TSTP Solution File: PUZ130+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PUZ130+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:23:13 EDT 2023
% Result : Theorem 5.16s 1.49s
% Output : Proof 7.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ130+1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 22:35:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.50/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.50/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.50/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.50/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.50/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.50/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.50/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.25/0.99 Prover 4: Preprocessing ...
% 2.25/0.99 Prover 1: Preprocessing ...
% 2.57/1.05 Prover 0: Preprocessing ...
% 2.57/1.05 Prover 2: Preprocessing ...
% 2.57/1.05 Prover 5: Preprocessing ...
% 2.57/1.05 Prover 6: Preprocessing ...
% 2.57/1.06 Prover 3: Preprocessing ...
% 4.13/1.30 Prover 1: Warning: ignoring some quantifiers
% 4.13/1.30 Prover 4: Warning: ignoring some quantifiers
% 4.13/1.31 Prover 2: Proving ...
% 4.13/1.31 Prover 5: Proving ...
% 4.13/1.32 Prover 6: Proving ...
% 4.13/1.32 Prover 1: Constructing countermodel ...
% 4.13/1.33 Prover 3: Warning: ignoring some quantifiers
% 4.13/1.33 Prover 4: Constructing countermodel ...
% 4.13/1.34 Prover 3: Constructing countermodel ...
% 4.13/1.34 Prover 0: Proving ...
% 5.16/1.48 Prover 0: proved (847ms)
% 5.16/1.49
% 5.16/1.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.16/1.49
% 5.16/1.49 Prover 3: stopped
% 5.16/1.49 Prover 6: stopped
% 5.16/1.49 Prover 5: stopped
% 5.16/1.49 Prover 2: stopped
% 5.16/1.49 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.16/1.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.16/1.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.16/1.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.16/1.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 5.82/1.53 Prover 8: Preprocessing ...
% 5.82/1.54 Prover 10: Preprocessing ...
% 5.82/1.54 Prover 11: Preprocessing ...
% 5.82/1.54 Prover 7: Preprocessing ...
% 5.82/1.56 Prover 13: Preprocessing ...
% 5.82/1.58 Prover 10: Warning: ignoring some quantifiers
% 5.82/1.58 Prover 7: Warning: ignoring some quantifiers
% 6.43/1.59 Prover 10: Constructing countermodel ...
% 6.43/1.59 Prover 7: Constructing countermodel ...
% 6.43/1.61 Prover 8: Warning: ignoring some quantifiers
% 6.43/1.62 Prover 11: Warning: ignoring some quantifiers
% 6.43/1.62 Prover 8: Constructing countermodel ...
% 6.43/1.62 Prover 1: gave up
% 6.43/1.64 Prover 4: Found proof (size 59)
% 6.43/1.64 Prover 4: proved (996ms)
% 6.43/1.64 Prover 7: stopped
% 6.43/1.64 Prover 8: stopped
% 6.43/1.64 Prover 11: Constructing countermodel ...
% 6.43/1.64 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 6.43/1.64 Prover 10: stopped
% 6.43/1.64 Prover 13: Warning: ignoring some quantifiers
% 6.43/1.64 Prover 11: stopped
% 6.43/1.65 Prover 13: Constructing countermodel ...
% 6.43/1.65 Prover 16: Preprocessing ...
% 6.43/1.65 Prover 13: stopped
% 6.43/1.68 Prover 16: Warning: ignoring some quantifiers
% 6.43/1.68 Prover 16: Constructing countermodel ...
