) = v6 & disjoint(v6, v4) = 0 &
% 12.57/2.47 in(v5, v4) = 0 & $i(v6) & $i(v5)))) & (v1 = 0 | ? [v4: $i] : (
% 12.57/2.47 ~ (v4 = empty_set) & subset(v4, v3) = 0 & $i(v4) & ! [v5: $i] :
% 12.57/2.47 ! [v6: $i] : ( ~ (fiber(v0, v5) = v6) | ~ (disjoint(v6, v4) = 0)
% 12.57/2.47 | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v4) =
% 12.57/2.47 v7))))))))
% 12.57/2.47
% 12.57/2.47 (d3_wellord1)
% 12.57/2.47 $i(empty_set) & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ! [v1:
% 12.57/2.47 $i] : ! [v2: int] : (v2 = 0 | ~ (is_well_founded_in(v0, v1) = v2) | ~
% 12.57/2.47 $i(v1) | ? [v3: $i] : ( ~ (v3 = empty_set) & subset(v3, v1) = 0 &
% 12.57/2.47 $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (fiber(v0, v4) = v5) | ~
% 12.57/2.47 (disjoint(v5, v3) = 0) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 12.57/2.47 in(v4, v3) = v6)))) & ! [v1: $i] : ( ~ (is_well_founded_in(v0,
% 12.57/2.47 v1) = 0) | ~ $i(v1) | ! [v2: $i] : (v2 = empty_set | ~
% 12.57/2.47 (subset(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 12.57/2.47 (fiber(v0, v3) = v4 & disjoint(v4, v2) = 0 & in(v3, v2) = 0 & $i(v4) &
% 12.57/2.47 $i(v3))))))
% 12.57/2.47
% 12.57/2.47 (t5_wellord1)
% 12.57/2.47 ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 12.57/2.47 (is_well_founded_in(v0, v2) = v3 & well_founded_relation(v0) = v1 &
% 12.57/2.48 relation_field(v0) = v2 & relation(v0) = 0 & $i(v2) & $i(v0) & ((v3 = 0 & ~
% 12.57/2.48 (v1 = 0)) | (v1 = 0 & ~ (v3 = 0))))
% 12.57/2.48
% 12.57/2.48 (function-axioms)
% 12.57/2.48 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.57/2.48 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 12.57/2.48 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.57/2.48 [v3: $i] : (v1 = v0 | ~ (is_well_founded_in(v3, v2) = v1) | ~
% 12.57/2.48 (is_well_founded_in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.57/2.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 12.57/2.48 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 12.57/2.48 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (fiber(v3, v2) = v1) | ~ (fiber(v3,
% 12.57/2.48 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 12.57/2.48 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~
% 12.57/2.48 (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.57/2.48 $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) =
% 12.57/2.48 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.57/2.48 $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 12.57/2.48 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1)
% 12.57/2.48 | ~ (powerset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 12.57/2.48 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 12.57/2.48 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 12.57/2.48 (relation_rng(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.57/2.48 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (well_founded_relation(v2)
% 12.57/2.48 = v1) | ~ (well_founded_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 12.57/2.48 ! [v2: $i] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2)
% 12.57/2.48 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.57/2.48 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 12.57/2.48 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 12.57/2.48 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 12.57/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.57/2.48 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 12.57/2.48 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 12.57/2.48 ~ (empty(v2) = v0))
