TSTP Solution File: SWV416+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV416+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 : n015.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 22:56:15 EDT 2023
% Result : Theorem 11.83s 2.38s
% Output : Proof 15.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV416+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 03:25:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.96/1.22 Prover 4: Preprocessing ...
% 3.96/1.22 Prover 1: Preprocessing ...
% 3.96/1.26 Prover 5: Preprocessing ...
% 3.96/1.26 Prover 2: Preprocessing ...
% 3.96/1.26 Prover 6: Preprocessing ...
% 3.96/1.26 Prover 3: Preprocessing ...
% 3.96/1.26 Prover 0: Preprocessing ...
% 9.29/1.99 Prover 1: Warning: ignoring some quantifiers
% 9.29/2.07 Prover 3: Warning: ignoring some quantifiers
% 9.29/2.07 Prover 6: Proving ...
% 9.29/2.07 Prover 5: Proving ...
% 9.29/2.14 Prover 3: Constructing countermodel ...
% 9.29/2.15 Prover 1: Constructing countermodel ...
% 10.52/2.19 Prover 2: Proving ...
% 11.07/2.27 Prover 4: Constructing countermodel ...
% 11.07/2.28 Prover 0: Proving ...
% 11.83/2.38 Prover 5: proved (1743ms)
% 11.83/2.38
% 11.83/2.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.83/2.38
% 11.83/2.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.83/2.38 Prover 3: stopped
% 11.83/2.39 Prover 0: stopped
% 12.30/2.41 Prover 6: stopped
% 12.30/2.41 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.30/2.41 Prover 2: stopped
% 12.30/2.42 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.30/2.42 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.30/2.42 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.30/2.44 Prover 7: Preprocessing ...
% 12.81/2.50 Prover 8: Preprocessing ...
% 12.81/2.52 Prover 11: Preprocessing ...
% 12.81/2.53 Prover 10: Preprocessing ...
% 12.81/2.54 Prover 13: Preprocessing ...
% 14.03/2.65 Prover 7: Warning: ignoring some quantifiers
% 14.03/2.66 Prover 1: Found proof (size 32)
% 14.03/2.67 Prover 1: proved (2042ms)
% 14.03/2.67 Prover 4: stopped
% 14.03/2.68 Prover 13: stopped
% 14.03/2.69 Prover 7: Constructing countermodel ...
% 14.03/2.72 Prover 7: stopped
% 14.03/2.72 Prover 10: Warning: ignoring some quantifiers
% 14.79/2.74 Prover 8: Warning: ignoring some quantifiers
% 14.79/2.74 Prover 10: Constructing countermodel ...
% 14.79/2.76 Prover 10: stopped
% 14.79/2.77 Prover 8: Constructing countermodel ...
% 14.79/2.78 Prover 8: stopped
% 15.17/2.82 Prover 11: Constructing countermodel ...
% 15.17/2.84 Prover 11: stopped
% 15.17/2.85
% 15.17/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.17/2.85
% 15.17/2.85 % SZS output start Proof for theBenchmark
% 15.17/2.86 Assumptions after simplification:
% 15.17/2.86 ---------------------------------
% 15.17/2.86
% 15.17/2.87 (ax56)
% 15.17/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (pi_sharp_remove(v0,
% 15.17/2.90 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 15.17/2.90 contains_pq(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 15.17/2.90 (pi_sharp_remove(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | contains_pq(v0, v1)
% 15.17/2.90 = 0)
% 15.17/2.90
% 15.17/2.90 (ax57)
% 15.17/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.17/2.90 (pi_sharp_remove(v2, v1) = v3) | ~ (i(v0) = v2) | ~ $i(v1) | ~ $i(v0) |
% 15.17/2.90 ? [v4: int] : ( ~ (v4 = 0) & pi_remove(v0, v1) = v4)) & ! [v0: $i] : !
