TSTP Solution File: SWV369+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV369+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 : n007.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 12.50s 2.34s
% Output : Proof 14.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV369+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 08:56:58 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.52/0.59 ________ _____
% 0.52/0.59 ___ __ \_________(_)________________________________
% 0.52/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.52/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.52/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.52/0.59
% 0.52/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.59 (2023-06-19)
% 0.52/0.59
% 0.52/0.59 (c) Philipp Rümmer, 2009-2023
% 0.52/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.59 Amanda Stjerna.
% 0.52/0.59 Free software under BSD-3-Clause.
% 0.52/0.59
% 0.52/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.59
% 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.61 Running up to 7 provers in parallel.
% 0.52/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.52/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.60/1.19 Prover 4: Preprocessing ...
% 3.60/1.20 Prover 1: Preprocessing ...
% 4.08/1.24 Prover 3: Preprocessing ...
% 4.08/1.24 Prover 2: Preprocessing ...
% 4.08/1.24 Prover 5: Preprocessing ...
% 4.08/1.24 Prover 6: Preprocessing ...
% 4.08/1.25 Prover 0: Preprocessing ...
% 8.81/1.92 Prover 1: Warning: ignoring some quantifiers
% 9.71/2.02 Prover 3: Warning: ignoring some quantifiers
% 9.71/2.03 Prover 1: Constructing countermodel ...
% 10.22/2.04 Prover 6: Proving ...
% 10.22/2.05 Prover 5: Proving ...
% 10.22/2.05 Prover 3: Constructing countermodel ...
% 10.40/2.10 Prover 2: Proving ...
% 10.84/2.13 Prover 4: Constructing countermodel ...
% 11.16/2.22 Prover 0: Proving ...
% 12.08/2.32 Prover 6: proved (1701ms)
% 12.50/2.34
% 12.50/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.50/2.34
% 12.50/2.34 Prover 3: proved (1726ms)
% 12.50/2.34
% 12.50/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.50/2.34
% 12.50/2.34 Prover 0: stopped
% 12.50/2.35 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.50/2.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.50/2.35 Prover 5: stopped
% 12.60/2.36 Prover 2: stopped
% 12.60/2.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.60/2.36 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.60/2.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.60/2.40 Prover 1: Found proof (size 22)
% 12.60/2.40 Prover 1: proved (1789ms)
% 12.60/2.40 Prover 4: stopped
% 12.60/2.41 Prover 10: Preprocessing ...
% 13.04/2.41 Prover 8: Preprocessing ...
% 13.04/2.43 Prover 7: Preprocessing ...
% 13.04/2.45 Prover 11: Preprocessing ...
% 13.04/2.45 Prover 13: Preprocessing ...
% 13.37/2.50 Prover 10: stopped
% 13.37/2.50 Prover 7: stopped
% 13.37/2.53 Prover 11: stopped
% 13.99/2.55 Prover 13: stopped
% 14.21/2.61 Prover 8: Warning: ignoring some quantifiers
% 14.21/2.63 Prover 8: Constructing countermodel ...
% 14.21/2.64 Prover 8: stopped
% 14.21/2.64
% 14.21/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.21/2.64
% 14.48/2.64 % SZS output start Proof for theBenchmark
% 14.48/2.64 Assumptions after simplification:
% 14.48/2.64 ---------------------------------
% 14.48/2.64
% 14.48/2.64 (ax20)
% 14.55/2.67 $i(create_slb) & ! [v0: $i] : ( ~ (contains_slb(create_slb, v0) = 0) | ~
% 14.55/2.67 $i(v0))
% 14.55/2.67
% 14.55/2.67 (ax39)
% 14.55/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.55/2.67 int] : (v5 = 0 | ~ (contains_cpq(v4, v3) = v5) | ~ (triple(v0, v1, v2) =
% 14.55/2.67 v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~
% 14.55/2.67 (v6 = 0) & contains_slb(v1, v3) = v6)) & ! [v0: $i] : ! [v1: $i] : !
