TSTP Solution File: MGT056+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : MGT056+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 09:16:30 EDT 2023
% Result : Theorem 7.16s 1.58s
% Output : Proof 9.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : MGT056+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Aug 28 06:36:45 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.51 ________ _____
% 0.16/0.51 ___ __ \_________(_)________________________________
% 0.16/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.51
% 0.16/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.51 (2023-06-19)
% 0.16/0.51
% 0.16/0.51 (c) Philipp Rümmer, 2009-2023
% 0.16/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.51 Amanda Stjerna.
% 0.16/0.51 Free software under BSD-3-Clause.
% 0.16/0.51
% 0.16/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.51
% 0.16/0.51 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.52 Running up to 7 provers in parallel.
% 0.16/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.27/0.91 Prover 1: Preprocessing ...
% 2.27/0.92 Prover 4: Preprocessing ...
% 2.65/0.95 Prover 6: Preprocessing ...
% 2.65/0.95 Prover 5: Preprocessing ...
% 2.65/0.95 Prover 2: Preprocessing ...
% 2.65/0.95 Prover 0: Preprocessing ...
% 2.65/0.95 Prover 3: Preprocessing ...
% 4.47/1.21 Prover 5: Proving ...
% 4.47/1.21 Prover 3: Warning: ignoring some quantifiers
% 4.47/1.21 Prover 1: Warning: ignoring some quantifiers
% 4.47/1.22 Prover 2: Proving ...
% 4.47/1.22 Prover 3: Constructing countermodel ...
% 4.47/1.23 Prover 6: Proving ...
% 4.47/1.24 Prover 1: Constructing countermodel ...
% 5.26/1.30 Prover 4: Constructing countermodel ...
% 5.26/1.39 Prover 0: Proving ...
% 6.07/1.58 Prover 3: proved (1035ms)
% 7.16/1.58
% 7.16/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.16/1.58
% 7.16/1.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.16/1.58 Prover 6: stopped
% 7.16/1.59 Prover 2: stopped
% 7.16/1.59 Prover 5: stopped
% 7.16/1.59 Prover 0: stopped
% 7.16/1.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.16/1.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.16/1.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.16/1.60 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.16/1.63 Prover 10: Preprocessing ...
% 7.47/1.64 Prover 7: Preprocessing ...
% 7.47/1.64 Prover 13: Preprocessing ...
% 7.47/1.64 Prover 11: Preprocessing ...
% 7.60/1.66 Prover 8: Preprocessing ...
% 7.60/1.68 Prover 7: Warning: ignoring some quantifiers
% 7.60/1.68 Prover 10: Warning: ignoring some quantifiers
% 7.60/1.69 Prover 7: Constructing countermodel ...
% 7.60/1.70 Prover 13: Warning: ignoring some quantifiers
% 7.60/1.70 Prover 10: Constructing countermodel ...
% 7.60/1.71 Prover 13: Constructing countermodel ...
% 8.10/1.76 Prover 8: Warning: ignoring some quantifiers
% 8.50/1.78 Prover 8: Constructing countermodel ...
% 8.50/1.83 Prover 11: Constructing countermodel ...
% 9.36/1.91 Prover 10: Found proof (size 31)
% 9.36/1.91 Prover 10: proved (315ms)
% 9.36/1.91 Prover 4: stopped
% 9.36/1.91 Prover 11: stopped
% 9.36/1.91 Prover 8: stopped
% 9.36/1.91 Prover 1: stopped
% 9.36/1.91 Prover 7: stopped
% 9.36/1.91 Prover 13: stopped
% 9.36/1.91
% 9.36/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.36/1.91
% 9.36/1.92 % SZS output start Proof for theBenchmark
