TSTP Solution File: LAT337+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT337+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 : n005.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 06:24:53 EDT 2023
% Result : Theorem 55.96s 8.28s
% Output : Proof 77.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT337+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.35 % Computer : n005.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Thu Aug 24 05:14:53 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.42/1.33 Prover 1: Preprocessing ...
% 4.42/1.33 Prover 4: Preprocessing ...
% 4.42/1.36 Prover 6: Preprocessing ...
% 4.42/1.36 Prover 5: Preprocessing ...
% 4.42/1.36 Prover 2: Preprocessing ...
% 4.42/1.36 Prover 0: Preprocessing ...
% 4.42/1.36 Prover 3: Preprocessing ...
% 10.68/2.24 Prover 1: Warning: ignoring some quantifiers
% 10.68/2.29 Prover 5: Proving ...
% 10.68/2.30 Prover 1: Constructing countermodel ...
% 11.39/2.31 Prover 2: Proving ...
% 11.39/2.37 Prover 3: Warning: ignoring some quantifiers
% 12.08/2.42 Prover 3: Constructing countermodel ...
% 12.08/2.43 Prover 6: Proving ...
% 14.33/2.76 Prover 4: Warning: ignoring some quantifiers
% 15.11/2.86 Prover 4: Constructing countermodel ...
% 17.34/3.13 Prover 0: Proving ...
% 55.96/8.28 Prover 0: proved (7573ms)
% 55.96/8.28
% 55.96/8.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.96/8.28
% 55.96/8.29 Prover 3: stopped
% 55.96/8.30 Prover 5: stopped
% 55.96/8.30 Prover 2: stopped
% 57.04/8.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 57.04/8.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 57.04/8.31 Prover 6: stopped
% 57.04/8.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 57.04/8.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 57.04/8.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 58.14/8.48 Prover 10: Preprocessing ...
% 58.14/8.53 Prover 8: Preprocessing ...
% 58.14/8.53 Prover 13: Preprocessing ...
% 58.82/8.55 Prover 7: Preprocessing ...
% 58.82/8.58 Prover 11: Preprocessing ...
% 59.21/8.64 Prover 10: Warning: ignoring some quantifiers
% 59.73/8.66 Prover 7: Warning: ignoring some quantifiers
% 59.73/8.66 Prover 10: Constructing countermodel ...
% 59.80/8.67 Prover 7: Constructing countermodel ...
% 60.16/8.73 Prover 13: Warning: ignoring some quantifiers
% 60.16/8.74 Prover 8: Warning: ignoring some quantifiers
% 60.45/8.75 Prover 13: Constructing countermodel ...
% 60.45/8.76 Prover 8: Constructing countermodel ...
% 62.87/9.14 Prover 11: Warning: ignoring some quantifiers
% 63.59/9.16 Prover 11: Constructing countermodel ...
% 76.74/10.90 Prover 10: Found proof (size 79)
% 76.74/10.90 Prover 10: proved (2597ms)
% 76.74/10.90 Prover 8: stopped
% 76.74/10.90 Prover 7: stopped
% 76.74/10.90 Prover 13: stopped
% 76.74/10.90 Prover 1: stopped
% 76.74/10.90 Prover 11: stopped
% 76.74/10.91 Prover 4: stopped
% 76.74/10.91
% 76.74/10.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 76.74/10.91
% 76.74/10.92 % SZS output start Proof for theBenchmark
% 76.74/10.92 Assumptions after simplification:
% 76.74/10.92 ---------------------------------
% 76.74/10.92
% 76.74/10.92 (cc1_lattices)
% 76.74/10.93 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.93 v9_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.93 l3_lattices(v0) | ~ v10_lattices(v0) | v8_lattices(v0) | v3_struct_0(v0)) &
% 76.74/10.93 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.93 v7_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.93 l3_lattices(v0) | ~ v10_lattices(v0) | v6_lattices(v0) | v3_struct_0(v0)) &
% 76.74/10.93 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.93 v5_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.93 l3_lattices(v0) | ~ v10_lattices(v0) | v4_lattices(v0) | v3_struct_0(v0))
% 76.74/10.93
% 76.74/10.93 (cc5_lattices)
% 76.74/10.93 ! [v0: $i] : ( ~ $i(v0) | ~ v17_lattices(v0) | ~ l3_lattices(v0) |
% 76.74/10.93 v16_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.93 v17_lattices(v0) | ~ l3_lattices(v0) | v11_lattices(v0) | v3_struct_0(v0))
% 76.74/10.93 & ! [v0: $i] : ( ~ $i(v0) | ~ v17_lattices(v0) | ~ l3_lattices(v0) |
% 76.74/10.93 v15_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.93 v17_lattices(v0) | ~ l3_lattices(v0) | v14_lattices(v0) | v3_struct_0(v0))
% 76.74/10.93 & ! [v0: $i] : ( ~ $i(v0) | ~ v17_lattices(v0) | ~ l3_lattices(v0) |
% 76.74/10.93 v13_lattices(v0) | v3_struct_0(v0))
% 76.74/10.93
% 76.74/10.93 (cc6_lattices)
% 76.74/10.93 ! [v0: $i] : ( ~ $i(v0) | ~ v16_lattices(v0) | ~ v11_lattices(v0) | ~
% 76.74/10.93 v15_lattices(v0) | ~ l3_lattices(v0) | v17_lattices(v0) | v3_struct_0(v0))
