TSTP Solution File: SWV384+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV384+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 : 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 22:56:07 EDT 2023
% Result : Theorem 11.58s 2.36s
% Output : Proof 14.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV384+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 : n016.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 03:49:30 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.62/0.61 ________ _____
% 0.62/0.61 ___ __ \_________(_)________________________________
% 0.62/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.61
% 0.62/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.61 (2023-06-19)
% 0.62/0.61
% 0.62/0.61 (c) Philipp Rümmer, 2009-2023
% 0.62/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.61 Amanda Stjerna.
% 0.62/0.61 Free software under BSD-3-Clause.
% 0.62/0.61
% 0.62/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.61
% 0.62/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.62/0.63 Running up to 7 provers in parallel.
% 0.68/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.68/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 3.73/1.24 Prover 1: Preprocessing ...
% 3.73/1.24 Prover 4: Preprocessing ...
% 3.78/1.28 Prover 6: Preprocessing ...
% 3.78/1.28 Prover 3: Preprocessing ...
% 3.78/1.28 Prover 0: Preprocessing ...
% 3.78/1.28 Prover 2: Preprocessing ...
% 3.78/1.28 Prover 5: Preprocessing ...
% 8.14/1.86 Prover 1: Warning: ignoring some quantifiers
% 8.14/1.92 Prover 3: Warning: ignoring some quantifiers
% 8.87/1.98 Prover 6: Proving ...
% 9.28/1.99 Prover 1: Constructing countermodel ...
% 9.28/2.00 Prover 3: Constructing countermodel ...
% 9.28/2.02 Prover 5: Proving ...
% 9.28/2.04 Prover 4: Constructing countermodel ...
% 9.77/2.10 Prover 2: Proving ...
% 9.77/2.10 Prover 0: Proving ...
% 11.58/2.36 Prover 5: proved (1718ms)
% 11.58/2.36
% 11.58/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.58/2.36
% 12.05/2.37 Prover 2: stopped
% 12.05/2.37 Prover 3: stopped
% 12.05/2.37 Prover 6: stopped
% 12.05/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.05/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.05/2.37 Prover 0: stopped
% 12.05/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.05/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.05/2.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.30/2.42 Prover 10: Preprocessing ...
% 12.53/2.43 Prover 8: Preprocessing ...
% 12.53/2.45 Prover 7: Preprocessing ...
% 12.53/2.46 Prover 1: Found proof (size 85)
% 12.53/2.46 Prover 1: proved (1829ms)
% 12.53/2.46 Prover 4: stopped
% 12.53/2.47 Prover 13: Preprocessing ...
% 12.53/2.47 Prover 11: Preprocessing ...
% 12.53/2.50 Prover 10: stopped
% 12.53/2.51 Prover 7: stopped
% 13.25/2.53 Prover 11: stopped
% 13.25/2.54 Prover 13: stopped
% 13.59/2.60 Prover 8: Warning: ignoring some quantifiers
% 13.59/2.62 Prover 8: Constructing countermodel ...
% 13.59/2.63 Prover 8: stopped
% 13.59/2.63
% 13.59/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.59/2.63
% 13.59/2.65 % SZS output start Proof for theBenchmark
% 13.59/2.65 Assumptions after simplification:
% 13.59/2.65 ---------------------------------
% 13.59/2.65
% 13.59/2.65 (ax41)
% 13.96/2.67 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad |
% 13.96/2.67 ~ (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ok(v3) =
% 13.96/2.67 0)
% 13.96/2.67
% 13.96/2.67 (l12_l13)
% 13.96/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1,
% 13.96/2.68 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 13.96/2.68 any] : ? [v6: $i] : ? [v7: any] : ? [v8: any] : (im_succ_cpq(v3) = v6 &
% 13.96/2.68 ok(v6) = v8 & ok(v3) = v5 & check_cpq(v6) = v7 & check_cpq(v3) = v4 &
% 13.96/2.68 $i(v6) & ( ~ (v8 = 0) | ~ (v7 = 0) | (v5 = 0 & v4 = 0))))
% 13.96/2.68
% 13.96/2.68 (l20_co)
% 13.96/2.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 13.96/2.68 any] : (ok(v3) = v5 & triple(v0, v1, v2) = v3 & check_cpq(v3) = v4 & $i(v3)
% 13.96/2.68 & $i(v2) & $i(v1) & $i(v0) & ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ?
