TSTP Solution File: LAT297+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT297+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 : n001.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 06:24:31 EDT 2023
% Result : Theorem 66.14s 9.62s
% Output : Proof 67.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT297+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 : n001.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 06:43:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.07/1.31 Prover 1: Preprocessing ...
% 4.07/1.31 Prover 4: Preprocessing ...
% 4.61/1.35 Prover 0: Preprocessing ...
% 4.61/1.35 Prover 5: Preprocessing ...
% 4.61/1.35 Prover 3: Preprocessing ...
% 4.61/1.35 Prover 6: Preprocessing ...
% 4.61/1.35 Prover 2: Preprocessing ...
% 11.19/2.27 Prover 1: Warning: ignoring some quantifiers
% 11.87/2.32 Prover 3: Warning: ignoring some quantifiers
% 11.87/2.33 Prover 5: Proving ...
% 12.07/2.35 Prover 2: Proving ...
% 12.07/2.36 Prover 3: Constructing countermodel ...
% 12.07/2.37 Prover 6: Proving ...
% 12.07/2.37 Prover 1: Constructing countermodel ...
% 14.87/2.82 Prover 4: Warning: ignoring some quantifiers
% 15.91/2.94 Prover 4: Constructing countermodel ...
% 18.32/3.23 Prover 0: Proving ...
% 25.65/4.45 Prover 3: gave up
% 25.65/4.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 29.18/4.66 Prover 7: Preprocessing ...
% 31.53/5.00 Prover 7: Warning: ignoring some quantifiers
% 32.32/5.04 Prover 7: Constructing countermodel ...
% 64.67/9.30 Prover 2: stopped
% 65.11/9.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 65.11/9.33 Prover 7: Found proof (size 130)
% 65.11/9.33 Prover 7: proved (4857ms)
% 65.11/9.33 Prover 5: stopped
% 65.11/9.33 Prover 4: stopped
% 65.11/9.33 Prover 1: stopped
% 65.11/9.33 Prover 6: stopped
% 65.11/9.34 Prover 0: stopped
% 65.31/9.40 Prover 8: Preprocessing ...
% 66.14/9.60 Prover 8: Warning: ignoring some quantifiers
% 66.14/9.62 Prover 8: Constructing countermodel ...
% 66.14/9.62 Prover 8: stopped
% 66.14/9.62
% 66.14/9.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.14/9.62
% 66.14/9.64 % SZS output start Proof for theBenchmark
% 66.14/9.65 Assumptions after simplification:
% 66.14/9.65 ---------------------------------
% 66.14/9.65
% 66.14/9.65 (antisymmetry_r2_hidden)
% 66.14/9.65 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v1, v0) | ~
% 66.14/9.66 r2_hidden(v0, v1))
% 66.14/9.66
% 66.14/9.66 (cc1_lattices)
% 66.14/9.66 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 66.14/9.66 v9_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 66.14/9.66 l3_lattices(v0) | ~ v10_lattices(v0) | v8_lattices(v0) | v3_struct_0(v0)) &
% 66.14/9.66 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 66.14/9.66 v7_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 66.14/9.66 l3_lattices(v0) | ~ v10_lattices(v0) | v6_lattices(v0) | v3_struct_0(v0)) &
% 66.14/9.66 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 66.14/9.66 v5_lattices(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 66.14/9.66 l3_lattices(v0) | ~ v10_lattices(v0) | v4_lattices(v0) | v3_struct_0(v0))
% 66.14/9.66
% 66.14/9.66 (commutativity_k3_lattices)
% 66.49/9.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0,
% 66.49/9.70 v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) |
% 66.49/9.70 ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3
% 66.49/9.70 & k3_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 &
% 66.49/9.70 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) & ! [v0:
% 66.49/9.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0, v1, v2)
% 66.49/9.70 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | ~
% 66.49/9.70 v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 &
% 66.49/9.70 k3_lattices(v0, v2, v1) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4)
% 66.49/9.70 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))))
% 66.49/9.70
% 66.49/9.70 (d10_lattice4)
% 66.49/9.71 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 66.49/9.71 l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] :
% 66.49/9.71 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 66.49/9.71 ! [v6: $i] : ( ~ (k4_lattices(v0, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) |
% 66.49/9.71 ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3) | ~
% 66.49/9.71 r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | ~
% 66.49/9.71 m1_subset_1(v3, v2) | r2_hidden(v6, v3)) & ! [v3: $i] : ! [v4: $i] :
% 66.49/9.71 ! [v5: $i] : ! [v6: $i] : ( ~ (k4_lattices(v0, v4, v5) = v6) | ~ $i(v5)
% 66.49/9.71 | ~ $i(v4) | ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3)
% 66.49/9.71 | ~ r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1)
% 66.49/9.71 | ~ m1_subset_1(v3, v2) | ? [v7: $i] : (k3_lattices(v0, v4, v5) = v7 &
% 66.49/9.71 $i(v7) & r2_hidden(v7, v3))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 66.49/9.71 : ! [v6: $i] : ( ~ (k3_lattices(v0, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4)
% 66.49/9.71 | ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3) | ~
% 66.49/9.71 r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | ~
% 66.49/9.71 m1_subset_1(v3, v2) | r2_hidden(v6, v3)) & ! [v3: $i] : ! [v4: $i] :
% 66.49/9.71 ! [v5: $i] : ! [v6: $i] : ( ~ (k3_lattices(v0, v4, v5) = v6) | ~ $i(v5)
% 66.49/9.71 | ~ $i(v4) | ~ $i(v3) | ~ m2_lattice4(v3, v0) | ~ r2_hidden(v5, v3)
% 66.49/9.71 | ~ r2_hidden(v4, v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1)
% 66.49/9.71 | ~ m1_subset_1(v3, v2) | ? [v7: $i] : (k4_lattices(v0, v4, v5) = v7 &
% 66.49/9.71 $i(v7) & r2_hidden(v7, v3))) & ! [v3: $i] : ( ~ $i(v3) | ~
% 66.49/9.71 m1_subset_1(v3, v2) | m2_lattice4(v3, v0) | ? [v4: $i] : ? [v5: $i] :
% 66.49/9.71 ? [v6: $i] : ? [v7: $i] : ($i(v5) & $i(v4) & r2_hidden(v5, v3) &
% 66.49/9.71 r2_hidden(v4, v3) & m1_subset_1(v5, v1) & m1_subset_1(v4, v1) &
% 66.49/9.71 ((k4_lattices(v0, v4, v5) = v6 & $i(v6) & ~ r2_hidden(v6, v3)) |
% 66.49/9.71 (k3_lattices(v0, v4, v5) = v7 & $i(v7) & ~ r2_hidden(v7, v3)))))))
% 66.49/9.71
% 66.49/9.71 (d1_lattices)
% 66.49/9.71 ! [v0: $i] : ! [v1: $i] : ( ~ (u2_lattices(v0) = v1) | ~ $i(v0) | ~
% 66.49/9.71 l2_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 &
% 66.49/9.71 $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (k2_binop_1(v2, v2,
% 66.49/9.71 v2, v1, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~ m1_subset_1(v4,
% 66.49/9.71 v2) | ~ m1_subset_1(v3, v2) | (k1_lattices(v0, v3, v4) = v5 &
% 66.49/9.71 $i(v5))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 66.49/9.71 (k1_lattices(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 66.49/9.71 m1_subset_1(v4, v2) | ~ m1_subset_1(v3, v2) | (k2_binop_1(v2, v2, v2,
% 66.49/9.71 v1, v3, v4) = v5 & $i(v5))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 66.49/9.71 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l2_lattices(v0) | v3_struct_0(v0) |
% 66.49/9.71 ? [v2: $i] : (u2_lattices(v0) = v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : !
% 66.49/9.71 [v5: $i] : ( ~ (k2_binop_1(v1, v1, v1, v2, v3, v4) = v5) | ~ $i(v4) | ~
% 66.49/9.71 $i(v3) | ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, v1) |
% 66.49/9.71 (k1_lattices(v0, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4: $i] :
% 66.49/9.71 ! [v5: $i] : ( ~ (k1_lattices(v0, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) |
% 66.49/9.71 ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, v1) | (k2_binop_1(v1, v1, v1,
% 66.49/9.71 v2, v3, v4) = v5 & $i(v5)))))
% 66.49/9.71
% 66.49/9.71 (d9_lattices)
% 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 66.49/9.72 (k1_lattices(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~ $i(v3) | ~
% 66.49/9.72 $i(v2) | ~ $i(v0) | ~ v9_lattices(v0) | ~ m1_subset_1(v3, v1) | ~
% 66.49/9.72 m1_subset_1(v2, v1) | ~ l3_lattices(v0) | k2_lattices(v0, v2, v4) = v2 |
% 66.49/9.72 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) |
% 66.49/9.72 ~ $i(v0) | ~ l3_lattices(v0) | v9_lattices(v0) | v3_struct_0(v0) | ? [v2:
% 66.49/9.72 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ( ~ (v5 = v2) &
% 66.49/9.72 k2_lattices(v0, v2, v4) = v5 & k1_lattices(v0, v2, v3) = v4 & $i(v5) &
% 66.49/9.72 $i(v4) & $i(v3) & $i(v2) & m1_subset_1(v3, v1) & m1_subset_1(v2, v1)))
% 66.49/9.72
% 66.49/9.72 (dt_k3_lattices)
% 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0,
% 66.49/9.72 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) |
% 66.49/9.72 ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : (u1_struct_0(v0) = v4 &
% 66.49/9.72 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4) |
% 66.49/9.72 m1_subset_1(v3, v4))))
% 66.49/9.72
% 66.49/9.72 (dt_l3_lattices)
% 66.49/9.72 ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l1_lattices(v0)) & ! [v0: $i]
% 66.49/9.72 : ( ~ $i(v0) | ~ l3_lattices(v0) | l2_lattices(v0))
% 66.49/9.72
% 66.49/9.72 (dt_m2_lattice4)
% 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 66.49/9.72 l3_lattices(v0) | ~ v10_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] :
% 66.49/9.72 (k1_zfmisc_1(v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~
% 66.49/9.72 m2_lattice4(v3, v0) | m1_subset_1(v3, v2))))
% 66.49/9.72
% 66.49/9.72 (redefinition_k3_lattices)
% 66.49/9.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_lattices(v0,
% 66.49/9.72 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) |
% 66.49/9.72 ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3
% 66.49/9.72 & k3_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 &
% 66.49/9.72 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) & ! [v0:
% 66.49/9.72 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k3_lattices(v0, v1, v2)
% 66.49/9.72 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l2_lattices(v0) | ~
% 66.49/9.72 v4_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 &
% 66.49/9.72 k1_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4)
% 66.49/9.72 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))))
% 66.49/9.72
% 66.49/9.72 (redefinition_k4_lattices)
% 66.49/9.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k2_lattices(v0,
% 66.49/9.73 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_lattices(v0) |
% 66.49/9.73 ~ v6_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3
% 66.49/9.73 & k4_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 &
% 66.49/9.73 $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4))))) & ! [v0:
% 66.49/9.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k4_lattices(v0, v1, v2)
% 66.49/9.73 = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_lattices(v0) | ~
% 66.49/9.73 v6_lattices(v0) | v3_struct_0(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 &
% 66.49/9.73 k2_lattices(v0, v1, v2) = v3 & $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4)
% 66.49/9.73 & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))))
% 66.49/9.73
% 66.49/9.73 (t13_filter_2)
% 66.49/9.73 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (u1_struct_0(v0) = v1
% 66.49/9.73 & k1_zfmisc_1(v1) = v2 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & m1_subset_1(v3,
% 66.49/9.73 v2) & l3_lattices(v0) & v10_lattices(v0) & ~ m2_lattice4(v3, v0) & ~
% 66.49/9.73 v3_struct_0(v0) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 66.49/9.73 (k4_lattices(v0, v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ r2_hidden(v6,
% 66.49/9.73 v3) | ~ m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | r2_hidden(v5,
% 66.49/9.73 v3)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (k4_lattices(v0,
% 66.49/9.73 v4, v5) = v6) | ~ $i(v5) | ~ $i(v4) | ~ r2_hidden(v6, v3) | ~
% 66.49/9.73 m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | r2_hidden(v4, v3)) & !
% 66.49/9.73 [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (k4_lattices(v0, v4, v5) = v6) |
% 66.49/9.73 ~ $i(v5) | ~ $i(v4) | ~ r2_hidden(v5, v3) | ~ r2_hidden(v4, v3) | ~
% 66.49/9.73 m1_subset_1(v5, v1) | ~ m1_subset_1(v4, v1) | r2_hidden(v6, v3)))
% 66.49/9.73
% 66.49/9.73 (t4_subset)
% 66.49/9.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_zfmisc_1(v2) =
% 66.49/9.73 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v0, v1) | ~
% 66.49/9.73 m1_subset_1(v1, v3) | m1_subset_1(v0, v2))
% 66.49/9.73
% 66.49/9.73 (function-axioms)
% 67.02/9.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 67.02/9.74 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (k2_binop_1(v7, v6, v5, v4,
% 67.02/9.74 v3, v2) = v1) | ~ (k2_binop_1(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 67.02/9.74 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 67.02/9.74 (k2_lattices(v4, v3, v2) = v1) | ~ (k2_lattices(v4, v3, v2) = v0)) & !
% 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 67.02/9.74 ~ (k1_lattices(v4, v3, v2) = v1) | ~ (k1_lattices(v4, v3, v2) = v0)) & !
% 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 67.02/9.74 ~ (k1_binop_1(v4, v3, v2) = v1) | ~ (k1_binop_1(v4, v3, v2) = v0)) & !
% 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 67.02/9.74 ~ (k4_lattices(v4, v3, v2) = v1) | ~ (k4_lattices(v4, v3, v2) = v0)) & !
% 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 67.02/9.74 ~ (k3_lattices(v4, v3, v2) = v1) | ~ (k3_lattices(v4, v3, v2) = v0)) & !
% 67.02/9.74 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 67.02/9.74 (k4_tarski(v3, v2) = v1) | ~ (k4_tarski(v3, v2) = v0)) & ! [v0: $i] : !
% 67.02/9.74 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k1_funct_1(v3, v2) = v1)
% 67.02/9.74 | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 67.02/9.74 ! [v3: $i] : (v1 = v0 | ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) =
% 67.02/9.74 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 67.02/9.74 ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i]
% 67.02/9.74 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~
% 67.02/9.74 (k1_tarski(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 67.02/9.74 ~ (u1_lattices(v2) = v1) | ~ (u1_lattices(v2) = v0)) & ! [v0: $i] : !
% 67.02/9.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u2_lattices(v2) = v1) | ~
% 67.02/9.74 (u2_lattices(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 67.02/9.74 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : !
% 67.02/9.74 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 67.02/9.74 (k1_zfmisc_1(v2) = v0))
% 67.02/9.74
% 67.02/9.74 Further assumptions not needed in the proof:
% 67.02/9.74 --------------------------------------------
% 67.02/9.74 cc1_funct_1, cc1_realset1, cc1_relset_1, cc2_funct_1, cc2_lattices,
% 67.02/9.74 commutativity_k2_tarski, commutativity_k4_lattices, d1_binop_1, d2_lattices,
% 67.02/9.74 d5_tarski, dt_k1_binop_1, dt_k1_funct_1, dt_k1_lattices, dt_k1_tarski,
% 67.02/9.74 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_binop_1, dt_k2_lattices, dt_k2_tarski,
% 67.02/9.74 dt_k2_zfmisc_1, dt_k4_lattices, dt_k4_tarski, dt_l1_lattices, dt_l1_struct_0,
% 67.02/9.74 dt_l2_lattices, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_lattices,
% 67.02/9.74 dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, existence_l1_struct_0,
% 67.02/9.74 existence_l2_lattices, existence_l3_lattices, existence_m1_relset_1,
% 67.02/9.74 existence_m1_subset_1, existence_m2_lattice4, existence_m2_relset_1,
% 67.02/9.74 fc1_struct_0, fc1_subset_1, fc1_xboole_0, fc2_lattice2, fc2_subset_1,
% 67.02/9.74 fc3_lattice2, fc3_realset1, fc3_subset_1, fc4_lattice2, fc4_subset_1,
% 67.02/9.74 fc5_lattice2, rc1_funct_1, rc1_lattice4, rc1_realset1, rc1_subset_1,
% 67.02/9.74 rc1_xboole_0, rc2_funct_1, rc2_realset1, rc2_subset_1, rc2_xboole_0,
% 67.02/9.74 rc3_funct_1, rc3_struct_0, rc5_struct_0, redefinition_k2_binop_1,
% 67.02/9.74 redefinition_m2_relset_1, reflexivity_r1_tarski, t1_subset, t2_subset,
% 67.02/9.74 t3_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 67.02/9.74
% 67.02/9.74 Those formulas are unsatisfiable:
% 67.02/9.74 ---------------------------------
% 67.02/9.74
% 67.02/9.74 Begin of proof
% 67.02/9.74 |
% 67.02/9.74 | ALPHA: (cc1_lattices) implies:
% 67.02/9.74 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 67.02/9.74 | v4_lattices(v0) | v3_struct_0(v0))
% 67.02/9.74 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 67.02/9.74 | v6_lattices(v0) | v3_struct_0(v0))
% 67.02/9.74 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v10_lattices(v0) |
% 67.02/9.74 | v9_lattices(v0) | v3_struct_0(v0))
% 67.02/9.74 |
% 67.02/9.74 | ALPHA: (commutativity_k3_lattices) implies:
% 67.02/9.75 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 67.02/9.75 | (k3_lattices(v0, v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 67.02/9.75 | ~ l2_lattices(v0) | ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4:
% 67.02/9.75 | $i] : ? [v5: $i] : ((v5 = v3 & k3_lattices(v0, v1, v2) = v3 &
% 67.02/9.75 | $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2,
% 67.02/9.75 | v4) | ~ m1_subset_1(v1, v4)))))
% 67.02/9.75 |
% 67.02/9.75 | ALPHA: (d1_lattices) implies:
% 67.02/9.75 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 67.02/9.75 | l2_lattices(v0) | v3_struct_0(v0) | ? [v2: $i] : (u2_lattices(v0) =
% 67.02/9.75 | v2 & $i(v2) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 67.02/9.75 | (k2_binop_1(v1, v1, v1, v2, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3)
% 67.02/9.75 | | ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3, v1) |
% 67.02/9.75 | (k1_lattices(v0, v3, v4) = v5 & $i(v5))) & ! [v3: $i] : ! [v4:
% 67.02/9.75 | $i] : ! [v5: $i] : ( ~ (k1_lattices(v0, v3, v4) = v5) | ~
% 67.02/9.75 | $i(v4) | ~ $i(v3) | ~ m1_subset_1(v4, v1) | ~ m1_subset_1(v3,
% 67.02/9.75 | v1) | (k2_binop_1(v1, v1, v1, v2, v3, v4) = v5 & $i(v5)))))
% 67.02/9.75 |
% 67.02/9.75 | ALPHA: (d9_lattices) implies:
% 67.02/9.75 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 67.02/9.75 | ~ (k1_lattices(v0, v2, v3) = v4) | ~ (u1_struct_0(v0) = v1) | ~
% 67.02/9.75 | $i(v3) | ~ $i(v2) | ~ $i(v0) | ~ v9_lattices(v0) | ~
% 67.02/9.75 | m1_subset_1(v3, v1) | ~ m1_subset_1(v2, v1) | ~ l3_lattices(v0) |
% 67.02/9.75 | k2_lattices(v0, v2, v4) = v2 | v3_struct_0(v0))
% 67.02/9.75 |
% 67.02/9.75 | ALPHA: (dt_l3_lattices) implies:
% 67.02/9.75 | (7) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l2_lattices(v0))
% 67.02/9.75 | (8) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | l1_lattices(v0))
% 67.02/9.75 |
% 67.02/9.75 | ALPHA: (redefinition_k3_lattices) implies:
% 67.02/9.75 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 67.02/9.75 | (k3_lattices(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 67.02/9.75 | ~ l2_lattices(v0) | ~ v4_lattices(v0) | v3_struct_0(v0) | ? [v4:
% 67.02/9.75 | $i] : ? [v5: $i] : ((v5 = v3 & k1_lattices(v0, v1, v2) = v3 &
% 67.02/9.75 | $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2,
% 67.02/9.75 | v4) | ~ m1_subset_1(v1, v4)))))
% 67.02/9.75 |
% 67.02/9.75 | ALPHA: (redefinition_k4_lattices) implies:
% 67.02/9.75 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 67.02/9.75 | (k2_lattices(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 67.02/9.75 | ~ l1_lattices(v0) | ~ v6_lattices(v0) | v3_struct_0(v0) | ? [v4:
% 67.02/9.75 | $i] : ? [v5: $i] : ((v5 = v3 & k4_lattices(v0, v1, v2) = v3 &
% 67.02/9.75 | $i(v3)) | (u1_struct_0(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2,
% 67.02/9.75 | v4) | ~ m1_subset_1(v1, v4)))))
% 67.02/9.75 |
% 67.02/9.75 | ALPHA: (function-axioms) implies:
% 67.02/9.75 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 67.02/9.76 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 67.02/9.76 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 67.02/9.76 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 67.02/9.76 |
% 67.02/9.76 | DELTA: instantiating (t13_filter_2) with fresh symbols all_87_0, all_87_1,
% 67.02/9.76 | all_87_2, all_87_3 gives:
% 67.02/9.76 | (13) u1_struct_0(all_87_3) = all_87_2 & k1_zfmisc_1(all_87_2) = all_87_1 &
% 67.02/9.76 | $i(all_87_0) & $i(all_87_1) & $i(all_87_2) & $i(all_87_3) &
% 67.02/9.76 | m1_subset_1(all_87_0, all_87_1) & l3_lattices(all_87_3) &
% 67.02/9.76 | v10_lattices(all_87_3) & ~ m2_lattice4(all_87_0, all_87_3) & ~
% 67.02/9.76 | v3_struct_0(all_87_3) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 67.02/9.76 | (k4_lattices(all_87_3, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 67.02/9.76 | r2_hidden(v2, all_87_0) | ~ m1_subset_1(v1, all_87_2) | ~
% 67.02/9.76 | m1_subset_1(v0, all_87_2) | r2_hidden(v1, all_87_0)) & ! [v0: $i] :
% 67.02/9.76 | ! [v1: $i] : ! [v2: $i] : ( ~ (k4_lattices(all_87_3, v0, v1) = v2) |
% 67.02/9.76 | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v2, all_87_0) | ~
% 67.02/9.76 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_87_2) |
% 67.02/9.76 | r2_hidden(v0, all_87_0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 67.02/9.76 | ( ~ (k4_lattices(all_87_3, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 67.02/9.76 | r2_hidden(v1, all_87_0) | ~ r2_hidden(v0, all_87_0) | ~
% 67.02/9.76 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_87_2) |
% 67.02/9.76 | r2_hidden(v2, all_87_0))
% 67.02/9.76 |
% 67.02/9.76 | ALPHA: (13) implies:
% 67.02/9.76 | (14) ~ v3_struct_0(all_87_3)
% 67.02/9.76 | (15) ~ m2_lattice4(all_87_0, all_87_3)
% 67.02/9.76 | (16) v10_lattices(all_87_3)
% 67.02/9.76 | (17) l3_lattices(all_87_3)
% 67.02/9.76 | (18) m1_subset_1(all_87_0, all_87_1)
% 67.02/9.76 | (19) $i(all_87_3)
% 67.02/9.76 | (20) $i(all_87_2)
% 67.02/9.76 | (21) $i(all_87_0)
% 67.02/9.76 | (22) k1_zfmisc_1(all_87_2) = all_87_1
% 67.02/9.76 | (23) u1_struct_0(all_87_3) = all_87_2
% 67.02/9.76 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k4_lattices(all_87_3,
% 67.02/9.76 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v1,
% 67.02/9.76 | all_87_0) | ~ r2_hidden(v0, all_87_0) | ~ m1_subset_1(v1,
% 67.02/9.76 | all_87_2) | ~ m1_subset_1(v0, all_87_2) | r2_hidden(v2,
% 67.02/9.76 | all_87_0))
% 67.02/9.76 | (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k4_lattices(all_87_3,
% 67.02/9.76 | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ r2_hidden(v2,
% 67.02/9.76 | all_87_0) | ~ m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0,
% 67.02/9.76 | all_87_2) | r2_hidden(v1, all_87_0))
% 67.02/9.76 |
% 67.02/9.77 | GROUND_INST: instantiating (3) with all_87_3, simplifying with (14), (16),
% 67.02/9.77 | (17), (19) gives:
% 67.02/9.77 | (26) v9_lattices(all_87_3)
% 67.02/9.77 |
% 67.02/9.77 | GROUND_INST: instantiating (2) with all_87_3, simplifying with (14), (16),
% 67.02/9.77 | (17), (19) gives:
% 67.02/9.77 | (27) v6_lattices(all_87_3)
% 67.02/9.77 |
% 67.02/9.77 | GROUND_INST: instantiating (1) with all_87_3, simplifying with (14), (16),
% 67.02/9.77 | (17), (19) gives:
% 67.02/9.77 | (28) v4_lattices(all_87_3)
% 67.02/9.77 |
% 67.02/9.77 | GROUND_INST: instantiating (8) with all_87_3, simplifying with (17), (19)
% 67.02/9.77 | gives:
% 67.19/9.77 | (29) l1_lattices(all_87_3)
% 67.19/9.77 |
% 67.19/9.77 | GROUND_INST: instantiating (7) with all_87_3, simplifying with (17), (19)
% 67.19/9.77 | gives:
% 67.19/9.77 | (30) l2_lattices(all_87_3)
% 67.19/9.77 |
% 67.19/9.77 | GROUND_INST: instantiating (d10_lattice4) with all_87_3, all_87_2, simplifying
% 67.19/9.77 | with (14), (16), (17), (19), (23) gives:
% 67.19/9.77 | (31) ? [v0: $i] : (k1_zfmisc_1(all_87_2) = v0 & $i(v0) & ! [v1: $i] : !