% 76.74/10.93
% 76.74/10.93 (cc7_lattices)
% 76.74/10.94 ! [v0: $i] : ( ~ $i(v0) | ~ v11_lattices(v0) | ~ l3_lattices(v0) | ~
% 76.74/10.94 v10_lattices(v0) | v12_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~
% 76.74/10.94 $i(v0) | ~ v11_lattices(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.94 v9_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.94 v11_lattices(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.94 v8_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.94 v11_lattices(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.94 v7_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.94 v11_lattices(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.94 v6_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.94 v11_lattices(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.94 v5_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 76.74/10.94 v11_lattices(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 76.74/10.94 v4_lattices(v0) | v3_struct_0(v0))
% 76.74/10.94
% 76.74/10.94 (dt_k22_filter_2)
% 77.21/10.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k22_filter_2(v0,
% 77.21/10.96 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ v1_xboole_0(v3) |
% 77.21/10.96 ~ l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] :
% 77.21/10.96 (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, v4) | ~
% 77.21/10.96 m1_subset_1(v1, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 77.21/10.96 [v3: $i] : ( ~ (k22_filter_2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 77.21/10.96 $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_lattice4(v3, v0) |
% 77.21/10.96 v3_struct_0(v0) | ? [v4: $i] : (u1_struct_0(v0) = v4 & $i(v4) & ( ~
% 77.21/10.96 m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))
% 77.21/10.96
% 77.21/10.96 (dt_m2_nat_lat)
% 77.21/10.96 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m2_nat_lat(v1, v0) |
% 77.21/10.96 ~ l3_lattices(v0) | ~ v10_lattices(v0) | ~ v3_struct_0(v1) |
% 77.21/10.96 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 77.21/10.96 m2_nat_lat(v1, v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.96 l3_lattices(v1) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1)
% 77.21/10.96 | ~ $i(v0) | ~ m2_nat_lat(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.96 v10_lattices(v0) | v10_lattices(v1) | v3_struct_0(v0))
% 77.21/10.96
% 77.21/10.96 (existence_m2_nat_lat)
% 77.21/10.96 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.96 v3_struct_0(v0) | ? [v1: $i] : ($i(v1) & m2_nat_lat(v1, v0)))
% 77.21/10.96
% 77.21/10.96 (fc5_filter_2)
% 77.21/10.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | ~ v3_struct_0(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) &
% 77.21/10.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v9_lattices(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v8_lattices(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v7_lattices(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v6_lattices(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v5_lattices(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v4_lattices(v2) | v1_xboole_0(v1) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v1_xboole_0(v1) | v3_lattices(v2) | v3_struct_0(v0)) & !
% 77.21/10.97 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ l3_lattices(v0) | ~
% 77.21/10.97 v10_lattices(v0) | v1_xboole_0(v1) | v10_lattices(v2) | v3_struct_0(v0))
% 77.21/10.97
% 77.21/10.97 (rc11_lattices)
% 77.21/10.97 ? [v0: $i] : ($i(v0) & v15_lattices(v0) & v14_lattices(v0) & v13_lattices(v0)
% 77.21/10.97 & v9_lattices(v0) & v8_lattices(v0) & v7_lattices(v0) & v6_lattices(v0) &
% 77.21/10.97 v5_lattices(v0) & v4_lattices(v0) & v3_lattices(v0) & l3_lattices(v0) &
% 77.21/10.97 v10_lattices(v0) & ~ v3_struct_0(v0))
% 77.21/10.97
% 77.21/10.97 (t78_filter_2)
% 77.21/10.97 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) = v2) | ~
% 77.21/10.97 $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~ v11_lattices(v0) | ~
% 77.21/10.97 l3_lattices(v0) | ~ v10_lattices(v0) | v11_lattices(v2) | v1_xboole_0(v1) |
% 77.21/10.97 v3_struct_0(v0))
% 77.21/10.97
% 77.21/10.97 (t86_filter_2)
% 77.21/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 77.21/10.98 $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~ (k22_filter_2(v0, v2, v3) = v4) |
% 77.21/10.98 ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~ $i(v2) | ~ $i(v0) | ~
% 77.21/10.98 v12_lattices(v0) | ~ v16_lattices(v0) | ~ v15_lattices(v0) | ~
% 77.21/10.98 r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1) |
