TSTP Solution File: SWV376+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV376+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 : n027.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 22:56:04 EDT 2023
% Result : Theorem 10.28s 2.37s
% Output : Proof 13.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 09:13:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 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 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 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 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 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 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
% 3.35/1.23 Prover 4: Preprocessing ...
% 3.35/1.23 Prover 1: Preprocessing ...
% 3.35/1.29 Prover 0: Preprocessing ...
% 3.35/1.29 Prover 6: Preprocessing ...
% 3.35/1.29 Prover 2: Preprocessing ...
% 3.35/1.29 Prover 5: Preprocessing ...
% 3.35/1.29 Prover 3: Preprocessing ...
% 8.89/2.02 Prover 1: Warning: ignoring some quantifiers
% 8.89/2.05 Prover 3: Warning: ignoring some quantifiers
% 9.59/2.10 Prover 3: Constructing countermodel ...
% 9.59/2.11 Prover 1: Constructing countermodel ...
% 9.59/2.11 Prover 4: Constructing countermodel ...
% 9.59/2.16 Prover 0: Proving ...
% 9.59/2.16 Prover 5: Proving ...
% 9.59/2.16 Prover 6: Proving ...
% 10.28/2.25 Prover 2: Proving ...
% 10.28/2.37 Prover 3: proved (1722ms)
% 10.28/2.37
% 10.28/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.28/2.37
% 10.28/2.37 Prover 6: stopped
% 10.28/2.37 Prover 2: stopped
% 10.28/2.39 Prover 0: stopped
% 10.28/2.40 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.28/2.40 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.28/2.40 Prover 5: stopped
% 10.28/2.40 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 10.28/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.28/2.40 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.76/2.45 Prover 7: Preprocessing ...
% 11.76/2.46 Prover 8: Preprocessing ...
% 11.76/2.47 Prover 10: Preprocessing ...
% 11.76/2.47 Prover 13: Preprocessing ...
% 11.76/2.48 Prover 11: Preprocessing ...
% 12.42/2.51 Prover 1: Found proof (size 49)
% 12.42/2.51 Prover 1: proved (1868ms)
% 12.42/2.51 Prover 7: stopped
% 12.42/2.52 Prover 4: stopped
% 12.42/2.56 Prover 13: stopped
% 12.42/2.56 Prover 10: stopped
% 12.42/2.57 Prover 11: stopped
% 12.98/2.62 Prover 8: Warning: ignoring some quantifiers
% 12.98/2.64 Prover 8: Constructing countermodel ...
% 12.98/2.65 Prover 8: stopped
% 12.98/2.65
% 12.98/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.98/2.65
% 12.98/2.66 % SZS output start Proof for theBenchmark
% 12.98/2.67 Assumptions after simplification:
% 12.98/2.67 ---------------------------------
% 12.98/2.67
% 12.98/2.67 (ax41)
% 13.53/2.69 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad |
% 13.53/2.69 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) =
% 13.53/2.69 0)
% 13.53/2.69
% 13.53/2.69 (l12_co)
% 13.53/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 13.53/2.70 = 0) & ok(v3) = v4 & triple(v0, v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) &
% 13.53/2.70 $i(v0) & ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (ok(v8) = 0
% 13.53/2.70 & triple(v5, v6, v7) = v8 & succ_cpq(v3, v8) = 0 & $i(v8) & $i(v7) &
% 13.53/2.70 $i(v6) & $i(v5)))
% 13.53/2.70
% 13.53/2.70 (l12_induction)
% 13.53/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.53/2.70 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ? [v9: $i] : ( ~ (v8 = 0)
% 13.53/2.70 & im_succ_cpq(v7) = v9 & ok(v9) = 0 & ok(v7) = v8 & triple(v3, v4, v5) = v7
% 13.53/2.70 & triple(v0, v1, v2) = v6 & succ_cpq(v6, v7) = 0 & $i(v9) & $i(v7) & $i(v6)
% 13.53/2.70 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) | ! [v0: $i] : !
