TSTP Solution File: ALG216+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG216+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n027.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 : Wed Aug 30 16:39:59 EDT 2023
% Result : Theorem 55.55s 8.44s
% Output : Proof 75.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG216+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n027.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 : Mon Aug 28 06:24:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 ________ _____
% 0.19/0.63 ___ __ \_________(_)________________________________
% 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.63
% 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.63 (2023-06-19)
% 0.19/0.63
% 0.19/0.63 (c) Philipp Rümmer, 2009-2023
% 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.63 Amanda Stjerna.
% 0.19/0.63 Free software under BSD-3-Clause.
% 0.19/0.63
% 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.63
% 0.19/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.65 Running up to 7 provers in parallel.
% 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 3.10/1.16 Prover 1: Preprocessing ...
% 3.10/1.16 Prover 4: Preprocessing ...
% 3.39/1.22 Prover 5: Preprocessing ...
% 3.39/1.22 Prover 0: Preprocessing ...
% 3.39/1.22 Prover 6: Preprocessing ...
% 3.39/1.22 Prover 3: Preprocessing ...
% 3.39/1.23 Prover 2: Preprocessing ...
% 9.16/2.08 Prover 5: Proving ...
% 9.16/2.08 Prover 1: Warning: ignoring some quantifiers
% 10.29/2.19 Prover 6: Proving ...
% 10.29/2.20 Prover 1: Constructing countermodel ...
% 10.29/2.21 Prover 3: Warning: ignoring some quantifiers
% 10.29/2.23 Prover 3: Constructing countermodel ...
% 11.51/2.34 Prover 2: Proving ...
% 21.24/3.68 Prover 3: gave up
% 21.24/3.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.47/3.83 Prover 7: Preprocessing ...
% 24.22/4.11 Prover 7: Warning: ignoring some quantifiers
% 24.22/4.14 Prover 7: Constructing countermodel ...
% 29.17/4.75 Prover 4: Warning: ignoring some quantifiers
% 30.27/4.89 Prover 1: gave up
% 30.27/4.90 Prover 4: Constructing countermodel ...
% 30.27/4.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 30.67/5.01 Prover 8: Preprocessing ...
% 30.67/5.11 Prover 0: Proving ...
% 30.98/5.23 Prover 8: Warning: ignoring some quantifiers
% 33.09/5.25 Prover 8: Constructing countermodel ...
% 46.67/7.05 Prover 8: gave up
% 46.67/7.06 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 47.38/7.16 Prover 9: Preprocessing ...
% 55.55/8.44 Prover 5: proved (7759ms)
% 55.55/8.44
% 55.55/8.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.55/8.44
% 55.55/8.45 Prover 6: stopped
% 55.70/8.45 Prover 2: stopped
% 55.70/8.46 Prover 0: stopped
% 55.70/8.47 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 55.70/8.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 55.70/8.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 55.70/8.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 58.21/8.54 Prover 10: Preprocessing ...
% 58.21/8.57 Prover 11: Preprocessing ...
% 58.21/8.58 Prover 13: Preprocessing ...
% 58.21/8.58 Prover 16: Preprocessing ...
% 58.87/8.62 Prover 10: Warning: ignoring some quantifiers
% 58.87/8.63 Prover 10: Constructing countermodel ...
% 59.50/8.70 Prover 13: Warning: ignoring some quantifiers
% 59.50/8.71 Prover 13: Constructing countermodel ...
% 59.50/8.76 Prover 16: Warning: ignoring some quantifiers
% 59.50/8.77 Prover 16: Constructing countermodel ...
% 60.50/9.05 Prover 9: Warning: ignoring some quantifiers
% 60.50/9.09 Prover 9: Constructing countermodel ...
% 60.50/9.10 Prover 9: stopped
% 60.50/9.10 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 60.50/9.19 Prover 19: Preprocessing ...
% 65.12/9.44 Prover 19: Warning: ignoring some quantifiers
% 65.12/9.45 Prover 19: Constructing countermodel ...
% 71.55/10.29 Prover 7: Found proof (size 136)
% 71.55/10.29 Prover 7: proved (6565ms)
% 71.76/10.29 Prover 16: stopped
% 71.76/10.29 Prover 19: stopped
% 71.76/10.29 Prover 10: stopped
% 71.76/10.29 Prover 13: stopped
% 71.76/10.29 Prover 4: stopped
% 73.89/10.85 Prover 11: Warning: ignoring some quantifiers
% 73.89/10.88 Prover 11: Constructing countermodel ...
% 73.89/10.90 Prover 11: stopped
% 73.89/10.90
% 73.89/10.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 73.89/10.90
% 74.28/10.92 % SZS output start Proof for theBenchmark
% 74.28/10.93 Assumptions after simplification:
% 74.28/10.93 ---------------------------------
% 74.28/10.93
% 74.28/10.93 (dt_k1_rlvect_1)
% 74.28/10.97 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) | ~
% 74.28/10.97 l2_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) &
% 74.28/10.97 m1_subset_1(v1, v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) =
% 74.28/10.97 v1) | ~ $i(v0) | ~ l2_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) = v2
% 74.28/10.97 & $i(v2) & m1_subset_1(v2, v1)))
% 74.28/10.97
% 74.28/10.97 (dt_l1_rlvect_1)
% 74.28/10.97 ! [v0: $i] : ( ~ $i(v0) | ~ l1_rlvect_1(v0) | l2_struct_0(v0))
% 74.28/10.97
% 74.28/10.97 (dt_l1_vectsp_2)
% 74.28/10.97 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ l1_struct_0(v0) | ~
% 74.28/10.97 l1_vectsp_2(v1, v0) | l1_rlvect_1(v1))
% 74.28/10.97
% 74.28/10.97 (dt_l2_struct_0)
% 74.28/10.97 ! [v0: $i] : ( ~ $i(v0) | ~ l2_struct_0(v0) | l1_struct_0(v0))
% 74.28/10.97
% 74.28/10.97 (dt_l2_vectsp_1)
% 74.28/10.97 ! [v0: $i] : ( ~ $i(v0) | ~ l2_vectsp_1(v0) | l2_struct_0(v0)) & ! [v0: $i]
% 74.28/10.97 : ( ~ $i(v0) | ~ l2_vectsp_1(v0) | l1_vectsp_1(v0))
% 74.28/10.97
% 74.28/10.97 (dt_l3_vectsp_1)
% 74.28/10.98 ! [v0: $i] : ( ~ $i(v0) | ~ l3_vectsp_1(v0) | l2_vectsp_1(v0)) & ! [v0: $i]
% 74.28/10.98 : ( ~ $i(v0) | ~ l3_vectsp_1(v0) | l1_rlvect_1(v0))
% 74.28/10.98
% 74.28/10.98 (rc2_rlvect_2)
% 74.28/10.98 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 74.28/10.98 l1_struct_0(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] :
% 74.28/10.98 (k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & v1_finset_1(v3) & m1_subset_1(v3,
% 74.28/10.98 v2) & ~ v1_xboole_0(v3)))
% 74.28/10.98
% 74.28/10.98 (rc4_struct_0)
% 74.28/10.98 ? [v0: $i] : ($i(v0) & l2_struct_0(v0) & ~ v3_struct_0(v0))
% 74.28/10.98
% 74.28/10.98 (t5_rmod_5)
% 74.62/10.99 ! [v0: $i] : ! [v1: $i] : ( ~ (k2_group_1(v0) = v1) | ~ $i(v0) | ~
% 74.62/10.99 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~
% 74.62/10.99 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~
% 74.62/10.99 v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0)
% 74.62/10.99 | ? [v2: $i] : (k1_rlvect_1(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] :
% 74.62/10.99 ( ~ (k1_rlvect_1(v3) = v4) | ~ $i(v3) | ~ l1_vectsp_2(v3, v0) | ~
% 74.62/10.99 v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~
% 74.62/10.99 v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5: $i] :
% 74.62/10.99 (u1_struct_0(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : (v2 = v1 |
% 74.62/10.99 ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ $i(v6) | ~ $i(v4) | ~
% 74.62/10.99 v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4,
% 74.62/10.99 v5)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1 | ~ (k8_rlvect_2(v3,
% 74.62/10.99 v4, v6) = v7) | ~ $i(v6) | ~ $i(v4) | ~ v1_rmod_5(v7, v0, v3)
% 74.62/10.99 | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)))) & ! [v3: $i] :
% 74.62/10.99 ! [v4: $i] : ( ~ (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ l1_vectsp_2(v3,
% 74.62/11.00 v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3)
% 74.62/11.00 | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5:
% 74.62/11.00 $i] : (k1_rlvect_1(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : (v2
% 74.62/11.00 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~ $i(v6) | ~
% 74.62/11.00 v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5,
% 74.62/11.00 v4)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1 | ~ (k8_rlvect_2(v3,
% 74.62/11.00 v5, v6) = v7) | ~ $i(v6) | ~ v1_rmod_5(v7, v0, v3) | ~
% 74.62/11.00 m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4)))))) & ! [v0: $i] : !
