TSTP Solution File: ALG222+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG222+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 : n032.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 : Wed Aug 30 16:40:02 EDT 2023
% Result : Theorem 100.82s 14.19s
% Output : Proof 101.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG222+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 02:40:45 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.51 ________ _____
% 0.14/0.51 ___ __ \_________(_)________________________________
% 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.51
% 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.51 (2023-06-19)
% 0.14/0.51
% 0.14/0.51 (c) Philipp Rümmer, 2009-2023
% 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.51 Amanda Stjerna.
% 0.14/0.51 Free software under BSD-3-Clause.
% 0.14/0.51
% 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.51
% 0.14/0.51 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.52 Running up to 7 provers in parallel.
% 0.14/0.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.53 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.53 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.53 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.53 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.99/1.20 Prover 1: Preprocessing ...
% 3.99/1.20 Prover 4: Preprocessing ...
% 4.35/1.24 Prover 2: Preprocessing ...
% 4.35/1.24 Prover 6: Preprocessing ...
% 4.35/1.25 Prover 5: Preprocessing ...
% 4.35/1.25 Prover 0: Preprocessing ...
% 4.35/1.25 Prover 3: Preprocessing ...
% 10.44/2.10 Prover 1: Warning: ignoring some quantifiers
% 10.44/2.14 Prover 5: Proving ...
% 10.44/2.21 Prover 2: Proving ...
% 10.44/2.25 Prover 1: Constructing countermodel ...
% 10.44/2.27 Prover 3: Warning: ignoring some quantifiers
% 10.44/2.31 Prover 3: Constructing countermodel ...
% 10.44/2.32 Prover 6: Proving ...
% 56.47/8.28 Prover 4: Warning: ignoring some quantifiers
% 58.54/8.51 Prover 4: Constructing countermodel ...
% 64.85/9.52 Prover 0: Proving ...
% 72.15/10.43 Prover 2: stopped
% 72.15/10.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.50/10.58 Prover 7: Preprocessing ...
% 74.53/10.70 Prover 7: Warning: ignoring some quantifiers
% 74.53/10.71 Prover 7: Constructing countermodel ...
% 98.40/13.86 Prover 5: stopped
% 98.40/13.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 98.99/14.06 Prover 8: Preprocessing ...
% 100.17/14.12 Prover 7: Found proof (size 173)
% 100.82/14.12 Prover 7: proved (3672ms)
% 100.82/14.12 Prover 6: stopped
% 100.82/14.12 Prover 1: stopped
% 100.82/14.13 Prover 0: stopped
% 100.82/14.13 Prover 4: stopped
% 100.82/14.13 Prover 3: stopped
% 100.82/14.18 Prover 8: Warning: ignoring some quantifiers
% 100.82/14.19 Prover 8: Constructing countermodel ...
% 100.82/14.19 Prover 8: stopped
% 100.82/14.19
% 100.82/14.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 100.82/14.19
% 100.82/14.21 % SZS output start Proof for theBenchmark
% 101.31/14.22 Assumptions after simplification:
% 101.31/14.22 ---------------------------------
% 101.31/14.22
% 101.31/14.22 (commutativity_k3_xboole_0)
% 101.31/14.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v1, v0) = v2) | ~
% 101.31/14.25 $i(v1) | ~ $i(v0) | (k3_xboole_0(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : !
% 101.31/14.25 [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~ $i(v1) | ~
% 101.31/14.25 $i(v0) | (k3_xboole_0(v1, v0) = v2 & $i(v2)))
% 101.31/14.26
% 101.31/14.26 (dt_k1_rmod_5)
% 101.31/14.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_rmod_5(v0, v1,
% 101.31/14.26 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) |
% 101.31/14.26 ~ v5_vectsp_2(v1, v0) | ~ l3_vectsp_1(v0) | ~ v2_vectsp_2(v0) | ~
% 101.31/14.26 v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~
% 101.31/14.26 v7_group_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~ v6_rlvect_1(v0)
% 101.31/14.26 | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~
% 101.31/14.26 v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | v3_vectsp_2(v3,
% 101.31/14.27 v0) | v10_vectsp_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v4: $i] :
% 101.31/14.27 ? [v5: $i] : (k1_zfmisc_1(v4) = v5 & u1_struct_0(v1) = v4 & $i(v5) & $i(v4)
% 101.31/14.27 & ~ m1_subset_1(v2, v5))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 101.31/14.27 [v3: $i] : ( ~ (k1_rmod_5(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 101.31/14.27 $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~
% 101.31/14.27 l3_vectsp_1(v0) | ~ v2_vectsp_2(v0) | ~ v8_vectsp_1(v0) | ~
% 101.31/14.27 v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v7_group_1(v0) | ~ v4_group_1(v0)
% 101.31/14.27 | ~ v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~
% 101.31/14.27 v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~
% 101.31/14.27 v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | m1_rmod_2(v3, v0, v1) |
% 101.31/14.27 v10_vectsp_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v4: $i] : ? [v5:
% 101.31/14.27 $i] : (k1_zfmisc_1(v4) = v5 & u1_struct_0(v1) = v4 & $i(v5) & $i(v4) & ~
% 101.31/14.27 m1_subset_1(v2, v5)))
% 101.31/14.27
% 101.31/14.27 (dt_k5_subset_1)
% 101.31/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k5_subset_1(v0,
% 101.31/14.27 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 101.31/14.27 (k1_zfmisc_1(v0) = v4 & $i(v4) & ( ~ m1_subset_1(v2, v4) | ~
% 101.31/14.27 m1_subset_1(v1, v4) | m1_subset_1(v3, v4))))
% 101.31/14.27
% 101.31/14.27 (redefinition_k5_subset_1)
% 101.31/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k5_subset_1(v0,
% 101.31/14.27 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ?
