TSTP Solution File: SWV383+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV383+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 : n004.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 9.50s 2.11s
% Output : Proof 11.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV383+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 09:18:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.66 ________ _____
% 0.20/0.66 ___ __ \_________(_)________________________________
% 0.20/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.66
% 0.20/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.66 (2023-06-19)
% 0.20/0.66
% 0.20/0.66 (c) Philipp Rümmer, 2009-2023
% 0.20/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.66 Amanda Stjerna.
% 0.20/0.66 Free software under BSD-3-Clause.
% 0.20/0.66
% 0.20/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.66
% 0.20/0.66 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.67 Running up to 7 provers in parallel.
% 0.65/0.69 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.69 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.69 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.65/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.07/1.21 Prover 4: Preprocessing ...
% 3.07/1.22 Prover 1: Preprocessing ...
% 3.07/1.25 Prover 0: Preprocessing ...
% 3.07/1.25 Prover 5: Preprocessing ...
% 3.07/1.25 Prover 6: Preprocessing ...
% 3.07/1.25 Prover 2: Preprocessing ...
% 3.07/1.25 Prover 3: Preprocessing ...
% 7.43/1.80 Prover 1: Warning: ignoring some quantifiers
% 7.43/1.87 Prover 3: Warning: ignoring some quantifiers
% 8.37/1.90 Prover 5: Proving ...
% 8.37/1.90 Prover 1: Constructing countermodel ...
% 8.37/1.91 Prover 6: Proving ...
% 8.37/1.92 Prover 3: Constructing countermodel ...
% 8.94/1.97 Prover 4: Constructing countermodel ...
% 8.94/2.00 Prover 0: Proving ...
% 9.26/2.02 Prover 2: Proving ...
% 9.50/2.10 Prover 3: proved (1419ms)
% 9.50/2.10
% 9.50/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.50/2.11
% 9.50/2.11 Prover 5: stopped
% 9.50/2.11 Prover 0: stopped
% 9.50/2.11 Prover 6: stopped
% 9.50/2.11 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.50/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.50/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.50/2.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.50/2.13 Prover 2: stopped
% 10.12/2.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.12/2.17 Prover 1: Found proof (size 21)
% 10.12/2.17 Prover 1: proved (1489ms)
% 10.12/2.17 Prover 4: stopped
% 10.12/2.18 Prover 11: Preprocessing ...
% 10.12/2.18 Prover 10: Preprocessing ...
% 10.50/2.19 Prover 8: Preprocessing ...
% 10.50/2.19 Prover 7: Preprocessing ...
% 10.50/2.19 Prover 13: Preprocessing ...
% 10.50/2.24 Prover 7: stopped
% 10.50/2.24 Prover 10: stopped
% 10.50/2.24 Prover 11: stopped
% 11.07/2.26 Prover 13: stopped
% 11.30/2.33 Prover 8: Warning: ignoring some quantifiers
% 11.30/2.36 Prover 8: Constructing countermodel ...
% 11.30/2.37 Prover 8: stopped
% 11.30/2.37
% 11.30/2.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.30/2.37
% 11.30/2.38 % SZS output start Proof for theBenchmark
% 11.30/2.38 Assumptions after simplification:
% 11.30/2.38 ---------------------------------
% 11.30/2.38
% 11.30/2.38 (l19_co)
% 11.57/2.41 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 11.57/2.41 = 0) & triple(v0, v1, v2) = v3 & check_cpq(v3) = v4 & $i(v3) & $i(v2) &
% 11.57/2.41 $i(v1) & $i(v0) & ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 11.57/2.41 (ok(v8) = 0 & triple(v5, v6, v7) = v8 & check_cpq(v8) = 0 & succ_cpq(v3, v8)
% 11.57/2.41 = 0 & $i(v8) & $i(v7) & $i(v6) & $i(v5)))
% 11.57/2.41
% 11.57/2.41 (l19_l20)
% 11.57/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1,
% 11.57/2.42 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v4: $i] : ! [v5:
% 11.57/2.42 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (triple(v4, v5, v6) = v7) | ~
% 11.57/2.42 (succ_cpq(v3, v7) = 0) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ? [v8: any]
% 11.57/2.42 : ? [v9: any] : (ok(v7) = v8 & check_cpq(v7) = v9 & ( ~ (v9 = 0) | ~ (v8
% 11.57/2.42 = 0)))) | (ok(v3) = 0 & check_cpq(v3) = 0))
% 11.57/2.42
% 11.57/2.42 (function-axioms)