% 77.21/10.98 ~ l3_lattices(v0) | ~ v10_lattices(v0) | ~ v3_struct_0(v5) |
% 77.21/10.98 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 77.21/10.98 ! [v4: $i] : ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~
% 77.21/10.98 (k22_filter_2(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 77.21/10.98 $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/10.98 v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3, v1) | ~
% 77.21/10.98 m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.98 v16_lattices(v5) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 77.21/10.98 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) =
% 77.21/10.98 v5) | ~ (k22_filter_2(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~
% 77.21/10.98 $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) |
% 77.21/10.98 ~ v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3, v1) |
% 77.21/10.98 ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.98 v15_lattices(v5) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 77.21/10.98 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) =
% 77.21/10.98 v5) | ~ (k22_filter_2(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~
% 77.21/10.98 $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) |
% 77.21/10.98 ~ v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3, v1) |
% 77.21/10.98 ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.98 l3_lattices(v5) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 77.21/10.98 : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) |
% 77.21/10.98 ~ (k22_filter_2(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) |
% 77.21/10.98 ~ $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/10.98 v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3, v1) | ~
% 77.21/10.98 m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.98 v10_lattices(v5) | v3_struct_0(v0))
% 77.21/10.98
% 77.21/10.98 (t87_filter_2)
% 77.21/10.98 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 77.21/10.98 $i] : (k23_filter_2(v0, v4) = v5 & k22_filter_2(v0, v2, v3) = v4 &
% 77.21/10.98 u1_struct_0(v0) = v1 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 77.21/10.98 r3_lattices(v0, v2, v3) & v17_lattices(v0) & m1_subset_1(v3, v1) &
% 77.21/10.98 m1_subset_1(v2, v1) & l3_lattices(v0) & v10_lattices(v0) & ~
% 77.21/10.98 v3_struct_0(v0) & ( ~ v17_lattices(v5) | ~ l3_lattices(v5) | ~
% 77.21/10.98 v10_lattices(v5) | v3_struct_0(v5)))
% 77.21/10.98
% 77.21/10.98 (function-axioms)
% 77.21/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 77.21/10.98 | ~ (k22_filter_2(v4, v3, v2) = v1) | ~ (k22_filter_2(v4, v3, v2) = v0)) &
% 77.21/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 77.21/10.98 | ~ (g3_lattices(v4, v3, v2) = v1) | ~ (g3_lattices(v4, v3, v2) = v0)) &
% 77.21/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 77.21/10.98 (k23_filter_2(v3, v2) = v1) | ~ (k23_filter_2(v3, v2) = v0)) & ! [v0: $i]
% 77.21/10.98 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2)
% 77.21/10.98 = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 77.21/10.98 [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) &
% 77.21/10.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1)
% 77.21/10.98 | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 77.21/10.98 = v0 | ~ (u2_lattices(v2) = v1) | ~ (u2_lattices(v2) = v0)) & ! [v0: $i]
% 77.21/10.98 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_lattices(v2) = v1) | ~
% 77.21/10.98 (u1_lattices(v2) = v0))
% 77.21/10.98
% 77.21/10.98 Further assumptions not needed in the proof:
% 77.21/10.98 --------------------------------------------
% 77.21/10.98 abstractness_v3_lattices, antisymmetry_r2_hidden, cc1_funct_1, cc1_relset_1,
% 77.21/10.98 cc2_funct_1, cc2_lattices, cc3_lattices, cc4_lattices, dt_g3_lattices,
% 77.21/10.98 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k23_filter_2, dt_k2_zfmisc_1, dt_l1_lattices,
% 77.21/10.98 dt_l1_struct_0, dt_l2_lattices, dt_l3_lattices, dt_m1_relset_1, dt_m1_subset_1,
% 77.21/10.98 dt_m2_lattice4, dt_m2_relset_1, dt_u1_lattices, dt_u1_struct_0, dt_u2_lattices,
% 77.21/10.98 existence_l1_lattices, existence_l1_struct_0, existence_l2_lattices,
% 77.21/10.98 existence_l3_lattices, existence_m1_relset_1, existence_m1_subset_1,
% 77.21/10.98 existence_m2_lattice4, existence_m2_relset_1, fc1_struct_0, fc1_subset_1,
% 77.21/10.98 fc1_xboole_0, fc2_lattice2, fc3_lattice2, fc3_lattices, fc4_lattice2,
% 77.21/10.98 fc4_subset_1, fc5_lattice2, free_g3_lattices, rc10_lattices, rc12_lattices,
% 77.21/10.98 rc13_lattices, rc1_funct_1, rc1_lattice4, rc1_nat_lat, rc1_subset_1,