% 13.53/2.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~
% 13.53/2.70 $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) = 0 | ! [v4: $i] : ! [v5: $i] : !
% 13.53/2.70 [v6: $i] : ! [v7: $i] : ( ~ (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3,
% 13.53/2.70 v7) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: int] : ( ~ (v8
% 13.53/2.70 = 0) & ok(v7) = v8)))
% 13.53/2.70
% 13.53/2.70 (l12_l13)
% 13.53/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1,
% 13.53/2.70 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 13.53/2.70 $i] : ? [v6: any] : (im_succ_cpq(v3) = v5 & ok(v5) = v6 & ok(v3) = v4 &
% 13.53/2.70 $i(v5) & ( ~ (v6 = 0) | v4 = 0)))
% 13.53/2.70
% 13.53/2.70 (function-axioms)
% 13.62/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 13.62/2.71 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 13.62/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.62/2.71 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 13.62/2.71 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.62/2.71 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 13.62/2.71 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 13.62/2.71 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 13.62/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.62/2.71 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 13.62/2.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.62/2.71 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 13.62/2.71 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 13.62/2.71 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.62/2.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 13.62/2.71 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.62/2.71 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 13.62/2.71 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.62/2.71 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 13.62/2.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 13.62/2.71 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 13.62/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.62/2.71 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 13.62/2.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.62/2.71 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 13.62/2.71 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 13.62/2.71 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.62/2.71 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.62/2.71 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 13.62/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.62/2.71 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 13.62/2.71 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (im_succ_cpq(v2) =
% 13.62/2.71 v1) | ~ (im_succ_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.62/2.71 : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) =
% 13.62/2.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 13.62/2.71 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 13.62/2.71 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 13.62/2.71 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.62/2.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 13.62/2.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.62/2.71 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 13.62/2.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 13.62/2.71 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.62/2.71 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 13.62/2.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.62/2.71 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 13.62/2.71 v0))
