TSTP Solution File: LAT313+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT313+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 : n010.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 06:24:40 EDT 2023
% Result : Theorem 12.76s 2.55s
% Output : Proof 26.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT313+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 : n010.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 : Thu Aug 24 04:21:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.17/1.16 Prover 1: Preprocessing ...
% 3.17/1.17 Prover 4: Preprocessing ...
% 3.40/1.22 Prover 3: Preprocessing ...
% 3.40/1.22 Prover 5: Preprocessing ...
% 3.40/1.22 Prover 2: Preprocessing ...
% 3.40/1.22 Prover 6: Preprocessing ...
% 3.40/1.23 Prover 0: Preprocessing ...
% 7.78/1.79 Prover 2: Proving ...
% 7.78/1.79 Prover 1: Warning: ignoring some quantifiers
% 7.78/1.82 Prover 5: Proving ...
% 7.78/1.83 Prover 3: Warning: ignoring some quantifiers
% 7.78/1.83 Prover 1: Constructing countermodel ...
% 7.78/1.85 Prover 3: Constructing countermodel ...
% 8.68/1.92 Prover 6: Proving ...
% 9.98/2.15 Prover 4: Warning: ignoring some quantifiers
% 10.49/2.21 Prover 4: Constructing countermodel ...
% 11.16/2.28 Prover 0: Proving ...
% 12.76/2.55 Prover 5: proved (1908ms)
% 12.76/2.55
% 12.76/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.76/2.55
% 12.76/2.55 Prover 3: stopped
% 12.76/2.55 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.76/2.55 Prover 2: stopped
% 12.76/2.55 Prover 6: stopped
% 12.76/2.55 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.76/2.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.76/2.56 Prover 0: stopped
% 12.76/2.56 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.49/2.57 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.67/2.66 Prover 7: Preprocessing ...
% 13.67/2.66 Prover 8: Preprocessing ...
% 13.67/2.66 Prover 13: Preprocessing ...
% 13.67/2.66 Prover 10: Preprocessing ...
% 13.67/2.69 Prover 11: Preprocessing ...
% 14.34/2.77 Prover 7: Warning: ignoring some quantifiers
% 14.34/2.77 Prover 7: Constructing countermodel ...
% 14.98/2.78 Prover 10: Warning: ignoring some quantifiers
% 14.98/2.79 Prover 10: Constructing countermodel ...
% 14.98/2.81 Prover 13: Warning: ignoring some quantifiers
% 14.98/2.82 Prover 13: Constructing countermodel ...
% 14.98/2.84 Prover 8: Warning: ignoring some quantifiers
% 15.55/2.85 Prover 8: Constructing countermodel ...
% 17.81/3.16 Prover 11: Warning: ignoring some quantifiers
% 17.97/3.18 Prover 11: Constructing countermodel ...
% 18.35/3.27 Prover 10: gave up
% 18.35/3.28 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 18.35/3.35 Prover 16: Preprocessing ...
% 19.88/3.44 Prover 16: Warning: ignoring some quantifiers
% 19.88/3.46 Prover 16: Constructing countermodel ...
% 26.12/4.29 Prover 16: Found proof (size 119)
% 26.12/4.29 Prover 16: proved (1011ms)
% 26.12/4.29 Prover 7: stopped
% 26.12/4.29 Prover 8: stopped
% 26.12/4.30 Prover 1: stopped
% 26.12/4.30 Prover 13: stopped
% 26.12/4.30 Prover 4: stopped
% 26.12/4.30 Prover 11: stopped
% 26.12/4.30
% 26.12/4.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.12/4.30
% 26.12/4.31 % SZS output start Proof for theBenchmark
% 26.65/4.31 Assumptions after simplification:
% 26.65/4.31 ---------------------------------
% 26.65/4.31
% 26.65/4.31 (d8_filter_2)
% 26.65/4.33 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.33 v3_struct_0(v0) | ? [v1: $i] : (k17_filter_2(v0) = v1 & u1_struct_0(v0) =
% 26.65/4.33 v1 & $i(v1)))
% 26.65/4.33
% 26.65/4.34 (dt_k17_filter_2)
% 26.65/4.34 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.34 v3_struct_0(v0) | ? [v1: $i] : (k17_filter_2(v0) = v1 & $i(v1) &
% 26.65/4.34 m2_filter_2(v1, v0)))
% 26.65/4.34
% 26.65/4.34 (dt_k6_lattices)
% 26.65/4.34 ! [v0: $i] : ( ~ $i(v0) | ~ l2_lattices(v0) | v3_struct_0(v0) | ? [v1: $i]
% 26.65/4.34 : ? [v2: $i] : (k6_lattices(v0) = v1 & u1_struct_0(v0) = v2 & $i(v2) &
% 26.65/4.34 $i(v1) & m1_subset_1(v1, v2)))
% 26.65/4.34
% 26.65/4.34 (dt_l1_lattices)
% 26.65/4.34 ! [v0: $i] : ( ~ $i(v0) | ~ l1_lattices(v0) | l1_struct_0(v0))
% 26.65/4.34
% 26.65/4.34 (dt_l3_lattices)
