TSTP Solution File: SYO899_8 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYO899_8 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 : Fri Sep 1 04:54:10 EDT 2023
% Result : Theorem 3.82s 1.39s
% Output : Proof 5.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO899_8 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n031.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 05:37:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.67 ________ _____
% 0.20/0.67 ___ __ \_________(_)________________________________
% 0.20/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.67
% 0.20/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.67 (2023-06-19)
% 0.20/0.67
% 0.20/0.67 (c) Philipp Rümmer, 2009-2023
% 0.20/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.67 Amanda Stjerna.
% 0.20/0.67 Free software under BSD-3-Clause.
% 0.20/0.67
% 0.20/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.67
% 0.20/0.67 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.68 Running up to 7 provers in parallel.
% 0.20/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.21/1.09 Prover 4: Preprocessing ...
% 2.21/1.09 Prover 1: Preprocessing ...
% 2.74/1.16 Prover 6: Preprocessing ...
% 2.74/1.16 Prover 2: Preprocessing ...
% 2.74/1.16 Prover 0: Preprocessing ...
% 2.74/1.16 Prover 5: Preprocessing ...
% 2.74/1.17 Prover 3: Preprocessing ...
% 3.50/1.27 Prover 3: Constructing countermodel ...
% 3.50/1.28 Prover 5: Proving ...
% 3.50/1.28 Prover 1: Constructing countermodel ...
% 3.50/1.28 Prover 4: Constructing countermodel ...
% 3.50/1.28 Prover 2: Proving ...
% 3.50/1.28 Prover 6: Proving ...
% 3.50/1.32 Prover 0: Proving ...
% 3.82/1.38 Prover 3: proved (692ms)
% 3.82/1.39
% 3.82/1.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.82/1.39
% 3.82/1.39 Prover 6: stopped
% 3.82/1.39 Prover 0: stopped
% 3.82/1.39 Prover 5: stopped
% 3.82/1.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 3.82/1.41 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 3.82/1.41 Prover 2: stopped
% 3.82/1.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 3.82/1.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 3.82/1.41 Prover 10: Preprocessing ...
% 3.82/1.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 3.82/1.41 Prover 11: Preprocessing ...
% 3.82/1.42 Prover 7: Preprocessing ...
% 3.82/1.42 Prover 10: Warning: ignoring some quantifiers
% 3.82/1.42 Prover 10: Constructing countermodel ...
% 4.69/1.42 Prover 13: Preprocessing ...
% 4.69/1.43 Prover 8: Preprocessing ...
% 4.69/1.43 Prover 1: Found proof (size 21)
% 4.69/1.43 Prover 1: proved (744ms)
% 4.69/1.43 Prover 4: stopped
% 4.69/1.44 Prover 7: Warning: ignoring some quantifiers
% 4.69/1.44 Prover 13: Warning: ignoring some quantifiers
% 4.69/1.44 Prover 7: Constructing countermodel ...
% 4.69/1.44 Prover 7: stopped
% 4.69/1.44 Prover 10: stopped
% 4.69/1.44 Prover 13: Constructing countermodel ...
% 4.69/1.44 Prover 13: stopped
% 4.92/1.45 Prover 8: Warning: ignoring some quantifiers
% 4.92/1.46 Prover 8: Constructing countermodel ...
% 4.92/1.46 Prover 11: Constructing countermodel ...