% 101.31/14.27 [v5: $i] : ((v5 = v3 & k3_xboole_0(v1, v2) = v3 & $i(v3)) | (k1_zfmisc_1(v0)
% 101.31/14.27 = v4 & $i(v4) & ( ~ m1_subset_1(v2, v4) | ~ m1_subset_1(v1, v4)))))
% 101.31/14.27
% 101.31/14.27 (t15_rmod_5)
% 101.31/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (u1_struct_0(v1) = v2) | ~
% 101.31/14.27 $i(v1) | ~ $i(v0) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~
% 101.31/14.27 l3_vectsp_1(v0) | ~ v2_vectsp_2(v0) | ~ v8_vectsp_1(v0) | ~
% 101.31/14.27 v7_vectsp_1(v0) | ~ v6_vectsp_1(v0) | ~ v7_group_1(v0) | ~ v4_group_1(v0)
% 101.31/14.27 | ~ v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~
% 101.31/14.27 v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~
% 101.31/14.27 v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | v10_vectsp_1(v0) | v3_struct_0(v1) |
% 101.31/14.27 v3_struct_0(v0) | ? [v3: $i] : (k1_zfmisc_1(v2) = v3 & $i(v3) & ! [v4: $i]
% 101.31/14.27 : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (k1_rmod_5(v0, v1, v6) =
% 101.31/14.27 v7) | ~ (k1_rmod_5(v0, v1, v4) = v5) | ~ $i(v6) | ~ $i(v4) | ~
% 101.31/14.27 r1_tarski(v4, v6) | ~ m1_subset_1(v6, v3) | ~ m1_subset_1(v4, v3) |
% 101.31/14.27 m1_rmod_2(v5, v0, v7))))
% 101.31/14.27
% 101.31/14.27 (t17_xboole_1)
% 101.31/14.27 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v0, v1) = v2) | ~
% 101.31/14.27 $i(v1) | ~ $i(v0) | r1_tarski(v2, v0))
% 101.31/14.27
% 101.31/14.28 (t18_rmod_5)
% 101.31/14.28 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 101.31/14.28 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] :
% 101.31/14.28 (k2_rmod_3(v0, v1, v5, v9) = v10 & k1_rmod_5(v0, v1, v7) = v8 & k1_rmod_5(v0,
% 101.31/14.28 v1, v6) = v9 & k1_rmod_5(v0, v1, v4) = v5 & k5_subset_1(v2, v4, v6) = v7 &
% 101.31/14.28 k1_zfmisc_1(v2) = v3 & u1_struct_0(v1) = v2 & $i(v10) & $i(v9) & $i(v8) &
% 101.31/14.28 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 101.31/14.28 m1_subset_1(v6, v3) & m1_subset_1(v4, v3) & l1_vectsp_2(v1, v0) &
% 101.31/14.28 v5_vectsp_2(v1, v0) & l3_vectsp_1(v0) & v2_vectsp_2(v0) & v8_vectsp_1(v0) &
% 101.31/14.28 v7_vectsp_1(v0) & v6_vectsp_1(v0) & v7_group_1(v0) & v4_group_1(v0) &
% 101.31/14.28 v6_rlvect_1(v1) & v6_rlvect_1(v0) & v5_rlvect_1(v1) & v5_rlvect_1(v0) &
% 101.31/14.28 v4_rlvect_1(v1) & v4_rlvect_1(v0) & v3_rlvect_1(v1) & v3_rlvect_1(v0) & ~
% 101.31/14.28 m1_rmod_2(v8, v0, v10) & ~ v10_vectsp_1(v0) & ~ v3_struct_0(v1) & ~
% 101.31/14.28 v3_struct_0(v0))
% 101.31/14.28
% 101.31/14.28 (t24_rmod_3)
% 101.31/14.28 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 101.31/14.28 $i] : ( ~ (k2_rmod_3(v0, v1, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 101.31/14.28 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ m1_rmod_2(v4, v0, v1) | ~ m1_rmod_2(v3,
% 101.31/14.28 v0, v1) | ~ m1_rmod_2(v2, v0, v4) | ~ m1_rmod_2(v2, v0, v3) | ~
% 101.31/14.28 m1_rmod_2(v2, v0, v1) | ~ l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~
% 101.31/14.28 l3_vectsp_1(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~
% 101.31/14.28 v6_vectsp_1(v0) | ~ v4_group_1(v0) | ~ v6_rlvect_1(v1) | ~
% 101.31/14.28 v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~ v5_rlvect_1(v0) | ~
% 101.31/14.28 v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~ v3_rlvect_1(v1) | ~
% 101.31/14.28 v3_rlvect_1(v0) | m1_rmod_2(v2, v0, v5) | v3_struct_0(v1) | v3_struct_0(v0))
% 101.31/14.28
% 101.31/14.28 (function-axioms)
% 101.31/14.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 101.31/14.29 $i] : ! [v6: $i] : (v1 = v0 | ~ (g1_vectsp_2(v6, v5, v4, v3, v2) = v1) |
% 101.31/14.29 ~ (g1_vectsp_2(v6, v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 101.31/14.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 101.31/14.29 (k2_rmod_3(v5, v4, v3, v2) = v1) | ~ (k2_rmod_3(v5, v4, v3, v2) = v0)) & !
% 101.31/14.29 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 101.31/14.29 ~ (k1_rmod_5(v4, v3, v2) = v1) | ~ (k1_rmod_5(v4, v3, v2) = v0)) & ! [v0:
% 101.31/14.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 101.31/14.29 (k5_subset_1(v4, v3, v2) = v1) | ~ (k5_subset_1(v4, v3, v2) = v0)) & !
% 101.31/14.29 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 101.31/14.29 (k3_xboole_0(v3, v2) = v1) | ~ (k3_xboole_0(v3, v2) = v0)) & ! [v0: $i] :
% 101.31/14.29 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) =
% 101.31/14.29 v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 101.31/14.29 $i] : ! [v3: $i] : (v1 = v0 | ~ (u1_vectsp_2(v3, v2) = v1) | ~
% 101.31/14.29 (u1_vectsp_2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 101.31/14.29 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0: $i]
% 101.31/14.29 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~
% 101.31/14.29 (u1_struct_0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 101.31/14.29 | ~ (u1_rlvect_1(v2) = v1) | ~ (u1_rlvect_1(v2) = v0)) & ! [v0: $i] : !
% 101.31/14.29 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u2_struct_0(v2) = v1) | ~
% 101.31/14.29 (u2_struct_0(v2) = v0))
% 101.31/14.29
% 101.31/14.29 Further assumptions not needed in the proof:
% 101.31/14.29 --------------------------------------------
% 101.31/14.29 abstractness_v3_vectsp_2, antisymmetry_r2_hidden, cc1_relset_1, cc2_vectsp_2,
% 101.31/14.29 cc3_vectsp_2, commutativity_k5_subset_1, dt_g1_vectsp_2, dt_k1_xboole_0,
% 101.31/14.29 dt_k1_zfmisc_1, dt_k2_rmod_3, dt_k2_zfmisc_1, dt_k3_xboole_0, dt_l1_group_1,
% 101.31/14.29 dt_l1_rlvect_1, dt_l1_struct_0, dt_l1_vectsp_1, dt_l1_vectsp_2, dt_l2_struct_0,
% 101.31/14.29 dt_l2_vectsp_1, dt_l3_vectsp_1, dt_m1_relset_1, dt_m1_rmod_2, dt_m1_subset_1,
% 101.31/14.29 dt_m2_relset_1, dt_u1_rlvect_1, dt_u1_struct_0, dt_u1_vectsp_2, dt_u2_struct_0,
% 101.31/14.29 existence_l1_group_1, existence_l1_rlvect_1, existence_l1_struct_0,
% 101.31/14.29 existence_l1_vectsp_1, existence_l1_vectsp_2, existence_l2_struct_0,
% 101.31/14.29 existence_l2_vectsp_1, existence_l3_vectsp_1, existence_m1_relset_1,
% 101.31/14.29 existence_m1_rmod_2, existence_m1_subset_1, existence_m2_relset_1, fc1_struct_0,
% 101.31/14.29 fc1_subset_1, fc1_vectsp_2, fc1_xboole_0, fc4_subset_1, free_g1_vectsp_2,