% 9.36/1.92 Assumptions after simplification:
% 9.36/1.92 ---------------------------------
% 9.36/1.92
% 9.36/1.92 (assumption_2)
% 9.77/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4 = v3
% 9.77/1.95 | ~ (hazard_of_mortality(v0, v2) = v4) | ~ (hazard_of_mortality(v0, v1) =
% 9.77/1.95 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ has_immunity(v0, v2) | ~
% 9.77/1.95 has_immunity(v0, v1) | ~ organization(v0))
% 9.77/1.95
% 9.77/1.95 (assumption_3)
% 9.77/1.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 9.77/1.95 (hazard_of_mortality(v0, v2) = v3) | ~ (hazard_of_mortality(v0, v1) = v4) |
% 9.77/1.95 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ has_immunity(v0, v1) | ~
% 9.77/1.95 organization(v0) | has_immunity(v0, v2) | greater(v3, v4))
% 9.77/1.95
% 9.77/1.95 (definition_1)
% 9.77/1.95 $i(eta) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (age(v0, v1) = v2) |
% 9.77/1.95 ~ $i(v1) | ~ $i(v0) | ~ has_immunity(v0, v1) | ~ has_endowment(v0) | ~
% 9.77/1.95 greater(v2, eta)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (age(v0,
% 9.77/1.95 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ has_endowment(v0) | ~
% 9.77/1.95 smaller_or_equal(v2, eta) | has_immunity(v0, v1)) & ! [v0: $i] : ( ~ $i(v0)
% 9.77/1.95 | ~ has_endowment(v0) | organization(v0)) & ? [v0: $i] : ( ~ $i(v0) |
% 9.77/1.95 has_endowment(v0) | ? [v1: $i] : ? [v2: $i] : ($i(v1) & ( ~
% 9.77/1.95 organization(v0) | (age(v0, v1) = v2 & $i(v2) & has_immunity(v0, v1) &
% 9.77/1.95 greater(v2, eta)) | (age(v0, v1) = v2 & $i(v2) & smaller_or_equal(v2,
% 9.77/1.96 eta) & ~ has_immunity(v0, v1)))))
% 9.77/1.96
% 9.77/1.96 (definition_greater_or_equal)
% 9.77/1.96 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 9.77/1.96 greater_or_equal(v0, v1) | greater(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (
% 9.77/1.96 ~ $i(v1) | ~ $i(v0) | ~ greater(v0, v1) | greater_or_equal(v0, v1)) & ?
% 9.77/1.96 [v0: $i] : ( ~ $i(v0) | greater_or_equal(v0, v0))
% 9.77/1.96
% 9.77/1.96 (definition_smaller)
% 9.77/1.96 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v1, v0) |
% 9.77/1.96 smaller(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 9.77/1.96 smaller(v0, v1) | greater(v1, v0))
% 9.77/1.96
% 9.77/1.96 (definition_smaller_or_equal)
% 9.77/1.96 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 9.77/1.96 smaller_or_equal(v0, v1) | smaller(v0, v1)) & ! [v0: $i] : ! [v1: $i] : (
% 9.77/1.96 ~ $i(v1) | ~ $i(v0) | ~ smaller(v0, v1) | smaller_or_equal(v0, v1)) & ?
% 9.77/1.96 [v0: $i] : ( ~ $i(v0) | smaller_or_equal(v0, v0))
% 9.77/1.96
% 9.77/1.96 (lemma_9)
% 9.77/1.96 $i(sigma) & $i(zero) & $i(eta) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 9.77/1.96 [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 9.77/1.96 : (hazard_of_mortality(v0, v2) = v7 & age(v0, v3) = v5 & age(v0, v2) = v4 &
% 9.77/1.96 age(v0, v1) = zero & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 9.77/1.96 $i(v0) & organization(v0) & has_endowment(v0) & greater(v5, eta) &
% 9.77/1.96 greater(sigma, zero) & greater_or_equal(eta, sigma) & smaller_or_equal(v4,
% 9.77/1.96 eta) & (( ~ (v8 = v7) & hazard_of_mortality(v0, v1) = v8 & $i(v8)) |
% 9.77/1.96 (hazard_of_mortality(v0, v3) = v6 & $i(v6) & ~ greater(v6, v7))))
% 9.77/1.96
% 9.77/1.96 (meaning_postulate_greater_transitive)
