TSTP Solution File: SWV417+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV417+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n003.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 22:56:16 EDT 2023
% Result : Theorem 14.32s 2.62s
% Output : Proof 20.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV417+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 06:38:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.63/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.63/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.63/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.63/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.63/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.63/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.63/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.83/1.22 Prover 4: Preprocessing ...
% 3.83/1.22 Prover 1: Preprocessing ...
% 3.83/1.28 Prover 2: Preprocessing ...
% 3.83/1.28 Prover 3: Preprocessing ...
% 3.83/1.28 Prover 0: Preprocessing ...
% 3.83/1.28 Prover 5: Preprocessing ...
% 3.83/1.28 Prover 6: Preprocessing ...
% 9.39/2.01 Prover 1: Warning: ignoring some quantifiers
% 10.12/2.08 Prover 6: Proving ...
% 10.87/2.14 Prover 1: Constructing countermodel ...
% 10.90/2.18 Prover 3: Warning: ignoring some quantifiers
% 11.30/2.21 Prover 3: Constructing countermodel ...
% 11.30/2.24 Prover 5: Proving ...
% 11.67/2.26 Prover 4: Constructing countermodel ...
% 11.67/2.31 Prover 2: Proving ...
% 12.42/2.35 Prover 0: Proving ...
% 14.32/2.61 Prover 5: proved (1977ms)
% 14.32/2.61
% 14.32/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.32/2.62
% 14.32/2.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.32/2.62 Prover 2: stopped
% 14.32/2.62 Prover 6: stopped
% 14.32/2.63 Prover 0: stopped
% 14.32/2.63 Prover 3: stopped
% 14.32/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.32/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.32/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.68/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.68/2.69 Prover 7: Preprocessing ...
% 14.68/2.70 Prover 8: Preprocessing ...
% 14.68/2.72 Prover 10: Preprocessing ...
% 14.68/2.72 Prover 13: Preprocessing ...
% 14.68/2.73 Prover 11: Preprocessing ...
% 16.25/2.86 Prover 1: gave up
% 16.25/2.86 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 16.63/2.92 Prover 16: Preprocessing ...
% 16.63/2.92 Prover 10: Warning: ignoring some quantifiers
% 16.63/2.92 Prover 7: Warning: ignoring some quantifiers
% 16.63/2.94 Prover 8: Warning: ignoring some quantifiers
% 16.63/2.96 Prover 10: Constructing countermodel ...
% 16.63/2.97 Prover 7: Constructing countermodel ...
% 16.63/2.99 Prover 8: Constructing countermodel ...
% 16.63/3.01 Prover 13: Warning: ignoring some quantifiers
% 17.17/3.07 Prover 13: Constructing countermodel ...
% 17.17/3.10 Prover 16: Warning: ignoring some quantifiers
% 18.29/3.12 Prover 16: Constructing countermodel ...
% 18.29/3.14 Prover 11: Constructing countermodel ...
