TSTP Solution File: LAT351+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT351+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 : n002.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 06:25:01 EDT 2023
% Result : Theorem 67.38s 9.48s
% Output : Proof 81.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT351+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.33 % Computer : n002.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Aug 24 10:23:46 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.79/1.54 Prover 4: Preprocessing ...
% 5.79/1.55 Prover 1: Preprocessing ...
% 5.79/1.58 Prover 0: Preprocessing ...
% 5.79/1.58 Prover 5: Preprocessing ...
% 5.79/1.58 Prover 6: Preprocessing ...
% 5.79/1.58 Prover 3: Preprocessing ...
% 5.79/1.58 Prover 2: Preprocessing ...
% 14.15/2.64 Prover 1: Warning: ignoring some quantifiers
% 14.42/2.72 Prover 5: Proving ...
% 14.99/2.76 Prover 1: Constructing countermodel ...
% 15.30/2.81 Prover 3: Warning: ignoring some quantifiers
% 15.96/2.86 Prover 3: Constructing countermodel ...
% 15.96/2.89 Prover 2: Proving ...
% 15.96/2.89 Prover 6: Proving ...
% 27.41/4.40 Prover 4: Warning: ignoring some quantifiers
% 27.88/4.49 Prover 4: Constructing countermodel ...
% 35.05/5.33 Prover 0: Proving ...
% 67.38/9.48 Prover 5: proved (8855ms)
% 67.38/9.48
% 67.38/9.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.38/9.48
% 67.38/9.48 Prover 3: stopped
% 67.38/9.48 Prover 2: stopped
% 67.38/9.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 67.38/9.48 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 67.38/9.48 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 67.38/9.49 Prover 6: stopped
% 67.38/9.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 67.75/9.52 Prover 0: stopped
% 67.75/9.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 69.52/9.76 Prover 7: Preprocessing ...
% 69.52/9.79 Prover 10: Preprocessing ...
% 69.92/9.80 Prover 8: Preprocessing ...
% 69.92/9.81 Prover 11: Preprocessing ...
% 69.92/9.82 Prover 13: Preprocessing ...
% 70.76/9.92 Prover 7: Warning: ignoring some quantifiers
% 70.76/9.94 Prover 7: Constructing countermodel ...
% 71.12/9.98 Prover 10: Warning: ignoring some quantifiers
% 71.12/10.02 Prover 10: Constructing countermodel ...
% 71.12/10.04 Prover 8: Warning: ignoring some quantifiers
% 71.12/10.04 Prover 13: Warning: ignoring some quantifiers
% 71.87/10.05 Prover 8: Constructing countermodel ...
% 71.87/10.06 Prover 13: Constructing countermodel ...
% 76.96/10.74 Prover 10: gave up
% 76.96/10.75 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 77.65/10.85 Prover 16: Preprocessing ...
% 79.28/11.01 Prover 16: Warning: ignoring some quantifiers
% 79.28/11.03 Prover 16: Constructing countermodel ...
% 79.28/11.07 Prover 7: Found proof (size 131)
% 79.28/11.07 Prover 7: proved (1587ms)
% 79.28/11.07 Prover 4: stopped
% 79.28/11.07 Prover 16: stopped
% 79.28/11.07 Prover 8: stopped
% 79.28/11.07 Prover 13: stopped
% 79.28/11.07 Prover 1: stopped
% 80.64/11.34 Prover 11: Warning: ignoring some quantifiers
% 81.04/11.38 Prover 11: Constructing countermodel ...
% 81.09/11.40 Prover 11: stopped
% 81.09/11.40
% 81.09/11.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.09/11.40
% 81.14/11.43 % SZS output start Proof for theBenchmark
% 81.14/11.44 Assumptions after simplification:
% 81.14/11.44 ---------------------------------
% 81.14/11.44
% 81.14/11.44 (abstractness_v1_orders_2)
% 81.14/11.48 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_orders_2(v0) = v1) | ~ $i(v0) | ~
% 81.14/11.48 v1_orders_2(v0) | ~ l1_orders_2(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 &
% 81.14/11.48 g1_orders_2(v2, v1) = v0 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.14/11.48 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ v1_orders_2(v0) | ~ l1_orders_2(v0)
% 81.14/11.49 | ? [v2: $i] : (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) = v0 & $i(v2)))
% 81.14/11.49
% 81.14/11.49 (cc1_waybel22)
% 81.14/11.49 ! [v0: $i] : ! [v1: $i] : ( ~ (k9_waybel_0(v0) = v1) | ~ $i(v0) | ~
% 81.14/11.49 v2_yellow_0(v0) | ~ l1_orders_2(v0) | ~ v4_orders_2(v0) | ~
% 81.14/11.49 v3_orders_2(v0) | ~ v2_orders_2(v0) | v3_struct_0(v0) | ? [v2: $i] : ?
% 81.14/11.49 [v3: $i] : (k2_yellow_1(v1) = v2 & u1_struct_0(v2) = v3 & $i(v3) & $i(v2) &
% 81.14/11.49 ! [v4: $i] : ( ~ $i(v4) | ~ m1_subset_1(v4, v3) | ~ v1_xboole_0(v4))))
% 81.14/11.49
% 81.14/11.49 (d2_waybel22)
% 81.14/11.49 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_waybel22(v0) = v1) | ~ $i(v0) |
% 81.14/11.49 (a_1_0_waybel22(v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.14/11.49 (a_1_0_waybel22(v0) = v1) | ~ $i(v0) | (k1_waybel22(v0) = v1 & $i(v1)))
% 81.14/11.49
% 81.14/11.49 (dt_k1_waybel22)
% 81.14/11.50 ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | ? [v2:
% 81.14/11.50 $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (k1_waybel22(v0) = v2 &
% 81.14/11.50 k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v1) = v3 &
% 81.14/11.50 $i(v5) & $i(v4) & $i(v3) & $i(v2) & m1_subset_1(v2, v5))) & ! [v0: $i] :
% 81.14/11.50 ! [v1: $i] : ( ~ (k1_waybel22(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3:
% 81.14/11.50 $i] : ? [v4: $i] : ? [v5: $i] : (k3_yellow_1(v0) = v2 & k1_zfmisc_1(v4)
% 81.14/11.50 = v5 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v2) = v3 & $i(v5) & $i(v4) &
% 81.14/11.50 $i(v3) & $i(v2) & m1_subset_1(v1, v5)))
% 81.14/11.50
% 81.14/11.50 (dt_k2_yellow_1)
% 81.14/11.50 ! [v0: $i] : ! [v1: $i] : ( ~ (k2_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.14/11.50 v1_orders_2(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k2_yellow_1(v0) = v1) |
% 81.14/11.50 ~ $i(v0) | l1_orders_2(v1))
% 81.14/11.50
% 81.14/11.50 (dt_k3_yellow_1)
% 81.14/11.50 ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.14/11.50 v1_orders_2(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) |
% 81.14/11.50 ~ $i(v0) | l1_orders_2(v1))
% 81.14/11.50
% 81.14/11.50 (dt_u1_orders_2)
% 81.14/11.50 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_orders_2(v0) = v1) | ~ $i(v0) | ~
% 81.14/11.50 l1_orders_2(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) &
% 81.14/11.50 m2_relset_1(v1, v2, v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.14/11.50 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ? [v2: $i] :
% 81.14/11.50 (u1_orders_2(v0) = v2 & $i(v2) & m2_relset_1(v2, v1, v1)))
% 81.14/11.50
% 81.14/11.50 (fc14_waybel_8)
% 81.58/11.51 ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.51 v3_struct_0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) |
% 81.58/11.51 ~ $i(v0) | v11_waybel_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.51 (k3_yellow_1(v0) = v1) | ~ $i(v0) | v10_waybel_1(v1)) & ! [v0: $i] : !