% 67.19/9.77 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (k4_lattices(all_87_3,
% 67.19/9.77 | v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 67.19/9.77 | m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) | ~
% 67.19/9.77 | r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~
% 67.19/9.77 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | r2_hidden(v4,
% 67.19/9.77 | v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 67.19/9.77 | ~ (k4_lattices(all_87_3, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 67.19/9.77 | ~ $i(v1) | ~ m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) |
% 67.19/9.77 | ~ r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~
% 67.19/9.77 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | ? [v5: $i] :
% 67.19/9.78 | (k3_lattices(all_87_3, v2, v3) = v5 & $i(v5) & r2_hidden(v5, v1)))
% 67.19/9.78 | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 67.19/9.78 | (k3_lattices(all_87_3, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 67.19/9.78 | $i(v1) | ~ m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) | ~
% 67.19/9.78 | r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~
% 67.19/9.78 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | r2_hidden(v4,
% 67.19/9.78 | v1)) & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 67.19/9.78 | ~ (k3_lattices(all_87_3, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) |
% 67.19/9.78 | ~ $i(v1) | ~ m2_lattice4(v1, all_87_3) | ~ r2_hidden(v3, v1) |
% 67.19/9.78 | ~ r2_hidden(v2, v1) | ~ m1_subset_1(v3, all_87_2) | ~
% 67.19/9.78 | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, v0) | ? [v5: $i] :
% 67.19/9.78 | (k4_lattices(all_87_3, v2, v3) = v5 & $i(v5) & r2_hidden(v5, v1)))
% 67.19/9.78 | & ! [v1: $i] : ( ~ $i(v1) | ~ m1_subset_1(v1, v0) |
% 67.19/9.78 | m2_lattice4(v1, all_87_3) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 67.19/9.78 | $i] : ? [v5: $i] : ($i(v3) & $i(v2) & r2_hidden(v3, v1) &
% 67.19/9.78 | r2_hidden(v2, v1) & m1_subset_1(v3, all_87_2) & m1_subset_1(v2,
% 67.19/9.78 | all_87_2) & ((k4_lattices(all_87_3, v2, v3) = v4 & $i(v4) & ~
% 67.19/9.78 | r2_hidden(v4, v1)) | (k3_lattices(all_87_3, v2, v3) = v5 &
% 67.19/9.78 | $i(v5) & ~ r2_hidden(v5, v1))))))
% 67.19/9.78 |
% 67.19/9.78 | GROUND_INST: instantiating (dt_m2_lattice4) with all_87_3, all_87_2,
% 67.19/9.78 | simplifying with (14), (16), (17), (19), (23) gives:
% 67.19/9.78 | (32) ? [v0: $i] : (k1_zfmisc_1(all_87_2) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 67.19/9.78 | $i(v1) | ~ m2_lattice4(v1, all_87_3) | m1_subset_1(v1, v0)))
% 67.19/9.78 |
% 67.19/9.78 | DELTA: instantiating (32) with fresh symbol all_106_0 gives:
% 67.19/9.78 | (33) k1_zfmisc_1(all_87_2) = all_106_0 & $i(all_106_0) & ! [v0: $i] : ( ~
% 67.19/9.78 | $i(v0) | ~ m2_lattice4(v0, all_87_3) | m1_subset_1(v0, all_106_0))
% 67.19/9.78 |
% 67.19/9.78 | ALPHA: (33) implies:
% 67.19/9.78 | (34) k1_zfmisc_1(all_87_2) = all_106_0
% 67.19/9.78 |
% 67.19/9.78 | DELTA: instantiating (31) with fresh symbol all_109_0 gives:
% 67.19/9.78 | (35) k1_zfmisc_1(all_87_2) = all_109_0 & $i(all_109_0) & ! [v0: $i] : !
% 67.19/9.78 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k4_lattices(all_87_3, v1,
% 67.19/9.78 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 67.19/9.78 | m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, v0) | ~ r2_hidden(v1,
% 67.19/9.78 | v0) | ~ m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, all_87_2)
% 67.19/9.78 | | ~ m1_subset_1(v0, all_109_0) | r2_hidden(v3, v0)) & ! [v0: $i] :
% 67.19/9.78 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k4_lattices(all_87_3,
% 67.19/9.78 | v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 67.19/9.78 | m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, v0) | ~ r2_hidden(v1,
% 67.19/9.78 | v0) | ~ m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, all_87_2)
% 67.19/9.78 | | ~ m1_subset_1(v0, all_109_0) | ? [v4: $i] :
% 67.19/9.78 | (k3_lattices(all_87_3, v1, v2) = v4 & $i(v4) & r2_hidden(v4, v0))) &
% 67.19/9.78 | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 67.19/9.78 | (k3_lattices(all_87_3, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 67.19/9.78 | $i(v0) | ~ m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2, v0) | ~
% 67.19/9.78 | r2_hidden(v1, v0) | ~ m1_subset_1(v2, all_87_2) | ~
% 67.19/9.78 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_109_0) |
% 67.19/9.78 | r2_hidden(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 67.19/9.78 | [v3: $i] : ( ~ (k3_lattices(all_87_3, v1, v2) = v3) | ~ $i(v2) | ~
% 67.19/9.79 | $i(v1) | ~ $i(v0) | ~ m2_lattice4(v0, all_87_3) | ~ r2_hidden(v2,
% 67.19/9.79 | v0) | ~ r2_hidden(v1, v0) | ~ m1_subset_1(v2, all_87_2) | ~
% 67.19/9.79 | m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_109_0) | ? [v4:
% 67.19/9.79 | $i] : (k4_lattices(all_87_3, v1, v2) = v4 & $i(v4) & r2_hidden(v4,
% 67.19/9.79 | v0))) & ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_109_0)
% 67.19/9.79 | | m2_lattice4(v0, all_87_3) | ? [v1: $i] : ? [v2: $i] : ? [v3:
% 67.19/9.79 | $i] : ? [v4: $i] : ($i(v2) & $i(v1) & r2_hidden(v2, v0) &
% 67.19/9.79 | r2_hidden(v1, v0) & m1_subset_1(v2, all_87_2) & m1_subset_1(v1,
% 67.19/9.79 | all_87_2) & ((k4_lattices(all_87_3, v1, v2) = v3 & $i(v3) & ~
% 67.19/9.79 | r2_hidden(v3, v0)) | (k3_lattices(all_87_3, v1, v2) = v4 &
% 67.19/9.79 | $i(v4) & ~ r2_hidden(v4, v0)))))
% 67.19/9.79 |
% 67.19/9.79 | ALPHA: (35) implies:
% 67.19/9.79 | (36) k1_zfmisc_1(all_87_2) = all_109_0
% 67.19/9.79 | (37) ! [v0: $i] : ( ~ $i(v0) | ~ m1_subset_1(v0, all_109_0) |
% 67.19/9.79 | m2_lattice4(v0, all_87_3) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i]
% 67.19/9.79 | : ? [v4: $i] : ($i(v2) & $i(v1) & r2_hidden(v2, v0) & r2_hidden(v1,
% 67.19/9.79 | v0) & m1_subset_1(v2, all_87_2) & m1_subset_1(v1, all_87_2) &
% 67.19/9.79 | ((k4_lattices(all_87_3, v1, v2) = v3 & $i(v3) & ~ r2_hidden(v3,
% 67.19/9.79 | v0)) | (k3_lattices(all_87_3, v1, v2) = v4 & $i(v4) & ~
% 67.19/9.79 | r2_hidden(v4, v0)))))
% 67.19/9.79 |
% 67.19/9.79 | GROUND_INST: instantiating (37) with all_87_0, simplifying with (15), (21)
% 67.19/9.79 | gives:
% 67.19/9.79 | (38) ~ m1_subset_1(all_87_0, all_109_0) | ? [v0: $i] : ? [v1: $i] : ?