% 13.96/2.68 [v9: $i] : (ok(v9) = 0 & triple(v6, v7, v8) = v9 & check_cpq(v9) = 0 &
% 13.96/2.68 succ_cpq(v3, v9) = 0 & $i(v9) & $i(v8) & $i(v7) & $i(v6)) & ( ~ (v5 = 0) |
% 13.96/2.68 ~ (v4 = 0)))
% 13.96/2.68
% 13.96/2.68 (l20_induction)
% 13.96/2.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.96/2.68 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: any] : ? [v10: $i]
% 13.96/2.68 : (im_succ_cpq(v7) = v10 & ok(v10) = 0 & ok(v7) = v9 & triple(v3, v4, v5) = v7
% 13.96/2.68 & triple(v0, v1, v2) = v6 & check_cpq(v10) = 0 & check_cpq(v7) = v8 &
% 13.96/2.68 succ_cpq(v6, v7) = 0 & $i(v10) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3)
% 13.96/2.68 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0))) | ! [v0: $i] : !
% 13.96/2.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, v2) = v3) | ~
% 13.96/2.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ! [v5: $i] : ! [v6: $i] :
% 13.96/2.68 ! [v7: $i] : ( ~ (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, v7) = 0) | ~
% 13.96/2.68 $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: any] : ? [v9: any] : (ok(v7) =
% 13.96/2.68 v8 & check_cpq(v7) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0)))) | (ok(v3) = 0 &
% 13.96/2.68 check_cpq(v3) = 0))
% 13.96/2.68
% 13.96/2.68 (function-axioms)
% 13.96/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 13.96/2.69 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 13.96/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.96/2.69 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 13.96/2.69 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 13.96/2.69 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 13.96/2.69 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 13.96/2.69 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 13.96/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.96/2.69 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 13.96/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.96/2.69 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 13.96/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 13.96/2.69 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.96/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 13.96/2.69 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.96/2.69 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 13.96/2.69 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.96/2.69 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 13.96/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 13.96/2.69 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 13.96/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.96/2.69 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 13.96/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.96/2.69 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 13.96/2.69 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 13.96/2.69 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.96/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.96/2.69 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 13.96/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.96/2.69 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 13.96/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (im_succ_cpq(v2) =
% 13.96/2.69 v1) | ~ (im_succ_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 13.96/2.69 : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) =
