TSTP Solution File: MGT039+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT039+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 09:16:23 EDT 2023
% Result : Theorem 8.59s 1.93s
% Output : Proof 14.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT039+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n016.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 06:40:59 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.20/0.65 ________ _____
% 0.20/0.65 ___ __ \_________(_)________________________________
% 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.65
% 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.65 (2023-06-19)
% 0.20/0.65
% 0.20/0.65 (c) Philipp Rümmer, 2009-2023
% 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.65 Amanda Stjerna.
% 0.20/0.65 Free software under BSD-3-Clause.
% 0.20/0.65
% 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.65
% 0.20/0.65 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.67 Running up to 7 provers in parallel.
% 0.20/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.74/1.08 Prover 1: Preprocessing ...
% 2.74/1.08 Prover 4: Preprocessing ...
% 3.01/1.12 Prover 3: Preprocessing ...
% 3.01/1.12 Prover 6: Preprocessing ...
% 3.01/1.12 Prover 0: Preprocessing ...
% 3.01/1.12 Prover 2: Preprocessing ...
% 3.01/1.12 Prover 5: Preprocessing ...
% 4.91/1.39 Prover 3: Constructing countermodel ...
% 4.91/1.39 Prover 1: Constructing countermodel ...
% 4.91/1.40 Prover 5: Proving ...
% 4.91/1.40 Prover 2: Proving ...
% 4.91/1.40 Prover 6: Proving ...
% 4.91/1.48 Prover 4: Constructing countermodel ...
% 4.91/1.51 Prover 0: Proving ...
% 6.39/1.62 Prover 3: gave up
% 6.39/1.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.66/1.66 Prover 7: Preprocessing ...
% 6.66/1.70 Prover 7: Warning: ignoring some quantifiers
% 6.66/1.71 Prover 7: Constructing countermodel ...
% 7.78/1.79 Prover 7: gave up
% 7.78/1.80 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.78/1.83 Prover 8: Preprocessing ...
% 8.59/1.92 Prover 2: proved (1246ms)
% 8.59/1.93
% 8.59/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.59/1.93
% 8.59/1.94 Prover 6: stopped
% 8.59/1.94 Prover 8: Warning: ignoring some quantifiers
% 8.59/1.94 Prover 0: stopped
% 8.90/1.95 Prover 5: stopped
% 8.90/1.96 Prover 8: Constructing countermodel ...
% 8.90/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.90/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.90/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.90/1.96 Prover 10: Preprocessing ...
% 8.90/1.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.90/1.99 Prover 11: Preprocessing ...
% 8.90/1.99 Prover 13: Preprocessing ...
% 8.90/2.01 Prover 16: Preprocessing ...
% 8.90/2.02 Prover 10: Warning: ignoring some quantifiers
% 8.90/2.02 Prover 10: Constructing countermodel ...
% 8.90/2.04 Prover 10: gave up
% 8.90/2.04 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 8.90/2.05 Prover 16: Warning: ignoring some quantifiers
% 8.90/2.05 Prover 16: Constructing countermodel ...
% 8.90/2.06 Prover 19: Preprocessing ...
% 8.90/2.09 Prover 13: Warning: ignoring some quantifiers
% 8.90/2.10 Prover 13: Constructing countermodel ...
% 10.22/2.19 Prover 19: Warning: ignoring some quantifiers
% 10.22/2.20 Prover 19: Constructing countermodel ...
% 10.72/2.23 Prover 11: Constructing countermodel ...
% 11.21/2.33 Prover 16: gave up
% 13.04/2.54 Prover 8: gave up
% 13.51/2.64 Prover 13: Found proof (size 138)
% 13.51/2.64 Prover 13: proved (691ms)
% 13.51/2.65 Prover 19: stopped
% 13.51/2.65 Prover 11: stopped
% 13.51/2.65 Prover 1: stopped
% 13.51/2.65 Prover 4: stopped
% 13.51/2.65
% 13.51/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.51/2.65
% 14.14/2.66 % SZS output start Proof for theBenchmark
% 14.14/2.67 Assumptions after simplification:
% 14.14/2.67 ---------------------------------
% 14.14/2.67
% 14.14/2.67 (l8)
% 14.25/2.69 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ! [v1: $i] : !
% 14.25/2.69 [v2: $i] : ( ~ (critical_point(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 14.25/2.69 greater(v1, v2) | ~ in_environment(v0, v1) | ~ environment(v0) |
% 14.25/2.69 selection_favors(efficient_producers, first_movers, v1)) & ! [v0: $i] : !
% 14.25/2.69 [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in_environment(v0, v1) | ~
% 14.25/2.69 environment(v0) | selection_favors(efficient_producers, first_movers, v1) |
% 14.25/2.69 ? [v2: $i] : (critical_point(v0) = v2 & $i(v2) & ~ greater(v1, v2)))
% 14.25/2.69
% 14.25/2.69 (mp3_favoured_trategy)
% 14.25/2.70 $i(efficient_producers) & $i(first_movers) & ! [v0: $i] : ( ~ $i(v0) | ~
% 14.25/2.70 propagation_strategy(efficient_producers) | ~
% 14.25/2.70 propagation_strategy(first_movers) | ~ observational_period(v0) |
% 14.25/2.70 selection_favors(efficient_producers, first_movers, v0) | ? [v1: $i] : ?
