TSTP Solution File: LAT292+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT292+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 : n003.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 06:24:27 EDT 2023
% Result : Theorem 37.29s 5.78s
% Output : Proof 46.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LAT292+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 07:27:37 EDT 2023
% 0.14/0.36 % 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
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 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 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 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 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 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
% 4.70/1.42 Prover 4: Preprocessing ...
% 4.70/1.43 Prover 1: Preprocessing ...
% 4.70/1.47 Prover 5: Preprocessing ...
% 4.70/1.47 Prover 2: Preprocessing ...
% 4.70/1.47 Prover 6: Preprocessing ...
% 4.70/1.47 Prover 3: Preprocessing ...
% 4.70/1.47 Prover 0: Preprocessing ...
% 12.36/2.46 Prover 5: Proving ...
% 12.36/2.52 Prover 1: Warning: ignoring some quantifiers
% 13.10/2.58 Prover 2: Proving ...
% 13.60/2.62 Prover 3: Warning: ignoring some quantifiers
% 13.60/2.64 Prover 1: Constructing countermodel ...
% 14.42/2.71 Prover 3: Constructing countermodel ...
% 14.67/2.77 Prover 6: Proving ...
% 18.68/3.32 Prover 4: Warning: ignoring some quantifiers
% 19.75/3.42 Prover 4: Constructing countermodel ...
% 20.47/3.53 Prover 0: Proving ...
% 37.29/5.78 Prover 2: proved (5113ms)
% 37.29/5.78
% 37.29/5.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.29/5.78
% 37.29/5.78 Prover 5: stopped
% 37.73/5.79 Prover 6: stopped
% 37.73/5.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 37.73/5.81 Prover 0: stopped
% 37.73/5.82 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 37.73/5.82 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 37.73/5.82 Prover 3: stopped
% 37.73/5.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 37.73/5.82 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 38.87/6.00 Prover 13: Preprocessing ...
% 38.87/6.01 Prover 7: Preprocessing ...
% 39.60/6.04 Prover 11: Preprocessing ...
% 39.60/6.06 Prover 10: Preprocessing ...
% 39.60/6.08 Prover 8: Preprocessing ...
% 40.05/6.12 Prover 7: Warning: ignoring some quantifiers
% 40.05/6.15 Prover 7: Constructing countermodel ...
% 40.61/6.22 Prover 10: Warning: ignoring some quantifiers
% 40.61/6.23 Prover 10: Constructing countermodel ...
% 40.61/6.30 Prover 13: Warning: ignoring some quantifiers
% 41.64/6.35 Prover 13: Constructing countermodel ...
% 41.64/6.36 Prover 8: Warning: ignoring some quantifiers
% 41.64/6.38 Prover 8: Constructing countermodel ...
% 43.36/6.56 Prover 10: gave up
% 43.36/6.58 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 43.36/6.61 Prover 11: Warning: ignoring some quantifiers
% 44.56/6.70 Prover 11: Constructing countermodel ...
% 44.56/6.71 Prover 16: Preprocessing ...
% 45.60/6.83 Prover 16: Warning: ignoring some quantifiers
% 45.60/6.84 Prover 16: Constructing countermodel ...