% 13.96/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 13.96/2.69 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 13.96/2.69 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 13.96/2.69 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.96/2.69 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 13.96/2.69 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.96/2.69 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 13.96/2.69 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 13.96/2.69 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 13.96/2.69 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 13.96/2.69 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.96/2.69 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 13.96/2.69 v0))
% 13.96/2.69
% 13.96/2.69 Further assumptions not needed in the proof:
% 13.96/2.69 --------------------------------------------
% 13.96/2.69 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 13.96/2.69 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax42, ax43, ax44,
% 13.96/2.69 ax45, ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest,
% 13.96/2.69 reflexivity, stricly_smaller_definition, totality, transitivity
% 13.96/2.69
% 13.96/2.69 Those formulas are unsatisfiable:
% 13.96/2.69 ---------------------------------
% 13.96/2.69
% 13.96/2.69 Begin of proof
% 13.96/2.69 |
% 13.96/2.69 | ALPHA: (ax41) implies:
% 13.96/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = bad | ~
% 13.96/2.69 | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.96/2.69 | ok(v3) = 0)
% 13.96/2.69 |
% 13.96/2.69 | ALPHA: (function-axioms) implies:
% 13.96/2.70 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.96/2.70 | (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 13.96/2.70 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.96/2.70 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 13.96/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 13.96/2.70 | (im_succ_cpq(v2) = v1) | ~ (im_succ_cpq(v2) = v0))
% 13.96/2.70 |
% 13.96/2.70 | DELTA: instantiating (l20_co) with fresh symbols all_47_0, all_47_1, all_47_2,
% 13.96/2.70 | all_47_3, all_47_4, all_47_5 gives:
% 13.96/2.70 | (5) ok(all_47_2) = all_47_0 & triple(all_47_5, all_47_4, all_47_3) =
% 13.96/2.70 | all_47_2 & check_cpq(all_47_2) = all_47_1 & $i(all_47_2) & $i(all_47_3)
% 13.96/2.70 | & $i(all_47_4) & $i(all_47_5) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i]
% 13.96/2.70 | : ? [v3: $i] : (ok(v3) = 0 & triple(v0, v1, v2) = v3 & check_cpq(v3) =
% 13.96/2.70 | 0 & succ_cpq(all_47_2, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) &
% 13.96/2.70 | ( ~ (all_47_0 = 0) | ~ (all_47_1 = 0))
% 13.96/2.70 |
% 13.96/2.70 | ALPHA: (5) implies:
% 13.96/2.70 | (6) $i(all_47_5)
% 13.96/2.70 | (7) $i(all_47_4)
% 14.12/2.70 | (8) $i(all_47_3)
% 14.12/2.70 | (9) check_cpq(all_47_2) = all_47_1
% 14.12/2.70 | (10) triple(all_47_5, all_47_4, all_47_3) = all_47_2
% 14.12/2.70 | (11) ok(all_47_2) = all_47_0
% 14.12/2.70 | (12) ~ (all_47_0 = 0) | ~ (all_47_1 = 0)
% 14.12/2.70 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ok(v3) = 0 &
% 14.12/2.70 | triple(v0, v1, v2) = v3 & check_cpq(v3) = 0 & succ_cpq(all_47_2, v3)
% 14.12/2.70 | = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.12/2.70 |
% 14.12/2.70 | DELTA: instantiating (13) with fresh symbols all_53_0, all_53_1, all_53_2,
% 14.12/2.70 | all_53_3 gives:
% 14.12/2.70 | (14) ok(all_53_0) = 0 & triple(all_53_3, all_53_2, all_53_1) = all_53_0 &
% 14.12/2.70 | check_cpq(all_53_0) = 0 & succ_cpq(all_47_2, all_53_0) = 0 &