% 20.10/3.38 Prover 16: Found proof (size 34)
% 20.10/3.38 Prover 16: proved (516ms)
% 20.10/3.38 Prover 11: stopped
% 20.10/3.38 Prover 7: stopped
% 20.10/3.38 Prover 4: stopped
% 20.10/3.38 Prover 13: stopped
% 20.10/3.38 Prover 8: stopped
% 20.10/3.38 Prover 10: stopped
% 20.10/3.38
% 20.10/3.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.10/3.38
% 20.10/3.39 % SZS output start Proof for theBenchmark
% 20.10/3.39 Assumptions after simplification:
% 20.10/3.39 ---------------------------------
% 20.10/3.39
% 20.10/3.39 (ax14)
% 20.54/3.41 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 20.54/3.42 issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) | findmin_pq_res(v0,
% 20.54/3.42 v1) = v1)
% 20.54/3.42
% 20.54/3.42 (ax58)
% 20.54/3.42 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ pi_sharp_find_min(v0,
% 20.54/3.42 v1) | issmallestelement_pq(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 20.54/3.42 $i(v1) | ~ $i(v0) | ~ pi_sharp_find_min(v0, v1) | contains_pq(v0, v1)) &
% 20.54/3.42 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 20.54/3.42 issmallestelement_pq(v0, v1) | ~ contains_pq(v0, v1) |
% 20.54/3.42 pi_sharp_find_min(v0, v1))
% 20.54/3.42
% 20.54/3.42 (ax59)
% 20.54/3.42 ! [v0: $i] : ( ~ $i(v0) | ~ pi_find_min(v0) | ? [v1: $i] : ? [v2: $i] :
% 20.54/3.42 (i(v0) = v1 & $i(v2) & $i(v1) & pi_sharp_find_min(v1, v2))) & ? [v0: $i] :
% 20.54/3.42 ( ~ $i(v0) | pi_find_min(v0) | ? [v1: $i] : (i(v0) = v1 & $i(v1) & ! [v2:
% 20.54/3.42 $i] : ( ~ $i(v2) | ~ pi_sharp_find_min(v1, v2))))
% 20.54/3.42
% 20.54/3.42 (co4)
% 20.54/3.42 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 20.54/3.42 $i] : ? [v6: $i] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & triple(v0, v1,
% 20.54/3.42 v2) = v3 & findmin_cpq_eff(v3) = v4 & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 20.54/3.42 $i(v2) & $i(v1) & $i(v0) & phi(v4) & pi_find_min(v3) & ! [v7: $i] : ( ~
% 20.54/3.42 $i(v7) | ~ pi_sharp_find_min(v5, v7) | ? [v8: $i] : ( ~ (v8 = v6) &
% 20.54/3.42 findmin_pq_res(v5, v7) = v8 & $i(v8))))
% 20.54/3.42
% 20.54/3.42 (main4_l7)
% 20.54/3.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1,
% 20.54/3.43 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5:
% 20.54/3.43 $i] : ? [v6: $i] : ((i(v3) = v5 & findmin_cpq_res(v3) = v6 & $i(v6) &
% 20.54/3.43 $i(v5) & pi_sharp_find_min(v5, v6)) | (findmin_cpq_eff(v3) = v4 & $i(v4)
% 20.54/3.43 & ~ phi(v4))))
% 20.54/3.43
% 20.54/3.43 (function-axioms)
% 20.54/3.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 20.54/3.44 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: $i]
% 20.54/3.44 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2)
% 20.54/3.44 = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.54/3.44 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~
% 20.54/3.44 (insert_pqp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.54/3.44 [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) =
% 20.54/3.44 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 20.54/3.44 ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: $i] :
% 20.54/3.44 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) =
% 20.54/3.44 v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.54/3.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~
% 20.54/3.44 (lookup_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.54/3.44 [v3: $i] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) =
% 20.54/3.44 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 20.54/3.44 ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 20.54/3.44 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 20.54/3.44 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.54/3.44 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~
% 20.54/3.44 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.54/3.44 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~
% 20.54/3.44 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.54/3.44 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~
% 20.54/3.44 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.54/3.44 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~
% 20.54/3.44 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.54/3.44 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) =
% 20.54/3.44 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 20.54/3.44 ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: $i] : !
% 20.54/3.44 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & !
% 20.54/3.44 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) =
% 20.54/3.44 v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.54/3.44 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2)
% 20.54/3.44 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.54/3.44 (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0: $i] :
% 20.54/3.44 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~
% 20.54/3.44 (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.54/3.44 (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 20.54/3.44
% 20.54/3.44 Further assumptions not needed in the proof:
% 20.54/3.44 --------------------------------------------
% 20.54/3.44 ax10, ax11, ax12, ax13, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, ax23,
% 20.54/3.44 ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 20.54/3.44 ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49,
% 20.54/3.44 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax6, ax60, ax61, ax62, ax7, ax8,
% 20.54/3.44 ax9, bottom_smallest, reflexivity, stricly_smaller_definition, totality,
% 20.54/3.44 transitivity
% 20.54/3.44
% 20.54/3.44 Those formulas are unsatisfiable:
% 20.54/3.44 ---------------------------------
% 20.54/3.44
% 20.54/3.44 Begin of proof
% 20.54/3.44 |
% 20.54/3.44 | ALPHA: (ax58) implies:
% 20.54/3.44 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 20.54/3.44 | pi_sharp_find_min(v0, v1) | contains_pq(v0, v1))
% 20.54/3.44 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 20.54/3.44 | pi_sharp_find_min(v0, v1) | issmallestelement_pq(v0, v1))
% 20.54/3.44 |
% 20.54/3.44 | ALPHA: (ax59) implies:
% 20.54/3.45 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ pi_find_min(v0) | ? [v1: $i] : ? [v2:
% 20.54/3.45 | $i] : (i(v0) = v1 & $i(v2) & $i(v1) & pi_sharp_find_min(v1, v2)))
% 20.54/3.45 |
% 20.54/3.45 | ALPHA: (function-axioms) implies:
% 20.54/3.45 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.54/3.45 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 20.54/3.45 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.54/3.45 | (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0))
% 20.54/3.45 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) |
% 20.54/3.45 | ~ (i(v2) = v0))
% 20.54/3.45 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.54/3.45 | (findmin_pq_res(v3, v2) = v1) | ~ (findmin_pq_res(v3, v2) = v0))
% 20.54/3.45 |
% 20.54/3.45 | DELTA: instantiating (co4) with fresh symbols all_88_0, all_88_1, all_88_2,
% 20.54/3.45 | all_88_3, all_88_4, all_88_5, all_88_6 gives:
% 20.54/3.45 | (8) i(all_88_3) = all_88_1 & findmin_cpq_res(all_88_3) = all_88_0 &
% 20.54/3.45 | triple(all_88_6, all_88_5, all_88_4) = all_88_3 &
% 20.54/3.45 | findmin_cpq_eff(all_88_3) = all_88_2 & $i(all_88_0) & $i(all_88_1) &
% 20.54/3.45 | $i(all_88_2) & $i(all_88_3) & $i(all_88_4) & $i(all_88_5) &
% 20.54/3.45 | $i(all_88_6) & phi(all_88_2) & pi_find_min(all_88_3) & ! [v0: $i] : (
% 20.54/3.45 | ~ $i(v0) | ~ pi_sharp_find_min(all_88_1, v0) | ? [v1: any] : ( ~
% 20.54/3.45 | (v1 = all_88_0) & findmin_pq_res(all_88_1, v0) = v1 & $i(v1)))
% 20.54/3.45 |
% 20.54/3.45 | ALPHA: (8) implies:
% 20.54/3.45 | (9) pi_find_min(all_88_3)
% 20.54/3.45 | (10) phi(all_88_2)
% 20.54/3.45 | (11) $i(all_88_6)
% 20.54/3.45 | (12) $i(all_88_5)
% 20.54/3.45 | (13) $i(all_88_4)
% 20.54/3.45 | (14) $i(all_88_3)
% 20.54/3.45 | (15) findmin_cpq_eff(all_88_3) = all_88_2
% 20.54/3.45 | (16) triple(all_88_6, all_88_5, all_88_4) = all_88_3
% 20.54/3.45 | (17) findmin_cpq_res(all_88_3) = all_88_0
% 20.54/3.45 | (18) i(all_88_3) = all_88_1
% 20.54/3.45 | (19) ! [v0: $i] : ( ~ $i(v0) | ~ pi_sharp_find_min(all_88_1, v0) | ?