% 15.17/2.90 [v1: $i] : ! [v2: $i] : ( ~ (pi_sharp_remove(v2, v1) = 0) | ~ (i(v0) = v2) |
% 15.17/2.90 ~ $i(v1) | ~ $i(v0) | pi_remove(v0, v1) = 0)
% 15.17/2.90
% 15.17/2.90 (co3)
% 15.17/2.90 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 15.17/2.90 $i] : ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (phi(v5) = 0
% 15.17/2.90 & pi_remove(v4, v3) = 0 & pi_sharp_remove(v6, v3) = v7 & i(v5) = v8 & i(v4)
% 15.17/2.90 = v6 & triple(v0, v1, v2) = v4 & remove_cpq(v4, v3) = v5 & remove_pq(v6, v3)
% 15.17/2.90 = v9 & $i(v9) & $i(v8) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 15.17/2.90 & $i(v0) & ( ~ (v9 = v8) | ~ (v7 = 0)))
% 15.17/2.90
% 15.17/2.90 (main3_li34)
% 15.17/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 15.17/2.90 $i] : ! [v6: $i] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~
% 15.17/2.90 (remove_pq(v5, v3) = v6) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 15.17/2.90 ? [v7: any] : ? [v8: $i] : ? [v9: $i] : (i(v8) = v9 & remove_cpq(v4, v3) =
% 15.17/2.90 v8 & contains_pq(v5, v3) = v7 & $i(v9) & $i(v8) & ( ~ (v7 = 0) | v9 =
% 15.17/2.90 v6)))
% 15.17/2.91
% 15.17/2.91 (function-axioms)
% 15.17/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 15.17/2.92 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 15.17/2.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.17/2.92 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 15.17/2.92 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.92 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) &
% 15.17/2.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 15.17/2.92 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~
% 15.17/2.92 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.92 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0:
% 15.17/2.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.17/2.92 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) =
% 15.17/2.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 15.17/2.92 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] :
% 15.17/2.92 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) =
% 15.17/2.92 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.92 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i]
% 15.17/2.92 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2)
% 15.17/2.92 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.17/2.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~
% 15.17/2.92 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 15.17/2.92 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.17/2.92 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 15.17/2.92 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.17/2.92 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 15.17/2.92 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 15.17/2.92 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 15.17/2.92 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.17/2.92 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 15.17/2.92 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.92 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 15.17/2.92 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 15.17/2.92 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 15.17/2.92 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~
% 15.17/2.92 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.17/2.92 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~
% 15.17/2.92 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.17/2.92 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~
% 15.17/2.92 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.17/2.92 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~
