TSTP Solution File: SEU010+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU010+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:42:17 EDT 2023
% Result : Theorem 35.06s 5.50s
% Output : Proof 35.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU010+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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 19:29:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 ________ _____
% 0.20/0.58 ___ __ \_________(_)________________________________
% 0.20/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.58 (2023-06-19)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2023
% 0.20/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.58 Amanda Stjerna.
% 0.20/0.58 Free software under BSD-3-Clause.
% 0.20/0.58
% 0.20/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.58
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.80/1.09 Prover 4: Preprocessing ...
% 2.80/1.09 Prover 1: Preprocessing ...
% 2.80/1.13 Prover 6: Preprocessing ...
% 2.80/1.13 Prover 3: Preprocessing ...
% 2.80/1.13 Prover 2: Preprocessing ...
% 2.80/1.13 Prover 5: Preprocessing ...
% 2.80/1.13 Prover 0: Preprocessing ...
% 5.75/1.57 Prover 1: Warning: ignoring some quantifiers
% 5.75/1.58 Prover 2: Proving ...
% 5.75/1.58 Prover 5: Proving ...
% 5.75/1.59 Prover 1: Constructing countermodel ...
% 5.75/1.60 Prover 3: Warning: ignoring some quantifiers
% 5.75/1.60 Prover 4: Warning: ignoring some quantifiers
% 6.34/1.60 Prover 6: Proving ...
% 6.34/1.61 Prover 3: Constructing countermodel ...
% 6.34/1.65 Prover 4: Constructing countermodel ...
% 6.84/1.70 Prover 0: Proving ...
% 35.06/5.46 Prover 4: Found proof (size 149)
% 35.06/5.46 Prover 4: proved (4847ms)
% 35.06/5.47 Prover 3: stopped
% 35.06/5.47 Prover 1: stopped
% 35.06/5.47 Prover 0: stopped
% 35.06/5.47 Prover 2: stopped
% 35.06/5.47 Prover 6: stopped
% 35.06/5.50 Prover 5: stopped
% 35.06/5.50
% 35.06/5.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.06/5.50
% 35.57/5.53 % SZS output start Proof for theBenchmark
% 35.57/5.53 Assumptions after simplification:
% 35.57/5.53 ---------------------------------
% 35.57/5.53
% 35.57/5.53 (dt_k5_relat_1)
% 35.57/5.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 35.57/5.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 35.57/5.56 (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) |
% 35.57/5.56 ~ (v3 = 0) | v5 = 0)))
% 35.57/5.56
% 35.57/5.56 (fc10_relat_1)
% 35.57/5.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v1, v0) =
% 35.57/5.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 35.57/5.56 ? [v6: any] : (empty(v2) = v5 & empty(v0) = v3 & relation(v2) = v6 &
% 35.57/5.56 relation(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 35.57/5.56
% 35.57/5.56 (fc1_funct_1)
% 35.57/5.56 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 35.57/5.56 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 35.57/5.56 ? [v6: any] : ? [v7: any] : ? [v8: any] : (function(v2) = v8 &
% 35.57/5.56 function(v1) = v6 & function(v0) = v4 & relation(v2) = v7 & relation(v1) =
% 35.57/5.56 v5 & relation(v0) = v3 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3
% 35.57/5.56 = 0) | (v8 = 0 & v7 = 0))))
% 35.57/5.56
% 35.57/5.56 (fc2_funct_1)
% 35.57/5.56 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) |
% 35.57/5.56 function(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) =
% 35.57/5.56 v1) | ~ $i(v0) | relation(v1) = 0)
% 35.57/5.56
% 35.57/5.56 (fc5_relat_1)
% 35.57/5.57 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 35.57/5.57 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 & empty(v3)
% 35.57/5.57 = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & !
% 35.57/5.57 [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 35.57/5.57 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 &
% 35.57/5.57 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0: $i] :
% 35.57/5.57 ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any]
% 35.57/5.57 : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & $i(v2) & ( ~
% 35.57/5.57 (v3 = 0) | v1 = 0)))
% 35.57/5.57
% 35.57/5.57 (fc6_relat_1)
% 35.57/5.57 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 35.57/5.57 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 & empty(v3)
% 35.57/5.57 = v4 & relation(v0) = v2 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 = 0)))) & !