% 81.58/11.51 [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | v2_waybel_1(v1)) & ! [v0:
% 81.58/11.51 $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.51 v9_waybel_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) |
% 81.58/11.51 ~ $i(v0) | v1_waybel_8(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.51 (k3_yellow_1(v0) = v1) | ~ $i(v0) | v2_waybel_3(v1)) & ! [v0: $i] : !
% 81.58/11.51 [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | v2_waybel_8(v1)) & ! [v0:
% 81.58/11.51 $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.51 v3_yellow_0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) |
% 81.58/11.51 ~ $i(v0) | v2_yellow_0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.51 (k3_yellow_1(v0) = v1) | ~ $i(v0) | v1_yellow_0(v1)) & ! [v0: $i] : !
% 81.58/11.51 [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | v25_waybel_0(v1)) & !
% 81.58/11.51 [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.51 v24_waybel_0(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) |
% 81.58/11.51 ~ $i(v0) | v1_orders_2(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.51 (k3_yellow_1(v0) = v1) | ~ $i(v0) | v3_waybel_3(v1)) & ! [v0: $i] : !
% 81.58/11.51 [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | v3_lattice3(v1)) & ! [v0:
% 81.58/11.51 $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.51 v2_lattice3(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) |
% 81.58/11.51 ~ $i(v0) | v1_lattice3(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.51 (k3_yellow_1(v0) = v1) | ~ $i(v0) | v4_orders_2(v1)) & ! [v0: $i] : !
% 81.58/11.51 [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | v3_orders_2(v1)) & ! [v0:
% 81.58/11.51 $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.51 v2_orders_2(v1))
% 81.58/11.51
% 81.58/11.51 (fc1_waybel22)
% 81.58/11.51 ! [v0: $i] : ! [v1: $i] : ( ~ (k9_waybel_0(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.51 v2_yellow_0(v0) | ~ l1_orders_2(v0) | ~ v2_lattice3(v0) | ~
% 81.58/11.51 v4_orders_2(v0) | ~ v3_orders_2(v0) | ~ v2_orders_2(v0) | v3_struct_0(v0)
% 81.58/11.51 | ? [v2: $i] : (k2_yellow_1(v1) = v2 & $i(v2) & v3_yellow_0(v2) &
% 81.58/11.51 v2_yellow_0(v2) & v1_yellow_0(v2) & v25_waybel_0(v2) & v24_waybel_0(v2) &
% 81.58/11.51 v1_orders_2(v2) & v3_waybel_3(v2) & v3_lattice3(v2) & v2_lattice3(v2) &
% 81.58/11.51 v1_lattice3(v2) & v4_orders_2(v2) & v3_orders_2(v2) & v2_orders_2(v2) & ~
% 81.58/11.51 v3_struct_0(v2)))
% 81.58/11.51
% 81.58/11.51 (fc2_waybel16)
% 81.58/11.51 ! [v0: $i] : ! [v1: $i] : ( ~ (k9_waybel_0(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.51 v2_yellow_0(v0) | ~ l1_orders_2(v0) | ~ v2_lattice3(v0) | ~
% 81.58/11.51 v4_orders_2(v0) | ~ v3_orders_2(v0) | ~ v2_orders_2(v0) | ? [v2: $i] :
% 81.58/11.51 (k2_yellow_1(v1) = v2 & $i(v2) & v1_yellow_0(v2) & v25_waybel_0(v2) &
% 81.58/11.51 v24_waybel_0(v2) & v1_orders_2(v2) & v3_lattice3(v2) & v2_lattice3(v2) &
% 81.58/11.51 v4_orders_2(v2) & v3_orders_2(v2) & v2_orders_2(v2) & ~ v3_struct_0(v2)))
% 81.58/11.51
% 81.58/11.51 (fc6_waybel_8)
% 81.58/11.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_orders_2(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.52 l1_orders_2(v0) | ~ v3_orders_2(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.52 (u1_struct_0(v0) = v2 & g1_orders_2(v2, v1) = v3 & $i(v3) & $i(v2) &
% 81.58/11.52 v1_orders_2(v3) & v3_orders_2(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.52 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v3_orders_2(v0)
% 81.58/11.52 | ? [v2: $i] : ? [v3: $i] : (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) =
% 81.58/11.52 v3 & $i(v3) & $i(v2) & v1_orders_2(v3) & v3_orders_2(v3)))
% 81.58/11.52
% 81.58/11.52 (fc7_waybel_8)
% 81.58/11.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_orders_2(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.52 l1_orders_2(v0) | ~ v4_orders_2(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.52 (u1_struct_0(v0) = v2 & g1_orders_2(v2, v1) = v3 & $i(v3) & $i(v2) &
% 81.58/11.52 v1_orders_2(v3) & v4_orders_2(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 81.58/11.52 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v4_orders_2(v0)
% 81.58/11.52 | ? [v2: $i] : ? [v3: $i] : (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) =
% 81.58/11.52 v3 & $i(v3) & $i(v2) & v1_orders_2(v3) & v4_orders_2(v3)))
% 81.58/11.52
% 81.58/11.52 (fc8_waybel_8)
% 81.58/11.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_orders_2(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.52 l1_orders_2(v0) | ~ v2_lattice3(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.52 (u1_struct_0(v0) = v2 & g1_orders_2(v2, v1) = v3 & $i(v3) & $i(v2) &
% 81.58/11.52 v1_orders_2(v3) & v2_lattice3(v3) & ~ v3_struct_0(v3))) & ! [v0: $i] :
% 81.58/11.52 ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~
% 81.58/11.52 v2_lattice3(v0) | ? [v2: $i] : ? [v3: $i] : (u1_orders_2(v0) = v2 &
% 81.58/11.52 g1_orders_2(v1, v2) = v3 & $i(v3) & $i(v2) & v1_orders_2(v3) &
% 81.58/11.52 v2_lattice3(v3) & ~ v3_struct_0(v3)))
% 81.58/11.52
% 81.58/11.52 (fc9_waybel_8)
% 81.58/11.52 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_orders_2(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.52 l1_orders_2(v0) | ~ v1_lattice3(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.52 (u1_struct_0(v0) = v2 & g1_orders_2(v2, v1) = v3 & $i(v3) & $i(v2) &
% 81.58/11.52 v1_orders_2(v3) & v1_lattice3(v3) & ~ v3_struct_0(v3))) & ! [v0: $i] :
% 81.58/11.52 ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~
% 81.58/11.52 v1_lattice3(v0) | ? [v2: $i] : ? [v3: $i] : (u1_orders_2(v0) = v2 &
% 81.58/11.52 g1_orders_2(v1, v2) = v3 & $i(v3) & $i(v2) & v1_orders_2(v3) &
% 81.58/11.52 v1_lattice3(v3) & ~ v3_struct_0(v3)))
% 81.58/11.52
% 81.58/11.52 (t10_waybel22)
% 81.58/11.52 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_card_1(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 81.58/11.52 : (k1_card_1(v2) = v1 & k1_waybel22(v0) = v2 & $i(v2) & $i(v1))) & ! [v0:
% 81.58/11.52 $i] : ! [v1: $i] : ( ~ (k1_waybel22(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 81.58/11.52 (k1_card_1(v1) = v2 & k1_card_1(v0) = v2 & $i(v2)))
% 81.58/11.52
% 81.58/11.52 (t16_waybel22)
% 81.58/11.53 ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | ? [v2:
% 81.58/11.53 $i] : ? [v3: $i] : ? [v4: $i] : (k1_waybel22(v0) = v4 & k9_waybel_0(v1)
% 81.58/11.53 = v2 & k2_yellow_1(v2) = v3 & $i(v4) & $i(v3) & $i(v2) & r1_waybel22(v3,