% 15.17/2.92 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 15.17/2.92 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) =
% 15.17/2.92 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.17/2.92 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~
% 15.17/2.92 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.92 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] :
% 15.17/2.92 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) =
% 15.17/2.92 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.92 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 15.17/2.92 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 15.17/2.92 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 15.17/2.92 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 15.17/2.92 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] :
% 15.17/2.92 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) =
% 15.17/2.92 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~
% 15.17/2.92 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.17/2.92 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 15.17/2.92 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2)
% 15.17/2.92 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 15.17/2.92 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 15.17/2.92 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 15.17/2.92 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.17/2.92 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 15.17/2.92 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.17/2.92 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 15.17/2.92 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 15.17/2.92 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 15.17/2.92 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 15.17/2.92 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.17/2.92 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 15.17/2.92 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 15.17/2.92 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 15.17/2.92
% 15.17/2.92 Further assumptions not needed in the proof:
% 15.17/2.92 --------------------------------------------
% 15.17/2.92 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22,
% 15.17/2.92 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35,
% 15.17/2.92 ax36, ax37, ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48,
% 15.17/2.92 ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax58, ax59, ax6, ax60, ax61, ax62,
% 15.17/2.92 ax7, ax8, ax9, bottom_smallest, main3_li12, reflexivity,
% 15.17/2.92 stricly_smaller_definition, totality, transitivity
% 15.17/2.92
% 15.17/2.92 Those formulas are unsatisfiable:
% 15.17/2.92 ---------------------------------
% 15.17/2.92
% 15.17/2.92 Begin of proof
% 15.17/2.92 |
% 15.17/2.92 | ALPHA: (ax56) implies:
% 15.17/2.92 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (pi_sharp_remove(v0, v1) = 0) | ~
% 15.17/2.92 | $i(v1) | ~ $i(v0) | contains_pq(v0, v1) = 0)
% 15.17/2.92 |
% 15.17/2.92 | ALPHA: (ax57) implies:
% 15.17/2.92 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 15.17/2.92 | (pi_sharp_remove(v2, v1) = v3) | ~ (i(v0) = v2) | ~ $i(v1) | ~
% 15.17/2.92 | $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & pi_remove(v0, v1) = v4))
% 15.17/2.92 |
% 15.17/2.92 | ALPHA: (function-axioms) implies:
% 15.17/2.92 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) |
% 15.17/2.92 | ~ (i(v2) = v0))
% 15.17/2.93 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.17/2.93 | ! [v3: $i] : (v1 = v0 | ~ (contains_pq(v3, v2) = v1) | ~
% 15.17/2.93 | (contains_pq(v3, v2) = v0))
% 15.17/2.93 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.17/2.93 | (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = v0))