% 7.04/1.68 Prover 16: stopped
% 7.04/1.68
% 7.04/1.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.04/1.68
% 7.09/1.70 % SZS output start Proof for theBenchmark
% 7.09/1.70 Assumptions after simplification:
% 7.09/1.70 ---------------------------------
% 7.09/1.70
% 7.09/1.70 (cat_chase_axiom)
% 7.21/1.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 7.21/1.73 | ~ (hates(v2, v3) = v4) | ~ (owner_of(v1) = v3) | ~ (owner_of(v0) = v2)
% 7.21/1.73 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 7.21/1.73 (chased(v1, v0) = v7 & dog(v1) = v6 & cat(v0) = v5 & ( ~ (v7 = 0) | ~ (v6 =
% 7.21/1.73 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (chased(v1, v0)
% 7.21/1.73 = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 7.21/1.73 ? [v5: $i] : ? [v6: any] : (hates(v4, v5) = v6 & owner_of(v1) = v5 &
% 7.21/1.73 owner_of(v0) = v4 & dog(v1) = v3 & cat(v0) = v2 & $i(v5) & $i(v4) & ( ~
% 7.21/1.73 (v3 = 0) | ~ (v2 = 0) | v6 = 0)))
% 7.21/1.73
% 7.21/1.73 (cat_pet_type)
% 7.21/1.74 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (pet(v0) = v1) | ~ $i(v0) | ? [v2:
% 7.21/1.74 int] : ( ~ (v2 = 0) & cat(v0) = v2)) & ! [v0: $i] : ( ~ (cat(v0) = 0) |
% 7.21/1.74 ~ $i(v0) | pet(v0) = 0)
% 7.21/1.74
% 7.21/1.74 (dog_pet_type)
% 7.21/1.74 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (pet(v0) = v1) | ~ $i(v0) | ? [v2:
% 7.21/1.74 int] : ( ~ (v2 = 0) & dog(v0) = v2)) & ! [v0: $i] : ( ~ (dog(v0) = 0) |
% 7.21/1.74 ~ $i(v0) | pet(v0) = 0)
% 7.21/1.74
% 7.21/1.74 (garfield_type)
% 7.21/1.74 cat(garfield) = 0 & $i(garfield)
% 7.21/1.74
% 7.21/1.74 (jon_conjecture)
% 7.21/1.74 $i(jon) & ? [v0: int] : ( ~ (v0 = 0) & hates(jon, jon) = v0)
% 7.21/1.74
% 7.21/1.74 (jon_g_owner_axiom)
% 7.21/1.74 owner(jon, garfield) = 0 & $i(jon) & $i(garfield)
% 7.21/1.74
% 7.21/1.74 (jon_o_owner_axiom)
% 7.21/1.74 owner(jon, odie) = 0 & $i(jon) & $i(odie)
% 7.21/1.74
% 7.21/1.74 (jon_type)
% 7.21/1.74 human(jon) = 0 & $i(jon)
% 7.21/1.74
% 7.21/1.74 (odie_chase_axiom)
% 7.21/1.74 chased(odie, garfield) = 0 & $i(odie) & $i(garfield)
% 7.21/1.74
% 7.21/1.74 (odie_type)
% 7.21/1.74 dog(odie) = 0 & $i(odie)
% 7.21/1.74
% 7.21/1.74 (owner_def)
% 7.21/1.74 ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (owner(v0, v1) = v2) | ~
% 7.21/1.74 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 7.21/1.74 (owner_of(v1) = v5 & human(v0) = v3 & pet(v1) = v4 & $i(v5) & ( ~ (v4 = 0) |
% 7.21/1.74 ~ (v3 = 0) | (( ~ (v5 = v0) | v2 = 0) & ( ~ (v2 = 0) | v5 = v0)))))
% 7.21/1.74
% 7.21/1.74 (function-axioms)
% 7.21/1.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.21/1.75 [v3: $i] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3, v2) = v0)) &
% 7.21/1.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.21/1.75 $i] : (v1 = v0 | ~ (hates(v3, v2) = v1) | ~ (hates(v3, v2) = v0)) & !
% 7.21/1.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 7.21/1.75 $i] : (v1 = v0 | ~ (owner(v3, v2) = v1) | ~ (owner(v3, v2) = v0)) & !