% 12.57/2.48
% 12.57/2.48 Further assumptions not needed in the proof:
% 12.57/2.48 --------------------------------------------
% 12.57/2.48 antisymmetry_r2_hidden, cc1_funct_1, cc2_funct_1, commutativity_k2_xboole_0,
% 12.57/2.48 d6_relat_1, dt_k1_relat_1, dt_k1_wellord1, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 12.57/2.48 dt_k2_relat_1, dt_k2_xboole_0, dt_k3_relat_1, dt_m1_subset_1,
% 12.57/2.48 existence_m1_subset_1, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 12.57/2.48 idempotence_k2_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0,
% 12.57/2.48 rc3_funct_1, reflexivity_r1_tarski, symmetry_r1_xboole_0, t1_boole, t1_subset,
% 12.57/2.48 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 12.57/2.48
% 12.57/2.48 Those formulas are unsatisfiable:
% 12.57/2.48 ---------------------------------
% 12.57/2.48
% 12.57/2.48 Begin of proof
% 12.57/2.48 |
% 12.57/2.48 | ALPHA: (d2_wellord1) implies:
% 12.57/2.49 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (well_founded_relation(v0) = v1) | ~
% 12.57/2.49 | $i(v0) | ? [v2: any] : ? [v3: $i] : (relation_field(v0) = v3 &
% 12.57/2.49 | relation(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v4:
% 12.57/2.49 | $i] : (v4 = empty_set | ~ (subset(v4, v3) = 0) | ~ $i(v4)
% 12.57/2.49 | | ? [v5: $i] : ? [v6: $i] : (fiber(v0, v5) = v6 &
% 12.57/2.49 | disjoint(v6, v4) = 0 & in(v5, v4) = 0 & $i(v6) &
% 12.57/2.49 | $i(v5)))) & (v1 = 0 | ? [v4: $i] : ( ~ (v4 = empty_set)
% 12.57/2.49 | & subset(v4, v3) = 0 & $i(v4) & ! [v5: $i] : ! [v6: $i] :
% 12.57/2.49 | ( ~ (fiber(v0, v5) = v6) | ~ (disjoint(v6, v4) = 0) | ~
% 12.57/2.49 | $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v4) =
% 12.57/2.49 | v7))))))))
% 12.57/2.49 |
% 12.57/2.49 | ALPHA: (d3_wellord1) implies:
% 12.57/2.49 | (2) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : !
% 12.57/2.49 | [v2: int] : (v2 = 0 | ~ (is_well_founded_in(v0, v1) = v2) | ~
% 12.57/2.49 | $i(v1) | ? [v3: $i] : ( ~ (v3 = empty_set) & subset(v3, v1) = 0
% 12.57/2.49 | & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (fiber(v0, v4) = v5)
% 12.57/2.49 | | ~ (disjoint(v5, v3) = 0) | ~ $i(v4) | ? [v6: int] : ( ~
% 12.57/2.49 | (v6 = 0) & in(v4, v3) = v6)))) & ! [v1: $i] : ( ~
% 12.57/2.49 | (is_well_founded_in(v0, v1) = 0) | ~ $i(v1) | ! [v2: $i] : (v2
% 12.57/2.49 | = empty_set | ~ (subset(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i]
% 12.57/2.49 | : ? [v4: $i] : (fiber(v0, v3) = v4 & disjoint(v4, v2) = 0 &
% 12.57/2.49 | in(v3, v2) = 0 & $i(v4) & $i(v3))))))
% 12.57/2.49 |
% 12.57/2.49 | ALPHA: (function-axioms) implies:
% 12.57/2.49 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.57/2.49 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 12.57/2.49 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.57/2.49 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 12.57/2.49 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.57/2.49 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 12.57/2.49 |
% 12.57/2.49 | DELTA: instantiating (t5_wellord1) with fresh symbols all_38_0, all_38_1,
% 12.57/2.49 | all_38_2, all_38_3 gives:
% 12.57/2.49 | (6) is_well_founded_in(all_38_3, all_38_1) = all_38_0 &
