TSTP Solution File: PUZ012_1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PUZ012_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n001.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 13:22:45 EDT 2023
% Result : Theorem 4.96s 1.44s
% Output : Proof 7.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ012_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n001.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 : Sat Aug 26 22:51:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.26/1.01 Prover 4: Preprocessing ...
% 2.26/1.01 Prover 1: Preprocessing ...
% 2.76/1.05 Prover 6: Preprocessing ...
% 2.76/1.05 Prover 2: Preprocessing ...
% 2.76/1.05 Prover 3: Preprocessing ...
% 2.76/1.05 Prover 5: Preprocessing ...
% 2.76/1.05 Prover 0: Preprocessing ...
% 3.69/1.18 Prover 2: Proving ...
% 3.69/1.18 Prover 5: Proving ...
% 3.69/1.20 Prover 6: Constructing countermodel ...
% 3.69/1.21 Prover 3: Constructing countermodel ...
% 4.21/1.23 Prover 1: Constructing countermodel ...
% 4.45/1.27 Prover 4: Constructing countermodel ...
% 4.45/1.29 Prover 0: Proving ...
% 4.96/1.44 Prover 3: proved (813ms)
% 4.96/1.44
% 4.96/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/1.44
% 4.96/1.44 Prover 6: proved (812ms)
% 4.96/1.44
% 4.96/1.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.96/1.44
% 4.96/1.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.96/1.44 Prover 0: stopped
% 4.96/1.44 Prover 2: stopped
% 4.96/1.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.96/1.45 Prover 5: stopped
% 4.96/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 4.96/1.45 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 4.96/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 4.96/1.48 Prover 11: Preprocessing ...
% 4.96/1.49 Prover 10: Preprocessing ...
% 4.96/1.49 Prover 7: Preprocessing ...
% 4.96/1.49 Prover 8: Preprocessing ...
% 4.96/1.50 Prover 13: Preprocessing ...
% 5.90/1.52 Prover 10: Warning: ignoring some quantifiers
% 5.90/1.53 Prover 7: Warning: ignoring some quantifiers
% 5.90/1.53 Prover 7: Constructing countermodel ...
% 5.90/1.53 Prover 10: Constructing countermodel ...
% 5.90/1.54 Prover 13: Warning: ignoring some quantifiers
% 5.90/1.54 Prover 13: Constructing countermodel ...
% 5.90/1.56 Prover 8: Warning: ignoring some quantifiers
% 5.90/1.56 Prover 8: Constructing countermodel ...
% 5.90/1.58 Prover 10: gave up
% 5.90/1.58 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.62/1.60 Prover 16: Preprocessing ...
% 6.62/1.61 Prover 11: Constructing countermodel ...
% 6.86/1.62 Prover 16: Warning: ignoring some quantifiers
% 6.86/1.63 Prover 7: gave up
% 6.96/1.63 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 6.96/1.63 Prover 16: Constructing countermodel ...
% 6.96/1.64 Prover 13: gave up
% 6.96/1.64 Prover 1: Found proof (size 63)
% 6.96/1.64 Prover 1: proved (1019ms)
% 6.96/1.64 Prover 8: stopped
% 6.96/1.64 Prover 11: stopped
% 6.96/1.64 Prover 16: stopped
% 6.96/1.64 Prover 4: stopped
% 6.96/1.65 Prover 19: Preprocessing ...
% 6.96/1.69 Prover 19: Warning: ignoring some quantifiers
% 6.96/1.70 Prover 19: Constructing countermodel ...