% 67.19/9.79 | [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) & r2_hidden(v1, all_87_0) &
% 67.19/9.79 | r2_hidden(v0, all_87_0) & m1_subset_1(v1, all_87_2) &
% 67.19/9.79 | m1_subset_1(v0, all_87_2) & ((k4_lattices(all_87_3, v0, v1) = v2 &
% 67.19/9.79 | $i(v2) & ~ r2_hidden(v2, all_87_0)) | (k3_lattices(all_87_3,
% 67.19/9.79 | v0, v1) = v3 & $i(v3) & ~ r2_hidden(v3, all_87_0))))
% 67.19/9.79 |
% 67.19/9.79 | GROUND_INST: instantiating (11) with all_87_1, all_109_0, all_87_2,
% 67.19/9.79 | simplifying with (22), (36) gives:
% 67.19/9.79 | (39) all_109_0 = all_87_1
% 67.19/9.79 |
% 67.19/9.79 | GROUND_INST: instantiating (11) with all_106_0, all_109_0, all_87_2,
% 67.19/9.79 | simplifying with (34), (36) gives:
% 67.19/9.79 | (40) all_109_0 = all_106_0
% 67.19/9.79 |
% 67.19/9.79 | COMBINE_EQS: (39), (40) imply:
% 67.19/9.79 | (41) all_106_0 = all_87_1
% 67.19/9.79 |
% 67.19/9.79 | BETA: splitting (38) gives:
% 67.19/9.79 |
% 67.19/9.79 | Case 1:
% 67.19/9.79 | |
% 67.19/9.79 | | (42) ~ m1_subset_1(all_87_0, all_109_0)
% 67.19/9.79 | |
% 67.19/9.79 | | REDUCE: (39), (42) imply:
% 67.19/9.79 | | (43) ~ m1_subset_1(all_87_0, all_87_1)
% 67.19/9.79 | |
% 67.19/9.79 | | PRED_UNIFY: (18), (43) imply:
% 67.19/9.79 | | (44) $false
% 67.19/9.79 | |
% 67.19/9.79 | | CLOSE: (44) is inconsistent.
% 67.19/9.79 | |
% 67.19/9.79 | Case 2:
% 67.19/9.79 | |
% 67.19/9.80 | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) &
% 67.19/9.80 | | $i(v0) & r2_hidden(v1, all_87_0) & r2_hidden(v0, all_87_0) &
% 67.19/9.80 | | m1_subset_1(v1, all_87_2) & m1_subset_1(v0, all_87_2) &
% 67.19/9.80 | | ((k4_lattices(all_87_3, v0, v1) = v2 & $i(v2) & ~ r2_hidden(v2,
% 67.19/9.80 | | all_87_0)) | (k3_lattices(all_87_3, v0, v1) = v3 & $i(v3) &
% 67.19/9.80 | | ~ r2_hidden(v3, all_87_0))))
% 67.19/9.80 | |
% 67.19/9.80 | | DELTA: instantiating (45) with fresh symbols all_120_0, all_120_1,
% 67.19/9.80 | | all_120_2, all_120_3 gives:
% 67.19/9.80 | | (46) $i(all_120_2) & $i(all_120_3) & r2_hidden(all_120_2, all_87_0) &
% 67.19/9.80 | | r2_hidden(all_120_3, all_87_0) & m1_subset_1(all_120_2, all_87_2) &
% 67.19/9.80 | | m1_subset_1(all_120_3, all_87_2) & ((k4_lattices(all_87_3,
% 67.19/9.80 | | all_120_3, all_120_2) = all_120_1 & $i(all_120_1) & ~
% 67.19/9.80 | | r2_hidden(all_120_1, all_87_0)) | (k3_lattices(all_87_3,
% 67.19/9.80 | | all_120_3, all_120_2) = all_120_0 & $i(all_120_0) & ~
% 67.19/9.80 | | r2_hidden(all_120_0, all_87_0)))
% 67.19/9.80 | |
% 67.19/9.80 | | ALPHA: (46) implies:
% 67.19/9.80 | | (47) m1_subset_1(all_120_3, all_87_2)
% 67.19/9.80 | | (48) m1_subset_1(all_120_2, all_87_2)
% 67.19/9.80 | | (49) r2_hidden(all_120_3, all_87_0)
% 67.19/9.80 | | (50) r2_hidden(all_120_2, all_87_0)
% 67.19/9.80 | | (51) $i(all_120_3)
% 67.19/9.80 | | (52) $i(all_120_2)
% 67.19/9.80 | | (53) (k4_lattices(all_87_3, all_120_3, all_120_2) = all_120_1 &
% 67.19/9.80 | | $i(all_120_1) & ~ r2_hidden(all_120_1, all_87_0)) |
% 67.19/9.80 | | (k3_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 &
% 67.19/9.80 | | $i(all_120_0) & ~ r2_hidden(all_120_0, all_87_0))
% 67.19/9.80 | |
% 67.19/9.80 | | GROUND_INST: instantiating (5) with all_87_3, all_87_2, simplifying with
% 67.19/9.80 | | (14), (19), (23), (30) gives:
% 67.19/9.80 | | (54) ? [v0: $i] : (u2_lattices(all_87_3) = v0 & $i(v0) & ! [v1: $i] :
% 67.19/9.80 | | ! [v2: $i] : ! [v3: $i] : ( ~ (k2_binop_1(all_87_2, all_87_2,
% 67.19/9.80 | | all_87_2, v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 67.19/9.80 | | m1_subset_1(v2, all_87_2) | ~ m1_subset_1(v1, all_87_2) |
% 67.19/9.80 | | (k1_lattices(all_87_3, v1, v2) = v3 & $i(v3))) & ! [v1: $i] :
% 67.19/9.80 | | ! [v2: $i] : ! [v3: $i] : ( ~ (k1_lattices(all_87_3, v1, v2) =
% 67.19/9.80 | | v3) | ~ $i(v2) | ~ $i(v1) | ~ m1_subset_1(v2, all_87_2) |
% 67.19/9.80 | | ~ m1_subset_1(v1, all_87_2) | (k2_binop_1(all_87_2, all_87_2,
% 67.19/9.80 | | all_87_2, v0, v1, v2) = v3 & $i(v3))))
% 67.19/9.80 | |
% 67.19/9.80 | | DELTA: instantiating (54) with fresh symbol all_140_0 gives:
% 67.19/9.80 | | (55) u2_lattices(all_87_3) = all_140_0 & $i(all_140_0) & ! [v0: $i] : !
% 67.19/9.80 | | [v1: $i] : ! [v2: $i] : ( ~ (k2_binop_1(all_87_2, all_87_2,
% 67.19/9.80 | | all_87_2, all_140_0, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 67.19/9.80 | | ~ m1_subset_1(v1, all_87_2) | ~ m1_subset_1(v0, all_87_2) |
% 67.19/9.80 | | (k1_lattices(all_87_3, v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 67.19/9.80 | | [v1: $i] : ! [v2: $i] : ( ~ (k1_lattices(all_87_3, v0, v1) = v2) |
% 67.19/9.80 | | ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1, all_87_2) | ~
% 67.19/9.80 | | m1_subset_1(v0, all_87_2) | (k2_binop_1(all_87_2, all_87_2,
% 67.19/9.80 | | all_87_2, all_140_0, v0, v1) = v2 & $i(v2)))
% 67.19/9.80 | |
% 67.19/9.80 | | ALPHA: (55) implies:
% 67.19/9.80 | | (56) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k1_lattices(all_87_3,
% 67.19/9.80 | | v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v1,
% 67.19/9.80 | | all_87_2) | ~ m1_subset_1(v0, all_87_2) | (k2_binop_1(all_87_2,
% 67.19/9.80 | | all_87_2, all_87_2, all_140_0, v0, v1) = v2 & $i(v2)))
% 67.19/9.80 | |
% 67.19/9.80 | | BETA: splitting (53) gives:
% 67.19/9.80 | |
% 67.19/9.80 | | Case 1:
% 67.19/9.80 | | |
% 67.19/9.80 | | | (57) k4_lattices(all_87_3, all_120_3, all_120_2) = all_120_1 &
% 67.19/9.80 | | | $i(all_120_1) & ~ r2_hidden(all_120_1, all_87_0)
% 67.19/9.81 | | |
% 67.19/9.81 | | | ALPHA: (57) implies:
% 67.19/9.81 | | | (58) ~ r2_hidden(all_120_1, all_87_0)
% 67.19/9.81 | | | (59) k4_lattices(all_87_3, all_120_3, all_120_2) = all_120_1
% 67.19/9.81 | | |
% 67.19/9.81 | | | GROUND_INST: instantiating (24) with all_120_3, all_120_2, all_120_1,
% 67.19/9.81 | | | simplifying with (47), (48), (49), (50), (51), (52), (58),
% 67.19/9.81 | | | (59) gives:
% 67.19/9.81 | | | (60) $false
% 67.19/9.81 | | |
% 67.19/9.81 | | | CLOSE: (60) is inconsistent.
