TSTP Solution File: SWV371+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV371+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 : n014.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 22:56:03 EDT 2023
% Result : Theorem 12.40s 2.39s
% Output : Proof 14.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV371+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 : n014.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 02:57:15 EDT 2023
% 0.13/0.35 % 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.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.91/1.23 Prover 1: Preprocessing ...
% 3.91/1.23 Prover 4: Preprocessing ...
% 4.25/1.26 Prover 6: Preprocessing ...
% 4.25/1.26 Prover 5: Preprocessing ...
% 4.25/1.26 Prover 2: Preprocessing ...
% 4.25/1.26 Prover 3: Preprocessing ...
% 4.25/1.28 Prover 0: Preprocessing ...
% 9.22/2.04 Prover 1: Warning: ignoring some quantifiers
% 9.22/2.12 Prover 1: Constructing countermodel ...
% 9.22/2.14 Prover 6: Proving ...
% 9.22/2.14 Prover 5: Proving ...
% 9.22/2.16 Prover 3: Warning: ignoring some quantifiers
% 10.55/2.20 Prover 3: Constructing countermodel ...
% 11.27/2.24 Prover 2: Proving ...
% 11.27/2.27 Prover 4: Constructing countermodel ...
% 11.70/2.29 Prover 0: Proving ...
% 12.40/2.39 Prover 3: proved (1757ms)
% 12.40/2.39
% 12.40/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.40/2.39
% 12.40/2.39 Prover 0: stopped
% 12.40/2.39 Prover 5: stopped
% 12.40/2.39 Prover 6: stopped
% 12.40/2.39 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.40/2.39 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.40/2.39 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.40/2.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.40/2.39 Prover 2: stopped
% 12.70/2.41 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.87/2.47 Prover 7: Preprocessing ...
% 12.87/2.49 Prover 8: Preprocessing ...
% 12.87/2.50 Prover 10: Preprocessing ...
% 12.87/2.50 Prover 11: Preprocessing ...
% 12.87/2.51 Prover 13: Preprocessing ...
% 12.87/2.52 Prover 1: Found proof (size 35)
% 12.87/2.52 Prover 1: proved (1888ms)
% 13.50/2.52 Prover 4: stopped
% 13.50/2.53 Prover 7: stopped
% 13.50/2.54 Prover 10: stopped
% 13.50/2.57 Prover 11: stopped
% 13.92/2.59 Prover 13: stopped
% 13.92/2.65 Prover 8: Warning: ignoring some quantifiers
% 14.40/2.68 Prover 8: Constructing countermodel ...
% 14.40/2.69 Prover 8: stopped
% 14.40/2.69
% 14.40/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.40/2.69
% 14.40/2.69 % SZS output start Proof for theBenchmark
% 14.40/2.70 Assumptions after simplification:
% 14.40/2.70 ---------------------------------
% 14.40/2.70
% 14.40/2.70 (ax58)
% 14.40/2.72 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pi_sharp_find_min(v0,
% 14.40/2.72 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 14.40/2.72 (issmallestelement_pq(v0, v1) = v4 & contains_pq(v0, v1) = v3 & ( ~ (v4 = 0)
% 14.40/2.72 | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 14.40/2.72 (pi_sharp_find_min(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 14.40/2.72 (issmallestelement_pq(v0, v1) = 0 & contains_pq(v0, v1) = 0))
% 14.40/2.72
% 14.40/2.72 (l7_co)
% 14.40/2.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 14.40/2.73 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & phi(v4) = 0 &
% 14.40/2.73 pi_sharp_find_min(v5, v6) = v7 & i(v3) = v5 & findmin_cpq_res(v3) = v6 &
% 14.40/2.73 triple(v0, v1, v2) = v3 & findmin_cpq_eff(v3) = v4 & $i(v6) & $i(v5) &
% 14.40/2.73 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 14.40/2.73
% 14.40/2.73 (l7_l8)
% 14.40/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.40/2.73 $i] : ! [v6: int] : (v6 = 0 | ~ (i(v3) = v4) | ~ (findmin_cpq_res(v3) =
% 14.40/2.73 v5) | ~ (triple(v0, v1, v2) = v3) | ~ (contains_pq(v4, v5) = v6) | ~
% 14.40/2.73 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 14.40/2.73 phi(v7) = v8 & findmin_cpq_eff(v3) = v7 & $i(v7)))
% 14.40/2.73
% 14.40/2.73 (l7_lX)
% 14.40/2.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.40/2.73 $i] : ! [v6: int] : (v6 = 0 | ~ (i(v3) = v4) | ~ (findmin_cpq_res(v3) =
% 14.40/2.73 v5) | ~ (triple(v0, v1, v2) = v3) | ~ (issmallestelement_pq(v4, v5) =
% 14.40/2.73 v6) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: $i] : ? [v8: int] : ( ~
% 14.40/2.73 (v8 = 0) & phi(v7) = v8 & findmin_cpq_eff(v3) = v7 & $i(v7)))
% 14.40/2.73
% 14.40/2.73 (function-axioms)
% 14.40/2.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 14.40/2.74 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 14.40/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.40/2.74 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 14.40/2.74 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.74 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) &