% 6.96/1.70 Prover 19: stopped
% 6.96/1.70
% 6.96/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.96/1.70
% 7.40/1.72 % SZS output start Proof for theBenchmark
% 7.40/1.72 Assumptions after simplification:
% 7.40/1.72 ---------------------------------
% 7.40/1.72
% 7.40/1.72 (apples_not_bananas)
% 7.40/1.75 fruit(bananas) & fruit(apples) & ? [v0: int] : ( ~ (v0 = 0) &
% 7.40/1.75 equal_fruits(apples, bananas) = v0)
% 7.40/1.75
% 7.40/1.75 (boxb_contains_apples)
% 7.40/1.75 contains(boxb, apples) = 0 & fruit(apples) & box(boxb)
% 7.40/1.75
% 7.40/1.75 (boxb_not_boxc)
% 7.40/1.75 box(boxc) & box(boxb) & ? [v0: int] : ( ~ (v0 = 0) & equal_boxes(boxb, boxc)
% 7.40/1.75 = v0)
% 7.40/1.75
% 7.40/1.75 (boxc_labelled_bananas)
% 7.40/1.75 label(boxc, bananas) = 0 & fruit(bananas) & box(boxc)
% 7.40/1.75
% 7.40/1.75 (contains_is_well_defined1)
% 7.40/1.75 ! [v0: box] : ! [v1: fruit] : ! [v2: fruit] : ! [v3: int] : (v3 = 0 | ~
% 7.40/1.75 (contains(v0, v1) = 0) | ~ (equal_fruits(v1, v2) = v3) | ~ fruit(v2) | ~
% 7.40/1.75 fruit(v1) | ~ box(v0) | ? [v4: int] : ( ~ (v4 = 0) & contains(v0, v2) =
% 7.40/1.75 v4))
% 7.40/1.75
% 7.40/1.75 (contains_is_well_defined2)
% 7.40/1.75 ! [v0: box] : ! [v1: fruit] : ! [v2: box] : ! [v3: int] : (v3 = 0 | ~
% 7.40/1.75 (contains(v0, v1) = 0) | ~ (equal_boxes(v0, v2) = v3) | ~ fruit(v1) | ~
% 7.40/1.75 box(v2) | ~ box(v0) | ? [v4: int] : ( ~ (v4 = 0) & contains(v2, v1) = v4))
% 7.40/1.75
% 7.40/1.75 (each_box_contains_something)
% 7.40/1.76 fruit(oranges) & fruit(bananas) & fruit(apples) & ! [v0: box] : ! [v1: int]
% 7.40/1.76 : (v1 = 0 | ~ (contains(v0, oranges) = v1) | ~ box(v0) | ? [v2: any] : ?
% 7.40/1.76 [v3: any] : (contains(v0, bananas) = v3 & contains(v0, apples) = v2 & (v3 =
% 7.40/1.76 0 | v2 = 0)))
% 7.40/1.76
% 7.40/1.76 (each_thing_is_in_a_box)
% 7.40/1.76 box(boxc) & box(boxb) & box(boxa) & ! [v0: fruit] : ! [v1: int] : (v1 = 0 |
% 7.40/1.76 ~ (contains(boxc, v0) = v1) | ~ fruit(v0) | ? [v2: any] : ? [v3: any] :
% 7.40/1.76 (contains(boxb, v0) = v3 & contains(boxa, v0) = v2 & (v3 = 0 | v2 = 0)))
% 7.40/1.76
% 7.40/1.76 (label_is_wrong)
% 7.40/1.76 ! [v0: box] : ! [v1: fruit] : ( ~ (label(v0, v1) = 0) | ~ fruit(v1) | ~
% 7.40/1.76 box(v0) | ? [v2: int] : ( ~ (v2 = 0) & contains(v0, v1) = v2))
% 7.40/1.76
% 7.40/1.76 (prove_boxa_contains_bananas_and_boxc_oranges)
% 7.40/1.76 fruit(oranges) & fruit(bananas) & box(boxc) & box(boxa) & ? [v0: any] : ?
% 7.40/1.76 [v1: any] : (contains(boxc, oranges) = v1 & contains(boxa, bananas) = v0 & ( ~
% 7.40/1.76 (v1 = 0) | ~ (v0 = 0)))
% 7.40/1.76
% 7.40/1.76 (function-axioms)
% 7.40/1.76 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: fruit] : !
% 7.40/1.76 [v3: box] : (v1 = v0 | ~ (label(v3, v2) = v1) | ~ (label(v3, v2) = v0)) & !
% 7.40/1.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: fruit] : !