% 7.21/1.75 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (owner_of(v2) = v1) | ~
% 7.21/1.75 (owner_of(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.21/1.75 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (human(v2) = v1) | ~
% 7.21/1.75 (human(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 7.21/1.75 : ! [v2: $i] : (v1 = v0 | ~ (pet(v2) = v1) | ~ (pet(v2) = v0)) & ! [v0:
% 7.21/1.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 7.21/1.75 ~ (dog(v2) = v1) | ~ (dog(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.21/1.75 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cat(v2) = v1) | ~
% 7.21/1.75 (cat(v2) = v0))
% 7.21/1.75
% 7.21/1.75 Further assumptions not needed in the proof:
% 7.21/1.75 --------------------------------------------
% 7.21/1.75 cat_type, dog_type, human_type, jon_only_g_owner_axiom, jon_only_o_owner_axiom,
% 7.21/1.75 owner_of_type, pet_owner_axiom, pet_type
% 7.21/1.75
% 7.21/1.75 Those formulas are unsatisfiable:
% 7.21/1.75 ---------------------------------
% 7.21/1.75
% 7.21/1.75 Begin of proof
% 7.21/1.75 |
% 7.21/1.75 | ALPHA: (garfield_type) implies:
% 7.21/1.75 | (1) cat(garfield) = 0
% 7.21/1.75 |
% 7.21/1.75 | ALPHA: (odie_type) implies:
% 7.21/1.75 | (2) dog(odie) = 0
% 7.21/1.75 |
% 7.21/1.75 | ALPHA: (dog_pet_type) implies:
% 7.21/1.75 | (3) ! [v0: $i] : ( ~ (dog(v0) = 0) | ~ $i(v0) | pet(v0) = 0)
% 7.21/1.75 |
% 7.21/1.75 | ALPHA: (cat_pet_type) implies:
% 7.21/1.75 | (4) ! [v0: $i] : ( ~ (cat(v0) = 0) | ~ $i(v0) | pet(v0) = 0)
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (jon_type) implies:
% 7.21/1.76 | (5) human(jon) = 0
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (jon_o_owner_axiom) implies:
% 7.21/1.76 | (6) owner(jon, odie) = 0
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (jon_g_owner_axiom) implies:
% 7.21/1.76 | (7) owner(jon, garfield) = 0
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (cat_chase_axiom) implies:
% 7.21/1.76 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (chased(v1, v0) = 0) | ~ $i(v1) | ~
% 7.21/1.76 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] : ?
% 7.21/1.76 | [v6: any] : (hates(v4, v5) = v6 & owner_of(v1) = v5 & owner_of(v0) =
% 7.21/1.76 | v4 & dog(v1) = v3 & cat(v0) = v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) |
% 7.21/1.76 | ~ (v2 = 0) | v6 = 0)))
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (odie_chase_axiom) implies:
% 7.21/1.76 | (9) $i(garfield)
% 7.21/1.76 | (10) $i(odie)
% 7.21/1.76 | (11) chased(odie, garfield) = 0
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (jon_conjecture) implies:
% 7.21/1.76 | (12) $i(jon)
% 7.21/1.76 | (13) ? [v0: int] : ( ~ (v0 = 0) & hates(jon, jon) = v0)
% 7.21/1.76 |
% 7.21/1.76 | ALPHA: (function-axioms) implies:
% 7.21/1.76 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.21/1.76 | : (v1 = v0 | ~ (cat(v2) = v1) | ~ (cat(v2) = v0))
% 7.21/1.76 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.21/1.76 | : (v1 = v0 | ~ (dog(v2) = v1) | ~ (dog(v2) = v0))
% 7.21/1.76 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.21/1.76 | : (v1 = v0 | ~ (pet(v2) = v1) | ~ (pet(v2) = v0))