% 101.31/14.29 idempotence_k3_xboole_0, idempotence_k5_subset_1, rc13_vectsp_2, rc16_vectsp_2,
% 101.31/14.29 rc1_rmod_2, rc1_subset_1, rc1_xboole_0, rc2_subset_1, rc2_xboole_0,
% 101.31/14.29 rc3_struct_0, rc4_struct_0, rc5_struct_0, rc8_vectsp_2, rc9_vectsp_2,
% 101.31/14.29 redefinition_m2_relset_1, reflexivity_r1_tarski, t1_subset, t2_boole, t2_subset,
% 101.31/14.29 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 101.31/14.29
% 101.31/14.29 Those formulas are unsatisfiable:
% 101.31/14.29 ---------------------------------
% 101.31/14.29
% 101.31/14.29 Begin of proof
% 101.31/14.29 |
% 101.31/14.29 | ALPHA: (commutativity_k3_xboole_0) implies:
% 101.31/14.29 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k3_xboole_0(v1, v0) =
% 101.31/14.29 | v2) | ~ $i(v1) | ~ $i(v0) | (k3_xboole_0(v0, v1) = v2 & $i(v2)))
% 101.31/14.29 |
% 101.31/14.29 | ALPHA: (dt_k1_rmod_5) implies:
% 101.31/14.29 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 101.31/14.29 | (k1_rmod_5(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 101.31/14.29 | l1_vectsp_2(v1, v0) | ~ v5_vectsp_2(v1, v0) | ~ l3_vectsp_1(v0) |
% 101.31/14.29 | ~ v2_vectsp_2(v0) | ~ v8_vectsp_1(v0) | ~ v7_vectsp_1(v0) | ~
% 101.31/14.29 | v6_vectsp_1(v0) | ~ v7_group_1(v0) | ~ v4_group_1(v0) | ~
% 101.31/14.29 | v6_rlvect_1(v1) | ~ v6_rlvect_1(v0) | ~ v5_rlvect_1(v1) | ~
% 101.31/14.29 | v5_rlvect_1(v0) | ~ v4_rlvect_1(v1) | ~ v4_rlvect_1(v0) | ~
% 101.31/14.29 | v3_rlvect_1(v1) | ~ v3_rlvect_1(v0) | m1_rmod_2(v3, v0, v1) |
% 101.31/14.29 | v10_vectsp_1(v0) | v3_struct_0(v1) | v3_struct_0(v0) | ? [v4: $i] :
% 101.31/14.29 | ? [v5: $i] : (k1_zfmisc_1(v4) = v5 & u1_struct_0(v1) = v4 & $i(v5) &
% 101.67/14.29 | $i(v4) & ~ m1_subset_1(v2, v5)))
% 101.67/14.29 |
% 101.67/14.29 | ALPHA: (function-axioms) implies:
% 101.67/14.29 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 101.67/14.29 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 101.67/14.29 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 101.67/14.29 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 101.67/14.29 |
% 101.67/14.29 | DELTA: instantiating (t18_rmod_5) with fresh symbols all_85_0, all_85_1,
% 101.67/14.29 | all_85_2, all_85_3, all_85_4, all_85_5, all_85_6, all_85_7, all_85_8,
% 101.67/14.29 | all_85_9, all_85_10 gives:
% 101.67/14.30 | (5) k2_rmod_3(all_85_10, all_85_9, all_85_5, all_85_1) = all_85_0 &
% 101.67/14.30 | k1_rmod_5(all_85_10, all_85_9, all_85_3) = all_85_2 &
% 101.67/14.30 | k1_rmod_5(all_85_10, all_85_9, all_85_4) = all_85_1 &
% 101.67/14.30 | k1_rmod_5(all_85_10, all_85_9, all_85_6) = all_85_5 &
% 101.67/14.30 | k5_subset_1(all_85_8, all_85_6, all_85_4) = all_85_3 &
% 101.67/14.30 | k1_zfmisc_1(all_85_8) = all_85_7 & u1_struct_0(all_85_9) = all_85_8 &
% 101.67/14.30 | $i(all_85_0) & $i(all_85_1) & $i(all_85_2) & $i(all_85_3) &
% 101.67/14.30 | $i(all_85_4) & $i(all_85_5) & $i(all_85_6) & $i(all_85_7) &
% 101.67/14.30 | $i(all_85_8) & $i(all_85_9) & $i(all_85_10) & m1_subset_1(all_85_4,
% 101.67/14.30 | all_85_7) & m1_subset_1(all_85_6, all_85_7) & l1_vectsp_2(all_85_9,
% 101.67/14.30 | all_85_10) & v5_vectsp_2(all_85_9, all_85_10) &
% 101.67/14.30 | l3_vectsp_1(all_85_10) & v2_vectsp_2(all_85_10) &
% 101.67/14.30 | v8_vectsp_1(all_85_10) & v7_vectsp_1(all_85_10) &
% 101.67/14.30 | v6_vectsp_1(all_85_10) & v7_group_1(all_85_10) & v4_group_1(all_85_10)
% 101.67/14.30 | & v6_rlvect_1(all_85_9) & v6_rlvect_1(all_85_10) &
% 101.67/14.30 | v5_rlvect_1(all_85_9) & v5_rlvect_1(all_85_10) & v4_rlvect_1(all_85_9)
% 101.67/14.30 | & v4_rlvect_1(all_85_10) & v3_rlvect_1(all_85_9) &
% 101.67/14.30 | v3_rlvect_1(all_85_10) & ~ m1_rmod_2(all_85_2, all_85_10, all_85_0) &
% 101.67/14.30 | ~ v10_vectsp_1(all_85_10) & ~ v3_struct_0(all_85_9) & ~
% 101.67/14.30 | v3_struct_0(all_85_10)
% 101.67/14.30 |
% 101.67/14.30 | ALPHA: (5) implies:
% 101.67/14.30 | (6) ~ v3_struct_0(all_85_10)
% 101.67/14.30 | (7) ~ v3_struct_0(all_85_9)
% 101.67/14.30 | (8) ~ v10_vectsp_1(all_85_10)
% 101.67/14.30 | (9) ~ m1_rmod_2(all_85_2, all_85_10, all_85_0)
% 101.67/14.30 | (10) v3_rlvect_1(all_85_10)
% 101.67/14.30 | (11) v3_rlvect_1(all_85_9)
% 101.67/14.30 | (12) v4_rlvect_1(all_85_10)
% 101.67/14.30 | (13) v4_rlvect_1(all_85_9)
% 101.67/14.30 | (14) v5_rlvect_1(all_85_10)
% 101.67/14.30 | (15) v5_rlvect_1(all_85_9)
% 101.67/14.30 | (16) v6_rlvect_1(all_85_10)
% 101.67/14.30 | (17) v6_rlvect_1(all_85_9)
% 101.67/14.30 | (18) v4_group_1(all_85_10)
% 101.67/14.30 | (19) v7_group_1(all_85_10)
% 101.67/14.30 | (20) v6_vectsp_1(all_85_10)
% 101.67/14.30 | (21) v7_vectsp_1(all_85_10)
% 101.67/14.30 | (22) v8_vectsp_1(all_85_10)
% 101.67/14.30 | (23) v2_vectsp_2(all_85_10)
% 101.67/14.30 | (24) l3_vectsp_1(all_85_10)
% 101.67/14.30 | (25) v5_vectsp_2(all_85_9, all_85_10)
% 101.67/14.30 | (26) l1_vectsp_2(all_85_9, all_85_10)
% 101.67/14.30 | (27) m1_subset_1(all_85_6, all_85_7)
% 101.67/14.30 | (28) m1_subset_1(all_85_4, all_85_7)
% 101.67/14.30 | (29) $i(all_85_10)
% 101.67/14.30 | (30) $i(all_85_9)
% 101.67/14.30 | (31) $i(all_85_8)
% 101.67/14.30 | (32) $i(all_85_6)
% 101.67/14.30 | (33) $i(all_85_5)
% 101.67/14.30 | (34) $i(all_85_4)
% 101.67/14.30 | (35) $i(all_85_3)
% 101.67/14.30 | (36) $i(all_85_2)
% 101.67/14.30 | (37) $i(all_85_1)
% 101.67/14.30 | (38) u1_struct_0(all_85_9) = all_85_8
% 101.67/14.30 | (39) k1_zfmisc_1(all_85_8) = all_85_7
% 101.67/14.30 | (40) k5_subset_1(all_85_8, all_85_6, all_85_4) = all_85_3
% 101.67/14.30 | (41) k1_rmod_5(all_85_10, all_85_9, all_85_6) = all_85_5
% 101.67/14.30 | (42) k1_rmod_5(all_85_10, all_85_9, all_85_4) = all_85_1
% 101.67/14.30 | (43) k1_rmod_5(all_85_10, all_85_9, all_85_3) = all_85_2
% 101.67/14.30 | (44) k2_rmod_3(all_85_10, all_85_9, all_85_5, all_85_1) = all_85_0
% 101.67/14.30 |
% 101.67/14.31 | GROUND_INST: instantiating (t15_rmod_5) with all_85_10, all_85_9, all_85_8,
% 101.67/14.31 | simplifying with (6), (7), (8), (10), (11), (12), (13), (14),
% 101.67/14.31 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 101.67/14.31 | (26), (29), (30), (38) gives:
% 101.67/14.31 | (45) ? [v0: $i] : (k1_zfmisc_1(all_85_8) = v0 & $i(v0) & ! [v1: $i] : !
