TSTP Solution File: SYO891_16 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.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 04:54:07 EDT 2023
% Result : Theorem 5.08s 1.52s
% Output : Proof 7.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO891_16 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n007.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 07:57:41 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
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.14/1.09 Prover 4: Preprocessing ...
% 2.83/1.10 Prover 1: Preprocessing ...
% 2.83/1.16 Prover 6: Preprocessing ...
% 2.83/1.16 Prover 3: Preprocessing ...
% 2.83/1.16 Prover 0: Preprocessing ...
% 2.83/1.16 Prover 5: Preprocessing ...
% 2.83/1.16 Prover 2: Preprocessing ...
% 4.44/1.36 Prover 5: Proving ...
% 4.44/1.36 Prover 2: Proving ...
% 4.44/1.37 Prover 1: Warning: ignoring some quantifiers
% 4.70/1.37 Prover 3: Warning: ignoring some quantifiers
% 4.70/1.38 Prover 6: Proving ...
% 4.75/1.38 Prover 3: Constructing countermodel ...
% 4.75/1.39 Prover 1: Constructing countermodel ...
% 5.08/1.49 Prover 4: Warning: ignoring some quantifiers
% 5.08/1.50 Prover 4: Constructing countermodel ...
% 5.08/1.51 Prover 2: proved (869ms)
% 5.08/1.52
% 5.08/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.08/1.52
% 5.08/1.52 Prover 6: stopped
% 5.08/1.52 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 5.08/1.52 Prover 5: stopped
% 5.79/1.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 5.79/1.52 Prover 3: proved (872ms)
% 5.79/1.52
% 5.79/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.79/1.52
% 5.79/1.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 5.79/1.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 5.79/1.56 Prover 10: Preprocessing ...
% 5.79/1.56 Prover 8: Preprocessing ...
% 5.79/1.57 Prover 7: Preprocessing ...
% 5.79/1.58 Prover 11: Preprocessing ...
% 6.28/1.60 Prover 7: Warning: ignoring some quantifiers
% 6.28/1.60 Prover 10: Warning: ignoring some quantifiers
% 6.28/1.60 Prover 10: Constructing countermodel ...
% 6.28/1.60 Prover 7: Constructing countermodel ...
% 6.28/1.63 Prover 0: Proving ...
% 6.28/1.63 Prover 1: Found proof (size 14)
% 6.28/1.63 Prover 1: proved (988ms)
% 6.28/1.63 Prover 7: stopped
% 6.28/1.63 Prover 4: stopped
% 6.28/1.63 Prover 0: stopped
% 6.28/1.63 Prover 10: stopped
% 6.28/1.65 Prover 8: Warning: ignoring some quantifiers
% 6.28/1.66 Prover 8: Constructing countermodel ...
% 6.28/1.67 Prover 8: stopped
% 6.95/1.71 Prover 11: Warning: ignoring some quantifiers
% 7.05/1.73 Prover 11: Constructing countermodel ...