% 81.58/11.53 v4))) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_waybel22(v0) = v1) | ~
% 81.58/11.53 $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k3_yellow_1(v0) = v2 &
% 81.58/11.53 k9_waybel_0(v2) = v3 & k2_yellow_1(v3) = v4 & $i(v4) & $i(v3) & $i(v2) &
% 81.58/11.53 r1_waybel22(v4, v1)))
% 81.58/11.53
% 81.58/11.53 (t17_waybel22)
% 81.58/11.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 81.58/11.53 (k1_card_1(v3) = v4) | ~ (k1_card_1(v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 81.58/11.53 $i(v1) | ~ $i(v0) | ~ r1_waybel22(v1, v3) | ~ r1_waybel22(v0, v2) | ~
% 81.58/11.53 l1_orders_2(v1) | ~ l1_orders_2(v0) | ~ v3_waybel_3(v1) | ~
% 81.58/11.53 v3_waybel_3(v0) | ~ v3_lattice3(v1) | ~ v3_lattice3(v0) | ~
% 81.58/11.53 v2_lattice3(v1) | ~ v2_lattice3(v0) | ~ v1_lattice3(v1) | ~
% 81.58/11.53 v1_lattice3(v0) | ~ v4_orders_2(v1) | ~ v4_orders_2(v0) | ~
% 81.58/11.53 v3_orders_2(v1) | ~ v3_orders_2(v0) | ~ v2_orders_2(v1) | ~
% 81.58/11.53 v2_orders_2(v0) | r5_waybel_1(v0, v1))
% 81.58/11.53
% 81.58/11.53 (t18_waybel22)
% 81.58/11.53 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 81.58/11.53 $i] : ? [v6: $i] : (k3_yellow_1(v0) = v3 & k1_card_1(v6) = v2 &
% 81.58/11.53 k1_card_1(v0) = v2 & k9_waybel_0(v3) = v4 & k2_yellow_1(v4) = v5 & $i(v6) &
% 81.58/11.53 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & r1_waybel22(v1, v6) &
% 81.58/11.53 l1_orders_2(v1) & v3_waybel_3(v1) & v3_lattice3(v1) & v2_lattice3(v1) &
% 81.58/11.53 v1_lattice3(v1) & v4_orders_2(v1) & v3_orders_2(v1) & v2_orders_2(v1) & ~
% 81.58/11.53 r5_waybel_1(v1, v5))
% 81.58/11.53
% 81.58/11.53 (function-axioms)
% 81.58/11.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 81.58/11.53 (k1_struct_0(v3, v2) = v1) | ~ (k1_struct_0(v3, v2) = v0)) & ! [v0: $i] :
% 81.58/11.53 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k7_waybel_0(v3, v2) =
% 81.58/11.53 v1) | ~ (k7_waybel_0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 81.58/11.53 $i] : ! [v3: $i] : (v1 = v0 | ~ (k5_waybel_0(v3, v2) = v1) | ~
% 81.58/11.53 (k5_waybel_0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 81.58/11.53 [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2)
% 81.58/11.53 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 81.58/11.53 | ~ (g1_orders_2(v3, v2) = v1) | ~ (g1_orders_2(v3, v2) = v0)) & ! [v0:
% 81.58/11.53 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~
% 81.58/11.53 (k1_tarski(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 81.58/11.53 ~ (k3_yellow_1(v2) = v1) | ~ (k3_yellow_1(v2) = v0)) & ! [v0: $i] : !
% 81.58/11.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_card_1(v2) = v1) | ~
% 81.58/11.53 (k1_card_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 81.58/11.53 ~ (k1_waybel22(v2) = v1) | ~ (k1_waybel22(v2) = v0)) & ! [v0: $i] : !
% 81.58/11.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (a_1_0_waybel22(v2) = v1) | ~
% 81.58/11.53 (a_1_0_waybel22(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 81.58/11.53 v0 | ~ (a_1_1_waybel_0(v2) = v1) | ~ (a_1_1_waybel_0(v2) = v0)) & ! [v0:
% 81.58/11.53 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k9_waybel_0(v2) = v1) | ~
% 81.58/11.53 (k9_waybel_0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 81.58/11.53 | ~ (k2_yellow_1(v2) = v1) | ~ (k2_yellow_1(v2) = v0)) & ! [v0: $i] : !
% 81.58/11.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 81.58/11.53 (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 81.58/11.53 | ~ (u1_orders_2(v2) = v1) | ~ (u1_orders_2(v2) = v0)) & ! [v0: $i] : !
% 81.58/11.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~
% 81.58/11.53 (u1_struct_0(v2) = v0))
% 81.58/11.53
% 81.58/11.53 Further assumptions not needed in the proof:
% 81.58/11.53 --------------------------------------------
% 81.58/11.53 antisymmetry_r2_hidden, cc10_waybel_0, cc11_waybel_0, cc12_waybel_0,
% 81.58/11.54 cc13_waybel_0, cc14_waybel_0, cc1_funct_1, cc1_lattice3, cc1_relset_1,
% 81.58/11.54 cc1_setfam_1, cc1_waybel_8, cc1_yellow_0, cc1_yellow_7, cc2_funct_1,
% 81.58/11.54 cc2_lattice3, cc2_waybel_5, cc2_waybel_8, cc2_yellow_0, cc3_waybel_5,
% 81.58/11.54 cc3_waybel_8, cc3_yellow_0, cc4_waybel_5, cc4_waybel_8, cc4_yellow_0,
% 81.58/11.54 cc5_waybel_0, cc5_yellow_0, cc9_waybel_0, d18_waybel_0, d24_waybel_0,
% 81.58/11.54 dt_g1_orders_2, dt_k1_card_1, dt_k1_struct_0, dt_k1_tarski, dt_k1_xboole_0,
% 81.58/11.54 dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k5_waybel_0, dt_k7_waybel_0, dt_k9_waybel_0,
% 81.58/11.54 dt_l1_orders_2, dt_l1_struct_0, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1,
% 81.58/11.54 dt_u1_struct_0, existence_l1_orders_2, existence_l1_struct_0,
% 81.58/11.54 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 81.58/11.54 fc10_waybel_0, fc10_waybel_8, fc11_waybel_8, fc12_waybel_0, fc12_waybel_8,
% 81.58/11.54 fc14_waybel_0, fc17_waybel_0, fc1_struct_0, fc1_subset_1, fc1_waybel16,
% 81.58/11.54 fc1_xboole_0, fc1_yellow_0, fc2_setfam_1, fc2_subset_1, fc4_subset_1,
% 81.58/11.54 fc4_waybel_8, fc5_waybel_8, fc8_waybel_0, fraenkel_a_1_0_waybel22,
% 81.58/11.54 fraenkel_a_1_1_waybel_0, free_g1_orders_2, rc10_waybel_0, rc12_waybel_0,
% 81.58/11.54 rc13_waybel_0, rc1_funct_1, rc1_lattice3, rc1_setfam_1, rc1_subset_1,
% 81.58/11.54 rc1_waybel_5, rc1_xboole_0, rc1_yellow_0, rc1_yellow_7, rc2_funct_1,
% 81.58/11.54 rc2_lattice3, rc2_subset_1, rc2_xboole_0, rc2_yellow_0, rc3_funct_1,
% 81.58/11.54 rc3_struct_0, rc5_struct_0, redefinition_k1_struct_0, redefinition_m2_relset_1,
% 81.58/11.54 reflexivity_r1_tarski, reflexivity_r5_waybel_1, t1_subset, t2_subset, t2_tarski,
% 81.58/11.54 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 81.58/11.54
% 81.58/11.54 Those formulas are unsatisfiable:
% 81.58/11.54 ---------------------------------
% 81.58/11.54
% 81.58/11.54 Begin of proof
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (abstractness_v1_orders_2) implies:
% 81.58/11.54 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.54 | v1_orders_2(v0) | ~ l1_orders_2(v0) | ? [v2: $i] : (u1_orders_2(v0)
% 81.58/11.54 | = v2 & g1_orders_2(v1, v2) = v0 & $i(v2)))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (d2_waybel22) implies:
% 81.58/11.54 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_waybel22(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | (a_1_0_waybel22(v0) = v1 & $i(v1)))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (dt_k1_waybel22) implies:
% 81.58/11.54 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) | ?