% 14.55/2.67 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (contains_cpq(v4, v3) = 0) | ~
% 14.55/2.67 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 14.55/2.67 contains_slb(v1, v3) = 0)
% 14.55/2.67
% 14.55/2.67 (ax54)
% 14.55/2.67 $i(create_slb) & $i(create_pq) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 14.55/2.67 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | i(v2) =
% 14.55/2.67 create_pq)
% 14.55/2.67
% 14.55/2.67 (ax8)
% 14.55/2.67 $i(create_pq) & ! [v0: $i] : ( ~ (contains_pq(create_pq, v0) = 0) | ~
% 14.55/2.67 $i(v0))
% 14.55/2.67
% 14.55/2.67 (l5_co)
% 14.55/2.67 $i(create_slb) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 14.55/2.67 [v4: any] : ? [v5: $i] : ? [v6: any] : (i(v3) = v5 & contains_cpq(v3, v2) =
% 14.55/2.67 v4 & triple(v0, create_slb, v1) = v3 & contains_pq(v5, v2) = v6 & $i(v5) &
% 14.55/2.67 $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 & ~ (v4 = 0)) | (v4 = 0 & ~
% 14.55/2.67 (v6 = 0))))
% 14.55/2.67
% 14.55/2.68 (function-axioms)
% 14.55/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 14.55/2.69 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0:
% 14.55/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.55/2.69 : ! [v4: $i] : (v1 = v0 | ~ (pair_in_list(v4, v3, v2) = v1) | ~
% 14.55/2.69 (pair_in_list(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.55/2.69 (pi_sharp_removemin(v3, v2) = v1) | ~ (pi_sharp_removemin(v3, v2) = v0)) &
% 14.55/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.55/2.69 $i] : (v1 = v0 | ~ (pi_sharp_find_min(v3, v2) = v1) | ~
% 14.55/2.69 (pi_sharp_find_min(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.55/2.70 (pi_remove(v3, v2) = v1) | ~ (pi_remove(v3, v2) = v0)) & ! [v0:
% 14.55/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.55/2.70 : (v1 = v0 | ~ (pi_sharp_remove(v3, v2) = v1) | ~ (pi_sharp_remove(v3, v2) =
% 14.55/2.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.55/2.70 ~ (remove_pqp(v3, v2) = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] :
% 14.55/2.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) =
% 14.55/2.70 v1) | ~ (insert_pqp(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.55/2.70 (contains_cpq(v3, v2) = v1) | ~ (contains_cpq(v3, v2) = v0)) & ! [v0: $i]
% 14.55/2.70 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2)
% 14.55/2.70 = v1) | ~ (remove_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.55/2.70 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_cpq(v3, v2) = v1) | ~
% 14.55/2.70 (insert_cpq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (succ_cpq(v3,
% 14.55/2.70 v2) = v1) | ~ (succ_cpq(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.55/2.70 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = v1) | ~
% 14.55/2.70 (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.55/2.70 [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ (lookup_slb(v3, v2) =
% 14.55/2.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.55/2.70 ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = v0)) & ! [v0:
% 14.55/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.55/2.70 : (v1 = v0 | ~ (contains_slb(v3, v2) = v1) | ~ (contains_slb(v3, v2) = v0))
% 14.55/2.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.55/2.70 (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 14.55/2.70 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~
% 14.55/2.70 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.55/2.70 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~
% 14.55/2.70 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.55/2.70 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~
% 14.55/2.70 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.55/2.70 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~
% 14.55/2.70 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.55/2.70 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~
% 14.55/2.70 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.55/2.70 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) =
% 14.55/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.55/2.70 $i] : ! [v3: $i] : (v1 = v0 | ~ (issmallestelement_pq(v3, v2) = v1) | ~
% 14.55/2.70 (issmallestelement_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.55/2.70 (contains_pq(v3, v2) = v1) | ~ (contains_pq(v3, v2) = v0)) & ! [v0: $i] :
% 14.55/2.70 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pq(v3, v2) =
% 14.55/2.70 v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.70 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.55/2.70 (strictly_less_than(v3, v2) = v1) | ~ (strictly_less_than(v3, v2) = v0)) &
% 14.55/2.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.55/2.70 $i] : (v1 = v0 | ~ (less_than(v3, v2) = v1) | ~ (less_than(v3, v2) = v0))
% 14.55/2.70 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 14.55/2.70 = v0 | ~ (phi(v2) = v1) | ~ (phi(v2) = v0)) & ! [v0: MultipleValueBool] :
% 14.55/2.70 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_removemin(v2) =
% 14.55/2.70 v1) | ~ (pi_removemin(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (pi_find_min(v2) = v1) | ~
% 14.55/2.70 (pi_find_min(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 14.55/2.70 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.55/2.70 $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = v1) | ~ (removemin_cpq_res(v2)
% 14.55/2.70 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.55/2.70 (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) & ! [v0: $i] :
% 14.55/2.70 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (findmin_pqp_res(v2) = v1) | ~
% 14.55/2.70 (findmin_pqp_res(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.55/2.70 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ok(v2) = v1) | ~ (ok(v2)
% 14.55/2.70 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.55/2.70 $i] : (v1 = v0 | ~ (check_cpq(v2) = v1) | ~ (check_cpq(v2) = v0)) & !