% 7.05/1.73 Prover 11: stopped
% 7.05/1.74
% 7.05/1.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.05/1.74
% 7.05/1.74 % SZS output start Proof for theBenchmark
% 7.05/1.74 Assumptions after simplification:
% 7.05/1.74 ---------------------------------
% 7.05/1.74
% 7.05/1.74 ($ki_exists_in_world_$i_cumul)
% 7.05/1.77 ! [v0: $ki_world] : ! [v1: $ki_world] : ! [v2: $i] : ( ~
% 7.05/1.77 ($ki_exists_in_world_$i(v0, v2) = 0) | ~ ($ki_accessible(v0, v1) = 0) | ~
% 7.05/1.77 $ki_world(v1) | ~ $ki_world(v0) | ~ $i(v2) | $ki_exists_in_world_$i(v1,
% 7.05/1.77 v2) = 0)
% 7.05/1.77
% 7.05/1.77 (verify)
% 7.05/1.78 $ki_world($ki_local_world) & ! [v0: $i] : ( ~
% 7.05/1.78 ($ki_exists_in_world_$i($ki_local_world, v0) = 0) | ~ $i(v0) | ! [v1:
% 7.05/1.78 $ki_world] : ( ~ ($ki_accessible($ki_local_world, v1) = 0) | ~
% 7.05/1.78 $ki_world(v1) | ? [v2: $i] : (qmltpeq(v1, v0, v2) = 0 &
% 7.05/1.78 $ki_exists_in_world_$i(v1, v2) = 0 & $i(v2)))) & ! [v0: $ki_world] : (
% 7.05/1.78 ~ ($ki_accessible($ki_local_world, v0) = 0) | ~ $ki_world(v0) | ! [v1: $i]
% 7.05/1.78 : ( ~ (p(v0, v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) &
% 7.05/1.78 $ki_exists_in_world_$i(v0, v1) = v2))) & ? [v0: $i] :
% 7.05/1.78 ($ki_exists_in_world_$i($ki_local_world, v0) = 0 & $i(v0) & ? [v1: $ki_world]
% 7.05/1.78 : (p(v1, v0) = 0 & $ki_accessible($ki_local_world, v1) = 0 & $ki_world(v1)))
% 7.05/1.78
% 7.05/1.78 (function-axioms)
% 7.05/1.78 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 7.05/1.78 [v3: $i] : ! [v4: $ki_world] : (v1 = v0 | ~ (qmltpeq(v4, v3, v2) = v1) | ~
% 7.05/1.78 (qmltpeq(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.05/1.78 MultipleValueBool] : ! [v2: $i] : ! [v3: $ki_world] : (v1 = v0 | ~ (p(v3,
% 7.05/1.78 v2) = v1) | ~ (p(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 7.05/1.78 MultipleValueBool] : ! [v2: $i] : ! [v3: $ki_world] : (v1 = v0 | ~
% 7.05/1.78 ($ki_exists_in_world_$i(v3, v2) = v1) | ~ ($ki_exists_in_world_$i(v3, v2) =
% 7.05/1.78 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 7.05/1.78 $ki_world] : ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_accessible(v3, v2) =
% 7.05/1.78 v1) | ~ ($ki_accessible(v3, v2) = v0))
% 7.05/1.78
% 7.05/1.78 Further assumptions not needed in the proof:
% 7.05/1.78 --------------------------------------------
% 7.05/1.78 $ki_exists_in_world_$i_nonempty, mrel_reflexive, mrel_transitive,
% 7.05/1.78 p_substitution_1, reflexivity, symmetry, transitivity
% 7.05/1.78
% 7.05/1.78 Those formulas are unsatisfiable:
% 7.05/1.78 ---------------------------------
% 7.05/1.78
% 7.05/1.78 Begin of proof
% 7.05/1.78 |
% 7.05/1.78 | ALPHA: (verify) implies:
% 7.05/1.78 | (1) $ki_world($ki_local_world)
% 7.05/1.79 | (2) ! [v0: $ki_world] : ( ~ ($ki_accessible($ki_local_world, v0) = 0) | ~
% 7.05/1.79 | $ki_world(v0) | ! [v1: $i] : ( ~ (p(v0, v1) = 0) | ~ $i(v1) | ?