% 7.21/1.76 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.21/1.76 | : (v1 = v0 | ~ (human(v2) = v1) | ~ (human(v2) = v0))
% 7.21/1.76 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (owner_of(v2)
% 7.21/1.76 | = v1) | ~ (owner_of(v2) = v0))
% 7.21/1.76 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 7.21/1.76 | : ! [v3: $i] : (v1 = v0 | ~ (hates(v3, v2) = v1) | ~ (hates(v3, v2)
% 7.21/1.76 | = v0))
% 7.21/1.76 |
% 7.21/1.77 | DELTA: instantiating (13) with fresh symbol all_10_0 gives:
% 7.21/1.77 | (20) ~ (all_10_0 = 0) & hates(jon, jon) = all_10_0
% 7.21/1.77 |
% 7.21/1.77 | ALPHA: (20) implies:
% 7.21/1.77 | (21) ~ (all_10_0 = 0)
% 7.21/1.77 | (22) hates(jon, jon) = all_10_0
% 7.21/1.77 |
% 7.21/1.77 | GROUND_INST: instantiating (4) with garfield, simplifying with (1), (9) gives:
% 7.21/1.77 | (23) pet(garfield) = 0
% 7.21/1.77 |
% 7.21/1.77 | GROUND_INST: instantiating (3) with odie, simplifying with (2), (10) gives:
% 7.21/1.77 | (24) pet(odie) = 0
% 7.21/1.77 |
% 7.21/1.77 | GROUND_INST: instantiating (owner_def) with jon, garfield, 0, simplifying with
% 7.21/1.77 | (7), (9), (12) gives:
% 7.21/1.77 | (25) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (owner_of(garfield) = v2 &
% 7.21/1.77 | human(jon) = v0 & pet(garfield) = v1 & $i(v2) & ( ~ (v1 = 0) | ~
% 7.21/1.77 | (v0 = 0) | v2 = jon))
% 7.21/1.77 |
% 7.21/1.77 | GROUND_INST: instantiating (owner_def) with jon, odie, 0, simplifying with
% 7.21/1.77 | (6), (10), (12) gives:
% 7.21/1.77 | (26) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (owner_of(odie) = v2 &
% 7.21/1.77 | human(jon) = v0 & pet(odie) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 =
% 7.21/1.77 | 0) | v2 = jon))
% 7.21/1.77 |
% 7.21/1.77 | GROUND_INST: instantiating (8) with garfield, odie, simplifying with (9),
% 7.21/1.77 | (10), (11) gives:
% 7.21/1.77 | (27) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] : ? [v4: any]
% 7.21/1.77 | : (hates(v2, v3) = v4 & owner_of(odie) = v3 & owner_of(garfield) = v2
% 7.21/1.77 | & dog(odie) = v1 & cat(garfield) = v0 & $i(v3) & $i(v2) & ( ~ (v1 =
% 7.21/1.77 | 0) | ~ (v0 = 0) | v4 = 0))
% 7.21/1.77 |
% 7.21/1.77 | DELTA: instantiating (26) with fresh symbols all_32_0, all_32_1, all_32_2
% 7.21/1.77 | gives:
% 7.21/1.77 | (28) owner_of(odie) = all_32_0 & human(jon) = all_32_2 & pet(odie) =
% 7.21/1.77 | all_32_1 & $i(all_32_0) & ( ~ (all_32_1 = 0) | ~ (all_32_2 = 0) |
% 7.21/1.77 | all_32_0 = jon)
% 7.21/1.77 |
% 7.21/1.77 | ALPHA: (28) implies:
% 7.21/1.77 | (29) pet(odie) = all_32_1
% 7.21/1.77 | (30) human(jon) = all_32_2
% 7.21/1.77 | (31) owner_of(odie) = all_32_0
% 7.21/1.77 | (32) ~ (all_32_1 = 0) | ~ (all_32_2 = 0) | all_32_0 = jon
% 7.21/1.77 |
% 7.21/1.77 | DELTA: instantiating (25) with fresh symbols all_34_0, all_34_1, all_34_2
% 7.21/1.77 | gives:
% 7.21/1.77 | (33) owner_of(garfield) = all_34_0 & human(jon) = all_34_2 & pet(garfield)
% 7.21/1.77 | = all_34_1 & $i(all_34_0) & ( ~ (all_34_1 = 0) | ~ (all_34_2 = 0) |
% 7.21/1.77 | all_34_0 = jon)
% 7.21/1.77 |
% 7.21/1.77 | ALPHA: (33) implies:
% 7.21/1.77 | (34) pet(garfield) = all_34_1
% 7.21/1.77 | (35) human(jon) = all_34_2