% 11.57/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 11.57/2.43 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 11.57/2.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.43 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 11.57/2.43 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.57/2.43 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 11.57/2.43 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 11.57/2.43 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 11.57/2.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.43 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 11.57/2.43 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.57/2.43 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 11.57/2.43 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 11.57/2.43 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.57/2.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 11.57/2.43 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 11.57/2.43 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 11.57/2.43 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 11.57/2.43 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 11.57/2.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 11.57/2.43 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 11.57/2.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.57/2.43 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 11.57/2.43 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.57/2.43 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 11.57/2.43 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 11.57/2.43 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.57/2.43 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.57/2.44 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 11.57/2.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.57/2.44 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 11.57/2.44 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.57/2.44 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 11.57/2.44 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 11.57/2.44 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.57/2.44 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 11.57/2.44 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 11.57/2.44 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.57/2.44 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 11.57/2.44 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.57/2.44 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 11.57/2.44 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 11.57/2.44 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.57/2.44 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 11.57/2.44 v1) | ~ (isnonempty_slb(v2) = v0))
% 11.57/2.44
% 11.57/2.44 Further assumptions not needed in the proof:
% 11.57/2.44 --------------------------------------------
% 11.57/2.44 ax18, ax19, ax20, ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30,
% 11.57/2.44 ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax40, ax41, ax42, ax43,
% 11.57/2.44 ax44, ax45, ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest,
% 11.57/2.44 reflexivity, stricly_smaller_definition, totality, transitivity
% 11.57/2.44
% 11.57/2.44 Those formulas are unsatisfiable:
% 11.57/2.44 ---------------------------------
% 11.57/2.44
% 11.57/2.44 Begin of proof
% 11.57/2.44 |
% 11.57/2.44 | ALPHA: (function-axioms) implies:
% 11.57/2.44 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.57/2.44 | (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 11.57/2.44 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.57/2.44 | (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0))
% 11.57/2.44 |
% 11.57/2.44 | DELTA: instantiating (l19_co) with fresh symbols all_45_0, all_45_1, all_45_2,
% 11.57/2.44 | all_45_3, all_45_4 gives:
% 11.57/2.44 | (3) ~ (all_45_0 = 0) & triple(all_45_4, all_45_3, all_45_2) = all_45_1 &
% 11.57/2.44 | check_cpq(all_45_1) = all_45_0 & $i(all_45_1) & $i(all_45_2) &
% 11.57/2.44 | $i(all_45_3) & $i(all_45_4) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 11.57/2.44 | ? [v3: $i] : (ok(v3) = 0 & triple(v0, v1, v2) = v3 & check_cpq(v3) = 0
% 11.57/2.44 | & succ_cpq(all_45_1, v3) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.57/2.44 |
% 11.57/2.44 | ALPHA: (3) implies:
% 11.57/2.44 | (4) ~ (all_45_0 = 0)
% 11.57/2.44 | (5) $i(all_45_4)
% 11.57/2.44 | (6) $i(all_45_3)
% 11.57/2.44 | (7) $i(all_45_2)
% 11.57/2.44 | (8) check_cpq(all_45_1) = all_45_0
% 11.57/2.45 | (9) triple(all_45_4, all_45_3, all_45_2) = all_45_1