% 14.55/2.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) =
% 14.55/2.70 v1) | ~ (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 14.55/2.70 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2)
% 14.55/2.70 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.55/2.70 $i] : (v1 = v0 | ~ (isnonempty_slb(v2) = v1) | ~ (isnonempty_slb(v2) =
% 14.55/2.70 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.55/2.70 $i] : (v1 = v0 | ~ (isnonempty_pq(v2) = v1) | ~ (isnonempty_pq(v2) = v0))
% 14.55/2.70
% 14.55/2.70 Further assumptions not needed in the proof:
% 14.55/2.70 --------------------------------------------
% 14.55/2.70 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax21, ax22, ax23,
% 14.55/2.70 ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 14.55/2.70 ax37, ax38, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax50,
% 14.55/2.70 ax51, ax52, ax53, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax7, ax9,
% 14.55/2.70 bottom_smallest, reflexivity, stricly_smaller_definition, totality, transitivity
% 14.55/2.70
% 14.55/2.70 Those formulas are unsatisfiable:
% 14.55/2.70 ---------------------------------
% 14.55/2.70
% 14.55/2.70 Begin of proof
% 14.55/2.70 |
% 14.55/2.70 | ALPHA: (ax8) implies:
% 14.55/2.70 | (1) ! [v0: $i] : ( ~ (contains_pq(create_pq, v0) = 0) | ~ $i(v0))
% 14.55/2.70 |
% 14.55/2.70 | ALPHA: (ax20) implies:
% 14.55/2.70 | (2) ! [v0: $i] : ( ~ (contains_slb(create_slb, v0) = 0) | ~ $i(v0))
% 14.55/2.70 |
% 14.55/2.70 | ALPHA: (ax39) implies:
% 14.55/2.70 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 14.55/2.70 | ~ (contains_cpq(v4, v3) = 0) | ~ (triple(v0, v1, v2) = v4) | ~
% 14.55/2.70 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | contains_slb(v1, v3) =
% 14.55/2.70 | 0)
% 14.55/2.70 |
% 14.55/2.70 | ALPHA: (ax54) implies:
% 14.55/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb,
% 14.55/2.70 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | i(v2) = create_pq)
% 14.55/2.70 |
% 14.55/2.70 | ALPHA: (l5_co) implies:
% 14.55/2.70 | (5) $i(create_slb)
% 14.55/2.70 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] :
% 14.55/2.70 | ? [v5: $i] : ? [v6: any] : (i(v3) = v5 & contains_cpq(v3, v2) = v4 &
% 14.55/2.70 | triple(v0, create_slb, v1) = v3 & contains_pq(v5, v2) = v6 & $i(v5) &
% 14.55/2.70 | $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 & ~ (v4 = 0)) | (v4 = 0
% 14.55/2.70 | & ~ (v6 = 0))))
% 14.55/2.70 |
% 14.55/2.70 | ALPHA: (function-axioms) implies:
% 14.55/2.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) |
% 14.55/2.70 | ~ (i(v2) = v0))
% 14.55/2.70 |
% 14.55/2.71 | DELTA: instantiating (6) with fresh symbols all_66_0, all_66_1, all_66_2,
% 14.55/2.71 | all_66_3, all_66_4, all_66_5, all_66_6 gives:
% 14.55/2.71 | (8) i(all_66_3) = all_66_1 & contains_cpq(all_66_3, all_66_4) = all_66_2 &
% 14.55/2.71 | triple(all_66_6, create_slb, all_66_5) = all_66_3 &
