TSTP Solution File: SEU019+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU019+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 : n011.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 17:42:18 EDT 2023
% Result : Theorem 7.67s 1.85s
% Output : Proof 11.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 17:00:06 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.53/1.05 Prover 4: Preprocessing ...
% 2.53/1.05 Prover 1: Preprocessing ...
% 2.87/1.09 Prover 3: Preprocessing ...
% 2.87/1.09 Prover 0: Preprocessing ...
% 2.87/1.09 Prover 5: Preprocessing ...
% 2.87/1.09 Prover 6: Preprocessing ...
% 2.87/1.09 Prover 2: Preprocessing ...
% 4.90/1.54 Prover 1: Warning: ignoring some quantifiers
% 6.14/1.56 Prover 3: Warning: ignoring some quantifiers
% 6.14/1.57 Prover 1: Constructing countermodel ...
% 6.14/1.58 Prover 2: Proving ...
% 6.14/1.58 Prover 5: Proving ...
% 6.14/1.59 Prover 3: Constructing countermodel ...
% 6.48/1.59 Prover 6: Proving ...
% 7.67/1.79 Prover 4: Warning: ignoring some quantifiers
% 7.67/1.84 Prover 3: proved (1218ms)
% 7.67/1.85
% 7.67/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.67/1.85
% 8.37/1.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.37/1.86 Prover 4: Constructing countermodel ...
% 8.37/1.86 Prover 5: stopped
% 8.37/1.86 Prover 6: stopped
% 8.37/1.86 Prover 2: stopped
% 8.37/1.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.37/1.87 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.37/1.87 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.37/1.88 Prover 0: Proving ...
% 8.37/1.88 Prover 0: stopped
% 8.68/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.68/1.91 Prover 7: Preprocessing ...
% 8.68/1.92 Prover 11: Preprocessing ...
% 8.68/1.92 Prover 8: Preprocessing ...
% 8.68/1.93 Prover 10: Preprocessing ...
% 9.05/1.94 Prover 13: Preprocessing ...
% 9.51/2.03 Prover 7: Warning: ignoring some quantifiers
% 9.51/2.04 Prover 7: Constructing countermodel ...
% 9.51/2.05 Prover 10: Warning: ignoring some quantifiers
% 9.51/2.05 Prover 13: Warning: ignoring some quantifiers
% 9.51/2.06 Prover 10: Constructing countermodel ...
% 9.51/2.06 Prover 1: Found proof (size 62)
% 9.51/2.06 Prover 1: proved (1438ms)
% 9.51/2.06 Prover 7: stopped
% 9.51/2.07 Prover 10: stopped
% 9.51/2.07 Prover 4: stopped
% 9.51/2.08 Prover 13: Constructing countermodel ...
% 9.51/2.09 Prover 13: stopped
% 9.51/2.11 Prover 8: Warning: ignoring some quantifiers
% 9.51/2.12 Prover 8: Constructing countermodel ...
% 9.51/2.13 Prover 8: stopped
% 9.51/2.18 Prover 11: Warning: ignoring some quantifiers
% 9.51/2.19 Prover 11: Constructing countermodel ...
% 9.51/2.20 Prover 11: stopped
% 9.51/2.20
% 9.51/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.51/2.20
% 10.61/2.21 % SZS output start Proof for theBenchmark
% 10.61/2.22 Assumptions after simplification:
% 10.61/2.22 ---------------------------------
% 10.61/2.22
% 10.61/2.22 (d8_funct_1)
% 10.61/2.25 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 10.61/2.25 any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0)
% 10.61/2.25 = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1
% 10.61/2.25 = 0) | ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~ (in(v6, v4) = 0)
% 10.61/2.25 | ~ (in(v5, v4) = 0) | ~ $i(v6) | ~ $i(v5) | ? [v7: $i] : ?
% 10.61/2.25 [v8: $i] : ( ~ (v8 = v7) & apply(v0, v6) = v8 & apply(v0, v5) = v7
% 10.61/2.25 & $i(v8) & $i(v7)))) & (v1 = 0 | ? [v5: $i] : ? [v6: $i] : ?