% 26.65/4.34 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l1_lattices(v0)) & ! [v0: $i]
% 26.65/4.34 : ( ~ $i(v0) | ~ l3_lattices(v0) | l2_lattices(v0))
% 26.65/4.34
% 26.65/4.34 (dt_m2_filter_2)
% 26.65/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ v1_xboole_0(v1) | ~
% 26.65/4.34 m2_filter_2(v1, v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.34 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 26.65/4.34 m2_filter_2(v1, v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.34 m2_lattice4(v1, v0) | v3_struct_0(v0))
% 26.65/4.34
% 26.65/4.34 (dt_m2_lattice4)
% 26.65/4.34 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.34 v3_struct_0(v0) | ? [v1: $i] : ? [v2: $i] : (k1_zfmisc_1(v1) = v2 &
% 26.65/4.34 u1_struct_0(v0) = v1 & $i(v2) & $i(v1) & ! [v3: $i] : ( ~ $i(v3) | ~
% 26.65/4.34 m2_lattice4(v3, v0) | m1_subset_1(v3, v2))))
% 26.65/4.34
% 26.65/4.34 (fc1_struct_0)
% 26.65/4.34 ! [v0: $i] : ( ~ $i(v0) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v1: $i]
% 26.65/4.34 : (u1_struct_0(v0) = v1 & $i(v1) & ~ v1_xboole_0(v1)))
% 26.65/4.34
% 26.65/4.34 (rc1_subset_1)
% 26.65/4.34 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_zfmisc_1(v0) = v1) | ~ $i(v0) |
% 26.65/4.34 v1_xboole_0(v0) | ? [v2: $i] : ($i(v2) & m1_subset_1(v2, v1) & ~
% 26.65/4.34 v1_xboole_0(v2)))
% 26.65/4.34
% 26.65/4.34 (rc5_struct_0)
% 26.65/4.35 ! [v0: $i] : ( ~ $i(v0) | ~ l1_struct_0(v0) | v3_struct_0(v0) | ? [v1: $i]
% 26.65/4.35 : ? [v2: $i] : ? [v3: $i] : (k1_zfmisc_1(v1) = v2 & u1_struct_0(v0) = v1 &
% 26.65/4.35 $i(v3) & $i(v2) & $i(v1) & m1_subset_1(v3, v2) & ~ v1_xboole_0(v3)))
% 26.65/4.35
% 26.65/4.35 (redefinition_r1_filter_2)
% 26.65/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 26.65/4.35 (k1_zfmisc_1(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.65/4.35 m1_subset_1(v2, v3) | ~ m1_subset_1(v1, v3) | ~ r1_filter_2(v0, v1, v2) |
% 26.65/4.35 v1_xboole_0(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 26.65/4.35 (k1_zfmisc_1(v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1, v2) |
% 26.65/4.35 v1_xboole_0(v0) | r1_filter_2(v0, v1, v1))
% 26.65/4.35
% 26.65/4.35 (reflexivity_r1_filter_2)
% 26.65/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_zfmisc_1(v0) =
% 26.65/4.35 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v2, v3) | ~
% 26.65/4.35 m1_subset_1(v1, v3) | v1_xboole_0(v0) | r1_filter_2(v0, v1, v1))
% 26.65/4.35
% 26.65/4.35 (t38_filter_2)
% 26.65/4.35 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.35 v3_struct_0(v0) | ? [v1: $i] : (u1_struct_0(v0) = v1 & $i(v1) & ! [v2: $i]
% 26.65/4.35 : ( ~ $i(v2) | ~ m2_filter_2(v2, v0) | ? [v3: $i] : (k19_filter_2(v0,
% 26.65/4.35 v2) = v3 & $i(v3) & r1_filter_2(v1, v3, v2)))))
% 26.65/4.35
% 26.65/4.35 (t42_filter_2)
% 26.65/4.35 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.35 v3_struct_0(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 26.65/4.35 (k6_lattices(v0) = v3 & k1_zfmisc_1(v1) = v2 & k17_filter_2(v0) = v4 &
% 26.65/4.35 u1_struct_0(v0) = v1 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & ! [v5: $i] : (
% 26.65/4.35 ~ $i(v5) | ~ m1_subset_1(v5, v2) | ~ r2_hidden(v3, v5) | ~
% 26.65/4.35 v14_lattices(v0) | v1_xboole_0(v5) | (k19_filter_2(v0, v5) = v1 &
% 26.65/4.35 r1_filter_2(v1, v1, v4)))))
% 26.65/4.35
% 26.65/4.35 (t43_filter_2)
% 26.65/4.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 26.65/4.35 (k6_lattices(v0) = v1 & k17_filter_2(v0) = v3 & u1_struct_0(v0) = v2 & $i(v4)
% 26.65/4.35 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r2_hidden(v1, v4) & v14_lattices(v0) &
% 26.65/4.35 m2_filter_2(v4, v0) & l3_lattices(v0) & v10_lattices(v0) & ~
% 26.65/4.35 v3_struct_0(v0) & ( ~ (v4 = v2) | ~ r1_filter_2(v2, v2, v3)))
% 26.65/4.35
% 26.65/4.35 (function-axioms)
% 26.65/4.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 26.65/4.35 (k19_filter_2(v3, v2) = v1) | ~ (k19_filter_2(v3, v2) = v0)) & ! [v0: $i]
% 26.65/4.35 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k6_lattices(v2) = v1) | ~
% 26.65/4.35 (k6_lattices(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 26.65/4.35 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : !
% 26.65/4.35 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k17_filter_2(v2) = v1) | ~
% 26.65/4.35 (k17_filter_2(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 26.65/4.35 v0 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 26.65/4.35
% 26.65/4.35 Further assumptions not needed in the proof:
% 26.65/4.35 --------------------------------------------
% 26.65/4.35 antisymmetry_r2_hidden, cc1_funct_1, cc1_lattices, cc2_lattices,
% 26.65/4.35 dt_k19_filter_2, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_l1_struct_0, dt_l2_lattices,
% 26.65/4.35 dt_m1_subset_1, dt_u1_struct_0, existence_l1_lattices, existence_l1_struct_0,
% 26.65/4.35 existence_l2_lattices, existence_l3_lattices, existence_m1_subset_1,
% 26.65/4.35 existence_m2_filter_2, existence_m2_lattice4, fc1_subset_1, fc1_xboole_0,
% 26.65/4.35 rc1_lattice4, rc1_xboole_0, rc2_subset_1, rc2_xboole_0, rc3_struct_0,
% 26.65/4.35 reflexivity_r1_tarski, symmetry_r1_filter_2, t1_subset, t2_subset, t3_subset,
% 26.65/4.35 t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 26.65/4.35
% 26.65/4.35 Those formulas are unsatisfiable:
% 26.65/4.35 ---------------------------------
% 26.65/4.35
% 26.65/4.35 Begin of proof
% 26.65/4.36 |
% 26.65/4.36 | ALPHA: (dt_l3_lattices) implies:
% 26.65/4.36 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l2_lattices(v0))
% 26.65/4.36 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l1_lattices(v0))
% 26.65/4.36 |
% 26.65/4.36 | ALPHA: (dt_m2_filter_2) implies:
% 26.65/4.36 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m2_filter_2(v1,
% 26.65/4.36 | v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) | m2_lattice4(v1,
% 26.65/4.36 | v0) | v3_struct_0(v0))
% 26.65/4.36 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ v1_xboole_0(v1)
% 26.65/4.36 | | ~ m2_filter_2(v1, v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 26.65/4.36 | v3_struct_0(v0))
% 26.65/4.36 |
% 26.65/4.36 | ALPHA: (redefinition_r1_filter_2) implies:
% 26.65/4.36 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v1 | ~
% 26.65/4.36 | (k1_zfmisc_1(v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 26.65/4.36 | m1_subset_1(v2, v3) | ~ m1_subset_1(v1, v3) | ~ r1_filter_2(v0, v1,
% 26.65/4.36 | v2) | v1_xboole_0(v0))
% 26.65/4.36 |
% 26.65/4.36 | ALPHA: (function-axioms) implies:
% 26.65/4.36 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.65/4.36 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 26.65/4.36 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.65/4.36 | (k17_filter_2(v2) = v1) | ~ (k17_filter_2(v2) = v0))
% 26.65/4.36 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.65/4.36 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 26.65/4.36 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 26.65/4.36 | (k6_lattices(v2) = v1) | ~ (k6_lattices(v2) = v0))
% 26.65/4.36 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 26.65/4.36 | (k19_filter_2(v3, v2) = v1) | ~ (k19_filter_2(v3, v2) = v0))
% 26.65/4.36 |
% 26.65/4.36 | DELTA: instantiating (t43_filter_2) with fresh symbols all_55_0, all_55_1,
% 26.65/4.36 | all_55_2, all_55_3, all_55_4 gives:
% 26.65/4.36 | (11) k6_lattices(all_55_4) = all_55_3 & k17_filter_2(all_55_4) = all_55_1 &
% 26.65/4.36 | u1_struct_0(all_55_4) = all_55_2 & $i(all_55_0) & $i(all_55_1) &
% 26.65/4.36 | $i(all_55_2) & $i(all_55_3) & $i(all_55_4) & r2_hidden(all_55_3,
% 26.65/4.36 | all_55_0) & v14_lattices(all_55_4) & m2_filter_2(all_55_0, all_55_4)
% 26.65/4.36 | & l3_lattices(all_55_4) & v10_lattices(all_55_4) & ~
% 26.65/4.36 | v3_struct_0(all_55_4) & ( ~ (all_55_0 = all_55_2) | ~
% 26.65/4.36 | r1_filter_2(all_55_2, all_55_2, all_55_1))
% 26.65/4.36 |
% 26.65/4.36 | ALPHA: (11) implies:
% 26.65/4.36 | (12) ~ v3_struct_0(all_55_4)
% 26.65/4.36 | (13) v10_lattices(all_55_4)
% 26.65/4.36 | (14) l3_lattices(all_55_4)
% 26.65/4.36 | (15) m2_filter_2(all_55_0, all_55_4)
% 26.65/4.36 | (16) v14_lattices(all_55_4)
% 26.65/4.36 | (17) r2_hidden(all_55_3, all_55_0)
% 26.65/4.36 | (18) $i(all_55_4)
% 26.65/4.36 | (19) $i(all_55_1)
% 26.65/4.36 | (20) $i(all_55_0)
% 26.65/4.37 | (21) u1_struct_0(all_55_4) = all_55_2
% 26.65/4.37 | (22) k17_filter_2(all_55_4) = all_55_1
% 26.65/4.37 | (23) k6_lattices(all_55_4) = all_55_3