% 12.57/2.49 | well_founded_relation(all_38_3) = all_38_2 & relation_field(all_38_3) =
% 12.57/2.49 | all_38_1 & relation(all_38_3) = 0 & $i(all_38_1) & $i(all_38_3) &
% 12.57/2.49 | ((all_38_0 = 0 & ~ (all_38_2 = 0)) | (all_38_2 = 0 & ~ (all_38_0 =
% 12.57/2.49 | 0)))
% 12.57/2.49 |
% 12.57/2.49 | ALPHA: (6) implies:
% 12.57/2.49 | (7) $i(all_38_3)
% 12.57/2.49 | (8) $i(all_38_1)
% 12.57/2.49 | (9) relation(all_38_3) = 0
% 12.57/2.49 | (10) relation_field(all_38_3) = all_38_1
% 12.57/2.49 | (11) well_founded_relation(all_38_3) = all_38_2
% 12.57/2.49 | (12) is_well_founded_in(all_38_3, all_38_1) = all_38_0
% 12.57/2.49 | (13) (all_38_0 = 0 & ~ (all_38_2 = 0)) | (all_38_2 = 0 & ~ (all_38_0 =
% 12.57/2.49 | 0))
% 12.57/2.49 |
% 12.57/2.50 | GROUND_INST: instantiating (2) with all_38_3, simplifying with (7), (9) gives:
% 12.57/2.50 | (14) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 12.57/2.50 | (is_well_founded_in(all_38_3, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 12.57/2.50 | ( ~ (v2 = empty_set) & subset(v2, v0) = 0 & $i(v2) & ! [v3: $i] :
% 12.57/2.50 | ! [v4: $i] : ( ~ (fiber(all_38_3, v3) = v4) | ~ (disjoint(v4, v2)
% 12.57/2.50 | = 0) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & in(v3, v2) =
% 12.57/2.50 | v5)))) & ! [v0: $i] : ( ~ (is_well_founded_in(all_38_3, v0) =
% 12.57/2.50 | 0) | ~ $i(v0) | ! [v1: $i] : (v1 = empty_set | ~ (subset(v1,
% 12.57/2.50 | v0) = 0) | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] :
% 12.57/2.50 | (fiber(all_38_3, v2) = v3 & disjoint(v3, v1) = 0 & in(v2, v1) = 0
% 12.57/2.50 | & $i(v3) & $i(v2))))
% 12.57/2.50 |
% 12.57/2.50 | ALPHA: (14) implies:
% 12.57/2.50 | (15) ! [v0: $i] : ( ~ (is_well_founded_in(all_38_3, v0) = 0) | ~ $i(v0) |
% 12.57/2.50 | ! [v1: $i] : (v1 = empty_set | ~ (subset(v1, v0) = 0) | ~ $i(v1)
% 12.57/2.50 | | ? [v2: $i] : ? [v3: $i] : (fiber(all_38_3, v2) = v3 &
% 12.57/2.50 | disjoint(v3, v1) = 0 & in(v2, v1) = 0 & $i(v3) & $i(v2))))
% 12.57/2.50 | (16) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 12.57/2.50 | (is_well_founded_in(all_38_3, v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 12.57/2.50 | ( ~ (v2 = empty_set) & subset(v2, v0) = 0 & $i(v2) & ! [v3: $i] :
% 12.57/2.50 | ! [v4: $i] : ( ~ (fiber(all_38_3, v3) = v4) | ~ (disjoint(v4, v2)
% 12.57/2.50 | = 0) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & in(v3, v2) =
% 12.57/2.50 | v5))))
% 12.57/2.50 |
% 12.57/2.50 | GROUND_INST: instantiating (1) with all_38_3, all_38_2, simplifying with (7),
% 12.57/2.50 | (11) gives:
% 12.75/2.50 | (17) ? [v0: any] : ? [v1: $i] : (relation_field(all_38_3) = v1 &
% 12.75/2.50 | relation(all_38_3) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_38_2 =
% 12.75/2.50 | 0) | ! [v2: $i] : (v2 = empty_set | ~ (subset(v2, v1) = 0)
% 12.75/2.50 | | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : (fiber(all_38_3,
% 12.75/2.50 | v3) = v4 & disjoint(v4, v2) = 0 & in(v3, v2) = 0 &
% 12.75/2.50 | $i(v4) & $i(v3)))) & (all_38_2 = 0 | ? [v2: $i] : ( ~ (v2
% 12.75/2.50 | = empty_set) & subset(v2, v1) = 0 & $i(v2) & ! [v3: $i] :
% 12.75/2.50 | ! [v4: $i] : ( ~ (fiber(all_38_3, v3) = v4) | ~
% 12.75/2.50 | (disjoint(v4, v2) = 0) | ~ $i(v3) | ? [v5: int] : ( ~
% 12.75/2.50 | (v5 = 0) & in(v3, v2) = v5)))))))
% 12.75/2.50 |
% 12.75/2.50 | GROUND_INST: instantiating (16) with all_38_1, all_38_0, simplifying with (8),
% 12.75/2.50 | (12) gives:
% 12.75/2.50 | (18) all_38_0 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0,
% 12.75/2.50 | all_38_1) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 12.75/2.50 | (fiber(all_38_3, v1) = v2) | ~ (disjoint(v2, v0) = 0) | ~ $i(v1)
% 12.75/2.50 | | ? [v3: int] : ( ~ (v3 = 0) & in(v1, v0) = v3)))
% 12.75/2.50 |
% 12.75/2.50 | DELTA: instantiating (17) with fresh symbols all_52_0, all_52_1 gives:
% 12.75/2.51 | (19) relation_field(all_38_3) = all_52_0 & relation(all_38_3) = all_52_1 &
% 12.75/2.51 | $i(all_52_0) & ( ~ (all_52_1 = 0) | (( ~ (all_38_2 = 0) | ! [v0: $i]
% 12.75/2.51 | : (v0 = empty_set | ~ (subset(v0, all_52_0) = 0) | ~ $i(v0) |
% 12.75/2.51 | ? [v1: $i] : ? [v2: $i] : (fiber(all_38_3, v1) = v2 &
% 12.75/2.51 | disjoint(v2, v0) = 0 & in(v1, v0) = 0 & $i(v2) & $i(v1)))) &
% 12.75/2.51 | (all_38_2 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0,
% 12.75/2.51 | all_52_0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 12.75/2.51 | (fiber(all_38_3, v1) = v2) | ~ (disjoint(v2, v0) = 0) | ~
% 12.75/2.51 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v1, v0) = v3))))))
% 12.75/2.51 |
% 12.75/2.51 | ALPHA: (19) implies:
% 12.75/2.51 | (20) $i(all_52_0)
% 12.75/2.51 | (21) relation(all_38_3) = all_52_1
% 12.75/2.51 | (22) relation_field(all_38_3) = all_52_0
% 12.75/2.51 | (23) ~ (all_52_1 = 0) | (( ~ (all_38_2 = 0) | ! [v0: $i] : (v0 =
% 12.75/2.51 | empty_set | ~ (subset(v0, all_52_0) = 0) | ~ $i(v0) | ? [v1:
% 12.75/2.51 | $i] : ? [v2: $i] : (fiber(all_38_3, v1) = v2 & disjoint(v2,
% 12.75/2.51 | v0) = 0 & in(v1, v0) = 0 & $i(v2) & $i(v1)))) & (all_38_2 =
% 12.75/2.51 | 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, all_52_0) = 0
% 12.75/2.51 | & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(all_38_3, v1)
% 12.75/2.51 | = v2) | ~ (disjoint(v2, v0) = 0) | ~ $i(v1) | ? [v3: int]
% 12.75/2.51 | : ( ~ (v3 = 0) & in(v1, v0) = v3)))))
% 12.75/2.51 |
% 12.75/2.51 | GROUND_INST: instantiating (3) with 0, all_52_1, all_38_3, simplifying with
% 12.75/2.51 | (9), (21) gives:
% 12.75/2.51 | (24) all_52_1 = 0
% 12.75/2.51 |
% 12.75/2.51 | GROUND_INST: instantiating (4) with all_38_1, all_52_0, all_38_3, simplifying
% 12.75/2.51 | with (10), (22) gives:
% 12.75/2.51 | (25) all_52_0 = all_38_1
% 12.75/2.51 |
% 12.75/2.51 | BETA: splitting (13) gives:
% 12.75/2.51 |
% 12.75/2.51 | Case 1:
% 12.75/2.51 | |
% 12.75/2.51 | | (26) all_38_0 = 0 & ~ (all_38_2 = 0)
% 12.75/2.51 | |
% 12.75/2.51 | | ALPHA: (26) implies:
% 12.75/2.51 | | (27) all_38_0 = 0
% 12.75/2.51 | | (28) ~ (all_38_2 = 0)
% 12.75/2.51 | |
% 12.75/2.51 | | REDUCE: (12), (27) imply:
% 12.75/2.51 | | (29) is_well_founded_in(all_38_3, all_38_1) = 0
% 12.75/2.51 | |
% 12.75/2.51 | | BETA: splitting (23) gives:
% 12.75/2.51 | |
% 12.75/2.51 | | Case 1:
% 12.75/2.51 | | |
% 12.75/2.51 | | | (30) ~ (all_52_1 = 0)
% 12.75/2.51 | | |
% 12.75/2.51 | | | REDUCE: (24), (30) imply:
% 12.75/2.51 | | | (31) $false
% 12.75/2.51 | | |
% 12.75/2.51 | | | CLOSE: (31) is inconsistent.
% 12.75/2.51 | | |
% 12.75/2.51 | | Case 2:
% 12.75/2.51 | | |
% 12.75/2.51 | | | (32) ( ~ (all_38_2 = 0) | ! [v0: $i] : (v0 = empty_set | ~
% 12.75/2.51 | | | (subset(v0, all_52_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 12.75/2.51 | | | $i] : (fiber(all_38_3, v1) = v2 & disjoint(v2, v0) = 0 &
% 12.75/2.51 | | | in(v1, v0) = 0 & $i(v2) & $i(v1)))) & (all_38_2 = 0 | ?