% 20.54/3.45 | [v1: any] : ( ~ (v1 = all_88_0) & findmin_pq_res(all_88_1, v0) = v1
% 20.54/3.45 | & $i(v1)))
% 20.54/3.45 |
% 20.54/3.45 | GROUND_INST: instantiating (3) with all_88_3, simplifying with (9), (14)
% 20.54/3.45 | gives:
% 20.54/3.45 | (20) ? [v0: $i] : ? [v1: $i] : (i(all_88_3) = v0 & $i(v1) & $i(v0) &
% 20.54/3.45 | pi_sharp_find_min(v0, v1))
% 20.54/3.45 |
% 20.54/3.45 | GROUND_INST: instantiating (main4_l7) with all_88_6, all_88_5, all_88_4,
% 20.54/3.45 | all_88_3, simplifying with (11), (12), (13), (16) gives:
% 20.54/3.45 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ((i(all_88_3) = v1 &
% 20.54/3.45 | findmin_cpq_res(all_88_3) = v2 & $i(v2) & $i(v1) &
% 20.54/3.45 | pi_sharp_find_min(v1, v2)) | (findmin_cpq_eff(all_88_3) = v0 &
% 20.54/3.45 | $i(v0) & ~ phi(v0)))
% 20.54/3.45 |
% 20.54/3.45 | DELTA: instantiating (20) with fresh symbols all_98_0, all_98_1 gives:
% 20.54/3.45 | (22) i(all_88_3) = all_98_1 & $i(all_98_0) & $i(all_98_1) &
% 20.54/3.45 | pi_sharp_find_min(all_98_1, all_98_0)
% 20.54/3.45 |
% 20.54/3.45 | ALPHA: (22) implies:
% 20.54/3.45 | (23) $i(all_98_1)
% 20.54/3.45 | (24) i(all_88_3) = all_98_1
% 20.54/3.45 |
% 20.54/3.45 | DELTA: instantiating (21) with fresh symbols all_100_0, all_100_1, all_100_2
% 20.54/3.46 | gives:
% 20.54/3.46 | (25) (i(all_88_3) = all_100_1 & findmin_cpq_res(all_88_3) = all_100_0 &
% 20.54/3.46 | $i(all_100_0) & $i(all_100_1) & pi_sharp_find_min(all_100_1,
% 20.54/3.46 | all_100_0)) | (findmin_cpq_eff(all_88_3) = all_100_2 &
% 20.54/3.46 | $i(all_100_2) & ~ phi(all_100_2))
% 20.54/3.46 |
% 20.54/3.46 | BETA: splitting (25) gives:
% 20.54/3.46 |
% 20.54/3.46 | Case 1:
% 20.54/3.46 | |
% 20.54/3.46 | | (26) i(all_88_3) = all_100_1 & findmin_cpq_res(all_88_3) = all_100_0 &
% 20.54/3.46 | | $i(all_100_0) & $i(all_100_1) & pi_sharp_find_min(all_100_1,
% 20.54/3.46 | | all_100_0)
% 20.54/3.46 | |
% 20.54/3.46 | | ALPHA: (26) implies:
% 20.54/3.46 | | (27) pi_sharp_find_min(all_100_1, all_100_0)
% 20.54/3.46 | | (28) $i(all_100_0)
% 20.54/3.46 | | (29) findmin_cpq_res(all_88_3) = all_100_0
% 20.54/3.46 | | (30) i(all_88_3) = all_100_1
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (5) with all_88_0, all_100_0, all_88_3,
% 20.54/3.46 | | simplifying with (17), (29) gives:
% 20.54/3.46 | | (31) all_100_0 = all_88_0
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (6) with all_88_1, all_100_1, all_88_3,
% 20.54/3.46 | | simplifying with (18), (30) gives:
% 20.54/3.46 | | (32) all_100_1 = all_88_1
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (6) with all_98_1, all_100_1, all_88_3,
% 20.54/3.46 | | simplifying with (24), (30) gives:
% 20.54/3.46 | | (33) all_100_1 = all_98_1
% 20.54/3.46 | |
% 20.54/3.46 | | COMBINE_EQS: (32), (33) imply:
% 20.54/3.46 | | (34) all_98_1 = all_88_1
% 20.54/3.46 | |
% 20.54/3.46 | | SIMP: (34) implies:
% 20.54/3.46 | | (35) all_98_1 = all_88_1
% 20.54/3.46 | |