% 45.60/6.92 Prover 13: Found proof (size 37)
% 45.60/6.92 Prover 13: proved (1094ms)
% 45.60/6.92 Prover 16: stopped
% 45.60/6.92 Prover 4: stopped
% 45.60/6.92 Prover 11: stopped
% 45.60/6.92 Prover 1: stopped
% 45.60/6.92 Prover 8: stopped
% 45.60/6.92 Prover 7: stopped
% 45.60/6.92
% 45.60/6.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.60/6.92
% 45.60/6.93 % SZS output start Proof for theBenchmark
% 45.60/6.93 Assumptions after simplification:
% 45.60/6.93 ---------------------------------
% 45.60/6.93
% 45.60/6.93 (d9_lopclset)
% 46.31/6.96 ! [v0: $i] : ! [v1: $i] : ( ~ (k12_lopclset(v0) = v1) | ~ $i(v0) | ~
% 46.31/6.96 l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.96 v3_realset2(v0) | v3_struct_0(v0) | ? [v2: $i] : (k11_lopclset(v0) = v2 &
% 46.31/6.96 k6_lopclset(v2) = v1 & $i(v2) & $i(v1))) & ! [v0: $i] : ( ~ $i(v0) | ~
% 46.31/6.96 l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.96 v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i] : ? [v2: $i] :
% 46.31/6.96 (k12_lopclset(v0) = v1 & k11_lopclset(v0) = v2 & k6_lopclset(v2) = v1 &
% 46.31/6.96 $i(v2) & $i(v1)))
% 46.31/6.96
% 46.31/6.96 (dt_k11_lopclset)
% 46.31/6.96 ! [v0: $i] : ! [v1: $i] : ( ~ (k11_lopclset(v0) = v1) | ~ $i(v0) | ~
% 46.31/6.96 l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.96 v1_pre_topc(v1) | v3_realset2(v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1:
% 46.31/6.96 $i] : ( ~ (k11_lopclset(v0) = v1) | ~ $i(v0) | ~ l3_lattices(v0) | ~
% 46.31/6.96 v17_lattices(v0) | ~ v10_lattices(v0) | l1_pre_topc(v1) | v3_realset2(v0) |
% 46.31/6.96 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k11_lopclset(v0) = v1) |
% 46.31/6.96 ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.96 v2_pre_topc(v1) | v3_realset2(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~
% 46.31/6.96 $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.96 v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i] : (k11_lopclset(v0) = v1 &
% 46.31/6.96 $i(v1) & v1_pre_topc(v1) & l1_pre_topc(v1) & v2_pre_topc(v1)))
% 46.31/6.96
% 46.31/6.96 (dt_k12_lopclset)
% 46.31/6.97 ! [v0: $i] : ! [v1: $i] : ( ~ (k12_lopclset(v0) = v1) | ~ $i(v0) | ~
% 46.31/6.97 l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) | ~
% 46.31/6.97 v3_struct_0(v1) | v3_realset2(v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1:
% 46.31/6.97 $i] : ( ~ (k12_lopclset(v0) = v1) | ~ $i(v0) | ~ l3_lattices(v0) | ~
% 46.31/6.97 v17_lattices(v0) | ~ v10_lattices(v0) | l3_lattices(v1) | v3_realset2(v0) |
% 46.31/6.97 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k12_lopclset(v0) = v1) |
% 46.31/6.97 ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.97 v3_realset2(v0) | v10_lattices(v1) | v3_struct_0(v0)) & ! [v0: $i] : ( ~
% 46.31/6.97 $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.97 v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i] : (k12_lopclset(v0) = v1 &
% 46.31/6.97 $i(v1) & l3_lattices(v1) & v10_lattices(v1) & ~ v3_struct_0(v1)))
% 46.31/6.97
% 46.31/6.97 (fc4_lopclset)
% 46.31/6.97 ! [v0: $i] : ! [v1: $i] : ( ~ (k11_lopclset(v0) = v1) | ~ $i(v0) | ~
% 46.31/6.97 l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) | ~
% 46.31/6.97 v3_struct_0(v1) | v3_realset2(v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1:
% 46.31/6.97 $i] : ( ~ (k11_lopclset(v0) = v1) | ~ $i(v0) | ~ l3_lattices(v0) | ~
% 46.31/6.97 v17_lattices(v0) | ~ v10_lattices(v0) | v1_pre_topc(v1) | v3_realset2(v0) |