% 14.25/2.70 [v2: $i] : (end_time(v1) = v2 & $i(v2) & $i(v1) & in_environment(v0, v1) &
% 14.25/2.70 environment(v1) & ~ selection_favors(efficient_producers, first_movers,
% 14.25/2.70 v2)))
% 14.25/2.70
% 14.25/2.70 (mp4_critical_point)
% 14.25/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (critical_point(v1) = v2) | ~
% 14.25/2.70 $i(v1) | ~ $i(v0) | ~ slow_change(v0) | ~ in_environment(v0, v1) | ~
% 14.25/2.70 environment(v1) | ~ observational_period(v0) | ? [v3: $i] : ($i(v3) &
% 14.25/2.70 greater(v3, v2) & in_environment(v1, v3))) & ! [v0: $i] : ! [v1: $i] : (
% 14.25/2.70 ~ $i(v1) | ~ $i(v0) | ~ slow_change(v0) | ~ in_environment(v0, v1) | ~
% 14.25/2.70 environment(v1) | ~ observational_period(v0) | ? [v2: $i] : ? [v3: $i] :
% 14.25/2.70 (critical_point(v1) = v2 & $i(v3) & $i(v2) & greater(v3, v2) &
% 14.25/2.70 in_environment(v1, v3)))
% 14.25/2.70
% 14.25/2.70 (mp_beginning_and_ending)
% 14.25/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (start_time(v0) = v2) | ~
% 14.25/2.70 $i(v1) | ~ $i(v0) | ~ greater(v1, v2) | ~ environment(v0) | ? [v3: $i] :
% 14.25/2.70 (end_time(v0) = v3 & $i(v3) & (greater_or_equal(v3, v1) | greater(v1, v3))))
% 14.25/2.70 & ? [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ environment(v1) | ?
% 14.25/2.70 [v2: $i] : ? [v3: $i] : (start_time(v1) = v2 & end_time(v1) = v3 & $i(v3) &
% 14.25/2.70 $i(v2) & ( ~ greater(v0, v2) | greater_or_equal(v3, v0) | greater(v0,
% 14.25/2.70 v3))))
% 14.25/2.70
% 14.25/2.70 (mp_environment_end_point)
% 14.25/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (end_time(v0) = v2) | ~ $i(v1)
% 14.25/2.71 | ~ $i(v0) | ~ in_environment(v0, v1) | ~ environment(v0) |
% 14.25/2.71 greater_or_equal(v2, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 14.25/2.71 $i(v0) | ~ in_environment(v0, v1) | ~ environment(v0) | ? [v2: $i] :
% 14.25/2.71 (end_time(v0) = v2 & $i(v2) & greater_or_equal(v2, v1)))
% 14.25/2.71
% 14.25/2.71 (mp_greater_or_equal)
% 14.25/2.71 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 14.25/2.71 greater_or_equal(v0, v1) | greater(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (
% 14.25/2.71 ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ?
% 14.25/2.71 [v0: $i] : ( ~ $i(v0) | greater_or_equal(v0, v0))
% 14.25/2.71
% 14.25/2.71 (mp_greater_transitivity)
% 14.25/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.25/2.71 ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 14.25/2.71
% 14.25/2.71 (mp_organizational_sets1)
% 14.25/2.71 $i(first_movers) & propagation_strategy(first_movers)
% 14.25/2.71
% 14.25/2.71 (mp_organizational_sets2)
% 14.25/2.71 $i(efficient_producers) & propagation_strategy(efficient_producers)
% 14.25/2.71
% 14.25/2.71 (mp_time_in_environment)
% 14.25/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (start_time(v0) = v2) | ~
% 14.25/2.71 $i(v1) | ~ $i(v0) | ~ greater_or_equal(v1, v2) | ~ environment(v0) |
% 14.25/2.71 in_environment(v0, v1) | ? [v3: $i] : (end_time(v0) = v3 & $i(v3) & ~
% 14.25/2.71 greater_or_equal(v3, v1))) & ? [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~
% 14.25/2.71 $i(v0) | ~ environment(v1) | in_environment(v1, v0) | ? [v2: $i] : ? [v3:
% 14.25/2.71 $i] : (start_time(v1) = v2 & end_time(v1) = v3 & $i(v3) & $i(v2) & ( ~
% 14.25/2.71 greater_or_equal(v3, v0) | ~ greater_or_equal(v0, v2))))
% 14.25/2.71
% 14.25/2.71 (mp_time_of_critical_point)
% 14.25/2.72 ! [v0: $i] : ! [v1: $i] : ( ~ (start_time(v0) = v1) | ~ $i(v0) | ~
% 14.25/2.72 environment(v0) | ? [v2: $i] : (critical_point(v0) = v2 & $i(v2) &
% 14.25/2.72 greater_or_equal(v2, v1))) & ! [v0: $i] : ( ~ $i(v0) | ~ environment(v0)
% 14.25/2.72 | ? [v1: $i] : ? [v2: $i] : (start_time(v0) = v2 & critical_point(v0) = v1
% 14.25/2.72 & $i(v2) & $i(v1) & greater_or_equal(v1, v2)))
% 14.25/2.72
% 14.25/2.72 (prove_t8)
% 14.25/2.72 $i(efficient_producers) & $i(first_movers) & ? [v0: $i] : ($i(v0) &
% 14.25/2.72 slow_change(v0) & observational_period(v0) & ~
% 14.25/2.72 selection_favors(efficient_producers, first_movers, v0))
% 14.25/2.72
% 14.25/2.72 (function-axioms)
% 14.25/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (start_time(v2) = v1)
% 14.25/2.72 | ~ (start_time(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 14.25/2.72 = v0 | ~ (critical_point(v2) = v1) | ~ (critical_point(v2) = v0)) & !