% 13.62/2.71
% 13.62/2.71 Further assumptions not needed in the proof:
% 13.63/2.71 --------------------------------------------
% 13.63/2.71 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 13.63/2.71 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax42, ax43, ax44,
% 13.63/2.71 ax45, ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest,
% 13.63/2.71 reflexivity, stricly_smaller_definition, totality, transitivity
% 13.63/2.71
% 13.63/2.71 Those formulas are unsatisfiable:
% 13.63/2.71 ---------------------------------
% 13.63/2.71
% 13.63/2.71 Begin of proof
% 13.63/2.72 |
% 13.63/2.72 | ALPHA: (ax41) implies:
% 13.63/2.72 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~
% 13.63/2.72 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.63/2.72 | ok(v3) = 0)
% 13.63/2.72 |
% 13.63/2.72 | ALPHA: (function-axioms) implies:
% 13.63/2.72 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.63/2.72 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 13.63/2.72 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 13.63/2.72 | (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(v2) = v0))
% 13.63/2.72 |
% 13.63/2.72 | DELTA: instantiating (l12_co) with fresh symbols all_45_0, all_45_1, all_45_2,
% 13.63/2.72 | all_45_3, all_45_4 gives:
% 13.63/2.72 | (4) ~ (all_45_0 = 0) & ok(all_45_1) = all_45_0 & triple(all_45_4,
% 13.63/2.72 | all_45_3, all_45_2) = all_45_1 & $i(all_45_1) & $i(all_45_2) &
% 13.63/2.72 | $i(all_45_3) & $i(all_45_4) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 13.63/2.72 | ? [v3: $i] : (ok(v3) = 0 & triple(v0, v1, v2) = v3 &
% 13.63/2.72 | succ_cpq(all_45_1, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.63/2.72 |
% 13.63/2.72 | ALPHA: (4) implies:
% 13.63/2.72 | (5) ~ (all_45_0 = 0)
% 13.63/2.72 | (6) $i(all_45_4)
% 13.63/2.72 | (7) $i(all_45_3)
% 13.63/2.72 | (8) $i(all_45_2)
% 13.63/2.72 | (9) triple(all_45_4, all_45_3, all_45_2) = all_45_1
% 13.63/2.72 | (10) ok(all_45_1) = all_45_0
% 13.63/2.72 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ok(v3) = 0 &
% 13.63/2.72 | triple(v0, v1, v2) = v3 & succ_cpq(all_45_1, v3) = 0 & $i(v3) &
% 13.63/2.72 | $i(v2) & $i(v1) & $i(v0))
% 13.63/2.72 |
% 13.63/2.72 | DELTA: instantiating (11) with fresh symbols all_53_0, all_53_1, all_53_2,
% 13.63/2.72 | all_53_3 gives:
% 13.63/2.72 | (12) ok(all_53_0) = 0 & triple(all_53_3, all_53_2, all_53_1) = all_53_0 &
% 13.63/2.72 | succ_cpq(all_45_1, all_53_0) = 0 & $i(all_53_0) & $i(all_53_1) &
% 13.63/2.72 | $i(all_53_2) & $i(all_53_3)
% 13.63/2.72 |
% 13.63/2.72 | ALPHA: (12) implies:
% 13.63/2.72 | (13) $i(all_53_3)
% 13.63/2.72 | (14) $i(all_53_2)
% 13.63/2.72 | (15) $i(all_53_1)
% 13.63/2.72 | (16) succ_cpq(all_45_1, all_53_0) = 0
% 13.63/2.72 | (17) triple(all_53_3, all_53_2, all_53_1) = all_53_0
% 13.63/2.72 | (18) ok(all_53_0) = 0
% 13.63/2.72 |
% 13.63/2.73 | GROUND_INST: instantiating (1) with all_45_4, all_45_3, all_45_2, all_45_1,
% 13.63/2.73 | simplifying with (6), (7), (8), (9) gives:
% 13.63/2.73 | (19) all_45_2 = bad | ok(all_45_1) = 0
% 13.63/2.73 |
