TSTP Solution File: PUZ130_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : PUZ130_1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 3.88s 1.34s
% Output : Proof 5.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PUZ130_1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 23:06:35 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.64 ________ _____
% 0.21/0.64 ___ __ \_________(_)________________________________
% 0.21/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.64
% 0.21/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.64 (2023-06-19)
% 0.21/0.64
% 0.21/0.64 (c) Philipp Rümmer, 2009-2023
% 0.21/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.64 Amanda Stjerna.
% 0.21/0.64 Free software under BSD-3-Clause.
% 0.21/0.64
% 0.21/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.64
% 0.21/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.65 Running up to 7 provers in parallel.
% 0.21/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.23/1.02 Prover 4: Preprocessing ...
% 2.23/1.02 Prover 1: Preprocessing ...
% 2.45/1.06 Prover 0: Preprocessing ...
% 2.45/1.06 Prover 6: Preprocessing ...
% 2.45/1.06 Prover 2: Preprocessing ...
% 2.45/1.06 Prover 3: Preprocessing ...
% 2.45/1.06 Prover 5: Preprocessing ...
% 3.43/1.22 Prover 6: Constructing countermodel ...
% 3.43/1.22 Prover 4: Constructing countermodel ...
% 3.43/1.22 Prover 1: Constructing countermodel ...
% 3.43/1.22 Prover 3: Constructing countermodel ...
% 3.43/1.23 Prover 0: Proving ...
% 3.43/1.23 Prover 2: Proving ...
% 3.43/1.23 Prover 5: Proving ...
% 3.88/1.34 Prover 0: proved (675ms)
% 3.88/1.34
% 3.88/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.88/1.34
% 3.88/1.34 Prover 6: stopped
% 3.88/1.34 Prover 3: stopped
% 3.88/1.34 Prover 2: proved (671ms)
% 3.88/1.34
% 3.88/1.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.88/1.34
% 3.88/1.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.88/1.35 Prover 5: stopped
% 3.88/1.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.88/1.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.88/1.35 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.88/1.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.88/1.37 Prover 7: Preprocessing ...
% 3.88/1.37 Prover 13: Preprocessing ...
% 3.88/1.38 Prover 10: Preprocessing ...
% 3.88/1.39 Prover 8: Preprocessing ...
% 3.88/1.39 Prover 11: Preprocessing ...
% 4.55/1.42 Prover 1: Found proof (size 27)
% 4.55/1.42 Prover 10: Constructing countermodel ...
% 4.55/1.42 Prover 1: proved (758ms)
% 4.55/1.42 Prover 7: Constructing countermodel ...
% 4.55/1.42 Prover 4: stopped
% 4.55/1.42 Prover 13: stopped
% 4.55/1.42 Prover 10: stopped
% 4.55/1.42 Prover 8: Warning: ignoring some quantifiers
% 4.55/1.43 Prover 7: stopped
% 4.55/1.43 Prover 8: Constructing countermodel ...
% 4.55/1.43 Prover 8: stopped
% 4.55/1.44 Prover 11: Constructing countermodel ...
% 5.03/1.45 Prover 11: stopped
% 5.03/1.45
% 5.03/1.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.45
% 5.03/1.45 % SZS output start Proof for theBenchmark
% 5.03/1.46 Assumptions after simplification:
% 5.03/1.46 ---------------------------------
% 5.03/1.46
% 5.03/1.46 (dog_chase_cat)
% 5.03/1.49 ! [v0: cat] : ! [v1: dog] : ! [v2: animal] : ! [v3: human] : ! [v4:
% 5.03/1.49 animal] : ! [v5: human] : ! [v6: int] : (v6 = 0 | ~ (hates(v3, v5) = v6)
% 5.03/1.49 | ~ (dog_to_animal(v1) = v4) | ~ (cat_to_animal(v0) = v2) | ~
% 5.03/1.49 (owner_of(v4) = v5) | ~ (owner_of(v2) = v3) | ~ dog(v1) | ~ cat(v0) | ?
% 5.03/1.49 [v7: int] : ( ~ (v7 = 0) & chased(v1, v0) = v7))
% 5.03/1.49
% 5.03/1.49 (jon_hates_jon)
% 5.03/1.49 human(jon) & ? [v0: int] : ( ~ (v0 = 0) & hates(jon, jon) = v0)
% 5.03/1.49
% 5.03/1.49 (jon_owns_garfield)
% 5.03/1.49 human(jon) & cat(garfield) & ? [v0: animal] : (cat_to_animal(garfield) = v0 &
% 5.03/1.49 owner_of(v0) = jon & animal(v0))
% 5.03/1.49
% 5.03/1.49 (jon_owns_odie)
% 5.03/1.49 human(jon) & dog(odie) & ? [v0: animal] : (dog_to_animal(odie) = v0 &
% 5.03/1.49 owner_of(v0) = jon & animal(v0))
% 5.03/1.49
% 5.03/1.49 (jon_owns_only)
% 5.03/1.49 human(jon) & dog(odie) & cat(garfield) & ? [v0: animal] : ? [v1: animal] :
% 5.03/1.49 (dog_to_animal(odie) = v1 & cat_to_animal(garfield) = v0 & animal(v1) &
% 5.03/1.49 animal(v0) & ! [v2: animal] : (v2 = v1 | v2 = v0 | ~ (owner_of(v2) = jon)
% 5.03/1.49 | ~ animal(v2)))
% 5.03/1.49
% 5.03/1.49 (odie_chased_garfield)
% 5.03/1.49 chased(odie, garfield) = 0 & dog(odie) & cat(garfield)
% 5.03/1.49
% 5.03/1.49 (function-axioms)
% 5.03/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: human] : !