% 15.17/2.93 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.17/2.93 | ! [v3: $i] : (v1 = v0 | ~ (pi_remove(v3, v2) = v1) | ~
% 15.17/2.93 | (pi_remove(v3, v2) = v0))
% 15.17/2.93 |
% 15.17/2.93 | DELTA: instantiating (co3) with fresh symbols all_70_0, all_70_1, all_70_2,
% 15.17/2.93 | all_70_3, all_70_4, all_70_5, all_70_6, all_70_7, all_70_8, all_70_9
% 15.17/2.93 | gives:
% 15.17/2.93 | (7) phi(all_70_4) = 0 & pi_remove(all_70_5, all_70_6) = 0 &
% 15.17/2.93 | pi_sharp_remove(all_70_3, all_70_6) = all_70_2 & i(all_70_4) = all_70_1
% 15.17/2.93 | & i(all_70_5) = all_70_3 & triple(all_70_9, all_70_8, all_70_7) =
% 15.17/2.93 | all_70_5 & remove_cpq(all_70_5, all_70_6) = all_70_4 &
% 15.17/2.93 | remove_pq(all_70_3, all_70_6) = all_70_0 & $i(all_70_0) & $i(all_70_1)
% 15.17/2.93 | & $i(all_70_3) & $i(all_70_4) & $i(all_70_5) & $i(all_70_6) &
% 15.17/2.93 | $i(all_70_7) & $i(all_70_8) & $i(all_70_9) & ( ~ (all_70_0 = all_70_1)
% 15.17/2.93 | | ~ (all_70_2 = 0))
% 15.17/2.93 |
% 15.17/2.93 | ALPHA: (7) implies:
% 15.17/2.93 | (8) $i(all_70_9)
% 15.17/2.93 | (9) $i(all_70_8)
% 15.17/2.93 | (10) $i(all_70_7)
% 15.17/2.93 | (11) $i(all_70_6)
% 15.17/2.93 | (12) $i(all_70_5)
% 15.17/2.93 | (13) $i(all_70_3)
% 15.17/2.93 | (14) remove_pq(all_70_3, all_70_6) = all_70_0
% 15.17/2.93 | (15) remove_cpq(all_70_5, all_70_6) = all_70_4
% 15.17/2.93 | (16) triple(all_70_9, all_70_8, all_70_7) = all_70_5
% 15.17/2.93 | (17) i(all_70_5) = all_70_3
% 15.17/2.93 | (18) i(all_70_4) = all_70_1
% 15.17/2.93 | (19) pi_sharp_remove(all_70_3, all_70_6) = all_70_2
% 15.17/2.93 | (20) pi_remove(all_70_5, all_70_6) = 0
% 15.17/2.93 | (21) ~ (all_70_0 = all_70_1) | ~ (all_70_2 = 0)
% 15.17/2.93 |
% 15.17/2.93 | GROUND_INST: instantiating (main3_li34) with all_70_9, all_70_8, all_70_7,
% 15.17/2.93 | all_70_6, all_70_5, all_70_3, all_70_0, simplifying with (8),
% 15.17/2.93 | (9), (10), (11), (14), (16), (17) gives:
% 15.17/2.93 | (22) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (i(v1) = v2 &
% 15.17/2.93 | remove_cpq(all_70_5, all_70_6) = v1 & contains_pq(all_70_3,
% 15.17/2.93 | all_70_6) = v0 & $i(v2) & $i(v1) & ( ~ (v0 = 0) | v2 = all_70_0))
% 15.17/2.93 |
% 15.17/2.93 | GROUND_INST: instantiating (2) with all_70_5, all_70_6, all_70_3, all_70_2,
% 15.17/2.93 | simplifying with (11), (12), (17), (19) gives:
% 15.17/2.93 | (23) all_70_2 = 0 | ? [v0: int] : ( ~ (v0 = 0) & pi_remove(all_70_5,
% 15.17/2.93 | all_70_6) = v0)
% 15.17/2.93 |
% 15.17/2.93 | DELTA: instantiating (22) with fresh symbols all_85_0, all_85_1, all_85_2
% 15.17/2.93 | gives:
% 15.17/2.93 | (24) i(all_85_1) = all_85_0 & remove_cpq(all_70_5, all_70_6) = all_85_1 &
% 15.17/2.93 | contains_pq(all_70_3, all_70_6) = all_85_2 & $i(all_85_0) &
% 15.17/2.93 | $i(all_85_1) & ( ~ (all_85_2 = 0) | all_85_0 = all_70_0)
% 15.17/2.93 |
% 15.17/2.93 | ALPHA: (24) implies:
% 15.17/2.93 | (25) contains_pq(all_70_3, all_70_6) = all_85_2
% 15.17/2.93 | (26) remove_cpq(all_70_5, all_70_6) = all_85_1
% 15.17/2.93 | (27) i(all_85_1) = all_85_0
% 15.17/2.93 | (28) ~ (all_85_2 = 0) | all_85_0 = all_70_0
% 15.17/2.93 |
% 15.17/2.93 | BETA: splitting (23) gives:
% 15.17/2.93 |
% 15.17/2.93 | Case 1:
% 15.17/2.93 | |
% 15.17/2.93 | | (29) all_70_2 = 0
% 15.17/2.93 | |
% 15.17/2.93 | | REDUCE: (19), (29) imply:
% 15.17/2.94 | | (30) pi_sharp_remove(all_70_3, all_70_6) = 0
% 15.17/2.94 | |
% 15.17/2.94 | | BETA: splitting (21) gives:
% 15.17/2.94 | |
% 15.17/2.94 | | Case 1:
% 15.17/2.94 | | |
% 15.17/2.94 | | | (31) ~ (all_70_2 = 0)
% 15.17/2.94 | | |
% 15.17/2.94 | | | REDUCE: (29), (31) imply:
% 15.17/2.94 | | | (32) $false
% 15.17/2.94 | | |
% 15.17/2.94 | | | CLOSE: (32) is inconsistent.