% 46.31/6.97 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k11_lopclset(v0) = v1) |
% 46.31/6.97 ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.97 v2_pre_topc(v1) | v3_realset2(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~
% 46.31/6.97 $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.97 v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i] : (k11_lopclset(v0) = v1 &
% 46.31/6.97 $i(v1) & v1_pre_topc(v1) & v2_pre_topc(v1) & ~ v3_struct_0(v1)))
% 46.31/6.97
% 46.31/6.97 (t43_lopclset)
% 46.31/6.97 ! [v0: $i] : ! [v1: $i] : ( ~ (k12_lopclset(v0) = v1) | ~ $i(v0) | ~
% 46.31/6.97 l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.97 r1_filter_1(v0, v1) | v3_realset2(v0) | v3_struct_0(v0)) & ! [v0: $i] : ( ~
% 46.31/6.97 $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) | ~ v10_lattices(v0) |
% 46.31/6.97 v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i] : (k12_lopclset(v0) = v1 &
% 46.31/6.97 $i(v1) & r1_filter_1(v0, v1)))
% 46.31/6.97
% 46.31/6.97 (t44_lopclset)
% 46.31/6.97 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & l3_lattices(v1) &
% 46.31/6.97 l3_lattices(v0) & v17_lattices(v1) & v17_lattices(v0) & v10_lattices(v1) &
% 46.31/6.97 v10_lattices(v0) & ~ v3_realset2(v1) & ~ v3_realset2(v0) & ~
% 46.31/6.97 v3_struct_0(v1) & ~ v3_struct_0(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 46.31/6.97 (k6_lopclset(v2) = v3) | ~ $i(v2) | ~ r1_filter_1(v1, v3) | ~
% 46.31/6.97 l1_pre_topc(v2) | ~ v2_pre_topc(v2) | v3_struct_0(v2)) & ! [v2: $i] : (
% 46.31/6.97 ~ $i(v2) | ~ l1_pre_topc(v2) | ~ v2_pre_topc(v2) | v3_struct_0(v2) | ?
% 46.31/6.97 [v3: $i] : (k6_lopclset(v2) = v3 & $i(v3) & ~ r1_filter_1(v0, v3))))
% 46.31/6.97
% 46.31/6.97 (function-axioms)
% 46.31/6.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 46.31/6.98 | ~ (g3_lattices(v4, v3, v2) = v1) | ~ (g3_lattices(v4, v3, v2) = v0)) &
% 46.31/6.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 46.31/6.98 (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] :
% 46.31/6.98 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (g1_pre_topc(v3, v2) =
% 46.31/6.98 v1) | ~ (g1_pre_topc(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 46.31/6.98 $i] : (v1 = v0 | ~ (k12_lopclset(v2) = v1) | ~ (k12_lopclset(v2) = v0)) &
% 46.31/6.98 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k11_lopclset(v2) = v1)
% 46.31/6.98 | ~ (k11_lopclset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 46.31/6.98 (v1 = v0 | ~ (k6_lopclset(v2) = v1) | ~ (k6_lopclset(v2) = v0)) & ! [v0:
% 46.31/6.98 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k4_lopclset(v2) = v1) | ~
% 46.31/6.98 (k4_lopclset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 46.31/6.98 | ~ (k5_lopclset(v2) = v1) | ~ (k5_lopclset(v2) = v0)) & ! [v0: $i] : !
% 46.31/6.98 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_lopclset(v2) = v1) | ~
% 46.31/6.98 (k1_lopclset(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 46.31/6.98 | ~ (a_1_0_lopclset(v2) = v1) | ~ (a_1_0_lopclset(v2) = v0)) & ! [v0: $i]
% 46.31/6.98 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 46.31/6.98 (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 46.31/6.98 | ~ (u2_lattices(v2) = v1) | ~ (u2_lattices(v2) = v0)) & ! [v0: $i] : !
% 46.31/6.98 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_lattices(v2) = v1) | ~
% 46.31/6.98 (u1_lattices(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 46.31/6.98 | ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : !
% 46.31/6.98 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_pre_topc(v2) = v1) | ~
% 46.31/6.98 (u1_pre_topc(v2) = v0))
% 46.31/6.98
% 46.31/6.98 Further assumptions not needed in the proof:
% 46.31/6.98 --------------------------------------------
% 46.31/6.98 abstractness_v1_pre_topc, abstractness_v3_lattices, antisymmetry_r2_hidden,
% 46.31/6.98 cc10_membered, cc11_membered, cc12_membered, cc13_membered, cc14_membered,
% 46.31/6.98 cc15_membered, cc16_membered, cc17_membered, cc18_membered, cc19_membered,
% 46.31/6.98 cc1_finset_1, cc1_finsub_1, cc1_funct_2, cc1_lattices, cc1_membered,
% 46.31/6.98 cc1_relset_1, cc20_membered, cc2_finset_1, cc2_finsub_1, cc2_lattices,
% 46.31/6.98 cc2_membered, cc3_lattices, cc3_membered, cc4_lattices, cc4_membered,
% 46.31/6.98 cc5_funct_2, cc5_lattices, cc6_funct_2, cc6_lattices, cc7_lattices, d1_lopclset,
% 46.31/6.98 d4_lopclset, dt_g1_pre_topc, dt_g3_lattices, dt_k1_lopclset, dt_k1_xboole_0,
% 46.31/6.98 dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k4_lopclset, dt_k5_lopclset, dt_k6_lopclset,
% 46.31/6.98 dt_l1_lattices, dt_l1_pre_topc, dt_l1_struct_0, dt_l2_lattices, dt_l3_lattices,
% 46.31/6.98 dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1, dt_u1_lattices, dt_u1_pre_topc,
% 46.31/6.98 dt_u1_struct_0, dt_u2_lattices, existence_l1_lattices, existence_l1_pre_topc,
% 46.31/6.98 existence_l1_struct_0, existence_l2_lattices, existence_l3_lattices,
% 46.31/6.98 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 46.31/6.98 fc14_finset_1, fc1_finsub_1, fc1_lopclset, fc1_struct_0, fc3_lattices,
% 46.31/6.98 fc6_membered, fraenkel_a_1_0_lopclset, free_g1_pre_topc, free_g3_lattices,
% 46.31/6.98 rc10_lattices, rc11_lattices, rc12_lattices, rc13_lattices, rc1_finset_1,
% 46.31/6.98 rc1_funct_2, rc1_lopclset, rc1_membered, rc1_pre_topc, rc2_partfun1,
% 46.31/6.98 rc2_pre_topc, rc3_finset_1, rc3_lattices, rc3_struct_0, rc4_finset_1,
% 46.31/6.98 rc5_struct_0, rc6_lattices, rc6_pre_topc, rc7_pre_topc, rc9_lattices,
% 46.31/6.98 redefinition_m2_relset_1, reflexivity_r1_filter_1, reflexivity_r1_tarski,
% 46.31/6.98 symmetry_r1_filter_1, t1_subset, t2_subset, t2_tarski, t3_subset, t4_subset,
% 46.31/6.98 t5_subset, t6_boole, t7_boole, t8_boole
% 46.31/6.98
% 46.31/6.98 Those formulas are unsatisfiable:
% 46.31/6.98 ---------------------------------
% 46.31/6.98
% 46.31/6.98 Begin of proof
% 46.31/6.98 |
% 46.31/6.98 | ALPHA: (d9_lopclset) implies:
% 46.31/6.98 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) |
% 46.31/6.98 | ~ v10_lattices(v0) | v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i]
% 46.31/6.98 | : ? [v2: $i] : (k12_lopclset(v0) = v1 & k11_lopclset(v0) = v2 &
% 46.31/6.98 | k6_lopclset(v2) = v1 & $i(v2) & $i(v1)))
% 46.31/6.98 |
% 46.31/6.98 | ALPHA: (dt_k11_lopclset) implies:
% 46.31/6.98 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) |