% 5.03/1.50 [v3: human] : (v1 = v0 | ~ (hates(v3, v2) = v1) | ~ (hates(v3, v2) = v0)) &
% 5.03/1.50 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: cat] : !
% 5.03/1.50 [v3: dog] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3, v2) = v0)) &
% 5.03/1.50 ! [v0: animal] : ! [v1: animal] : ! [v2: dog] : (v1 = v0 | ~
% 5.03/1.50 (dog_to_animal(v2) = v1) | ~ (dog_to_animal(v2) = v0)) & ! [v0: animal] :
% 5.03/1.50 ! [v1: animal] : ! [v2: cat] : (v1 = v0 | ~ (cat_to_animal(v2) = v1) | ~
% 5.03/1.50 (cat_to_animal(v2) = v0)) & ! [v0: human] : ! [v1: human] : ! [v2:
% 5.03/1.50 animal] : (v1 = v0 | ~ (owner_of(v2) = v1) | ~ (owner_of(v2) = v0))
% 5.03/1.50
% 5.03/1.50 Further assumptions not needed in the proof:
% 5.03/1.50 --------------------------------------------
% 5.03/1.50 human_owner
% 5.03/1.50
% 5.03/1.50 Those formulas are unsatisfiable:
% 5.03/1.50 ---------------------------------
% 5.03/1.50
% 5.03/1.50 Begin of proof
% 5.03/1.50 |
% 5.03/1.50 | ALPHA: (jon_owns_garfield) implies:
% 5.03/1.50 | (1) ? [v0: animal] : (cat_to_animal(garfield) = v0 & owner_of(v0) = jon &
% 5.03/1.50 | animal(v0))
% 5.03/1.50 |
% 5.03/1.50 | ALPHA: (jon_owns_odie) implies:
% 5.03/1.50 | (2) ? [v0: animal] : (dog_to_animal(odie) = v0 & owner_of(v0) = jon &
% 5.03/1.50 | animal(v0))
% 5.03/1.50 |
% 5.03/1.50 | ALPHA: (jon_owns_only) implies:
% 5.03/1.50 | (3) ? [v0: animal] : ? [v1: animal] : (dog_to_animal(odie) = v1 &
% 5.03/1.50 | cat_to_animal(garfield) = v0 & animal(v1) & animal(v0) & ! [v2:
% 5.03/1.50 | animal] : (v2 = v1 | v2 = v0 | ~ (owner_of(v2) = jon) | ~
% 5.03/1.50 | animal(v2)))
% 5.03/1.50 |
% 5.03/1.50 | ALPHA: (odie_chased_garfield) implies:
% 5.03/1.51 | (4) cat(garfield)
% 5.03/1.51 | (5) dog(odie)
% 5.03/1.51 | (6) chased(odie, garfield) = 0
% 5.03/1.51 |
% 5.03/1.51 | ALPHA: (jon_hates_jon) implies:
% 5.03/1.51 | (7) ? [v0: int] : ( ~ (v0 = 0) & hates(jon, jon) = v0)
% 5.03/1.51 |
% 5.03/1.51 | ALPHA: (function-axioms) implies:
% 5.03/1.51 | (8) ! [v0: animal] : ! [v1: animal] : ! [v2: cat] : (v1 = v0 | ~
% 5.03/1.51 | (cat_to_animal(v2) = v1) | ~ (cat_to_animal(v2) = v0))
% 5.03/1.51 | (9) ! [v0: animal] : ! [v1: animal] : ! [v2: dog] : (v1 = v0 | ~
% 5.03/1.51 | (dog_to_animal(v2) = v1) | ~ (dog_to_animal(v2) = v0))
% 5.03/1.51 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: cat]
% 5.03/1.51 | : ! [v3: dog] : (v1 = v0 | ~ (chased(v3, v2) = v1) | ~ (chased(v3,
% 5.03/1.51 | v2) = v0))
% 5.03/1.51 |
% 5.03/1.51 | DELTA: instantiating (7) with fresh symbol all_14_0 gives:
% 5.03/1.51 | (11) ~ (all_14_0 = 0) & hates(jon, jon) = all_14_0
% 5.03/1.51 |
% 5.03/1.51 | ALPHA: (11) implies:
% 5.03/1.51 | (12) ~ (all_14_0 = 0)
% 5.03/1.51 | (13) hates(jon, jon) = all_14_0
% 5.03/1.51 |
% 5.03/1.51 | DELTA: instantiating (1) with fresh symbol all_16_0 gives:
% 5.03/1.51 | (14) cat_to_animal(garfield) = all_16_0 & owner_of(all_16_0) = jon &
% 5.03/1.51 | animal(all_16_0)
% 5.03/1.51 |