% 14.12/2.70 | $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3)
% 14.12/2.70 |
% 14.12/2.70 | ALPHA: (14) implies:
% 14.12/2.70 | (15) $i(all_53_3)
% 14.12/2.70 | (16) $i(all_53_2)
% 14.12/2.70 | (17) $i(all_53_1)
% 14.12/2.70 | (18) succ_cpq(all_47_2, all_53_0) = 0
% 14.12/2.70 | (19) check_cpq(all_53_0) = 0
% 14.12/2.70 | (20) triple(all_53_3, all_53_2, all_53_1) = all_53_0
% 14.12/2.70 | (21) ok(all_53_0) = 0
% 14.12/2.70 |
% 14.12/2.70 | GROUND_INST: instantiating (1) with all_47_5, all_47_4, all_47_3, all_47_2,
% 14.12/2.70 | simplifying with (6), (7), (8), (10) gives:
% 14.12/2.70 | (22) all_47_3 = bad | ok(all_47_2) = 0
% 14.12/2.70 |
% 14.12/2.70 | GROUND_INST: instantiating (l12_l13) with all_47_5, all_47_4, all_47_3,
% 14.12/2.70 | all_47_2, simplifying with (6), (7), (8), (10) gives:
% 14.12/2.70 | (23) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4:
% 14.12/2.70 | any] : (im_succ_cpq(all_47_2) = v2 & ok(v2) = v4 & ok(all_47_2) = v1
% 14.12/2.70 | & check_cpq(v2) = v3 & check_cpq(all_47_2) = v0 & $i(v2) & ( ~ (v4 =
% 14.12/2.70 | 0) | ~ (v3 = 0) | (v1 = 0 & v0 = 0)))
% 14.12/2.70 |
% 14.12/2.71 | GROUND_INST: instantiating (l12_l13) with all_53_3, all_53_2, all_53_1,
% 14.12/2.71 | all_53_0, simplifying with (15), (16), (17), (20) gives:
% 14.12/2.71 | (24) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4:
% 14.12/2.71 | any] : (im_succ_cpq(all_53_0) = v2 & ok(v2) = v4 & ok(all_53_0) = v1
% 14.12/2.71 | & check_cpq(v2) = v3 & check_cpq(all_53_0) = v0 & $i(v2) & ( ~ (v4 =
% 14.12/2.71 | 0) | ~ (v3 = 0) | (v1 = 0 & v0 = 0)))
% 14.12/2.71 |
% 14.12/2.71 | DELTA: instantiating (24) with fresh symbols all_60_0, all_60_1, all_60_2,
% 14.12/2.71 | all_60_3, all_60_4 gives:
% 14.12/2.71 | (25) im_succ_cpq(all_53_0) = all_60_2 & ok(all_60_2) = all_60_0 &
% 14.12/2.71 | ok(all_53_0) = all_60_3 & check_cpq(all_60_2) = all_60_1 &
% 14.12/2.71 | check_cpq(all_53_0) = all_60_4 & $i(all_60_2) & ( ~ (all_60_0 = 0) |
% 14.12/2.71 | ~ (all_60_1 = 0) | (all_60_3 = 0 & all_60_4 = 0))
% 14.12/2.71 |
% 14.12/2.71 | ALPHA: (25) implies:
% 14.12/2.71 | (26) check_cpq(all_53_0) = all_60_4
% 14.12/2.71 | (27) ok(all_53_0) = all_60_3
% 14.12/2.71 |
% 14.12/2.71 | DELTA: instantiating (23) with fresh symbols all_62_0, all_62_1, all_62_2,
% 14.12/2.71 | all_62_3, all_62_4 gives:
% 14.12/2.71 | (28) im_succ_cpq(all_47_2) = all_62_2 & ok(all_62_2) = all_62_0 &
% 14.12/2.71 | ok(all_47_2) = all_62_3 & check_cpq(all_62_2) = all_62_1 &
% 14.12/2.71 | check_cpq(all_47_2) = all_62_4 & $i(all_62_2) & ( ~ (all_62_0 = 0) |
% 14.12/2.71 | ~ (all_62_1 = 0) | (all_62_3 = 0 & all_62_4 = 0))
% 14.12/2.71 |
% 14.12/2.71 | ALPHA: (28) implies:
% 14.12/2.71 | (29) check_cpq(all_47_2) = all_62_4
% 14.12/2.71 | (30) ok(all_47_2) = all_62_3
% 14.12/2.71 |
% 14.12/2.71 | GROUND_INST: instantiating (2) with all_47_1, all_62_4, all_47_2, simplifying
% 14.12/2.71 | with (9), (29) gives:
% 14.12/2.71 | (31) all_62_4 = all_47_1
% 14.12/2.71 |
% 14.12/2.71 | GROUND_INST: instantiating (2) with 0, all_60_4, all_53_0, simplifying with
% 14.12/2.71 | (19), (26) gives:
% 14.12/2.71 | (32) all_60_4 = 0
% 14.12/2.71 |
% 14.12/2.71 | GROUND_INST: instantiating (3) with all_47_0, all_62_3, all_47_2, simplifying
% 14.12/2.71 | with (11), (30) gives:
% 14.12/2.71 | (33) all_62_3 = all_47_0
% 14.12/2.71 |
% 14.12/2.71 | GROUND_INST: instantiating (3) with 0, all_60_3, all_53_0, simplifying with
% 14.12/2.71 | (21), (27) gives:
% 14.12/2.71 | (34) all_60_3 = 0
% 14.12/2.71 |