% 35.57/5.57 [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 35.57/5.57 any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 & empty(v0) = v2 &
% 35.57/5.57 relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0: $i] :
% 35.57/5.57 ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: any]
% 35.57/5.57 : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 & $i(v2) & ( ~
% 35.57/5.57 (v3 = 0) | v1 = 0)))
% 35.57/5.57
% 35.57/5.57 (fc9_relat_1)
% 35.57/5.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_composition(v0, v1) =
% 35.57/5.58 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 35.57/5.58 ? [v6: any] : (empty(v2) = v5 & empty(v0) = v3 & relation(v2) = v6 &
% 35.57/5.58 relation(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 35.57/5.58
% 35.57/5.58 (reflexivity_r1_tarski)
% 35.57/5.58 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0, v0) = v1) | ~ $i(v0))
% 35.57/5.58
% 35.57/5.58 (t42_funct_1)
% 35.92/5.58 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 35.92/5.58 $i] : ? [v6: $i] : (identity_relation(v4) = v5 & identity_relation(v1) = v2
% 35.92/5.58 & relation_composition(v2, v0) = v3 & relation_composition(v0, v5) = v6 &
% 35.92/5.58 relation_rng(v0) = v4 & relation_dom(v0) = v1 & function(v0) = 0 &
% 35.92/5.58 relation(v0) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 35.92/5.58 $i(v0) & ( ~ (v6 = v0) | ~ (v3 = v0)))
% 35.92/5.58
% 35.92/5.58 (t77_relat_1)
% 35.92/5.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 35.92/5.59 (identity_relation(v0) = v2) | ~ (relation_composition(v2, v1) = v3) | ~
% 35.92/5.59 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (subset(v5,
% 35.92/5.59 v0) = v6 & relation_dom(v1) = v5 & relation(v1) = v4 & $i(v5) & ( ~ (v6
% 35.92/5.59 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 35.92/5.59 (subset(v2, v0) = 0) | ~ (relation_dom(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 35.92/5.59 ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (identity_relation(v0) = v4 &
% 35.92/5.59 relation_composition(v4, v1) = v5 & relation(v1) = v3 & $i(v5) & $i(v4) &
% 35.92/5.59 ( ~ (v3 = 0) | v5 = v1)))
% 35.92/5.59
% 35.92/5.59 (t79_relat_1)
% 35.92/5.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 35.92/5.59 (identity_relation(v0) = v2) | ~ (relation_composition(v1, v2) = v3) | ~
% 35.92/5.59 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (subset(v5,
% 35.92/5.59 v0) = v6 & relation_rng(v1) = v5 & relation(v1) = v4 & $i(v5) & ( ~ (v6
% 35.92/5.59 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 35.92/5.59 (subset(v2, v0) = 0) | ~ (relation_rng(v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 35.92/5.59 ? [v3: any] : ? [v4: $i] : ? [v5: $i] : (identity_relation(v0) = v4 &
% 35.92/5.59 relation_composition(v1, v4) = v5 & relation(v1) = v3 & $i(v5) & $i(v4) &
% 35.92/5.59 ( ~ (v3 = 0) | v5 = v1)))
% 35.92/5.59
% 35.92/5.59 (function-axioms)
% 35.92/5.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 35.92/5.60 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 35.92/5.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 35.92/5.60 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 35.92/5.60 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 35.92/5.60 $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 35.92/5.60 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 35.92/5.60 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 35.92/5.60 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 35.92/5.60 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0:
% 35.92/5.60 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 35.92/5.60 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 35.92/5.60 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 35.92/5.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 35.92/5.60 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 35.92/5.60 : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) &
% 35.92/5.60 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 35.92/5.60 v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2)
% 35.92/5.60 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 35.92/5.60 $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0:
% 35.92/5.60 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 35.92/5.60 ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 35.92/5.60
% 35.92/5.60 Further assumptions not needed in the proof:
% 35.92/5.60 --------------------------------------------
% 35.92/5.60 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, dt_k6_relat_1,
% 35.92/5.60 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 35.92/5.60 fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0,
% 35.92/5.60 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_relat_1, t1_subset, t2_subset,
% 35.92/5.60 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 35.92/5.60
% 35.92/5.60 Those formulas are unsatisfiable:
% 35.92/5.60 ---------------------------------
% 35.92/5.60
% 35.92/5.60 Begin of proof
% 35.92/5.60 |
% 35.92/5.60 | ALPHA: (fc5_relat_1) implies:
% 35.92/5.60 | (1) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 35.92/5.60 | [v2: $i] : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 &
% 35.92/5.60 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 35.92/5.60 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 35.92/5.60 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 &