% 13.63/2.73 | GROUND_INST: instantiating (l12_l13) with all_45_4, all_45_3, all_45_2,
% 13.63/2.73 | all_45_1, simplifying with (6), (7), (8), (9) gives:
% 13.63/2.73 | (20) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_45_1) =
% 13.63/2.73 | v1 & ok(v1) = v2 & ok(all_45_1) = v0 & $i(v1) & ( ~ (v2 = 0) | v0 =
% 13.63/2.73 | 0))
% 13.63/2.73 |
% 13.63/2.73 | GROUND_INST: instantiating (l12_l13) with all_53_3, all_53_2, all_53_1,
% 13.63/2.73 | all_53_0, simplifying with (13), (14), (15), (17) gives:
% 13.63/2.73 | (21) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_53_0) =
% 13.63/2.73 | v1 & ok(v1) = v2 & ok(all_53_0) = v0 & $i(v1) & ( ~ (v2 = 0) | v0 =
% 13.63/2.73 | 0))
% 13.63/2.73 |
% 13.63/2.73 | DELTA: instantiating (21) with fresh symbols all_60_0, all_60_1, all_60_2
% 13.63/2.73 | gives:
% 13.63/2.73 | (22) im_succ_cpq(all_53_0) = all_60_1 & ok(all_60_1) = all_60_0 &
% 13.63/2.73 | ok(all_53_0) = all_60_2 & $i(all_60_1) & ( ~ (all_60_0 = 0) | all_60_2
% 13.63/2.73 | = 0)
% 13.63/2.73 |
% 13.63/2.73 | ALPHA: (22) implies:
% 13.63/2.73 | (23) ok(all_53_0) = all_60_2
% 13.63/2.73 |
% 13.63/2.73 | DELTA: instantiating (20) with fresh symbols all_62_0, all_62_1, all_62_2
% 13.63/2.73 | gives:
% 13.63/2.73 | (24) im_succ_cpq(all_45_1) = all_62_1 & ok(all_62_1) = all_62_0 &
% 13.63/2.73 | ok(all_45_1) = all_62_2 & $i(all_62_1) & ( ~ (all_62_0 = 0) | all_62_2
% 13.63/2.73 | = 0)
% 13.63/2.73 |
% 13.63/2.73 | ALPHA: (24) implies:
% 13.63/2.73 | (25) ok(all_45_1) = all_62_2
% 13.63/2.73 |
% 13.63/2.73 | BETA: splitting (19) gives:
% 13.63/2.73 |
% 13.63/2.73 | Case 1:
% 13.63/2.73 | |
% 13.63/2.73 | | (26) ok(all_45_1) = 0
% 13.63/2.73 | |
% 13.63/2.73 | | GROUND_INST: instantiating (2) with all_45_0, all_62_2, all_45_1,
% 13.63/2.73 | | simplifying with (10), (25) gives:
% 13.63/2.73 | | (27) all_62_2 = all_45_0
% 13.63/2.73 | |
% 13.63/2.73 | | GROUND_INST: instantiating (2) with 0, all_62_2, all_45_1, simplifying with
% 13.63/2.73 | | (25), (26) gives:
% 13.63/2.73 | | (28) all_62_2 = 0
% 13.63/2.73 | |
% 13.63/2.73 | | COMBINE_EQS: (27), (28) imply:
% 13.63/2.73 | | (29) all_45_0 = 0
% 13.63/2.73 | |
% 13.63/2.73 | | SIMP: (29) implies:
% 13.63/2.73 | | (30) all_45_0 = 0
% 13.63/2.73 | |
% 13.63/2.73 | | REDUCE: (5), (30) imply:
% 13.63/2.73 | | (31) $false
% 13.63/2.73 | |
% 13.63/2.73 | | CLOSE: (31) is inconsistent.
% 13.63/2.73 | |
% 13.63/2.73 | Case 2:
% 13.63/2.73 | |
% 13.63/2.73 | | (32) all_45_2 = bad
% 13.63/2.73 | | (33) ~ (ok(all_45_1) = 0)
% 13.63/2.73 | |
% 13.63/2.73 | | REDUCE: (9), (32) imply:
% 13.63/2.73 | | (34) triple(all_45_4, all_45_3, bad) = all_45_1
% 13.63/2.73 | |
% 13.63/2.73 | | REDUCE: (8), (32) imply:
% 13.63/2.73 | | (35) $i(bad)
% 13.63/2.73 | |
% 13.63/2.73 | | GROUND_INST: instantiating (2) with 0, all_60_2, all_53_0, simplifying with
% 13.63/2.73 | | (18), (23) gives:
% 13.63/2.73 | | (36) all_60_2 = 0
% 13.63/2.73 | |
% 13.63/2.73 | | BETA: splitting (l12_induction) gives:
% 13.63/2.73 | |
% 13.63/2.73 | | Case 1:
% 13.63/2.73 | | |
% 13.63/2.74 | | | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 13.63/2.74 | | | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] :
% 13.63/2.74 | | | ? [v9: $i] : ( ~ (v8 = 0) & im_succ_cpq(v7) = v9 & ok(v9) = 0 &
% 13.63/2.74 | | | ok(v7) = v8 & triple(v3, v4, v5) = v7 & triple(v0, v1, v2) = v6
% 13.63/2.74 | | | & succ_cpq(v6, v7) = 0 & $i(v9) & $i(v7) & $i(v6) & $i(v5) &