% 46.31/6.98 | ~ v10_lattices(v0) | v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i]
% 46.31/6.98 | : (k11_lopclset(v0) = v1 & $i(v1) & v1_pre_topc(v1) & l1_pre_topc(v1)
% 46.31/6.98 | & v2_pre_topc(v1)))
% 46.31/6.98 |
% 46.31/6.98 | ALPHA: (dt_k12_lopclset) implies:
% 46.31/6.98 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) |
% 46.31/6.98 | ~ v10_lattices(v0) | v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i]
% 46.31/6.98 | : (k12_lopclset(v0) = v1 & $i(v1) & l3_lattices(v1) &
% 46.31/6.98 | v10_lattices(v1) & ~ v3_struct_0(v1)))
% 46.31/6.98 |
% 46.31/6.98 | ALPHA: (fc4_lopclset) implies:
% 46.31/6.98 | (4) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) |
% 46.31/6.98 | ~ v10_lattices(v0) | v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i]
% 46.31/6.98 | : (k11_lopclset(v0) = v1 & $i(v1) & v1_pre_topc(v1) & v2_pre_topc(v1)
% 46.31/6.98 | & ~ v3_struct_0(v1)))
% 46.31/6.98 |
% 46.31/6.98 | ALPHA: (t43_lopclset) implies:
% 46.31/6.98 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ l3_lattices(v0) | ~ v17_lattices(v0) |
% 46.31/6.98 | ~ v10_lattices(v0) | v3_realset2(v0) | v3_struct_0(v0) | ? [v1: $i]
% 46.31/6.98 | : (k12_lopclset(v0) = v1 & $i(v1) & r1_filter_1(v0, v1)))
% 46.31/6.98 |
% 46.31/6.98 | ALPHA: (function-axioms) implies:
% 46.31/6.98 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 46.31/6.98 | (k11_lopclset(v2) = v1) | ~ (k11_lopclset(v2) = v0))
% 46.31/6.98 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 46.31/6.98 | (k12_lopclset(v2) = v1) | ~ (k12_lopclset(v2) = v0))
% 46.31/6.98 |
% 46.31/6.98 | DELTA: instantiating (t44_lopclset) with fresh symbols all_135_0, all_135_1
% 46.31/6.98 | gives:
% 46.31/6.99 | (8) $i(all_135_0) & $i(all_135_1) & l3_lattices(all_135_0) &
% 46.31/6.99 | l3_lattices(all_135_1) & v17_lattices(all_135_0) &
% 46.31/6.99 | v17_lattices(all_135_1) & v10_lattices(all_135_0) &
% 46.31/6.99 | v10_lattices(all_135_1) & ~ v3_realset2(all_135_0) & ~
% 46.31/6.99 | v3_realset2(all_135_1) & ~ v3_struct_0(all_135_0) & ~
% 46.31/6.99 | v3_struct_0(all_135_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 46.31/6.99 | (k6_lopclset(v0) = v1) | ~ $i(v0) | ~ r1_filter_1(all_135_0, v1) |
% 46.31/6.99 | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0) | v3_struct_0(v0)) & ! [v0:
% 46.31/6.99 | $i] : ( ~ $i(v0) | ~ l1_pre_topc(v0) | ~ v2_pre_topc(v0) |
% 46.31/6.99 | v3_struct_0(v0) | ? [v1: $i] : (k6_lopclset(v0) = v1 & $i(v1) & ~
% 46.31/6.99 | r1_filter_1(all_135_1, v1)))
% 46.31/6.99 |
% 46.31/6.99 | ALPHA: (8) implies:
% 46.31/6.99 | (9) ~ v3_struct_0(all_135_0)
% 46.31/6.99 | (10) ~ v3_realset2(all_135_0)
% 46.31/6.99 | (11) v10_lattices(all_135_0)
% 46.31/6.99 | (12) v17_lattices(all_135_0)
% 46.31/6.99 | (13) l3_lattices(all_135_0)
% 46.31/6.99 | (14) $i(all_135_0)
% 46.31/6.99 | (15) ! [v0: $i] : ! [v1: $i] : ( ~ (k6_lopclset(v0) = v1) | ~ $i(v0) |