% 26.65/4.37 | (24) ~ (all_55_0 = all_55_2) | ~ r1_filter_2(all_55_2, all_55_2,
% 26.65/4.37 | all_55_1)
% 26.65/4.37 |
% 26.65/4.37 | GROUND_INST: instantiating (t42_filter_2) with all_55_4, simplifying with
% 26.65/4.37 | (12), (13), (14), (18) gives:
% 26.65/4.37 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 26.65/4.37 | (k6_lattices(all_55_4) = v2 & k1_zfmisc_1(v0) = v1 &
% 26.65/4.37 | k17_filter_2(all_55_4) = v3 & u1_struct_0(all_55_4) = v0 & $i(v3) &
% 26.65/4.37 | $i(v2) & $i(v1) & $i(v0) & ! [v4: $i] : ( ~ $i(v4) | ~
% 26.65/4.37 | m1_subset_1(v4, v1) | ~ r2_hidden(v2, v4) | ~
% 26.65/4.37 | v14_lattices(all_55_4) | v1_xboole_0(v4) | (k19_filter_2(all_55_4,
% 26.65/4.37 | v4) = v0 & r1_filter_2(v0, v0, v3))))
% 26.65/4.37 |
% 26.65/4.37 | GROUND_INST: instantiating (dt_m2_lattice4) with all_55_4, simplifying with
% 26.65/4.37 | (12), (13), (14), (18) gives:
% 26.65/4.37 | (26) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(v0) = v1 &
% 26.65/4.37 | u1_struct_0(all_55_4) = v0 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~
% 26.65/4.37 | $i(v2) | ~ m2_lattice4(v2, all_55_4) | m1_subset_1(v2, v1)))
% 26.65/4.37 |
% 26.65/4.37 | GROUND_INST: instantiating (d8_filter_2) with all_55_4, simplifying with (12),
% 26.65/4.37 | (13), (14), (18) gives:
% 26.92/4.37 | (27) ? [v0: $i] : (k17_filter_2(all_55_4) = v0 & u1_struct_0(all_55_4) =
% 26.92/4.37 | v0 & $i(v0))
% 26.92/4.37 |
% 26.92/4.37 | GROUND_INST: instantiating (dt_k17_filter_2) with all_55_4, simplifying with
% 26.92/4.37 | (12), (13), (14), (18) gives:
% 26.92/4.37 | (28) ? [v0: $i] : (k17_filter_2(all_55_4) = v0 & $i(v0) & m2_filter_2(v0,
% 26.92/4.37 | all_55_4))
% 26.92/4.37 |
% 26.92/4.37 | GROUND_INST: instantiating (t38_filter_2) with all_55_4, simplifying with
% 26.92/4.37 | (12), (13), (14), (18) gives:
% 26.92/4.37 | (29) ? [v0: $i] : (u1_struct_0(all_55_4) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 26.92/4.37 | $i(v1) | ~ m2_filter_2(v1, all_55_4) | ? [v2: $i] :
% 26.92/4.37 | (k19_filter_2(all_55_4, v1) = v2 & $i(v2) & r1_filter_2(v0, v2,
% 26.92/4.37 | v1))))
% 26.92/4.37 |
% 26.92/4.37 | GROUND_INST: instantiating (2) with all_55_4, simplifying with (14), (18)
% 26.92/4.37 | gives:
% 26.92/4.37 | (30) l1_lattices(all_55_4)
% 26.92/4.37 |
% 26.92/4.37 | GROUND_INST: instantiating (1) with all_55_4, simplifying with (14), (18)
% 26.92/4.37 | gives:
% 26.92/4.37 | (31) l2_lattices(all_55_4)
% 26.92/4.37 |
% 26.92/4.37 | GROUND_INST: instantiating (3) with all_55_4, all_55_0, simplifying with (12),
% 26.92/4.37 | (13), (14), (15), (18), (20) gives:
% 26.92/4.37 | (32) m2_lattice4(all_55_0, all_55_4)
% 26.92/4.37 |
% 26.92/4.37 | DELTA: instantiating (28) with fresh symbol all_75_0 gives:
% 26.92/4.37 | (33) k17_filter_2(all_55_4) = all_75_0 & $i(all_75_0) &
% 26.92/4.37 | m2_filter_2(all_75_0, all_55_4)
% 26.92/4.37 |
% 26.92/4.37 | ALPHA: (33) implies:
% 26.92/4.37 | (34) m2_filter_2(all_75_0, all_55_4)
% 26.92/4.37 | (35) k17_filter_2(all_55_4) = all_75_0
% 26.92/4.37 |
% 26.92/4.37 | DELTA: instantiating (27) with fresh symbol all_77_0 gives:
% 26.92/4.37 | (36) k17_filter_2(all_55_4) = all_77_0 & u1_struct_0(all_55_4) = all_77_0 &
% 26.92/4.37 | $i(all_77_0)
% 26.92/4.37 |
% 26.92/4.37 | ALPHA: (36) implies:
% 26.92/4.37 | (37) u1_struct_0(all_55_4) = all_77_0
% 26.92/4.37 | (38) k17_filter_2(all_55_4) = all_77_0
% 26.92/4.37 |
% 26.92/4.37 | DELTA: instantiating (26) with fresh symbols all_79_0, all_79_1 gives:
% 26.92/4.37 | (39) k1_zfmisc_1(all_79_1) = all_79_0 & u1_struct_0(all_55_4) = all_79_1 &
% 26.92/4.37 | $i(all_79_0) & $i(all_79_1) & ! [v0: $i] : ( ~ $i(v0) | ~
% 26.92/4.37 | m2_lattice4(v0, all_55_4) | m1_subset_1(v0, all_79_0))
% 26.92/4.37 |
% 26.92/4.37 | ALPHA: (39) implies:
% 26.92/4.38 | (40) u1_struct_0(all_55_4) = all_79_1
% 26.92/4.38 | (41) k1_zfmisc_1(all_79_1) = all_79_0
% 26.92/4.38 | (42) ! [v0: $i] : ( ~ $i(v0) | ~ m2_lattice4(v0, all_55_4) |
% 26.92/4.38 | m1_subset_1(v0, all_79_0))
% 26.92/4.38 |
% 26.92/4.38 | DELTA: instantiating (29) with fresh symbol all_82_0 gives:
% 26.92/4.38 | (43) u1_struct_0(all_55_4) = all_82_0 & $i(all_82_0) & ! [v0: $i] : ( ~
% 26.92/4.38 | $i(v0) | ~ m2_filter_2(v0, all_55_4) | ? [v1: $i] :