% 7.21/1.77 | (36) owner_of(garfield) = all_34_0
% 7.21/1.77 | (37) ~ (all_34_1 = 0) | ~ (all_34_2 = 0) | all_34_0 = jon
% 7.21/1.77 |
% 7.21/1.77 | DELTA: instantiating (27) with fresh symbols all_36_0, all_36_1, all_36_2,
% 7.21/1.77 | all_36_3, all_36_4 gives:
% 7.21/1.78 | (38) hates(all_36_2, all_36_1) = all_36_0 & owner_of(odie) = all_36_1 &
% 7.21/1.78 | owner_of(garfield) = all_36_2 & dog(odie) = all_36_3 & cat(garfield) =
% 7.21/1.78 | all_36_4 & $i(all_36_1) & $i(all_36_2) & ( ~ (all_36_3 = 0) | ~
% 7.21/1.78 | (all_36_4 = 0) | all_36_0 = 0)
% 7.21/1.78 |
% 7.21/1.78 | ALPHA: (38) implies:
% 7.21/1.78 | (39) cat(garfield) = all_36_4
% 7.21/1.78 | (40) dog(odie) = all_36_3
% 7.21/1.78 | (41) owner_of(garfield) = all_36_2
% 7.21/1.78 | (42) owner_of(odie) = all_36_1
% 7.21/1.78 | (43) hates(all_36_2, all_36_1) = all_36_0
% 7.21/1.78 | (44) ~ (all_36_3 = 0) | ~ (all_36_4 = 0) | all_36_0 = 0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (14) with 0, all_36_4, garfield, simplifying with
% 7.21/1.78 | (1), (39) gives:
% 7.21/1.78 | (45) all_36_4 = 0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (15) with 0, all_36_3, odie, simplifying with (2),
% 7.21/1.78 | (40) gives:
% 7.21/1.78 | (46) all_36_3 = 0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (16) with 0, all_34_1, garfield, simplifying with
% 7.21/1.78 | (23), (34) gives:
% 7.21/1.78 | (47) all_34_1 = 0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (16) with 0, all_32_1, odie, simplifying with (24),
% 7.21/1.78 | (29) gives:
% 7.21/1.78 | (48) all_32_1 = 0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (17) with 0, all_34_2, jon, simplifying with (5),
% 7.21/1.78 | (35) gives:
% 7.21/1.78 | (49) all_34_2 = 0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (17) with all_32_2, all_34_2, jon, simplifying with
% 7.21/1.78 | (30), (35) gives:
% 7.21/1.78 | (50) all_34_2 = all_32_2
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (18) with all_34_0, all_36_2, garfield, simplifying
% 7.21/1.78 | with (36), (41) gives:
% 7.21/1.78 | (51) all_36_2 = all_34_0
% 7.21/1.78 |
% 7.21/1.78 | GROUND_INST: instantiating (18) with all_32_0, all_36_1, odie, simplifying
% 7.21/1.78 | with (31), (42) gives:
% 7.21/1.78 | (52) all_36_1 = all_32_0
% 7.21/1.78 |
% 7.21/1.78 | COMBINE_EQS: (49), (50) imply:
% 7.21/1.78 | (53) all_32_2 = 0
% 7.21/1.78 |
% 7.21/1.78 | REDUCE: (43), (51), (52) imply:
% 7.21/1.78 | (54) hates(all_34_0, all_32_0) = all_36_0
% 7.21/1.78 |
% 7.21/1.78 | BETA: splitting (32) gives:
% 7.21/1.78 |
% 7.21/1.78 | Case 1:
% 7.21/1.78 | |
% 7.21/1.78 | | (55) ~ (all_32_1 = 0)
% 7.21/1.78 | |
% 7.21/1.78 | | REDUCE: (48), (55) imply:
% 7.21/1.78 | | (56) $false
% 7.21/1.78 | |
% 7.21/1.78 | | CLOSE: (56) is inconsistent.
% 7.21/1.78 | |
% 7.21/1.78 | Case 2:
% 7.21/1.78 | |
% 7.21/1.78 | | (57) ~ (all_32_2 = 0) | all_32_0 = jon
% 7.21/1.78 | |
% 7.21/1.78 | | BETA: splitting (57) gives:
% 7.21/1.78 | |
% 7.21/1.78 | | Case 1:
% 7.21/1.78 | | |
% 7.21/1.78 | | | (58) ~ (all_32_2 = 0)
% 7.21/1.78 | | |
% 7.21/1.78 | | | REDUCE: (53), (58) imply:
% 7.21/1.78 | | | (59) $false
% 7.21/1.78 | | |
% 7.21/1.78 | | | CLOSE: (59) is inconsistent.