% 10.61/2.25 [v7: $i] : ( ~ (v6 = v5) & apply(v0, v6) = v7 & apply(v0, v5) = v7 &
% 10.61/2.25 in(v6, v4) = 0 & in(v5, v4) = 0 & $i(v7) & $i(v6) & $i(v5)))))))
% 10.61/2.25
% 10.61/2.25 (fc2_funct_1)
% 10.61/2.25 ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~ $i(v0) |
% 10.61/2.25 relation(v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) =
% 10.61/2.25 v1) | ~ $i(v0) | function(v1) = 0)
% 10.61/2.25
% 10.61/2.25 (fc5_relat_1)
% 10.61/2.25 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 10.61/2.25 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 10.61/2.25 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 10.61/2.25
% 10.61/2.25 (t34_funct_1)
% 10.61/2.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity_relation(v0) = v2) |
% 10.61/2.25 ~ (function(v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: $i] :
% 10.61/2.25 (relation_dom(v1) = v4 & relation(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | (( ~
% 10.61/2.25 (v4 = v0) | v2 = v1 | ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) &
% 10.61/2.25 apply(v1, v5) = v6 & in(v5, v0) = 0 & $i(v6) & $i(v5))) & ( ~ (v2
% 10.61/2.25 = v1) | (v4 = v0 & ! [v5: $i] : ! [v6: $i] : (v6 = v5 | ~
% 10.61/2.25 (apply(v1, v5) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) &
% 10.61/2.25 in(v5, v0) = v7))))))))
% 10.61/2.25
% 10.61/2.25 (t52_funct_1)
% 10.61/2.26 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 10.61/2.26 identity_relation(v0) = v1 & one_to_one(v1) = v2 & $i(v1) & $i(v0))
% 10.61/2.26
% 10.61/2.26 (function-axioms)
% 10.61/2.26 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.61/2.26 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 10.61/2.26 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.61/2.26 $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & !
% 10.61/2.26 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3,
% 10.61/2.26 v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.61/2.26 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 10.61/2.26 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.61/2.26 $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 10.61/2.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.61/2.26 ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) =
% 10.61/2.26 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.61/2.26 (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0:
% 10.61/2.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.61/2.26 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.61/2.26 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 10.61/2.26 (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.61/2.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 10.61/2.26 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.61/2.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 10.61/2.26 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.61/2.26 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 10.61/2.26 (empty(v2) = v0))
% 10.61/2.26
% 10.61/2.26 Further assumptions not needed in the proof:
% 10.61/2.26 --------------------------------------------
% 10.61/2.26 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, dt_k6_relat_1,
% 10.61/2.26 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 10.61/2.26 fc7_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_relat_1,
% 10.61/2.26 rc2_subset_1, rc2_xboole_0, rc3_relat_1, reflexivity_r1_tarski, t1_subset,
% 10.61/2.26 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 10.61/2.26
% 10.61/2.26 Those formulas are unsatisfiable:
% 10.61/2.26 ---------------------------------
% 10.61/2.26
% 10.61/2.26 Begin of proof
% 10.61/2.26 |
% 10.61/2.26 | ALPHA: (fc2_funct_1) implies:
% 10.61/2.26 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~
% 10.61/2.26 | $i(v0) | function(v1) = 0)
% 10.61/2.27 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (identity_relation(v0) = v1) | ~
% 10.61/2.27 | $i(v0) | relation(v1) = 0)
% 10.61/2.27 |
% 10.61/2.27 | ALPHA: (function-axioms) implies:
% 10.61/2.27 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.61/2.27 | (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 10.61/2.27 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.61/2.27 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 10.61/2.27 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.61/2.27 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 10.61/2.27 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.61/2.27 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.61/2.27 |
% 10.61/2.27 | DELTA: instantiating (t52_funct_1) with fresh symbols all_39_0, all_39_1,
% 10.61/2.27 | all_39_2 gives:
% 10.61/2.27 | (7) ~ (all_39_0 = 0) & identity_relation(all_39_2) = all_39_1 &
% 10.61/2.27 | one_to_one(all_39_1) = all_39_0 & $i(all_39_1) & $i(all_39_2)
% 10.61/2.27 |
% 10.61/2.27 | ALPHA: (7) implies:
% 10.61/2.27 | (8) ~ (all_39_0 = 0)
% 10.61/2.27 | (9) $i(all_39_2)
% 10.61/2.27 | (10) $i(all_39_1)
% 10.61/2.27 | (11) one_to_one(all_39_1) = all_39_0
% 10.61/2.27 | (12) identity_relation(all_39_2) = all_39_1
% 10.61/2.27 |
% 10.61/2.27 | GROUND_INST: instantiating (d8_funct_1) with all_39_1, all_39_0, simplifying
% 10.61/2.27 | with (10), (11) gives:
% 10.61/2.27 | (13) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(all_39_1) =
% 10.61/2.27 | v2 & relation(all_39_1) = v0 & function(all_39_1) = v1 & $i(v2) & (
% 10.61/2.27 | ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (all_39_0 = 0) | ! [v3: $i] : !