% 14.12/2.71 | BETA: splitting (l20_induction) gives:
% 14.12/2.71 |
% 14.12/2.71 | Case 1:
% 14.12/2.71 | |
% 14.12/2.71 | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 14.12/2.71 | | : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9:
% 14.12/2.71 | | any] : ? [v10: $i] : (im_succ_cpq(v7) = v10 & ok(v10) = 0 &
% 14.12/2.71 | | ok(v7) = v9 & triple(v3, v4, v5) = v7 & triple(v0, v1, v2) = v6 &
% 14.12/2.71 | | check_cpq(v10) = 0 & check_cpq(v7) = v8 & succ_cpq(v6, v7) = 0 &
% 14.12/2.71 | | $i(v10) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 14.12/2.71 | | $i(v1) & $i(v0) & ( ~ (v9 = 0) | ~ (v8 = 0)))
% 14.12/2.71 | |
% 14.12/2.71 | | DELTA: instantiating (35) with fresh symbols all_74_0, all_74_1, all_74_2,
% 14.12/2.71 | | all_74_3, all_74_4, all_74_5, all_74_6, all_74_7, all_74_8, all_74_9,
% 14.12/2.71 | | all_74_10 gives:
% 14.12/2.71 | | (36) im_succ_cpq(all_74_3) = all_74_0 & ok(all_74_0) = 0 & ok(all_74_3) =
% 14.12/2.71 | | all_74_1 & triple(all_74_7, all_74_6, all_74_5) = all_74_3 &
% 14.12/2.71 | | triple(all_74_10, all_74_9, all_74_8) = all_74_4 &
% 14.12/2.71 | | check_cpq(all_74_0) = 0 & check_cpq(all_74_3) = all_74_2 &
% 14.12/2.71 | | succ_cpq(all_74_4, all_74_3) = 0 & $i(all_74_0) & $i(all_74_3) &
% 14.12/2.71 | | $i(all_74_4) & $i(all_74_5) & $i(all_74_6) & $i(all_74_7) &
% 14.12/2.71 | | $i(all_74_8) & $i(all_74_9) & $i(all_74_10) & ( ~ (all_74_1 = 0) |
% 14.12/2.71 | | ~ (all_74_2 = 0))
% 14.12/2.71 | |
% 14.12/2.71 | | ALPHA: (36) implies:
% 14.12/2.71 | | (37) $i(all_74_7)
% 14.12/2.71 | | (38) $i(all_74_6)
% 14.12/2.71 | | (39) $i(all_74_5)
% 14.12/2.71 | | (40) check_cpq(all_74_3) = all_74_2
% 14.12/2.71 | | (41) check_cpq(all_74_0) = 0
% 14.12/2.71 | | (42) triple(all_74_7, all_74_6, all_74_5) = all_74_3
% 14.12/2.71 | | (43) ok(all_74_3) = all_74_1
% 14.12/2.71 | | (44) ok(all_74_0) = 0
% 14.12/2.71 | | (45) im_succ_cpq(all_74_3) = all_74_0
% 14.12/2.71 | | (46) ~ (all_74_1 = 0) | ~ (all_74_2 = 0)
% 14.12/2.71 | |
% 14.12/2.72 | | GROUND_INST: instantiating (l12_l13) with all_74_7, all_74_6, all_74_5,
% 14.12/2.72 | | all_74_3, simplifying with (37), (38), (39), (42) gives:
% 14.12/2.72 | | (47) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] : ? [v4:
% 14.12/2.72 | | any] : (im_succ_cpq(all_74_3) = v2 & ok(v2) = v4 & ok(all_74_3) =
% 14.12/2.72 | | v1 & check_cpq(v2) = v3 & check_cpq(all_74_3) = v0 & $i(v2) & ( ~
% 14.12/2.72 | | (v4 = 0) | ~ (v3 = 0) | (v1 = 0 & v0 = 0)))
% 14.12/2.72 | |
% 14.12/2.72 | | DELTA: instantiating (47) with fresh symbols all_81_0, all_81_1, all_81_2,
% 14.12/2.72 | | all_81_3, all_81_4 gives:
% 14.12/2.72 | | (48) im_succ_cpq(all_74_3) = all_81_2 & ok(all_81_2) = all_81_0 &
% 14.12/2.72 | | ok(all_74_3) = all_81_3 & check_cpq(all_81_2) = all_81_1 &
% 14.12/2.72 | | check_cpq(all_74_3) = all_81_4 & $i(all_81_2) & ( ~ (all_81_0 = 0) |
% 14.12/2.72 | | ~ (all_81_1 = 0) | (all_81_3 = 0 & all_81_4 = 0))
% 14.12/2.72 | |
% 14.12/2.72 | | ALPHA: (48) implies:
% 14.12/2.72 | | (49) check_cpq(all_74_3) = all_81_4
% 14.12/2.72 | | (50) check_cpq(all_81_2) = all_81_1
% 14.12/2.72 | | (51) ok(all_74_3) = all_81_3
% 14.12/2.72 | | (52) ok(all_81_2) = all_81_0
% 14.12/2.72 | | (53) im_succ_cpq(all_74_3) = all_81_2
% 14.12/2.72 | | (54) ~ (all_81_0 = 0) | ~ (all_81_1 = 0) | (all_81_3 = 0 & all_81_4 =
% 14.12/2.72 | | 0)
% 14.12/2.72 | |
% 14.12/2.72 | | GROUND_INST: instantiating (2) with all_74_2, all_81_4, all_74_3,
% 14.12/2.72 | | simplifying with (40), (49) gives:
% 14.12/2.72 | | (55) all_81_4 = all_74_2