% 14.55/2.71 | contains_pq(all_66_1, all_66_4) = all_66_0 & $i(all_66_1) &
% 14.55/2.71 | $i(all_66_3) & $i(all_66_4) & $i(all_66_5) & $i(all_66_6) & ((all_66_0
% 14.55/2.71 | = 0 & ~ (all_66_2 = 0)) | (all_66_2 = 0 & ~ (all_66_0 = 0)))
% 14.55/2.71 |
% 14.55/2.71 | ALPHA: (8) implies:
% 14.55/2.71 | (9) $i(all_66_6)
% 14.55/2.71 | (10) $i(all_66_5)
% 14.55/2.71 | (11) $i(all_66_4)
% 14.55/2.71 | (12) contains_pq(all_66_1, all_66_4) = all_66_0
% 14.55/2.71 | (13) triple(all_66_6, create_slb, all_66_5) = all_66_3
% 14.55/2.71 | (14) contains_cpq(all_66_3, all_66_4) = all_66_2
% 14.55/2.71 | (15) i(all_66_3) = all_66_1
% 14.55/2.71 | (16) (all_66_0 = 0 & ~ (all_66_2 = 0)) | (all_66_2 = 0 & ~ (all_66_0 =
% 14.55/2.71 | 0))
% 14.55/2.71 |
% 14.55/2.71 | GROUND_INST: instantiating (4) with all_66_6, all_66_5, all_66_3, simplifying
% 14.55/2.71 | with (9), (10), (13) gives:
% 14.55/2.71 | (17) i(all_66_3) = create_pq
% 14.55/2.71 |
% 14.55/2.71 | GROUND_INST: instantiating (7) with all_66_1, create_pq, all_66_3, simplifying
% 14.55/2.71 | with (15), (17) gives:
% 14.55/2.71 | (18) all_66_1 = create_pq
% 14.55/2.71 |
% 14.55/2.71 | REDUCE: (12), (18) imply:
% 14.55/2.71 | (19) contains_pq(create_pq, all_66_4) = all_66_0
% 14.55/2.71 |
% 14.55/2.71 | BETA: splitting (16) gives:
% 14.55/2.71 |
% 14.55/2.71 | Case 1:
% 14.55/2.71 | |
% 14.55/2.71 | | (20) all_66_0 = 0 & ~ (all_66_2 = 0)
% 14.55/2.71 | |
% 14.55/2.71 | | ALPHA: (20) implies:
% 14.55/2.71 | | (21) all_66_0 = 0
% 14.55/2.71 | |
% 14.55/2.71 | | REDUCE: (19), (21) imply:
% 14.55/2.71 | | (22) contains_pq(create_pq, all_66_4) = 0
% 14.55/2.71 | |
% 14.55/2.71 | | GROUND_INST: instantiating (1) with all_66_4, simplifying with (11), (22)
% 14.55/2.71 | | gives:
% 14.55/2.71 | | (23) $false
% 14.55/2.71 | |
% 14.55/2.71 | | CLOSE: (23) is inconsistent.
% 14.55/2.71 | |
% 14.55/2.71 | Case 2:
% 14.55/2.71 | |
% 14.55/2.71 | | (24) all_66_2 = 0 & ~ (all_66_0 = 0)
% 14.55/2.71 | |
% 14.55/2.71 | | ALPHA: (24) implies:
% 14.55/2.71 | | (25) all_66_2 = 0
% 14.55/2.71 | |
% 14.55/2.71 | | REDUCE: (14), (25) imply:
% 14.55/2.71 | | (26) contains_cpq(all_66_3, all_66_4) = 0
% 14.55/2.71 | |
% 14.55/2.71 | | GROUND_INST: instantiating (3) with all_66_6, create_slb, all_66_5,
% 14.55/2.71 | | all_66_4, all_66_3, simplifying with (5), (9), (10), (11),
% 14.55/2.71 | | (13), (26) gives:
% 14.55/2.71 | | (27) contains_slb(create_slb, all_66_4) = 0
% 14.55/2.71 | |
% 14.55/2.71 | | GROUND_INST: instantiating (2) with all_66_4, simplifying with (11), (27)
% 14.55/2.71 | | gives:
% 14.55/2.71 | | (28) $false
% 14.55/2.71 | |
% 14.55/2.71 | | CLOSE: (28) is inconsistent.
% 14.55/2.71 | |
% 14.55/2.71 | End of split
% 14.55/2.71 |
% 14.55/2.71 End of proof
% 14.55/2.71 % SZS output end Proof for theBenchmark
% 14.55/2.71
% 14.55/2.71 2120ms
%------------------------------------------------------------------------------