% 101.67/14.31 | [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (k1_rmod_5(all_85_10,
% 101.67/14.31 | all_85_9, v3) = v4) | ~ (k1_rmod_5(all_85_10, all_85_9, v1) =
% 101.67/14.31 | v2) | ~ $i(v3) | ~ $i(v1) | ~ r1_tarski(v1, v3) | ~
% 101.67/14.31 | m1_subset_1(v3, v0) | ~ m1_subset_1(v1, v0) | m1_rmod_2(v2,
% 101.67/14.31 | all_85_10, v4)))
% 101.67/14.31 |
% 101.67/14.31 | GROUND_INST: instantiating (redefinition_k5_subset_1) with all_85_8, all_85_6,
% 101.67/14.31 | all_85_4, all_85_3, simplifying with (31), (32), (34), (40)
% 101.67/14.31 | gives:
% 101.67/14.31 | (46) ? [v0: $i] : ? [v1: int] : ((v1 = all_85_3 & k3_xboole_0(all_85_6,
% 101.67/14.31 | all_85_4) = all_85_3 & $i(all_85_3)) | (k1_zfmisc_1(all_85_8) =
% 101.67/14.31 | v0 & $i(v0) & ( ~ m1_subset_1(all_85_4, v0) | ~
% 101.67/14.31 | m1_subset_1(all_85_6, v0))))
% 101.67/14.31 |
% 101.67/14.31 | GROUND_INST: instantiating (dt_k5_subset_1) with all_85_8, all_85_6, all_85_4,
% 101.67/14.31 | all_85_3, simplifying with (31), (32), (34), (40) gives:
% 101.67/14.31 | (47) ? [v0: $i] : (k1_zfmisc_1(all_85_8) = v0 & $i(v0) & ( ~
% 101.67/14.31 | m1_subset_1(all_85_4, v0) | ~ m1_subset_1(all_85_6, v0) |
% 101.67/14.31 | m1_subset_1(all_85_3, v0)))
% 101.67/14.31 |
% 101.67/14.31 | GROUND_INST: instantiating (2) with all_85_10, all_85_9, all_85_6, all_85_5,
% 101.67/14.31 | simplifying with (6), (7), (8), (10), (11), (12), (13), (14),
% 101.67/14.31 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 101.67/14.31 | (26), (29), (30), (32), (41) gives:
% 101.67/14.31 | (48) m1_rmod_2(all_85_5, all_85_10, all_85_9) | ? [v0: $i] : ? [v1: $i] :
% 101.67/14.31 | (k1_zfmisc_1(v0) = v1 & u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) &
% 101.67/14.31 | ~ m1_subset_1(all_85_6, v1))
% 101.67/14.31 |
% 101.67/14.31 | GROUND_INST: instantiating (2) with all_85_10, all_85_9, all_85_4, all_85_1,
% 101.67/14.31 | simplifying with (6), (7), (8), (10), (11), (12), (13), (14),
% 101.67/14.31 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 101.67/14.31 | (26), (29), (30), (34), (42) gives:
% 101.67/14.31 | (49) m1_rmod_2(all_85_1, all_85_10, all_85_9) | ? [v0: $i] : ? [v1: $i] :
% 101.67/14.31 | (k1_zfmisc_1(v0) = v1 & u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) &
% 101.67/14.31 | ~ m1_subset_1(all_85_4, v1))
% 101.67/14.31 |
% 101.67/14.31 | GROUND_INST: instantiating (2) with all_85_10, all_85_9, all_85_3, all_85_2,
% 101.67/14.32 | simplifying with (6), (7), (8), (10), (11), (12), (13), (14),
% 101.67/14.32 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 101.67/14.32 | (26), (29), (30), (35), (43) gives:
% 101.67/14.32 | (50) m1_rmod_2(all_85_2, all_85_10, all_85_9) | ? [v0: $i] : ? [v1: $i] :
% 101.67/14.32 | (k1_zfmisc_1(v0) = v1 & u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) &
% 101.67/14.32 | ~ m1_subset_1(all_85_3, v1))
% 101.67/14.32 |
% 101.67/14.32 | DELTA: instantiating (47) with fresh symbol all_113_0 gives:
% 101.67/14.32 | (51) k1_zfmisc_1(all_85_8) = all_113_0 & $i(all_113_0) & ( ~
% 101.67/14.32 | m1_subset_1(all_85_4, all_113_0) | ~ m1_subset_1(all_85_6,
% 101.67/14.32 | all_113_0) | m1_subset_1(all_85_3, all_113_0))
% 101.67/14.32 |
% 101.67/14.32 | ALPHA: (51) implies:
% 101.67/14.32 | (52) k1_zfmisc_1(all_85_8) = all_113_0
% 101.67/14.32 | (53) ~ m1_subset_1(all_85_4, all_113_0) | ~ m1_subset_1(all_85_6,
% 101.67/14.32 | all_113_0) | m1_subset_1(all_85_3, all_113_0)
% 101.67/14.32 |
% 101.67/14.32 | DELTA: instantiating (46) with fresh symbols all_116_0, all_116_1 gives:
% 101.67/14.32 | (54) (all_116_0 = all_85_3 & k3_xboole_0(all_85_6, all_85_4) = all_85_3 &
% 101.67/14.32 | $i(all_85_3)) | (k1_zfmisc_1(all_85_8) = all_116_1 & $i(all_116_1) &
% 101.67/14.32 | ( ~ m1_subset_1(all_85_4, all_116_1) | ~ m1_subset_1(all_85_6,
% 101.67/14.32 | all_116_1)))
% 101.67/14.32 |
% 101.67/14.32 | DELTA: instantiating (45) with fresh symbol all_123_0 gives:
% 101.67/14.32 | (55) k1_zfmisc_1(all_85_8) = all_123_0 & $i(all_123_0) & ! [v0: $i] : !