% 77.21/10.98 rc1_xboole_0, rc2_funct_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 77.21/10.98 rc3_lattices, rc3_struct_0, rc5_struct_0, rc6_lattices, rc9_lattices,
% 77.21/10.98 redefinition_m2_relset_1, redefinition_r3_lattices, reflexivity_r1_tarski,
% 77.21/10.98 reflexivity_r3_lattices, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 77.21/10.98 t6_boole, t7_boole, t8_boole
% 77.21/10.98
% 77.21/10.98 Those formulas are unsatisfiable:
% 77.21/10.98 ---------------------------------
% 77.21/10.98
% 77.21/10.98 Begin of proof
% 77.21/10.98 |
% 77.21/10.98 | ALPHA: (cc1_lattices) implies:
% 77.21/10.98 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.98 | v8_lattices(v0) | v3_struct_0(v0))
% 77.21/10.98 |
% 77.21/10.98 | ALPHA: (cc5_lattices) implies:
% 77.21/10.98 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ v17_lattices(v0) | ~ l3_lattices(v0) |
% 77.21/10.98 | v15_lattices(v0) | v3_struct_0(v0))
% 77.21/10.98 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ v17_lattices(v0) | ~ l3_lattices(v0) |
% 77.21/10.98 | v11_lattices(v0) | v3_struct_0(v0))
% 77.21/10.99 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ v17_lattices(v0) | ~ l3_lattices(v0) |
% 77.21/10.99 | v16_lattices(v0) | v3_struct_0(v0))
% 77.21/10.99 |
% 77.21/10.99 | ALPHA: (cc7_lattices) implies:
% 77.21/10.99 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ v11_lattices(v0) | ~ l3_lattices(v0) |
% 77.21/10.99 | ~ v10_lattices(v0) | v12_lattices(v0) | v3_struct_0(v0))
% 77.21/10.99 |
% 77.21/10.99 | ALPHA: (dt_k22_filter_2) implies:
% 77.21/10.99 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 77.21/10.99 | (k22_filter_2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 77.21/10.99 | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_lattice4(v3, v0) |
% 77.21/10.99 | v3_struct_0(v0) | ? [v4: $i] : (u1_struct_0(v0) = v4 & $i(v4) & ( ~
% 77.21/10.99 | m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))
% 77.21/10.99 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 77.21/10.99 | (k22_filter_2(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 77.21/10.99 | ~ v1_xboole_0(v3) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 77.21/10.99 | v3_struct_0(v0) | ? [v4: $i] : (u1_struct_0(v0) = v4 & $i(v4) & ( ~
% 77.21/10.99 | m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))
% 77.21/10.99 |
% 77.21/10.99 | ALPHA: (dt_m2_nat_lat) implies:
% 77.21/10.99 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m2_nat_lat(v1,
% 77.21/10.99 | v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | v10_lattices(v1) |
% 77.21/10.99 | v3_struct_0(v0))
% 77.21/10.99 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m2_nat_lat(v1,
% 77.21/10.99 | v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | l3_lattices(v1) |
% 77.21/10.99 | v3_struct_0(v0))
% 77.21/10.99 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m2_nat_lat(v1,
% 77.21/10.99 | v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | ~
% 77.21/10.99 | v3_struct_0(v1) | v3_struct_0(v0))
% 77.21/10.99 |
% 77.21/10.99 | ALPHA: (fc5_filter_2) implies:
% 77.21/10.99 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k23_filter_2(v0, v1) =
% 77.21/10.99 | v2) | ~ $i(v1) | ~ $i(v0) | ~ m2_lattice4(v1, v0) | ~
% 77.21/10.99 | l3_lattices(v0) | ~ v10_lattices(v0) | v1_xboole_0(v1) |
% 77.21/10.99 | v3_lattices(v2) | v3_struct_0(v0))
% 77.21/10.99 |
% 77.21/10.99 | ALPHA: (t86_filter_2) implies:
% 77.21/10.99 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.21/10.99 | ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~ (k22_filter_2(v0,
% 77.21/10.99 | v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 77.21/10.99 | $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/10.99 | v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3,
% 77.21/10.99 | v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~
% 77.21/10.99 | v10_lattices(v0) | v10_lattices(v5) | v3_struct_0(v0))
% 77.21/10.99 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.21/10.99 | ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~ (k22_filter_2(v0,
% 77.21/10.99 | v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 77.21/10.99 | $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/10.99 | v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3,
% 77.21/10.99 | v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~
% 77.21/10.99 | v10_lattices(v0) | l3_lattices(v5) | v3_struct_0(v0))
% 77.21/10.99 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.21/10.99 | ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~ (k22_filter_2(v0,