% 7.40/1.76 [v3: box] : (v1 = v0 | ~ (contains(v3, v2) = v1) | ~ (contains(v3, v2) =
% 7.40/1.76 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.40/1.76 box] : ! [v3: box] : (v1 = v0 | ~ (equal_boxes(v3, v2) = v1) | ~
% 7.40/1.76 (equal_boxes(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.40/1.76 MultipleValueBool] : ! [v2: fruit] : ! [v3: fruit] : (v1 = v0 | ~
% 7.40/1.76 (equal_fruits(v3, v2) = v1) | ~ (equal_fruits(v3, v2) = v0))
% 7.40/1.76
% 7.40/1.76 Further assumptions not needed in the proof:
% 7.40/1.76 --------------------------------------------
% 7.40/1.76 apples_not_oranges, bananas_not_oranges, boxa_labelled_apples, boxa_not_boxb,
% 7.40/1.76 boxa_not_boxc, boxb_labelled_oranges, reflexivity_for_boxes,
% 7.40/1.76 reflexivity_for_fruits
% 7.40/1.76
% 7.40/1.76 Those formulas are unsatisfiable:
% 7.40/1.76 ---------------------------------
% 7.40/1.76
% 7.40/1.76 Begin of proof
% 7.40/1.76 |
% 7.40/1.76 | ALPHA: (each_thing_is_in_a_box) implies:
% 7.40/1.77 | (1) ! [v0: fruit] : ! [v1: int] : (v1 = 0 | ~ (contains(boxc, v0) = v1)
% 7.40/1.77 | | ~ fruit(v0) | ? [v2: any] : ? [v3: any] : (contains(boxb, v0) =
% 7.40/1.77 | v3 & contains(boxa, v0) = v2 & (v3 = 0 | v2 = 0)))
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (each_box_contains_something) implies:
% 7.40/1.77 | (2) ! [v0: box] : ! [v1: int] : (v1 = 0 | ~ (contains(v0, oranges) = v1)
% 7.40/1.77 | | ~ box(v0) | ? [v2: any] : ? [v3: any] : (contains(v0, bananas) =
% 7.40/1.77 | v3 & contains(v0, apples) = v2 & (v3 = 0 | v2 = 0)))
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (boxb_not_boxc) implies:
% 7.40/1.77 | (3) ? [v0: int] : ( ~ (v0 = 0) & equal_boxes(boxb, boxc) = v0)
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (apples_not_bananas) implies:
% 7.40/1.77 | (4) ? [v0: int] : ( ~ (v0 = 0) & equal_fruits(apples, bananas) = v0)
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (boxc_labelled_bananas) implies:
% 7.40/1.77 | (5) label(boxc, bananas) = 0
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (boxb_contains_apples) implies:
% 7.40/1.77 | (6) box(boxb)
% 7.40/1.77 | (7) fruit(apples)
% 7.40/1.77 | (8) contains(boxb, apples) = 0
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (prove_boxa_contains_bananas_and_boxc_oranges) implies:
% 7.40/1.77 | (9) box(boxc)
% 7.40/1.77 | (10) fruit(bananas)
% 7.40/1.77 | (11) ? [v0: any] : ? [v1: any] : (contains(boxc, oranges) = v1 &
% 7.40/1.77 | contains(boxa, bananas) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (function-axioms) implies:
% 7.40/1.77 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.40/1.77 | fruit] : ! [v3: box] : (v1 = v0 | ~ (contains(v3, v2) = v1) | ~
% 7.40/1.77 | (contains(v3, v2) = v0))
% 7.40/1.77 |
% 7.40/1.77 | DELTA: instantiating (4) with fresh symbol all_15_0 gives:
% 7.40/1.77 | (13) ~ (all_15_0 = 0) & equal_fruits(apples, bananas) = all_15_0
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (13) implies:
% 7.40/1.77 | (14) ~ (all_15_0 = 0)
% 7.40/1.77 | (15) equal_fruits(apples, bananas) = all_15_0
% 7.40/1.77 |
% 7.40/1.77 | DELTA: instantiating (3) with fresh symbol all_25_0 gives:
% 7.40/1.77 | (16) ~ (all_25_0 = 0) & equal_boxes(boxb, boxc) = all_25_0
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (16) implies:
% 7.40/1.77 | (17) ~ (all_25_0 = 0)
% 7.40/1.77 | (18) equal_boxes(boxb, boxc) = all_25_0
% 7.40/1.77 |
% 7.40/1.77 | DELTA: instantiating (11) with fresh symbols all_27_0, all_27_1 gives:
% 7.40/1.77 | (19) contains(boxc, oranges) = all_27_0 & contains(boxa, bananas) =
% 7.40/1.77 | all_27_1 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0))
% 7.40/1.77 |
% 7.40/1.77 | ALPHA: (19) implies:
% 7.40/1.78 | (20) contains(boxa, bananas) = all_27_1
% 7.40/1.78 | (21) contains(boxc, oranges) = all_27_0
% 7.40/1.78 | (22) ~ (all_27_0 = 0) | ~ (all_27_1 = 0)
% 7.40/1.78 |
% 7.40/1.78 | GROUND_INST: instantiating (contains_is_well_defined2) with boxb, apples,
% 7.40/1.78 | boxc, all_25_0, simplifying with (6), (7), (8), (9), (18) gives:
% 7.40/1.78 | (23) all_25_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & contains(boxc, apples) =
% 7.40/1.78 | v0)
% 7.40/1.78 |
% 7.40/1.78 | GROUND_INST: instantiating (contains_is_well_defined1) with boxb, apples,
% 7.40/1.78 | bananas, all_15_0, simplifying with (6), (7), (8), (10), (15)
% 7.40/1.78 | gives:
% 7.40/1.78 | (24) all_15_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & contains(boxb, bananas) =
% 7.40/1.78 | v0)
% 7.40/1.78 |
% 7.40/1.78 | GROUND_INST: instantiating (2) with boxc, all_27_0, simplifying with (9), (21)
% 7.40/1.78 | gives:
% 7.40/1.78 | (25) all_27_0 = 0 | ? [v0: any] : ? [v1: any] : (contains(boxc, bananas)
% 7.40/1.78 | = v1 & contains(boxc, apples) = v0 & (v1 = 0 | v0 = 0))
% 7.40/1.78 |
% 7.75/1.78 | GROUND_INST: instantiating (label_is_wrong) with boxc, bananas, simplifying
% 7.75/1.78 | with (5), (9), (10) gives:
% 7.75/1.78 | (26) ? [v0: int] : ( ~ (v0 = 0) & contains(boxc, bananas) = v0)
% 7.75/1.78 |
% 7.75/1.78 | DELTA: instantiating (26) with fresh symbol all_34_0 gives:
% 7.75/1.78 | (27) ~ (all_34_0 = 0) & contains(boxc, bananas) = all_34_0
% 7.75/1.78 |
% 7.75/1.78 | ALPHA: (27) implies:
% 7.75/1.78 | (28) ~ (all_34_0 = 0)
% 7.75/1.78 | (29) contains(boxc, bananas) = all_34_0
% 7.75/1.78 |
% 7.75/1.78 | BETA: splitting (24) gives:
% 7.75/1.78 |
% 7.75/1.78 | Case 1:
% 7.75/1.78 | |
% 7.75/1.78 | | (30) all_15_0 = 0
% 7.75/1.78 | |
% 7.75/1.78 | | REDUCE: (14), (30) imply:
% 7.75/1.78 | | (31) $false
% 7.75/1.78 | |
% 7.75/1.78 | | CLOSE: (31) is inconsistent.
% 7.75/1.78 | |
% 7.75/1.78 | Case 2:
% 7.75/1.78 | |
% 7.75/1.78 | | (32) ? [v0: int] : ( ~ (v0 = 0) & contains(boxb, bananas) = v0)
% 7.75/1.78 | |
% 7.75/1.78 | | DELTA: instantiating (32) with fresh symbol all_44_0 gives:
% 7.75/1.78 | | (33) ~ (all_44_0 = 0) & contains(boxb, bananas) = all_44_0
% 7.75/1.78 | |
% 7.75/1.78 | | ALPHA: (33) implies:
% 7.75/1.78 | | (34) ~ (all_44_0 = 0)
% 7.75/1.78 | | (35) contains(boxb, bananas) = all_44_0
% 7.75/1.78 | |
% 7.75/1.79 | | BETA: splitting (23) gives:
% 7.75/1.79 | |
% 7.75/1.79 | | Case 1:
% 7.75/1.79 | | |
% 7.75/1.79 | | | (36) all_25_0 = 0
% 7.75/1.79 | | |
% 7.75/1.79 | | | REDUCE: (17), (36) imply:
% 7.75/1.79 | | | (37) $false
% 7.75/1.79 | | |
% 7.75/1.79 | | | CLOSE: (37) is inconsistent.
