TSTP Solution File: SWV405+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV405+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 : n019.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 22:56:12 EDT 2023
% Result : Theorem 9.35s 2.07s
% Output : Proof 11.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV405+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n019.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 07:03:27 EDT 2023
% 0.13/0.34 % 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.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.37/1.18 Prover 4: Preprocessing ...
% 3.37/1.19 Prover 1: Preprocessing ...
% 3.37/1.22 Prover 2: Preprocessing ...
% 3.37/1.22 Prover 5: Preprocessing ...
% 3.37/1.22 Prover 0: Preprocessing ...
% 3.37/1.22 Prover 6: Preprocessing ...
% 3.37/1.22 Prover 3: Preprocessing ...
% 7.54/1.83 Prover 1: Warning: ignoring some quantifiers
% 7.54/1.84 Prover 3: Warning: ignoring some quantifiers
% 8.21/1.86 Prover 6: Proving ...
% 8.21/1.87 Prover 5: Proving ...
% 8.21/1.89 Prover 3: Constructing countermodel ...
% 8.51/1.89 Prover 1: Constructing countermodel ...
% 8.51/1.90 Prover 4: Constructing countermodel ...
% 8.85/1.94 Prover 0: Proving ...
% 8.91/1.97 Prover 2: Proving ...
% 9.35/2.06 Prover 3: proved (1435ms)
% 9.35/2.06
% 9.35/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.35/2.07
% 9.35/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.35/2.07 Prover 0: stopped
% 9.35/2.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.35/2.08 Prover 6: stopped
% 9.35/2.10 Prover 2: stopped
% 9.35/2.10 Prover 5: stopped
% 9.35/2.11 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.35/2.11 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.35/2.11 Prover 1: Found proof (size 17)
% 9.35/2.11 Prover 1: proved (1487ms)
% 9.35/2.11 Prover 4: Found proof (size 15)
% 9.35/2.11 Prover 4: proved (1474ms)
% 9.35/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.35/2.12 Prover 8: Preprocessing ...
% 9.35/2.16 Prover 11: Preprocessing ...
% 9.35/2.16 Prover 13: Preprocessing ...
% 9.35/2.16 Prover 10: Preprocessing ...
% 9.35/2.16 Prover 7: Preprocessing ...
% 9.99/2.22 Prover 7: stopped
% 9.99/2.23 Prover 10: stopped
% 9.99/2.23 Prover 11: stopped
% 9.99/2.26 Prover 13: stopped
% 9.99/2.28 Prover 8: Warning: ignoring some quantifiers
% 9.99/2.30 Prover 8: Constructing countermodel ...
% 11.25/2.31 Prover 8: stopped
% 11.25/2.31
% 11.25/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.25/2.31
% 11.25/2.31 % SZS output start Proof for theBenchmark
% 11.25/2.31 Assumptions after simplification:
% 11.25/2.31 ---------------------------------
% 11.25/2.31
% 11.25/2.31 (ax22)
% 11.25/2.34 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ( ~ (pair_in_list(create_slb, v0,
% 11.25/2.34 v1) = 0) | ~ $i(v1) | ~ $i(v0))
% 11.25/2.34
% 11.25/2.34 (ax36)
% 11.25/2.34 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0,
% 11.25/2.34 create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | check_cpq(v2) = 0)
% 11.25/2.34
% 11.25/2.34 (l41_co)
% 11.25/2.34 $i(create_slb) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] :
% 11.25/2.34 (triple(v0, create_slb, v1) = v2 & check_cpq(v2) = v3 & $i(v2) & $i(v1) &
% 11.25/2.34 $i(v0) & ((v3 = 0 & ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0)
% 11.25/2.34 & pair_in_list(create_slb, v4, v5) = 0 & less_than(v5, v4) = v6 &
% 11.25/2.34 $i(v5) & $i(v4))) | ( ~ (v3 = 0) & ! [v4: $i] : ! [v5: $i] : ( ~
% 11.25/2.34 (pair_in_list(create_slb, v4, v5) = 0) | ~ $i(v5) | ~ $i(v4) |
% 11.25/2.34 less_than(v5, v4) = 0))))
% 11.25/2.34
% 11.25/2.34 (function-axioms)
% 11.44/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 11.44/2.35 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 11.44/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.44/2.35 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 11.44/2.35 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.44/2.35 ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2)
% 11.44/2.35 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 11.44/2.35 | ~ (insert_pqp(v3, v2) = v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0:
% 11.44/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.44/2.35 : (v1 = v0 | ~ (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0))
% 11.44/2.35 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.44/2.35 (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : !
% 11.44/2.35 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1)
% 11.44/2.35 | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.44/2.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 11.44/2.35 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 11.44/2.35 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 11.44/2.35 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 11.44/2.35 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 11.44/2.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 11.44/2.35 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 11.44/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.44/2.35 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 11.44/2.35 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.44/2.35 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 11.44/2.35 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 11.44/2.35 (insert_slb(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.44/2.35 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.44/2.35 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 11.44/2.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.44/2.35 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 11.44/2.35 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.44/2.35 (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0:
% 11.44/2.35 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) |
% 11.44/2.35 ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.44/2.35 (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & !
% 11.44/2.35 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 11.44/2.35 | ~ (ok(v2) = v1) | ~ (ok(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.44/2.35 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) |
% 11.44/2.35 ~ (check_cpq(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.44/2.35 | ~ (removemin_cpq_eff(v2) = v1) | ~ (removemin_cpq_eff(v2) = v0)) & !
% 11.44/2.36 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) =
% 11.44/2.36 v1) | ~ (findmin_cpq_eff(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 11.44/2.36 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isnonempty_slb(v2) =
% 11.44/2.36 v1) | ~ (isnonempty_slb(v2) = v0))
% 11.44/2.36
% 11.44/2.36 Further assumptions not needed in the proof:
% 11.44/2.36 --------------------------------------------
% 11.44/2.36 ax18, ax19, ax20, ax21, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31,
% 11.44/2.36 ax32, ax33, ax34, ax35, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45,
% 11.44/2.36 ax46, ax47, ax48, ax49, ax50, ax51, ax52, ax53, bottom_smallest, reflexivity,
% 11.44/2.36 stricly_smaller_definition, totality, transitivity
% 11.44/2.36
% 11.44/2.36 Those formulas are unsatisfiable:
% 11.44/2.36 ---------------------------------
% 11.44/2.36
% 11.44/2.36 Begin of proof
% 11.44/2.36 |
% 11.44/2.36 | ALPHA: (ax22) implies:
% 11.44/2.36 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (pair_in_list(create_slb, v0, v1) = 0)
% 11.44/2.36 | | ~ $i(v1) | ~ $i(v0))
% 11.44/2.36 |
% 11.44/2.36 | ALPHA: (ax36) implies:
% 11.44/2.36 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb,
% 11.44/2.36 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | check_cpq(v2) = 0)
% 11.44/2.36 |
% 11.44/2.36 | ALPHA: (l41_co) implies:
% 11.44/2.36 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (triple(v0,
% 11.44/2.36 | create_slb, v1) = v2 & check_cpq(v2) = v3 & $i(v2) & $i(v1) &
% 11.44/2.36 | $i(v0) & ((v3 = 0 & ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~
% 11.44/2.36 | (v6 = 0) & pair_in_list(create_slb, v4, v5) = 0 & less_than(v5,
% 11.44/2.36 | v4) = v6 & $i(v5) & $i(v4))) | ( ~ (v3 = 0) & ! [v4: $i] :
% 11.44/2.36 | ! [v5: $i] : ( ~ (pair_in_list(create_slb, v4, v5) = 0) | ~
% 11.44/2.36 | $i(v5) | ~ $i(v4) | less_than(v5, v4) = 0))))
% 11.44/2.36 |
% 11.44/2.36 | ALPHA: (function-axioms) implies:
% 11.44/2.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.44/2.36 | (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0))
% 11.44/2.36 |
% 11.44/2.36 | DELTA: instantiating (3) with fresh symbols all_44_0, all_44_1, all_44_2,
% 11.44/2.36 | all_44_3 gives:
% 11.44/2.36 | (5) triple(all_44_3, create_slb, all_44_2) = all_44_1 & check_cpq(all_44_1)
% 11.44/2.36 | = all_44_0 & $i(all_44_1) & $i(all_44_2) & $i(all_44_3) & ((all_44_0 =
% 11.44/2.36 | 0 & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 11.44/2.36 | pair_in_list(create_slb, v0, v1) = 0 & less_than(v1, v0) = v2 &
% 11.44/2.36 | $i(v1) & $i(v0))) | ( ~ (all_44_0 = 0) & ! [v0: $i] : ! [v1:
% 11.44/2.36 | $i] : ( ~ (pair_in_list(create_slb, v0, v1) = 0) | ~ $i(v1) | ~
% 11.44/2.36 | $i(v0) | less_than(v1, v0) = 0)))
% 11.44/2.36 |
% 11.44/2.36 | ALPHA: (5) implies:
% 11.44/2.36 | (6) $i(all_44_3)
% 11.44/2.36 | (7) $i(all_44_2)
% 11.44/2.36 | (8) check_cpq(all_44_1) = all_44_0
% 11.44/2.36 | (9) triple(all_44_3, create_slb, all_44_2) = all_44_1
% 11.44/2.37 | (10) (all_44_0 = 0 & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 =
% 11.44/2.37 | 0) & pair_in_list(create_slb, v0, v1) = 0 & less_than(v1, v0) =
% 11.44/2.37 | v2 & $i(v1) & $i(v0))) | ( ~ (all_44_0 = 0) & ! [v0: $i] : !