% 77.21/10.99 | v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 77.21/10.99 | $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/10.99 | v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3,
% 77.21/10.99 | v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~
% 77.21/10.99 | v10_lattices(v0) | v15_lattices(v5) | v3_struct_0(v0))
% 77.21/10.99 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.21/10.99 | ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~ (k22_filter_2(v0,
% 77.21/10.99 | v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 77.21/10.99 | $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/10.99 | v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3,
% 77.21/10.99 | v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~
% 77.21/10.99 | v10_lattices(v0) | v16_lattices(v5) | v3_struct_0(v0))
% 77.21/10.99 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 77.21/11.00 | ! [v5: $i] : ( ~ (k23_filter_2(v0, v4) = v5) | ~ (k22_filter_2(v0,
% 77.21/11.00 | v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 77.21/11.00 | $i(v2) | ~ $i(v0) | ~ v12_lattices(v0) | ~ v16_lattices(v0) | ~
% 77.21/11.00 | v15_lattices(v0) | ~ r3_lattices(v0, v2, v3) | ~ m1_subset_1(v3,
% 77.21/11.00 | v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) | ~
% 77.21/11.00 | v10_lattices(v0) | ~ v3_struct_0(v5) | v3_struct_0(v0))
% 77.21/11.00 |
% 77.21/11.00 | ALPHA: (function-axioms) implies:
% 77.21/11.00 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 77.21/11.00 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 77.21/11.00 |
% 77.21/11.00 | DELTA: instantiating (rc11_lattices) with fresh symbol all_88_0 gives:
% 77.21/11.00 | (18) $i(all_88_0) & v15_lattices(all_88_0) & v14_lattices(all_88_0) &
% 77.21/11.00 | v13_lattices(all_88_0) & v9_lattices(all_88_0) & v8_lattices(all_88_0)
% 77.21/11.00 | & v7_lattices(all_88_0) & v6_lattices(all_88_0) &
% 77.21/11.00 | v5_lattices(all_88_0) & v4_lattices(all_88_0) & v3_lattices(all_88_0)
% 77.21/11.00 | & l3_lattices(all_88_0) & v10_lattices(all_88_0) & ~
% 77.21/11.00 | v3_struct_0(all_88_0)
% 77.21/11.00 |
% 77.21/11.00 | ALPHA: (18) implies:
% 77.21/11.00 | (19) ~ v3_struct_0(all_88_0)
% 77.21/11.00 | (20) v10_lattices(all_88_0)
% 77.21/11.00 | (21) l3_lattices(all_88_0)
% 77.21/11.00 | (22) $i(all_88_0)
% 77.21/11.00 |
% 77.21/11.00 | DELTA: instantiating (t87_filter_2) with fresh symbols all_96_0, all_96_1,
% 77.21/11.00 | all_96_2, all_96_3, all_96_4, all_96_5 gives:
% 77.21/11.00 | (23) k23_filter_2(all_96_5, all_96_1) = all_96_0 & k22_filter_2(all_96_5,
% 77.21/11.00 | all_96_3, all_96_2) = all_96_1 & u1_struct_0(all_96_5) = all_96_4 &
% 77.21/11.00 | $i(all_96_0) & $i(all_96_1) & $i(all_96_2) & $i(all_96_3) &
% 77.21/11.00 | $i(all_96_4) & $i(all_96_5) & r3_lattices(all_96_5, all_96_3,
% 77.21/11.00 | all_96_2) & v17_lattices(all_96_5) & m1_subset_1(all_96_2, all_96_4)
% 77.21/11.00 | & m1_subset_1(all_96_3, all_96_4) & l3_lattices(all_96_5) &
% 77.21/11.00 | v10_lattices(all_96_5) & ~ v3_struct_0(all_96_5) & ( ~
% 77.21/11.00 | v17_lattices(all_96_0) | ~ l3_lattices(all_96_0) | ~
% 77.21/11.00 | v10_lattices(all_96_0) | v3_struct_0(all_96_0))
% 77.21/11.00 |
% 77.21/11.00 | ALPHA: (23) implies:
% 77.21/11.00 | (24) ~ v3_struct_0(all_96_5)
% 77.21/11.00 | (25) v10_lattices(all_96_5)
% 77.21/11.00 | (26) l3_lattices(all_96_5)
% 77.21/11.00 | (27) m1_subset_1(all_96_3, all_96_4)
% 77.21/11.00 | (28) m1_subset_1(all_96_2, all_96_4)
% 77.21/11.00 | (29) v17_lattices(all_96_5)
% 77.21/11.00 | (30) r3_lattices(all_96_5, all_96_3, all_96_2)
% 77.21/11.00 | (31) $i(all_96_5)
% 77.21/11.00 | (32) $i(all_96_3)
% 77.21/11.00 | (33) $i(all_96_2)
% 77.21/11.00 | (34) $i(all_96_1)
% 77.21/11.00 | (35) $i(all_96_0)
% 77.21/11.00 | (36) u1_struct_0(all_96_5) = all_96_4
% 77.21/11.00 | (37) k22_filter_2(all_96_5, all_96_3, all_96_2) = all_96_1
% 77.21/11.00 | (38) k23_filter_2(all_96_5, all_96_1) = all_96_0
% 77.21/11.00 | (39) ~ v17_lattices(all_96_0) | ~ l3_lattices(all_96_0) | ~
% 77.21/11.00 | v10_lattices(all_96_0) | v3_struct_0(all_96_0)
% 77.21/11.00 |
% 77.21/11.00 | GROUND_INST: instantiating (existence_m2_nat_lat) with all_88_0, simplifying
% 77.21/11.00 | with (19), (20), (21), (22) gives:
% 77.21/11.00 | (40) ? [v0: $i] : ($i(v0) & m2_nat_lat(v0, all_88_0))
% 77.21/11.00 |
% 77.21/11.00 | GROUND_INST: instantiating (4) with all_96_5, simplifying with (24), (26),
% 77.21/11.00 | (29), (31) gives:
% 77.21/11.00 | (41) v16_lattices(all_96_5)
% 77.21/11.00 |
% 77.21/11.00 | GROUND_INST: instantiating (3) with all_96_5, simplifying with (24), (26),
% 77.21/11.00 | (29), (31) gives:
% 77.21/11.00 | (42) v11_lattices(all_96_5)
% 77.21/11.00 |