% 81.58/11.54 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (k1_waybel22(v0)
% 81.58/11.54 | = v2 & k1_zfmisc_1(v4) = v5 & k1_zfmisc_1(v3) = v4 &
% 81.58/11.54 | u1_struct_0(v1) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) &
% 81.58/11.54 | m1_subset_1(v2, v5)))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (dt_k2_yellow_1) implies:
% 81.58/11.54 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | l1_orders_2(v1))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (dt_k3_yellow_1) implies:
% 81.58/11.54 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | l1_orders_2(v1))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (dt_u1_orders_2) implies:
% 81.58/11.54 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 81.58/11.54 | l1_orders_2(v0) | ? [v2: $i] : (u1_orders_2(v0) = v2 & $i(v2) &
% 81.58/11.54 | m2_relset_1(v2, v1, v1)))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (fc14_waybel_8) implies:
% 81.58/11.54 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v2_orders_2(v1))
% 81.58/11.54 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v3_orders_2(v1))
% 81.58/11.54 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v4_orders_2(v1))
% 81.58/11.54 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v1_lattice3(v1))
% 81.58/11.54 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v2_lattice3(v1))
% 81.58/11.54 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v1_orders_2(v1))
% 81.58/11.54 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.54 | v2_yellow_0(v1))
% 81.58/11.54 |
% 81.58/11.54 | ALPHA: (fc6_waybel_8) implies:
% 81.58/11.55 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 81.58/11.55 | ~ l1_orders_2(v0) | ~ v3_orders_2(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.55 | (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) = v3 & $i(v3) & $i(v2) &
% 81.58/11.55 | v1_orders_2(v3) & v3_orders_2(v3)))
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (fc7_waybel_8) implies:
% 81.58/11.55 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 81.58/11.55 | ~ l1_orders_2(v0) | ~ v4_orders_2(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.55 | (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) = v3 & $i(v3) & $i(v2) &
% 81.58/11.55 | v1_orders_2(v3) & v4_orders_2(v3)))
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (fc8_waybel_8) implies:
% 81.58/11.55 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 81.58/11.55 | ~ l1_orders_2(v0) | ~ v2_lattice3(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.55 | (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) = v3 & $i(v3) & $i(v2) &
% 81.58/11.55 | v1_orders_2(v3) & v2_lattice3(v3) & ~ v3_struct_0(v3)))
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (fc9_waybel_8) implies:
% 81.58/11.55 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 81.58/11.55 | ~ l1_orders_2(v0) | ~ v1_lattice3(v0) | ? [v2: $i] : ? [v3: $i] :
% 81.58/11.55 | (u1_orders_2(v0) = v2 & g1_orders_2(v1, v2) = v3 & $i(v3) & $i(v2) &
% 81.58/11.55 | v1_orders_2(v3) & v1_lattice3(v3) & ~ v3_struct_0(v3)))
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (t10_waybel22) implies:
% 81.58/11.55 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_card_1(v0) = v1) | ~ $i(v0) | ?
% 81.58/11.55 | [v2: $i] : (k1_card_1(v2) = v1 & k1_waybel22(v0) = v2 & $i(v2) &
% 81.58/11.55 | $i(v1)))
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (t16_waybel22) implies:
% 81.58/11.55 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (k3_yellow_1(v0) = v1) | ~ $i(v0) |
% 81.58/11.55 | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_waybel22(v0) = v4 &
% 81.58/11.55 | k9_waybel_0(v1) = v2 & k2_yellow_1(v2) = v3 & $i(v4) & $i(v3) &
% 81.58/11.55 | $i(v2) & r1_waybel22(v3, v4)))
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (function-axioms) implies:
% 81.58/11.55 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.58/11.55 | (u1_orders_2(v2) = v1) | ~ (u1_orders_2(v2) = v0))
% 81.58/11.55 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.58/11.55 | (k2_yellow_1(v2) = v1) | ~ (k2_yellow_1(v2) = v0))
% 81.58/11.55 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.58/11.55 | (k9_waybel_0(v2) = v1) | ~ (k9_waybel_0(v2) = v0))
% 81.58/11.55 | (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 81.58/11.55 | (k1_waybel22(v2) = v1) | ~ (k1_waybel22(v2) = v0))
% 81.58/11.55 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 81.58/11.55 | (g1_orders_2(v3, v2) = v1) | ~ (g1_orders_2(v3, v2) = v0))
% 81.58/11.55 |
% 81.58/11.55 | DELTA: instantiating (t18_waybel22) with fresh symbols all_138_0, all_138_1,
% 81.58/11.55 | all_138_2, all_138_3, all_138_4, all_138_5, all_138_6 gives:
% 81.58/11.55 | (25) k3_yellow_1(all_138_6) = all_138_3 & k1_card_1(all_138_0) = all_138_4
% 81.58/11.55 | & k1_card_1(all_138_6) = all_138_4 & k9_waybel_0(all_138_3) =
% 81.58/11.55 | all_138_2 & k2_yellow_1(all_138_2) = all_138_1 & $i(all_138_0) &
% 81.58/11.55 | $i(all_138_1) & $i(all_138_2) & $i(all_138_3) & $i(all_138_4) &
% 81.58/11.55 | $i(all_138_5) & $i(all_138_6) & r1_waybel22(all_138_5, all_138_0) &
% 81.58/11.55 | l1_orders_2(all_138_5) & v3_waybel_3(all_138_5) &
% 81.58/11.55 | v3_lattice3(all_138_5) & v2_lattice3(all_138_5) &
% 81.58/11.55 | v1_lattice3(all_138_5) & v4_orders_2(all_138_5) &
% 81.58/11.55 | v3_orders_2(all_138_5) & v2_orders_2(all_138_5) & ~
% 81.58/11.55 | r5_waybel_1(all_138_5, all_138_1)
% 81.58/11.55 |
% 81.58/11.55 | ALPHA: (25) implies:
% 81.58/11.55 | (26) ~ r5_waybel_1(all_138_5, all_138_1)
% 81.58/11.55 | (27) v2_orders_2(all_138_5)
% 81.58/11.55 | (28) v3_orders_2(all_138_5)
% 81.58/11.56 | (29) v4_orders_2(all_138_5)
% 81.58/11.56 | (30) v1_lattice3(all_138_5)
% 81.58/11.56 | (31) v2_lattice3(all_138_5)
% 81.58/11.56 | (32) v3_lattice3(all_138_5)
% 81.58/11.56 | (33) v3_waybel_3(all_138_5)
% 81.58/11.56 | (34) l1_orders_2(all_138_5)
% 81.58/11.56 | (35) r1_waybel22(all_138_5, all_138_0)