% 35.92/5.60 | empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 35.92/5.60 | v2 = 0)))
% 35.92/5.60 |
% 35.92/5.60 | ALPHA: (fc6_relat_1) implies:
% 35.92/5.61 | (3) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 35.92/5.61 | [v2: $i] : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 &
% 35.92/5.61 | empty(v0) = v1 & $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 35.92/5.61 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 35.92/5.61 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (empty(v1) = v4 &
% 35.92/5.61 | empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 35.92/5.61 | v2 = 0)))
% 35.92/5.61 |
% 35.92/5.61 | ALPHA: (fc2_funct_1) implies:
% 35.92/5.61 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~
% 35.92/5.61 | $i(v0) | relation(v1) = 0)
% 35.92/5.61 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~
% 35.92/5.61 | $i(v0) | function(v1) = 0)
% 35.92/5.61 |
% 35.92/5.61 | ALPHA: (t77_relat_1) implies:
% 35.92/5.61 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 35.92/5.61 | (identity_relation(v0) = v2) | ~ (relation_composition(v2, v1) = v3)
% 35.92/5.61 | | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 35.92/5.61 | (subset(v5, v0) = v6 & relation_dom(v1) = v5 & relation(v1) = v4 &
% 35.92/5.61 | $i(v5) & ( ~ (v6 = 0) | ~ (v4 = 0))))
% 35.92/5.61 |
% 35.92/5.61 | ALPHA: (t79_relat_1) implies:
% 35.92/5.61 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 35.92/5.61 | (identity_relation(v0) = v2) | ~ (relation_composition(v1, v2) = v3)
% 35.92/5.61 | | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] :
% 35.92/5.61 | (subset(v5, v0) = v6 & relation_rng(v1) = v5 & relation(v1) = v4 &
% 35.92/5.61 | $i(v5) & ( ~ (v6 = 0) | ~ (v4 = 0))))
% 35.92/5.61 |
% 35.92/5.61 | ALPHA: (function-axioms) implies:
% 35.92/5.61 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 35.92/5.61 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 35.92/5.61 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 35.92/5.61 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 35.92/5.61 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 35.92/5.61 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 35.92/5.61 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 35.92/5.61 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 35.92/5.61 |
% 35.92/5.61 | DELTA: instantiating (t42_funct_1) with fresh symbols all_44_0, all_44_1,
% 35.92/5.61 | all_44_2, all_44_3, all_44_4, all_44_5, all_44_6 gives:
% 35.92/5.61 | (13) identity_relation(all_44_2) = all_44_1 & identity_relation(all_44_5) =
% 35.92/5.61 | all_44_4 & relation_composition(all_44_4, all_44_6) = all_44_3 &
% 35.92/5.61 | relation_composition(all_44_6, all_44_1) = all_44_0 &
% 35.92/5.61 | relation_rng(all_44_6) = all_44_2 & relation_dom(all_44_6) = all_44_5
% 35.92/5.61 | & function(all_44_6) = 0 & relation(all_44_6) = 0 & $i(all_44_0) &
% 35.92/5.61 | $i(all_44_1) & $i(all_44_2) & $i(all_44_3) & $i(all_44_4) &
% 35.92/5.61 | $i(all_44_5) & $i(all_44_6) & ( ~ (all_44_0 = all_44_6) | ~ (all_44_3
% 35.92/5.61 | = all_44_6))
% 35.92/5.62 |
% 35.92/5.62 | ALPHA: (13) implies:
% 35.92/5.62 | (14) $i(all_44_6)
% 35.92/5.62 | (15) $i(all_44_5)
% 35.92/5.62 | (16) $i(all_44_4)
% 35.92/5.62 | (17) $i(all_44_2)
% 35.92/5.62 | (18) $i(all_44_1)
% 35.92/5.62 | (19) $i(all_44_0)
% 35.92/5.62 | (20) relation(all_44_6) = 0
% 35.92/5.62 | (21) function(all_44_6) = 0
% 35.92/5.62 | (22) relation_dom(all_44_6) = all_44_5
% 35.92/5.62 | (23) relation_rng(all_44_6) = all_44_2
% 35.92/5.62 | (24) relation_composition(all_44_6, all_44_1) = all_44_0
% 35.92/5.62 | (25) relation_composition(all_44_4, all_44_6) = all_44_3
% 35.92/5.62 | (26) identity_relation(all_44_5) = all_44_4
% 35.92/5.62 | (27) identity_relation(all_44_2) = all_44_1
% 35.92/5.62 | (28) ~ (all_44_0 = all_44_6) | ~ (all_44_3 = all_44_6)
% 35.92/5.62 |
% 35.92/5.62 | GROUND_INST: instantiating (3) with all_44_6, simplifying with (14), (20)
% 35.92/5.62 | gives:
% 35.92/5.62 | (29) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_rng(all_44_6) =
% 35.92/5.62 | v1 & empty(v1) = v2 & empty(all_44_6) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 35.92/5.62 | v0 = 0))
% 35.92/5.62 |
% 35.92/5.62 | GROUND_INST: instantiating (1) with all_44_6, simplifying with (14), (20)
% 35.92/5.62 | gives:
% 35.92/5.62 | (30) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (relation_dom(all_44_6) =
% 35.92/5.62 | v1 & empty(v1) = v2 & empty(all_44_6) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 35.92/5.62 | v0 = 0))
% 35.92/5.62 |
% 35.92/5.62 | GROUND_INST: instantiating (2) with all_44_6, all_44_5, simplifying with (14),
% 35.92/5.62 | (22) gives:
% 35.92/5.62 | (31) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_44_5) = v2 &
% 35.92/5.62 | empty(all_44_6) = v0 & relation(all_44_6) = v1 & ( ~ (v2 = 0) | ~
% 35.92/5.62 | (v1 = 0) | v0 = 0))
% 35.92/5.62 |
% 35.92/5.62 | GROUND_INST: instantiating (4) with all_44_6, all_44_2, simplifying with (14),
% 35.92/5.62 | (23) gives:
% 35.92/5.62 | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (empty(all_44_2) = v2 &
% 35.92/5.62 | empty(all_44_6) = v0 & relation(all_44_6) = v1 & ( ~ (v2 = 0) | ~
% 35.92/5.62 | (v1 = 0) | v0 = 0))
% 35.92/5.62 |
% 35.92/5.62 | GROUND_INST: instantiating (fc10_relat_1) with all_44_1, all_44_6, all_44_0,
% 35.92/5.62 | simplifying with (14), (18), (24) gives:
% 35.92/5.62 | (33) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 35.92/5.62 | (empty(all_44_0) = v2 & empty(all_44_1) = v0 & relation(all_44_0) = v3
% 35.92/5.62 | & relation(all_44_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 &
% 35.92/5.62 | v2 = 0)))
% 35.92/5.62 |
% 35.92/5.62 | GROUND_INST: instantiating (fc1_funct_1) with all_44_6, all_44_1, all_44_0,
% 35.92/5.62 | simplifying with (14), (18), (24) gives:
% 35.92/5.62 | (34) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 35.92/5.62 | any] : ? [v5: any] : (function(all_44_0) = v5 & function(all_44_1)
% 35.92/5.63 | = v3 & function(all_44_6) = v1 & relation(all_44_0) = v4 &
% 35.92/5.63 | relation(all_44_1) = v2 & relation(all_44_6) = v0 & ( ~ (v3 = 0) |
% 35.92/5.63 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v5 = 0 & v4 = 0)))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (fc9_relat_1) with all_44_6, all_44_1, all_44_0,
% 35.92/5.63 | simplifying with (14), (18), (24) gives:
% 35.92/5.63 | (35) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 35.92/5.63 | (empty(all_44_0) = v2 & empty(all_44_6) = v0 & relation(all_44_0) = v3
% 35.92/5.63 | & relation(all_44_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 &
% 35.92/5.63 | v2 = 0)))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (dt_k5_relat_1) with all_44_6, all_44_1, all_44_0,
% 35.92/5.63 | simplifying with (14), (18), (24) gives:
% 35.92/5.63 | (36) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_44_0) = v2
% 35.92/5.63 | & relation(all_44_1) = v1 & relation(all_44_6) = v0 & ( ~ (v1 = 0) |
% 35.92/5.63 | ~ (v0 = 0) | v2 = 0))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (fc1_funct_1) with all_44_4, all_44_6, all_44_3,
% 35.92/5.63 | simplifying with (14), (16), (25) gives:
% 35.92/5.63 | (37) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] : ? [v4:
% 35.92/5.63 | any] : ? [v5: any] : (function(all_44_3) = v5 & function(all_44_4)
% 35.92/5.63 | = v1 & function(all_44_6) = v3 & relation(all_44_3) = v4 &
% 35.92/5.63 | relation(all_44_4) = v0 & relation(all_44_6) = v2 & ( ~ (v3 = 0) |
% 35.92/5.63 | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0) | (v5 = 0 & v4 = 0)))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (fc9_relat_1) with all_44_4, all_44_6, all_44_3,
% 35.92/5.63 | simplifying with (14), (16), (25) gives:
% 35.92/5.63 | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 35.92/5.63 | (empty(all_44_3) = v2 & empty(all_44_4) = v0 & relation(all_44_3) = v3
% 35.92/5.63 | & relation(all_44_6) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 &
% 35.92/5.63 | v2 = 0)))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (dt_k5_relat_1) with all_44_4, all_44_6, all_44_3,
% 35.92/5.63 | simplifying with (14), (16), (25) gives:
% 35.92/5.63 | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_44_3) = v2
% 35.92/5.63 | & relation(all_44_4) = v0 & relation(all_44_6) = v1 & ( ~ (v1 = 0) |
% 35.92/5.63 | ~ (v0 = 0) | v2 = 0))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (7) with all_44_5, all_44_6, all_44_4, all_44_3,
% 35.92/5.63 | simplifying with (14), (15), (25), (26) gives:
% 35.92/5.63 | (40) all_44_3 = all_44_6 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 35.92/5.63 | (subset(v1, all_44_5) = v2 & relation_dom(all_44_6) = v1 &
% 35.92/5.63 | relation(all_44_6) = v0 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 35.92/5.63 |
% 35.92/5.63 | GROUND_INST: instantiating (8) with all_44_2, all_44_6, all_44_1, all_44_0,
% 35.92/5.63 | simplifying with (14), (17), (24), (27) gives:
% 35.92/5.64 | (41) all_44_0 = all_44_6 | ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 35.92/5.64 | (subset(v1, all_44_2) = v2 & relation_rng(all_44_6) = v1 &
% 35.92/5.64 | relation(all_44_6) = v0 & $i(v1) & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 35.92/5.64 |
% 35.92/5.64 | GROUND_INST: instantiating (6) with all_44_2, all_44_1, simplifying with (17),
% 35.92/5.64 | (27) gives:
% 35.92/5.64 | (42) function(all_44_1) = 0
% 35.92/5.64 |
% 35.92/5.64 | GROUND_INST: instantiating (5) with all_44_2, all_44_1, simplifying with (17),
% 35.92/5.64 | (27) gives:
% 35.92/5.64 | (43) relation(all_44_1) = 0
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (39) with fresh symbols all_64_0, all_64_1, all_64_2
% 35.92/5.64 | gives:
% 35.92/5.64 | (44) relation(all_44_3) = all_64_0 & relation(all_44_4) = all_64_2 &
% 35.92/5.64 | relation(all_44_6) = all_64_1 & ( ~ (all_64_1 = 0) | ~ (all_64_2 = 0)
% 35.92/5.64 | | all_64_0 = 0)
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (44) implies:
% 35.92/5.64 | (45) relation(all_44_6) = all_64_1
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (32) with fresh symbols all_68_0, all_68_1, all_68_2
% 35.92/5.64 | gives:
% 35.92/5.64 | (46) empty(all_44_2) = all_68_0 & empty(all_44_6) = all_68_2 &
% 35.92/5.64 | relation(all_44_6) = all_68_1 & ( ~ (all_68_0 = 0) | ~ (all_68_1 = 0)
% 35.92/5.64 | | all_68_2 = 0)
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (46) implies:
% 35.92/5.64 | (47) relation(all_44_6) = all_68_1
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (31) with fresh symbols all_70_0, all_70_1, all_70_2
% 35.92/5.64 | gives:
% 35.92/5.64 | (48) empty(all_44_5) = all_70_0 & empty(all_44_6) = all_70_2 &
% 35.92/5.64 | relation(all_44_6) = all_70_1 & ( ~ (all_70_0 = 0) | ~ (all_70_1 = 0)
% 35.92/5.64 | | all_70_2 = 0)
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (48) implies:
% 35.92/5.64 | (49) relation(all_44_6) = all_70_1