% 7.21/1.78 | | |
% 7.21/1.78 | | Case 2:
% 7.21/1.78 | | |
% 7.21/1.78 | | | (60) all_32_0 = jon
% 7.21/1.78 | | |
% 7.21/1.78 | | | REDUCE: (54), (60) imply:
% 7.21/1.78 | | | (61) hates(all_34_0, jon) = all_36_0
% 7.21/1.78 | | |
% 7.21/1.78 | | | BETA: splitting (37) gives:
% 7.21/1.78 | | |
% 7.21/1.78 | | | Case 1:
% 7.21/1.78 | | | |
% 7.21/1.78 | | | | (62) ~ (all_34_1 = 0)
% 7.21/1.78 | | | |
% 7.21/1.78 | | | | REDUCE: (47), (62) imply:
% 7.21/1.78 | | | | (63) $false
% 7.21/1.78 | | | |
% 7.21/1.78 | | | | CLOSE: (63) is inconsistent.
% 7.21/1.78 | | | |
% 7.21/1.78 | | | Case 2:
% 7.21/1.78 | | | |
% 7.21/1.78 | | | | (64) ~ (all_34_2 = 0) | all_34_0 = jon
% 7.21/1.78 | | | |
% 7.21/1.78 | | | | BETA: splitting (64) gives:
% 7.21/1.78 | | | |
% 7.21/1.78 | | | | Case 1:
% 7.21/1.78 | | | | |
% 7.21/1.78 | | | | | (65) ~ (all_34_2 = 0)
% 7.21/1.78 | | | | |
% 7.21/1.78 | | | | | REDUCE: (49), (65) imply:
% 7.21/1.78 | | | | | (66) $false
% 7.21/1.78 | | | | |
% 7.21/1.78 | | | | | CLOSE: (66) is inconsistent.
% 7.21/1.78 | | | | |
% 7.21/1.78 | | | | Case 2:
% 7.21/1.78 | | | | |
% 7.21/1.78 | | | | | (67) all_34_0 = jon
% 7.21/1.78 | | | | |
% 7.21/1.78 | | | | | REDUCE: (61), (67) imply:
% 7.21/1.79 | | | | | (68) hates(jon, jon) = all_36_0
% 7.21/1.79 | | | | |
% 7.21/1.79 | | | | | BETA: splitting (44) gives:
% 7.21/1.79 | | | | |
% 7.21/1.79 | | | | | Case 1:
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | | (69) ~ (all_36_3 = 0)
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | | REDUCE: (46), (69) imply:
% 7.21/1.79 | | | | | | (70) $false
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | | CLOSE: (70) is inconsistent.
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | Case 2:
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | | (71) ~ (all_36_4 = 0) | all_36_0 = 0
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | | BETA: splitting (71) gives:
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | | Case 1:
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | (72) ~ (all_36_4 = 0)
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | REDUCE: (45), (72) imply:
% 7.21/1.79 | | | | | | | (73) $false
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | CLOSE: (73) is inconsistent.
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | Case 2:
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | (74) all_36_0 = 0
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | REDUCE: (68), (74) imply:
% 7.21/1.79 | | | | | | | (75) hates(jon, jon) = 0
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | GROUND_INST: instantiating (19) with all_10_0, 0, jon, jon,
% 7.21/1.79 | | | | | | | simplifying with (22), (75) gives:
% 7.21/1.79 | | | | | | | (76) all_10_0 = 0
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | REDUCE: (21), (76) imply:
% 7.21/1.79 | | | | | | | (77) $false
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | | CLOSE: (77) is inconsistent.
% 7.21/1.79 | | | | | | |
% 7.21/1.79 | | | | | | End of split
% 7.21/1.79 | | | | | |
% 7.21/1.79 | | | | | End of split
% 7.21/1.79 | | | | |
% 7.21/1.79 | | | | End of split
% 7.21/1.79 | | | |
% 7.21/1.79 | | | End of split
% 7.21/1.79 | | |
% 7.21/1.79 | | End of split
% 7.21/1.79 | |
% 7.21/1.79 | End of split
% 7.21/1.79 |
% 7.21/1.79 End of proof
% 7.21/1.79 % SZS output end Proof for theBenchmark
% 7.21/1.79
% 7.21/1.79 1170ms
%------------------------------------------------------------------------------