% 7.05/1.79 | [v2: int] : ( ~ (v2 = 0) & $ki_exists_in_world_$i(v0, v1) = v2)))
% 7.05/1.79 | (3) ? [v0: $i] : ($ki_exists_in_world_$i($ki_local_world, v0) = 0 & $i(v0)
% 7.05/1.79 | & ? [v1: $ki_world] : (p(v1, v0) = 0 &
% 7.05/1.79 | $ki_accessible($ki_local_world, v1) = 0 & $ki_world(v1)))
% 7.05/1.79 |
% 7.05/1.79 | ALPHA: (function-axioms) implies:
% 7.05/1.79 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 7.05/1.79 | ! [v3: $ki_world] : (v1 = v0 | ~ ($ki_exists_in_world_$i(v3, v2) =
% 7.05/1.79 | v1) | ~ ($ki_exists_in_world_$i(v3, v2) = v0))
% 7.05/1.79 |
% 7.05/1.79 | DELTA: instantiating (3) with fresh symbol all_15_0 gives:
% 7.05/1.79 | (5) $ki_exists_in_world_$i($ki_local_world, all_15_0) = 0 & $i(all_15_0) &
% 7.05/1.79 | ? [v0: $ki_world] : (p(v0, all_15_0) = 0 &
% 7.05/1.79 | $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0))
% 7.05/1.79 |
% 7.05/1.79 | ALPHA: (5) implies:
% 7.05/1.79 | (6) $i(all_15_0)
% 7.05/1.79 | (7) $ki_exists_in_world_$i($ki_local_world, all_15_0) = 0
% 7.05/1.79 | (8) ? [v0: $ki_world] : (p(v0, all_15_0) = 0 &
% 7.05/1.79 | $ki_accessible($ki_local_world, v0) = 0 & $ki_world(v0))
% 7.05/1.79 |
% 7.05/1.79 | DELTA: instantiating (8) with fresh symbol all_17_0 gives:
% 7.05/1.79 | (9) p(all_17_0, all_15_0) = 0 & $ki_accessible($ki_local_world, all_17_0) =
% 7.05/1.79 | 0 & $ki_world(all_17_0)
% 7.05/1.79 |
% 7.05/1.79 | ALPHA: (9) implies:
% 7.05/1.79 | (10) $ki_world(all_17_0)
% 7.05/1.80 | (11) $ki_accessible($ki_local_world, all_17_0) = 0
% 7.05/1.80 | (12) p(all_17_0, all_15_0) = 0
% 7.05/1.80 |
% 7.05/1.80 | GROUND_INST: instantiating (2) with all_17_0, simplifying with (10), (11)
% 7.05/1.80 | gives:
% 7.05/1.80 | (13) ! [v0: $i] : ( ~ (p(all_17_0, v0) = 0) | ~ $i(v0) | ? [v1: int] : (
% 7.05/1.80 | ~ (v1 = 0) & $ki_exists_in_world_$i(all_17_0, v0) = v1))
% 7.05/1.80 |
% 7.05/1.80 | GROUND_INST: instantiating ($ki_exists_in_world_$i_cumul) with
% 7.05/1.80 | $ki_local_world, all_17_0, all_15_0, simplifying with (1), (6),
% 7.05/1.80 | (7), (10), (11) gives:
% 7.05/1.80 | (14) $ki_exists_in_world_$i(all_17_0, all_15_0) = 0
% 7.05/1.80 |
% 7.05/1.80 | GROUND_INST: instantiating (13) with all_15_0, simplifying with (6), (12)
% 7.05/1.80 | gives:
% 7.05/1.80 | (15) ? [v0: int] : ( ~ (v0 = 0) & $ki_exists_in_world_$i(all_17_0,
% 7.05/1.80 | all_15_0) = v0)
% 7.05/1.80 |
% 7.05/1.80 | DELTA: instantiating (15) with fresh symbol all_31_0 gives:
% 7.05/1.80 | (16) ~ (all_31_0 = 0) & $ki_exists_in_world_$i(all_17_0, all_15_0) =
% 7.05/1.80 | all_31_0
% 7.05/1.80 |
% 7.05/1.80 | ALPHA: (16) implies:
% 7.05/1.80 | (17) ~ (all_31_0 = 0)
% 7.05/1.80 | (18) $ki_exists_in_world_$i(all_17_0, all_15_0) = all_31_0
% 7.05/1.80 |
% 7.05/1.80 | GROUND_INST: instantiating (4) with 0, all_31_0, all_15_0, all_17_0,
% 7.05/1.80 | simplifying with (14), (18) gives:
% 7.05/1.80 | (19) all_31_0 = 0
% 7.05/1.80 |
% 7.05/1.80 | REDUCE: (17), (19) imply:
% 7.05/1.80 | (20) $false
% 7.05/1.80 |
% 7.05/1.80 | CLOSE: (20) is inconsistent.
% 7.05/1.80 |
% 7.05/1.80 End of proof
% 7.05/1.80 % SZS output end Proof for theBenchmark
% 7.05/1.80
% 7.05/1.80 1178ms
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