% 26.92/4.38 | (k19_filter_2(all_55_4, v0) = v1 & $i(v1) & r1_filter_2(all_82_0,
% 26.92/4.38 | v1, v0)))
% 26.92/4.38 |
% 26.92/4.38 | ALPHA: (43) implies:
% 26.92/4.38 | (44) u1_struct_0(all_55_4) = all_82_0
% 26.92/4.38 | (45) ! [v0: $i] : ( ~ $i(v0) | ~ m2_filter_2(v0, all_55_4) | ? [v1: $i]
% 26.92/4.38 | : (k19_filter_2(all_55_4, v0) = v1 & $i(v1) & r1_filter_2(all_82_0,
% 26.92/4.38 | v1, v0)))
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (45) with all_55_0, simplifying with (15), (20)
% 26.92/4.38 | gives:
% 26.92/4.38 | (46) ? [v0: $i] : (k19_filter_2(all_55_4, all_55_0) = v0 & $i(v0) &
% 26.92/4.38 | r1_filter_2(all_82_0, v0, all_55_0))
% 26.92/4.38 |
% 26.92/4.38 | DELTA: instantiating (25) with fresh symbols all_87_0, all_87_1, all_87_2,
% 26.92/4.38 | all_87_3 gives:
% 26.92/4.38 | (47) k6_lattices(all_55_4) = all_87_1 & k1_zfmisc_1(all_87_3) = all_87_2 &
% 26.92/4.38 | k17_filter_2(all_55_4) = all_87_0 & u1_struct_0(all_55_4) = all_87_3 &
% 26.92/4.38 | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) & ! [v0:
% 26.92/4.38 | $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_87_2) | ~
% 26.92/4.38 | r2_hidden(all_87_1, v0) | ~ v14_lattices(all_55_4) |
% 26.92/4.38 | v1_xboole_0(v0) | (k19_filter_2(all_55_4, v0) = all_87_3 &
% 26.92/4.38 | r1_filter_2(all_87_3, all_87_3, all_87_0)))
% 26.92/4.38 |
% 26.92/4.38 | ALPHA: (47) implies:
% 26.92/4.38 | (48) u1_struct_0(all_55_4) = all_87_3
% 26.92/4.38 | (49) k17_filter_2(all_55_4) = all_87_0
% 26.92/4.38 | (50) k1_zfmisc_1(all_87_3) = all_87_2
% 26.92/4.38 | (51) k6_lattices(all_55_4) = all_87_1
% 26.92/4.38 | (52) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_87_2) | ~
% 26.92/4.38 | r2_hidden(all_87_1, v0) | ~ v14_lattices(all_55_4) |
% 26.92/4.38 | v1_xboole_0(v0) | (k19_filter_2(all_55_4, v0) = all_87_3 &
% 26.92/4.38 | r1_filter_2(all_87_3, all_87_3, all_87_0)))
% 26.92/4.38 |
% 26.92/4.38 | DELTA: instantiating (46) with fresh symbol all_90_0 gives:
% 26.92/4.38 | (53) k19_filter_2(all_55_4, all_55_0) = all_90_0 & $i(all_90_0) &
% 26.92/4.38 | r1_filter_2(all_82_0, all_90_0, all_55_0)
% 26.92/4.38 |
% 26.92/4.38 | ALPHA: (53) implies:
% 26.92/4.38 | (54) r1_filter_2(all_82_0, all_90_0, all_55_0)
% 26.92/4.38 | (55) k19_filter_2(all_55_4, all_55_0) = all_90_0
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (6) with all_77_0, all_79_1, all_55_4, simplifying
% 26.92/4.38 | with (37), (40) gives:
% 26.92/4.38 | (56) all_79_1 = all_77_0
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (6) with all_79_1, all_82_0, all_55_4, simplifying
% 26.92/4.38 | with (40), (44) gives:
% 26.92/4.38 | (57) all_82_0 = all_79_1
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (6) with all_55_2, all_87_3, all_55_4, simplifying
% 26.92/4.38 | with (21), (48) gives:
% 26.92/4.38 | (58) all_87_3 = all_55_2
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (6) with all_82_0, all_87_3, all_55_4, simplifying
% 26.92/4.38 | with (44), (48) gives:
% 26.92/4.38 | (59) all_87_3 = all_82_0
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (7) with all_55_1, all_77_0, all_55_4, simplifying
% 26.92/4.38 | with (22), (38) gives:
% 26.92/4.38 | (60) all_77_0 = all_55_1
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (7) with all_77_0, all_87_0, all_55_4, simplifying
% 26.92/4.38 | with (38), (49) gives:
% 26.92/4.38 | (61) all_87_0 = all_77_0
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (7) with all_75_0, all_87_0, all_55_4, simplifying
% 26.92/4.38 | with (35), (49) gives:
% 26.92/4.38 | (62) all_87_0 = all_75_0
% 26.92/4.38 |
% 26.92/4.38 | GROUND_INST: instantiating (8) with all_79_0, all_87_2, all_79_1, simplifying
% 26.92/4.38 | with (41) gives:
% 26.92/4.38 | (63) all_87_2 = all_79_0 | ~ (k1_zfmisc_1(all_79_1) = all_87_2)
% 26.92/4.38 |
% 26.92/4.39 | GROUND_INST: instantiating (9) with all_55_3, all_87_1, all_55_4, simplifying
% 26.92/4.39 | with (23), (51) gives:
% 26.92/4.39 | (64) all_87_1 = all_55_3
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (61), (62) imply:
% 26.92/4.39 | (65) all_77_0 = all_75_0
% 26.92/4.39 |
% 26.92/4.39 | SIMP: (65) implies:
% 26.92/4.39 | (66) all_77_0 = all_75_0
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (58), (59) imply:
% 26.92/4.39 | (67) all_82_0 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | SIMP: (67) implies:
% 26.92/4.39 | (68) all_82_0 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (57), (68) imply:
% 26.92/4.39 | (69) all_79_1 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | SIMP: (69) implies:
% 26.92/4.39 | (70) all_79_1 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (56), (70) imply:
% 26.92/4.39 | (71) all_77_0 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (60), (66) imply:
% 26.92/4.39 | (72) all_75_0 = all_55_1
% 26.92/4.39 |
% 26.92/4.39 | SIMP: (72) implies:
% 26.92/4.39 | (73) all_75_0 = all_55_1
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (60), (71) imply:
% 26.92/4.39 | (74) all_55_1 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | COMBINE_EQS: (73), (74) imply:
% 26.92/4.39 | (75) all_75_0 = all_55_2
% 26.92/4.39 |
% 26.92/4.39 | REDUCE: (50), (58) imply:
% 26.92/4.39 | (76) k1_zfmisc_1(all_55_2) = all_87_2
% 26.92/4.39 |
% 26.92/4.39 | REDUCE: (19), (74) imply:
% 26.92/4.39 | (77) $i(all_55_2)
% 26.92/4.39 |
% 26.92/4.39 | REDUCE: (54), (68) imply:
% 26.92/4.39 | (78) r1_filter_2(all_55_2, all_90_0, all_55_0)
% 26.92/4.39 |
% 26.92/4.39 | REDUCE: (34), (75) imply:
% 26.92/4.39 | (79) m2_filter_2(all_55_2, all_55_4)
% 26.92/4.39 |
% 26.92/4.39 | BETA: splitting (63) gives:
% 26.92/4.39 |
% 26.92/4.39 | Case 1:
% 26.92/4.39 | |
% 26.92/4.39 | | (80) ~ (k1_zfmisc_1(all_79_1) = all_87_2)
% 26.92/4.39 | |
% 26.92/4.39 | | REDUCE: (70), (80) imply:
% 26.92/4.39 | | (81) ~ (k1_zfmisc_1(all_55_2) = all_87_2)
% 26.92/4.39 | |
% 26.92/4.39 | | PRED_UNIFY: (76), (81) imply:
% 26.92/4.39 | | (82) $false
% 26.92/4.39 | |
% 26.92/4.39 | | CLOSE: (82) is inconsistent.
% 26.92/4.39 | |
% 26.92/4.39 | Case 2:
% 26.92/4.39 | |
% 26.92/4.39 | | (83) all_87_2 = all_79_0
% 26.92/4.39 | |
% 26.92/4.39 | | REDUCE: (76), (83) imply:
% 26.92/4.39 | | (84) k1_zfmisc_1(all_55_2) = all_79_0
% 26.92/4.39 | |
% 26.92/4.39 | | GROUND_INST: instantiating (3) with all_55_4, all_55_2, simplifying with
% 26.92/4.39 | | (12), (13), (14), (18), (77), (79) gives:
% 26.92/4.39 | | (85) m2_lattice4(all_55_2, all_55_4)
% 26.92/4.39 | |
% 26.92/4.39 | | GROUND_INST: instantiating (dt_k6_lattices) with all_55_4, simplifying with
% 26.92/4.39 | | (12), (18), (31) gives:
% 26.92/4.39 | | (86) ? [v0: $i] : ? [v1: $i] : (k6_lattices(all_55_4) = v0 &
% 26.92/4.39 | | u1_struct_0(all_55_4) = v1 & $i(v1) & $i(v0) & m1_subset_1(v0,
% 26.92/4.40 | | v1))
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (dt_l1_lattices) with all_55_4, simplifying with
% 26.92/4.40 | | (18), (30) gives:
% 26.92/4.40 | | (87) l1_struct_0(all_55_4)
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (42) with all_55_0, simplifying with (20), (32)
% 26.92/4.40 | | gives:
% 26.92/4.40 | | (88) m1_subset_1(all_55_0, all_79_0)
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (rc1_subset_1) with all_55_2, all_79_0,
% 26.92/4.40 | | simplifying with (77), (84) gives:
% 26.92/4.40 | | (89) v1_xboole_0(all_55_2) | ? [v0: $i] : ($i(v0) & m1_subset_1(v0,
% 26.92/4.40 | | all_79_0) & ~ v1_xboole_0(v0))
% 26.92/4.40 | |
% 26.92/4.40 | | DELTA: instantiating (86) with fresh symbols all_112_0, all_112_1 gives:
% 26.92/4.40 | | (90) k6_lattices(all_55_4) = all_112_1 & u1_struct_0(all_55_4) =
% 26.92/4.40 | | all_112_0 & $i(all_112_0) & $i(all_112_1) & m1_subset_1(all_112_1,
% 26.92/4.40 | | all_112_0)
% 26.92/4.40 | |
% 26.92/4.40 | | ALPHA: (90) implies:
% 26.92/4.40 | | (91) $i(all_112_0)
% 26.92/4.40 | | (92) u1_struct_0(all_55_4) = all_112_0
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (6) with all_55_2, all_112_0, all_55_4,
% 26.92/4.40 | | simplifying with (21), (92) gives:
% 26.92/4.40 | | (93) all_112_0 = all_55_2
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (rc5_struct_0) with all_55_4, simplifying with
% 26.92/4.40 | | (12), (18), (87) gives:
% 26.92/4.40 | | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_zfmisc_1(v0) = v1 &
% 26.92/4.40 | | u1_struct_0(all_55_4) = v0 & $i(v2) & $i(v1) & $i(v0) &
% 26.92/4.40 | | m1_subset_1(v2, v1) & ~ v1_xboole_0(v2))
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (fc1_struct_0) with all_55_4, simplifying with
% 26.92/4.40 | | (12), (18), (87) gives:
% 26.92/4.40 | | (95) ? [v0: $i] : (u1_struct_0(all_55_4) = v0 & $i(v0) & ~
% 26.92/4.40 | | v1_xboole_0(v0))
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (42) with all_55_2, simplifying with (77), (85)
% 26.92/4.40 | | gives:
% 26.92/4.40 | | (96) m1_subset_1(all_55_2, all_79_0)
% 26.92/4.40 | |
% 26.92/4.40 | | DELTA: instantiating (95) with fresh symbol all_124_0 gives:
% 26.92/4.40 | | (97) u1_struct_0(all_55_4) = all_124_0 & $i(all_124_0) & ~
% 26.92/4.40 | | v1_xboole_0(all_124_0)
% 26.92/4.40 | |
% 26.92/4.40 | | ALPHA: (97) implies:
% 26.92/4.40 | | (98) ~ v1_xboole_0(all_124_0)
% 26.92/4.40 | | (99) $i(all_124_0)
% 26.92/4.40 | | (100) u1_struct_0(all_55_4) = all_124_0
% 26.92/4.40 | |
% 26.92/4.40 | | DELTA: instantiating (94) with fresh symbols all_126_0, all_126_1, all_126_2
% 26.92/4.40 | | gives:
% 26.92/4.40 | | (101) k1_zfmisc_1(all_126_2) = all_126_1 & u1_struct_0(all_55_4) =
% 26.92/4.40 | | all_126_2 & $i(all_126_0) & $i(all_126_1) & $i(all_126_2) &
% 26.92/4.40 | | m1_subset_1(all_126_0, all_126_1) & ~ v1_xboole_0(all_126_0)
% 26.92/4.40 | |
% 26.92/4.40 | | ALPHA: (101) implies:
% 26.92/4.40 | | (102) u1_struct_0(all_55_4) = all_126_2
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (6) with all_55_2, all_126_2, all_55_4,
% 26.92/4.40 | | simplifying with (21), (102) gives:
% 26.92/4.40 | | (103) all_126_2 = all_55_2
% 26.92/4.40 | |
% 26.92/4.40 | | GROUND_INST: instantiating (6) with all_124_0, all_126_2, all_55_4,
% 26.92/4.40 | | simplifying with (100), (102) gives:
% 26.92/4.40 | | (104) all_126_2 = all_124_0
% 26.92/4.40 | |
% 26.92/4.40 | | COMBINE_EQS: (103), (104) imply:
% 26.92/4.40 | | (105) all_124_0 = all_55_2
% 26.92/4.40 | |
% 26.92/4.40 | | REDUCE: (98), (105) imply:
% 26.92/4.40 | | (106) ~ v1_xboole_0(all_55_2)
% 26.92/4.40 | |
% 26.92/4.40 | | BETA: splitting (89) gives:
% 26.92/4.40 | |
% 26.92/4.40 | | Case 1:
% 26.92/4.40 | | |
% 26.92/4.40 | | | (107) v1_xboole_0(all_55_2)
% 26.92/4.40 | | |
% 26.92/4.40 | | | PRED_UNIFY: (106), (107) imply:
% 26.92/4.40 | | | (108) $false
% 26.92/4.40 | | |
% 26.92/4.40 | | | CLOSE: (108) is inconsistent.
% 26.92/4.40 | | |
% 26.92/4.40 | | Case 2:
% 26.92/4.40 | | |
% 26.92/4.40 | | | (109) ? [v0: $i] : ($i(v0) & m1_subset_1(v0, all_79_0) & ~
% 26.92/4.40 | | | v1_xboole_0(v0))
% 26.92/4.40 | | |
% 26.92/4.40 | | | DELTA: instantiating (109) with fresh symbol all_143_0 gives:
% 26.92/4.40 | | | (110) $i(all_143_0) & m1_subset_1(all_143_0, all_79_0) & ~
% 26.92/4.40 | | | v1_xboole_0(all_143_0)
% 26.92/4.40 | | |
% 26.92/4.40 | | | ALPHA: (110) implies:
% 26.92/4.40 | | | (111) m1_subset_1(all_143_0, all_79_0)
% 26.92/4.40 | | | (112) $i(all_143_0)
% 26.92/4.40 | | |
% 26.92/4.40 | | | GROUND_INST: instantiating (5) with all_55_2, all_55_2, all_55_0,
% 26.92/4.40 | | | all_79_0, simplifying with (20), (77), (84), (88), (96),
% 26.92/4.40 | | | (106) gives:
% 26.92/4.40 | | | (113) all_55_0 = all_55_2 | ~ r1_filter_2(all_55_2, all_55_2,
% 26.92/4.40 | | | all_55_0)
% 26.92/4.40 | | |
% 26.92/4.40 | | | GROUND_INST: instantiating (52) with all_55_0, simplifying with (16), (20)
% 26.92/4.41 | | | gives:
% 26.92/4.41 | | | (114) ~ m1_subset_1(all_55_0, all_87_2) | ~ r2_hidden(all_87_1,
% 26.92/4.41 | | | all_55_0) | v1_xboole_0(all_55_0) | (k19_filter_2(all_55_4,
% 26.92/4.41 | | | all_55_0) = all_87_3 & r1_filter_2(all_87_3, all_87_3,
% 26.92/4.41 | | | all_87_0))
% 26.92/4.41 | | |
% 26.92/4.41 | | | GROUND_INST: instantiating (reflexivity_r1_filter_2) with all_55_2,
% 26.92/4.41 | | | all_55_2, all_143_0, all_79_0, simplifying with (77), (84),
% 26.92/4.41 | | | (96), (106), (111), (112) gives:
% 26.92/4.41 | | | (115) r1_filter_2(all_55_2, all_55_2, all_55_2)
% 26.92/4.41 | | |
% 26.92/4.41 | | | BETA: splitting (24) gives:
% 26.92/4.41 | | |
% 26.92/4.41 | | | Case 1:
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | (116) ~ r1_filter_2(all_55_2, all_55_2, all_55_1)
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | REDUCE: (74), (116) imply:
% 26.92/4.41 | | | | (117) ~ r1_filter_2(all_55_2, all_55_2, all_55_2)
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | PRED_UNIFY: (115), (117) imply:
% 26.92/4.41 | | | | (118) $false
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | CLOSE: (118) is inconsistent.