% 81.58/11.56 | (36) $i(all_138_6)
% 81.58/11.56 | (37) $i(all_138_5)
% 81.58/11.56 | (38) $i(all_138_3)
% 81.58/11.56 | (39) $i(all_138_2)
% 81.58/11.56 | (40) $i(all_138_0)
% 81.58/11.56 | (41) k2_yellow_1(all_138_2) = all_138_1
% 81.58/11.56 | (42) k9_waybel_0(all_138_3) = all_138_2
% 81.58/11.56 | (43) k1_card_1(all_138_6) = all_138_4
% 81.58/11.56 | (44) k1_card_1(all_138_0) = all_138_4
% 81.58/11.56 | (45) k3_yellow_1(all_138_6) = all_138_3
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (4) with all_138_2, all_138_1, simplifying with
% 81.58/11.56 | (39), (41) gives:
% 81.58/11.56 | (46) l1_orders_2(all_138_1)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (18) with all_138_6, all_138_4, simplifying with
% 81.58/11.56 | (36), (43) gives:
% 81.58/11.56 | (47) ? [v0: $i] : (k1_card_1(v0) = all_138_4 & k1_waybel22(all_138_6) = v0
% 81.58/11.56 | & $i(v0) & $i(all_138_4))
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (13) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (48) v2_yellow_0(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (12) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (49) v1_orders_2(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (5) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (50) l1_orders_2(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (11) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (51) v2_lattice3(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (10) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (52) v1_lattice3(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (9) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (53) v4_orders_2(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (8) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (54) v3_orders_2(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (7) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (55) v2_orders_2(all_138_3)
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (3) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 81.58/11.56 | (k1_waybel22(all_138_6) = v0 & k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v1)
% 81.58/11.56 | = v2 & u1_struct_0(all_138_3) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 81.58/11.56 | $i(v0) & m1_subset_1(v0, v3))
% 81.58/11.56 |
% 81.58/11.56 | GROUND_INST: instantiating (19) with all_138_6, all_138_3, simplifying with
% 81.58/11.56 | (36), (45) gives:
% 81.58/11.56 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_waybel22(all_138_6) = v2
% 81.58/11.56 | & k9_waybel_0(all_138_3) = v0 & k2_yellow_1(v0) = v1 & $i(v2) &
% 81.58/11.56 | $i(v1) & $i(v0) & r1_waybel22(v1, v2))
% 81.58/11.56 |
% 81.58/11.56 | DELTA: instantiating (47) with fresh symbol all_154_0 gives:
% 81.58/11.56 | (58) k1_card_1(all_154_0) = all_138_4 & k1_waybel22(all_138_6) = all_154_0
% 81.58/11.56 | & $i(all_154_0) & $i(all_138_4)
% 81.58/11.56 |
% 81.58/11.56 | ALPHA: (58) implies:
% 81.58/11.56 | (59) k1_waybel22(all_138_6) = all_154_0
% 81.58/11.56 | (60) k1_card_1(all_154_0) = all_138_4
% 81.58/11.56 |
% 81.58/11.56 | DELTA: instantiating (57) with fresh symbols all_158_0, all_158_1, all_158_2
% 81.58/11.56 | gives:
% 81.58/11.56 | (61) k1_waybel22(all_138_6) = all_158_0 & k9_waybel_0(all_138_3) =
% 81.58/11.56 | all_158_2 & k2_yellow_1(all_158_2) = all_158_1 & $i(all_158_0) &
% 81.58/11.56 | $i(all_158_1) & $i(all_158_2) & r1_waybel22(all_158_1, all_158_0)
% 81.58/11.56 |
% 81.58/11.56 | ALPHA: (61) implies:
% 81.58/11.56 | (62) r1_waybel22(all_158_1, all_158_0)
% 81.58/11.56 | (63) k2_yellow_1(all_158_2) = all_158_1
% 81.58/11.57 | (64) k9_waybel_0(all_138_3) = all_158_2
% 81.58/11.57 | (65) k1_waybel22(all_138_6) = all_158_0
% 81.58/11.57 |
% 81.58/11.57 | DELTA: instantiating (56) with fresh symbols all_160_0, all_160_1, all_160_2,
% 81.58/11.57 | all_160_3 gives:
% 81.58/11.57 | (66) k1_waybel22(all_138_6) = all_160_3 & k1_zfmisc_1(all_160_1) =
% 81.58/11.57 | all_160_0 & k1_zfmisc_1(all_160_2) = all_160_1 &
% 81.58/11.57 | u1_struct_0(all_138_3) = all_160_2 & $i(all_160_0) & $i(all_160_1) &
% 81.58/11.57 | $i(all_160_2) & $i(all_160_3) & m1_subset_1(all_160_3, all_160_0)
% 81.58/11.57 |
% 81.58/11.57 | ALPHA: (66) implies:
% 81.58/11.57 | (67) u1_struct_0(all_138_3) = all_160_2
% 81.58/11.57 | (68) k1_waybel22(all_138_6) = all_160_3
% 81.58/11.57 |
% 81.58/11.57 | GROUND_INST: instantiating (21) with all_138_1, all_158_1, all_138_2,
% 81.58/11.57 | simplifying with (41) gives:
% 81.58/11.57 | (69) all_158_1 = all_138_1 | ~ (k2_yellow_1(all_138_2) = all_158_1)
% 81.58/11.57 |
% 81.58/11.57 | GROUND_INST: instantiating (22) with all_138_2, all_158_2, all_138_3,
% 81.58/11.57 | simplifying with (42), (64) gives:
% 81.58/11.57 | (70) all_158_2 = all_138_2
% 81.58/11.57 |
% 81.58/11.57 | GROUND_INST: instantiating (23) with all_158_0, all_160_3, all_138_6,
% 81.58/11.57 | simplifying with (65), (68) gives:
% 81.58/11.57 | (71) all_160_3 = all_158_0
% 81.58/11.57 |
% 81.58/11.57 | GROUND_INST: instantiating (23) with all_154_0, all_160_3, all_138_6,
% 81.58/11.57 | simplifying with (59), (68) gives:
% 81.58/11.57 | (72) all_160_3 = all_154_0
% 81.58/11.57 |
% 81.58/11.57 | COMBINE_EQS: (71), (72) imply:
% 81.58/11.57 | (73) all_158_0 = all_154_0
% 81.58/11.57 |
% 81.58/11.57 | SIMP: (73) implies:
% 81.58/11.57 | (74) all_158_0 = all_154_0
% 81.58/11.57 |
% 81.58/11.57 | REDUCE: (63), (70) imply:
% 81.58/11.57 | (75) k2_yellow_1(all_138_2) = all_158_1
% 81.58/11.57 |
% 81.58/11.57 | REDUCE: (62), (74) imply:
% 81.58/11.57 | (76) r1_waybel22(all_158_1, all_154_0)
% 81.58/11.57 |
% 81.58/11.57 | BETA: splitting (69) gives:
% 81.58/11.57 |
% 81.58/11.57 | Case 1:
% 81.58/11.57 | |
% 81.58/11.57 | | (77) ~ (k2_yellow_1(all_138_2) = all_158_1)
% 81.58/11.57 | |
% 81.58/11.57 | | PRED_UNIFY: (75), (77) imply:
% 81.58/11.57 | | (78) $false
% 81.58/11.57 | |
% 81.58/11.57 | | CLOSE: (78) is inconsistent.