% 9.77/1.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 9.77/1.96 ~ greater(v1, v2) | ~ greater(v0, v1) | greater(v0, v2))
% 9.77/1.96
% 9.77/1.96 Further assumptions not needed in the proof:
% 9.77/1.96 --------------------------------------------
% 9.77/1.97 meaning_postulate_greater_comparable, meaning_postulate_greater_strict
% 9.77/1.97
% 9.77/1.97 Those formulas are unsatisfiable:
% 9.77/1.97 ---------------------------------
% 9.77/1.97
% 9.77/1.97 Begin of proof
% 9.77/1.97 |
% 9.77/1.97 | ALPHA: (definition_smaller_or_equal) implies:
% 9.77/1.97 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ smaller(v0, v1)
% 9.77/1.97 | | smaller_or_equal(v0, v1))
% 9.77/1.97 |
% 9.77/1.97 | ALPHA: (definition_greater_or_equal) implies:
% 9.77/1.97 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 9.77/1.97 | greater_or_equal(v0, v1) | greater(v0, v1))
% 9.77/1.97 |
% 9.77/1.97 | ALPHA: (definition_smaller) implies:
% 9.77/1.97 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ greater(v1, v0)
% 9.77/1.97 | | smaller(v0, v1))
% 9.77/1.97 |
% 9.77/1.97 | ALPHA: (definition_1) implies:
% 9.77/1.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (age(v0, v1) = v2) | ~
% 9.77/1.97 | $i(v1) | ~ $i(v0) | ~ has_endowment(v0) | ~ smaller_or_equal(v2,
% 9.77/1.97 | eta) | has_immunity(v0, v1))
% 9.77/1.97 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (age(v0, v1) = v2) | ~
% 9.77/1.97 | $i(v1) | ~ $i(v0) | ~ has_immunity(v0, v1) | ~ has_endowment(v0) |
% 9.77/1.97 | ~ greater(v2, eta))
% 9.77/1.97 |
% 9.77/1.97 | ALPHA: (lemma_9) implies:
% 9.77/1.97 | (6) $i(eta)
% 9.77/1.97 | (7) $i(zero)
% 9.77/1.97 | (8) $i(sigma)
% 9.77/1.98 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 9.77/1.98 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 9.77/1.98 | (hazard_of_mortality(v0, v2) = v7 & age(v0, v3) = v5 & age(v0, v2) = v4
% 9.77/1.98 | & age(v0, v1) = zero & $i(v7) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 9.77/1.98 | $i(v1) & $i(v0) & organization(v0) & has_endowment(v0) & greater(v5,
% 9.77/1.98 | eta) & greater(sigma, zero) & greater_or_equal(eta, sigma) &
% 9.77/1.98 | smaller_or_equal(v4, eta) & (( ~ (v8 = v7) & hazard_of_mortality(v0,
% 9.77/1.98 | v1) = v8 & $i(v8)) | (hazard_of_mortality(v0, v3) = v6 & $i(v6)
% 9.77/1.98 | & ~ greater(v6, v7))))
% 9.77/1.98 |
% 9.77/1.98 | DELTA: instantiating (9) with fresh symbols all_16_0, all_16_1, all_16_2,
% 9.77/1.98 | all_16_3, all_16_4, all_16_5, all_16_6, all_16_7, all_16_8 gives:
% 9.77/1.98 | (10) hazard_of_mortality(all_16_8, all_16_6) = all_16_1 & age(all_16_8,
% 9.77/1.98 | all_16_5) = all_16_3 & age(all_16_8, all_16_6) = all_16_4 &
% 9.77/1.98 | age(all_16_8, all_16_7) = zero & $i(all_16_1) & $i(all_16_3) &
% 9.77/1.98 | $i(all_16_4) & $i(all_16_5) & $i(all_16_6) & $i(all_16_7) &
% 9.77/1.98 | $i(all_16_8) & organization(all_16_8) & has_endowment(all_16_8) &
% 9.77/1.98 | greater(all_16_3, eta) & greater(sigma, zero) & greater_or_equal(eta,
% 9.77/1.98 | sigma) & smaller_or_equal(all_16_4, eta) & (( ~ (all_16_0 =
% 9.77/1.98 | all_16_1) & hazard_of_mortality(all_16_8, all_16_7) = all_16_0 &
% 9.77/1.98 | $i(all_16_0)) | (hazard_of_mortality(all_16_8, all_16_5) =
% 9.77/1.98 | all_16_2 & $i(all_16_2) & ~ greater(all_16_2, all_16_1)))
% 9.77/1.98 |
% 9.77/1.98 | ALPHA: (10) implies:
% 9.77/1.98 | (11) smaller_or_equal(all_16_4, eta)