% 14.25/2.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (end_time(v2) = v1) | ~
% 14.25/2.72 (end_time(v2) = v0))
% 14.25/2.72
% 14.25/2.72 Those formulas are unsatisfiable:
% 14.25/2.72 ---------------------------------
% 14.25/2.72
% 14.25/2.72 Begin of proof
% 14.25/2.72 |
% 14.25/2.72 | ALPHA: (mp3_favoured_trategy) implies:
% 14.25/2.72 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ propagation_strategy(efficient_producers)
% 14.25/2.72 | | ~ propagation_strategy(first_movers) | ~ observational_period(v0)
% 14.25/2.72 | | selection_favors(efficient_producers, first_movers, v0) | ? [v1:
% 14.25/2.72 | $i] : ? [v2: $i] : (end_time(v1) = v2 & $i(v2) & $i(v1) &
% 14.25/2.72 | in_environment(v0, v1) & environment(v1) & ~
% 14.25/2.72 | selection_favors(efficient_producers, first_movers, v2)))
% 14.25/2.72 |
% 14.25/2.72 | ALPHA: (mp4_critical_point) implies:
% 14.25/2.72 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ slow_change(v0)
% 14.25/2.72 | | ~ in_environment(v0, v1) | ~ environment(v1) | ~
% 14.25/2.72 | observational_period(v0) | ? [v2: $i] : ? [v3: $i] :
% 14.25/2.72 | (critical_point(v1) = v2 & $i(v3) & $i(v2) & greater(v3, v2) &
% 14.25/2.72 | in_environment(v1, v3)))
% 14.25/2.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (critical_point(v1) = v2)
% 14.25/2.72 | | ~ $i(v1) | ~ $i(v0) | ~ slow_change(v0) | ~ in_environment(v0,
% 14.25/2.72 | v1) | ~ environment(v1) | ~ observational_period(v0) | ? [v3:
% 14.25/2.72 | $i] : ($i(v3) & greater(v3, v2) & in_environment(v1, v3)))
% 14.25/2.72 |
% 14.25/2.72 | ALPHA: (mp_organizational_sets1) implies:
% 14.25/2.72 | (4) propagation_strategy(first_movers)
% 14.25/2.72 |
% 14.25/2.72 | ALPHA: (mp_organizational_sets2) implies:
% 14.25/2.72 | (5) propagation_strategy(efficient_producers)
% 14.25/2.72 |
% 14.25/2.72 | ALPHA: (mp_time_in_environment) implies:
% 14.25/2.73 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (start_time(v0) = v2) |
% 14.25/2.73 | ~ $i(v1) | ~ $i(v0) | ~ greater_or_equal(v1, v2) | ~
% 14.25/2.73 | environment(v0) | in_environment(v0, v1) | ? [v3: $i] :
% 14.25/2.73 | (end_time(v0) = v3 & $i(v3) & ~ greater_or_equal(v3, v1)))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (mp_environment_end_point) implies:
% 14.25/2.73 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 14.25/2.73 | in_environment(v0, v1) | ~ environment(v0) | ? [v2: $i] :
% 14.25/2.73 | (end_time(v0) = v2 & $i(v2) & greater_or_equal(v2, v1)))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (mp_time_of_critical_point) implies:
% 14.25/2.73 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ environment(v0) | ? [v1: $i] : ? [v2:
% 14.25/2.73 | $i] : (start_time(v0) = v2 & critical_point(v0) = v1 & $i(v2) &
% 14.25/2.73 | $i(v1) & greater_or_equal(v1, v2)))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (mp_greater_or_equal) implies:
% 14.25/2.73 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1)
% 14.25/2.73 | | greater_or_equal(v0, v1))
% 14.25/2.73 | (10) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 14.25/2.73 | greater_or_equal(v0, v1) | greater(v0, v1))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (mp_beginning_and_ending) implies:
% 14.25/2.73 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (start_time(v0) = v2) |
% 14.25/2.73 | ~ $i(v1) | ~ $i(v0) | ~ greater(v1, v2) | ~ environment(v0) | ?
% 14.25/2.73 | [v3: $i] : (end_time(v0) = v3 & $i(v3) & (greater_or_equal(v3, v1) |
% 14.25/2.73 | greater(v1, v3))))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (l8) implies:
% 14.25/2.73 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (critical_point(v0) =
% 14.25/2.73 | v2) | ~ $i(v1) | ~ $i(v0) | ~ greater(v1, v2) | ~
% 14.25/2.73 | in_environment(v0, v1) | ~ environment(v0) |
% 14.25/2.73 | selection_favors(efficient_producers, first_movers, v1))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (prove_t8) implies:
% 14.25/2.73 | (13) ? [v0: $i] : ($i(v0) & slow_change(v0) & observational_period(v0) &
% 14.25/2.73 | ~ selection_favors(efficient_producers, first_movers, v0))
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (function-axioms) implies:
% 14.25/2.73 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (end_time(v2)
% 14.25/2.73 | = v1) | ~ (end_time(v2) = v0))
% 14.25/2.73 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.25/2.73 | (critical_point(v2) = v1) | ~ (critical_point(v2) = v0))
% 14.25/2.73 |
% 14.25/2.73 | DELTA: instantiating (13) with fresh symbol all_14_0 gives:
% 14.25/2.73 | (16) $i(all_14_0) & slow_change(all_14_0) & observational_period(all_14_0)
% 14.25/2.73 | & ~ selection_favors(efficient_producers, first_movers, all_14_0)
% 14.25/2.73 |
% 14.25/2.73 | ALPHA: (16) implies:
% 14.25/2.73 | (17) ~ selection_favors(efficient_producers, first_movers, all_14_0)
% 14.25/2.74 | (18) observational_period(all_14_0)
% 14.25/2.74 | (19) slow_change(all_14_0)
% 14.25/2.74 | (20) $i(all_14_0)
% 14.25/2.74 |
% 14.25/2.74 | GROUND_INST: instantiating (1) with all_14_0, simplifying with (4), (5), (17),
% 14.25/2.74 | (18), (20) gives:
% 14.25/2.74 | (21) ? [v0: $i] : ? [v1: $i] : (end_time(v0) = v1 & $i(v1) & $i(v0) &
% 14.25/2.74 | in_environment(all_14_0, v0) & environment(v0) & ~
% 14.25/2.74 | selection_favors(efficient_producers, first_movers, v1))
% 14.25/2.74 |
% 14.25/2.74 | DELTA: instantiating (21) with fresh symbols all_25_0, all_25_1 gives:
% 14.25/2.74 | (22) end_time(all_25_1) = all_25_0 & $i(all_25_0) & $i(all_25_1) &
% 14.25/2.74 | in_environment(all_14_0, all_25_1) & environment(all_25_1) & ~
% 14.25/2.74 | selection_favors(efficient_producers, first_movers, all_25_0)
% 14.25/2.74 |
% 14.25/2.74 | ALPHA: (22) implies:
% 14.25/2.74 | (23) ~ selection_favors(efficient_producers, first_movers, all_25_0)
% 14.25/2.74 | (24) environment(all_25_1)
% 14.25/2.74 | (25) in_environment(all_14_0, all_25_1)
% 14.25/2.74 | (26) $i(all_25_1)
% 14.25/2.74 | (27) end_time(all_25_1) = all_25_0
% 14.25/2.74 |
% 14.25/2.74 | GROUND_INST: instantiating (8) with all_25_1, simplifying with (24), (26)
% 14.25/2.74 | gives:
% 14.25/2.74 | (28) ? [v0: $i] : ? [v1: $i] : (start_time(all_25_1) = v1 &
% 14.25/2.74 | critical_point(all_25_1) = v0 & $i(v1) & $i(v0) &
% 14.25/2.74 | greater_or_equal(v0, v1))
% 14.25/2.74 |
% 14.25/2.74 | GROUND_INST: instantiating (2) with all_14_0, all_25_1, simplifying with (18),
% 14.25/2.74 | (19), (20), (24), (25), (26) gives:
% 14.25/2.74 | (29) ? [v0: $i] : ? [v1: $i] : (critical_point(all_25_1) = v0 & $i(v1) &
% 14.25/2.74 | $i(v0) & greater(v1, v0) & in_environment(all_25_1, v1))
% 14.25/2.74 |
% 14.25/2.74 | DELTA: instantiating (29) with fresh symbols all_32_0, all_32_1 gives:
% 14.25/2.74 | (30) critical_point(all_25_1) = all_32_1 & $i(all_32_0) & $i(all_32_1) &
% 14.25/2.74 | greater(all_32_0, all_32_1) & in_environment(all_25_1, all_32_0)
% 14.25/2.74 |
% 14.25/2.74 | ALPHA: (30) implies:
% 14.25/2.74 | (31) in_environment(all_25_1, all_32_0)
% 14.25/2.74 | (32) greater(all_32_0, all_32_1)
% 14.25/2.74 | (33) $i(all_32_0)
% 14.25/2.74 | (34) critical_point(all_25_1) = all_32_1
% 14.25/2.74 |
% 14.25/2.74 | DELTA: instantiating (28) with fresh symbols all_34_0, all_34_1 gives:
% 14.25/2.74 | (35) start_time(all_25_1) = all_34_0 & critical_point(all_25_1) = all_34_1
% 14.25/2.74 | & $i(all_34_0) & $i(all_34_1) & greater_or_equal(all_34_1, all_34_0)
% 14.25/2.74 |
% 14.25/2.74 | ALPHA: (35) implies:
% 14.25/2.74 | (36) greater_or_equal(all_34_1, all_34_0)
% 14.25/2.74 | (37) $i(all_34_1)
% 14.25/2.74 | (38) $i(all_34_0)
% 14.25/2.74 | (39) critical_point(all_25_1) = all_34_1
% 14.25/2.74 | (40) start_time(all_25_1) = all_34_0
% 14.25/2.74 |
% 14.25/2.74 | GROUND_INST: instantiating (15) with all_32_1, all_34_1, all_25_1, simplifying
% 14.25/2.74 | with (34), (39) gives:
% 14.25/2.74 | (41) all_34_1 = all_32_1
% 14.25/2.74 |
% 14.25/2.74 | REDUCE: (37), (41) imply:
% 14.25/2.74 | (42) $i(all_32_1)
% 14.25/2.74 |
% 14.25/2.75 | REDUCE: (36), (41) imply:
% 14.25/2.75 | (43) greater_or_equal(all_32_1, all_34_0)
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (7) with all_25_1, all_32_0, simplifying with (24),
% 14.25/2.75 | (26), (31), (33) gives:
% 14.25/2.75 | (44) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) & greater_or_equal(v0,
% 14.25/2.75 | all_32_0))
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (9) with all_32_0, all_32_1, simplifying with (32),
% 14.25/2.75 | (33), (42) gives:
% 14.25/2.75 | (45) greater_or_equal(all_32_0, all_32_1)
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (10) with all_32_1, all_34_0, simplifying with
% 14.25/2.75 | (38), (42), (43) gives:
% 14.25/2.75 | (46) all_34_0 = all_32_1 | greater(all_32_1, all_34_0)
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (3) with all_14_0, all_25_1, all_32_1, simplifying
% 14.25/2.75 | with (18), (19), (20), (24), (25), (26), (34) gives:
% 14.25/2.75 | (47) ? [v0: $i] : ($i(v0) & greater(v0, all_32_1) &
% 14.25/2.75 | in_environment(all_25_1, v0))