% 14.40/2.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.40/2.74 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~
% 14.40/2.74 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.74 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0:
% 14.40/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.40/2.74 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) =
% 14.40/2.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.40/2.74 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] :
% 14.40/2.74 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) =
% 14.40/2.74 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.74 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i]
% 14.40/2.74 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2)
% 14.40/2.74 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.40/2.74 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~
% 14.40/2.74 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 14.40/2.74 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.40/2.74 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 14.40/2.74 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.40/2.74 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 14.40/2.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.40/2.74 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 14.40/2.74 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.40/2.74 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 14.40/2.74 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.74 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 14.40/2.74 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 14.40/2.74 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.40/2.74 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~
% 14.40/2.74 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~
% 14.40/2.74 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~
% 14.40/2.74 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~
% 14.40/2.74 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.40/2.74 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) =
% 14.40/2.74 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.40/2.74 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~
% 14.40/2.74 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.74 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] :
% 14.40/2.74 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) =
% 14.40/2.74 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.40/2.74 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 14.40/2.74 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.40/2.74 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 14.40/2.74 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 14.40/2.74 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] :
% 14.40/2.74 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) =
% 14.40/2.74 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~
% 14.40/2.74 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 14.40/2.74 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.40/2.74 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2)
% 14.40/2.74 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.40/2.74 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 14.40/2.74 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 14.40/2.74 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.40/2.74 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 14.40/2.74 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.40/2.74 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 14.40/2.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 14.40/2.74 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.40/2.74 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 14.40/2.74 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.40/2.74 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 14.40/2.74 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.40/2.74 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 14.40/2.74
% 14.40/2.74 Further assumptions not needed in the proof:
% 14.40/2.74 --------------------------------------------
% 14.40/2.74 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22,
% 14.40/2.74 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35,
% 14.40/2.74 ax36, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48,
% 14.40/2.74 ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax59, ax6, ax60, ax61,
% 14.40/2.74 ax62, ax7, ax8, ax9, bottom_smallest, reflexivity, stricly_smaller_definition,
% 14.40/2.74 totality, transitivity
% 14.40/2.74
% 14.40/2.74 Those formulas are unsatisfiable:
% 14.40/2.74 ---------------------------------
% 14.40/2.74
% 14.40/2.74 Begin of proof
% 14.40/2.75 |
% 14.40/2.75 | ALPHA: (ax58) implies:
% 14.40/2.75 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 14.40/2.75 | (pi_sharp_find_min(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 14.40/2.75 | any] : ? [v4: any] : (issmallestelement_pq(v0, v1) = v4 &
% 14.40/2.75 | contains_pq(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 14.40/2.75 |
% 14.40/2.75 | ALPHA: (function-axioms) implies:
% 14.40/2.75 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.40/2.75 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0))
% 14.40/2.75 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.40/2.75 | (v1 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0))
% 14.40/2.75 |
% 14.40/2.75 | DELTA: instantiating (l7_co) with fresh symbols all_68_0, all_68_1, all_68_2,
% 14.40/2.75 | all_68_3, all_68_4, all_68_5, all_68_6, all_68_7 gives:
% 14.40/2.75 | (4) ~ (all_68_0 = 0) & phi(all_68_3) = 0 & pi_sharp_find_min(all_68_2,
% 14.40/2.75 | all_68_1) = all_68_0 & i(all_68_4) = all_68_2 &
% 14.40/2.75 | findmin_cpq_res(all_68_4) = all_68_1 & triple(all_68_7, all_68_6,
% 14.40/2.75 | all_68_5) = all_68_4 & findmin_cpq_eff(all_68_4) = all_68_3 &
% 14.40/2.75 | $i(all_68_1) & $i(all_68_2) & $i(all_68_3) & $i(all_68_4) &
% 14.40/2.75 | $i(all_68_5) & $i(all_68_6) & $i(all_68_7)
% 14.40/2.75 |
% 14.40/2.75 | ALPHA: (4) implies:
% 14.40/2.75 | (5) ~ (all_68_0 = 0)
% 14.40/2.75 | (6) $i(all_68_7)
% 14.40/2.75 | (7) $i(all_68_6)
% 14.40/2.75 | (8) $i(all_68_5)
% 14.40/2.75 | (9) $i(all_68_2)
% 14.40/2.75 | (10) $i(all_68_1)
% 14.40/2.75 | (11) findmin_cpq_eff(all_68_4) = all_68_3
% 14.40/2.75 | (12) triple(all_68_7, all_68_6, all_68_5) = all_68_4
% 14.40/2.75 | (13) findmin_cpq_res(all_68_4) = all_68_1
% 14.40/2.75 | (14) i(all_68_4) = all_68_2
% 14.40/2.75 | (15) pi_sharp_find_min(all_68_2, all_68_1) = all_68_0
% 14.40/2.75 | (16) phi(all_68_3) = 0
% 14.40/2.75 |
% 14.40/2.75 | GROUND_INST: instantiating (1) with all_68_2, all_68_1, all_68_0, simplifying
% 14.40/2.75 | with (9), (10), (15) gives:
% 14.40/2.75 | (17) all_68_0 = 0 | ? [v0: any] : ? [v1: any] :
% 14.40/2.75 | (issmallestelement_pq(all_68_2, all_68_1) = v1 & contains_pq(all_68_2,
% 14.40/2.75 | all_68_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.40/2.75 |
% 14.40/2.75 | BETA: splitting (17) gives:
% 14.40/2.75 |
% 14.40/2.75 | Case 1:
% 14.40/2.75 | |
% 14.40/2.75 | | (18) all_68_0 = 0
% 14.40/2.75 | |
% 14.40/2.75 | | REDUCE: (5), (18) imply:
% 14.40/2.75 | | (19) $false
% 14.40/2.76 | |
% 14.40/2.76 | | CLOSE: (19) is inconsistent.
% 14.40/2.76 | |
% 14.40/2.76 | Case 2:
% 14.40/2.76 | |
% 14.40/2.76 | | (20) ? [v0: any] : ? [v1: any] : (issmallestelement_pq(all_68_2,
% 14.40/2.76 | | all_68_1) = v1 & contains_pq(all_68_2, all_68_1) = v0 & ( ~ (v1
% 14.40/2.76 | | = 0) | ~ (v0 = 0)))
% 14.40/2.76 | |
% 14.40/2.76 | | DELTA: instantiating (20) with fresh symbols all_87_0, all_87_1 gives:
% 14.40/2.76 | | (21) issmallestelement_pq(all_68_2, all_68_1) = all_87_0 &
% 14.40/2.76 | | contains_pq(all_68_2, all_68_1) = all_87_1 & ( ~ (all_87_0 = 0) | ~
% 14.40/2.76 | | (all_87_1 = 0))
% 14.40/2.76 | |
% 14.40/2.76 | | ALPHA: (21) implies:
% 14.40/2.76 | | (22) contains_pq(all_68_2, all_68_1) = all_87_1
% 14.40/2.76 | | (23) issmallestelement_pq(all_68_2, all_68_1) = all_87_0
% 14.40/2.76 | | (24) ~ (all_87_0 = 0) | ~ (all_87_1 = 0)
% 14.40/2.76 | |
% 14.40/2.76 | | GROUND_INST: instantiating (l7_l8) with all_68_7, all_68_6, all_68_5,
% 14.40/2.76 | | all_68_4, all_68_2, all_68_1, all_87_1, simplifying with (6),
% 14.40/2.76 | | (7), (8), (12), (13), (14), (22) gives:
% 14.40/2.76 | | (25) all_87_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) =
% 14.40/2.76 | | v1 & findmin_cpq_eff(all_68_4) = v0 & $i(v0))
% 14.40/2.76 | |
% 14.40/2.76 | | GROUND_INST: instantiating (l7_lX) with all_68_7, all_68_6, all_68_5,
% 14.40/2.76 | | all_68_4, all_68_2, all_68_1, all_87_0, simplifying with (6),
% 14.40/2.76 | | (7), (8), (12), (13), (14), (23) gives:
% 14.40/2.76 | | (26) all_87_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) =
% 14.40/2.76 | | v1 & findmin_cpq_eff(all_68_4) = v0 & $i(v0))
% 14.40/2.76 | |
% 14.40/2.76 | | BETA: splitting (26) gives:
% 14.40/2.76 | |
% 14.40/2.76 | | Case 1:
% 14.40/2.76 | | |
% 14.40/2.76 | | | (27) all_87_0 = 0
% 14.40/2.76 | | |
% 14.40/2.76 | | | BETA: splitting (24) gives:
% 14.40/2.76 | | |
% 14.40/2.76 | | | Case 1:
% 14.40/2.76 | | | |
% 14.40/2.76 | | | | (28) ~ (all_87_0 = 0)
% 14.40/2.76 | | | |
% 14.40/2.76 | | | | REDUCE: (27), (28) imply:
% 14.40/2.76 | | | | (29) $false
% 14.40/2.76 | | | |
% 14.40/2.76 | | | | CLOSE: (29) is inconsistent.