% 101.67/14.32 | [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_rmod_5(all_85_10,
% 101.67/14.32 | all_85_9, v2) = v3) | ~ (k1_rmod_5(all_85_10, all_85_9, v0) =
% 101.67/14.32 | v1) | ~ $i(v2) | ~ $i(v0) | ~ r1_tarski(v0, v2) | ~
% 101.67/14.32 | m1_subset_1(v2, all_123_0) | ~ m1_subset_1(v0, all_123_0) |
% 101.67/14.32 | m1_rmod_2(v1, all_85_10, v3))
% 101.67/14.32 |
% 101.67/14.32 | ALPHA: (55) implies:
% 101.67/14.32 | (56) k1_zfmisc_1(all_85_8) = all_123_0
% 101.67/14.32 | (57) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 101.67/14.32 | (k1_rmod_5(all_85_10, all_85_9, v2) = v3) | ~ (k1_rmod_5(all_85_10,
% 101.67/14.32 | all_85_9, v0) = v1) | ~ $i(v2) | ~ $i(v0) | ~ r1_tarski(v0,
% 101.67/14.32 | v2) | ~ m1_subset_1(v2, all_123_0) | ~ m1_subset_1(v0,
% 101.67/14.32 | all_123_0) | m1_rmod_2(v1, all_85_10, v3))
% 101.67/14.32 |
% 101.67/14.32 | GROUND_INST: instantiating (4) with all_85_7, all_123_0, all_85_8, simplifying
% 101.67/14.32 | with (39), (56) gives:
% 101.67/14.32 | (58) all_123_0 = all_85_7
% 101.67/14.32 |
% 101.67/14.32 | GROUND_INST: instantiating (4) with all_113_0, all_123_0, all_85_8,
% 101.67/14.32 | simplifying with (52), (56) gives:
% 101.67/14.32 | (59) all_123_0 = all_113_0
% 101.67/14.32 |
% 101.67/14.32 | COMBINE_EQS: (58), (59) imply:
% 101.67/14.32 | (60) all_113_0 = all_85_7
% 101.67/14.32 |
% 101.67/14.32 | BETA: splitting (48) gives:
% 101.67/14.32 |
% 101.67/14.32 | Case 1:
% 101.67/14.32 | |
% 101.67/14.32 | | (61) m1_rmod_2(all_85_5, all_85_10, all_85_9)
% 101.67/14.32 | |
% 101.67/14.32 | | BETA: splitting (53) gives:
% 101.67/14.32 | |
% 101.67/14.32 | | Case 1:
% 101.67/14.32 | | |
% 101.67/14.32 | | | (62) ~ m1_subset_1(all_85_4, all_113_0)
% 101.67/14.32 | | |
% 101.67/14.32 | | | REDUCE: (60), (62) imply:
% 101.67/14.32 | | | (63) ~ m1_subset_1(all_85_4, all_85_7)
% 101.67/14.32 | | |
% 101.67/14.32 | | | PRED_UNIFY: (28), (63) imply:
% 101.67/14.32 | | | (64) $false
% 101.67/14.32 | | |
% 101.67/14.32 | | | CLOSE: (64) is inconsistent.
% 101.67/14.32 | | |
% 101.67/14.32 | | Case 2:
% 101.67/14.32 | | |
% 101.67/14.32 | | | (65) m1_subset_1(all_85_4, all_113_0)
% 101.67/14.32 | | | (66) ~ m1_subset_1(all_85_6, all_113_0) | m1_subset_1(all_85_3,
% 101.67/14.32 | | | all_113_0)
% 101.67/14.32 | | |
% 101.67/14.32 | | | BETA: splitting (49) gives:
% 101.67/14.32 | | |
% 101.67/14.32 | | | Case 1:
% 101.67/14.32 | | | |
% 101.67/14.32 | | | | (67) m1_rmod_2(all_85_1, all_85_10, all_85_9)
% 101.67/14.32 | | | |
% 101.67/14.32 | | | | BETA: splitting (66) gives:
% 101.67/14.32 | | | |
% 101.67/14.32 | | | | Case 1:
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | (68) ~ m1_subset_1(all_85_6, all_113_0)
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | REDUCE: (60), (68) imply:
% 101.67/14.32 | | | | | (69) ~ m1_subset_1(all_85_6, all_85_7)
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | PRED_UNIFY: (27), (69) imply:
% 101.67/14.32 | | | | | (70) $false
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | CLOSE: (70) is inconsistent.
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | Case 2:
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | (71) m1_subset_1(all_85_6, all_113_0)
% 101.67/14.32 | | | | | (72) m1_subset_1(all_85_3, all_113_0)
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | REDUCE: (60), (72) imply:
% 101.67/14.32 | | | | | (73) m1_subset_1(all_85_3, all_85_7)
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | BETA: splitting (50) gives:
% 101.67/14.32 | | | | |
% 101.67/14.32 | | | | | Case 1:
% 101.67/14.32 | | | | | |
% 101.67/14.32 | | | | | | (74) m1_rmod_2(all_85_2, all_85_10, all_85_9)
% 101.67/14.32 | | | | | |
% 101.67/14.32 | | | | | | BETA: splitting (54) gives:
% 101.67/14.32 | | | | | |
% 101.67/14.32 | | | | | | Case 1:
% 101.67/14.32 | | | | | | |
% 101.67/14.32 | | | | | | | (75) all_116_0 = all_85_3 & k3_xboole_0(all_85_6, all_85_4) =
% 101.67/14.32 | | | | | | | all_85_3 & $i(all_85_3)
% 101.67/14.32 | | | | | | |
% 101.67/14.32 | | | | | | | ALPHA: (75) implies:
% 101.67/14.32 | | | | | | | (76) k3_xboole_0(all_85_6, all_85_4) = all_85_3
% 101.67/14.32 | | | | | | |
% 101.67/14.32 | | | | | | | GROUND_INST: instantiating (1) with all_85_4, all_85_6, all_85_3,
% 101.67/14.32 | | | | | | | simplifying with (32), (34), (76) gives:
% 101.67/14.32 | | | | | | | (77) k3_xboole_0(all_85_4, all_85_6) = all_85_3 & $i(all_85_3)
% 101.67/14.32 | | | | | | |
% 101.67/14.32 | | | | | | | ALPHA: (77) implies:
% 101.67/14.33 | | | | | | | (78) k3_xboole_0(all_85_4, all_85_6) = all_85_3
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | GROUND_INST: instantiating (t17_xboole_1) with all_85_6, all_85_4,
% 101.67/14.33 | | | | | | | all_85_3, simplifying with (32), (34), (76) gives:
% 101.67/14.33 | | | | | | | (79) r1_tarski(all_85_3, all_85_6)
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | GROUND_INST: instantiating (57) with all_85_3, all_85_2, all_85_6,
% 101.67/14.33 | | | | | | | all_85_5, simplifying with (32), (35), (41), (43),
% 101.67/14.33 | | | | | | | (79) gives:
% 101.67/14.33 | | | | | | | (80) ~ m1_subset_1(all_85_3, all_123_0) | ~
% 101.67/14.33 | | | | | | | m1_subset_1(all_85_6, all_123_0) | m1_rmod_2(all_85_2,
% 101.67/14.33 | | | | | | | all_85_10, all_85_5)
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | GROUND_INST: instantiating (t17_xboole_1) with all_85_4, all_85_6,
% 101.67/14.33 | | | | | | | all_85_3, simplifying with (32), (34), (78) gives:
% 101.67/14.33 | | | | | | | (81) r1_tarski(all_85_3, all_85_4)
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | BETA: splitting (80) gives:
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | Case 1:
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | (82) ~ m1_subset_1(all_85_3, all_123_0)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | REDUCE: (58), (82) imply:
% 101.67/14.33 | | | | | | | | (83) ~ m1_subset_1(all_85_3, all_85_7)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | PRED_UNIFY: (73), (83) imply:
% 101.67/14.33 | | | | | | | | (84) $false
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | CLOSE: (84) is inconsistent.