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (12) with all_25_1, all_32_0, all_32_1, simplifying
% 14.25/2.75 | with (24), (26), (31), (32), (33), (34) gives:
% 14.25/2.75 | (48) selection_favors(efficient_producers, first_movers, all_32_0)
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (6) with all_25_1, all_32_1, all_34_0, simplifying
% 14.25/2.75 | with (24), (26), (40), (42), (43) gives:
% 14.25/2.75 | (49) in_environment(all_25_1, all_32_1) | ? [v0: $i] : (end_time(all_25_1)
% 14.25/2.75 | = v0 & $i(v0) & ~ greater_or_equal(v0, all_32_1))
% 14.25/2.75 |
% 14.25/2.75 | DELTA: instantiating (44) with fresh symbol all_46_0 gives:
% 14.25/2.75 | (50) end_time(all_25_1) = all_46_0 & $i(all_46_0) &
% 14.25/2.75 | greater_or_equal(all_46_0, all_32_0)
% 14.25/2.75 |
% 14.25/2.75 | ALPHA: (50) implies:
% 14.25/2.75 | (51) greater_or_equal(all_46_0, all_32_0)
% 14.25/2.75 | (52) $i(all_46_0)
% 14.25/2.75 | (53) end_time(all_25_1) = all_46_0
% 14.25/2.75 |
% 14.25/2.75 | DELTA: instantiating (47) with fresh symbol all_48_0 gives:
% 14.25/2.75 | (54) $i(all_48_0) & greater(all_48_0, all_32_1) & in_environment(all_25_1,
% 14.25/2.75 | all_48_0)
% 14.25/2.75 |
% 14.25/2.75 | ALPHA: (54) implies:
% 14.25/2.75 | (55) in_environment(all_25_1, all_48_0)
% 14.25/2.75 | (56) $i(all_48_0)
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (14) with all_25_0, all_46_0, all_25_1, simplifying
% 14.25/2.75 | with (27), (53) gives:
% 14.25/2.75 | (57) all_46_0 = all_25_0
% 14.25/2.75 |
% 14.25/2.75 | REDUCE: (52), (57) imply:
% 14.25/2.75 | (58) $i(all_25_0)
% 14.25/2.75 |
% 14.25/2.75 | REDUCE: (51), (57) imply:
% 14.25/2.75 | (59) greater_or_equal(all_25_0, all_32_0)
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (7) with all_25_1, all_48_0, simplifying with (24),
% 14.25/2.75 | (26), (55), (56) gives:
% 14.25/2.75 | (60) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) & greater_or_equal(v0,
% 14.25/2.75 | all_48_0))
% 14.25/2.75 |
% 14.25/2.75 | GROUND_INST: instantiating (10) with all_25_0, all_32_0, simplifying with
% 14.25/2.75 | (33), (58), (59) gives:
% 14.25/2.75 | (61) all_32_0 = all_25_0 | greater(all_25_0, all_32_0)
% 14.25/2.75 |
% 14.25/2.75 | DELTA: instantiating (60) with fresh symbol all_60_0 gives:
% 14.25/2.76 | (62) end_time(all_25_1) = all_60_0 & $i(all_60_0) &
% 14.25/2.76 | greater_or_equal(all_60_0, all_48_0)
% 14.25/2.76 |
% 14.25/2.76 | ALPHA: (62) implies:
% 14.25/2.76 | (63) end_time(all_25_1) = all_60_0
% 14.25/2.76 |
% 14.25/2.76 | GROUND_INST: instantiating (14) with all_25_0, all_60_0, all_25_1, simplifying
% 14.25/2.76 | with (27), (63) gives:
% 14.25/2.76 | (64) all_60_0 = all_25_0
% 14.25/2.76 |
% 14.25/2.76 | BETA: splitting (49) gives:
% 14.25/2.76 |
% 14.25/2.76 | Case 1:
% 14.25/2.76 | |
% 14.25/2.76 | | (65) in_environment(all_25_1, all_32_1)
% 14.25/2.76 | |
% 14.25/2.76 | | GROUND_INST: instantiating (7) with all_25_1, all_32_1, simplifying with
% 14.25/2.76 | | (24), (26), (42), (65) gives:
% 14.25/2.76 | | (66) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) &
% 14.25/2.76 | | greater_or_equal(v0, all_32_1))
% 14.25/2.76 | |
% 14.25/2.76 | | DELTA: instantiating (66) with fresh symbol all_106_0 gives:
% 14.25/2.76 | | (67) end_time(all_25_1) = all_106_0 & $i(all_106_0) &
% 14.25/2.76 | | greater_or_equal(all_106_0, all_32_1)
% 14.25/2.76 | |
% 14.25/2.76 | | ALPHA: (67) implies:
% 14.25/2.76 | | (68) greater_or_equal(all_106_0, all_32_1)
% 14.25/2.76 | | (69) $i(all_106_0)
% 14.25/2.76 | | (70) end_time(all_25_1) = all_106_0
% 14.25/2.76 | |
% 14.25/2.76 | | GROUND_INST: instantiating (14) with all_25_0, all_106_0, all_25_1,
% 14.25/2.76 | | simplifying with (27), (70) gives:
% 14.25/2.76 | | (71) all_106_0 = all_25_0
% 14.25/2.76 | |
% 14.25/2.76 | | REDUCE: (68), (71) imply:
% 14.25/2.76 | | (72) greater_or_equal(all_25_0, all_32_1)
% 14.25/2.76 | |
% 14.25/2.76 | | BETA: splitting (46) gives:
% 14.25/2.76 | |
% 14.25/2.76 | | Case 1:
% 14.25/2.76 | | |
% 14.25/2.76 | | | (73) greater(all_32_1, all_34_0)
% 14.25/2.76 | | |
% 14.25/2.76 | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_32_0,
% 14.25/2.76 | | | all_32_1, all_34_0, simplifying with (32), (33), (38), (42),
% 14.25/2.76 | | | (73) gives:
% 14.25/2.76 | | | (74) greater(all_32_0, all_34_0)
% 14.25/2.76 | | |
% 14.25/2.76 | | | BETA: splitting (61) gives:
% 14.25/2.76 | | |
% 14.25/2.76 | | | Case 1:
% 14.25/2.76 | | | |
% 14.25/2.76 | | | | (75) greater(all_25_0, all_32_0)