% 10.61/2.27 | [v4: $i] : (v4 = v3 | ~ (in(v4, v2) = 0) | ~ (in(v3, v2) =
% 10.61/2.27 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: $i] : ? [v6: $i] : (
% 10.61/2.27 | ~ (v6 = v5) & apply(all_39_1, v4) = v6 & apply(all_39_1,
% 10.61/2.27 | v3) = v5 & $i(v6) & $i(v5)))) & (all_39_0 = 0 | ? [v3:
% 10.61/2.27 | $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v4 = v3) &
% 10.61/2.27 | apply(all_39_1, v4) = v5 & apply(all_39_1, v3) = v5 & in(v4,
% 10.61/2.27 | v2) = 0 & in(v3, v2) = 0 & $i(v5) & $i(v4) & $i(v3))))))
% 10.61/2.27 |
% 10.61/2.27 | GROUND_INST: instantiating (2) with all_39_2, all_39_1, simplifying with (9),
% 10.61/2.27 | (12) gives:
% 10.61/2.27 | (14) relation(all_39_1) = 0
% 10.61/2.27 |
% 10.61/2.27 | GROUND_INST: instantiating (1) with all_39_2, all_39_1, simplifying with (9),
% 10.61/2.27 | (12) gives:
% 10.61/2.27 | (15) function(all_39_1) = 0
% 10.61/2.27 |
% 10.61/2.27 | DELTA: instantiating (13) with fresh symbols all_49_0, all_49_1, all_49_2
% 10.61/2.27 | gives:
% 10.61/2.28 | (16) relation_dom(all_39_1) = all_49_0 & relation(all_39_1) = all_49_2 &
% 10.61/2.28 | function(all_39_1) = all_49_1 & $i(all_49_0) & ( ~ (all_49_1 = 0) | ~
% 10.61/2.28 | (all_49_2 = 0) | (( ~ (all_39_0 = 0) | ! [v0: $i] : ! [v1: $i] :
% 10.61/2.28 | (v1 = v0 | ~ (in(v1, all_49_0) = 0) | ~ (in(v0, all_49_0) = 0)
% 10.61/2.28 | | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3
% 10.61/2.28 | = v2) & apply(all_39_1, v1) = v3 & apply(all_39_1, v0) =
% 10.61/2.28 | v2 & $i(v3) & $i(v2)))) & (all_39_0 = 0 | ? [v0: $i] : ?