% 74.62/11.00 [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) | ~ l3_vectsp_1(v0) | ~
% 74.62/11.00 v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~
% 74.62/11.00 v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~
% 74.62/11.00 v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2: $i] :
% 74.62/11.00 (k2_group_1(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~
% 74.62/11.00 (k1_rlvect_1(v3) = v4) | ~ $i(v3) | ~ l1_vectsp_2(v3, v0) | ~
% 74.62/11.00 v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~
% 74.62/11.00 v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5: $i] :
% 74.62/11.00 (u1_struct_0(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : (v2 = v1 |
% 74.62/11.00 ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ $i(v6) | ~ $i(v4) | ~
% 74.62/11.00 v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4,
% 74.62/11.00 v5)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1 | ~ (k8_rlvect_2(v3,
% 74.62/11.00 v4, v6) = v7) | ~ $i(v6) | ~ $i(v4) | ~ v1_rmod_5(v7, v0, v3)
% 74.62/11.00 | ~ m1_subset_1(v6, v5) | ~ m1_subset_1(v4, v5)))) & ! [v3: $i] :
% 74.62/11.00 ! [v4: $i] : ( ~ (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ l1_vectsp_2(v3,
% 74.62/11.00 v0) | ~ v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3)
% 74.62/11.00 | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5:
% 74.62/11.00 $i] : (k1_rlvect_1(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : (v2
% 74.62/11.00 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~ $i(v6) | ~
% 74.62/11.00 v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~ m1_subset_1(v5,
% 74.62/11.00 v4)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1 | ~ (k8_rlvect_2(v3,
% 74.62/11.00 v5, v6) = v7) | ~ $i(v6) | ~ v1_rmod_5(v7, v0, v3) | ~
% 74.62/11.00 m1_subset_1(v6, v4) | ~ m1_subset_1(v5, v4))))))
% 74.62/11.00
% 74.62/11.00 (t6_rmod_5)
% 74.62/11.00 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 74.62/11.00 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v2 = v1) &
% 74.62/11.00 k2_group_1(v0) = v2 & k1_rlvect_1(v3) = v5 & k1_rlvect_1(v0) = v1 &
% 74.62/11.00 u1_struct_0(v3) = v4 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 74.62/11.00 $i(v0) & m1_subset_1(v6, v4) & l1_vectsp_2(v3, v0) & v5_vectsp_2(v3, v0) &
% 74.62/11.00 l3_vectsp_1(v0) & v8_vectsp_1(v0) & v7_vectsp_1(v0) & v6_vectsp_1(v0) &
% 74.62/11.00 v4_group_1(v0) & v6_rlvect_1(v3) & v6_rlvect_1(v0) & v5_rlvect_1(v3) &
% 74.62/11.00 v5_rlvect_1(v0) & v4_rlvect_1(v3) & v4_rlvect_1(v0) & v3_rlvect_1(v3) &
% 74.62/11.00 v3_rlvect_1(v0) & ~ v3_struct_0(v3) & ~ v3_struct_0(v0) &
% 74.62/11.00 ((k8_rlvect_2(v3, v6, v5) = v7 & $i(v7) & v1_rmod_5(v7, v0, v3)) |
% 74.62/11.00 (k8_rlvect_2(v3, v5, v6) = v8 & $i(v8) & v1_rmod_5(v8, v0, v3))))
% 74.62/11.00
% 74.62/11.00 (function-axioms)
% 74.62/11.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 74.62/11.01 | ~ (k8_rlvect_2(v4, v3, v2) = v1) | ~ (k8_rlvect_2(v4, v3, v2) = v0)) &
% 74.62/11.01 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 74.62/11.01 (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = v0)) & ! [v0: $i] : !
% 74.62/11.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k2_group_1(v2) = v1) | ~
% 74.62/11.01 (k2_group_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 74.62/11.01 | ~ (k1_rlvect_1(v2) = v1) | ~ (k1_rlvect_1(v2) = v0)) & ! [v0: $i] : !
% 74.62/11.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~
% 74.62/11.01 (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 74.62/11.01 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 74.62/11.01
% 74.62/11.01 Further assumptions not needed in the proof:
% 74.62/11.01 --------------------------------------------
% 74.62/11.01 antisymmetry_r2_hidden, commutativity_k2_tarski, commutativity_k8_rlvect_2,
% 74.62/11.01 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_group_1, dt_k2_tarski, dt_k8_rlvect_2,
% 74.62/11.01 dt_l1_group_1, dt_l1_struct_0, dt_l1_vectsp_1, dt_m1_subset_1, dt_u1_struct_0,
% 74.62/11.01 existence_l1_group_1, existence_l1_rlvect_1, existence_l1_struct_0,
% 74.62/11.01 existence_l1_vectsp_1, existence_l1_vectsp_2, existence_l2_struct_0,
% 74.62/11.01 existence_l2_vectsp_1, existence_l3_vectsp_1, existence_m1_subset_1,
% 74.62/11.01 fc1_struct_0, fc1_subset_1, fc1_xboole_0, fc3_subset_1, rc1_subset_1,
% 74.62/11.01 rc1_xboole_0, rc2_subset_1, rc2_xboole_0, rc3_struct_0, rc5_struct_0,
% 74.62/11.01 rc9_vectsp_2, redefinition_k8_rlvect_2, reflexivity_r1_tarski, t1_subset,
% 74.62/11.01 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 74.62/11.01
% 74.62/11.01 Those formulas are unsatisfiable:
% 74.62/11.01 ---------------------------------
% 74.62/11.01
% 74.62/11.01 Begin of proof
% 74.62/11.01 |
% 74.62/11.01 | ALPHA: (dt_l2_vectsp_1) implies:
% 74.62/11.01 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ l2_vectsp_1(v0) | l2_struct_0(v0))
% 74.62/11.01 |
% 74.62/11.01 | ALPHA: (dt_k1_rlvect_1) implies:
% 74.62/11.01 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 74.62/11.01 | l2_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) = v2 & $i(v2) &
% 74.62/11.01 | m1_subset_1(v2, v1)))
% 74.62/11.02 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) | ~
% 74.62/11.02 | l2_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) &
% 74.62/11.02 | m1_subset_1(v1, v2)))
% 74.62/11.02 |
% 74.62/11.02 | ALPHA: (dt_l3_vectsp_1) implies:
% 74.62/11.02 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ l3_vectsp_1(v0) | l2_vectsp_1(v0))
% 74.62/11.02 |
% 74.62/11.02 | ALPHA: (t5_rmod_5) implies:
% 74.62/11.02 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) | ~
% 74.62/11.02 | l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~
% 74.62/11.02 | v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~
% 74.62/11.02 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) |
% 74.62/11.02 | v3_struct_0(v0) | ? [v2: $i] : (k2_group_1(v0) = v2 & $i(v2) & !
% 74.62/11.02 | [v3: $i] : ! [v4: $i] : ( ~ (k1_rlvect_1(v3) = v4) | ~ $i(v3) |
% 74.62/11.02 | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~
% 74.62/11.02 | v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~
% 74.62/11.02 | v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5: $i] :
% 74.62/11.02 | (u1_struct_0(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : (v2
% 74.62/11.02 | = v1 | ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ $i(v6) | ~
% 74.62/11.02 | $i(v4) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) |
% 74.62/11.02 | ~ m1_subset_1(v4, v5)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1
% 74.62/11.02 | | ~ (k8_rlvect_2(v3, v4, v6) = v7) | ~ $i(v6) | ~ $i(v4) |
% 74.62/11.02 | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~
% 74.62/11.02 | m1_subset_1(v4, v5)))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 74.62/11.03 | (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ l1_vectsp_2(v3, v0) | ~
% 74.62/11.03 | v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) |
% 74.62/11.03 | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ?
% 74.62/11.03 | [v5: $i] : (k1_rlvect_1(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7:
% 74.62/11.03 | $i] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~
% 74.62/11.03 | $i(v6) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) |
% 74.62/11.03 | ~ m1_subset_1(v5, v4)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1
% 74.62/11.03 | | ~ (k8_rlvect_2(v3, v5, v6) = v7) | ~ $i(v6) | ~
% 74.62/11.03 | v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~
% 74.62/11.03 | m1_subset_1(v5, v4))))))
% 74.62/11.03 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_group_1(v0) = v1) | ~ $i(v0) | ~
% 74.62/11.03 | l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~
% 74.62/11.03 | v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v0) | ~
% 74.62/11.03 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) |
% 74.62/11.03 | v3_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) = v2 & $i(v2) & !