% 81.58/11.57 | |
% 81.58/11.57 | Case 2:
% 81.58/11.57 | |
% 81.58/11.57 | | (79) all_158_1 = all_138_1
% 81.58/11.57 | |
% 81.58/11.57 | | REDUCE: (76), (79) imply:
% 81.58/11.57 | | (80) r1_waybel22(all_138_1, all_154_0)
% 81.58/11.57 | |
% 81.58/11.57 | | GROUND_INST: instantiating (fc1_waybel22) with all_138_3, all_138_2,
% 81.58/11.57 | | simplifying with (38), (42), (48), (50), (51), (53), (54), (55)
% 81.58/11.57 | | gives:
% 81.58/11.57 | | (81) v3_struct_0(all_138_3) | ? [v0: $i] : (k2_yellow_1(all_138_2) = v0
% 81.58/11.57 | | & $i(v0) & v3_yellow_0(v0) & v2_yellow_0(v0) & v1_yellow_0(v0) &
% 81.58/11.57 | | v25_waybel_0(v0) & v24_waybel_0(v0) & v1_orders_2(v0) &
% 81.58/11.57 | | v3_waybel_3(v0) & v3_lattice3(v0) & v2_lattice3(v0) &
% 81.58/11.57 | | v1_lattice3(v0) & v4_orders_2(v0) & v3_orders_2(v0) &
% 81.58/11.57 | | v2_orders_2(v0) & ~ v3_struct_0(v0))
% 81.58/11.57 | |
% 81.58/11.57 | | GROUND_INST: instantiating (fc2_waybel16) with all_138_3, all_138_2,
% 81.58/11.57 | | simplifying with (38), (42), (48), (50), (51), (53), (54), (55)
% 81.58/11.57 | | gives:
% 81.58/11.58 | | (82) ? [v0: $i] : (k2_yellow_1(all_138_2) = v0 & $i(v0) &
% 81.58/11.58 | | v1_yellow_0(v0) & v25_waybel_0(v0) & v24_waybel_0(v0) &
% 81.58/11.58 | | v1_orders_2(v0) & v3_lattice3(v0) & v2_lattice3(v0) &
% 81.58/11.58 | | v4_orders_2(v0) & v3_orders_2(v0) & v2_orders_2(v0) & ~
% 81.58/11.58 | | v3_struct_0(v0))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (cc1_waybel22) with all_138_3, all_138_2,
% 81.58/11.58 | | simplifying with (38), (42), (48), (50), (53), (54), (55)
% 81.58/11.58 | | gives:
% 81.58/11.58 | | (83) v3_struct_0(all_138_3) | ? [v0: $i] : ? [v1: $i] :
% 81.58/11.58 | | (k2_yellow_1(all_138_2) = v0 & u1_struct_0(v0) = v1 & $i(v1) &
% 81.58/11.58 | | $i(v0) & ! [v2: $i] : ( ~ $i(v2) | ~ m1_subset_1(v2, v1) | ~
% 81.58/11.58 | | v1_xboole_0(v2)))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (1) with all_138_3, all_160_2, simplifying with
% 81.58/11.58 | | (38), (49), (50), (67) gives:
% 81.58/11.58 | | (84) ? [v0: $i] : (u1_orders_2(all_138_3) = v0 & g1_orders_2(all_160_2,
% 81.58/11.58 | | v0) = all_138_3 & $i(v0))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (16) with all_138_3, all_160_2, simplifying with
% 81.58/11.58 | | (38), (50), (51), (67) gives:
% 81.58/11.58 | | (85) ? [v0: $i] : ? [v1: $i] : (u1_orders_2(all_138_3) = v0 &
% 81.58/11.58 | | g1_orders_2(all_160_2, v0) = v1 & $i(v1) & $i(v0) &
% 81.58/11.58 | | v1_orders_2(v1) & v2_lattice3(v1) & ~ v3_struct_0(v1))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (17) with all_138_3, all_160_2, simplifying with
% 81.58/11.58 | | (38), (50), (52), (67) gives:
% 81.58/11.58 | | (86) ? [v0: $i] : ? [v1: $i] : (u1_orders_2(all_138_3) = v0 &
% 81.58/11.58 | | g1_orders_2(all_160_2, v0) = v1 & $i(v1) & $i(v0) &
% 81.58/11.58 | | v1_orders_2(v1) & v1_lattice3(v1) & ~ v3_struct_0(v1))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (15) with all_138_3, all_160_2, simplifying with
% 81.58/11.58 | | (38), (50), (53), (67) gives:
% 81.58/11.58 | | (87) ? [v0: $i] : ? [v1: $i] : (u1_orders_2(all_138_3) = v0 &
% 81.58/11.58 | | g1_orders_2(all_160_2, v0) = v1 & $i(v1) & $i(v0) &
% 81.58/11.58 | | v1_orders_2(v1) & v4_orders_2(v1))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (14) with all_138_3, all_160_2, simplifying with
% 81.58/11.58 | | (38), (50), (54), (67) gives:
% 81.58/11.58 | | (88) ? [v0: $i] : ? [v1: $i] : (u1_orders_2(all_138_3) = v0 &
% 81.58/11.58 | | g1_orders_2(all_160_2, v0) = v1 & $i(v1) & $i(v0) &
% 81.58/11.58 | | v1_orders_2(v1) & v3_orders_2(v1))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (6) with all_138_3, all_160_2, simplifying with
% 81.58/11.58 | | (38), (50), (67) gives:
% 81.58/11.58 | | (89) ? [v0: $i] : (u1_orders_2(all_138_3) = v0 & $i(v0) &
% 81.58/11.58 | | m2_relset_1(v0, all_160_2, all_160_2))
% 81.58/11.58 | |
% 81.58/11.58 | | GROUND_INST: instantiating (2) with all_138_6, all_154_0, simplifying with
% 81.58/11.58 | | (36), (59) gives:
% 81.58/11.58 | | (90) a_1_0_waybel22(all_138_6) = all_154_0 & $i(all_154_0)
% 81.58/11.58 | |
% 81.58/11.58 | | ALPHA: (90) implies:
% 81.58/11.58 | | (91) $i(all_154_0)
% 81.58/11.58 | |
% 81.58/11.58 | | DELTA: instantiating (84) with fresh symbol all_198_0 gives:
% 81.58/11.58 | | (92) u1_orders_2(all_138_3) = all_198_0 & g1_orders_2(all_160_2,
% 81.58/11.58 | | all_198_0) = all_138_3 & $i(all_198_0)
% 81.58/11.58 | |
% 81.58/11.58 | | ALPHA: (92) implies:
% 81.58/11.58 | | (93) g1_orders_2(all_160_2, all_198_0) = all_138_3
% 81.58/11.58 | | (94) u1_orders_2(all_138_3) = all_198_0
% 81.58/11.58 | |
% 81.58/11.58 | | DELTA: instantiating (89) with fresh symbol all_200_0 gives:
% 81.58/11.58 | | (95) u1_orders_2(all_138_3) = all_200_0 & $i(all_200_0) &
% 81.58/11.58 | | m2_relset_1(all_200_0, all_160_2, all_160_2)
% 81.58/11.58 | |
% 81.58/11.58 | | ALPHA: (95) implies:
% 81.58/11.58 | | (96) u1_orders_2(all_138_3) = all_200_0
% 81.58/11.58 | |
% 81.58/11.58 | | DELTA: instantiating (88) with fresh symbols all_208_0, all_208_1 gives:
% 81.58/11.58 | | (97) u1_orders_2(all_138_3) = all_208_1 & g1_orders_2(all_160_2,
% 81.58/11.58 | | all_208_1) = all_208_0 & $i(all_208_0) & $i(all_208_1) &
% 81.58/11.58 | | v1_orders_2(all_208_0) & v3_orders_2(all_208_0)
% 81.58/11.58 | |
% 81.58/11.58 | | ALPHA: (97) implies:
% 81.58/11.58 | | (98) u1_orders_2(all_138_3) = all_208_1
% 81.58/11.58 | |
% 81.58/11.58 | | DELTA: instantiating (87) with fresh symbols all_210_0, all_210_1 gives:
% 81.58/11.58 | | (99) u1_orders_2(all_138_3) = all_210_1 & g1_orders_2(all_160_2,
% 81.58/11.58 | | all_210_1) = all_210_0 & $i(all_210_0) & $i(all_210_1) &
% 81.58/11.58 | | v1_orders_2(all_210_0) & v4_orders_2(all_210_0)
% 81.58/11.58 | |
% 81.58/11.58 | | ALPHA: (99) implies:
% 81.58/11.58 | | (100) g1_orders_2(all_160_2, all_210_1) = all_210_0
% 81.58/11.58 | | (101) u1_orders_2(all_138_3) = all_210_1
% 81.58/11.58 | |