% 10.61/2.28 | [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & apply(all_39_1, v1) =
% 10.61/2.28 | v2 & apply(all_39_1, v0) = v2 & in(v1, all_49_0) = 0 & in(v0,
% 10.61/2.28 | all_49_0) = 0 & $i(v2) & $i(v1) & $i(v0)))))
% 10.61/2.28 |
% 10.61/2.28 | ALPHA: (16) implies:
% 10.61/2.28 | (17) function(all_39_1) = all_49_1
% 10.61/2.28 | (18) relation(all_39_1) = all_49_2
% 10.61/2.28 | (19) relation_dom(all_39_1) = all_49_0
% 10.61/2.28 | (20) ~ (all_49_1 = 0) | ~ (all_49_2 = 0) | (( ~ (all_39_0 = 0) | ! [v0:
% 10.61/2.28 | $i] : ! [v1: $i] : (v1 = v0 | ~ (in(v1, all_49_0) = 0) | ~
% 10.61/2.28 | (in(v0, all_49_0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 10.61/2.28 | ? [v3: $i] : ( ~ (v3 = v2) & apply(all_39_1, v1) = v3 &
% 10.61/2.28 | apply(all_39_1, v0) = v2 & $i(v3) & $i(v2)))) & (all_39_0 = 0
% 10.61/2.28 | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 10.61/2.28 | apply(all_39_1, v1) = v2 & apply(all_39_1, v0) = v2 & in(v1,
% 10.61/2.28 | all_49_0) = 0 & in(v0, all_49_0) = 0 & $i(v2) & $i(v1) &
% 10.61/2.28 | $i(v0))))
% 10.61/2.28 |
% 10.61/2.28 | GROUND_INST: instantiating (3) with 0, all_49_1, all_39_1, simplifying with
% 10.61/2.28 | (15), (17) gives:
% 10.61/2.28 | (21) all_49_1 = 0
% 10.61/2.28 |
% 10.61/2.28 | GROUND_INST: instantiating (4) with 0, all_49_2, all_39_1, simplifying with
% 10.61/2.28 | (14), (18) gives:
% 10.61/2.28 | (22) all_49_2 = 0
% 10.61/2.28 |
% 10.61/2.28 | BETA: splitting (20) gives:
% 10.61/2.28 |
% 10.61/2.28 | Case 1:
% 10.61/2.28 | |
% 10.61/2.28 | | (23) ~ (all_49_1 = 0)
% 10.61/2.28 | |
% 10.61/2.28 | | REDUCE: (21), (23) imply:
% 10.61/2.28 | | (24) $false
% 10.61/2.28 | |
% 10.61/2.28 | | CLOSE: (24) is inconsistent.
% 10.61/2.28 | |
% 10.61/2.28 | Case 2:
% 10.61/2.28 | |
% 10.61/2.29 | | (25) ~ (all_49_2 = 0) | (( ~ (all_39_0 = 0) | ! [v0: $i] : ! [v1: $i]
% 10.61/2.29 | | : (v1 = v0 | ~ (in(v1, all_49_0) = 0) | ~ (in(v0, all_49_0) =
% 10.61/2.29 | | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~
% 10.61/2.29 | | (v3 = v2) & apply(all_39_1, v1) = v3 & apply(all_39_1, v0) =
% 10.61/2.29 | | v2 & $i(v3) & $i(v2)))) & (all_39_0 = 0 | ? [v0: $i] : ?
% 10.61/2.29 | | [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & apply(all_39_1, v1) =
% 10.61/2.29 | | v2 & apply(all_39_1, v0) = v2 & in(v1, all_49_0) = 0 & in(v0,
% 10.61/2.29 | | all_49_0) = 0 & $i(v2) & $i(v1) & $i(v0))))
% 10.61/2.29 | |
% 10.61/2.29 | | BETA: splitting (25) gives:
% 10.61/2.29 | |
% 10.61/2.29 | | Case 1:
% 10.61/2.29 | | |
% 10.61/2.29 | | | (26) ~ (all_49_2 = 0)
% 10.61/2.29 | | |
% 10.61/2.29 | | | REDUCE: (22), (26) imply:
% 10.61/2.29 | | | (27) $false
% 10.61/2.29 | | |
% 10.61/2.29 | | | CLOSE: (27) is inconsistent.
% 10.61/2.29 | | |
% 10.61/2.29 | | Case 2:
% 10.61/2.29 | | |
% 10.61/2.29 | | | (28) ( ~ (all_39_0 = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 10.61/2.29 | | | (in(v1, all_49_0) = 0) | ~ (in(v0, all_49_0) = 0) | ~ $i(v1)
% 10.61/2.29 | | | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) &
% 10.61/2.29 | | | apply(all_39_1, v1) = v3 & apply(all_39_1, v0) = v2 & $i(v3)
% 10.61/2.29 | | | & $i(v2)))) & (all_39_0 = 0 | ? [v0: $i] : ? [v1: $i] : ?