% 14.25/2.76 | | | |
% 14.25/2.76 | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_25_0,
% 14.25/2.76 | | | | all_32_0, all_34_0, simplifying with (33), (38), (58),
% 14.25/2.76 | | | | (74), (75) gives:
% 14.25/2.76 | | | | (76) greater(all_25_0, all_34_0)
% 14.25/2.76 | | | |
% 14.25/2.76 | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_25_0,
% 14.25/2.76 | | | | all_32_0, all_32_1, simplifying with (32), (33), (42),
% 14.25/2.76 | | | | (58), (75) gives:
% 14.25/2.76 | | | | (77) greater(all_25_0, all_32_1)
% 14.25/2.76 | | | |
% 14.25/2.76 | | | | GROUND_INST: instantiating (11) with all_25_1, all_25_0, all_34_0,
% 14.25/2.76 | | | | simplifying with (24), (26), (40), (58), (76) gives:
% 14.25/2.76 | | | | (78) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) &
% 14.25/2.76 | | | | (greater_or_equal(v0, all_25_0) | greater(all_25_0, v0)))
% 14.25/2.76 | | | |
% 14.25/2.76 | | | | GROUND_INST: instantiating (9) with all_25_0, all_34_0, simplifying with
% 14.25/2.76 | | | | (38), (58), (76) gives:
% 14.25/2.76 | | | | (79) greater_or_equal(all_25_0, all_34_0)
% 14.25/2.76 | | | |
% 14.25/2.76 | | | | DELTA: instantiating (78) with fresh symbol all_150_0 gives:
% 14.25/2.76 | | | | (80) end_time(all_25_1) = all_150_0 & $i(all_150_0) &
% 14.25/2.76 | | | | (greater_or_equal(all_150_0, all_25_0) | greater(all_25_0,
% 14.25/2.77 | | | | all_150_0))
% 14.25/2.77 | | | |
% 14.25/2.77 | | | | ALPHA: (80) implies:
% 14.25/2.77 | | | | (81) $i(all_150_0)
% 14.25/2.77 | | | | (82) end_time(all_25_1) = all_150_0
% 14.25/2.77 | | | | (83) greater_or_equal(all_150_0, all_25_0) | greater(all_25_0,
% 14.25/2.77 | | | | all_150_0)
% 14.25/2.77 | | | |
% 14.25/2.77 | | | | GROUND_INST: instantiating (14) with all_25_0, all_150_0, all_25_1,
% 14.25/2.77 | | | | simplifying with (27), (82) gives:
% 14.25/2.77 | | | | (84) all_150_0 = all_25_0
% 14.25/2.77 | | | |
% 14.25/2.77 | | | | GROUND_INST: instantiating (6) with all_25_1, all_25_0, all_34_0,
% 14.25/2.77 | | | | simplifying with (24), (26), (40), (58), (79) gives:
% 14.25/2.77 | | | | (85) in_environment(all_25_1, all_25_0) | ? [v0: $i] :
% 14.25/2.77 | | | | (end_time(all_25_1) = v0 & $i(v0) & ~ greater_or_equal(v0,
% 14.25/2.77 | | | | all_25_0))
% 14.25/2.77 | | | |
% 14.25/2.77 | | | | BETA: splitting (83) gives:
% 14.25/2.77 | | | |
% 14.25/2.77 | | | | Case 1:
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | (86) greater_or_equal(all_150_0, all_25_0)
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | REDUCE: (84), (86) imply:
% 14.25/2.77 | | | | | (87) greater_or_equal(all_25_0, all_25_0)
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | BETA: splitting (85) gives:
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | Case 1:
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | (88) in_environment(all_25_1, all_25_0)
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | GROUND_INST: instantiating (12) with all_25_1, all_25_0, all_32_1,
% 14.25/2.77 | | | | | | simplifying with (23), (24), (26), (34), (58), (77),
% 14.25/2.77 | | | | | | (88) gives:
% 14.25/2.77 | | | | | | (89) $false
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | CLOSE: (89) is inconsistent.
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | Case 2:
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | (90) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) & ~
% 14.25/2.77 | | | | | | greater_or_equal(v0, all_25_0))
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | DELTA: instantiating (90) with fresh symbol all_225_0 gives:
% 14.25/2.77 | | | | | | (91) end_time(all_25_1) = all_225_0 & $i(all_225_0) & ~
% 14.25/2.77 | | | | | | greater_or_equal(all_225_0, all_25_0)
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | ALPHA: (91) implies:
% 14.25/2.77 | | | | | | (92) ~ greater_or_equal(all_225_0, all_25_0)
% 14.25/2.77 | | | | | | (93) end_time(all_25_1) = all_225_0
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | GROUND_INST: instantiating (14) with all_25_0, all_225_0, all_25_1,
% 14.25/2.77 | | | | | | simplifying with (27), (93) gives:
% 14.25/2.77 | | | | | | (94) all_225_0 = all_25_0
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | REDUCE: (92), (94) imply:
% 14.25/2.77 | | | | | | (95) ~ greater_or_equal(all_25_0, all_25_0)
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | PRED_UNIFY: (87), (95) imply:
% 14.25/2.77 | | | | | | (96) $false
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | | CLOSE: (96) is inconsistent.