% 11.57/2.45 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (ok(v3) = 0 &
% 11.57/2.45 | triple(v0, v1, v2) = v3 & check_cpq(v3) = 0 & succ_cpq(all_45_1, v3)
% 11.57/2.45 | = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.57/2.45 |
% 11.57/2.45 | DELTA: instantiating (10) with fresh symbols all_53_0, all_53_1, all_53_2,
% 11.57/2.45 | all_53_3 gives:
% 11.57/2.45 | (11) ok(all_53_0) = 0 & triple(all_53_3, all_53_2, all_53_1) = all_53_0 &
% 11.57/2.45 | check_cpq(all_53_0) = 0 & succ_cpq(all_45_1, all_53_0) = 0 &
% 11.57/2.45 | $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3)
% 11.57/2.45 |
% 11.57/2.45 | ALPHA: (11) implies:
% 11.57/2.45 | (12) $i(all_53_3)
% 11.57/2.45 | (13) $i(all_53_2)
% 11.57/2.45 | (14) $i(all_53_1)
% 11.57/2.45 | (15) succ_cpq(all_45_1, all_53_0) = 0
% 11.57/2.45 | (16) check_cpq(all_53_0) = 0
% 11.57/2.45 | (17) triple(all_53_3, all_53_2, all_53_1) = all_53_0
% 11.57/2.45 | (18) ok(all_53_0) = 0
% 11.57/2.45 |
% 11.57/2.45 | GROUND_INST: instantiating (l19_l20) with all_45_4, all_45_3, all_45_2,
% 11.57/2.45 | all_45_1, simplifying with (5), (6), (7), (9) gives:
% 11.57/2.45 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.57/2.45 | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_45_1, v3) = 0) | ~
% 11.57/2.45 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 11.57/2.45 | (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0)))) |
% 11.57/2.45 | (ok(all_45_1) = 0 & check_cpq(all_45_1) = 0)
% 11.57/2.45 |
% 11.57/2.45 | BETA: splitting (19) gives:
% 11.57/2.45 |
% 11.57/2.45 | Case 1:
% 11.57/2.45 | |
% 11.57/2.45 | | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.57/2.45 | | (triple(v0, v1, v2) = v3) | ~ (succ_cpq(all_45_1, v3) = 0) | ~
% 11.57/2.45 | | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 11.57/2.45 | | (ok(v3) = v4 & check_cpq(v3) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 11.57/2.45 | |
% 11.57/2.45 | | GROUND_INST: instantiating (20) with all_53_3, all_53_2, all_53_1, all_53_0,
% 11.57/2.45 | | simplifying with (12), (13), (14), (15), (17) gives:
% 11.57/2.45 | | (21) ? [v0: any] : ? [v1: any] : (ok(all_53_0) = v0 &
% 11.57/2.45 | | check_cpq(all_53_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 11.57/2.45 | |
% 11.57/2.45 | | DELTA: instantiating (21) with fresh symbols all_62_0, all_62_1 gives:
% 11.57/2.45 | | (22) ok(all_53_0) = all_62_1 & check_cpq(all_53_0) = all_62_0 & ( ~
% 11.57/2.45 | | (all_62_0 = 0) | ~ (all_62_1 = 0))
% 11.57/2.45 | |
% 11.57/2.45 | | ALPHA: (22) implies:
% 11.57/2.46 | | (23) check_cpq(all_53_0) = all_62_0
% 11.57/2.46 | | (24) ok(all_53_0) = all_62_1
% 11.57/2.46 | | (25) ~ (all_62_0 = 0) | ~ (all_62_1 = 0)
% 11.57/2.46 | |
% 11.57/2.46 | | GROUND_INST: instantiating (1) with 0, all_62_0, all_53_0, simplifying with
% 11.57/2.46 | | (16), (23) gives:
% 11.57/2.46 | | (26) all_62_0 = 0
% 11.57/2.46 | |
% 11.57/2.46 | | GROUND_INST: instantiating (2) with 0, all_62_1, all_53_0, simplifying with
% 11.57/2.46 | | (18), (24) gives:
% 11.57/2.46 | | (27) all_62_1 = 0
% 11.57/2.46 | |
% 11.57/2.46 | | BETA: splitting (25) gives:
% 11.57/2.46 | |
% 11.57/2.46 | | Case 1:
% 11.57/2.46 | | |
% 11.57/2.46 | | | (28) ~ (all_62_0 = 0)
% 11.57/2.46 | | |
% 11.57/2.46 | | | REDUCE: (26), (28) imply:
% 11.57/2.46 | | | (29) $false
% 11.57/2.46 | | |
% 11.57/2.46 | | | CLOSE: (29) is inconsistent.
% 11.57/2.46 | | |
% 11.57/2.46 | | Case 2:
% 11.57/2.46 | | |
% 11.57/2.46 | | | (30) ~ (all_62_1 = 0)
% 11.57/2.46 | | |
% 11.57/2.46 | | | REDUCE: (27), (30) imply:
% 11.57/2.46 | | | (31) $false
% 11.57/2.46 | | |
% 11.57/2.46 | | | CLOSE: (31) is inconsistent.
% 11.57/2.46 | | |
% 11.57/2.46 | | End of split
% 11.57/2.46 | |
% 11.57/2.46 | Case 2:
% 11.57/2.46 | |
% 11.57/2.46 | | (32) ok(all_45_1) = 0 & check_cpq(all_45_1) = 0
% 11.57/2.46 | |
% 11.57/2.46 | | ALPHA: (32) implies:
% 11.57/2.46 | | (33) check_cpq(all_45_1) = 0
% 11.57/2.46 | |
% 11.57/2.46 | | GROUND_INST: instantiating (1) with all_45_0, 0, all_45_1, simplifying with
% 11.57/2.46 | | (8), (33) gives:
% 11.57/2.46 | | (34) all_45_0 = 0
% 11.57/2.46 | |
% 11.57/2.46 | | REDUCE: (4), (34) imply:
% 11.57/2.46 | | (35) $false
% 11.57/2.46 | |
% 11.57/2.46 | | CLOSE: (35) is inconsistent.
% 11.57/2.46 | |
% 11.57/2.46 | End of split
% 11.57/2.46 |
% 11.57/2.46 End of proof
% 11.57/2.46 % SZS output end Proof for theBenchmark
% 11.57/2.46
% 11.57/2.46 1799ms
%------------------------------------------------------------------------------