% 9.77/1.98 | (12) greater_or_equal(eta, sigma)
% 9.77/1.98 | (13) greater(sigma, zero)
% 9.77/1.98 | (14) greater(all_16_3, eta)
% 9.77/1.98 | (15) has_endowment(all_16_8)
% 9.77/1.98 | (16) organization(all_16_8)
% 9.77/1.98 | (17) $i(all_16_8)
% 9.77/1.98 | (18) $i(all_16_7)
% 9.77/1.98 | (19) $i(all_16_6)
% 9.77/1.98 | (20) $i(all_16_5)
% 9.77/1.98 | (21) age(all_16_8, all_16_7) = zero
% 9.77/1.98 | (22) age(all_16_8, all_16_6) = all_16_4
% 9.77/1.98 | (23) age(all_16_8, all_16_5) = all_16_3
% 9.77/1.98 | (24) hazard_of_mortality(all_16_8, all_16_6) = all_16_1
% 9.77/1.98 | (25) ( ~ (all_16_0 = all_16_1) & hazard_of_mortality(all_16_8, all_16_7) =
% 9.77/1.98 | all_16_0 & $i(all_16_0)) | (hazard_of_mortality(all_16_8, all_16_5)
% 9.77/1.98 | = all_16_2 & $i(all_16_2) & ~ greater(all_16_2, all_16_1))
% 9.77/1.98 |
% 9.77/1.98 | GROUND_INST: instantiating (2) with eta, sigma, simplifying with (6), (8),
% 9.77/1.98 | (12) gives:
% 9.77/1.98 | (26) sigma = eta | greater(eta, sigma)
% 9.77/1.98 |
% 9.77/1.98 | GROUND_INST: instantiating (3) with zero, sigma, simplifying with (7), (8),
% 9.77/1.98 | (13) gives:
% 9.77/1.98 | (27) smaller(zero, sigma)
% 9.77/1.98 |
% 9.77/1.98 | GROUND_INST: instantiating (4) with all_16_8, all_16_6, all_16_4, simplifying
% 9.77/1.98 | with (11), (15), (17), (19), (22) gives:
% 9.77/1.98 | (28) has_immunity(all_16_8, all_16_6)
% 9.77/1.99 |
% 9.77/1.99 | GROUND_INST: instantiating (1) with zero, sigma, simplifying with (7), (8),
% 9.77/1.99 | (27) gives:
% 9.77/1.99 | (29) smaller_or_equal(zero, sigma)
% 9.77/1.99 |
% 9.77/1.99 | BETA: splitting (25) gives:
% 9.77/1.99 |
% 9.77/1.99 | Case 1:
% 9.77/1.99 | |
% 9.77/1.99 | | (30) ~ (all_16_0 = all_16_1) & hazard_of_mortality(all_16_8, all_16_7) =
% 9.77/1.99 | | all_16_0 & $i(all_16_0)
% 9.77/1.99 | |
% 9.77/1.99 | | ALPHA: (30) implies:
% 9.77/1.99 | | (31) ~ (all_16_0 = all_16_1)
% 9.77/1.99 | | (32) hazard_of_mortality(all_16_8, all_16_7) = all_16_0
% 9.77/1.99 | |
% 9.77/1.99 | | BETA: splitting (26) gives:
% 9.77/1.99 | |
% 9.77/1.99 | | Case 1:
% 9.77/1.99 | | |
% 9.77/1.99 | | | (33) greater(eta, sigma)
% 9.77/1.99 | | |
% 9.77/1.99 | | | GROUND_INST: instantiating (meaning_postulate_greater_transitive) with
% 9.77/1.99 | | | eta, sigma, zero, simplifying with (6), (7), (8), (13), (33)
% 9.77/1.99 | | | gives:
% 9.77/1.99 | | | (34) greater(eta, zero)
% 9.77/1.99 | | |
% 9.77/1.99 | | | GROUND_INST: instantiating (3) with zero, eta, simplifying with (6), (7),
% 9.77/1.99 | | | (34) gives:
% 9.77/1.99 | | | (35) smaller(zero, eta)
% 9.77/1.99 | | |
% 9.77/1.99 | | | GROUND_INST: instantiating (1) with zero, eta, simplifying with (6), (7),
% 9.77/1.99 | | | (35) gives:
% 9.77/1.99 | | | (36) smaller_or_equal(zero, eta)
% 9.77/1.99 | | |
% 9.77/1.99 | | | REF_CLOSE: (4), (15), (16), (17), (18), (19), (21), (24), (28), (31),
% 9.77/1.99 | | | (32), (36), (assumption_2) are inconsistent by sub-proof #1.
% 9.77/1.99 | | |
% 9.77/1.99 | | Case 2:
% 9.77/1.99 | | |
% 9.77/1.99 | | | (37) sigma = eta
% 9.77/1.99 | | |
% 9.77/1.99 | | | REDUCE: (29), (37) imply:
% 9.77/1.99 | | | (38) smaller_or_equal(zero, eta)
% 9.77/1.99 | | |
% 9.77/1.99 | | | REF_CLOSE: (4), (15), (16), (17), (18), (19), (21), (24), (28), (31),
% 9.77/1.99 | | | (32), (38), (assumption_2) are inconsistent by sub-proof #1.