% 12.75/2.51 | | | [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, all_52_0) = 0 &
% 12.75/2.51 | | | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(all_38_3, v1)
% 12.75/2.51 | | | = v2) | ~ (disjoint(v2, v0) = 0) | ~ $i(v1) | ? [v3:
% 12.75/2.51 | | | int] : ( ~ (v3 = 0) & in(v1, v0) = v3))))
% 12.75/2.51 | | |
% 12.75/2.51 | | | ALPHA: (32) implies:
% 12.75/2.52 | | | (33) all_38_2 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0,
% 12.75/2.52 | | | all_52_0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~
% 12.75/2.52 | | | (fiber(all_38_3, v1) = v2) | ~ (disjoint(v2, v0) = 0) | ~
% 12.75/2.52 | | | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v1, v0) = v3)))
% 12.75/2.52 | | |
% 12.75/2.52 | | | BETA: splitting (33) gives:
% 12.75/2.52 | | |
% 12.75/2.52 | | | Case 1:
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | (34) all_38_2 = 0
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | REDUCE: (28), (34) imply:
% 12.75/2.52 | | | | (35) $false
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | CLOSE: (35) is inconsistent.
% 12.75/2.52 | | | |
% 12.75/2.52 | | | Case 2:
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | (36) ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, all_52_0) = 0 &
% 12.75/2.52 | | | | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(all_38_3, v1)
% 12.75/2.52 | | | | = v2) | ~ (disjoint(v2, v0) = 0) | ~ $i(v1) | ? [v3:
% 12.75/2.52 | | | | int] : ( ~ (v3 = 0) & in(v1, v0) = v3)))
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | DELTA: instantiating (36) with fresh symbol all_89_0 gives:
% 12.75/2.52 | | | | (37) ~ (all_89_0 = empty_set) & subset(all_89_0, all_52_0) = 0 &
% 12.75/2.52 | | | | $i(all_89_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (fiber(all_38_3,
% 12.75/2.52 | | | | v0) = v1) | ~ (disjoint(v1, all_89_0) = 0) | ~ $i(v0) |
% 12.75/2.52 | | | | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_89_0) = v2))
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | ALPHA: (37) implies:
% 12.75/2.52 | | | | (38) ~ (all_89_0 = empty_set)
% 12.75/2.52 | | | | (39) $i(all_89_0)
% 12.75/2.52 | | | | (40) subset(all_89_0, all_52_0) = 0
% 12.75/2.52 | | | | (41) ! [v0: $i] : ! [v1: $i] : ( ~ (fiber(all_38_3, v0) = v1) | ~
% 12.75/2.52 | | | | (disjoint(v1, all_89_0) = 0) | ~ $i(v0) | ? [v2: int] : ( ~
% 12.75/2.52 | | | | (v2 = 0) & in(v0, all_89_0) = v2))
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | REDUCE: (25), (40) imply:
% 12.75/2.52 | | | | (42) subset(all_89_0, all_38_1) = 0
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | GROUND_INST: instantiating (15) with all_38_1, simplifying with (8),
% 12.75/2.52 | | | | (29) gives:
% 12.75/2.52 | | | | (43) ! [v0: $i] : (v0 = empty_set | ~ (subset(v0, all_38_1) = 0) |
% 12.75/2.52 | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (fiber(all_38_3, v1) =
% 12.75/2.52 | | | | v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0 & $i(v2) &
% 12.75/2.52 | | | | $i(v1)))
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | GROUND_INST: instantiating (43) with all_89_0, simplifying with (39),
% 12.75/2.52 | | | | (42) gives:
% 12.75/2.52 | | | | (44) all_89_0 = empty_set | ? [v0: $i] : ? [v1: $i] :
% 12.75/2.52 | | | | (fiber(all_38_3, v0) = v1 & disjoint(v1, all_89_0) = 0 & in(v0,
% 12.75/2.52 | | | | all_89_0) = 0 & $i(v1) & $i(v0))
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | BETA: splitting (44) gives:
% 12.75/2.52 | | | |
% 12.75/2.52 | | | | Case 1:
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | | (45) all_89_0 = empty_set
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | | REDUCE: (38), (45) imply:
% 12.75/2.52 | | | | | (46) $false
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | | CLOSE: (46) is inconsistent.