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | Case 2:
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | (85) m1_subset_1(all_85_3, all_123_0)
% 101.67/14.33 | | | | | | | | (86) ~ m1_subset_1(all_85_6, all_123_0) |
% 101.67/14.33 | | | | | | | | m1_rmod_2(all_85_2, all_85_10, all_85_5)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | BETA: splitting (86) gives:
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | Case 1:
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | (87) ~ m1_subset_1(all_85_6, all_123_0)
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | REDUCE: (58), (87) imply:
% 101.67/14.33 | | | | | | | | | (88) ~ m1_subset_1(all_85_6, all_85_7)
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | PRED_UNIFY: (27), (88) imply:
% 101.67/14.33 | | | | | | | | | (89) $false
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | CLOSE: (89) is inconsistent.
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | Case 2:
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | (90) m1_rmod_2(all_85_2, all_85_10, all_85_5)
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | GROUND_INST: instantiating (57) with all_85_3, all_85_2,
% 101.67/14.33 | | | | | | | | | all_85_4, all_85_1, simplifying with (34), (35),
% 101.67/14.33 | | | | | | | | | (42), (43), (81) gives:
% 101.67/14.33 | | | | | | | | | (91) ~ m1_subset_1(all_85_3, all_123_0) | ~
% 101.67/14.33 | | | | | | | | | m1_subset_1(all_85_4, all_123_0) | m1_rmod_2(all_85_2,
% 101.67/14.33 | | | | | | | | | all_85_10, all_85_1)
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | BETA: splitting (91) gives:
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | | Case 1:
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | (92) ~ m1_subset_1(all_85_3, all_123_0)
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | REDUCE: (58), (92) imply:
% 101.67/14.33 | | | | | | | | | | (93) ~ m1_subset_1(all_85_3, all_85_7)
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | PRED_UNIFY: (73), (93) imply:
% 101.67/14.33 | | | | | | | | | | (94) $false
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | CLOSE: (94) is inconsistent.
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | Case 2:
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | (95) ~ m1_subset_1(all_85_4, all_123_0) |
% 101.67/14.33 | | | | | | | | | | m1_rmod_2(all_85_2, all_85_10, all_85_1)
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | BETA: splitting (95) gives:
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | Case 1:
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | (96) ~ m1_subset_1(all_85_4, all_123_0)
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | REDUCE: (58), (96) imply:
% 101.67/14.33 | | | | | | | | | | | (97) ~ m1_subset_1(all_85_4, all_85_7)
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | PRED_UNIFY: (28), (97) imply:
% 101.67/14.33 | | | | | | | | | | | (98) $false
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | CLOSE: (98) is inconsistent.
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | Case 2:
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | (99) m1_rmod_2(all_85_2, all_85_10, all_85_1)
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | GROUND_INST: instantiating (t24_rmod_3) with all_85_10,
% 101.67/14.33 | | | | | | | | | | | all_85_9, all_85_2, all_85_5, all_85_1, all_85_0,
% 101.67/14.33 | | | | | | | | | | | simplifying with (6), (7), (9), (10), (11), (12),
% 101.67/14.33 | | | | | | | | | | | (13), (14), (15), (16), (17), (18), (20), (21),
% 101.67/14.33 | | | | | | | | | | | (22), (24), (25), (26), (29), (30), (33), (36),
% 101.67/14.33 | | | | | | | | | | | (37), (44), (61), (67), (74), (90), (99) gives:
% 101.67/14.33 | | | | | | | | | | | (100) $false
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | | CLOSE: (100) is inconsistent.
% 101.67/14.33 | | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | | End of split
% 101.67/14.33 | | | | | | | | | |
% 101.67/14.33 | | | | | | | | | End of split
% 101.67/14.33 | | | | | | | | |
% 101.67/14.33 | | | | | | | | End of split
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | End of split
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | Case 2:
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | (101) k1_zfmisc_1(all_85_8) = all_116_1 & $i(all_116_1) & ( ~
% 101.67/14.33 | | | | | | | m1_subset_1(all_85_4, all_116_1) | ~
% 101.67/14.33 | | | | | | | m1_subset_1(all_85_6, all_116_1))
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | ALPHA: (101) implies:
% 101.67/14.33 | | | | | | | (102) k1_zfmisc_1(all_85_8) = all_116_1
% 101.67/14.33 | | | | | | | (103) ~ m1_subset_1(all_85_4, all_116_1) | ~
% 101.67/14.33 | | | | | | | m1_subset_1(all_85_6, all_116_1)
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | GROUND_INST: instantiating (4) with all_85_7, all_116_1, all_85_8,
% 101.67/14.33 | | | | | | | simplifying with (39), (102) gives:
% 101.67/14.33 | | | | | | | (104) all_116_1 = all_85_7
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | BETA: splitting (103) gives:
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | | Case 1:
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | (105) ~ m1_subset_1(all_85_4, all_116_1)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | REDUCE: (104), (105) imply:
% 101.67/14.33 | | | | | | | | (106) ~ m1_subset_1(all_85_4, all_85_7)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | PRED_UNIFY: (28), (106) imply:
% 101.67/14.33 | | | | | | | | (107) $false
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | CLOSE: (107) is inconsistent.
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | Case 2:
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | (108) ~ m1_subset_1(all_85_6, all_116_1)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | REDUCE: (104), (108) imply:
% 101.67/14.33 | | | | | | | | (109) ~ m1_subset_1(all_85_6, all_85_7)
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | PRED_UNIFY: (27), (109) imply:
% 101.67/14.33 | | | | | | | | (110) $false
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | | CLOSE: (110) is inconsistent.