% 20.54/3.46 | | REDUCE: (28), (31) imply:
% 20.54/3.46 | | (36) $i(all_88_0)
% 20.54/3.46 | |
% 20.54/3.46 | | REDUCE: (23), (35) imply:
% 20.54/3.46 | | (37) $i(all_88_1)
% 20.54/3.46 | |
% 20.54/3.46 | | REDUCE: (27), (31), (32) imply:
% 20.54/3.46 | | (38) pi_sharp_find_min(all_88_1, all_88_0)
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (19) with all_88_0, simplifying with (36), (38)
% 20.54/3.46 | | gives:
% 20.54/3.46 | | (39) ? [v0: any] : ( ~ (v0 = all_88_0) & findmin_pq_res(all_88_1,
% 20.54/3.46 | | all_88_0) = v0 & $i(v0))
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (2) with all_88_1, all_88_0, simplifying with
% 20.54/3.46 | | (36), (37), (38) gives:
% 20.54/3.46 | | (40) issmallestelement_pq(all_88_1, all_88_0)
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (1) with all_88_1, all_88_0, simplifying with
% 20.54/3.46 | | (36), (37), (38) gives:
% 20.54/3.46 | | (41) contains_pq(all_88_1, all_88_0)
% 20.54/3.46 | |
% 20.54/3.46 | | DELTA: instantiating (39) with fresh symbol all_117_0 gives:
% 20.54/3.46 | | (42) ~ (all_117_0 = all_88_0) & findmin_pq_res(all_88_1, all_88_0) =
% 20.54/3.46 | | all_117_0 & $i(all_117_0)
% 20.54/3.46 | |
% 20.54/3.46 | | ALPHA: (42) implies:
% 20.54/3.46 | | (43) ~ (all_117_0 = all_88_0)
% 20.54/3.46 | | (44) findmin_pq_res(all_88_1, all_88_0) = all_117_0
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (ax14) with all_88_1, all_88_0, simplifying with
% 20.54/3.46 | | (36), (37), (40), (41) gives:
% 20.54/3.46 | | (45) findmin_pq_res(all_88_1, all_88_0) = all_88_0
% 20.54/3.46 | |
% 20.54/3.46 | | GROUND_INST: instantiating (7) with all_117_0, all_88_0, all_88_0, all_88_1,
% 20.54/3.46 | | simplifying with (44), (45) gives:
% 20.54/3.46 | | (46) all_117_0 = all_88_0
% 20.54/3.46 | |
% 20.54/3.46 | | REDUCE: (43), (46) imply:
% 20.79/3.46 | | (47) $false
% 20.79/3.46 | |
% 20.79/3.46 | | CLOSE: (47) is inconsistent.
% 20.79/3.46 | |
% 20.79/3.46 | Case 2:
% 20.79/3.46 | |
% 20.79/3.46 | | (48) findmin_cpq_eff(all_88_3) = all_100_2 & $i(all_100_2) & ~
% 20.79/3.46 | | phi(all_100_2)
% 20.79/3.46 | |
% 20.79/3.46 | | ALPHA: (48) implies:
% 20.79/3.46 | | (49) ~ phi(all_100_2)
% 20.79/3.46 | | (50) findmin_cpq_eff(all_88_3) = all_100_2
% 20.79/3.46 | |
% 20.79/3.47 | | GROUND_INST: instantiating (4) with all_88_2, all_100_2, all_88_3,
% 20.79/3.47 | | simplifying with (15), (50) gives:
% 20.79/3.47 | | (51) all_100_2 = all_88_2
% 20.79/3.47 | |
% 20.79/3.47 | | PRED_UNIFY: (10), (49) imply:
% 20.79/3.47 | | (52) ~ (all_100_2 = all_88_2)
% 20.79/3.47 | |
% 20.79/3.47 | | REDUCE: (51), (52) imply:
% 20.79/3.47 | | (53) $false
% 20.79/3.47 | |
% 20.79/3.47 | | CLOSE: (53) is inconsistent.
% 20.79/3.47 | |
% 20.79/3.47 | End of split
% 20.79/3.47 |
% 20.79/3.47 End of proof
% 20.79/3.47 % SZS output end Proof for theBenchmark
% 20.79/3.47
% 20.79/3.47 2857ms
%------------------------------------------------------------------------------