% 9.77/1.99 | | |
% 9.77/1.99 | | End of split
% 9.77/1.99 | |
% 9.77/1.99 | Case 2:
% 9.77/1.99 | |
% 9.77/1.99 | | (39) hazard_of_mortality(all_16_8, all_16_5) = all_16_2 & $i(all_16_2) &
% 9.77/1.99 | | ~ greater(all_16_2, all_16_1)
% 9.77/1.99 | |
% 9.77/1.99 | | ALPHA: (39) implies:
% 9.77/1.99 | | (40) ~ greater(all_16_2, all_16_1)
% 9.77/1.99 | | (41) hazard_of_mortality(all_16_8, all_16_5) = all_16_2
% 9.77/1.99 | |
% 9.77/2.00 | | GROUND_INST: instantiating (assumption_3) with all_16_8, all_16_6, all_16_5,
% 9.77/2.00 | | all_16_2, all_16_1, simplifying with (16), (17), (19), (20),
% 9.77/2.00 | | (24), (28), (40), (41) gives:
% 9.77/2.00 | | (42) has_immunity(all_16_8, all_16_5)
% 9.77/2.00 | |
% 9.77/2.00 | | GROUND_INST: instantiating (5) with all_16_8, all_16_5, all_16_3,
% 9.77/2.00 | | simplifying with (14), (15), (17), (20), (23), (42) gives:
% 9.77/2.00 | | (43) $false
% 9.77/2.00 | |
% 9.77/2.00 | | CLOSE: (43) is inconsistent.
% 9.77/2.00 | |
% 9.77/2.00 | End of split
% 9.77/2.00 |
% 9.77/2.00 End of proof
% 9.77/2.00
% 9.77/2.00 Sub-proof #1 shows that the following formulas are inconsistent:
% 9.77/2.00 ----------------------------------------------------------------
% 9.77/2.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (age(v0, v1) = v2) | ~
% 9.77/2.00 $i(v1) | ~ $i(v0) | ~ has_endowment(v0) | ~ smaller_or_equal(v2,
% 9.77/2.00 eta) | has_immunity(v0, v1))
% 9.77/2.00 (2) organization(all_16_8)
% 9.77/2.00 (3) has_immunity(all_16_8, all_16_6)
% 9.77/2.00 (4) ~ (all_16_0 = all_16_1)
% 9.77/2.00 (5) smaller_or_equal(zero, eta)
% 9.77/2.00 (6) hazard_of_mortality(all_16_8, all_16_6) = all_16_1
% 9.77/2.00 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v4
% 9.77/2.00 = v3 | ~ (hazard_of_mortality(v0, v2) = v4) | ~
% 9.77/2.00 (hazard_of_mortality(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 9.77/2.00 | ~ has_immunity(v0, v2) | ~ has_immunity(v0, v1) | ~
% 9.77/2.00 organization(v0))
% 9.77/2.00 (8) $i(all_16_6)
% 9.77/2.00 (9) hazard_of_mortality(all_16_8, all_16_7) = all_16_0
% 9.77/2.00 (10) has_endowment(all_16_8)
% 9.77/2.00 (11) $i(all_16_7)
% 9.77/2.00 (12) age(all_16_8, all_16_7) = zero
% 9.77/2.00 (13) $i(all_16_8)
% 9.77/2.00
% 9.77/2.00 Begin of proof
% 9.77/2.00 |
% 9.77/2.00 | GROUND_INST: instantiating (1) with all_16_8, all_16_7, zero, simplifying with
% 9.77/2.00 | (5), (10), (11), (12), (13) gives:
% 9.77/2.00 | (14) has_immunity(all_16_8, all_16_7)
% 9.77/2.00 |
% 9.77/2.00 | GROUND_INST: instantiating (7) with all_16_8, all_16_7, all_16_6, all_16_0,
% 9.77/2.00 | all_16_1, simplifying with (2), (3), (6), (8), (9), (11), (13),
% 9.77/2.00 | (14) gives:
% 9.77/2.00 | (15) all_16_0 = all_16_1
% 9.77/2.00 |
% 9.77/2.00 | REDUCE: (4), (15) imply:
% 9.77/2.00 | (16) $false
% 9.77/2.00 |
% 9.77/2.00 | CLOSE: (16) is inconsistent.
% 9.77/2.00 |
% 9.77/2.00 End of proof
% 9.77/2.00 % SZS output end Proof for theBenchmark
% 9.77/2.00
% 9.77/2.00 1488ms
%------------------------------------------------------------------------------