% 101.67/14.33 | | | | | | | |
% 101.67/14.33 | | | | | | | End of split
% 101.67/14.33 | | | | | | |
% 101.67/14.33 | | | | | | End of split
% 101.67/14.33 | | | | | |
% 101.67/14.33 | | | | | Case 2:
% 101.67/14.33 | | | | | |
% 101.67/14.33 | | | | | | (111) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(v0) = v1 &
% 101.67/14.33 | | | | | | u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) & ~
% 101.67/14.33 | | | | | | m1_subset_1(all_85_3, v1))
% 101.67/14.33 | | | | | |
% 101.67/14.33 | | | | | | DELTA: instantiating (111) with fresh symbols all_158_0, all_158_1
% 101.67/14.33 | | | | | | gives:
% 101.67/14.33 | | | | | | (112) k1_zfmisc_1(all_158_1) = all_158_0 & u1_struct_0(all_85_9)
% 101.67/14.33 | | | | | | = all_158_1 & $i(all_158_0) & $i(all_158_1) & ~
% 101.67/14.33 | | | | | | m1_subset_1(all_85_3, all_158_0)
% 101.67/14.33 | | | | | |
% 101.67/14.33 | | | | | | ALPHA: (112) implies:
% 101.67/14.33 | | | | | | (113) ~ m1_subset_1(all_85_3, all_158_0)
% 101.67/14.33 | | | | | | (114) u1_struct_0(all_85_9) = all_158_1
% 101.67/14.33 | | | | | | (115) k1_zfmisc_1(all_158_1) = all_158_0
% 101.67/14.33 | | | | | |
% 101.67/14.33 | | | | | | GROUND_INST: instantiating (3) with all_85_8, all_158_1, all_85_9,
% 101.67/14.33 | | | | | | simplifying with (38), (114) gives:
% 101.67/14.33 | | | | | | (116) all_158_1 = all_85_8
% 101.67/14.33 | | | | | |
% 101.67/14.33 | | | | | | GROUND_INST: instantiating (4) with all_85_7, all_158_0, all_85_8,
% 101.67/14.33 | | | | | | simplifying with (39) gives:
% 101.67/14.33 | | | | | | (117) all_158_0 = all_85_7 | ~ (k1_zfmisc_1(all_85_8) =
% 101.67/14.33 | | | | | | all_158_0)
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | PRED_UNIFY: (73), (113) imply:
% 101.67/14.34 | | | | | | (118) ~ (all_158_0 = all_85_7)
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | REDUCE: (115), (116) imply:
% 101.67/14.34 | | | | | | (119) k1_zfmisc_1(all_85_8) = all_158_0
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | BETA: splitting (117) gives:
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | Case 1:
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | | (120) ~ (k1_zfmisc_1(all_85_8) = all_158_0)
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | | PRED_UNIFY: (119), (120) imply:
% 101.67/14.34 | | | | | | | (121) $false
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | | CLOSE: (121) is inconsistent.
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | Case 2:
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | | (122) all_158_0 = all_85_7
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | | REDUCE: (118), (122) imply:
% 101.67/14.34 | | | | | | | (123) $false
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | | CLOSE: (123) is inconsistent.
% 101.67/14.34 | | | | | | |
% 101.67/14.34 | | | | | | End of split
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | End of split
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | End of split
% 101.67/14.34 | | | |
% 101.67/14.34 | | | Case 2:
% 101.67/14.34 | | | |
% 101.67/14.34 | | | | (124) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(v0) = v1 &
% 101.67/14.34 | | | | u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) & ~
% 101.67/14.34 | | | | m1_subset_1(all_85_4, v1))
% 101.67/14.34 | | | |
% 101.67/14.34 | | | | DELTA: instantiating (124) with fresh symbols all_146_0, all_146_1
% 101.67/14.34 | | | | gives:
% 101.67/14.34 | | | | (125) k1_zfmisc_1(all_146_1) = all_146_0 & u1_struct_0(all_85_9) =
% 101.67/14.34 | | | | all_146_1 & $i(all_146_0) & $i(all_146_1) & ~
% 101.67/14.34 | | | | m1_subset_1(all_85_4, all_146_0)
% 101.67/14.34 | | | |
% 101.67/14.34 | | | | ALPHA: (125) implies:
% 101.67/14.34 | | | | (126) u1_struct_0(all_85_9) = all_146_1
% 101.67/14.34 | | | | (127) k1_zfmisc_1(all_146_1) = all_146_0
% 101.67/14.34 | | | |
% 101.67/14.34 | | | | BETA: splitting (50) gives:
% 101.67/14.34 | | | |
% 101.67/14.34 | | | | Case 1:
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | DELTA: instantiating (124) with fresh symbols all_164_0, all_164_1
% 101.67/14.34 | | | | | gives:
% 101.67/14.34 | | | | | (128) k1_zfmisc_1(all_164_1) = all_164_0 & u1_struct_0(all_85_9) =
% 101.67/14.34 | | | | | all_164_1 & $i(all_164_0) & $i(all_164_1) & ~
% 101.67/14.34 | | | | | m1_subset_1(all_85_4, all_164_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | ALPHA: (128) implies:
% 101.67/14.34 | | | | | (129) ~ m1_subset_1(all_85_4, all_164_0)
% 101.67/14.34 | | | | | (130) u1_struct_0(all_85_9) = all_164_1
% 101.67/14.34 | | | | | (131) k1_zfmisc_1(all_164_1) = all_164_0
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (3) with all_85_8, all_164_1, all_85_9,
% 101.67/14.34 | | | | | simplifying with (38), (130) gives:
% 101.67/14.34 | | | | | (132) all_164_1 = all_85_8
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (3) with all_146_1, all_164_1, all_85_9,
% 101.67/14.34 | | | | | simplifying with (126), (130) gives:
% 101.67/14.34 | | | | | (133) all_164_1 = all_146_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (4) with all_85_7, all_164_0, all_85_8,
% 101.67/14.34 | | | | | simplifying with (39) gives:
% 101.67/14.34 | | | | | (134) all_164_0 = all_85_7 | ~ (k1_zfmisc_1(all_85_8) = all_164_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | PRED_UNIFY: (28), (129) imply:
% 101.67/14.34 | | | | | (135) ~ (all_164_0 = all_85_7)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | COMBINE_EQS: (132), (133) imply:
% 101.67/14.34 | | | | | (136) all_146_1 = all_85_8
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | REDUCE: (131), (132) imply:
% 101.67/14.34 | | | | | (137) k1_zfmisc_1(all_85_8) = all_164_0
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | BETA: splitting (134) gives:
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | Case 1:
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | (138) ~ (k1_zfmisc_1(all_85_8) = all_164_0)
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | PRED_UNIFY: (137), (138) imply:
% 101.67/14.34 | | | | | | (139) $false
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | CLOSE: (139) is inconsistent.
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | Case 2:
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | (140) all_164_0 = all_85_7
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | REDUCE: (135), (140) imply:
% 101.67/14.34 | | | | | | (141) $false
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | | CLOSE: (141) is inconsistent.