% 14.12/2.72 | |
% 14.12/2.72 | | GROUND_INST: instantiating (3) with all_74_1, all_81_3, all_74_3,
% 14.12/2.72 | | simplifying with (43), (51) gives:
% 14.12/2.72 | | (56) all_81_3 = all_74_1
% 14.12/2.72 | |
% 14.12/2.72 | | GROUND_INST: instantiating (4) with all_74_0, all_81_2, all_74_3,
% 14.12/2.72 | | simplifying with (45), (53) gives:
% 14.12/2.72 | | (57) all_81_2 = all_74_0
% 14.12/2.72 | |
% 14.12/2.72 | | REDUCE: (52), (57) imply:
% 14.12/2.72 | | (58) ok(all_74_0) = all_81_0
% 14.12/2.72 | |
% 14.12/2.72 | | REDUCE: (50), (57) imply:
% 14.12/2.72 | | (59) check_cpq(all_74_0) = all_81_1
% 14.12/2.72 | |
% 14.12/2.72 | | GROUND_INST: instantiating (2) with 0, all_81_1, all_74_0, simplifying with
% 14.12/2.72 | | (41), (59) gives:
% 14.12/2.72 | | (60) all_81_1 = 0
% 14.12/2.72 | |
% 14.12/2.72 | | GROUND_INST: instantiating (3) with 0, all_81_0, all_74_0, simplifying with
% 14.12/2.72 | | (44), (58) gives:
% 14.12/2.72 | | (61) all_81_0 = 0
% 14.12/2.72 | |
% 14.12/2.72 | | BETA: splitting (54) gives:
% 14.12/2.72 | |
% 14.12/2.72 | | Case 1:
% 14.12/2.72 | | |
% 14.12/2.72 | | | (62) ~ (all_81_0 = 0)
% 14.12/2.72 | | |
% 14.12/2.72 | | | REDUCE: (61), (62) imply:
% 14.12/2.72 | | | (63) $false
% 14.12/2.72 | | |
% 14.12/2.72 | | | CLOSE: (63) is inconsistent.
% 14.12/2.72 | | |
% 14.12/2.72 | | Case 2:
% 14.12/2.72 | | |
% 14.12/2.72 | | | (64) ~ (all_81_1 = 0) | (all_81_3 = 0 & all_81_4 = 0)
% 14.12/2.72 | | |
% 14.12/2.72 | | | BETA: splitting (64) gives:
% 14.12/2.72 | | |
% 14.12/2.72 | | | Case 1:
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | (65) ~ (all_81_1 = 0)
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | REDUCE: (60), (65) imply:
% 14.12/2.72 | | | | (66) $false
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | CLOSE: (66) is inconsistent.
% 14.12/2.72 | | | |
% 14.12/2.72 | | | Case 2:
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | (67) all_81_3 = 0 & all_81_4 = 0
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | ALPHA: (67) implies:
% 14.12/2.72 | | | | (68) all_81_4 = 0
% 14.12/2.72 | | | | (69) all_81_3 = 0
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | COMBINE_EQS: (56), (69) imply:
% 14.12/2.72 | | | | (70) all_74_1 = 0
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | SIMP: (70) implies:
% 14.12/2.72 | | | | (71) all_74_1 = 0
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | COMBINE_EQS: (55), (68) imply:
% 14.12/2.72 | | | | (72) all_74_2 = 0
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | BETA: splitting (46) gives:
% 14.12/2.72 | | | |
% 14.12/2.72 | | | | Case 1:
% 14.12/2.72 | | | | |
% 14.12/2.72 | | | | | (73) ~ (all_74_1 = 0)
% 14.12/2.72 | | | | |
% 14.12/2.72 | | | | | REDUCE: (71), (73) imply:
% 14.12/2.72 | | | | | (74) $false
% 14.12/2.72 | | | | |
% 14.12/2.72 | | | | | CLOSE: (74) is inconsistent.
% 14.12/2.72 | | | | |
% 14.12/2.72 | | | | Case 2:
% 14.12/2.72 | | | | |
% 14.12/2.72 | | | | | (75) ~ (all_74_2 = 0)
% 14.12/2.72 | | | | |
% 14.12/2.73 | | | | | REDUCE: (72), (75) imply:
% 14.12/2.73 | | | | | (76) $false
% 14.12/2.73 | | | | |
% 14.12/2.73 | | | | | CLOSE: (76) is inconsistent.
% 14.12/2.73 | | | | |
% 14.12/2.73 | | | | End of split
% 14.12/2.73 | | | |
% 14.12/2.73 | | | End of split
% 14.12/2.73 | | |
% 14.12/2.73 | | End of split
% 14.12/2.73 | |
% 14.12/2.73 | Case 2:
% 14.12/2.73 | |
% 14.12/2.73 | | (77) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.12/2.73 | | (triple(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | !
% 14.12/2.73 | | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 14.12/2.73 | | (triple(v4, v5, v6) = v7) | ~ (succ_cpq(v3, v7) = 0) | ~
% 14.12/2.73 | | $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: any] : ? [v9: any] :
% 14.12/2.73 | | (ok(v7) = v8 & check_cpq(v7) = v9 & ( ~ (v9 = 0) | ~ (v8 =
% 14.12/2.73 | | 0)))) | (ok(v3) = 0 & check_cpq(v3) = 0))
% 14.12/2.73 | |
% 14.12/2.73 | | GROUND_INST: instantiating (77) with all_47_5, all_47_4, all_47_3, all_47_2,
% 14.12/2.73 | | simplifying with (6), (7), (8), (10) gives:
% 14.12/2.73 | | (78) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.12/2.73 | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_47_2, v3) = 0) | ~
% 14.12/2.73 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 14.12/2.73 | | (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 14.12/2.73 | | | (ok(all_47_2) = 0 & check_cpq(all_47_2) = 0)
% 14.12/2.73 | |
% 14.12/2.73 | | BETA: splitting (12) gives:
% 14.12/2.73 | |
% 14.12/2.73 | | Case 1:
% 14.12/2.73 | | |
% 14.12/2.73 | | | (79) ~ (all_47_0 = 0)
% 14.12/2.73 | | |
% 14.12/2.73 | | | BETA: splitting (22) gives:
% 14.12/2.73 | | |
% 14.12/2.73 | | | Case 1:
% 14.12/2.73 | | | |
% 14.12/2.73 | | | | (80) ok(all_47_2) = 0
% 14.12/2.73 | | | |
% 14.27/2.73 | | | | GROUND_INST: instantiating (3) with all_47_0, 0, all_47_2, simplifying
% 14.27/2.73 | | | | with (11), (80) gives:
% 14.27/2.73 | | | | (81) all_47_0 = 0
% 14.27/2.73 | | | |
% 14.27/2.73 | | | | REDUCE: (79), (81) imply:
% 14.27/2.73 | | | | (82) $false
% 14.27/2.73 | | | |
% 14.27/2.73 | | | | CLOSE: (82) is inconsistent.
% 14.27/2.73 | | | |
% 14.27/2.73 | | | Case 2:
% 14.27/2.73 | | | |
% 14.27/2.73 | | | | (83) ~ (ok(all_47_2) = 0)
% 14.27/2.73 | | | |
% 14.27/2.73 | | | | BETA: splitting (78) gives:
% 14.27/2.73 | | | |
% 14.27/2.73 | | | | Case 1:
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | (84) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.27/2.73 | | | | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_47_2, v3) = 0)
% 14.27/2.73 | | | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 14.27/2.73 | | | | | any] : (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) |
% 14.27/2.73 | | | | | ~ (v4 = 0))))
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | GROUND_INST: instantiating (84) with all_53_3, all_53_2, all_53_1,
% 14.27/2.73 | | | | | all_53_0, simplifying with (15), (16), (17), (18), (20)
% 14.27/2.73 | | | | | gives:
% 14.27/2.73 | | | | | (85) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 &
% 14.27/2.73 | | | | | check_cpq(all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | REF_CLOSE: (2), (3), (19), (21), (85) are inconsistent by sub-proof
% 14.27/2.73 | | | | | #1.
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | Case 2:
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | (86) ok(all_47_2) = 0 & check_cpq(all_47_2) = 0
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | ALPHA: (86) implies:
% 14.27/2.73 | | | | | (87) ok(all_47_2) = 0
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | PRED_UNIFY: (83), (87) imply:
% 14.27/2.73 | | | | | (88) $false
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | | CLOSE: (88) is inconsistent.
% 14.27/2.73 | | | | |
% 14.27/2.73 | | | | End of split
% 14.27/2.73 | | | |
% 14.27/2.73 | | | End of split
% 14.27/2.73 | | |
% 14.27/2.73 | | Case 2:
% 14.27/2.73 | | |
% 14.27/2.74 | | | (89) ~ (all_47_1 = 0)
% 14.27/2.74 | | |
% 14.27/2.74 | | | BETA: splitting (78) gives:
% 14.27/2.74 | | |
% 14.27/2.74 | | | Case 1:
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | (90) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 14.27/2.74 | | | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_47_2, v3) = 0) |
% 14.27/2.74 | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any]
% 14.27/2.74 | | | | : (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | ~ (v4 =
% 14.27/2.74 | | | | 0))))
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | GROUND_INST: instantiating (90) with all_53_3, all_53_2, all_53_1,
% 14.27/2.74 | | | | all_53_0, simplifying with (15), (16), (17), (18), (20)
% 14.27/2.74 | | | | gives:
% 14.27/2.74 | | | | (91) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 &
% 14.27/2.74 | | | | check_cpq(all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | REF_CLOSE: (2), (3), (19), (21), (91) are inconsistent by sub-proof #1.