% 74.62/11.03 | [v3: $i] : ! [v4: $i] : ( ~ (k1_rlvect_1(v3) = v4) | ~ $i(v3) |
% 74.62/11.03 | ~ l1_vectsp_2(v3, v0) | ~ v5_vectsp_2(v3, v0) | ~
% 74.62/11.03 | v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) | ~ v4_rlvect_1(v3) | ~
% 74.62/11.03 | v3_rlvect_1(v3) | v3_struct_0(v3) | ? [v5: $i] :
% 74.62/11.03 | (u1_struct_0(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7: $i] : (v2
% 74.62/11.03 | = v1 | ~ (k8_rlvect_2(v3, v6, v4) = v7) | ~ $i(v6) | ~
% 74.62/11.03 | $i(v4) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) |
% 74.62/11.03 | ~ m1_subset_1(v4, v5)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1
% 74.62/11.03 | | ~ (k8_rlvect_2(v3, v4, v6) = v7) | ~ $i(v6) | ~ $i(v4) |
% 74.62/11.03 | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v5) | ~
% 74.62/11.03 | m1_subset_1(v4, v5)))) & ! [v3: $i] : ! [v4: $i] : ( ~
% 74.62/11.03 | (u1_struct_0(v3) = v4) | ~ $i(v3) | ~ l1_vectsp_2(v3, v0) | ~
% 74.62/11.03 | v5_vectsp_2(v3, v0) | ~ v6_rlvect_1(v3) | ~ v5_rlvect_1(v3) |
% 74.62/11.03 | ~ v4_rlvect_1(v3) | ~ v3_rlvect_1(v3) | v3_struct_0(v3) | ?
% 74.62/11.03 | [v5: $i] : (k1_rlvect_1(v3) = v5 & $i(v5) & ! [v6: $i] : ! [v7:
% 74.62/11.03 | $i] : (v2 = v1 | ~ (k8_rlvect_2(v3, v6, v5) = v7) | ~
% 74.62/11.03 | $i(v6) | ~ v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) |
% 74.62/11.03 | ~ m1_subset_1(v5, v4)) & ! [v6: $i] : ! [v7: $i] : (v2 = v1
% 74.62/11.03 | | ~ (k8_rlvect_2(v3, v5, v6) = v7) | ~ $i(v6) | ~
% 74.62/11.03 | v1_rmod_5(v7, v0, v3) | ~ m1_subset_1(v6, v4) | ~
% 74.62/11.03 | m1_subset_1(v5, v4))))))
% 74.62/11.03 |
% 74.62/11.03 | ALPHA: (function-axioms) implies:
% 74.62/11.04 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 74.62/11.04 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 74.62/11.04 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 74.62/11.04 | (k1_rlvect_1(v2) = v1) | ~ (k1_rlvect_1(v2) = v0))
% 74.62/11.04 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k2_group_1(v2)
% 74.62/11.04 | = v1) | ~ (k2_group_1(v2) = v0))
% 74.62/11.04 |
% 74.62/11.04 | DELTA: instantiating (rc4_struct_0) with fresh symbol all_57_0 gives:
% 74.62/11.04 | (10) $i(all_57_0) & l2_struct_0(all_57_0) & ~ v3_struct_0(all_57_0)
% 74.62/11.04 |
% 74.62/11.04 | ALPHA: (10) implies:
% 74.62/11.04 | (11) ~ v3_struct_0(all_57_0)
% 74.62/11.04 | (12) l2_struct_0(all_57_0)
% 74.62/11.04 | (13) $i(all_57_0)
% 74.62/11.04 |
% 74.62/11.04 | DELTA: instantiating (t6_rmod_5) with fresh symbols all_60_0, all_60_1,
% 74.62/11.04 | all_60_2, all_60_3, all_60_4, all_60_5, all_60_6, all_60_7, all_60_8
% 74.62/11.04 | gives:
% 74.62/11.04 | (14) ~ (all_60_6 = all_60_7) & k2_group_1(all_60_8) = all_60_6 &
% 74.62/11.04 | k1_rlvect_1(all_60_5) = all_60_3 & k1_rlvect_1(all_60_8) = all_60_7 &
% 74.62/11.04 | u1_struct_0(all_60_5) = all_60_4 & $i(all_60_2) & $i(all_60_3) &
% 74.62/11.04 | $i(all_60_4) & $i(all_60_5) & $i(all_60_6) & $i(all_60_7) &
% 74.62/11.04 | $i(all_60_8) & m1_subset_1(all_60_2, all_60_4) & l1_vectsp_2(all_60_5,
% 74.62/11.04 | all_60_8) & v5_vectsp_2(all_60_5, all_60_8) & l3_vectsp_1(all_60_8)
% 74.62/11.04 | & v8_vectsp_1(all_60_8) & v7_vectsp_1(all_60_8) &
% 74.62/11.04 | v6_vectsp_1(all_60_8) & v4_group_1(all_60_8) & v6_rlvect_1(all_60_5) &
% 74.62/11.04 | v6_rlvect_1(all_60_8) & v5_rlvect_1(all_60_5) & v5_rlvect_1(all_60_8)
% 74.62/11.04 | & v4_rlvect_1(all_60_5) & v4_rlvect_1(all_60_8) &
% 74.62/11.04 | v3_rlvect_1(all_60_5) & v3_rlvect_1(all_60_8) & ~
% 74.62/11.04 | v3_struct_0(all_60_5) & ~ v3_struct_0(all_60_8) &
% 74.62/11.04 | ((k8_rlvect_2(all_60_5, all_60_2, all_60_3) = all_60_1 & $i(all_60_1)
% 74.62/11.04 | & v1_rmod_5(all_60_1, all_60_8, all_60_5)) |
% 74.62/11.04 | (k8_rlvect_2(all_60_5, all_60_3, all_60_2) = all_60_0 & $i(all_60_0)
% 74.62/11.04 | & v1_rmod_5(all_60_0, all_60_8, all_60_5)))
% 74.62/11.04 |
% 74.62/11.04 | ALPHA: (14) implies:
% 74.62/11.04 | (15) ~ (all_60_6 = all_60_7)
% 74.62/11.04 | (16) ~ v3_struct_0(all_60_8)
% 74.62/11.04 | (17) ~ v3_struct_0(all_60_5)
% 74.62/11.04 | (18) v3_rlvect_1(all_60_8)
% 74.62/11.04 | (19) v3_rlvect_1(all_60_5)
% 74.62/11.04 | (20) v4_rlvect_1(all_60_8)
% 74.62/11.04 | (21) v4_rlvect_1(all_60_5)
% 74.62/11.04 | (22) v5_rlvect_1(all_60_8)
% 74.62/11.04 | (23) v5_rlvect_1(all_60_5)
% 74.62/11.05 | (24) v6_rlvect_1(all_60_8)
% 74.62/11.05 | (25) v6_rlvect_1(all_60_5)
% 74.62/11.05 | (26) v4_group_1(all_60_8)
% 74.62/11.05 | (27) v6_vectsp_1(all_60_8)
% 74.62/11.05 | (28) v7_vectsp_1(all_60_8)
% 74.62/11.05 | (29) v8_vectsp_1(all_60_8)
% 74.62/11.05 | (30) l3_vectsp_1(all_60_8)
% 74.62/11.05 | (31) v5_vectsp_2(all_60_5, all_60_8)
% 74.62/11.05 | (32) l1_vectsp_2(all_60_5, all_60_8)
% 74.62/11.05 | (33) m1_subset_1(all_60_2, all_60_4)
% 74.62/11.05 | (34) $i(all_60_8)
% 74.62/11.05 | (35) $i(all_60_5)
% 74.62/11.05 | (36) $i(all_60_2)
% 74.62/11.05 | (37) u1_struct_0(all_60_5) = all_60_4
% 74.62/11.05 | (38) k1_rlvect_1(all_60_8) = all_60_7
% 74.62/11.05 | (39) k1_rlvect_1(all_60_5) = all_60_3
% 74.62/11.05 | (40) k2_group_1(all_60_8) = all_60_6
% 74.62/11.05 | (41) (k8_rlvect_2(all_60_5, all_60_2, all_60_3) = all_60_1 & $i(all_60_1) &
% 74.62/11.05 | v1_rmod_5(all_60_1, all_60_8, all_60_5)) | (k8_rlvect_2(all_60_5,
% 74.62/11.05 | all_60_3, all_60_2) = all_60_0 & $i(all_60_0) &
% 74.62/11.05 | v1_rmod_5(all_60_0, all_60_8, all_60_5))
% 74.62/11.05 |
% 74.62/11.05 | GROUND_INST: instantiating (8) with all_60_7, all_60_3, all_60_8, simplifying
% 74.62/11.05 | with (38) gives:
% 74.62/11.05 | (42) all_60_3 = all_60_7 | ~ (k1_rlvect_1(all_60_8) = all_60_3)
% 74.62/11.05 |
% 74.62/11.05 | GROUND_INST: instantiating (4) with all_60_8, simplifying with (30), (34)
% 74.62/11.05 | gives:
% 74.62/11.05 | (43) l2_vectsp_1(all_60_8)
% 74.62/11.05 |
% 74.62/11.05 | GROUND_INST: instantiating (dt_l2_struct_0) with all_57_0, simplifying with
% 74.62/11.05 | (12), (13) gives:
% 74.62/11.05 | (44) l1_struct_0(all_57_0)
% 74.62/11.05 |
% 74.62/11.05 | GROUND_INST: instantiating (2) with all_57_0, all_60_4, simplifying with (12),
% 74.62/11.05 | (13) gives:
% 74.62/11.05 | (45) ~ (u1_struct_0(all_57_0) = all_60_4) | ? [v0: $i] :
% 74.62/11.05 | (k1_rlvect_1(all_57_0) = v0 & $i(v0) & m1_subset_1(v0, all_60_4))
% 74.62/11.05 |
% 74.62/11.05 | GROUND_INST: instantiating (5) with all_60_8, all_60_7, simplifying with (16),
% 74.62/11.05 | (18), (20), (22), (24), (26), (27), (28), (29), (30), (34), (38)
% 74.62/11.05 | gives:
% 74.62/11.06 | (46) ? [v0: $i] : (k2_group_1(all_60_8) = v0 & $i(v0) & ! [v1: $i] : !