% 81.58/11.58 | | DELTA: instantiating (86) with fresh symbols all_212_0, all_212_1 gives:
% 81.58/11.58 | | (102) u1_orders_2(all_138_3) = all_212_1 & g1_orders_2(all_160_2,
% 81.58/11.58 | | all_212_1) = all_212_0 & $i(all_212_0) & $i(all_212_1) &
% 81.58/11.58 | | v1_orders_2(all_212_0) & v1_lattice3(all_212_0) & ~
% 81.58/11.58 | | v3_struct_0(all_212_0)
% 81.58/11.58 | |
% 81.58/11.58 | | ALPHA: (102) implies:
% 81.58/11.58 | | (103) ~ v3_struct_0(all_212_0)
% 81.58/11.59 | | (104) g1_orders_2(all_160_2, all_212_1) = all_212_0
% 81.58/11.59 | | (105) u1_orders_2(all_138_3) = all_212_1
% 81.58/11.59 | |
% 81.58/11.59 | | DELTA: instantiating (85) with fresh symbols all_214_0, all_214_1 gives:
% 81.58/11.59 | | (106) u1_orders_2(all_138_3) = all_214_1 & g1_orders_2(all_160_2,
% 81.58/11.59 | | all_214_1) = all_214_0 & $i(all_214_0) & $i(all_214_1) &
% 81.58/11.59 | | v1_orders_2(all_214_0) & v2_lattice3(all_214_0) & ~
% 81.58/11.59 | | v3_struct_0(all_214_0)
% 81.58/11.59 | |
% 81.58/11.59 | | ALPHA: (106) implies:
% 81.58/11.59 | | (107) u1_orders_2(all_138_3) = all_214_1
% 81.58/11.59 | |
% 81.58/11.59 | | DELTA: instantiating (82) with fresh symbol all_220_0 gives:
% 81.58/11.59 | | (108) k2_yellow_1(all_138_2) = all_220_0 & $i(all_220_0) &
% 81.58/11.59 | | v1_yellow_0(all_220_0) & v25_waybel_0(all_220_0) &
% 81.58/11.59 | | v24_waybel_0(all_220_0) & v1_orders_2(all_220_0) &
% 81.58/11.59 | | v3_lattice3(all_220_0) & v2_lattice3(all_220_0) &
% 81.58/11.59 | | v4_orders_2(all_220_0) & v3_orders_2(all_220_0) &
% 81.58/11.59 | | v2_orders_2(all_220_0) & ~ v3_struct_0(all_220_0)
% 81.58/11.59 | |
% 81.58/11.59 | | ALPHA: (108) implies:
% 81.58/11.59 | | (109) k2_yellow_1(all_138_2) = all_220_0
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (24) with all_138_3, all_210_0, all_198_0,
% 81.58/11.59 | | all_160_2, simplifying with (93) gives:
% 81.58/11.59 | | (110) all_210_0 = all_138_3 | ~ (g1_orders_2(all_160_2, all_198_0) =
% 81.58/11.59 | | all_210_0)
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (24) with all_210_0, all_212_0, all_210_1,
% 81.58/11.59 | | all_160_2, simplifying with (100) gives:
% 81.58/11.59 | | (111) all_212_0 = all_210_0 | ~ (g1_orders_2(all_160_2, all_210_1) =
% 81.58/11.59 | | all_212_0)
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (20) with all_208_1, all_210_1, all_138_3,
% 81.58/11.59 | | simplifying with (98), (101) gives:
% 81.58/11.59 | | (112) all_210_1 = all_208_1
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (20) with all_200_0, all_210_1, all_138_3,
% 81.58/11.59 | | simplifying with (96), (101) gives:
% 81.58/11.59 | | (113) all_210_1 = all_200_0
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (20) with all_208_1, all_212_1, all_138_3,
% 81.58/11.59 | | simplifying with (98), (105) gives:
% 81.58/11.59 | | (114) all_212_1 = all_208_1
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (20) with all_212_1, all_214_1, all_138_3,
% 81.58/11.59 | | simplifying with (105), (107) gives:
% 81.58/11.59 | | (115) all_214_1 = all_212_1
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (20) with all_198_0, all_214_1, all_138_3,
% 81.58/11.59 | | simplifying with (94), (107) gives:
% 81.58/11.59 | | (116) all_214_1 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | GROUND_INST: instantiating (21) with all_138_1, all_220_0, all_138_2,
% 81.58/11.59 | | simplifying with (41), (109) gives:
% 81.58/11.59 | | (117) all_220_0 = all_138_1
% 81.58/11.59 | |
% 81.58/11.59 | | COMBINE_EQS: (115), (116) imply:
% 81.58/11.59 | | (118) all_212_1 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | SIMP: (118) implies:
% 81.58/11.59 | | (119) all_212_1 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | COMBINE_EQS: (114), (119) imply:
% 81.58/11.59 | | (120) all_208_1 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | SIMP: (120) implies:
% 81.58/11.59 | | (121) all_208_1 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | COMBINE_EQS: (112), (113) imply:
% 81.58/11.59 | | (122) all_208_1 = all_200_0
% 81.58/11.59 | |
% 81.58/11.59 | | SIMP: (122) implies:
% 81.58/11.59 | | (123) all_208_1 = all_200_0
% 81.58/11.59 | |
% 81.58/11.59 | | COMBINE_EQS: (121), (123) imply:
% 81.58/11.59 | | (124) all_200_0 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | SIMP: (124) implies:
% 81.58/11.59 | | (125) all_200_0 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | COMBINE_EQS: (113), (125) imply:
% 81.58/11.59 | | (126) all_210_1 = all_198_0
% 81.58/11.59 | |
% 81.58/11.59 | | REDUCE: (104), (119) imply:
% 81.58/11.59 | | (127) g1_orders_2(all_160_2, all_198_0) = all_212_0
% 81.58/11.59 | |
% 81.58/11.59 | | BETA: splitting (111) gives:
% 81.58/11.59 | |
% 81.58/11.59 | | Case 1:
% 81.58/11.59 | | |
% 81.58/11.59 | | | (128) ~ (g1_orders_2(all_160_2, all_210_1) = all_212_0)
% 81.58/11.59 | | |
% 81.58/11.59 | | | REDUCE: (126), (128) imply:
% 81.58/11.59 | | | (129) ~ (g1_orders_2(all_160_2, all_198_0) = all_212_0)
% 81.58/11.59 | | |
% 81.58/11.59 | | | PRED_UNIFY: (127), (129) imply:
% 81.58/11.59 | | | (130) $false
% 81.58/11.59 | | |
% 81.58/11.59 | | | CLOSE: (130) is inconsistent.
% 81.58/11.59 | | |
% 81.58/11.59 | | Case 2:
% 81.58/11.59 | | |
% 81.58/11.59 | | | (131) all_212_0 = all_210_0
% 81.58/11.59 | | |
% 81.58/11.59 | | | REDUCE: (127), (131) imply:
% 81.58/11.59 | | | (132) g1_orders_2(all_160_2, all_198_0) = all_210_0
% 81.58/11.59 | | |
% 81.58/11.59 | | | REDUCE: (103), (131) imply:
% 81.58/11.59 | | | (133) ~ v3_struct_0(all_210_0)
% 81.58/11.59 | | |
% 81.58/11.59 | | | BETA: splitting (110) gives:
% 81.58/11.59 | | |
% 81.58/11.59 | | | Case 1:
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | (134) ~ (g1_orders_2(all_160_2, all_198_0) = all_210_0)
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | PRED_UNIFY: (132), (134) imply:
% 81.58/11.59 | | | | (135) $false
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | CLOSE: (135) is inconsistent.