% 67.19/9.81 | | |
% 67.19/9.81 | | Case 2:
% 67.19/9.81 | | |
% 67.19/9.81 | | | (61) k3_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 &
% 67.19/9.81 | | | $i(all_120_0) & ~ r2_hidden(all_120_0, all_87_0)
% 67.19/9.81 | | |
% 67.19/9.81 | | | ALPHA: (61) implies:
% 67.19/9.81 | | | (62) ~ r2_hidden(all_120_0, all_87_0)
% 67.19/9.81 | | | (63) k3_lattices(all_87_3, all_120_3, all_120_2) = all_120_0
% 67.19/9.81 | | |
% 67.19/9.81 | | | GROUND_INST: instantiating (t4_subset) with all_87_2, all_87_2, all_87_2,
% 67.19/9.81 | | | all_87_1, simplifying with (20), (22) gives:
% 67.19/9.81 | | | (64) ~ r2_hidden(all_87_2, all_87_2) | ~ m1_subset_1(all_87_2,
% 67.19/9.81 | | | all_87_1) | m1_subset_1(all_87_2, all_87_2)
% 67.19/9.81 | | |
% 67.19/9.81 | | | GROUND_INST: instantiating (4) with all_87_3, all_120_2, all_120_3,
% 67.19/9.81 | | | all_120_0, simplifying with (14), (19), (28), (30), (51),
% 67.19/9.81 | | | (52), (63) gives:
% 67.19/9.81 | | | (65) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_0 &
% 67.19/9.81 | | | k3_lattices(all_87_3, all_120_2, all_120_3) = all_120_0 &
% 67.19/9.81 | | | $i(all_120_0)) | (u1_struct_0(all_87_3) = v0 & $i(v0) & ( ~
% 67.19/9.81 | | | m1_subset_1(all_120_2, v0) | ~ m1_subset_1(all_120_3,
% 67.19/9.81 | | | v0))))
% 67.19/9.81 | | |
% 67.19/9.81 | | | GROUND_INST: instantiating (9) with all_87_3, all_120_3, all_120_2,
% 67.19/9.81 | | | all_120_0, simplifying with (14), (19), (28), (30), (51),
% 67.19/9.81 | | | (52), (63) gives:
% 67.19/9.81 | | | (66) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_0 &
% 67.19/9.81 | | | k1_lattices(all_87_3, all_120_3, all_120_2) = all_120_0 &
% 67.19/9.81 | | | $i(all_120_0)) | (u1_struct_0(all_87_3) = v0 & $i(v0) & ( ~
% 67.19/9.81 | | | m1_subset_1(all_120_2, v0) | ~ m1_subset_1(all_120_3,
% 67.19/9.81 | | | v0))))
% 67.19/9.81 | | |
% 67.19/9.81 | | | GROUND_INST: instantiating (dt_k3_lattices) with all_87_3, all_120_3,
% 67.19/9.81 | | | all_120_2, all_120_0, simplifying with (14), (19), (28),
% 67.19/9.81 | | | (30), (51), (52), (63) gives:
% 67.19/9.81 | | | (67) ? [v0: $i] : (u1_struct_0(all_87_3) = v0 & $i(v0) & ( ~
% 67.19/9.81 | | | m1_subset_1(all_120_2, v0) | ~ m1_subset_1(all_120_3, v0) |
% 67.19/9.81 | | | m1_subset_1(all_120_0, v0)))
% 67.19/9.81 | | |
% 67.19/9.81 | | | DELTA: instantiating (67) with fresh symbol all_492_0 gives:
% 67.19/9.81 | | | (68) u1_struct_0(all_87_3) = all_492_0 & $i(all_492_0) & ( ~
% 67.19/9.81 | | | m1_subset_1(all_120_2, all_492_0) | ~ m1_subset_1(all_120_3,
% 67.19/9.81 | | | all_492_0) | m1_subset_1(all_120_0, all_492_0))
% 67.19/9.81 | | |
% 67.19/9.81 | | | ALPHA: (68) implies:
% 67.19/9.82 | | | (69) $i(all_492_0)
% 67.19/9.82 | | | (70) u1_struct_0(all_87_3) = all_492_0
% 67.19/9.82 | | | (71) ~ m1_subset_1(all_120_2, all_492_0) | ~ m1_subset_1(all_120_3,
% 67.19/9.82 | | | all_492_0) | m1_subset_1(all_120_0, all_492_0)
% 67.19/9.82 | | |
% 67.19/9.82 | | | DELTA: instantiating (66) with fresh symbols all_494_0, all_494_1 gives:
% 67.19/9.82 | | | (72) (all_494_0 = all_120_0 & k1_lattices(all_87_3, all_120_3,
% 67.19/9.82 | | | all_120_2) = all_120_0 & $i(all_120_0)) |
% 67.19/9.82 | | | (u1_struct_0(all_87_3) = all_494_1 & $i(all_494_1) & ( ~
% 67.19/9.82 | | | m1_subset_1(all_120_2, all_494_1) | ~ m1_subset_1(all_120_3,
% 67.19/9.82 | | | all_494_1)))
% 67.19/9.82 | | |
% 67.19/9.82 | | | DELTA: instantiating (65) with fresh symbols all_495_0, all_495_1 gives:
% 67.19/9.82 | | | (73) (all_495_0 = all_120_0 & k3_lattices(all_87_3, all_120_2,
% 67.19/9.82 | | | all_120_3) = all_120_0 & $i(all_120_0)) |
% 67.19/9.82 | | | (u1_struct_0(all_87_3) = all_495_1 & $i(all_495_1) & ( ~
% 67.19/9.82 | | | m1_subset_1(all_120_2, all_495_1) | ~ m1_subset_1(all_120_3,
% 67.19/9.82 | | | all_495_1)))
% 67.19/9.82 | | |
% 67.19/9.82 | | | BETA: splitting (73) gives:
% 67.19/9.82 | | |
% 67.19/9.82 | | | Case 1:
% 67.19/9.82 | | | |
% 67.19/9.82 | | | | (74) all_495_0 = all_120_0 & k3_lattices(all_87_3, all_120_2,
% 67.19/9.82 | | | | all_120_3) = all_120_0 & $i(all_120_0)
% 67.19/9.82 | | | |
% 67.19/9.82 | | | | ALPHA: (74) implies:
% 67.19/9.82 | | | | (75) k3_lattices(all_87_3, all_120_2, all_120_3) = all_120_0
% 67.19/9.82 | | | |
% 67.19/9.82 | | | | GROUND_INST: instantiating (12) with all_87_2, all_492_0, all_87_3,
% 67.19/9.82 | | | | simplifying with (23), (70) gives:
% 67.19/9.82 | | | | (76) all_492_0 = all_87_2
% 67.19/9.82 | | | |
% 67.19/9.82 | | | | BETA: splitting (71) gives:
% 67.19/9.82 | | | |
% 67.19/9.82 | | | | Case 1:
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | (77) ~ m1_subset_1(all_120_2, all_492_0)
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | REDUCE: (76), (77) imply:
% 67.19/9.82 | | | | | (78) ~ m1_subset_1(all_120_2, all_87_2)
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | PRED_UNIFY: (48), (78) imply:
% 67.19/9.82 | | | | | (79) $false
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | CLOSE: (79) is inconsistent.
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | Case 2:
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | (80) m1_subset_1(all_120_2, all_492_0)
% 67.19/9.82 | | | | | (81) ~ m1_subset_1(all_120_3, all_492_0) | m1_subset_1(all_120_0,
% 67.19/9.82 | | | | | all_492_0)
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | BETA: splitting (81) gives:
% 67.19/9.82 | | | | |
% 67.19/9.82 | | | | | Case 1:
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | (82) ~ m1_subset_1(all_120_3, all_492_0)
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | REDUCE: (76), (82) imply:
% 67.19/9.82 | | | | | | (83) ~ m1_subset_1(all_120_3, all_87_2)
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | PRED_UNIFY: (47), (83) imply:
% 67.19/9.82 | | | | | | (84) $false
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | CLOSE: (84) is inconsistent.