% 74.62/11.06 | [v2: $i] : ( ~ (k1_rlvect_1(v1) = v2) | ~ $i(v1) | ~
% 74.62/11.06 | l1_vectsp_2(v1, all_60_8) | ~ v5_vectsp_2(v1, all_60_8) | ~
% 74.62/11.06 | v6_rlvect_1(v1) | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~
% 74.62/11.06 | v3_rlvect_1(v1) | v3_struct_0(v1) | ? [v3: $i] : (u1_struct_0(v1)
% 74.62/11.06 | = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v0 = all_60_7 | ~
% 74.62/11.06 | (k8_rlvect_2(v1, v4, v2) = v5) | ~ $i(v4) | ~ $i(v2) | ~
% 74.62/11.06 | v1_rmod_5(v5, all_60_8, v1) | ~ m1_subset_1(v4, v3) | ~
% 74.62/11.06 | m1_subset_1(v2, v3)) & ! [v4: $i] : ! [v5: $i] : (v0 =
% 74.62/11.06 | all_60_7 | ~ (k8_rlvect_2(v1, v2, v4) = v5) | ~ $i(v4) | ~
% 74.62/11.06 | $i(v2) | ~ v1_rmod_5(v5, all_60_8, v1) | ~ m1_subset_1(v4,
% 74.62/11.06 | v3) | ~ m1_subset_1(v2, v3)))) & ! [v1: $i] : ! [v2: $i]
% 74.62/11.06 | : ( ~ (u1_struct_0(v1) = v2) | ~ $i(v1) | ~ l1_vectsp_2(v1,
% 74.62/11.06 | all_60_8) | ~ v5_vectsp_2(v1, all_60_8) | ~ v6_rlvect_1(v1) |
% 74.62/11.06 | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~ v3_rlvect_1(v1) |
% 74.62/11.06 | v3_struct_0(v1) | ? [v3: $i] : (k1_rlvect_1(v1) = v3 & $i(v3) &
% 74.62/11.06 | ! [v4: $i] : ! [v5: $i] : (v0 = all_60_7 | ~ (k8_rlvect_2(v1,
% 74.62/11.06 | v4, v3) = v5) | ~ $i(v4) | ~ v1_rmod_5(v5, all_60_8, v1)
% 74.62/11.06 | | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)) & ! [v4:
% 74.62/11.06 | $i] : ! [v5: $i] : (v0 = all_60_7 | ~ (k8_rlvect_2(v1, v3,
% 74.62/11.06 | v4) = v5) | ~ $i(v4) | ~ v1_rmod_5(v5, all_60_8, v1) |
% 74.62/11.06 | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)))))
% 74.62/11.06 |
% 74.62/11.06 | GROUND_INST: instantiating (6) with all_60_8, all_60_6, simplifying with (16),
% 74.62/11.06 | (18), (20), (22), (24), (26), (27), (28), (29), (30), (34), (40)
% 74.62/11.06 | gives:
% 74.62/11.07 | (47) ? [v0: $i] : (k1_rlvect_1(all_60_8) = v0 & $i(v0) & ! [v1: $i] : !
% 74.62/11.07 | [v2: $i] : ( ~ (k1_rlvect_1(v1) = v2) | ~ $i(v1) | ~
% 74.62/11.07 | l1_vectsp_2(v1, all_60_8) | ~ v5_vectsp_2(v1, all_60_8) | ~
% 74.62/11.07 | v6_rlvect_1(v1) | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~
% 74.62/11.07 | v3_rlvect_1(v1) | v3_struct_0(v1) | ? [v3: $i] : (u1_struct_0(v1)
% 74.62/11.07 | = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : (v0 = all_60_6 | ~
% 74.62/11.07 | (k8_rlvect_2(v1, v4, v2) = v5) | ~ $i(v4) | ~ $i(v2) | ~
% 74.62/11.07 | v1_rmod_5(v5, all_60_8, v1) | ~ m1_subset_1(v4, v3) | ~
% 74.62/11.07 | m1_subset_1(v2, v3)) & ! [v4: $i] : ! [v5: $i] : (v0 =
% 74.62/11.07 | all_60_6 | ~ (k8_rlvect_2(v1, v2, v4) = v5) | ~ $i(v4) | ~
% 74.62/11.07 | $i(v2) | ~ v1_rmod_5(v5, all_60_8, v1) | ~ m1_subset_1(v4,
% 74.62/11.07 | v3) | ~ m1_subset_1(v2, v3)))) & ! [v1: $i] : ! [v2: $i]
% 74.62/11.07 | : ( ~ (u1_struct_0(v1) = v2) | ~ $i(v1) | ~ l1_vectsp_2(v1,
% 74.62/11.07 | all_60_8) | ~ v5_vectsp_2(v1, all_60_8) | ~ v6_rlvect_1(v1) |
% 74.62/11.07 | ~ v5_rlvect_1(v1) | ~ v4_rlvect_1(v1) | ~ v3_rlvect_1(v1) |
% 74.62/11.07 | v3_struct_0(v1) | ? [v3: $i] : (k1_rlvect_1(v1) = v3 & $i(v3) &
% 74.62/11.07 | ! [v4: $i] : ! [v5: $i] : (v0 = all_60_6 | ~ (k8_rlvect_2(v1,
% 74.62/11.07 | v4, v3) = v5) | ~ $i(v4) | ~ v1_rmod_5(v5, all_60_8, v1)
% 74.62/11.07 | | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)) & ! [v4:
% 74.62/11.07 | $i] : ! [v5: $i] : (v0 = all_60_6 | ~ (k8_rlvect_2(v1, v3,
% 74.62/11.07 | v4) = v5) | ~ $i(v4) | ~ v1_rmod_5(v5, all_60_8, v1) |
% 74.62/11.07 | ~ m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2)))))
% 74.62/11.07 |
% 74.62/11.07 | DELTA: instantiating (47) with fresh symbol all_80_0 gives:
% 74.62/11.07 | (48) k1_rlvect_1(all_60_8) = all_80_0 & $i(all_80_0) & ! [v0: $i] : !
% 74.62/11.07 | [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) | ~ l1_vectsp_2(v0,
% 74.62/11.07 | all_60_8) | ~ v5_vectsp_2(v0, all_60_8) | ~ v6_rlvect_1(v0) | ~
% 74.62/11.07 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) |
% 74.62/11.07 | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & !
% 74.62/11.07 | [v3: $i] : ! [v4: $i] : (all_80_0 = all_60_6 | ~
% 74.62/11.07 | (k8_rlvect_2(v0, v3, v1) = v4) | ~ $i(v3) | ~ $i(v1) | ~
% 74.62/11.07 | v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2) | ~
% 74.62/11.07 | m1_subset_1(v1, v2)) & ! [v3: $i] : ! [v4: $i] : (all_80_0 =
% 74.62/11.07 | all_60_6 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ $i(v3) | ~
% 74.62/11.07 | $i(v1) | ~ v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2)
% 74.62/11.07 | | ~ m1_subset_1(v1, v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 74.62/11.07 | (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_vectsp_2(v0, all_60_8) |
% 74.62/11.07 | ~ v5_vectsp_2(v0, all_60_8) | ~ v6_rlvect_1(v0) | ~
% 74.62/11.07 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) |
% 74.62/11.07 | v3_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) = v2 & $i(v2) & !