% 14.40/2.76 | | | |
% 14.40/2.76 | | | Case 2:
% 14.40/2.76 | | | |
% 14.40/2.76 | | | | (30) ~ (all_87_1 = 0)
% 14.40/2.76 | | | |
% 14.40/2.76 | | | | BETA: splitting (25) gives:
% 14.40/2.76 | | | |
% 14.40/2.76 | | | | Case 1:
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | (31) all_87_1 = 0
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | REDUCE: (30), (31) imply:
% 14.40/2.76 | | | | | (32) $false
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | CLOSE: (32) is inconsistent.
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | Case 2:
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) = v1 &
% 14.40/2.76 | | | | | findmin_cpq_eff(all_68_4) = v0 & $i(v0))
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | DELTA: instantiating (33) with fresh symbols all_108_0, all_108_1
% 14.40/2.76 | | | | | gives:
% 14.40/2.76 | | | | | (34) ~ (all_108_0 = 0) & phi(all_108_1) = all_108_0 &
% 14.40/2.76 | | | | | findmin_cpq_eff(all_68_4) = all_108_1 & $i(all_108_1)
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | ALPHA: (34) implies:
% 14.40/2.76 | | | | | (35) ~ (all_108_0 = 0)
% 14.40/2.76 | | | | | (36) findmin_cpq_eff(all_68_4) = all_108_1
% 14.40/2.76 | | | | | (37) phi(all_108_1) = all_108_0
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | GROUND_INST: instantiating (2) with all_68_3, all_108_1, all_68_4,
% 14.40/2.76 | | | | | simplifying with (11), (36) gives:
% 14.40/2.76 | | | | | (38) all_108_1 = all_68_3
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | REDUCE: (37), (38) imply:
% 14.40/2.76 | | | | | (39) phi(all_68_3) = all_108_0
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | GROUND_INST: instantiating (3) with 0, all_108_0, all_68_3,
% 14.40/2.76 | | | | | simplifying with (16), (39) gives:
% 14.40/2.76 | | | | | (40) all_108_0 = 0
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | REDUCE: (35), (40) imply:
% 14.40/2.76 | | | | | (41) $false
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | | CLOSE: (41) is inconsistent.
% 14.40/2.76 | | | | |
% 14.40/2.76 | | | | End of split
% 14.40/2.76 | | | |
% 14.40/2.76 | | | End of split
% 14.40/2.76 | | |
% 14.40/2.76 | | Case 2:
% 14.40/2.76 | | |
% 14.40/2.77 | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & phi(v0) = v1 &
% 14.40/2.77 | | | findmin_cpq_eff(all_68_4) = v0 & $i(v0))
% 14.40/2.77 | | |
% 14.40/2.77 | | | DELTA: instantiating (42) with fresh symbols all_100_0, all_100_1 gives:
% 14.40/2.77 | | | (43) ~ (all_100_0 = 0) & phi(all_100_1) = all_100_0 &
% 14.40/2.77 | | | findmin_cpq_eff(all_68_4) = all_100_1 & $i(all_100_1)
% 14.40/2.77 | | |
% 14.40/2.77 | | | ALPHA: (43) implies:
% 14.40/2.77 | | | (44) ~ (all_100_0 = 0)
% 14.40/2.77 | | | (45) findmin_cpq_eff(all_68_4) = all_100_1
% 14.40/2.77 | | | (46) phi(all_100_1) = all_100_0
% 14.40/2.77 | | |
% 14.40/2.77 | | | GROUND_INST: instantiating (2) with all_68_3, all_100_1, all_68_4,
% 14.40/2.77 | | | simplifying with (11), (45) gives:
% 14.40/2.77 | | | (47) all_100_1 = all_68_3
% 14.40/2.77 | | |
% 14.40/2.77 | | | REDUCE: (46), (47) imply:
% 14.40/2.77 | | | (48) phi(all_68_3) = all_100_0
% 14.40/2.77 | | |
% 14.40/2.77 | | | GROUND_INST: instantiating (3) with 0, all_100_0, all_68_3, simplifying
% 14.40/2.77 | | | with (16), (48) gives:
% 14.40/2.77 | | | (49) all_100_0 = 0
% 14.40/2.77 | | |
% 14.40/2.77 | | | REDUCE: (44), (49) imply:
% 14.40/2.77 | | | (50) $false
% 14.40/2.77 | | |
% 14.40/2.77 | | | CLOSE: (50) is inconsistent.
% 14.40/2.77 | | |
% 14.40/2.77 | | End of split
% 14.40/2.77 | |
% 14.40/2.77 | End of split
% 14.40/2.77 |
% 14.40/2.77 End of proof
% 14.40/2.77 % SZS output end Proof for theBenchmark
% 14.40/2.77
% 14.40/2.77 2159ms
%------------------------------------------------------------------------------