% 15.17/2.94 | | |
% 15.17/2.94 | | Case 2:
% 15.17/2.94 | | |
% 15.17/2.94 | | | (33) ~ (all_70_0 = all_70_1)
% 15.17/2.94 | | |
% 15.17/2.94 | | | GROUND_INST: instantiating (5) with all_70_4, all_85_1, all_70_6,
% 15.17/2.94 | | | all_70_5, simplifying with (15), (26) gives:
% 15.17/2.94 | | | (34) all_85_1 = all_70_4
% 15.17/2.94 | | |
% 15.17/2.94 | | | REDUCE: (27), (34) imply:
% 15.17/2.94 | | | (35) i(all_70_4) = all_85_0
% 15.17/2.94 | | |
% 15.17/2.94 | | | GROUND_INST: instantiating (3) with all_70_1, all_85_0, all_70_4,
% 15.17/2.94 | | | simplifying with (18), (35) gives:
% 15.17/2.94 | | | (36) all_85_0 = all_70_1
% 15.17/2.94 | | |
% 15.17/2.94 | | | BETA: splitting (28) gives:
% 15.17/2.94 | | |
% 15.17/2.94 | | | Case 1:
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | (37) ~ (all_85_2 = 0)
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | GROUND_INST: instantiating (1) with all_70_3, all_70_6, simplifying with
% 15.17/2.94 | | | | (11), (13), (30) gives:
% 15.17/2.94 | | | | (38) contains_pq(all_70_3, all_70_6) = 0
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | GROUND_INST: instantiating (4) with all_85_2, 0, all_70_6, all_70_3,
% 15.17/2.94 | | | | simplifying with (25), (38) gives:
% 15.17/2.94 | | | | (39) all_85_2 = 0
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | REDUCE: (37), (39) imply:
% 15.17/2.94 | | | | (40) $false
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | CLOSE: (40) is inconsistent.
% 15.17/2.94 | | | |
% 15.17/2.94 | | | Case 2:
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | (41) all_85_0 = all_70_0
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | COMBINE_EQS: (36), (41) imply:
% 15.17/2.94 | | | | (42) all_70_0 = all_70_1
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | SIMP: (42) implies:
% 15.17/2.94 | | | | (43) all_70_0 = all_70_1
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | REDUCE: (33), (43) imply:
% 15.17/2.94 | | | | (44) $false
% 15.17/2.94 | | | |
% 15.17/2.94 | | | | CLOSE: (44) is inconsistent.
% 15.17/2.94 | | | |
% 15.17/2.94 | | | End of split
% 15.17/2.94 | | |
% 15.17/2.94 | | End of split
% 15.17/2.94 | |
% 15.17/2.94 | Case 2:
% 15.17/2.94 | |
% 15.17/2.94 | | (45) ? [v0: int] : ( ~ (v0 = 0) & pi_remove(all_70_5, all_70_6) = v0)
% 15.17/2.94 | |
% 15.17/2.94 | | DELTA: instantiating (45) with fresh symbol all_93_0 gives:
% 15.17/2.94 | | (46) ~ (all_93_0 = 0) & pi_remove(all_70_5, all_70_6) = all_93_0
% 15.17/2.94 | |
% 15.17/2.94 | | ALPHA: (46) implies:
% 15.17/2.94 | | (47) ~ (all_93_0 = 0)
% 15.17/2.94 | | (48) pi_remove(all_70_5, all_70_6) = all_93_0
% 15.17/2.94 | |
% 15.17/2.94 | | GROUND_INST: instantiating (6) with 0, all_93_0, all_70_6, all_70_5,
% 15.17/2.94 | | simplifying with (20), (48) gives:
% 15.17/2.94 | | (49) all_93_0 = 0
% 15.17/2.94 | |
% 15.17/2.94 | | REDUCE: (47), (49) imply:
% 15.17/2.94 | | (50) $false
% 15.17/2.94 | |
% 15.17/2.94 | | CLOSE: (50) is inconsistent.
% 15.17/2.94 | |
% 15.17/2.94 | End of split
% 15.17/2.94 |
% 15.17/2.94 End of proof
% 15.17/2.94 % SZS output end Proof for theBenchmark
% 15.17/2.94
% 15.17/2.94 2340ms
%------------------------------------------------------------------------------