% 77.21/11.00 | GROUND_INST: instantiating (2) with all_96_5, simplifying with (24), (26),
% 77.21/11.00 | (29), (31) gives:
% 77.21/11.00 | (43) v15_lattices(all_96_5)
% 77.21/11.00 |
% 77.21/11.00 | GROUND_INST: instantiating (6) with all_96_5, all_96_3, all_96_2, all_96_1,
% 77.21/11.00 | simplifying with (24), (25), (26), (31), (32), (33), (37) gives:
% 77.21/11.00 | (44) m2_lattice4(all_96_1, all_96_5) | ? [v0: $i] : (u1_struct_0(all_96_5)
% 77.21/11.00 | = v0 & $i(v0) & ( ~ m1_subset_1(all_96_2, v0) | ~
% 77.21/11.00 | m1_subset_1(all_96_3, v0)))
% 77.21/11.00 |
% 77.21/11.00 | DELTA: instantiating (40) with fresh symbol all_126_0 gives:
% 77.21/11.00 | (45) $i(all_126_0) & m2_nat_lat(all_126_0, all_88_0)
% 77.21/11.00 |
% 77.21/11.00 | ALPHA: (45) implies:
% 77.21/11.00 | (46) m2_nat_lat(all_126_0, all_88_0)
% 77.21/11.00 | (47) $i(all_126_0)
% 77.21/11.00 |
% 77.21/11.00 | BETA: splitting (44) gives:
% 77.21/11.00 |
% 77.21/11.01 | Case 1:
% 77.21/11.01 | |
% 77.21/11.01 | | (48) m2_lattice4(all_96_1, all_96_5)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (5) with all_96_5, simplifying with (24), (25),
% 77.21/11.01 | | (26), (31), (42) gives:
% 77.21/11.01 | | (49) v12_lattices(all_96_5)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (t78_filter_2) with all_96_5, all_96_1, all_96_0,
% 77.21/11.01 | | simplifying with (24), (25), (26), (31), (34), (38), (42), (48)
% 77.21/11.01 | | gives:
% 77.21/11.01 | | (50) v11_lattices(all_96_0) | v1_xboole_0(all_96_1)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (11) with all_96_5, all_96_1, all_96_0,
% 77.21/11.01 | | simplifying with (24), (25), (26), (31), (34), (38), (48)
% 77.21/11.01 | | gives:
% 77.21/11.01 | | (51) v1_xboole_0(all_96_1) | v3_lattices(all_96_0)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (9) with all_88_0, all_126_0, simplifying with
% 77.21/11.01 | | (19), (20), (21), (22), (46), (47) gives:
% 77.21/11.01 | | (52) l3_lattices(all_126_0)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (8) with all_88_0, all_126_0, simplifying with
% 77.21/11.01 | | (19), (20), (21), (22), (46), (47) gives:
% 77.21/11.01 | | (53) v10_lattices(all_126_0)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (1) with all_126_0, simplifying with (47), (52),
% 77.21/11.01 | | (53) gives:
% 77.21/11.01 | | (54) v8_lattices(all_126_0) | v3_struct_0(all_126_0)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (15) with all_96_5, all_96_4, all_96_3, all_96_2,
% 77.21/11.01 | | all_96_1, all_96_0, simplifying with (24), (25), (26), (27),
% 77.21/11.01 | | (28), (30), (31), (32), (33), (36), (37), (38), (41), (43),
% 77.21/11.01 | | (49) gives:
% 77.21/11.01 | | (55) v16_lattices(all_96_0)
% 77.21/11.01 | |
% 77.21/11.01 | | GROUND_INST: instantiating (14) with all_96_5, all_96_4, all_96_3, all_96_2,
% 77.21/11.01 | | all_96_1, all_96_0, simplifying with (24), (25), (26), (27),
% 77.21/11.01 | | (28), (30), (31), (32), (33), (36), (37), (38), (41), (43),
% 77.21/11.01 | | (49) gives:
% 77.21/11.01 | | (56) v15_lattices(all_96_0)
% 77.21/11.01 | |
% 77.21/11.02 | | GROUND_INST: instantiating (13) with all_96_5, all_96_4, all_96_3, all_96_2,
% 77.21/11.02 | | all_96_1, all_96_0, simplifying with (24), (25), (26), (27),
% 77.21/11.02 | | (28), (30), (31), (32), (33), (36), (37), (38), (41), (43),
% 77.21/11.02 | | (49) gives:
% 77.21/11.02 | | (57) l3_lattices(all_96_0)
% 77.21/11.02 | |
% 77.21/11.02 | | GROUND_INST: instantiating (12) with all_96_5, all_96_4, all_96_3, all_96_2,
% 77.21/11.02 | | all_96_1, all_96_0, simplifying with (24), (25), (26), (27),
% 77.21/11.02 | | (28), (30), (31), (32), (33), (36), (37), (38), (41), (43),
% 77.21/11.02 | | (49) gives:
% 77.21/11.02 | | (58) v10_lattices(all_96_0)
% 77.21/11.02 | |
% 77.21/11.02 | | BETA: splitting (39) gives:
% 77.21/11.02 | |
% 77.21/11.02 | | Case 1:
% 77.21/11.02 | | |
% 77.21/11.02 | | | (59) ~ v17_lattices(all_96_0)
% 77.21/11.02 | | |
% 77.21/11.02 | | | BETA: splitting (51) gives:
% 77.21/11.02 | | |
% 77.21/11.02 | | | Case 1:
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | (60) v1_xboole_0(all_96_1)
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | GROUND_INST: instantiating (7) with all_96_5, all_96_3, all_96_2,
% 77.21/11.02 | | | | all_96_1, simplifying with (24), (25), (26), (31), (32),
% 77.21/11.02 | | | | (33), (37), (60) gives:
% 77.21/11.02 | | | | (61) ? [v0: $i] : (u1_struct_0(all_96_5) = v0 & $i(v0) & ( ~
% 77.21/11.02 | | | | m1_subset_1(all_96_2, v0) | ~ m1_subset_1(all_96_3, v0)))
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | DELTA: instantiating (61) with fresh symbol all_671_0 gives:
% 77.21/11.02 | | | | (62) u1_struct_0(all_96_5) = all_671_0 & $i(all_671_0) & ( ~
% 77.21/11.02 | | | | m1_subset_1(all_96_2, all_671_0) | ~ m1_subset_1(all_96_3,
% 77.21/11.02 | | | | all_671_0))
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | ALPHA: (62) implies:
% 77.21/11.02 | | | | (63) u1_struct_0(all_96_5) = all_671_0
% 77.21/11.02 | | | | (64) ~ m1_subset_1(all_96_2, all_671_0) | ~ m1_subset_1(all_96_3,
% 77.21/11.02 | | | | all_671_0)
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | GROUND_INST: instantiating (17) with all_96_4, all_671_0, all_96_5,
% 77.21/11.02 | | | | simplifying with (36), (63) gives:
% 77.21/11.02 | | | | (65) all_671_0 = all_96_4
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | BETA: splitting (64) gives:
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | Case 1:
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | (66) ~ m1_subset_1(all_96_2, all_671_0)
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | REDUCE: (65), (66) imply:
% 77.21/11.02 | | | | | (67) ~ m1_subset_1(all_96_2, all_96_4)
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | PRED_UNIFY: (28), (67) imply:
% 77.21/11.02 | | | | | (68) $false
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | CLOSE: (68) is inconsistent.
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | Case 2:
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | (69) ~ m1_subset_1(all_96_3, all_671_0)
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | REDUCE: (65), (69) imply:
% 77.21/11.02 | | | | | (70) ~ m1_subset_1(all_96_3, all_96_4)
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | PRED_UNIFY: (27), (70) imply:
% 77.21/11.02 | | | | | (71) $false
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | CLOSE: (71) is inconsistent.
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | End of split
% 77.21/11.02 | | | |
% 77.21/11.02 | | | Case 2:
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | (72) ~ v1_xboole_0(all_96_1)
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | BETA: splitting (50) gives:
% 77.21/11.02 | | | |
% 77.21/11.02 | | | | Case 1:
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | (73) v11_lattices(all_96_0)
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | BETA: splitting (54) gives:
% 77.21/11.02 | | | | |
% 77.21/11.02 | | | | | Case 1:
% 77.21/11.02 | | | | | |
% 77.21/11.02 | | | | | |
% 77.21/11.02 | | | | | | GROUND_INST: instantiating (cc6_lattices) with all_96_0, simplifying
% 77.21/11.02 | | | | | | with (35), (55), (56), (57), (59), (73) gives:
% 77.21/11.02 | | | | | | (74) v3_struct_0(all_96_0)
% 77.21/11.02 | | | | | |
% 77.21/11.03 | | | | | | GROUND_INST: instantiating (16) with all_96_5, all_96_4, all_96_3,
% 77.21/11.03 | | | | | | all_96_2, all_96_1, all_96_0, simplifying with (24),
% 77.21/11.03 | | | | | | (25), (26), (27), (28), (30), (31), (32), (33), (36),
% 77.21/11.03 | | | | | | (37), (38), (41), (43), (49), (74) gives:
% 77.21/11.03 | | | | | | (75) $false
% 77.21/11.03 | | | | | |
% 77.21/11.03 | | | | | | CLOSE: (75) is inconsistent.
% 77.21/11.03 | | | | | |
% 77.21/11.03 | | | | | Case 2:
% 77.21/11.03 | | | | | |
% 77.21/11.03 | | | | | | (76) v3_struct_0(all_126_0)
% 77.21/11.03 | | | | | |
% 77.21/11.03 | | | | | | GROUND_INST: instantiating (10) with all_88_0, all_126_0,
% 77.21/11.03 | | | | | | simplifying with (19), (20), (21), (22), (46), (47),
% 77.21/11.03 | | | | | | (76) gives:
% 77.21/11.03 | | | | | | (77) $false
% 77.21/11.03 | | | | | |
% 77.21/11.03 | | | | | | CLOSE: (77) is inconsistent.
% 77.21/11.03 | | | | | |
% 77.21/11.03 | | | | | End of split
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | Case 2:
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | (78) v1_xboole_0(all_96_1)
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | PRED_UNIFY: (72), (78) imply:
% 77.21/11.03 | | | | | (79) $false
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | CLOSE: (79) is inconsistent.
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | End of split
% 77.21/11.03 | | | |
% 77.21/11.03 | | | End of split
% 77.21/11.03 | | |
% 77.21/11.03 | | Case 2:
% 77.21/11.03 | | |
% 77.21/11.03 | | | (80) ~ l3_lattices(all_96_0) | ~ v10_lattices(all_96_0) |
% 77.21/11.03 | | | v3_struct_0(all_96_0)
% 77.21/11.03 | | |
% 77.21/11.03 | | | BETA: splitting (80) gives:
% 77.21/11.03 | | |
% 77.21/11.03 | | | Case 1:
% 77.21/11.03 | | | |
% 77.21/11.03 | | | | (81) ~ l3_lattices(all_96_0)
% 77.21/11.03 | | | |
% 77.21/11.03 | | | | PRED_UNIFY: (57), (81) imply:
% 77.21/11.03 | | | | (82) $false
% 77.21/11.03 | | | |
% 77.21/11.03 | | | | CLOSE: (82) is inconsistent.