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | Case 2:
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | | (47) ? [v0: $i] : ? [v1: $i] : (fiber(all_38_3, v0) = v1 &
% 12.75/2.52 | | | | | disjoint(v1, all_89_0) = 0 & in(v0, all_89_0) = 0 & $i(v1) &
% 12.75/2.52 | | | | | $i(v0))
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | | DELTA: instantiating (47) with fresh symbols all_106_0, all_106_1
% 12.75/2.52 | | | | | gives:
% 12.75/2.52 | | | | | (48) fiber(all_38_3, all_106_1) = all_106_0 & disjoint(all_106_0,
% 12.75/2.52 | | | | | all_89_0) = 0 & in(all_106_1, all_89_0) = 0 & $i(all_106_0)
% 12.75/2.52 | | | | | & $i(all_106_1)
% 12.75/2.52 | | | | |
% 12.75/2.52 | | | | | ALPHA: (48) implies:
% 12.75/2.52 | | | | | (49) $i(all_106_1)
% 12.75/2.52 | | | | | (50) in(all_106_1, all_89_0) = 0
% 12.75/2.52 | | | | | (51) disjoint(all_106_0, all_89_0) = 0
% 12.75/2.53 | | | | | (52) fiber(all_38_3, all_106_1) = all_106_0
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | | GROUND_INST: instantiating (41) with all_106_1, all_106_0, simplifying
% 12.75/2.53 | | | | | with (49), (51), (52) gives:
% 12.75/2.53 | | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & in(all_106_1, all_89_0) = v0)
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | | DELTA: instantiating (53) with fresh symbol all_118_0 gives:
% 12.75/2.53 | | | | | (54) ~ (all_118_0 = 0) & in(all_106_1, all_89_0) = all_118_0
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | | ALPHA: (54) implies:
% 12.75/2.53 | | | | | (55) ~ (all_118_0 = 0)
% 12.75/2.53 | | | | | (56) in(all_106_1, all_89_0) = all_118_0
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | | GROUND_INST: instantiating (5) with 0, all_118_0, all_89_0, all_106_1,
% 12.75/2.53 | | | | | simplifying with (50), (56) gives:
% 12.75/2.53 | | | | | (57) all_118_0 = 0
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | | REDUCE: (55), (57) imply:
% 12.75/2.53 | | | | | (58) $false
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | | CLOSE: (58) is inconsistent.
% 12.75/2.53 | | | | |
% 12.75/2.53 | | | | End of split
% 12.75/2.53 | | | |
% 12.75/2.53 | | | End of split
% 12.75/2.53 | | |
% 12.75/2.53 | | End of split
% 12.75/2.53 | |
% 12.75/2.53 | Case 2:
% 12.75/2.53 | |
% 12.75/2.53 | | (59) all_38_2 = 0 & ~ (all_38_0 = 0)
% 12.75/2.53 | |
% 12.75/2.53 | | ALPHA: (59) implies:
% 12.75/2.53 | | (60) all_38_2 = 0
% 12.75/2.53 | | (61) ~ (all_38_0 = 0)
% 12.75/2.53 | |
% 12.75/2.53 | | BETA: splitting (23) gives:
% 12.75/2.53 | |
% 12.75/2.53 | | Case 1:
% 12.75/2.53 | | |
% 12.75/2.53 | | | (62) ~ (all_52_1 = 0)
% 12.75/2.53 | | |
% 12.75/2.53 | | | REDUCE: (24), (62) imply:
% 12.75/2.53 | | | (63) $false
% 12.75/2.53 | | |
% 12.75/2.53 | | | CLOSE: (63) is inconsistent.
% 12.75/2.53 | | |
% 12.75/2.53 | | Case 2:
% 12.75/2.53 | | |
% 12.75/2.53 | | | (64) ( ~ (all_38_2 = 0) | ! [v0: $i] : (v0 = empty_set | ~
% 12.75/2.53 | | | (subset(v0, all_52_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 12.75/2.53 | | | $i] : (fiber(all_38_3, v1) = v2 & disjoint(v2, v0) = 0 &
% 12.75/2.53 | | | in(v1, v0) = 0 & $i(v2) & $i(v1)))) & (all_38_2 = 0 | ?