% 13.63/2.74 | | | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 13.63/2.74 | | |
% 13.63/2.74 | | | DELTA: instantiating (37) with fresh symbols all_82_0, all_82_1, all_82_2,
% 13.63/2.74 | | | all_82_3, all_82_4, all_82_5, all_82_6, all_82_7, all_82_8,
% 13.63/2.74 | | | all_82_9 gives:
% 13.63/2.74 | | | (38) ~ (all_82_1 = 0) & im_succ_cpq(all_82_2) = all_82_0 &
% 13.63/2.74 | | | ok(all_82_0) = 0 & ok(all_82_2) = all_82_1 & triple(all_82_6,
% 13.63/2.74 | | | all_82_5, all_82_4) = all_82_2 & triple(all_82_9, all_82_8,
% 13.63/2.74 | | | all_82_7) = all_82_3 & succ_cpq(all_82_3, all_82_2) = 0 &
% 13.63/2.74 | | | $i(all_82_0) & $i(all_82_2) & $i(all_82_3) & $i(all_82_4) &
% 13.63/2.74 | | | $i(all_82_5) & $i(all_82_6) & $i(all_82_7) & $i(all_82_8) &
% 13.63/2.74 | | | $i(all_82_9)
% 13.63/2.74 | | |
% 13.63/2.74 | | | ALPHA: (38) implies:
% 13.63/2.74 | | | (39) ~ (all_82_1 = 0)
% 13.63/2.74 | | | (40) $i(all_82_6)
% 13.63/2.74 | | | (41) $i(all_82_5)
% 13.63/2.74 | | | (42) $i(all_82_4)
% 13.63/2.74 | | | (43) triple(all_82_6, all_82_5, all_82_4) = all_82_2
% 13.63/2.74 | | | (44) ok(all_82_2) = all_82_1
% 13.63/2.74 | | | (45) ok(all_82_0) = 0
% 13.63/2.74 | | | (46) im_succ_cpq(all_82_2) = all_82_0
% 13.63/2.74 | | |
% 13.63/2.74 | | | GROUND_INST: instantiating (l12_l13) with all_82_6, all_82_5, all_82_4,
% 13.63/2.74 | | | all_82_2, simplifying with (40), (41), (42), (43) gives:
% 13.63/2.74 | | | (47) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (im_succ_cpq(all_82_2)
% 13.63/2.74 | | | = v1 & ok(v1) = v2 & ok(all_82_2) = v0 & $i(v1) & ( ~ (v2 = 0) |
% 13.63/2.74 | | | v0 = 0))
% 13.63/2.74 | | |
% 13.63/2.74 | | | DELTA: instantiating (47) with fresh symbols all_89_0, all_89_1, all_89_2
% 13.63/2.74 | | | gives:
% 13.63/2.74 | | | (48) im_succ_cpq(all_82_2) = all_89_1 & ok(all_89_1) = all_89_0 &
% 13.63/2.74 | | | ok(all_82_2) = all_89_2 & $i(all_89_1) & ( ~ (all_89_0 = 0) |
% 13.63/2.74 | | | all_89_2 = 0)
% 13.63/2.74 | | |
% 13.63/2.74 | | | ALPHA: (48) implies:
% 13.63/2.74 | | | (49) ok(all_82_2) = all_89_2
% 13.63/2.74 | | | (50) ok(all_89_1) = all_89_0
% 13.63/2.74 | | | (51) im_succ_cpq(all_82_2) = all_89_1
% 13.63/2.74 | | | (52) ~ (all_89_0 = 0) | all_89_2 = 0
% 13.63/2.74 | | |
% 13.63/2.74 | | | GROUND_INST: instantiating (2) with all_82_1, all_89_2, all_82_2,
% 13.63/2.74 | | | simplifying with (44), (49) gives:
% 13.63/2.74 | | | (53) all_89_2 = all_82_1
% 13.63/2.74 | | |
% 13.63/2.74 | | | GROUND_INST: instantiating (3) with all_82_0, all_89_1, all_82_2,
% 13.63/2.74 | | | simplifying with (46), (51) gives:
% 13.63/2.74 | | | (54) all_89_1 = all_82_0
% 13.63/2.74 | | |
% 13.63/2.74 | | | REDUCE: (50), (54) imply:
% 13.63/2.74 | | | (55) ok(all_82_0) = all_89_0
% 13.63/2.74 | | |
% 13.63/2.74 | | | BETA: splitting (52) gives:
% 13.63/2.74 | | |
% 13.63/2.74 | | | Case 1:
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | (56) ~ (all_89_0 = 0)
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | GROUND_INST: instantiating (2) with 0, all_89_0, all_82_0, simplifying
% 13.63/2.74 | | | | with (45), (55) gives:
% 13.63/2.74 | | | | (57) all_89_0 = 0
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | REDUCE: (56), (57) imply:
% 13.63/2.74 | | | | (58) $false
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | CLOSE: (58) is inconsistent.