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (30) with fresh symbols all_76_0, all_76_1, all_76_2
% 35.92/5.64 | gives:
% 35.92/5.64 | (50) relation_dom(all_44_6) = all_76_1 & empty(all_76_1) = all_76_0 &
% 35.92/5.64 | empty(all_44_6) = all_76_2 & $i(all_76_1) & ( ~ (all_76_0 = 0) |
% 35.92/5.64 | all_76_2 = 0)
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (50) implies:
% 35.92/5.64 | (51) relation_dom(all_44_6) = all_76_1
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (29) with fresh symbols all_78_0, all_78_1, all_78_2
% 35.92/5.64 | gives:
% 35.92/5.64 | (52) relation_rng(all_44_6) = all_78_1 & empty(all_78_1) = all_78_0 &
% 35.92/5.64 | empty(all_44_6) = all_78_2 & $i(all_78_1) & ( ~ (all_78_0 = 0) |
% 35.92/5.64 | all_78_2 = 0)
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (52) implies:
% 35.92/5.64 | (53) relation_rng(all_44_6) = all_78_1
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (36) with fresh symbols all_80_0, all_80_1, all_80_2
% 35.92/5.64 | gives:
% 35.92/5.64 | (54) relation(all_44_0) = all_80_0 & relation(all_44_1) = all_80_1 &
% 35.92/5.64 | relation(all_44_6) = all_80_2 & ( ~ (all_80_1 = 0) | ~ (all_80_2 = 0)
% 35.92/5.64 | | all_80_0 = 0)
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (54) implies:
% 35.92/5.64 | (55) relation(all_44_6) = all_80_2
% 35.92/5.64 | (56) relation(all_44_0) = all_80_0
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (38) with fresh symbols all_100_0, all_100_1, all_100_2,
% 35.92/5.64 | all_100_3 gives:
% 35.92/5.64 | (57) empty(all_44_3) = all_100_1 & empty(all_44_4) = all_100_3 &
% 35.92/5.64 | relation(all_44_3) = all_100_0 & relation(all_44_6) = all_100_2 & ( ~
% 35.92/5.64 | (all_100_2 = 0) | ~ (all_100_3 = 0) | (all_100_0 = 0 & all_100_1 =
% 35.92/5.64 | 0))
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (57) implies:
% 35.92/5.64 | (58) relation(all_44_6) = all_100_2
% 35.92/5.64 |
% 35.92/5.64 | DELTA: instantiating (35) with fresh symbols all_102_0, all_102_1, all_102_2,
% 35.92/5.64 | all_102_3 gives:
% 35.92/5.64 | (59) empty(all_44_0) = all_102_1 & empty(all_44_6) = all_102_3 &
% 35.92/5.64 | relation(all_44_0) = all_102_0 & relation(all_44_1) = all_102_2 & ( ~
% 35.92/5.64 | (all_102_2 = 0) | ~ (all_102_3 = 0) | (all_102_0 = 0 & all_102_1 =
% 35.92/5.64 | 0))
% 35.92/5.64 |
% 35.92/5.64 | ALPHA: (59) implies:
% 35.92/5.65 | (60) relation(all_44_1) = all_102_2
% 35.92/5.65 | (61) relation(all_44_0) = all_102_0
% 35.92/5.65 |
% 35.92/5.65 | DELTA: instantiating (33) with fresh symbols all_106_0, all_106_1, all_106_2,
% 35.92/5.65 | all_106_3 gives:
% 35.92/5.65 | (62) empty(all_44_0) = all_106_1 & empty(all_44_1) = all_106_3 &
% 35.92/5.65 | relation(all_44_0) = all_106_0 & relation(all_44_6) = all_106_2 & ( ~
% 35.92/5.65 | (all_106_2 = 0) | ~ (all_106_3 = 0) | (all_106_0 = 0 & all_106_1 =
% 35.92/5.65 | 0))
% 35.92/5.65 |
% 35.92/5.65 | ALPHA: (62) implies:
% 35.92/5.65 | (63) relation(all_44_6) = all_106_2
% 35.92/5.65 | (64) relation(all_44_0) = all_106_0
% 35.92/5.65 |
% 35.92/5.65 | DELTA: instantiating (34) with fresh symbols all_108_0, all_108_1, all_108_2,
% 35.92/5.65 | all_108_3, all_108_4, all_108_5 gives:
% 35.92/5.65 | (65) function(all_44_0) = all_108_0 & function(all_44_1) = all_108_2 &
% 35.92/5.65 | function(all_44_6) = all_108_4 & relation(all_44_0) = all_108_1 &
% 35.92/5.65 | relation(all_44_1) = all_108_3 & relation(all_44_6) = all_108_5 & ( ~
% 35.92/5.65 | (all_108_2 = 0) | ~ (all_108_3 = 0) | ~ (all_108_4 = 0) | ~
% 35.92/5.65 | (all_108_5 = 0) | (all_108_0 = 0 & all_108_1 = 0))
% 35.92/5.65 |
% 35.92/5.65 | ALPHA: (65) implies:
% 35.92/5.65 | (66) relation(all_44_6) = all_108_5
% 35.92/5.65 | (67) relation(all_44_1) = all_108_3
% 35.92/5.65 | (68) relation(all_44_0) = all_108_1
% 35.92/5.65 | (69) function(all_44_6) = all_108_4
% 35.92/5.65 | (70) function(all_44_1) = all_108_2
% 35.92/5.65 | (71) ~ (all_108_2 = 0) | ~ (all_108_3 = 0) | ~ (all_108_4 = 0) | ~
% 35.92/5.65 | (all_108_5 = 0) | (all_108_0 = 0 & all_108_1 = 0)
% 35.92/5.65 |
% 35.92/5.65 | DELTA: instantiating (37) with fresh symbols all_110_0, all_110_1, all_110_2,
% 35.92/5.65 | all_110_3, all_110_4, all_110_5 gives:
% 35.92/5.65 | (72) function(all_44_3) = all_110_0 & function(all_44_4) = all_110_4 &
% 35.92/5.65 | function(all_44_6) = all_110_2 & relation(all_44_3) = all_110_1 &
% 35.92/5.65 | relation(all_44_4) = all_110_5 & relation(all_44_6) = all_110_3 & ( ~
% 35.92/5.65 | (all_110_2 = 0) | ~ (all_110_3 = 0) | ~ (all_110_4 = 0) | ~
% 35.92/5.65 | (all_110_5 = 0) | (all_110_0 = 0 & all_110_1 = 0))
% 35.92/5.65 |
% 35.92/5.65 | ALPHA: (72) implies:
% 35.92/5.65 | (73) relation(all_44_6) = all_110_3
% 35.92/5.65 | (74) function(all_44_6) = all_110_2
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with 0, all_68_1, all_44_6, simplifying with
% 35.92/5.65 | (20), (47) gives:
% 35.92/5.65 | (75) all_68_1 = 0
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_68_1, all_80_2, all_44_6, simplifying
% 35.92/5.65 | with (47), (55) gives:
% 35.92/5.65 | (76) all_80_2 = all_68_1
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_64_1, all_80_2, all_44_6, simplifying
% 35.92/5.65 | with (45), (55) gives:
% 35.92/5.65 | (77) all_80_2 = all_64_1
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_80_2, all_100_2, all_44_6, simplifying
% 35.92/5.65 | with (55), (58) gives:
% 35.92/5.65 | (78) all_100_2 = all_80_2