% 81.58/11.59 | | | |
% 81.58/11.59 | | | Case 2:
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | (136) all_210_0 = all_138_3
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | REDUCE: (133), (136) imply:
% 81.58/11.59 | | | | (137) ~ v3_struct_0(all_138_3)
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | BETA: splitting (81) gives:
% 81.58/11.59 | | | |
% 81.58/11.59 | | | | Case 1:
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | (138) v3_struct_0(all_138_3)
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | PRED_UNIFY: (137), (138) imply:
% 81.58/11.59 | | | | | (139) $false
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | CLOSE: (139) is inconsistent.
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | Case 2:
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | (140) ? [v0: $i] : (k2_yellow_1(all_138_2) = v0 & $i(v0) &
% 81.58/11.59 | | | | | v3_yellow_0(v0) & v2_yellow_0(v0) & v1_yellow_0(v0) &
% 81.58/11.59 | | | | | v25_waybel_0(v0) & v24_waybel_0(v0) & v1_orders_2(v0) &
% 81.58/11.59 | | | | | v3_waybel_3(v0) & v3_lattice3(v0) & v2_lattice3(v0) &
% 81.58/11.59 | | | | | v1_lattice3(v0) & v4_orders_2(v0) & v3_orders_2(v0) &
% 81.58/11.59 | | | | | v2_orders_2(v0) & ~ v3_struct_0(v0))
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | DELTA: instantiating (140) with fresh symbol all_246_0 gives:
% 81.58/11.59 | | | | | (141) k2_yellow_1(all_138_2) = all_246_0 & $i(all_246_0) &
% 81.58/11.59 | | | | | v3_yellow_0(all_246_0) & v2_yellow_0(all_246_0) &
% 81.58/11.59 | | | | | v1_yellow_0(all_246_0) & v25_waybel_0(all_246_0) &
% 81.58/11.59 | | | | | v24_waybel_0(all_246_0) & v1_orders_2(all_246_0) &
% 81.58/11.59 | | | | | v3_waybel_3(all_246_0) & v3_lattice3(all_246_0) &
% 81.58/11.59 | | | | | v2_lattice3(all_246_0) & v1_lattice3(all_246_0) &
% 81.58/11.59 | | | | | v4_orders_2(all_246_0) & v3_orders_2(all_246_0) &
% 81.58/11.59 | | | | | v2_orders_2(all_246_0) & ~ v3_struct_0(all_246_0)
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | ALPHA: (141) implies:
% 81.58/11.59 | | | | | (142) v2_orders_2(all_246_0)
% 81.58/11.59 | | | | | (143) v3_orders_2(all_246_0)
% 81.58/11.59 | | | | | (144) v4_orders_2(all_246_0)
% 81.58/11.59 | | | | | (145) v1_lattice3(all_246_0)
% 81.58/11.59 | | | | | (146) v2_lattice3(all_246_0)
% 81.58/11.59 | | | | | (147) v3_lattice3(all_246_0)
% 81.58/11.59 | | | | | (148) v3_waybel_3(all_246_0)
% 81.58/11.59 | | | | | (149) $i(all_246_0)
% 81.58/11.59 | | | | | (150) k2_yellow_1(all_138_2) = all_246_0
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | BETA: splitting (83) gives:
% 81.58/11.59 | | | | |
% 81.58/11.59 | | | | | Case 1:
% 81.58/11.59 | | | | | |
% 81.58/11.59 | | | | | | (151) v3_struct_0(all_138_3)
% 81.58/11.59 | | | | | |
% 81.58/11.59 | | | | | | PRED_UNIFY: (137), (151) imply:
% 81.58/11.59 | | | | | | (152) $false
% 81.58/11.59 | | | | | |
% 81.58/11.59 | | | | | | CLOSE: (152) is inconsistent.
% 81.58/11.59 | | | | | |
% 81.58/11.59 | | | | | Case 2:
% 81.58/11.59 | | | | | |
% 81.58/11.59 | | | | | | (153) ? [v0: $i] : ? [v1: $i] : (k2_yellow_1(all_138_2) = v0 &
% 81.58/11.60 | | | | | | u1_struct_0(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : (
% 81.58/11.60 | | | | | | ~ $i(v2) | ~ m1_subset_1(v2, v1) | ~
% 81.58/11.60 | | | | | | v1_xboole_0(v2)))
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | DELTA: instantiating (153) with fresh symbols all_264_0, all_264_1
% 81.58/11.60 | | | | | | gives:
% 81.58/11.60 | | | | | | (154) k2_yellow_1(all_138_2) = all_264_1 & u1_struct_0(all_264_1)
% 81.58/11.60 | | | | | | = all_264_0 & $i(all_264_0) & $i(all_264_1) & ! [v0: $i] :
% 81.58/11.60 | | | | | | ( ~ $i(v0) | ~ m1_subset_1(v0, all_264_0) | ~
% 81.58/11.60 | | | | | | v1_xboole_0(v0))
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | ALPHA: (154) implies:
% 81.58/11.60 | | | | | | (155) k2_yellow_1(all_138_2) = all_264_1
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | GROUND_INST: instantiating (21) with all_138_1, all_264_1,
% 81.58/11.60 | | | | | | all_138_2, simplifying with (41), (155) gives:
% 81.58/11.60 | | | | | | (156) all_264_1 = all_138_1
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | GROUND_INST: instantiating (21) with all_246_0, all_264_1,
% 81.58/11.60 | | | | | | all_138_2, simplifying with (150), (155) gives:
% 81.58/11.60 | | | | | | (157) all_264_1 = all_246_0
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | COMBINE_EQS: (156), (157) imply:
% 81.58/11.60 | | | | | | (158) all_246_0 = all_138_1
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (149), (158) imply:
% 81.58/11.60 | | | | | | (159) $i(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (148), (158) imply:
% 81.58/11.60 | | | | | | (160) v3_waybel_3(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (147), (158) imply:
% 81.58/11.60 | | | | | | (161) v3_lattice3(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (146), (158) imply:
% 81.58/11.60 | | | | | | (162) v2_lattice3(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (145), (158) imply:
% 81.58/11.60 | | | | | | (163) v1_lattice3(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (144), (158) imply:
% 81.58/11.60 | | | | | | (164) v4_orders_2(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (143), (158) imply:
% 81.58/11.60 | | | | | | (165) v3_orders_2(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | REDUCE: (142), (158) imply:
% 81.58/11.60 | | | | | | (166) v2_orders_2(all_138_1)
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | GROUND_INST: instantiating (t17_waybel22) with all_138_5, all_138_1,
% 81.58/11.60 | | | | | | all_138_0, all_154_0, all_138_4, simplifying with (26),
% 81.58/11.60 | | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 81.58/11.60 | | | | | | (37), (40), (44), (46), (60), (80), (91), (159), (160),
% 81.58/11.60 | | | | | | (161), (162), (163), (164), (165), (166) gives:
% 81.58/11.60 | | | | | | (167) $false
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | | CLOSE: (167) is inconsistent.
% 81.58/11.60 | | | | | |
% 81.58/11.60 | | | | | End of split
% 81.58/11.60 | | | | |
% 81.58/11.60 | | | | End of split
% 81.58/11.60 | | | |
% 81.58/11.60 | | | End of split
% 81.58/11.60 | | |
% 81.58/11.60 | | End of split
% 81.58/11.60 | |
% 81.58/11.60 | End of split
% 81.58/11.60 |
% 81.58/11.60 End of proof
% 81.58/11.60 % SZS output end Proof for theBenchmark
% 81.58/11.60
% 81.58/11.60 11003ms
%------------------------------------------------------------------------------