% 14.25/2.77 | | | | | |
% 14.25/2.77 | | | | | End of split
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | Case 2:
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | (97) ~ greater_or_equal(all_150_0, all_25_0)
% 14.25/2.77 | | | | | (98) greater(all_25_0, all_150_0)
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | REDUCE: (84), (98) imply:
% 14.25/2.77 | | | | | (99) greater(all_25_0, all_25_0)
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | REDUCE: (84), (97) imply:
% 14.25/2.77 | | | | | (100) ~ greater_or_equal(all_25_0, all_25_0)
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | GROUND_INST: instantiating (9) with all_25_0, all_25_0, simplifying
% 14.25/2.77 | | | | | with (58), (99), (100) gives:
% 14.25/2.77 | | | | | (101) $false
% 14.25/2.77 | | | | |
% 14.25/2.77 | | | | | CLOSE: (101) is inconsistent.
% 14.25/2.77 | | | | |
% 14.25/2.78 | | | | End of split
% 14.25/2.78 | | | |
% 14.25/2.78 | | | Case 2:
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | (102) all_32_0 = all_25_0
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | REDUCE: (48), (102) imply:
% 14.25/2.78 | | | | (103) selection_favors(efficient_producers, first_movers, all_25_0)
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | PRED_UNIFY: (23), (103) imply:
% 14.25/2.78 | | | | (104) $false
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | CLOSE: (104) is inconsistent.
% 14.25/2.78 | | | |
% 14.25/2.78 | | | End of split
% 14.25/2.78 | | |
% 14.25/2.78 | | Case 2:
% 14.25/2.78 | | |
% 14.25/2.78 | | | (105) all_34_0 = all_32_1
% 14.25/2.78 | | |
% 14.25/2.78 | | | REDUCE: (40), (105) imply:
% 14.25/2.78 | | | (106) start_time(all_25_1) = all_32_1
% 14.25/2.78 | | |
% 14.25/2.78 | | | GROUND_INST: instantiating (6) with all_25_1, all_25_0, all_32_1,
% 14.25/2.78 | | | simplifying with (24), (26), (58), (72), (106) gives:
% 14.25/2.78 | | | (107) in_environment(all_25_1, all_25_0) | ? [v0: $i] :
% 14.25/2.78 | | | (end_time(all_25_1) = v0 & $i(v0) & ~ greater_or_equal(v0,
% 14.25/2.78 | | | all_25_0))
% 14.25/2.78 | | |
% 14.25/2.78 | | | BETA: splitting (61) gives:
% 14.25/2.78 | | |
% 14.25/2.78 | | | Case 1:
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | (108) greater(all_25_0, all_32_0)
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_25_0,
% 14.25/2.78 | | | | all_32_0, all_32_1, simplifying with (32), (33), (42),
% 14.25/2.78 | | | | (58), (108) gives:
% 14.25/2.78 | | | | (109) greater(all_25_0, all_32_1)
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | GROUND_INST: instantiating (11) with all_25_1, all_25_0, all_32_1,
% 14.25/2.78 | | | | simplifying with (24), (26), (58), (106), (109) gives:
% 14.25/2.78 | | | | (110) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) &
% 14.25/2.78 | | | | (greater_or_equal(v0, all_25_0) | greater(all_25_0, v0)))
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | DELTA: instantiating (110) with fresh symbol all_137_0 gives:
% 14.25/2.78 | | | | (111) end_time(all_25_1) = all_137_0 & $i(all_137_0) &
% 14.25/2.78 | | | | (greater_or_equal(all_137_0, all_25_0) | greater(all_25_0,
% 14.25/2.78 | | | | all_137_0))
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | ALPHA: (111) implies:
% 14.25/2.78 | | | | (112) $i(all_137_0)
% 14.25/2.78 | | | | (113) end_time(all_25_1) = all_137_0
% 14.25/2.78 | | | | (114) greater_or_equal(all_137_0, all_25_0) | greater(all_25_0,
% 14.25/2.78 | | | | all_137_0)
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | GROUND_INST: instantiating (14) with all_25_0, all_137_0, all_25_1,
% 14.25/2.78 | | | | simplifying with (27), (113) gives:
% 14.25/2.78 | | | | (115) all_137_0 = all_25_0
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | BETA: splitting (107) gives:
% 14.25/2.78 | | | |
% 14.25/2.78 | | | | Case 1:
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | (116) in_environment(all_25_1, all_25_0)
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | GROUND_INST: instantiating (12) with all_25_1, all_25_0, all_32_1,
% 14.25/2.78 | | | | | simplifying with (23), (24), (26), (34), (58), (109),
% 14.25/2.78 | | | | | (116) gives:
% 14.25/2.78 | | | | | (117) $false
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | CLOSE: (117) is inconsistent.
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | Case 2:
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | (118) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) & ~
% 14.25/2.78 | | | | | greater_or_equal(v0, all_25_0))
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | DELTA: instantiating (118) with fresh symbol all_164_0 gives:
% 14.25/2.78 | | | | | (119) end_time(all_25_1) = all_164_0 & $i(all_164_0) & ~
% 14.25/2.78 | | | | | greater_or_equal(all_164_0, all_25_0)
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | ALPHA: (119) implies:
% 14.25/2.78 | | | | | (120) ~ greater_or_equal(all_164_0, all_25_0)
% 14.25/2.78 | | | | | (121) $i(all_164_0)
% 14.25/2.78 | | | | | (122) end_time(all_25_1) = all_164_0
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | GROUND_INST: instantiating (14) with all_25_0, all_164_0, all_25_1,
% 14.25/2.78 | | | | | simplifying with (27), (122) gives:
% 14.25/2.78 | | | | | (123) all_164_0 = all_25_0
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | REDUCE: (120), (123) imply:
% 14.25/2.78 | | | | | (124) ~ greater_or_equal(all_25_0, all_25_0)
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | BETA: splitting (114) gives:
% 14.25/2.78 | | | | |
% 14.25/2.78 | | | | | Case 1:
% 14.25/2.78 | | | | | |
% 14.25/2.78 | | | | | | (125) greater_or_equal(all_137_0, all_25_0)
% 14.25/2.78 | | | | | |
% 14.25/2.78 | | | | | | REDUCE: (115), (125) imply:
% 14.25/2.79 | | | | | | (126) greater_or_equal(all_25_0, all_25_0)
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | | PRED_UNIFY: (124), (126) imply:
% 14.25/2.79 | | | | | | (127) $false
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | | CLOSE: (127) is inconsistent.