% 26.92/4.41 | | | |
% 26.92/4.41 | | | Case 2:
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | (119) ~ (all_55_0 = all_55_2)
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | BETA: splitting (113) gives:
% 26.92/4.41 | | | |
% 26.92/4.41 | | | | Case 1:
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | (120) ~ r1_filter_2(all_55_2, all_55_2, all_55_0)
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | PRED_UNIFY: (78), (120) imply:
% 26.92/4.41 | | | | | (121) ~ (all_90_0 = all_55_2)
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | BETA: splitting (114) gives:
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | Case 1:
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | (122) ~ m1_subset_1(all_55_0, all_87_2)
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | REDUCE: (83), (122) imply:
% 26.92/4.41 | | | | | | (123) ~ m1_subset_1(all_55_0, all_79_0)
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | PRED_UNIFY: (88), (123) imply:
% 26.92/4.41 | | | | | | (124) $false
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | CLOSE: (124) is inconsistent.
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | Case 2:
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | (125) ~ r2_hidden(all_87_1, all_55_0) | v1_xboole_0(all_55_0) |
% 26.92/4.41 | | | | | | (k19_filter_2(all_55_4, all_55_0) = all_87_3 &
% 26.92/4.41 | | | | | | r1_filter_2(all_87_3, all_87_3, all_87_0))
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | BETA: splitting (125) gives:
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | | Case 1:
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | (126) ~ r2_hidden(all_87_1, all_55_0)
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | REDUCE: (64), (126) imply:
% 26.92/4.41 | | | | | | | (127) ~ r2_hidden(all_55_3, all_55_0)
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | PRED_UNIFY: (17), (127) imply:
% 26.92/4.41 | | | | | | | (128) $false
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | CLOSE: (128) is inconsistent.
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | Case 2:
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | (129) v1_xboole_0(all_55_0) | (k19_filter_2(all_55_4, all_55_0)
% 26.92/4.41 | | | | | | | = all_87_3 & r1_filter_2(all_87_3, all_87_3, all_87_0))
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | BETA: splitting (129) gives:
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | | Case 1:
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | (130) v1_xboole_0(all_55_0)
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | GROUND_INST: instantiating (4) with all_55_4, all_55_0,
% 26.92/4.41 | | | | | | | | simplifying with (12), (13), (14), (15), (18),
% 26.92/4.41 | | | | | | | | (20), (130) gives:
% 26.92/4.41 | | | | | | | | (131) $false
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | CLOSE: (131) is inconsistent.
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | Case 2:
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | (132) k19_filter_2(all_55_4, all_55_0) = all_87_3 &
% 26.92/4.41 | | | | | | | | r1_filter_2(all_87_3, all_87_3, all_87_0)
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | ALPHA: (132) implies:
% 26.92/4.41 | | | | | | | | (133) k19_filter_2(all_55_4, all_55_0) = all_87_3
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | REDUCE: (58), (133) imply:
% 26.92/4.41 | | | | | | | | (134) k19_filter_2(all_55_4, all_55_0) = all_55_2
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | GROUND_INST: instantiating (10) with all_90_0, all_55_2,
% 26.92/4.41 | | | | | | | | all_55_0, all_55_4, simplifying with (55), (134)
% 26.92/4.41 | | | | | | | | gives:
% 26.92/4.41 | | | | | | | | (135) all_90_0 = all_55_2
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | REDUCE: (121), (135) imply:
% 26.92/4.41 | | | | | | | | (136) $false
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | | CLOSE: (136) is inconsistent.
% 26.92/4.41 | | | | | | | |
% 26.92/4.41 | | | | | | | End of split
% 26.92/4.41 | | | | | | |
% 26.92/4.41 | | | | | | End of split
% 26.92/4.41 | | | | | |
% 26.92/4.41 | | | | | End of split
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | Case 2:
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | (137) all_55_0 = all_55_2
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | REDUCE: (119), (137) imply:
% 26.92/4.41 | | | | | (138) $false
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | | CLOSE: (138) is inconsistent.
% 26.92/4.41 | | | | |
% 26.92/4.41 | | | | End of split
% 26.92/4.41 | | | |
% 26.92/4.41 | | | End of split
% 26.92/4.41 | | |
% 26.92/4.41 | | End of split
% 26.92/4.41 | |
% 26.92/4.41 | End of split
% 26.92/4.41 |
% 26.92/4.41 End of proof
% 26.92/4.41 % SZS output end Proof for theBenchmark
% 26.92/4.41
% 26.92/4.41 3799ms
%------------------------------------------------------------------------------