% 7.75/1.79 | | |
% 7.75/1.79 | | Case 2:
% 7.75/1.79 | | |
% 7.75/1.79 | | | (38) ? [v0: int] : ( ~ (v0 = 0) & contains(boxc, apples) = v0)
% 7.75/1.79 | | |
% 7.75/1.79 | | | DELTA: instantiating (38) with fresh symbol all_49_0 gives:
% 7.75/1.79 | | | (39) ~ (all_49_0 = 0) & contains(boxc, apples) = all_49_0
% 7.75/1.79 | | |
% 7.75/1.79 | | | ALPHA: (39) implies:
% 7.75/1.79 | | | (40) ~ (all_49_0 = 0)
% 7.75/1.79 | | | (41) contains(boxc, apples) = all_49_0
% 7.75/1.79 | | |
% 7.75/1.79 | | | BETA: splitting (25) gives:
% 7.75/1.79 | | |
% 7.75/1.79 | | | Case 1:
% 7.75/1.79 | | | |
% 7.75/1.79 | | | | (42) all_27_0 = 0
% 7.75/1.79 | | | |
% 7.75/1.79 | | | | BETA: splitting (22) gives:
% 7.75/1.79 | | | |
% 7.75/1.79 | | | | Case 1:
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | (43) ~ (all_27_0 = 0)
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | REDUCE: (42), (43) imply:
% 7.75/1.79 | | | | | (44) $false
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | CLOSE: (44) is inconsistent.
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | Case 2:
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | (45) ~ (all_27_1 = 0)
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | GROUND_INST: instantiating (1) with bananas, all_34_0, simplifying
% 7.75/1.79 | | | | | with (10), (29) gives:
% 7.75/1.79 | | | | | (46) all_34_0 = 0 | ? [v0: any] : ? [v1: any] : (contains(boxb,
% 7.75/1.79 | | | | | bananas) = v1 & contains(boxa, bananas) = v0 & (v1 = 0 |
% 7.75/1.79 | | | | | v0 = 0))
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | BETA: splitting (46) gives:
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | | Case 1:
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | (47) all_34_0 = 0
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | REDUCE: (28), (47) imply:
% 7.75/1.79 | | | | | | (48) $false
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | CLOSE: (48) is inconsistent.
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | Case 2:
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | (49) ? [v0: any] : ? [v1: any] : (contains(boxb, bananas) = v1
% 7.75/1.79 | | | | | | & contains(boxa, bananas) = v0 & (v1 = 0 | v0 = 0))
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | DELTA: instantiating (49) with fresh symbols all_66_0, all_66_1
% 7.75/1.79 | | | | | | gives:
% 7.75/1.79 | | | | | | (50) contains(boxb, bananas) = all_66_0 & contains(boxa, bananas)
% 7.75/1.79 | | | | | | = all_66_1 & (all_66_0 = 0 | all_66_1 = 0)
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | ALPHA: (50) implies:
% 7.75/1.79 | | | | | | (51) contains(boxa, bananas) = all_66_1
% 7.75/1.79 | | | | | | (52) contains(boxb, bananas) = all_66_0
% 7.75/1.79 | | | | | | (53) all_66_0 = 0 | all_66_1 = 0
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | GROUND_INST: instantiating (12) with all_27_1, all_66_1, bananas,
% 7.75/1.79 | | | | | | boxa, simplifying with (20), (51) gives:
% 7.75/1.79 | | | | | | (54) all_66_1 = all_27_1
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | GROUND_INST: instantiating (12) with all_44_0, all_66_0, bananas,
% 7.75/1.79 | | | | | | boxb, simplifying with (35), (52) gives:
% 7.75/1.79 | | | | | | (55) all_66_0 = all_44_0
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | BETA: splitting (53) gives:
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | | Case 1:
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | (56) all_66_0 = 0
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | COMBINE_EQS: (55), (56) imply:
% 7.75/1.79 | | | | | | | (57) all_44_0 = 0
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | REDUCE: (34), (57) imply:
% 7.75/1.79 | | | | | | | (58) $false
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | CLOSE: (58) is inconsistent.