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | Case 2:
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | | (128) ~ greater_or_equal(all_137_0, all_25_0)
% 14.25/2.79 | | | | | | (129) greater(all_25_0, all_137_0)
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | | REDUCE: (115), (129) imply:
% 14.25/2.79 | | | | | | (130) greater(all_25_0, all_25_0)
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | | GROUND_INST: instantiating (9) with all_25_0, all_25_0, simplifying
% 14.25/2.79 | | | | | | with (58), (124), (130) gives:
% 14.25/2.79 | | | | | | (131) $false
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | | CLOSE: (131) is inconsistent.
% 14.25/2.79 | | | | | |
% 14.25/2.79 | | | | | End of split
% 14.25/2.79 | | | | |
% 14.25/2.79 | | | | End of split
% 14.25/2.79 | | | |
% 14.25/2.79 | | | Case 2:
% 14.25/2.79 | | | |
% 14.25/2.79 | | | | (132) all_32_0 = all_25_0
% 14.25/2.79 | | | |
% 14.25/2.79 | | | | REDUCE: (48), (132) imply:
% 14.25/2.79 | | | | (133) selection_favors(efficient_producers, first_movers, all_25_0)
% 14.25/2.79 | | | |
% 14.25/2.79 | | | | PRED_UNIFY: (23), (133) imply:
% 14.25/2.79 | | | | (134) $false
% 14.25/2.79 | | | |
% 14.25/2.79 | | | | CLOSE: (134) is inconsistent.
% 14.25/2.79 | | | |
% 14.25/2.79 | | | End of split
% 14.25/2.79 | | |
% 14.25/2.79 | | End of split
% 14.25/2.79 | |
% 14.25/2.79 | Case 2:
% 14.25/2.79 | |
% 14.25/2.79 | | (135) ? [v0: $i] : (end_time(all_25_1) = v0 & $i(v0) & ~
% 14.25/2.79 | | greater_or_equal(v0, all_32_1))
% 14.25/2.79 | |
% 14.25/2.79 | | DELTA: instantiating (135) with fresh symbol all_100_0 gives:
% 14.25/2.79 | | (136) end_time(all_25_1) = all_100_0 & $i(all_100_0) & ~
% 14.25/2.79 | | greater_or_equal(all_100_0, all_32_1)
% 14.25/2.79 | |
% 14.25/2.79 | | ALPHA: (136) implies:
% 14.25/2.79 | | (137) end_time(all_25_1) = all_100_0
% 14.25/2.79 | | (138) $i(all_100_0)
% 14.25/2.79 | | (139) ~ greater_or_equal(all_100_0, all_32_1)
% 14.25/2.79 | |
% 14.25/2.79 | | GROUND_INST: instantiating (14) with all_25_0, all_100_0, all_25_1,
% 14.25/2.79 | | simplifying with (27), (137) gives:
% 14.25/2.79 | | (140) all_100_0 = all_25_0
% 14.25/2.79 | |
% 14.25/2.79 | | REDUCE: (139), (140) imply:
% 14.25/2.79 | | (141) ~ greater_or_equal(all_25_0, all_32_1)
% 14.25/2.79 | |
% 14.25/2.79 | | BETA: splitting (61) gives:
% 14.25/2.79 | |
% 14.25/2.79 | | Case 1:
% 14.25/2.79 | | |
% 14.25/2.79 | | | (142) greater(all_25_0, all_32_0)
% 14.25/2.79 | | |
% 14.25/2.79 | | | GROUND_INST: instantiating (mp_greater_transitivity) with all_25_0,
% 14.25/2.79 | | | all_32_0, all_32_1, simplifying with (32), (33), (42), (58),
% 14.25/2.79 | | | (142) gives:
% 14.25/2.79 | | | (143) greater(all_25_0, all_32_1)
% 14.25/2.79 | | |
% 14.25/2.79 | | | GROUND_INST: instantiating (9) with all_25_0, all_32_1, simplifying with
% 14.25/2.79 | | | (42), (58), (141), (143) gives:
% 14.25/2.79 | | | (144) $false
% 14.25/2.79 | | |
% 14.25/2.79 | | | CLOSE: (144) is inconsistent.
% 14.25/2.79 | | |
% 14.25/2.79 | | Case 2:
% 14.25/2.79 | | |
% 14.25/2.79 | | | (145) all_32_0 = all_25_0
% 14.25/2.79 | | |
% 14.25/2.79 | | | REDUCE: (45), (145) imply:
% 14.25/2.79 | | | (146) greater_or_equal(all_25_0, all_32_1)
% 14.25/2.79 | | |
% 14.25/2.79 | | | PRED_UNIFY: (141), (146) imply:
% 14.25/2.79 | | | (147) $false
% 14.25/2.79 | | |
% 14.25/2.79 | | | CLOSE: (147) is inconsistent.
% 14.25/2.79 | | |
% 14.25/2.79 | | End of split
% 14.25/2.79 | |
% 14.25/2.79 | End of split
% 14.25/2.79 |
% 14.25/2.79 End of proof
% 14.25/2.79 % SZS output end Proof for theBenchmark
% 14.25/2.79
% 14.25/2.79 2140ms
%------------------------------------------------------------------------------