% 74.62/11.07 | [v3: $i] : ! [v4: $i] : (all_80_0 = all_60_6 | ~
% 74.62/11.07 | (k8_rlvect_2(v0, v3, v2) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 74.62/11.07 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 74.62/11.07 | v1)) & ! [v3: $i] : ! [v4: $i] : (all_80_0 = all_60_6 | ~
% 74.62/11.07 | (k8_rlvect_2(v0, v2, v3) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 74.62/11.07 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 74.62/11.07 | v1))))
% 74.62/11.07 |
% 74.62/11.07 | ALPHA: (48) implies:
% 75.02/11.07 | (49) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 75.02/11.07 | ~ l1_vectsp_2(v0, all_60_8) | ~ v5_vectsp_2(v0, all_60_8) | ~
% 75.02/11.07 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~
% 75.02/11.07 | v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) =
% 75.02/11.07 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : (all_80_0 = all_60_6 |
% 75.02/11.07 | ~ (k8_rlvect_2(v0, v3, v2) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 75.02/11.07 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 75.02/11.07 | v1)) & ! [v3: $i] : ! [v4: $i] : (all_80_0 = all_60_6 | ~
% 75.02/11.07 | (k8_rlvect_2(v0, v2, v3) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 75.02/11.07 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 75.02/11.07 | v1))))
% 75.02/11.08 | (50) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) |
% 75.02/11.08 | ~ l1_vectsp_2(v0, all_60_8) | ~ v5_vectsp_2(v0, all_60_8) | ~
% 75.02/11.08 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~
% 75.02/11.08 | v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) =
% 75.02/11.08 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : (all_80_0 = all_60_6 |
% 75.02/11.08 | ~ (k8_rlvect_2(v0, v3, v1) = v4) | ~ $i(v3) | ~ $i(v1) | ~
% 75.02/11.08 | v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2) | ~
% 75.02/11.08 | m1_subset_1(v1, v2)) & ! [v3: $i] : ! [v4: $i] : (all_80_0 =
% 75.02/11.08 | all_60_6 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ $i(v3) | ~
% 75.02/11.08 | $i(v1) | ~ v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2)
% 75.02/11.08 | | ~ m1_subset_1(v1, v2))))
% 75.02/11.08 |
% 75.02/11.08 | GROUND_INST: instantiating (49) with all_60_5, all_60_4, simplifying with
% 75.02/11.08 | (17), (19), (21), (23), (25), (31), (32), (35), (37) gives:
% 75.04/11.08 | (51) ? [v0: $i] : (k1_rlvect_1(all_60_5) = v0 & $i(v0) & ! [v1: $i] : !
% 75.04/11.08 | [v2: $i] : (all_80_0 = all_60_6 | ~ (k8_rlvect_2(all_60_5, v1, v0)
% 75.04/11.08 | = v2) | ~ $i(v1) | ~ v1_rmod_5(v2, all_60_8, all_60_5) | ~
% 75.04/11.08 | m1_subset_1(v1, all_60_4) | ~ m1_subset_1(v0, all_60_4)) & !
% 75.04/11.08 | [v1: $i] : ! [v2: $i] : (all_80_0 = all_60_6 | ~
% 75.04/11.08 | (k8_rlvect_2(all_60_5, v0, v1) = v2) | ~ $i(v1) | ~
% 75.04/11.08 | v1_rmod_5(v2, all_60_8, all_60_5) | ~ m1_subset_1(v1, all_60_4) |
% 75.04/11.08 | ~ m1_subset_1(v0, all_60_4)))
% 75.04/11.08 |
% 75.04/11.08 | GROUND_INST: instantiating (50) with all_60_5, all_60_3, simplifying with
% 75.04/11.08 | (17), (19), (21), (23), (25), (31), (32), (35), (39) gives:
% 75.04/11.08 | (52) ? [v0: $i] : (u1_struct_0(all_60_5) = v0 & $i(v0) & ! [v1: $i] : !
% 75.04/11.08 | [v2: $i] : (all_80_0 = all_60_6 | ~ (k8_rlvect_2(all_60_5, v1,
% 75.04/11.08 | all_60_3) = v2) | ~ $i(v1) | ~ $i(all_60_3) | ~
% 75.04/11.08 | v1_rmod_5(v2, all_60_8, all_60_5) | ~ m1_subset_1(v1, v0) | ~
% 75.04/11.08 | m1_subset_1(all_60_3, v0)) & ! [v1: $i] : ! [v2: $i] : (all_80_0
% 75.04/11.08 | = all_60_6 | ~ (k8_rlvect_2(all_60_5, all_60_3, v1) = v2) | ~
% 75.04/11.08 | $i(v1) | ~ $i(all_60_3) | ~ v1_rmod_5(v2, all_60_8, all_60_5) |
% 75.04/11.08 | ~ m1_subset_1(v1, v0) | ~ m1_subset_1(all_60_3, v0)))
% 75.04/11.08 |
% 75.04/11.08 | DELTA: instantiating (51) with fresh symbol all_83_0 gives:
% 75.04/11.08 | (53) k1_rlvect_1(all_60_5) = all_83_0 & $i(all_83_0) & ! [v0: $i] : !
% 75.04/11.08 | [v1: $i] : (all_80_0 = all_60_6 | ~ (k8_rlvect_2(all_60_5, v0,
% 75.04/11.08 | all_83_0) = v1) | ~ $i(v0) | ~ v1_rmod_5(v1, all_60_8,
% 75.04/11.08 | all_60_5) | ~ m1_subset_1(v0, all_60_4) | ~
% 75.04/11.08 | m1_subset_1(all_83_0, all_60_4)) & ! [v0: $i] : ! [v1: $i] :
% 75.04/11.08 | (all_80_0 = all_60_6 | ~ (k8_rlvect_2(all_60_5, all_83_0, v0) = v1) |
% 75.04/11.08 | ~ $i(v0) | ~ v1_rmod_5(v1, all_60_8, all_60_5) | ~
% 75.04/11.08 | m1_subset_1(v0, all_60_4) | ~ m1_subset_1(all_83_0, all_60_4))
% 75.04/11.08 |
% 75.04/11.08 | ALPHA: (53) implies:
% 75.04/11.08 | (54) k1_rlvect_1(all_60_5) = all_83_0
% 75.04/11.08 |
% 75.04/11.08 | DELTA: instantiating (52) with fresh symbol all_86_0 gives:
% 75.04/11.09 | (55) u1_struct_0(all_60_5) = all_86_0 & $i(all_86_0) & ! [v0: $i] : !
% 75.04/11.09 | [v1: $i] : (all_80_0 = all_60_6 | ~ (k8_rlvect_2(all_60_5, v0,
% 75.04/11.09 | all_60_3) = v1) | ~ $i(v0) | ~ $i(all_60_3) | ~ v1_rmod_5(v1,
% 75.04/11.09 | all_60_8, all_60_5) | ~ m1_subset_1(v0, all_86_0) | ~
% 75.04/11.09 | m1_subset_1(all_60_3, all_86_0)) & ! [v0: $i] : ! [v1: $i] :
% 75.04/11.09 | (all_80_0 = all_60_6 | ~ (k8_rlvect_2(all_60_5, all_60_3, v0) = v1) |
% 75.04/11.09 | ~ $i(v0) | ~ $i(all_60_3) | ~ v1_rmod_5(v1, all_60_8, all_60_5) |
% 75.04/11.09 | ~ m1_subset_1(v0, all_86_0) | ~ m1_subset_1(all_60_3, all_86_0))
% 75.04/11.09 |
% 75.04/11.09 | ALPHA: (55) implies:
% 75.04/11.09 | (56) u1_struct_0(all_60_5) = all_86_0
% 75.04/11.09 |
% 75.04/11.09 | DELTA: instantiating (46) with fresh symbol all_89_0 gives:
% 75.04/11.09 | (57) k2_group_1(all_60_8) = all_89_0 & $i(all_89_0) & ! [v0: $i] : ! [v1:
% 75.04/11.09 | $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) | ~ l1_vectsp_2(v0,
% 75.04/11.09 | all_60_8) | ~ v5_vectsp_2(v0, all_60_8) | ~ v6_rlvect_1(v0) | ~
% 75.04/11.09 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) |
% 75.04/11.09 | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) & !
% 75.04/11.09 | [v3: $i] : ! [v4: $i] : (all_89_0 = all_60_7 | ~
% 75.04/11.09 | (k8_rlvect_2(v0, v3, v1) = v4) | ~ $i(v3) | ~ $i(v1) | ~
% 75.04/11.09 | v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2) | ~
% 75.04/11.09 | m1_subset_1(v1, v2)) & ! [v3: $i] : ! [v4: $i] : (all_89_0 =
% 75.04/11.09 | all_60_7 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ $i(v3) | ~
% 75.04/11.09 | $i(v1) | ~ v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2)
% 75.04/11.09 | | ~ m1_subset_1(v1, v2)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 75.04/11.09 | (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_vectsp_2(v0, all_60_8) |
% 75.04/11.09 | ~ v5_vectsp_2(v0, all_60_8) | ~ v6_rlvect_1(v0) | ~
% 75.04/11.09 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v0) |
% 75.04/11.09 | v3_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) = v2 & $i(v2) & !