% 4.92/1.46 Prover 8: stopped
% 4.92/1.46 Prover 11: stopped
% 4.92/1.46
% 4.92/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/1.46
% 4.92/1.47 % SZS output start Proof for theBenchmark
% 4.92/1.47 Assumptions after simplification:
% 4.92/1.47 ---------------------------------
% 4.92/1.47
% 4.92/1.47 (mrel_reflexive)
% 4.92/1.50 ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ ($ki_accessible(v0, v0) = v1)
% 4.92/1.50 | ~ $ki_world(v0))
% 4.92/1.50
% 4.92/1.50 (verify)
% 4.92/1.51 $ki_world($ki_local_world) & ! [v0: $ki_world] : ( ~
% 4.92/1.51 ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v0) | p(v0) = 0) &
% 4.92/1.51 ! [v0: $ki_world] : ( ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 4.92/1.51 $ki_world(v0) | ? [v1: int] : ( ~ (v1 = 0) & q(v0) = v1)) & ? [v0:
% 4.92/1.51 $ki_world] : ? [v1: any] : (p(v0) = v1 & $ki_accessible($ki_local_world,
% 4.92/1.51 v0) = 0 & $ki_world(v0) & ( ~ (v1 = 0) | ! [v2: $ki_world] : ! [v3: int]
% 4.92/1.51 : (v3 = 0 | ~ (q(v2) = v3) | ~ $ki_world(v2) | ? [v4: int] : ( ~ (v4 =
% 4.92/1.51 0) & $ki_accessible(v0, v2) = v4))))
% 4.92/1.51
% 4.92/1.51 (function-axioms)
% 4.92/1.51 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $ki_world] :
% 4.92/1.51 ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3, v2) = v1) | ~
% 4.92/1.51 ($ki_accessible(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 4.92/1.51 MultipleValueBool] : ! [v2: $ki_world] : (v1 = v0 | ~ (p(v2) = v1) | ~
% 4.92/1.51 (p(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : !
% 4.92/1.51 [v2: $ki_world] : (v1 = v0 | ~ (q(v2) = v1) | ~ (q(v2) = v0))
% 4.92/1.51
% 4.92/1.51 Those formulas are unsatisfiable:
% 4.92/1.51 ---------------------------------
% 4.92/1.51
% 4.92/1.51 Begin of proof
% 4.92/1.51 |
% 4.92/1.51 | ALPHA: (verify) implies:
% 4.92/1.52 | (1) ! [v0: $ki_world] : ( ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 4.92/1.52 | $ki_world(v0) | ? [v1: int] : ( ~ (v1 = 0) & q(v0) = v1))
% 4.92/1.52 | (2) ! [v0: $ki_world] : ( ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 4.92/1.52 | $ki_world(v0) | p(v0) = 0)
% 4.92/1.52 | (3) ? [v0: $ki_world] : ? [v1: any] : (p(v0) = v1 &
% 4.92/1.52 | $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0) & ( ~ (v1 =
% 4.92/1.52 | 0) | ! [v2: $ki_world] : ! [v3: int] : (v3 = 0 | ~ (q(v2) =
% 4.92/1.52 | v3) | ~ $ki_world(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 4.92/1.52 | $ki_accessible(v0, v2) = v4))))
% 4.92/1.52 |
% 4.92/1.52 | ALPHA: (function-axioms) implies:
% 4.92/1.52 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 4.92/1.52 | $ki_world] : (v1 = v0 | ~ (p(v2) = v1) | ~ (p(v2) = v0))
% 4.92/1.52 |
% 4.92/1.52 | DELTA: instantiating (3) with fresh symbols all_8_0, all_8_1 gives:
% 4.92/1.52 | (5) p(all_8_1) = all_8_0 & $ki_accessible($ki_local_world, all_8_1) = 0 &
% 4.92/1.52 | $ki_world(all_8_1) & ( ~ (all_8_0 = 0) | ! [v0: $ki_world] : ! [v1:
% 4.92/1.52 | int] : (v1 = 0 | ~ (q(v0) = v1) | ~ $ki_world(v0) | ? [v2: int]
% 4.92/1.52 | : ( ~ (v2 = 0) & $ki_accessible(all_8_1, v0) = v2)))
% 4.92/1.52 |
% 4.92/1.52 | ALPHA: (5) implies:
% 4.92/1.52 | (6) $ki_world(all_8_1)
% 4.92/1.52 | (7) $ki_accessible($ki_local_world, all_8_1) = 0
% 4.92/1.52 | (8) p(all_8_1) = all_8_0
% 4.92/1.52 | (9) ~ (all_8_0 = 0) | ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~
% 4.92/1.52 | (q(v0) = v1) | ~ $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 4.92/1.52 | $ki_accessible(all_8_1, v0) = v2))
% 4.92/1.53 |
% 4.92/1.53 | GROUND_INST: instantiating (2) with all_8_1, simplifying with (6), (7) gives:
% 4.92/1.53 | (10) p(all_8_1) = 0
% 4.92/1.53 |
% 4.92/1.53 | GROUND_INST: instantiating (1) with all_8_1, simplifying with (6), (7) gives:
% 4.92/1.53 | (11) ? [v0: int] : ( ~ (v0 = 0) & q(all_8_1) = v0)
% 4.92/1.53 |
% 4.92/1.53 | DELTA: instantiating (11) with fresh symbol all_16_0 gives:
% 5.29/1.53 | (12) ~ (all_16_0 = 0) & q(all_8_1) = all_16_0
% 5.29/1.53 |
% 5.29/1.53 | ALPHA: (12) implies:
% 5.29/1.53 | (13) ~ (all_16_0 = 0)
% 5.29/1.53 | (14) q(all_8_1) = all_16_0
% 5.29/1.53 |
% 5.29/1.53 | GROUND_INST: instantiating (4) with all_8_0, 0, all_8_1, simplifying with (8),
% 5.29/1.53 | (10) gives:
% 5.29/1.53 | (15) all_8_0 = 0
% 5.29/1.53 |
% 5.29/1.53 | BETA: splitting (9) gives:
% 5.29/1.53 |
% 5.29/1.53 | Case 1:
% 5.29/1.53 | |
% 5.29/1.53 | | (16) ~ (all_8_0 = 0)
% 5.29/1.53 | |
% 5.29/1.53 | | REDUCE: (15), (16) imply:
% 5.29/1.53 | | (17) $false
% 5.29/1.53 | |
% 5.29/1.53 | | CLOSE: (17) is inconsistent.