% 46.31/6.99 | ~ r1_filter_1(all_135_0, v1) | ~ l1_pre_topc(v0) | ~
% 46.31/6.99 | v2_pre_topc(v0) | v3_struct_0(v0))
% 46.31/6.99 |
% 46.31/6.99 | GROUND_INST: instantiating (1) with all_135_0, simplifying with (9), (10),
% 46.31/6.99 | (11), (12), (13), (14) gives:
% 46.31/6.99 | (16) ? [v0: $i] : ? [v1: $i] : (k12_lopclset(all_135_0) = v0 &
% 46.31/6.99 | k11_lopclset(all_135_0) = v1 & k6_lopclset(v1) = v0 & $i(v1) &
% 46.31/6.99 | $i(v0))
% 46.31/6.99 |
% 46.31/6.99 | GROUND_INST: instantiating (5) with all_135_0, simplifying with (9), (10),
% 46.31/6.99 | (11), (12), (13), (14) gives:
% 46.31/6.99 | (17) ? [v0: $i] : (k12_lopclset(all_135_0) = v0 & $i(v0) &
% 46.31/6.99 | r1_filter_1(all_135_0, v0))
% 46.31/6.99 |
% 46.31/6.99 | GROUND_INST: instantiating (3) with all_135_0, simplifying with (9), (10),
% 46.31/6.99 | (11), (12), (13), (14) gives:
% 46.31/6.99 | (18) ? [v0: $i] : (k12_lopclset(all_135_0) = v0 & $i(v0) & l3_lattices(v0)
% 46.31/6.99 | & v10_lattices(v0) & ~ v3_struct_0(v0))
% 46.31/6.99 |
% 46.31/6.99 | GROUND_INST: instantiating (2) with all_135_0, simplifying with (9), (10),
% 46.31/6.99 | (11), (12), (13), (14) gives:
% 46.31/6.99 | (19) ? [v0: $i] : (k11_lopclset(all_135_0) = v0 & $i(v0) & v1_pre_topc(v0)
% 46.31/6.99 | & l1_pre_topc(v0) & v2_pre_topc(v0))
% 46.31/6.99 |
% 46.31/6.99 | GROUND_INST: instantiating (4) with all_135_0, simplifying with (9), (10),
% 46.31/6.99 | (11), (12), (13), (14) gives:
% 46.31/6.99 | (20) ? [v0: $i] : (k11_lopclset(all_135_0) = v0 & $i(v0) & v1_pre_topc(v0)
% 46.31/6.99 | & v2_pre_topc(v0) & ~ v3_struct_0(v0))
% 46.31/6.99 |
% 46.31/6.99 | DELTA: instantiating (17) with fresh symbol all_152_0 gives:
% 46.31/6.99 | (21) k12_lopclset(all_135_0) = all_152_0 & $i(all_152_0) &
% 46.31/6.99 | r1_filter_1(all_135_0, all_152_0)
% 46.31/6.99 |
% 46.31/6.99 | ALPHA: (21) implies:
% 46.31/6.99 | (22) r1_filter_1(all_135_0, all_152_0)
% 46.31/6.99 | (23) k12_lopclset(all_135_0) = all_152_0
% 46.31/6.99 |
% 46.31/6.99 | DELTA: instantiating (16) with fresh symbols all_166_0, all_166_1 gives:
% 46.31/6.99 | (24) k12_lopclset(all_135_0) = all_166_1 & k11_lopclset(all_135_0) =
% 46.31/6.99 | all_166_0 & k6_lopclset(all_166_0) = all_166_1 & $i(all_166_0) &
% 46.31/6.99 | $i(all_166_1)
% 46.31/6.99 |
% 46.31/6.99 | ALPHA: (24) implies:
% 46.31/6.99 | (25) k6_lopclset(all_166_0) = all_166_1
% 46.31/6.99 | (26) k11_lopclset(all_135_0) = all_166_0
% 46.31/6.99 | (27) k12_lopclset(all_135_0) = all_166_1
% 46.31/6.99 |
% 46.31/6.99 | DELTA: instantiating (20) with fresh symbol all_168_0 gives:
% 46.31/6.99 | (28) k11_lopclset(all_135_0) = all_168_0 & $i(all_168_0) &
% 46.31/6.99 | v1_pre_topc(all_168_0) & v2_pre_topc(all_168_0) & ~
% 46.31/6.99 | v3_struct_0(all_168_0)
% 46.31/6.99 |
% 46.31/6.99 | ALPHA: (28) implies:
% 46.31/6.99 | (29) ~ v3_struct_0(all_168_0)