% 75.04/11.09 | [v3: $i] : ! [v4: $i] : (all_89_0 = all_60_7 | ~
% 75.04/11.09 | (k8_rlvect_2(v0, v3, v2) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 75.04/11.09 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 75.04/11.09 | v1)) & ! [v3: $i] : ! [v4: $i] : (all_89_0 = all_60_7 | ~
% 75.04/11.09 | (k8_rlvect_2(v0, v2, v3) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 75.04/11.09 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 75.04/11.09 | v1))))
% 75.04/11.09 |
% 75.04/11.09 | ALPHA: (57) implies:
% 75.04/11.09 | (58) k2_group_1(all_60_8) = all_89_0
% 75.04/11.09 | (59) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 75.04/11.09 | ~ l1_vectsp_2(v0, all_60_8) | ~ v5_vectsp_2(v0, all_60_8) | ~
% 75.04/11.09 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~
% 75.04/11.09 | v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (k1_rlvect_1(v0) =
% 75.04/11.09 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : (all_89_0 = all_60_7 |
% 75.04/11.09 | ~ (k8_rlvect_2(v0, v3, v2) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 75.04/11.09 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 75.04/11.09 | v1)) & ! [v3: $i] : ! [v4: $i] : (all_89_0 = all_60_7 | ~
% 75.04/11.09 | (k8_rlvect_2(v0, v2, v3) = v4) | ~ $i(v3) | ~ v1_rmod_5(v4,
% 75.04/11.09 | all_60_8, v0) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2,
% 75.04/11.09 | v1))))
% 75.04/11.10 | (60) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_rlvect_1(v0) = v1) | ~ $i(v0) |
% 75.04/11.10 | ~ l1_vectsp_2(v0, all_60_8) | ~ v5_vectsp_2(v0, all_60_8) | ~
% 75.04/11.10 | v6_rlvect_1(v0) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v0) | ~
% 75.04/11.10 | v3_rlvect_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) =
% 75.04/11.10 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : (all_89_0 = all_60_7 |
% 75.04/11.10 | ~ (k8_rlvect_2(v0, v3, v1) = v4) | ~ $i(v3) | ~ $i(v1) | ~
% 75.04/11.10 | v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2) | ~
% 75.04/11.10 | m1_subset_1(v1, v2)) & ! [v3: $i] : ! [v4: $i] : (all_89_0 =
% 75.04/11.10 | all_60_7 | ~ (k8_rlvect_2(v0, v1, v3) = v4) | ~ $i(v3) | ~
% 75.04/11.10 | $i(v1) | ~ v1_rmod_5(v4, all_60_8, v0) | ~ m1_subset_1(v3, v2)
% 75.04/11.10 | | ~ m1_subset_1(v1, v2))))
% 75.04/11.10 |
% 75.04/11.10 | GROUND_INST: instantiating (59) with all_60_5, all_60_4, simplifying with
% 75.04/11.10 | (17), (19), (21), (23), (25), (31), (32), (35), (37) gives:
% 75.04/11.10 | (61) ? [v0: $i] : (k1_rlvect_1(all_60_5) = v0 & $i(v0) & ! [v1: $i] : !
% 75.04/11.10 | [v2: $i] : (all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, v1, v0)
% 75.04/11.10 | = v2) | ~ $i(v1) | ~ v1_rmod_5(v2, all_60_8, all_60_5) | ~
% 75.04/11.10 | m1_subset_1(v1, all_60_4) | ~ m1_subset_1(v0, all_60_4)) & !
% 75.04/11.10 | [v1: $i] : ! [v2: $i] : (all_89_0 = all_60_7 | ~
% 75.04/11.10 | (k8_rlvect_2(all_60_5, v0, v1) = v2) | ~ $i(v1) | ~
% 75.04/11.10 | v1_rmod_5(v2, all_60_8, all_60_5) | ~ m1_subset_1(v1, all_60_4) |
% 75.04/11.10 | ~ m1_subset_1(v0, all_60_4)))
% 75.04/11.10 |
% 75.04/11.10 | GROUND_INST: instantiating (60) with all_60_5, all_60_3, simplifying with
% 75.04/11.10 | (17), (19), (21), (23), (25), (31), (32), (35), (39) gives:
% 75.04/11.10 | (62) ? [v0: $i] : (u1_struct_0(all_60_5) = v0 & $i(v0) & ! [v1: $i] : !
% 75.04/11.10 | [v2: $i] : (all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, v1,
% 75.04/11.10 | all_60_3) = v2) | ~ $i(v1) | ~ $i(all_60_3) | ~
% 75.04/11.10 | v1_rmod_5(v2, all_60_8, all_60_5) | ~ m1_subset_1(v1, v0) | ~
% 75.04/11.10 | m1_subset_1(all_60_3, v0)) & ! [v1: $i] : ! [v2: $i] : (all_89_0
% 75.04/11.10 | = all_60_7 | ~ (k8_rlvect_2(all_60_5, all_60_3, v1) = v2) | ~
% 75.04/11.10 | $i(v1) | ~ $i(all_60_3) | ~ v1_rmod_5(v2, all_60_8, all_60_5) |
% 75.04/11.10 | ~ m1_subset_1(v1, v0) | ~ m1_subset_1(all_60_3, v0)))
% 75.04/11.10 |
% 75.04/11.10 | DELTA: instantiating (61) with fresh symbol all_92_0 gives:
% 75.14/11.10 | (63) k1_rlvect_1(all_60_5) = all_92_0 & $i(all_92_0) & ! [v0: $i] : !
% 75.14/11.10 | [v1: $i] : (all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, v0,
% 75.14/11.10 | all_92_0) = v1) | ~ $i(v0) | ~ v1_rmod_5(v1, all_60_8,
% 75.14/11.10 | all_60_5) | ~ m1_subset_1(v0, all_60_4) | ~
% 75.14/11.10 | m1_subset_1(all_92_0, all_60_4)) & ! [v0: $i] : ! [v1: $i] :
% 75.14/11.10 | (all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, all_92_0, v0) = v1) |
% 75.14/11.10 | ~ $i(v0) | ~ v1_rmod_5(v1, all_60_8, all_60_5) | ~
% 75.14/11.10 | m1_subset_1(v0, all_60_4) | ~ m1_subset_1(all_92_0, all_60_4))
% 75.14/11.10 |
% 75.14/11.10 | ALPHA: (63) implies:
% 75.14/11.10 | (64) k1_rlvect_1(all_60_5) = all_92_0
% 75.14/11.10 | (65) ! [v0: $i] : ! [v1: $i] : (all_89_0 = all_60_7 | ~
% 75.14/11.10 | (k8_rlvect_2(all_60_5, all_92_0, v0) = v1) | ~ $i(v0) | ~
% 75.14/11.10 | v1_rmod_5(v1, all_60_8, all_60_5) | ~ m1_subset_1(v0, all_60_4) |
% 75.14/11.10 | ~ m1_subset_1(all_92_0, all_60_4))
% 75.14/11.10 |
% 75.14/11.10 | DELTA: instantiating (62) with fresh symbol all_95_0 gives:
% 75.14/11.11 | (66) u1_struct_0(all_60_5) = all_95_0 & $i(all_95_0) & ! [v0: $i] : !
% 75.14/11.11 | [v1: $i] : (all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, v0,
% 75.14/11.11 | all_60_3) = v1) | ~ $i(v0) | ~ $i(all_60_3) | ~ v1_rmod_5(v1,
% 75.14/11.11 | all_60_8, all_60_5) | ~ m1_subset_1(v0, all_95_0) | ~
% 75.14/11.11 | m1_subset_1(all_60_3, all_95_0)) & ! [v0: $i] : ! [v1: $i] :
% 75.14/11.11 | (all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, all_60_3, v0) = v1) |
% 75.14/11.11 | ~ $i(v0) | ~ $i(all_60_3) | ~ v1_rmod_5(v1, all_60_8, all_60_5) |
% 75.14/11.11 | ~ m1_subset_1(v0, all_95_0) | ~ m1_subset_1(all_60_3, all_95_0))
% 75.14/11.11 |
% 75.14/11.11 | ALPHA: (66) implies:
% 75.14/11.11 | (67) u1_struct_0(all_60_5) = all_95_0
% 75.14/11.11 | (68) ! [v0: $i] : ! [v1: $i] : (all_89_0 = all_60_7 | ~
% 75.14/11.11 | (k8_rlvect_2(all_60_5, all_60_3, v0) = v1) | ~ $i(v0) | ~
% 75.14/11.11 | $i(all_60_3) | ~ v1_rmod_5(v1, all_60_8, all_60_5) | ~
% 75.14/11.11 | m1_subset_1(v0, all_95_0) | ~ m1_subset_1(all_60_3, all_95_0))
% 75.14/11.11 | (69) ! [v0: $i] : ! [v1: $i] : (all_89_0 = all_60_7 | ~
% 75.14/11.11 | (k8_rlvect_2(all_60_5, v0, all_60_3) = v1) | ~ $i(v0) | ~
% 75.14/11.11 | $i(all_60_3) | ~ v1_rmod_5(v1, all_60_8, all_60_5) | ~
% 75.14/11.11 | m1_subset_1(v0, all_95_0) | ~ m1_subset_1(all_60_3, all_95_0))
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (7) with all_60_4, all_95_0, all_60_5, simplifying
% 75.14/11.11 | with (37), (67) gives:
% 75.14/11.11 | (70) all_95_0 = all_60_4
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (7) with all_86_0, all_95_0, all_60_5, simplifying
% 75.14/11.11 | with (56), (67) gives:
% 75.14/11.11 | (71) all_95_0 = all_86_0