% 5.29/1.53 | |
% 5.29/1.53 | Case 2:
% 5.29/1.53 | |
% 5.29/1.53 | | (18) ! [v0: $ki_world] : ! [v1: int] : (v1 = 0 | ~ (q(v0) = v1) | ~
% 5.29/1.53 | | $ki_world(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 5.29/1.53 | | $ki_accessible(all_8_1, v0) = v2))
% 5.29/1.53 | |
% 5.29/1.53 | | GROUND_INST: instantiating (18) with all_8_1, all_16_0, simplifying with
% 5.29/1.53 | | (6), (14) gives:
% 5.29/1.53 | | (19) all_16_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(all_8_1,
% 5.29/1.53 | | all_8_1) = v0)
% 5.29/1.53 | |
% 5.29/1.53 | | BETA: splitting (19) gives:
% 5.29/1.53 | |
% 5.29/1.53 | | Case 1:
% 5.29/1.53 | | |
% 5.29/1.53 | | | (20) all_16_0 = 0
% 5.29/1.53 | | |
% 5.29/1.53 | | | REDUCE: (13), (20) imply:
% 5.29/1.53 | | | (21) $false
% 5.29/1.53 | | |
% 5.29/1.53 | | | CLOSE: (21) is inconsistent.
% 5.29/1.53 | | |
% 5.29/1.53 | | Case 2:
% 5.29/1.53 | | |
% 5.29/1.53 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & $ki_accessible(all_8_1, all_8_1) =
% 5.29/1.53 | | | v0)
% 5.29/1.53 | | |
% 5.29/1.53 | | | DELTA: instantiating (22) with fresh symbol all_34_0 gives:
% 5.29/1.53 | | | (23) ~ (all_34_0 = 0) & $ki_accessible(all_8_1, all_8_1) = all_34_0
% 5.29/1.53 | | |
% 5.29/1.53 | | | ALPHA: (23) implies:
% 5.29/1.54 | | | (24) ~ (all_34_0 = 0)
% 5.29/1.54 | | | (25) $ki_accessible(all_8_1, all_8_1) = all_34_0
% 5.29/1.54 | | |
% 5.29/1.54 | | | GROUND_INST: instantiating (mrel_reflexive) with all_8_1, all_34_0,
% 5.29/1.54 | | | simplifying with (6), (25) gives:
% 5.29/1.54 | | | (26) all_34_0 = 0
% 5.29/1.54 | | |
% 5.29/1.54 | | | REDUCE: (24), (26) imply:
% 5.29/1.54 | | | (27) $false
% 5.29/1.54 | | |
% 5.29/1.54 | | | CLOSE: (27) is inconsistent.
% 5.29/1.54 | | |
% 5.29/1.54 | | End of split
% 5.29/1.54 | |
% 5.29/1.54 | End of split
% 5.29/1.54 |
% 5.29/1.54 End of proof
% 5.29/1.54 % SZS output end Proof for theBenchmark
% 5.29/1.54
% 5.29/1.54 867ms
%------------------------------------------------------------------------------