% 46.31/6.99 | (30) v2_pre_topc(all_168_0)
% 46.31/6.99 | (31) $i(all_168_0)
% 46.31/6.99 | (32) k11_lopclset(all_135_0) = all_168_0
% 46.31/6.99 |
% 46.31/6.99 | DELTA: instantiating (19) with fresh symbol all_184_0 gives:
% 46.31/6.99 | (33) k11_lopclset(all_135_0) = all_184_0 & $i(all_184_0) &
% 46.31/6.99 | v1_pre_topc(all_184_0) & l1_pre_topc(all_184_0) &
% 46.31/6.99 | v2_pre_topc(all_184_0)
% 46.31/6.99 |
% 46.31/6.99 | ALPHA: (33) implies:
% 46.31/6.99 | (34) l1_pre_topc(all_184_0)
% 46.31/6.99 | (35) k11_lopclset(all_135_0) = all_184_0
% 46.31/6.99 |
% 46.31/6.99 | DELTA: instantiating (18) with fresh symbol all_186_0 gives:
% 46.31/6.99 | (36) k12_lopclset(all_135_0) = all_186_0 & $i(all_186_0) &
% 46.31/6.99 | l3_lattices(all_186_0) & v10_lattices(all_186_0) & ~
% 46.31/6.99 | v3_struct_0(all_186_0)
% 46.31/6.99 |
% 46.31/6.99 | ALPHA: (36) implies:
% 46.31/7.00 | (37) k12_lopclset(all_135_0) = all_186_0
% 46.31/7.00 |
% 46.31/7.00 | GROUND_INST: instantiating (6) with all_168_0, all_184_0, all_135_0,
% 46.31/7.00 | simplifying with (32), (35) gives:
% 46.31/7.00 | (38) all_184_0 = all_168_0
% 46.31/7.00 |
% 46.31/7.00 | GROUND_INST: instantiating (6) with all_166_0, all_184_0, all_135_0,
% 46.31/7.00 | simplifying with (26), (35) gives:
% 46.31/7.00 | (39) all_184_0 = all_166_0
% 46.31/7.00 |
% 46.31/7.00 | GROUND_INST: instantiating (7) with all_166_1, all_186_0, all_135_0,
% 46.31/7.00 | simplifying with (27), (37) gives:
% 46.31/7.00 | (40) all_186_0 = all_166_1
% 46.31/7.00 |
% 46.31/7.00 | GROUND_INST: instantiating (7) with all_152_0, all_186_0, all_135_0,
% 46.31/7.00 | simplifying with (23), (37) gives:
% 46.31/7.00 | (41) all_186_0 = all_152_0
% 46.31/7.00 |
% 46.31/7.00 | COMBINE_EQS: (40), (41) imply:
% 46.31/7.00 | (42) all_166_1 = all_152_0
% 46.31/7.00 |
% 46.31/7.00 | COMBINE_EQS: (38), (39) imply:
% 46.31/7.00 | (43) all_168_0 = all_166_0
% 46.31/7.00 |
% 46.31/7.00 | REDUCE: (25), (42) imply:
% 46.31/7.00 | (44) k6_lopclset(all_166_0) = all_152_0
% 46.31/7.00 |
% 46.31/7.00 | REDUCE: (31), (43) imply:
% 46.31/7.00 | (45) $i(all_166_0)
% 46.31/7.00 |
% 46.31/7.00 | REDUCE: (34), (39) imply:
% 46.31/7.00 | (46) l1_pre_topc(all_166_0)
% 46.31/7.00 |
% 46.31/7.00 | REDUCE: (30), (43) imply:
% 46.31/7.00 | (47) v2_pre_topc(all_166_0)
% 46.31/7.00 |
% 46.31/7.00 | REDUCE: (29), (43) imply:
% 46.31/7.00 | (48) ~ v3_struct_0(all_166_0)
% 46.31/7.00 |
% 46.31/7.00 | GROUND_INST: instantiating (15) with all_166_0, all_152_0, simplifying with
% 46.31/7.00 | (22), (44), (45), (46), (47), (48) gives:
% 46.31/7.00 | (49) $false
% 46.31/7.00 |
% 46.31/7.00 | CLOSE: (49) is inconsistent.
% 46.31/7.00 |
% 46.31/7.00 End of proof
% 46.31/7.00 % SZS output end Proof for theBenchmark
% 46.31/7.00
% 46.31/7.00 6376ms
%------------------------------------------------------------------------------