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (8) with all_60_3, all_92_0, all_60_5, simplifying
% 75.14/11.11 | with (39), (64) gives:
% 75.14/11.11 | (72) all_92_0 = all_60_3
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (8) with all_83_0, all_92_0, all_60_5, simplifying
% 75.14/11.11 | with (54), (64) gives:
% 75.14/11.11 | (73) all_92_0 = all_83_0
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (9) with all_60_6, all_89_0, all_60_8, simplifying
% 75.14/11.11 | with (40), (58) gives:
% 75.14/11.11 | (74) all_89_0 = all_60_6
% 75.14/11.11 |
% 75.14/11.11 | COMBINE_EQS: (70), (71) imply:
% 75.14/11.11 | (75) all_86_0 = all_60_4
% 75.14/11.11 |
% 75.14/11.11 | SIMP: (75) implies:
% 75.14/11.11 | (76) all_86_0 = all_60_4
% 75.14/11.11 |
% 75.14/11.11 | COMBINE_EQS: (72), (73) imply:
% 75.14/11.11 | (77) all_83_0 = all_60_3
% 75.14/11.11 |
% 75.14/11.11 | SIMP: (77) implies:
% 75.14/11.11 | (78) all_83_0 = all_60_3
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (rc2_rlvect_2) with all_57_0, all_60_4, simplifying
% 75.14/11.11 | with (11), (13), (44) gives:
% 75.14/11.11 | (79) ~ (u1_struct_0(all_57_0) = all_60_4) | ? [v0: $i] : ? [v1: $i] :
% 75.14/11.11 | (k1_zfmisc_1(all_60_4) = v0 & $i(v1) & $i(v0) & v1_finset_1(v1) &
% 75.14/11.11 | m1_subset_1(v1, v0) & ~ v1_xboole_0(v1))
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (1) with all_60_8, simplifying with (34), (43)
% 75.14/11.11 | gives:
% 75.14/11.11 | (80) l2_struct_0(all_60_8)
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (dt_l2_struct_0) with all_60_8, simplifying with
% 75.14/11.11 | (34), (80) gives:
% 75.14/11.11 | (81) l1_struct_0(all_60_8)
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (dt_l1_vectsp_2) with all_60_8, all_60_5,
% 75.14/11.11 | simplifying with (32), (34), (35), (81) gives:
% 75.14/11.11 | (82) l1_rlvect_1(all_60_5)
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (3) with all_60_5, all_60_3, simplifying with (35),
% 75.14/11.11 | (39) gives:
% 75.14/11.11 | (83) ~ l2_struct_0(all_60_5) | ? [v0: $i] : (u1_struct_0(all_60_5) = v0 &
% 75.14/11.11 | $i(v0) & m1_subset_1(all_60_3, v0))
% 75.14/11.11 |
% 75.14/11.11 | GROUND_INST: instantiating (2) with all_60_5, all_60_4, simplifying with (35),
% 75.14/11.11 | (37) gives:
% 75.14/11.12 | (84) ~ l2_struct_0(all_60_5) | ? [v0: $i] : (k1_rlvect_1(all_60_5) = v0 &
% 75.14/11.12 | $i(v0) & m1_subset_1(v0, all_60_4))
% 75.14/11.12 |
% 75.14/11.12 | GROUND_INST: instantiating (dt_l1_rlvect_1) with all_60_5, simplifying with
% 75.14/11.12 | (35), (82) gives:
% 75.14/11.12 | (85) l2_struct_0(all_60_5)
% 75.14/11.12 |
% 75.14/11.12 | BETA: splitting (83) gives:
% 75.14/11.12 |
% 75.14/11.12 | Case 1:
% 75.14/11.12 | |
% 75.14/11.12 | | (86) ~ l2_struct_0(all_60_5)
% 75.14/11.12 | |
% 75.14/11.12 | | PRED_UNIFY: (85), (86) imply:
% 75.14/11.12 | | (87) $false
% 75.14/11.12 | |
% 75.14/11.12 | | CLOSE: (87) is inconsistent.
% 75.14/11.12 | |
% 75.14/11.12 | Case 2:
% 75.14/11.12 | |
% 75.14/11.12 | | (88) ? [v0: $i] : (u1_struct_0(all_60_5) = v0 & $i(v0) &
% 75.14/11.12 | | m1_subset_1(all_60_3, v0))
% 75.14/11.12 | |
% 75.14/11.12 | | DELTA: instantiating (88) with fresh symbol all_204_0 gives:
% 75.14/11.12 | | (89) u1_struct_0(all_60_5) = all_204_0 & $i(all_204_0) &
% 75.14/11.12 | | m1_subset_1(all_60_3, all_204_0)
% 75.14/11.12 | |
% 75.14/11.12 | | ALPHA: (89) implies:
% 75.14/11.12 | | (90) m1_subset_1(all_60_3, all_204_0)
% 75.14/11.12 | | (91) u1_struct_0(all_60_5) = all_204_0
% 75.14/11.12 | |
% 75.22/11.12 | | BETA: splitting (84) gives:
% 75.22/11.12 | |
% 75.22/11.12 | | Case 1:
% 75.22/11.12 | | |
% 75.22/11.12 | | | (92) ~ l2_struct_0(all_60_5)
% 75.22/11.12 | | |
% 75.22/11.12 | | | PRED_UNIFY: (85), (92) imply:
% 75.22/11.12 | | | (93) $false
% 75.22/11.12 | | |
% 75.22/11.12 | | | CLOSE: (93) is inconsistent.
% 75.22/11.12 | | |
% 75.22/11.12 | | Case 2:
% 75.22/11.12 | | |
% 75.22/11.12 | | | (94) ? [v0: $i] : (k1_rlvect_1(all_60_5) = v0 & $i(v0) &
% 75.22/11.12 | | | m1_subset_1(v0, all_60_4))
% 75.22/11.12 | | |
% 75.22/11.12 | | | DELTA: instantiating (94) with fresh symbol all_210_0 gives:
% 75.22/11.12 | | | (95) k1_rlvect_1(all_60_5) = all_210_0 & $i(all_210_0) &
% 75.22/11.12 | | | m1_subset_1(all_210_0, all_60_4)
% 75.22/11.12 | | |
% 75.22/11.12 | | | ALPHA: (95) implies:
% 75.22/11.12 | | | (96) $i(all_210_0)
% 75.22/11.12 | | | (97) k1_rlvect_1(all_60_5) = all_210_0
% 75.22/11.12 | | |
% 75.22/11.12 | | | GROUND_INST: instantiating (7) with all_60_4, all_204_0, all_60_5,
% 75.22/11.12 | | | simplifying with (37), (91) gives:
% 75.22/11.12 | | | (98) all_204_0 = all_60_4
% 75.22/11.12 | | |
% 75.22/11.12 | | | GROUND_INST: instantiating (8) with all_60_3, all_210_0, all_60_5,
% 75.22/11.12 | | | simplifying with (39), (97) gives:
% 75.22/11.12 | | | (99) all_210_0 = all_60_3
% 75.22/11.12 | | |
% 75.22/11.12 | | | REDUCE: (96), (99) imply:
% 75.22/11.12 | | | (100) $i(all_60_3)
% 75.22/11.12 | | |
% 75.22/11.12 | | | REDUCE: (90), (98) imply:
% 75.22/11.12 | | | (101) m1_subset_1(all_60_3, all_60_4)
% 75.22/11.12 | | |
% 75.22/11.12 | | | BETA: splitting (41) gives:
% 75.22/11.12 | | |
% 75.22/11.12 | | | Case 1:
% 75.22/11.12 | | | |
% 75.22/11.12 | | | | (102) k8_rlvect_2(all_60_5, all_60_2, all_60_3) = all_60_1 &
% 75.22/11.12 | | | | $i(all_60_1) & v1_rmod_5(all_60_1, all_60_8, all_60_5)
% 75.22/11.12 | | | |
% 75.22/11.12 | | | | ALPHA: (102) implies:
% 75.22/11.12 | | | | (103) v1_rmod_5(all_60_1, all_60_8, all_60_5)
% 75.22/11.12 | | | | (104) k8_rlvect_2(all_60_5, all_60_2, all_60_3) = all_60_1
% 75.22/11.12 | | | |
% 75.22/11.12 | | | | BETA: splitting (45) gives:
% 75.22/11.12 | | | |
% 75.22/11.12 | | | | Case 1:
% 75.22/11.12 | | | | |
% 75.22/11.12 | | | | |
% 75.22/11.12 | | | | | GROUND_INST: instantiating (69) with all_60_2, all_60_1, simplifying
% 75.22/11.12 | | | | | with (36), (100), (103), (104) gives:
% 75.22/11.12 | | | | | (105) all_89_0 = all_60_7 | ~ m1_subset_1(all_60_2, all_95_0) | ~
% 75.22/11.12 | | | | | m1_subset_1(all_60_3, all_95_0)
% 75.22/11.12 | | | | |
% 75.22/11.12 | | | | | REF_CLOSE: (15), (33), (70), (74), (101), (105) are inconsistent by
% 75.22/11.12 | | | | | sub-proof #1.
% 75.22/11.12 | | | | |
% 75.22/11.13 | | | | Case 2:
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | (106) u1_struct_0(all_57_0) = all_60_4
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | BETA: splitting (79) gives:
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | Case 1:
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | (107) ~ (u1_struct_0(all_57_0) = all_60_4)
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | PRED_UNIFY: (106), (107) imply:
% 75.22/11.13 | | | | | | (108) $false
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | CLOSE: (108) is inconsistent.