% 10.61/2.29 | | | [v2: $i] : ( ~ (v1 = v0) & apply(all_39_1, v1) = v2 &
% 10.61/2.29 | | | apply(all_39_1, v0) = v2 & in(v1, all_49_0) = 0 & in(v0,
% 10.61/2.29 | | | all_49_0) = 0 & $i(v2) & $i(v1) & $i(v0)))
% 10.61/2.29 | | |
% 10.61/2.29 | | | ALPHA: (28) implies:
% 10.61/2.29 | | | (29) all_39_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 =
% 10.61/2.29 | | | v0) & apply(all_39_1, v1) = v2 & apply(all_39_1, v0) = v2 &
% 10.61/2.29 | | | in(v1, all_49_0) = 0 & in(v0, all_49_0) = 0 & $i(v2) & $i(v1) &
% 10.61/2.29 | | | $i(v0))
% 10.61/2.29 | | |
% 10.61/2.29 | | | BETA: splitting (29) gives:
% 10.61/2.29 | | |
% 10.61/2.29 | | | Case 1:
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | (30) all_39_0 = 0
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | REDUCE: (8), (30) imply:
% 10.61/2.29 | | | | (31) $false
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | CLOSE: (31) is inconsistent.
% 10.61/2.29 | | | |
% 10.61/2.29 | | | Case 2:
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 10.61/2.29 | | | | apply(all_39_1, v1) = v2 & apply(all_39_1, v0) = v2 & in(v1,
% 10.61/2.29 | | | | all_49_0) = 0 & in(v0, all_49_0) = 0 & $i(v2) & $i(v1) &
% 10.61/2.29 | | | | $i(v0))
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | DELTA: instantiating (32) with fresh symbols all_67_0, all_67_1,
% 10.61/2.29 | | | | all_67_2 gives:
% 10.61/2.29 | | | | (33) ~ (all_67_1 = all_67_2) & apply(all_39_1, all_67_1) = all_67_0
% 10.61/2.29 | | | | & apply(all_39_1, all_67_2) = all_67_0 & in(all_67_1, all_49_0)
% 10.61/2.29 | | | | = 0 & in(all_67_2, all_49_0) = 0 & $i(all_67_0) & $i(all_67_1) &
% 10.61/2.29 | | | | $i(all_67_2)
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | ALPHA: (33) implies:
% 10.61/2.29 | | | | (34) ~ (all_67_1 = all_67_2)
% 10.61/2.29 | | | | (35) $i(all_67_2)
% 10.61/2.29 | | | | (36) $i(all_67_1)
% 10.61/2.29 | | | | (37) in(all_67_2, all_49_0) = 0
% 10.61/2.29 | | | | (38) in(all_67_1, all_49_0) = 0
% 10.61/2.29 | | | | (39) apply(all_39_1, all_67_2) = all_67_0
% 10.61/2.29 | | | | (40) apply(all_39_1, all_67_1) = all_67_0
% 10.61/2.29 | | | |
% 10.61/2.29 | | | | GROUND_INST: instantiating (t34_funct_1) with all_39_2, all_39_1,
% 10.61/2.29 | | | | all_39_1, simplifying with (9), (10), (12), (15) gives:
% 10.61/2.30 | | | | (41) ? [v0: any] : ? [v1: $i] : (relation_dom(all_39_1) = v1 &
% 10.61/2.30 | | | | relation(all_39_1) = v0 & $i(v1) & ( ~ (v0 = 0) | (v1 =
% 10.61/2.30 | | | | all_39_2 & ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 10.61/2.30 | | | | (apply(all_39_1, v2) = v3) | ~ $i(v2) | ? [v4: int] :
% 10.61/2.30 | | | | ( ~ (v4 = 0) & in(v2, all_39_2) = v4)))))
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | GROUND_INST: instantiating (fc5_relat_1) with all_39_1, all_49_0,
% 10.61/2.30 | | | | simplifying with (10), (19) gives:
% 10.61/2.30 | | | | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_39_1)
% 10.61/2.30 | | | | = v1 & empty(all_49_0) = v2 & empty(all_39_1) = v0 & ( ~ (v2 =
% 10.61/2.30 | | | | 0) | ~ (v1 = 0) | v0 = 0))
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | DELTA: instantiating (42) with fresh symbols all_80_0, all_80_1,
% 10.61/2.30 | | | | all_80_2 gives:
% 10.61/2.30 | | | | (43) relation(all_39_1) = all_80_1 & empty(all_49_0) = all_80_0 &
% 10.61/2.30 | | | | empty(all_39_1) = all_80_2 & ( ~ (all_80_0 = 0) | ~ (all_80_1 =
% 10.61/2.30 | | | | 0) | all_80_2 = 0)
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | ALPHA: (43) implies:
% 10.61/2.30 | | | | (44) relation(all_39_1) = all_80_1