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_100_2, all_106_2, all_44_6,
% 35.92/5.65 | simplifying with (58), (63) gives:
% 35.92/5.65 | (79) all_106_2 = all_100_2
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_106_2, all_108_5, all_44_6,
% 35.92/5.65 | simplifying with (63), (66) gives:
% 35.92/5.65 | (80) all_108_5 = all_106_2
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_108_5, all_110_3, all_44_6,
% 35.92/5.65 | simplifying with (66), (73) gives:
% 35.92/5.65 | (81) all_110_3 = all_108_5
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_70_1, all_110_3, all_44_6, simplifying
% 35.92/5.65 | with (49), (73) gives:
% 35.92/5.65 | (82) all_110_3 = all_70_1
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_102_2, all_108_3, all_44_1,
% 35.92/5.65 | simplifying with (60), (67) gives:
% 35.92/5.65 | (83) all_108_3 = all_102_2
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with 0, all_108_3, all_44_1, simplifying with
% 35.92/5.65 | (43), (67) gives:
% 35.92/5.65 | (84) all_108_3 = 0
% 35.92/5.65 |
% 35.92/5.65 | GROUND_INST: instantiating (9) with all_106_0, all_108_1, all_44_0,
% 35.92/5.65 | simplifying with (64), (68) gives:
% 35.92/5.65 | (85) all_108_1 = all_106_0
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (9) with all_102_0, all_108_1, all_44_0,
% 35.92/5.66 | simplifying with (61), (68) gives:
% 35.92/5.66 | (86) all_108_1 = all_102_0
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (9) with all_80_0, all_108_1, all_44_0, simplifying
% 35.92/5.66 | with (56), (68) gives:
% 35.92/5.66 | (87) all_108_1 = all_80_0
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (10) with 0, all_110_2, all_44_6, simplifying with
% 35.92/5.66 | (21), (74) gives:
% 35.92/5.66 | (88) all_110_2 = 0
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (10) with all_108_4, all_110_2, all_44_6,
% 35.92/5.66 | simplifying with (69), (74) gives:
% 35.92/5.66 | (89) all_110_2 = all_108_4
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (10) with 0, all_108_2, all_44_1, simplifying with
% 35.92/5.66 | (42), (70) gives:
% 35.92/5.66 | (90) all_108_2 = 0
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (11) with all_44_5, all_76_1, all_44_6, simplifying
% 35.92/5.66 | with (22), (51) gives:
% 35.92/5.66 | (91) all_76_1 = all_44_5
% 35.92/5.66 |
% 35.92/5.66 | GROUND_INST: instantiating (12) with all_44_2, all_78_1, all_44_6, simplifying
% 35.92/5.66 | with (23), (53) gives:
% 35.92/5.66 | (92) all_78_1 = all_44_2
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (88), (89) imply:
% 35.92/5.66 | (93) all_108_4 = 0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (81), (82) imply:
% 35.92/5.66 | (94) all_108_5 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | SIMP: (94) implies:
% 35.92/5.66 | (95) all_108_5 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (85), (86) imply:
% 35.92/5.66 | (96) all_106_0 = all_102_0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (85), (87) imply:
% 35.92/5.66 | (97) all_106_0 = all_80_0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (83), (84) imply:
% 35.92/5.66 | (98) all_102_2 = 0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (80), (95) imply:
% 35.92/5.66 | (99) all_106_2 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | SIMP: (99) implies:
% 35.92/5.66 | (100) all_106_2 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (96), (97) imply:
% 35.92/5.66 | (101) all_102_0 = all_80_0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (79), (100) imply:
% 35.92/5.66 | (102) all_100_2 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | SIMP: (102) implies:
% 35.92/5.66 | (103) all_100_2 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (78), (103) imply:
% 35.92/5.66 | (104) all_80_2 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | SIMP: (104) implies:
% 35.92/5.66 | (105) all_80_2 = all_70_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (76), (105) imply:
% 35.92/5.66 | (106) all_70_1 = all_68_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (77), (105) imply:
% 35.92/5.66 | (107) all_70_1 = all_64_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (106), (107) imply:
% 35.92/5.66 | (108) all_68_1 = all_64_1
% 35.92/5.66 |
% 35.92/5.66 | SIMP: (108) implies:
% 35.92/5.66 | (109) all_68_1 = all_64_1
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (75), (109) imply:
% 35.92/5.66 | (110) all_64_1 = 0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (107), (110) imply:
% 35.92/5.66 | (111) all_70_1 = 0
% 35.92/5.66 |
% 35.92/5.66 | COMBINE_EQS: (95), (111) imply:
% 35.92/5.66 | (112) all_108_5 = 0
% 35.92/5.66 |
% 35.92/5.66 | BETA: splitting (71) gives:
% 35.92/5.66 |
% 35.92/5.66 | Case 1:
% 35.92/5.66 | |
% 35.92/5.66 | | (113) ~ (all_108_2 = 0)
% 35.92/5.66 | |
% 35.92/5.66 | | REDUCE: (90), (113) imply:
% 35.92/5.66 | | (114) $false
% 35.92/5.66 | |
% 35.92/5.66 | | CLOSE: (114) is inconsistent.
% 35.92/5.66 | |
% 35.92/5.66 | Case 2:
% 35.92/5.66 | |
% 35.92/5.66 | | (115) ~ (all_108_3 = 0) | ~ (all_108_4 = 0) | ~ (all_108_5 = 0) |
% 35.92/5.66 | | (all_108_0 = 0 & all_108_1 = 0)
% 35.92/5.66 | |
% 35.92/5.66 | | BETA: splitting (115) gives:
% 35.92/5.66 | |
% 35.92/5.66 | | Case 1:
% 35.92/5.66 | | |
% 35.92/5.66 | | | (116) ~ (all_108_3 = 0)
% 35.92/5.66 | | |
% 35.92/5.66 | | | REDUCE: (84), (116) imply:
% 35.92/5.66 | | | (117) $false
% 35.92/5.66 | | |
% 35.92/5.66 | | | CLOSE: (117) is inconsistent.