% 11.44/2.37 | [v1: $i] : ( ~ (pair_in_list(create_slb, v0, v1) = 0) | ~ $i(v1) |
% 11.44/2.37 | ~ $i(v0) | less_than(v1, v0) = 0))
% 11.44/2.37 |
% 11.44/2.37 | GROUND_INST: instantiating (2) with all_44_3, all_44_2, all_44_1, simplifying
% 11.44/2.37 | with (6), (7), (9) gives:
% 11.44/2.37 | (11) check_cpq(all_44_1) = 0
% 11.44/2.37 |
% 11.44/2.37 | GROUND_INST: instantiating (4) with all_44_0, 0, all_44_1, simplifying with
% 11.44/2.37 | (8), (11) gives:
% 11.44/2.37 | (12) all_44_0 = 0
% 11.44/2.37 |
% 11.44/2.37 | BETA: splitting (10) gives:
% 11.44/2.37 |
% 11.44/2.37 | Case 1:
% 11.44/2.37 | |
% 11.44/2.37 | | (13) all_44_0 = 0 & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 =
% 11.44/2.37 | | 0) & pair_in_list(create_slb, v0, v1) = 0 & less_than(v1, v0) =
% 11.44/2.37 | | v2 & $i(v1) & $i(v0))
% 11.44/2.37 | |
% 11.44/2.37 | | ALPHA: (13) implies:
% 11.44/2.37 | | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 11.44/2.37 | | pair_in_list(create_slb, v0, v1) = 0 & less_than(v1, v0) = v2 &
% 11.44/2.37 | | $i(v1) & $i(v0))
% 11.44/2.37 | |
% 11.44/2.37 | | DELTA: instantiating (14) with fresh symbols all_68_0, all_68_1, all_68_2
% 11.44/2.37 | | gives:
% 11.44/2.37 | | (15) ~ (all_68_0 = 0) & pair_in_list(create_slb, all_68_2, all_68_1) = 0
% 11.44/2.37 | | & less_than(all_68_1, all_68_2) = all_68_0 & $i(all_68_1) &
% 11.44/2.37 | | $i(all_68_2)
% 11.44/2.37 | |
% 11.44/2.37 | | ALPHA: (15) implies:
% 11.44/2.37 | | (16) $i(all_68_2)
% 11.44/2.37 | | (17) $i(all_68_1)
% 11.44/2.37 | | (18) pair_in_list(create_slb, all_68_2, all_68_1) = 0
% 11.44/2.37 | |
% 11.44/2.37 | | GROUND_INST: instantiating (1) with all_68_2, all_68_1, simplifying with
% 11.44/2.37 | | (16), (17), (18) gives:
% 11.44/2.37 | | (19) $false
% 11.44/2.37 | |
% 11.44/2.37 | | CLOSE: (19) is inconsistent.
% 11.44/2.37 | |
% 11.44/2.37 | Case 2:
% 11.44/2.37 | |
% 11.44/2.37 | | (20) ~ (all_44_0 = 0) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.44/2.37 | | (pair_in_list(create_slb, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 11.44/2.37 | | less_than(v1, v0) = 0)
% 11.44/2.37 | |
% 11.44/2.37 | | ALPHA: (20) implies:
% 11.44/2.37 | | (21) ~ (all_44_0 = 0)
% 11.44/2.37 | |
% 11.44/2.37 | | REDUCE: (12), (21) imply:
% 11.44/2.37 | | (22) $false
% 11.44/2.37 | |
% 11.44/2.37 | | CLOSE: (22) is inconsistent.
% 11.44/2.37 | |
% 11.44/2.37 | End of split
% 11.44/2.37 |
% 11.44/2.37 End of proof
% 11.44/2.37 % SZS output end Proof for theBenchmark
% 11.44/2.37
% 11.44/2.37 1765ms
%------------------------------------------------------------------------------