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | DELTA: instantiating (41) with fresh symbols all_88_0, all_88_1 gives:
% 10.61/2.30 | | | | (45) relation_dom(all_39_1) = all_88_0 & relation(all_39_1) =
% 10.61/2.30 | | | | all_88_1 & $i(all_88_0) & ( ~ (all_88_1 = 0) | (all_88_0 =
% 10.61/2.30 | | | | all_39_2 & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 10.61/2.30 | | | | (apply(all_39_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : (
% 10.61/2.30 | | | | ~ (v2 = 0) & in(v0, all_39_2) = v2))))
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | ALPHA: (45) implies:
% 10.61/2.30 | | | | (46) relation(all_39_1) = all_88_1
% 10.61/2.30 | | | | (47) relation_dom(all_39_1) = all_88_0
% 10.61/2.30 | | | | (48) ~ (all_88_1 = 0) | (all_88_0 = all_39_2 & ! [v0: $i] : ! [v1:
% 10.61/2.30 | | | | $i] : (v1 = v0 | ~ (apply(all_39_1, v0) = v1) | ~ $i(v0) |
% 10.61/2.30 | | | | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_39_2) = v2)))
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | GROUND_INST: instantiating (4) with 0, all_88_1, all_39_1, simplifying
% 10.61/2.30 | | | | with (14), (46) gives:
% 10.61/2.30 | | | | (49) all_88_1 = 0
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | GROUND_INST: instantiating (4) with all_80_1, all_88_1, all_39_1,
% 10.61/2.30 | | | | simplifying with (44), (46) gives:
% 10.61/2.30 | | | | (50) all_88_1 = all_80_1
% 10.61/2.30 | | | |
% 10.61/2.30 | | | | GROUND_INST: instantiating (5) with all_49_0, all_88_0, all_39_1,
% 11.18/2.30 | | | | simplifying with (19), (47) gives:
% 11.18/2.30 | | | | (51) all_88_0 = all_49_0
% 11.18/2.30 | | | |
% 11.18/2.30 | | | | COMBINE_EQS: (49), (50) imply:
% 11.18/2.30 | | | | (52) all_80_1 = 0
% 11.18/2.30 | | | |
% 11.18/2.30 | | | | BETA: splitting (48) gives:
% 11.18/2.30 | | | |
% 11.18/2.30 | | | | Case 1:
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | (53) ~ (all_88_1 = 0)
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | REDUCE: (49), (53) imply:
% 11.18/2.30 | | | | | (54) $false
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | CLOSE: (54) is inconsistent.
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | Case 2:
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | (55) all_88_0 = all_39_2 & ! [v0: $i] : ! [v1: $i] : (v1 = v0 |
% 11.18/2.30 | | | | | ~ (apply(all_39_1, v0) = v1) | ~ $i(v0) | ? [v2: int] : (
% 11.18/2.30 | | | | | ~ (v2 = 0) & in(v0, all_39_2) = v2))
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | ALPHA: (55) implies:
% 11.18/2.30 | | | | | (56) all_88_0 = all_39_2
% 11.18/2.30 | | | | | (57) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (apply(all_39_1, v0)
% 11.18/2.30 | | | | | = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0,
% 11.18/2.30 | | | | | all_39_2) = v2))
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | COMBINE_EQS: (51), (56) imply:
% 11.18/2.30 | | | | | (58) all_49_0 = all_39_2
% 11.18/2.30 | | | | |
% 11.18/2.30 | | | | | GROUND_INST: instantiating (57) with all_67_2, all_67_0, simplifying
% 11.18/2.30 | | | | | with (35), (39) gives:
% 11.18/2.31 | | | | | (59) all_67_0 = all_67_2 | ? [v0: int] : ( ~ (v0 = 0) &
% 11.18/2.31 | | | | | in(all_67_2, all_39_2) = v0)
% 11.18/2.31 | | | | |
% 11.18/2.31 | | | | | GROUND_INST: instantiating (57) with all_67_1, all_67_0, simplifying
% 11.18/2.31 | | | | | with (36), (40) gives:
% 11.18/2.31 | | | | | (60) all_67_0 = all_67_1 | ? [v0: int] : ( ~ (v0 = 0) &
% 11.18/2.31 | | | | | in(all_67_1, all_39_2) = v0)