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | Case 2:
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | (85) m1_subset_1(all_120_3, all_492_0)
% 67.19/9.82 | | | | | | (86) m1_subset_1(all_120_0, all_492_0)
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | REDUCE: (76), (86) imply:
% 67.19/9.82 | | | | | | (87) m1_subset_1(all_120_0, all_87_2)
% 67.19/9.82 | | | | | |
% 67.19/9.82 | | | | | | BETA: splitting (72) gives:
% 67.19/9.82 | | | | | |
% 67.19/9.83 | | | | | | Case 1:
% 67.19/9.83 | | | | | | |
% 67.19/9.83 | | | | | | | (88) all_494_0 = all_120_0 & k1_lattices(all_87_3, all_120_3,
% 67.19/9.83 | | | | | | | all_120_2) = all_120_0 & $i(all_120_0)
% 67.19/9.83 | | | | | | |
% 67.19/9.83 | | | | | | | ALPHA: (88) implies:
% 67.19/9.83 | | | | | | | (89) k1_lattices(all_87_3, all_120_3, all_120_2) = all_120_0
% 67.19/9.83 | | | | | | |
% 67.19/9.83 | | | | | | | GROUND_INST: instantiating (9) with all_87_3, all_120_2,
% 67.19/9.83 | | | | | | | all_120_3, all_120_0, simplifying with (14), (19),
% 67.19/9.83 | | | | | | | (28), (30), (51), (52), (75) gives:
% 67.19/9.83 | | | | | | | (90) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_0 &
% 67.19/9.83 | | | | | | | k1_lattices(all_87_3, all_120_2, all_120_3) =
% 67.19/9.83 | | | | | | | all_120_0 & $i(all_120_0)) | (u1_struct_0(all_87_3) =
% 67.19/9.83 | | | | | | | v0 & $i(v0) & ( ~ m1_subset_1(all_120_2, v0) | ~
% 67.19/9.83 | | | | | | | m1_subset_1(all_120_3, v0))))
% 67.19/9.83 | | | | | | |
% 67.48/9.83 | | | | | | | GROUND_INST: instantiating (6) with all_87_3, all_87_2, all_120_3,
% 67.48/9.83 | | | | | | | all_120_2, all_120_0, simplifying with (14), (17),
% 67.48/9.83 | | | | | | | (19), (23), (26), (47), (48), (51), (52), (89) gives:
% 67.48/9.83 | | | | | | | (91) k2_lattices(all_87_3, all_120_3, all_120_0) = all_120_3
% 67.48/9.83 | | | | | | |
% 67.48/9.83 | | | | | | | DELTA: instantiating (90) with fresh symbols all_677_0, all_677_1
% 67.48/9.83 | | | | | | | gives:
% 67.48/9.83 | | | | | | | (92) (all_677_0 = all_120_0 & k1_lattices(all_87_3, all_120_2,
% 67.48/9.83 | | | | | | | all_120_3) = all_120_0 & $i(all_120_0)) |
% 67.48/9.83 | | | | | | | (u1_struct_0(all_87_3) = all_677_1 & $i(all_677_1) & ( ~
% 67.48/9.83 | | | | | | | m1_subset_1(all_120_2, all_677_1) | ~
% 67.48/9.83 | | | | | | | m1_subset_1(all_120_3, all_677_1)))
% 67.48/9.83 | | | | | | |
% 67.48/9.83 | | | | | | | BETA: splitting (92) gives:
% 67.48/9.83 | | | | | | |
% 67.48/9.83 | | | | | | | Case 1:
% 67.48/9.83 | | | | | | | |
% 67.48/9.83 | | | | | | | | (93) all_677_0 = all_120_0 & k1_lattices(all_87_3, all_120_2,
% 67.48/9.83 | | | | | | | | all_120_3) = all_120_0 & $i(all_120_0)
% 67.48/9.83 | | | | | | | |
% 67.48/9.83 | | | | | | | | ALPHA: (93) implies:
% 67.48/9.83 | | | | | | | | (94) k1_lattices(all_87_3, all_120_2, all_120_3) = all_120_0
% 67.48/9.83 | | | | | | | |
% 67.48/9.83 | | | | | | | | BETA: splitting (64) gives:
% 67.48/9.83 | | | | | | | |
% 67.48/9.83 | | | | | | | | Case 1:
% 67.48/9.83 | | | | | | | | |
% 67.48/9.83 | | | | | | | | |
% 67.48/9.83 | | | | | | | | | GROUND_INST: instantiating (56) with all_120_2, all_120_3,
% 67.48/9.83 | | | | | | | | | all_120_0, simplifying with (47), (48), (51),
% 67.48/9.83 | | | | | | | | | (52), (94) gives:
% 67.48/9.83 | | | | | | | | | (95) k2_binop_1(all_87_2, all_87_2, all_87_2, all_140_0,
% 67.48/9.83 | | | | | | | | | all_120_2, all_120_3) = all_120_0 & $i(all_120_0)
% 67.48/9.83 | | | | | | | | |
% 67.48/9.83 | | | | | | | | | ALPHA: (95) implies:
% 67.48/9.83 | | | | | | | | | (96) $i(all_120_0)
% 67.48/9.83 | | | | | | | | |
% 67.48/9.84 | | | | | | | | | GROUND_INST: instantiating (10) with all_87_3, all_120_3,
% 67.48/9.84 | | | | | | | | | all_120_0, all_120_3, simplifying with (14), (19),
% 67.48/9.84 | | | | | | | | | (27), (29), (51), (91), (96) gives:
% 67.48/9.84 | | | | | | | | | (97) ? [v0: $i] : ? [v1: int] : ((v1 = all_120_3 &
% 67.48/9.84 | | | | | | | | | k4_lattices(all_87_3, all_120_3, all_120_0) =
% 67.48/9.84 | | | | | | | | | all_120_3) | (u1_struct_0(all_87_3) = v0 & $i(v0)
% 67.48/9.84 | | | | | | | | | & ( ~ m1_subset_1(all_120_0, v0) | ~
% 67.48/9.84 | | | | | | | | | m1_subset_1(all_120_3, v0))))
% 67.48/9.84 | | | | | | | | |
% 67.48/9.84 | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_742_0,
% 67.48/9.84 | | | | | | | | | all_742_1 gives:
% 67.48/9.84 | | | | | | | | | (98) (all_742_0 = all_120_3 & k4_lattices(all_87_3,
% 67.48/9.84 | | | | | | | | | all_120_3, all_120_0) = all_120_3) |
% 67.48/9.84 | | | | | | | | | (u1_struct_0(all_87_3) = all_742_1 & $i(all_742_1) & (
% 67.48/9.84 | | | | | | | | | ~ m1_subset_1(all_120_0, all_742_1) | ~
% 67.48/9.84 | | | | | | | | | m1_subset_1(all_120_3, all_742_1)))
% 67.48/9.84 | | | | | | | | |
% 67.48/9.84 | | | | | | | | | BETA: splitting (98) gives:
% 67.48/9.84 | | | | | | | | |
% 67.48/9.84 | | | | | | | | | Case 1:
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | (99) all_742_0 = all_120_3 & k4_lattices(all_87_3,
% 67.48/9.84 | | | | | | | | | | all_120_3, all_120_0) = all_120_3
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | ALPHA: (99) implies:
% 67.48/9.84 | | | | | | | | | | (100) k4_lattices(all_87_3, all_120_3, all_120_0) =
% 67.48/9.84 | | | | | | | | | | all_120_3
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | GROUND_INST: instantiating (25) with all_120_3, all_120_0,
% 67.48/9.84 | | | | | | | | | | all_120_3, simplifying with (47), (49), (51),
% 67.48/9.84 | | | | | | | | | | (62), (87), (96), (100) gives:
% 67.48/9.84 | | | | | | | | | | (101) $false
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | CLOSE: (101) is inconsistent.
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | Case 2:
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | (102) u1_struct_0(all_87_3) = all_742_1 & $i(all_742_1) &
% 67.48/9.84 | | | | | | | | | | ( ~ m1_subset_1(all_120_0, all_742_1) | ~
% 67.48/9.84 | | | | | | | | | | m1_subset_1(all_120_3, all_742_1))
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | ALPHA: (102) implies:
% 67.48/9.84 | | | | | | | | | | (103) u1_struct_0(all_87_3) = all_742_1
% 67.48/9.84 | | | | | | | | | | (104) ~ m1_subset_1(all_120_0, all_742_1) | ~
% 67.48/9.84 | | | | | | | | | | m1_subset_1(all_120_3, all_742_1)
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | GROUND_INST: instantiating (12) with all_87_2, all_742_1,
% 67.48/9.84 | | | | | | | | | | all_87_3, simplifying with (23), (103) gives:
% 67.48/9.84 | | | | | | | | | | (105) all_742_1 = all_87_2
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | BETA: splitting (104) gives:
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | Case 1:
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | (106) ~ m1_subset_1(all_120_0, all_742_1)
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | REDUCE: (105), (106) imply:
% 67.48/9.84 | | | | | | | | | | | (107) ~ m1_subset_1(all_120_0, all_87_2)
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | PRED_UNIFY: (87), (107) imply:
% 67.48/9.84 | | | | | | | | | | | (108) $false
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | CLOSE: (108) is inconsistent.