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | Case 2:
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | (59) all_66_1 = 0
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | COMBINE_EQS: (54), (59) imply:
% 7.75/1.79 | | | | | | | (60) all_27_1 = 0
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | SIMP: (60) implies:
% 7.75/1.79 | | | | | | | (61) all_27_1 = 0
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | REDUCE: (45), (61) imply:
% 7.75/1.79 | | | | | | | (62) $false
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | | CLOSE: (62) is inconsistent.
% 7.75/1.79 | | | | | | |
% 7.75/1.79 | | | | | | End of split
% 7.75/1.79 | | | | | |
% 7.75/1.79 | | | | | End of split
% 7.75/1.79 | | | | |
% 7.75/1.79 | | | | End of split
% 7.75/1.79 | | | |
% 7.75/1.79 | | | Case 2:
% 7.75/1.79 | | | |
% 7.75/1.79 | | | | (63) ? [v0: any] : ? [v1: any] : (contains(boxc, bananas) = v1 &
% 7.75/1.79 | | | | contains(boxc, apples) = v0 & (v1 = 0 | v0 = 0))
% 7.75/1.79 | | | |
% 7.75/1.79 | | | | DELTA: instantiating (63) with fresh symbols all_55_0, all_55_1 gives:
% 7.75/1.80 | | | | (64) contains(boxc, bananas) = all_55_0 & contains(boxc, apples) =
% 7.75/1.80 | | | | all_55_1 & (all_55_0 = 0 | all_55_1 = 0)
% 7.75/1.80 | | | |
% 7.75/1.80 | | | | ALPHA: (64) implies:
% 7.75/1.80 | | | | (65) contains(boxc, apples) = all_55_1
% 7.75/1.80 | | | | (66) contains(boxc, bananas) = all_55_0
% 7.75/1.80 | | | | (67) all_55_0 = 0 | all_55_1 = 0
% 7.75/1.80 | | | |
% 7.75/1.80 | | | | GROUND_INST: instantiating (12) with all_49_0, all_55_1, apples, boxc,
% 7.75/1.80 | | | | simplifying with (41), (65) gives:
% 7.75/1.80 | | | | (68) all_55_1 = all_49_0
% 7.75/1.80 | | | |
% 7.75/1.80 | | | | GROUND_INST: instantiating (12) with all_34_0, all_55_0, bananas, boxc,
% 7.75/1.80 | | | | simplifying with (29), (66) gives:
% 7.75/1.80 | | | | (69) all_55_0 = all_34_0
% 7.75/1.80 | | | |
% 7.75/1.80 | | | | BETA: splitting (67) gives:
% 7.75/1.80 | | | |
% 7.75/1.80 | | | | Case 1:
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | (70) all_55_0 = 0
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | COMBINE_EQS: (69), (70) imply:
% 7.75/1.80 | | | | | (71) all_34_0 = 0
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | SIMP: (71) implies:
% 7.75/1.80 | | | | | (72) all_34_0 = 0
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | REDUCE: (28), (72) imply:
% 7.75/1.80 | | | | | (73) $false
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | CLOSE: (73) is inconsistent.
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | Case 2:
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | (74) all_55_1 = 0
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | COMBINE_EQS: (68), (74) imply:
% 7.75/1.80 | | | | | (75) all_49_0 = 0
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | REDUCE: (40), (75) imply:
% 7.75/1.80 | | | | | (76) $false
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | | CLOSE: (76) is inconsistent.
% 7.75/1.80 | | | | |
% 7.75/1.80 | | | | End of split
% 7.75/1.80 | | | |
% 7.75/1.80 | | | End of split
% 7.75/1.80 | | |
% 7.75/1.80 | | End of split
% 7.75/1.80 | |
% 7.75/1.80 | End of split
% 7.75/1.80 |
% 7.75/1.80 End of proof
% 7.75/1.80 % SZS output end Proof for theBenchmark
% 7.75/1.80
% 7.75/1.80 1198ms
%------------------------------------------------------------------------------