% 35.92/5.66 | | |
% 35.92/5.66 | | Case 2:
% 35.92/5.66 | | |
% 35.92/5.66 | | | (118) ~ (all_108_4 = 0) | ~ (all_108_5 = 0) | (all_108_0 = 0 &
% 35.92/5.66 | | | all_108_1 = 0)
% 35.92/5.66 | | |
% 35.92/5.66 | | | BETA: splitting (118) gives:
% 35.92/5.66 | | |
% 35.92/5.66 | | | Case 1:
% 35.92/5.66 | | | |
% 35.92/5.66 | | | | (119) ~ (all_108_4 = 0)
% 35.92/5.66 | | | |
% 35.92/5.67 | | | | REDUCE: (93), (119) imply:
% 35.92/5.67 | | | | (120) $false
% 35.92/5.67 | | | |
% 35.92/5.67 | | | | CLOSE: (120) is inconsistent.
% 35.92/5.67 | | | |
% 35.92/5.67 | | | Case 2:
% 35.92/5.67 | | | |
% 35.92/5.67 | | | | (121) ~ (all_108_5 = 0) | (all_108_0 = 0 & all_108_1 = 0)
% 35.92/5.67 | | | |
% 35.92/5.67 | | | | BETA: splitting (121) gives:
% 35.92/5.67 | | | |
% 35.92/5.67 | | | | Case 1:
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | (122) ~ (all_108_5 = 0)
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | REDUCE: (112), (122) imply:
% 35.92/5.67 | | | | | (123) $false
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | CLOSE: (123) is inconsistent.
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | Case 2:
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | (124) all_108_0 = 0 & all_108_1 = 0
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | ALPHA: (124) implies:
% 35.92/5.67 | | | | | (125) all_108_1 = 0
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | COMBINE_EQS: (87), (125) imply:
% 35.92/5.67 | | | | | (126) all_80_0 = 0
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | REDUCE: (56), (126) imply:
% 35.92/5.67 | | | | | (127) relation(all_44_0) = 0
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | GROUND_INST: instantiating (1) with all_44_0, simplifying with (19),
% 35.92/5.67 | | | | | (127) gives:
% 35.92/5.67 | | | | | (128) ? [v0: any] : ? [v1: $i] : ? [v2: any] :
% 35.92/5.67 | | | | | (relation_dom(all_44_0) = v1 & empty(v1) = v2 &
% 35.92/5.67 | | | | | empty(all_44_0) = v0 & $i(v1) & ( ~ (v2 = 0) | v0 = 0))
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | DELTA: instantiating (128) with fresh symbols all_291_0, all_291_1,
% 35.92/5.67 | | | | | all_291_2 gives:
% 35.92/5.67 | | | | | (129) relation_dom(all_44_0) = all_291_1 & empty(all_291_1) =
% 35.92/5.67 | | | | | all_291_0 & empty(all_44_0) = all_291_2 & $i(all_291_1) & ( ~
% 35.92/5.67 | | | | | (all_291_0 = 0) | all_291_2 = 0)
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | ALPHA: (129) implies:
% 35.92/5.67 | | | | | (130) $i(all_291_1)
% 35.92/5.67 | | | | | (131) relation_dom(all_44_0) = all_291_1
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | BETA: splitting (28) gives:
% 35.92/5.67 | | | | |
% 35.92/5.67 | | | | | Case 1:
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | (132) ~ (all_44_0 = all_44_6)
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | BETA: splitting (41) gives:
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | Case 1:
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | (133) all_44_0 = all_44_6
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | REDUCE: (132), (133) imply:
% 35.92/5.67 | | | | | | | (134) $false
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | CLOSE: (134) is inconsistent.
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | Case 2:
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | (135) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (subset(v1,
% 35.92/5.67 | | | | | | | all_44_2) = v2 & relation_rng(all_44_6) = v1 &
% 35.92/5.67 | | | | | | | relation(all_44_6) = v0 & $i(v1) & ( ~ (v2 = 0) | ~
% 35.92/5.67 | | | | | | | (v0 = 0)))
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | DELTA: instantiating (135) with fresh symbols all_400_0,
% 35.92/5.67 | | | | | | | all_400_1, all_400_2 gives:
% 35.92/5.67 | | | | | | | (136) subset(all_400_1, all_44_2) = all_400_0 &
% 35.92/5.67 | | | | | | | relation_rng(all_44_6) = all_400_1 & relation(all_44_6) =
% 35.92/5.67 | | | | | | | all_400_2 & $i(all_400_1) & ( ~ (all_400_0 = 0) | ~
% 35.92/5.67 | | | | | | | (all_400_2 = 0))
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | ALPHA: (136) implies:
% 35.92/5.67 | | | | | | | (137) $i(all_400_1)
% 35.92/5.67 | | | | | | | (138) relation(all_44_6) = all_400_2
% 35.92/5.67 | | | | | | | (139) relation_rng(all_44_6) = all_400_1
% 35.92/5.67 | | | | | | | (140) subset(all_400_1, all_44_2) = all_400_0
% 35.92/5.67 | | | | | | | (141) ~ (all_400_0 = 0) | ~ (all_400_2 = 0)
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | GROUND_INST: instantiating (9) with 0, all_400_2, all_44_6,
% 35.92/5.67 | | | | | | | simplifying with (20), (138) gives:
% 35.92/5.67 | | | | | | | (142) all_400_2 = 0
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | GROUND_INST: instantiating (12) with all_44_2, all_400_1,
% 35.92/5.67 | | | | | | | all_44_6, simplifying with (23), (139) gives:
% 35.92/5.67 | | | | | | | (143) all_400_1 = all_44_2
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | REDUCE: (140), (143) imply:
% 35.92/5.67 | | | | | | | (144) subset(all_44_2, all_44_2) = all_400_0
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | BETA: splitting (141) gives:
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | Case 1:
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | (145) ~ (all_400_0 = 0)
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | GROUND_INST: instantiating (reflexivity_r1_tarski) with
% 35.92/5.67 | | | | | | | | all_44_2, all_400_0, simplifying with (17), (144)
% 35.92/5.67 | | | | | | | | gives:
% 35.92/5.67 | | | | | | | | (146) all_400_0 = 0
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | REDUCE: (145), (146) imply:
% 35.92/5.67 | | | | | | | | (147) $false
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | CLOSE: (147) is inconsistent.