% 12.75/2.53 | | | [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, all_52_0) = 0 &
% 12.75/2.53 | | | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(all_38_3, v1)
% 12.75/2.53 | | | = v2) | ~ (disjoint(v2, v0) = 0) | ~ $i(v1) | ? [v3:
% 12.75/2.53 | | | int] : ( ~ (v3 = 0) & in(v1, v0) = v3))))
% 12.75/2.53 | | |
% 12.75/2.53 | | | ALPHA: (64) implies:
% 12.75/2.53 | | | (65) ~ (all_38_2 = 0) | ! [v0: $i] : (v0 = empty_set | ~ (subset(v0,
% 12.75/2.53 | | | all_52_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 12.75/2.53 | | | (fiber(all_38_3, v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) =
% 12.75/2.53 | | | 0 & $i(v2) & $i(v1)))
% 12.75/2.53 | | |
% 12.91/2.53 | | | BETA: splitting (18) gives:
% 12.91/2.53 | | |
% 12.91/2.53 | | | Case 1:
% 12.91/2.53 | | | |
% 12.91/2.53 | | | | (66) all_38_0 = 0
% 12.91/2.53 | | | |
% 12.91/2.53 | | | | REDUCE: (61), (66) imply:
% 12.91/2.53 | | | | (67) $false
% 12.91/2.53 | | | |
% 12.91/2.53 | | | | CLOSE: (67) is inconsistent.
% 12.91/2.53 | | | |
% 12.91/2.53 | | | Case 2:
% 12.91/2.53 | | | |
% 12.91/2.53 | | | | (68) ? [v0: $i] : ( ~ (v0 = empty_set) & subset(v0, all_38_1) = 0 &
% 12.91/2.53 | | | | $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (fiber(all_38_3, v1)
% 12.91/2.53 | | | | = v2) | ~ (disjoint(v2, v0) = 0) | ~ $i(v1) | ? [v3:
% 12.91/2.53 | | | | int] : ( ~ (v3 = 0) & in(v1, v0) = v3)))
% 12.91/2.53 | | | |
% 12.91/2.53 | | | | DELTA: instantiating (68) with fresh symbol all_88_0 gives:
% 12.91/2.53 | | | | (69) ~ (all_88_0 = empty_set) & subset(all_88_0, all_38_1) = 0 &
% 12.91/2.53 | | | | $i(all_88_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (fiber(all_38_3,
% 12.91/2.53 | | | | v0) = v1) | ~ (disjoint(v1, all_88_0) = 0) | ~ $i(v0) |
% 12.91/2.53 | | | | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_88_0) = v2))
% 12.91/2.53 | | | |
% 12.91/2.53 | | | | ALPHA: (69) implies:
% 12.91/2.53 | | | | (70) ~ (all_88_0 = empty_set)
% 12.91/2.53 | | | | (71) $i(all_88_0)
% 12.91/2.53 | | | | (72) subset(all_88_0, all_38_1) = 0
% 12.91/2.54 | | | | (73) ! [v0: $i] : ! [v1: $i] : ( ~ (fiber(all_38_3, v0) = v1) | ~
% 12.91/2.54 | | | | (disjoint(v1, all_88_0) = 0) | ~ $i(v0) | ? [v2: int] : ( ~
% 12.91/2.54 | | | | (v2 = 0) & in(v0, all_88_0) = v2))
% 12.91/2.54 | | | |
% 12.91/2.54 | | | | BETA: splitting (65) gives:
% 12.91/2.54 | | | |
% 12.91/2.54 | | | | Case 1:
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | (74) ~ (all_38_2 = 0)
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | REDUCE: (60), (74) imply:
% 12.91/2.54 | | | | | (75) $false
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | CLOSE: (75) is inconsistent.
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | Case 2:
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | (76) ! [v0: $i] : (v0 = empty_set | ~ (subset(v0, all_52_0) = 0)
% 12.91/2.54 | | | | | | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (fiber(all_38_3,
% 12.91/2.54 | | | | | v1) = v2 & disjoint(v2, v0) = 0 & in(v1, v0) = 0 &
% 12.91/2.54 | | | | | $i(v2) & $i(v1)))
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | GROUND_INST: instantiating (76) with all_88_0, simplifying with (71)
% 12.91/2.54 | | | | | gives:
% 12.91/2.54 | | | | | (77) all_88_0 = empty_set | ~ (subset(all_88_0, all_52_0) = 0) |
% 12.91/2.54 | | | | | ? [v0: $i] : ? [v1: $i] : (fiber(all_38_3, v0) = v1 &
% 12.91/2.54 | | | | | disjoint(v1, all_88_0) = 0 & in(v0, all_88_0) = 0 & $i(v1) &
% 12.91/2.54 | | | | | $i(v0))
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | BETA: splitting (77) gives:
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | | Case 1:
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | (78) ~ (subset(all_88_0, all_52_0) = 0)
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | REDUCE: (25), (78) imply:
% 12.91/2.54 | | | | | | (79) ~ (subset(all_88_0, all_38_1) = 0)
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | PRED_UNIFY: (72), (79) imply:
% 12.91/2.54 | | | | | | (80) $false
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | CLOSE: (80) is inconsistent.