% 13.63/2.74 | | | |
% 13.63/2.74 | | | Case 2:
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | (59) all_89_2 = 0
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | COMBINE_EQS: (53), (59) imply:
% 13.63/2.74 | | | | (60) all_82_1 = 0
% 13.63/2.74 | | | |
% 13.63/2.74 | | | | REDUCE: (39), (60) imply:
% 13.63/2.75 | | | | (61) $false
% 13.63/2.75 | | | |
% 13.63/2.75 | | | | CLOSE: (61) is inconsistent.
% 13.63/2.75 | | | |
% 13.63/2.75 | | | End of split
% 13.63/2.75 | | |
% 13.63/2.75 | | Case 2:
% 13.63/2.75 | | |
% 13.63/2.75 | | | (62) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.63/2.75 | | | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.63/2.75 | | | ok(v3) = 0 | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7:
% 13.63/2.75 | | | $i] : ( ~ (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, v7) =
% 13.63/2.75 | | | 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: int] : ( ~
% 13.63/2.75 | | | (v8 = 0) & ok(v7) = v8)))
% 13.63/2.75 | | |
% 13.63/2.75 | | | GROUND_INST: instantiating (62) with all_45_4, all_45_3, bad, all_45_1,
% 13.63/2.75 | | | simplifying with (6), (7), (33), (34), (35) gives:
% 13.63/2.75 | | | (63) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 13.63/2.75 | | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_45_1, v3) = 0) | ~
% 13.63/2.75 | | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 13.63/2.75 | | | ok(v3) = v4))
% 13.63/2.75 | | |
% 13.63/2.75 | | | GROUND_INST: instantiating (63) with all_53_3, all_53_2, all_53_1,
% 13.63/2.75 | | | all_53_0, simplifying with (13), (14), (15), (16), (17)
% 13.63/2.75 | | | gives:
% 13.63/2.75 | | | (64) ? [v0: int] : ( ~ (v0 = 0) & ok(all_53_0) = v0)
% 13.63/2.75 | | |
% 13.63/2.75 | | | DELTA: instantiating (64) with fresh symbol all_84_0 gives:
% 13.63/2.75 | | | (65) ~ (all_84_0 = 0) & ok(all_53_0) = all_84_0
% 13.63/2.75 | | |
% 13.63/2.75 | | | ALPHA: (65) implies:
% 13.63/2.75 | | | (66) ~ (all_84_0 = 0)
% 13.63/2.75 | | | (67) ok(all_53_0) = all_84_0
% 13.63/2.75 | | |
% 13.63/2.75 | | | GROUND_INST: instantiating (2) with 0, all_84_0, all_53_0, simplifying
% 13.63/2.75 | | | with (18), (67) gives:
% 13.63/2.75 | | | (68) all_84_0 = 0
% 13.63/2.75 | | |
% 13.63/2.75 | | | REDUCE: (66), (68) imply:
% 13.63/2.75 | | | (69) $false
% 13.63/2.75 | | |
% 13.63/2.75 | | | CLOSE: (69) is inconsistent.
% 13.63/2.75 | | |
% 13.63/2.75 | | End of split
% 13.63/2.75 | |
% 13.63/2.75 | End of split
% 13.63/2.75 |
% 13.63/2.75 End of proof
% 13.63/2.75 % SZS output end Proof for theBenchmark
% 13.63/2.75
% 13.63/2.75 2125ms
%------------------------------------------------------------------------------