% 5.03/1.51 | ALPHA: (14) implies:
% 5.03/1.51 | (15) owner_of(all_16_0) = jon
% 5.03/1.51 | (16) cat_to_animal(garfield) = all_16_0
% 5.03/1.51 |
% 5.03/1.51 | DELTA: instantiating (2) with fresh symbol all_18_0 gives:
% 5.03/1.51 | (17) dog_to_animal(odie) = all_18_0 & owner_of(all_18_0) = jon &
% 5.03/1.51 | animal(all_18_0)
% 5.03/1.51 |
% 5.03/1.51 | ALPHA: (17) implies:
% 5.03/1.51 | (18) owner_of(all_18_0) = jon
% 5.03/1.51 | (19) dog_to_animal(odie) = all_18_0
% 5.03/1.51 |
% 5.03/1.51 | DELTA: instantiating (3) with fresh symbols all_20_0, all_20_1 gives:
% 5.03/1.52 | (20) dog_to_animal(odie) = all_20_0 & cat_to_animal(garfield) = all_20_1 &
% 5.03/1.52 | animal(all_20_0) & animal(all_20_1) & ! [v0: any] : (v0 = all_20_0 |
% 5.03/1.52 | v0 = all_20_1 | ~ (owner_of(v0) = jon) | ~ animal(v0))
% 5.03/1.52 |
% 5.03/1.52 | ALPHA: (20) implies:
% 5.03/1.52 | (21) cat_to_animal(garfield) = all_20_1
% 5.03/1.52 | (22) dog_to_animal(odie) = all_20_0
% 5.03/1.52 |
% 5.03/1.52 | GROUND_INST: instantiating (8) with all_16_0, all_20_1, garfield, simplifying
% 5.03/1.52 | with (16), (21) gives:
% 5.03/1.52 | (23) all_20_1 = all_16_0
% 5.03/1.52 |
% 5.03/1.52 | GROUND_INST: instantiating (9) with all_18_0, all_20_0, odie, simplifying with
% 5.03/1.52 | (19), (22) gives:
% 5.03/1.52 | (24) all_20_0 = all_18_0
% 5.03/1.52 |
% 5.03/1.52 | GROUND_INST: instantiating (dog_chase_cat) with garfield, odie, all_16_0, jon,
% 5.03/1.52 | all_18_0, jon, all_14_0, simplifying with (4), (5), (13), (15),
% 5.03/1.52 | (16), (18), (19) gives:
% 5.03/1.52 | (25) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & chased(odie, garfield) =
% 5.03/1.52 | v0)
% 5.03/1.52 |
% 5.03/1.52 | BETA: splitting (25) gives:
% 5.03/1.52 |
% 5.03/1.52 | Case 1:
% 5.03/1.52 | |
% 5.03/1.52 | | (26) all_14_0 = 0
% 5.03/1.52 | |
% 5.03/1.52 | | REDUCE: (12), (26) imply:
% 5.03/1.52 | | (27) $false
% 5.03/1.52 | |
% 5.03/1.52 | | CLOSE: (27) is inconsistent.
% 5.03/1.52 | |
% 5.03/1.52 | Case 2:
% 5.03/1.52 | |
% 5.03/1.52 | | (28) ? [v0: int] : ( ~ (v0 = 0) & chased(odie, garfield) = v0)
% 5.03/1.52 | |
% 5.03/1.52 | | DELTA: instantiating (28) with fresh symbol all_34_0 gives:
% 5.03/1.52 | | (29) ~ (all_34_0 = 0) & chased(odie, garfield) = all_34_0
% 5.03/1.52 | |
% 5.03/1.52 | | ALPHA: (29) implies:
% 5.03/1.52 | | (30) ~ (all_34_0 = 0)
% 5.03/1.52 | | (31) chased(odie, garfield) = all_34_0
% 5.03/1.52 | |
% 5.03/1.52 | | GROUND_INST: instantiating (10) with 0, all_34_0, garfield, odie,
% 5.03/1.52 | | simplifying with (6), (31) gives:
% 5.03/1.52 | | (32) all_34_0 = 0
% 5.03/1.52 | |
% 5.03/1.52 | | REDUCE: (30), (32) imply:
% 5.03/1.52 | | (33) $false
% 5.03/1.52 | |
% 5.03/1.52 | | CLOSE: (33) is inconsistent.
% 5.03/1.52 | |
% 5.03/1.52 | End of split
% 5.03/1.52 |
% 5.03/1.52 End of proof
% 5.03/1.52 % SZS output end Proof for theBenchmark
% 5.03/1.53
% 5.03/1.53 882ms
%------------------------------------------------------------------------------