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | Case 2:
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | GROUND_INST: instantiating (69) with all_60_2, all_60_1, simplifying
% 75.22/11.13 | | | | | | with (36), (100), (103), (104) gives:
% 75.22/11.13 | | | | | | (109) all_89_0 = all_60_7 | ~ m1_subset_1(all_60_2, all_95_0) |
% 75.22/11.13 | | | | | | ~ m1_subset_1(all_60_3, all_95_0)
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | REF_CLOSE: (15), (33), (70), (74), (101), (109) are inconsistent by
% 75.22/11.13 | | | | | | sub-proof #1.
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | End of split
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | End of split
% 75.22/11.13 | | | |
% 75.22/11.13 | | | Case 2:
% 75.22/11.13 | | | |
% 75.22/11.13 | | | | (110) k8_rlvect_2(all_60_5, all_60_3, all_60_2) = all_60_0 &
% 75.22/11.13 | | | | $i(all_60_0) & v1_rmod_5(all_60_0, all_60_8, all_60_5)
% 75.22/11.13 | | | |
% 75.22/11.13 | | | | ALPHA: (110) implies:
% 75.22/11.13 | | | | (111) v1_rmod_5(all_60_0, all_60_8, all_60_5)
% 75.22/11.13 | | | | (112) k8_rlvect_2(all_60_5, all_60_3, all_60_2) = all_60_0
% 75.22/11.13 | | | |
% 75.22/11.13 | | | | BETA: splitting (42) gives:
% 75.22/11.13 | | | |
% 75.22/11.13 | | | | Case 1:
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | GROUND_INST: instantiating (68) with all_60_2, all_60_0, simplifying
% 75.22/11.13 | | | | | with (36), (100), (111), (112) gives:
% 75.22/11.13 | | | | | (113) all_89_0 = all_60_7 | ~ m1_subset_1(all_60_2, all_95_0) | ~
% 75.22/11.13 | | | | | m1_subset_1(all_60_3, all_95_0)
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | REF_CLOSE: (15), (33), (70), (74), (101), (113) are inconsistent by
% 75.22/11.13 | | | | | sub-proof #1.
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | Case 2:
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | (114) all_60_3 = all_60_7
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | COMBINE_EQS: (72), (114) imply:
% 75.22/11.13 | | | | | (115) all_92_0 = all_60_7
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | REDUCE: (112), (114) imply:
% 75.22/11.13 | | | | | (116) k8_rlvect_2(all_60_5, all_60_7, all_60_2) = all_60_0
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | REDUCE: (101), (114) imply:
% 75.22/11.13 | | | | | (117) m1_subset_1(all_60_7, all_60_4)
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | GROUND_INST: instantiating (65) with all_60_2, all_60_0, simplifying
% 75.22/11.13 | | | | | with (33), (36), (111) gives:
% 75.22/11.13 | | | | | (118) all_89_0 = all_60_7 | ~ (k8_rlvect_2(all_60_5, all_92_0,
% 75.22/11.13 | | | | | all_60_2) = all_60_0) | ~ m1_subset_1(all_92_0,
% 75.22/11.13 | | | | | all_60_4)
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | BETA: splitting (118) gives:
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | | Case 1:
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | (119) ~ (k8_rlvect_2(all_60_5, all_92_0, all_60_2) = all_60_0)
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | REDUCE: (115), (119) imply:
% 75.22/11.13 | | | | | | (120) ~ (k8_rlvect_2(all_60_5, all_60_7, all_60_2) = all_60_0)
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | PRED_UNIFY: (116), (120) imply:
% 75.22/11.13 | | | | | | (121) $false
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | CLOSE: (121) is inconsistent.
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | Case 2:
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | (122) all_89_0 = all_60_7 | ~ m1_subset_1(all_92_0, all_60_4)
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | BETA: splitting (122) gives:
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | | Case 1:
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | (123) ~ m1_subset_1(all_92_0, all_60_4)
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | REDUCE: (115), (123) imply:
% 75.22/11.13 | | | | | | | (124) ~ m1_subset_1(all_60_7, all_60_4)
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | PRED_UNIFY: (117), (124) imply:
% 75.22/11.13 | | | | | | | (125) $false
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | CLOSE: (125) is inconsistent.
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | Case 2:
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | (126) all_89_0 = all_60_7
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | COMBINE_EQS: (74), (126) imply:
% 75.22/11.13 | | | | | | | (127) all_60_6 = all_60_7
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | SIMP: (127) implies:
% 75.22/11.13 | | | | | | | (128) all_60_6 = all_60_7
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | REDUCE: (15), (128) imply:
% 75.22/11.13 | | | | | | | (129) $false
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | | CLOSE: (129) is inconsistent.
% 75.22/11.13 | | | | | | |
% 75.22/11.13 | | | | | | End of split
% 75.22/11.13 | | | | | |
% 75.22/11.13 | | | | | End of split
% 75.22/11.13 | | | | |
% 75.22/11.13 | | | | End of split
% 75.22/11.13 | | | |
% 75.22/11.13 | | | End of split
% 75.22/11.13 | | |
% 75.22/11.13 | | End of split
% 75.22/11.13 | |
% 75.22/11.13 | End of split
% 75.22/11.13 |
% 75.22/11.13 End of proof
% 75.22/11.13
% 75.22/11.13 Sub-proof #1 shows that the following formulas are inconsistent:
% 75.22/11.13 ----------------------------------------------------------------
% 75.22/11.13 (1) all_89_0 = all_60_6
% 75.22/11.13 (2) m1_subset_1(all_60_3, all_60_4)
% 75.22/11.13 (3) all_95_0 = all_60_4
% 75.22/11.14 (4) m1_subset_1(all_60_2, all_60_4)
% 75.22/11.14 (5) all_89_0 = all_60_7 | ~ m1_subset_1(all_60_2, all_95_0) | ~
% 75.22/11.14 m1_subset_1(all_60_3, all_95_0)
% 75.22/11.14 (6) ~ (all_60_6 = all_60_7)
% 75.22/11.14
% 75.22/11.14 Begin of proof
% 75.22/11.14 |
% 75.22/11.14 | BETA: splitting (5) gives:
% 75.22/11.14 |
% 75.22/11.14 | Case 1:
% 75.22/11.14 | |
% 75.22/11.14 | | (7) ~ m1_subset_1(all_60_2, all_95_0)
% 75.22/11.14 | |
% 75.22/11.14 | | REDUCE: (3), (7) imply:
% 75.22/11.14 | | (8) ~ m1_subset_1(all_60_2, all_60_4)
% 75.22/11.14 | |
% 75.22/11.14 | | PRED_UNIFY: (4), (8) imply:
% 75.22/11.14 | | (9) $false
% 75.22/11.14 | |
% 75.22/11.14 | | CLOSE: (9) is inconsistent.
% 75.22/11.14 | |
% 75.22/11.14 | Case 2:
% 75.22/11.14 | |
% 75.22/11.14 | | (10) all_89_0 = all_60_7 | ~ m1_subset_1(all_60_3, all_95_0)
% 75.22/11.14 | |
% 75.22/11.14 | | BETA: splitting (10) gives:
% 75.22/11.14 | |
% 75.22/11.14 | | Case 1:
% 75.22/11.14 | | |
% 75.22/11.14 | | | (11) ~ m1_subset_1(all_60_3, all_95_0)
% 75.22/11.14 | | |
% 75.22/11.14 | | | REDUCE: (3), (11) imply:
% 75.22/11.14 | | | (12) ~ m1_subset_1(all_60_3, all_60_4)
% 75.22/11.14 | | |
% 75.22/11.14 | | | PRED_UNIFY: (2), (12) imply:
% 75.22/11.14 | | | (13) $false
% 75.22/11.14 | | |
% 75.22/11.14 | | | CLOSE: (13) is inconsistent.
% 75.22/11.14 | | |
% 75.22/11.14 | | Case 2:
% 75.22/11.14 | | |
% 75.22/11.14 | | | (14) all_89_0 = all_60_7
% 75.22/11.14 | | |
% 75.22/11.14 | | | COMBINE_EQS: (1), (14) imply:
% 75.22/11.14 | | | (15) all_60_6 = all_60_7
% 75.22/11.14 | | |
% 75.22/11.14 | | | SIMP: (15) implies:
% 75.22/11.14 | | | (16) all_60_6 = all_60_7
% 75.22/11.14 | | |
% 75.22/11.14 | | | REDUCE: (6), (16) imply:
% 75.22/11.14 | | | (17) $false
% 75.22/11.14 | | |
% 75.22/11.14 | | | CLOSE: (17) is inconsistent.
% 75.22/11.14 | | |
% 75.22/11.14 | | End of split
% 75.22/11.14 | |
% 75.22/11.14 | End of split
% 75.22/11.14 |
% 75.22/11.14 End of proof
% 75.22/11.14 % SZS output end Proof for theBenchmark
% 75.22/11.14
% 75.22/11.14 10506ms
%------------------------------------------------------------------------------