% 14.27/2.74 | | | |
% 14.27/2.74 | | | Case 2:
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | (92) ok(all_47_2) = 0 & check_cpq(all_47_2) = 0
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | ALPHA: (92) implies:
% 14.27/2.74 | | | | (93) check_cpq(all_47_2) = 0
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | GROUND_INST: instantiating (2) with all_47_1, 0, all_47_2, simplifying
% 14.27/2.74 | | | | with (9), (93) gives:
% 14.27/2.74 | | | | (94) all_47_1 = 0
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | REDUCE: (89), (94) imply:
% 14.27/2.74 | | | | (95) $false
% 14.27/2.74 | | | |
% 14.27/2.74 | | | | CLOSE: (95) is inconsistent.
% 14.27/2.74 | | | |
% 14.27/2.74 | | | End of split
% 14.27/2.74 | | |
% 14.27/2.74 | | End of split
% 14.27/2.74 | |
% 14.27/2.74 | End of split
% 14.27/2.74 |
% 14.27/2.74 End of proof
% 14.27/2.74
% 14.27/2.74 Sub-proof #1 shows that the following formulas are inconsistent:
% 14.27/2.74 ----------------------------------------------------------------
% 14.27/2.74 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.27/2.74 (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 14.27/2.74 (2) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 & check_cpq(all_53_0) =
% 14.27/2.74 v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.27/2.74 (3) check_cpq(all_53_0) = 0
% 14.27/2.74 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.27/2.74 (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 14.27/2.74 (5) ok(all_53_0) = 0
% 14.27/2.74
% 14.27/2.74 Begin of proof
% 14.27/2.74 |
% 14.27/2.74 | DELTA: instantiating (2) with fresh symbols all_87_0, all_87_1 gives:
% 14.27/2.74 | (6) ok(all_53_0) = all_87_1 & check_cpq(all_53_0) = all_87_0 & ( ~
% 14.27/2.74 | (all_87_0 = 0) | ~ (all_87_1 = 0))
% 14.27/2.74 |
% 14.27/2.74 | ALPHA: (6) implies:
% 14.27/2.74 | (7) check_cpq(all_53_0) = all_87_0
% 14.27/2.74 | (8) ok(all_53_0) = all_87_1
% 14.27/2.74 | (9) ~ (all_87_0 = 0) | ~ (all_87_1 = 0)
% 14.27/2.74 |
% 14.27/2.74 | GROUND_INST: instantiating (4) with 0, all_87_0, all_53_0, simplifying with
% 14.27/2.74 | (3), (7) gives:
% 14.27/2.74 | (10) all_87_0 = 0
% 14.27/2.74 |
% 14.27/2.74 | GROUND_INST: instantiating (1) with 0, all_87_1, all_53_0, simplifying with
% 14.27/2.74 | (5), (8) gives:
% 14.27/2.74 | (11) all_87_1 = 0
% 14.27/2.74 |
% 14.27/2.74 | BETA: splitting (9) gives:
% 14.27/2.74 |
% 14.27/2.74 | Case 1:
% 14.27/2.74 | |
% 14.27/2.74 | | (12) ~ (all_87_0 = 0)
% 14.27/2.74 | |
% 14.27/2.74 | | REDUCE: (10), (12) imply:
% 14.27/2.74 | | (13) $false
% 14.27/2.74 | |
% 14.27/2.74 | | CLOSE: (13) is inconsistent.
% 14.27/2.74 | |
% 14.27/2.74 | Case 2:
% 14.27/2.74 | |
% 14.27/2.74 | | (14) ~ (all_87_1 = 0)
% 14.27/2.74 | |
% 14.27/2.74 | | REDUCE: (11), (14) imply:
% 14.27/2.74 | | (15) $false
% 14.27/2.74 | |
% 14.27/2.74 | | CLOSE: (15) is inconsistent.
% 14.27/2.74 | |
% 14.27/2.74 | End of split
% 14.27/2.74 |
% 14.27/2.74 End of proof
% 14.27/2.74 % SZS output end Proof for theBenchmark
% 14.27/2.74
% 14.27/2.74 2127ms
%------------------------------------------------------------------------------