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | Case 2:
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | (81) all_88_0 = empty_set | ? [v0: $i] : ? [v1: $i] :
% 12.91/2.54 | | | | | | (fiber(all_38_3, v0) = v1 & disjoint(v1, all_88_0) = 0 &
% 12.91/2.54 | | | | | | in(v0, all_88_0) = 0 & $i(v1) & $i(v0))
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | BETA: splitting (81) gives:
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | | Case 1:
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | (82) all_88_0 = empty_set
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | REDUCE: (70), (82) imply:
% 12.91/2.54 | | | | | | | (83) $false
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | CLOSE: (83) is inconsistent.
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | Case 2:
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | (84) ? [v0: $i] : ? [v1: $i] : (fiber(all_38_3, v0) = v1 &
% 12.91/2.54 | | | | | | | disjoint(v1, all_88_0) = 0 & in(v0, all_88_0) = 0 &
% 12.91/2.54 | | | | | | | $i(v1) & $i(v0))
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | DELTA: instantiating (84) with fresh symbols all_176_0, all_176_1
% 12.91/2.54 | | | | | | | gives:
% 12.91/2.54 | | | | | | | (85) fiber(all_38_3, all_176_1) = all_176_0 &
% 12.91/2.54 | | | | | | | disjoint(all_176_0, all_88_0) = 0 & in(all_176_1,
% 12.91/2.54 | | | | | | | all_88_0) = 0 & $i(all_176_0) & $i(all_176_1)
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | ALPHA: (85) implies:
% 12.91/2.54 | | | | | | | (86) $i(all_176_1)
% 12.91/2.54 | | | | | | | (87) in(all_176_1, all_88_0) = 0
% 12.91/2.54 | | | | | | | (88) disjoint(all_176_0, all_88_0) = 0
% 12.91/2.54 | | | | | | | (89) fiber(all_38_3, all_176_1) = all_176_0
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | GROUND_INST: instantiating (73) with all_176_1, all_176_0,
% 12.91/2.54 | | | | | | | simplifying with (86), (88), (89) gives:
% 12.91/2.54 | | | | | | | (90) ? [v0: int] : ( ~ (v0 = 0) & in(all_176_1, all_88_0) =
% 12.91/2.54 | | | | | | | v0)
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | DELTA: instantiating (90) with fresh symbol all_184_0 gives:
% 12.91/2.54 | | | | | | | (91) ~ (all_184_0 = 0) & in(all_176_1, all_88_0) = all_184_0
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | ALPHA: (91) implies:
% 12.91/2.54 | | | | | | | (92) ~ (all_184_0 = 0)
% 12.91/2.54 | | | | | | | (93) in(all_176_1, all_88_0) = all_184_0
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | GROUND_INST: instantiating (5) with 0, all_184_0, all_88_0,
% 12.91/2.54 | | | | | | | all_176_1, simplifying with (87), (93) gives:
% 12.91/2.54 | | | | | | | (94) all_184_0 = 0
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | REDUCE: (92), (94) imply:
% 12.91/2.54 | | | | | | | (95) $false
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | | CLOSE: (95) is inconsistent.
% 12.91/2.54 | | | | | | |
% 12.91/2.54 | | | | | | End of split
% 12.91/2.54 | | | | | |
% 12.91/2.54 | | | | | End of split
% 12.91/2.54 | | | | |
% 12.91/2.54 | | | | End of split
% 12.91/2.54 | | | |
% 12.91/2.55 | | | End of split
% 12.91/2.55 | | |
% 12.91/2.55 | | End of split
% 12.91/2.55 | |
% 12.91/2.55 | End of split
% 12.91/2.55 |
% 12.91/2.55 End of proof
% 12.91/2.55 % SZS output end Proof for theBenchmark
% 12.91/2.55
% 12.91/2.55 1915ms
%------------------------------------------------------------------------------