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | Case 2:
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | (109) ~ m1_subset_1(all_120_3, all_742_1)
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | REDUCE: (105), (109) imply:
% 67.48/9.84 | | | | | | | | | | | (110) ~ m1_subset_1(all_120_3, all_87_2)
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | PRED_UNIFY: (47), (110) imply:
% 67.48/9.84 | | | | | | | | | | | (111) $false
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 67.48/9.84 | | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | | End of split
% 67.48/9.84 | | | | | | | | | |
% 67.48/9.84 | | | | | | | | | End of split
% 67.48/9.84 | | | | | | | | |
% 67.48/9.84 | | | | | | | | Case 2:
% 67.48/9.84 | | | | | | | | |
% 67.48/9.84 | | | | | | | | | (112) r2_hidden(all_87_2, all_87_2)
% 67.48/9.84 | | | | | | | | |
% 67.48/9.84 | | | | | | | | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with
% 67.48/9.84 | | | | | | | | | all_87_2, all_87_2, simplifying with (20), (112)
% 67.48/9.84 | | | | | | | | | gives:
% 67.48/9.85 | | | | | | | | | (113) $false
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | CLOSE: (113) is inconsistent.
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | End of split
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | Case 2:
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | (114) u1_struct_0(all_87_3) = all_677_1 & $i(all_677_1) & ( ~
% 67.48/9.85 | | | | | | | | m1_subset_1(all_120_2, all_677_1) | ~
% 67.48/9.85 | | | | | | | | m1_subset_1(all_120_3, all_677_1))
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | ALPHA: (114) implies:
% 67.48/9.85 | | | | | | | | (115) u1_struct_0(all_87_3) = all_677_1
% 67.48/9.85 | | | | | | | | (116) ~ m1_subset_1(all_120_2, all_677_1) | ~
% 67.48/9.85 | | | | | | | | m1_subset_1(all_120_3, all_677_1)
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | GROUND_INST: instantiating (12) with all_87_2, all_677_1,
% 67.48/9.85 | | | | | | | | all_87_3, simplifying with (23), (115) gives:
% 67.48/9.85 | | | | | | | | (117) all_677_1 = all_87_2
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | BETA: splitting (116) gives:
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | Case 1:
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | (118) ~ m1_subset_1(all_120_2, all_677_1)
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | REDUCE: (117), (118) imply:
% 67.48/9.85 | | | | | | | | | (119) ~ m1_subset_1(all_120_2, all_87_2)
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | PRED_UNIFY: (48), (119) imply:
% 67.48/9.85 | | | | | | | | | (120) $false
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | CLOSE: (120) is inconsistent.
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | Case 2:
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | (121) ~ m1_subset_1(all_120_3, all_677_1)
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | REDUCE: (117), (121) imply:
% 67.48/9.85 | | | | | | | | | (122) ~ m1_subset_1(all_120_3, all_87_2)
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | PRED_UNIFY: (47), (122) imply:
% 67.48/9.85 | | | | | | | | | (123) $false
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | | CLOSE: (123) is inconsistent.
% 67.48/9.85 | | | | | | | | |
% 67.48/9.85 | | | | | | | | End of split
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | End of split
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | Case 2:
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | | (124) u1_struct_0(all_87_3) = all_494_1 & $i(all_494_1) & ( ~
% 67.48/9.85 | | | | | | | m1_subset_1(all_120_2, all_494_1) | ~
% 67.48/9.85 | | | | | | | m1_subset_1(all_120_3, all_494_1))
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | | ALPHA: (124) implies:
% 67.48/9.85 | | | | | | | (125) u1_struct_0(all_87_3) = all_494_1
% 67.48/9.85 | | | | | | | (126) ~ m1_subset_1(all_120_2, all_494_1) | ~
% 67.48/9.85 | | | | | | | m1_subset_1(all_120_3, all_494_1)
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | | GROUND_INST: instantiating (12) with all_87_2, all_494_1,
% 67.48/9.85 | | | | | | | all_87_3, simplifying with (23), (125) gives:
% 67.48/9.85 | | | | | | | (127) all_494_1 = all_87_2
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | | BETA: splitting (126) gives:
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | | Case 1:
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | (128) ~ m1_subset_1(all_120_2, all_494_1)
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | REDUCE: (127), (128) imply:
% 67.48/9.85 | | | | | | | | (129) ~ m1_subset_1(all_120_2, all_87_2)
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | PRED_UNIFY: (48), (129) imply:
% 67.48/9.85 | | | | | | | | (130) $false
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | CLOSE: (130) is inconsistent.
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | Case 2:
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | (131) ~ m1_subset_1(all_120_3, all_494_1)
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | REDUCE: (127), (131) imply:
% 67.48/9.85 | | | | | | | | (132) ~ m1_subset_1(all_120_3, all_87_2)
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | PRED_UNIFY: (47), (132) imply:
% 67.48/9.85 | | | | | | | | (133) $false
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | | CLOSE: (133) is inconsistent.
% 67.48/9.85 | | | | | | | |
% 67.48/9.85 | | | | | | | End of split
% 67.48/9.85 | | | | | | |
% 67.48/9.85 | | | | | | End of split
% 67.48/9.85 | | | | | |
% 67.48/9.85 | | | | | End of split
% 67.48/9.85 | | | | |
% 67.48/9.85 | | | | End of split
% 67.48/9.85 | | | |
% 67.48/9.85 | | | Case 2:
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | (134) u1_struct_0(all_87_3) = all_495_1 & $i(all_495_1) & ( ~
% 67.48/9.86 | | | | m1_subset_1(all_120_2, all_495_1) | ~ m1_subset_1(all_120_3,
% 67.48/9.86 | | | | all_495_1))
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | ALPHA: (134) implies:
% 67.48/9.86 | | | | (135) u1_struct_0(all_87_3) = all_495_1
% 67.48/9.86 | | | | (136) ~ m1_subset_1(all_120_2, all_495_1) | ~
% 67.48/9.86 | | | | m1_subset_1(all_120_3, all_495_1)
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | GROUND_INST: instantiating (12) with all_87_2, all_495_1, all_87_3,
% 67.48/9.86 | | | | simplifying with (23), (135) gives:
% 67.48/9.86 | | | | (137) all_495_1 = all_87_2
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | GROUND_INST: instantiating (12) with all_492_0, all_495_1, all_87_3,
% 67.48/9.86 | | | | simplifying with (70), (135) gives:
% 67.48/9.86 | | | | (138) all_495_1 = all_492_0
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | COMBINE_EQS: (137), (138) imply:
% 67.48/9.86 | | | | (139) all_492_0 = all_87_2
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | BETA: splitting (136) gives:
% 67.48/9.86 | | | |
% 67.48/9.86 | | | | Case 1:
% 67.48/9.86 | | | | |
% 67.48/9.86 | | | | | (140) ~ m1_subset_1(all_120_2, all_495_1)
% 67.48/9.86 | | | | |
% 67.48/9.86 | | | | | REDUCE: (137), (140) imply:
% 67.48/9.86 | | | | | (141) ~ m1_subset_1(all_120_2, all_87_2)
% 67.48/9.86 | | | | |
% 67.61/9.86 | | | | | PRED_UNIFY: (48), (141) imply:
% 67.61/9.86 | | | | | (142) $false
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | | CLOSE: (142) is inconsistent.
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | Case 2:
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | | (143) ~ m1_subset_1(all_120_3, all_495_1)
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | | REDUCE: (137), (143) imply:
% 67.61/9.86 | | | | | (144) ~ m1_subset_1(all_120_3, all_87_2)
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | | PRED_UNIFY: (47), (144) imply:
% 67.61/9.86 | | | | | (145) $false
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | | CLOSE: (145) is inconsistent.
% 67.61/9.86 | | | | |
% 67.61/9.86 | | | | End of split
% 67.61/9.86 | | | |
% 67.61/9.86 | | | End of split
% 67.61/9.86 | | |
% 67.61/9.86 | | End of split
% 67.61/9.86 | |
% 67.61/9.86 | End of split
% 67.61/9.86 |
% 67.61/9.86 End of proof
% 67.61/9.86 % SZS output end Proof for theBenchmark
% 67.61/9.86
% 67.61/9.86 9235ms
%------------------------------------------------------------------------------