% 77.21/11.03 | | | |
% 77.21/11.03 | | | Case 2:
% 77.21/11.03 | | | |
% 77.21/11.03 | | | | (83) ~ v10_lattices(all_96_0) | v3_struct_0(all_96_0)
% 77.21/11.03 | | | |
% 77.21/11.03 | | | | BETA: splitting (83) gives:
% 77.21/11.03 | | | |
% 77.21/11.03 | | | | Case 1:
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | (84) ~ v10_lattices(all_96_0)
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | PRED_UNIFY: (58), (84) imply:
% 77.21/11.03 | | | | | (85) $false
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | CLOSE: (85) is inconsistent.
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | Case 2:
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | (86) v3_struct_0(all_96_0)
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | GROUND_INST: instantiating (16) with all_96_5, all_96_4, all_96_3,
% 77.21/11.03 | | | | | all_96_2, all_96_1, all_96_0, simplifying with (24),
% 77.21/11.03 | | | | | (25), (26), (27), (28), (30), (31), (32), (33), (36),
% 77.21/11.03 | | | | | (37), (38), (41), (43), (49), (86) gives:
% 77.21/11.03 | | | | | (87) $false
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | | CLOSE: (87) is inconsistent.
% 77.21/11.03 | | | | |
% 77.21/11.03 | | | | End of split
% 77.21/11.03 | | | |
% 77.21/11.03 | | | End of split
% 77.21/11.03 | | |
% 77.21/11.03 | | End of split
% 77.21/11.03 | |
% 77.21/11.03 | Case 2:
% 77.21/11.03 | |
% 77.21/11.03 | | (88) ? [v0: $i] : (u1_struct_0(all_96_5) = v0 & $i(v0) & ( ~
% 77.21/11.03 | | m1_subset_1(all_96_2, v0) | ~ m1_subset_1(all_96_3, v0)))
% 77.21/11.03 | |
% 77.21/11.03 | | DELTA: instantiating (88) with fresh symbol all_159_0 gives:
% 77.21/11.03 | | (89) u1_struct_0(all_96_5) = all_159_0 & $i(all_159_0) & ( ~
% 77.21/11.03 | | m1_subset_1(all_96_2, all_159_0) | ~ m1_subset_1(all_96_3,
% 77.21/11.03 | | all_159_0))
% 77.21/11.03 | |
% 77.21/11.03 | | ALPHA: (89) implies:
% 77.21/11.03 | | (90) u1_struct_0(all_96_5) = all_159_0
% 77.21/11.03 | | (91) ~ m1_subset_1(all_96_2, all_159_0) | ~ m1_subset_1(all_96_3,
% 77.21/11.03 | | all_159_0)
% 77.21/11.03 | |
% 77.21/11.03 | | GROUND_INST: instantiating (17) with all_96_4, all_159_0, all_96_5,
% 77.21/11.03 | | simplifying with (36), (90) gives:
% 77.21/11.03 | | (92) all_159_0 = all_96_4
% 77.21/11.03 | |
% 77.21/11.03 | | BETA: splitting (91) gives:
% 77.21/11.03 | |
% 77.21/11.03 | | Case 1:
% 77.21/11.03 | | |
% 77.21/11.03 | | | (93) ~ m1_subset_1(all_96_2, all_159_0)
% 77.21/11.03 | | |
% 77.21/11.03 | | | REDUCE: (92), (93) imply:
% 77.21/11.03 | | | (94) ~ m1_subset_1(all_96_2, all_96_4)
% 77.21/11.03 | | |
% 77.21/11.03 | | | PRED_UNIFY: (28), (94) imply:
% 77.21/11.03 | | | (95) $false
% 77.21/11.03 | | |
% 77.21/11.03 | | | CLOSE: (95) is inconsistent.
% 77.21/11.03 | | |
% 77.21/11.03 | | Case 2:
% 77.21/11.03 | | |
% 77.21/11.03 | | | (96) ~ m1_subset_1(all_96_3, all_159_0)
% 77.21/11.03 | | |
% 77.21/11.03 | | | REDUCE: (92), (96) imply:
% 77.21/11.03 | | | (97) ~ m1_subset_1(all_96_3, all_96_4)
% 77.21/11.03 | | |
% 77.21/11.03 | | | PRED_UNIFY: (27), (97) imply:
% 77.21/11.03 | | | (98) $false
% 77.21/11.03 | | |
% 77.21/11.03 | | | CLOSE: (98) is inconsistent.
% 77.21/11.03 | | |
% 77.21/11.03 | | End of split
% 77.21/11.03 | |
% 77.21/11.03 | End of split
% 77.21/11.03 |
% 77.21/11.03 End of proof
% 77.21/11.03 % SZS output end Proof for theBenchmark
% 77.21/11.03
% 77.21/11.03 10422ms
%------------------------------------------------------------------------------