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | Case 2:
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | (148) ~ (all_400_2 = 0)
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | REDUCE: (142), (148) imply:
% 35.92/5.67 | | | | | | | | (149) $false
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | | CLOSE: (149) is inconsistent.
% 35.92/5.67 | | | | | | | |
% 35.92/5.67 | | | | | | | End of split
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | End of split
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | Case 2:
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | (150) all_44_0 = all_44_6
% 35.92/5.67 | | | | | | (151) ~ (all_44_3 = all_44_6)
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | REDUCE: (131), (150) imply:
% 35.92/5.67 | | | | | | (152) relation_dom(all_44_6) = all_291_1
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | BETA: splitting (40) gives:
% 35.92/5.67 | | | | | |
% 35.92/5.67 | | | | | | Case 1:
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | (153) all_44_3 = all_44_6
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | REDUCE: (151), (153) imply:
% 35.92/5.67 | | | | | | | (154) $false
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | CLOSE: (154) is inconsistent.
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | Case 2:
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | (155) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (subset(v1,
% 35.92/5.67 | | | | | | | all_44_5) = v2 & relation_dom(all_44_6) = v1 &
% 35.92/5.67 | | | | | | | relation(all_44_6) = v0 & $i(v1) & ( ~ (v2 = 0) | ~
% 35.92/5.67 | | | | | | | (v0 = 0)))
% 35.92/5.67 | | | | | | |
% 35.92/5.67 | | | | | | | DELTA: instantiating (155) with fresh symbols all_400_0,
% 35.92/5.67 | | | | | | | all_400_1, all_400_2 gives:
% 35.92/5.68 | | | | | | | (156) subset(all_400_1, all_44_5) = all_400_0 &
% 35.92/5.68 | | | | | | | relation_dom(all_44_6) = all_400_1 & relation(all_44_6) =
% 35.92/5.68 | | | | | | | all_400_2 & $i(all_400_1) & ( ~ (all_400_0 = 0) | ~
% 35.92/5.68 | | | | | | | (all_400_2 = 0))
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | ALPHA: (156) implies:
% 35.92/5.68 | | | | | | | (157) relation(all_44_6) = all_400_2
% 35.92/5.68 | | | | | | | (158) relation_dom(all_44_6) = all_400_1
% 35.92/5.68 | | | | | | | (159) subset(all_400_1, all_44_5) = all_400_0
% 35.92/5.68 | | | | | | | (160) ~ (all_400_0 = 0) | ~ (all_400_2 = 0)
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | GROUND_INST: instantiating (9) with 0, all_400_2, all_44_6,
% 35.92/5.68 | | | | | | | simplifying with (20), (157) gives:
% 35.92/5.68 | | | | | | | (161) all_400_2 = 0
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | GROUND_INST: instantiating (11) with all_44_5, all_400_1,
% 35.92/5.68 | | | | | | | all_44_6, simplifying with (22), (158) gives:
% 35.92/5.68 | | | | | | | (162) all_400_1 = all_44_5
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | GROUND_INST: instantiating (11) with all_291_1, all_400_1,
% 35.92/5.68 | | | | | | | all_44_6, simplifying with (152), (158) gives:
% 35.92/5.68 | | | | | | | (163) all_400_1 = all_291_1
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | COMBINE_EQS: (162), (163) imply:
% 35.92/5.68 | | | | | | | (164) all_291_1 = all_44_5
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | SIMP: (164) implies:
% 35.92/5.68 | | | | | | | (165) all_291_1 = all_44_5
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | REDUCE: (159), (162) imply:
% 35.92/5.68 | | | | | | | (166) subset(all_44_5, all_44_5) = all_400_0
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | BETA: splitting (160) gives:
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | | Case 1:
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | (167) ~ (all_400_0 = 0)
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | GROUND_INST: instantiating (reflexivity_r1_tarski) with
% 35.92/5.68 | | | | | | | | all_44_5, all_400_0, simplifying with (15), (166)
% 35.92/5.68 | | | | | | | | gives:
% 35.92/5.68 | | | | | | | | (168) all_400_0 = 0
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | REDUCE: (167), (168) imply:
% 35.92/5.68 | | | | | | | | (169) $false
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | CLOSE: (169) is inconsistent.
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | Case 2:
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | (170) ~ (all_400_2 = 0)
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | REDUCE: (161), (170) imply:
% 35.92/5.68 | | | | | | | | (171) $false
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | | CLOSE: (171) is inconsistent.
% 35.92/5.68 | | | | | | | |
% 35.92/5.68 | | | | | | | End of split
% 35.92/5.68 | | | | | | |
% 35.92/5.68 | | | | | | End of split
% 35.92/5.68 | | | | | |
% 35.92/5.68 | | | | | End of split
% 35.92/5.68 | | | | |
% 35.92/5.68 | | | | End of split
% 35.92/5.68 | | | |
% 35.92/5.68 | | | End of split
% 35.92/5.68 | | |
% 35.92/5.68 | | End of split
% 35.92/5.68 | |
% 35.92/5.68 | End of split
% 35.92/5.68 |
% 35.92/5.68 End of proof
% 35.92/5.68 % SZS output end Proof for theBenchmark
% 35.92/5.68
% 35.92/5.68 5093ms
%------------------------------------------------------------------------------