% 11.18/2.31 | | | | |
% 11.18/2.31 | | | | | REDUCE: (38), (58) imply:
% 11.18/2.31 | | | | | (61) in(all_67_1, all_39_2) = 0
% 11.18/2.31 | | | | |
% 11.18/2.31 | | | | | REDUCE: (37), (58) imply:
% 11.18/2.31 | | | | | (62) in(all_67_2, all_39_2) = 0
% 11.18/2.31 | | | | |
% 11.18/2.31 | | | | | BETA: splitting (60) gives:
% 11.18/2.31 | | | | |
% 11.18/2.31 | | | | | Case 1:
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | (63) all_67_0 = all_67_1
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | BETA: splitting (59) gives:
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | Case 1:
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | (64) all_67_0 = all_67_2
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | COMBINE_EQS: (63), (64) imply:
% 11.18/2.31 | | | | | | | (65) all_67_1 = all_67_2
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | REDUCE: (34), (65) imply:
% 11.18/2.31 | | | | | | | (66) $false
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | CLOSE: (66) is inconsistent.
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | Case 2:
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | (67) ? [v0: int] : ( ~ (v0 = 0) & in(all_67_2, all_39_2) = v0)
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | DELTA: instantiating (67) with fresh symbol all_111_0 gives:
% 11.18/2.31 | | | | | | | (68) ~ (all_111_0 = 0) & in(all_67_2, all_39_2) = all_111_0
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | ALPHA: (68) implies:
% 11.18/2.31 | | | | | | | (69) ~ (all_111_0 = 0)
% 11.18/2.31 | | | | | | | (70) in(all_67_2, all_39_2) = all_111_0
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | GROUND_INST: instantiating (6) with 0, all_111_0, all_39_2,
% 11.18/2.31 | | | | | | | all_67_2, simplifying with (62), (70) gives:
% 11.18/2.31 | | | | | | | (71) all_111_0 = 0
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | REDUCE: (69), (71) imply:
% 11.18/2.31 | | | | | | | (72) $false
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | | CLOSE: (72) is inconsistent.
% 11.18/2.31 | | | | | | |
% 11.18/2.31 | | | | | | End of split
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | Case 2:
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & in(all_67_1, all_39_2) = v0)
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | DELTA: instantiating (73) with fresh symbol all_107_0 gives:
% 11.18/2.31 | | | | | | (74) ~ (all_107_0 = 0) & in(all_67_1, all_39_2) = all_107_0
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | ALPHA: (74) implies:
% 11.18/2.31 | | | | | | (75) ~ (all_107_0 = 0)
% 11.18/2.31 | | | | | | (76) in(all_67_1, all_39_2) = all_107_0
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | GROUND_INST: instantiating (6) with 0, all_107_0, all_39_2,
% 11.18/2.31 | | | | | | all_67_1, simplifying with (61), (76) gives:
% 11.18/2.31 | | | | | | (77) all_107_0 = 0
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | REDUCE: (75), (77) imply:
% 11.18/2.31 | | | | | | (78) $false
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | | CLOSE: (78) is inconsistent.
% 11.18/2.31 | | | | | |
% 11.18/2.31 | | | | | End of split
% 11.18/2.31 | | | | |
% 11.18/2.31 | | | | End of split
% 11.18/2.31 | | | |
% 11.18/2.31 | | | End of split
% 11.18/2.31 | | |
% 11.18/2.31 | | End of split
% 11.18/2.31 | |
% 11.18/2.31 | End of split
% 11.18/2.31 |
% 11.18/2.31 End of proof
% 11.18/2.31 % SZS output end Proof for theBenchmark
% 11.18/2.31
% 11.18/2.31 1705ms
%------------------------------------------------------------------------------