% 101.67/14.34 | | | | | |
% 101.67/14.34 | | | | | End of split
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | Case 2:
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | (142) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(v0) = v1 &
% 101.67/14.34 | | | | | u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) & ~
% 101.67/14.34 | | | | | m1_subset_1(all_85_3, v1))
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | DELTA: instantiating (142) with fresh symbols all_160_0, all_160_1
% 101.67/14.34 | | | | | gives:
% 101.67/14.34 | | | | | (143) k1_zfmisc_1(all_160_1) = all_160_0 & u1_struct_0(all_85_9) =
% 101.67/14.34 | | | | | all_160_1 & $i(all_160_0) & $i(all_160_1) & ~
% 101.67/14.34 | | | | | m1_subset_1(all_85_3, all_160_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | ALPHA: (143) implies:
% 101.67/14.34 | | | | | (144) u1_struct_0(all_85_9) = all_160_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | DELTA: instantiating (124) with fresh symbols all_166_0, all_166_1
% 101.67/14.34 | | | | | gives:
% 101.67/14.34 | | | | | (145) k1_zfmisc_1(all_166_1) = all_166_0 & u1_struct_0(all_85_9) =
% 101.67/14.34 | | | | | all_166_1 & $i(all_166_0) & $i(all_166_1) & ~
% 101.67/14.34 | | | | | m1_subset_1(all_85_4, all_166_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | ALPHA: (145) implies:
% 101.67/14.34 | | | | | (146) ~ m1_subset_1(all_85_4, all_166_0)
% 101.67/14.34 | | | | | (147) u1_struct_0(all_85_9) = all_166_1
% 101.67/14.34 | | | | | (148) k1_zfmisc_1(all_166_1) = all_166_0
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | DELTA: instantiating (142) with fresh symbols all_172_0, all_172_1
% 101.67/14.34 | | | | | gives:
% 101.67/14.34 | | | | | (149) k1_zfmisc_1(all_172_1) = all_172_0 & u1_struct_0(all_85_9) =
% 101.67/14.34 | | | | | all_172_1 & $i(all_172_0) & $i(all_172_1) & ~
% 101.67/14.34 | | | | | m1_subset_1(all_85_3, all_172_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | ALPHA: (149) implies:
% 101.67/14.34 | | | | | (150) u1_struct_0(all_85_9) = all_172_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (3) with all_85_8, all_166_1, all_85_9,
% 101.67/14.34 | | | | | simplifying with (38), (147) gives:
% 101.67/14.34 | | | | | (151) all_166_1 = all_85_8
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (3) with all_160_1, all_166_1, all_85_9,
% 101.67/14.34 | | | | | simplifying with (144), (147) gives:
% 101.67/14.34 | | | | | (152) all_166_1 = all_160_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (3) with all_166_1, all_172_1, all_85_9,
% 101.67/14.34 | | | | | simplifying with (147), (150) gives:
% 101.67/14.34 | | | | | (153) all_172_1 = all_166_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (3) with all_146_1, all_172_1, all_85_9,
% 101.67/14.34 | | | | | simplifying with (126), (150) gives:
% 101.67/14.34 | | | | | (154) all_172_1 = all_146_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (4) with all_85_7, all_166_0, all_85_8,
% 101.67/14.34 | | | | | simplifying with (39) gives:
% 101.67/14.34 | | | | | (155) all_166_0 = all_85_7 | ~ (k1_zfmisc_1(all_85_8) = all_166_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | GROUND_INST: instantiating (4) with all_146_0, all_166_0, all_146_1,
% 101.67/14.34 | | | | | simplifying with (127) gives:
% 101.67/14.34 | | | | | (156) all_166_0 = all_146_0 | ~ (k1_zfmisc_1(all_146_1) =
% 101.67/14.34 | | | | | all_166_0)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | PRED_UNIFY: (28), (146) imply:
% 101.67/14.34 | | | | | (157) ~ (all_166_0 = all_85_7)
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | COMBINE_EQS: (153), (154) imply:
% 101.67/14.34 | | | | | (158) all_166_1 = all_146_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | SIMP: (158) implies:
% 101.67/14.34 | | | | | (159) all_166_1 = all_146_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | COMBINE_EQS: (151), (152) imply:
% 101.67/14.34 | | | | | (160) all_160_1 = all_85_8
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | COMBINE_EQS: (152), (159) imply:
% 101.67/14.34 | | | | | (161) all_160_1 = all_146_1
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | COMBINE_EQS: (160), (161) imply:
% 101.67/14.34 | | | | | (162) all_146_1 = all_85_8
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | SIMP: (162) implies:
% 101.67/14.34 | | | | | (163) all_146_1 = all_85_8
% 101.67/14.34 | | | | |
% 101.67/14.34 | | | | | REDUCE: (148), (151) imply:
% 101.67/14.35 | | | | | (164) k1_zfmisc_1(all_85_8) = all_166_0
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | BETA: splitting (156) gives:
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | Case 1:
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | (165) ~ (k1_zfmisc_1(all_146_1) = all_166_0)
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | REDUCE: (163), (165) imply:
% 101.67/14.35 | | | | | | (166) ~ (k1_zfmisc_1(all_85_8) = all_166_0)
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | PRED_UNIFY: (164), (166) imply:
% 101.67/14.35 | | | | | | (167) $false
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | CLOSE: (167) is inconsistent.
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | Case 2:
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | (168) all_166_0 = all_146_0
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | REDUCE: (157), (168) imply:
% 101.67/14.35 | | | | | | (169) ~ (all_146_0 = all_85_7)
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | REDUCE: (164), (168) imply:
% 101.67/14.35 | | | | | | (170) k1_zfmisc_1(all_85_8) = all_146_0
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | BETA: splitting (155) gives:
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | | Case 1:
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | (171) ~ (k1_zfmisc_1(all_85_8) = all_166_0)
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | REDUCE: (168), (171) imply:
% 101.67/14.35 | | | | | | | (172) ~ (k1_zfmisc_1(all_85_8) = all_146_0)
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | PRED_UNIFY: (170), (172) imply:
% 101.67/14.35 | | | | | | | (173) $false
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | CLOSE: (173) is inconsistent.
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | Case 2:
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | (174) all_166_0 = all_85_7
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | COMBINE_EQS: (168), (174) imply:
% 101.67/14.35 | | | | | | | (175) all_146_0 = all_85_7
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | REDUCE: (169), (175) imply:
% 101.67/14.35 | | | | | | | (176) $false
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | | CLOSE: (176) is inconsistent.
% 101.67/14.35 | | | | | | |
% 101.67/14.35 | | | | | | End of split
% 101.67/14.35 | | | | | |
% 101.67/14.35 | | | | | End of split
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | End of split
% 101.67/14.35 | | | |
% 101.67/14.35 | | | End of split
% 101.67/14.35 | | |
% 101.67/14.35 | | End of split
% 101.67/14.35 | |
% 101.67/14.35 | Case 2:
% 101.67/14.35 | |
% 101.67/14.35 | | (177) ? [v0: $i] : ? [v1: $i] : (k1_zfmisc_1(v0) = v1 &
% 101.67/14.35 | | u1_struct_0(all_85_9) = v0 & $i(v1) & $i(v0) & ~
% 101.67/14.35 | | m1_subset_1(all_85_6, v1))
% 101.67/14.35 | |
% 101.67/14.35 | | DELTA: instantiating (177) with fresh symbols all_134_0, all_134_1 gives:
% 101.67/14.35 | | (178) k1_zfmisc_1(all_134_1) = all_134_0 & u1_struct_0(all_85_9) =
% 101.67/14.35 | | all_134_1 & $i(all_134_0) & $i(all_134_1) & ~
% 101.67/14.35 | | m1_subset_1(all_85_6, all_134_0)
% 101.67/14.35 | |
% 101.67/14.35 | | ALPHA: (178) implies:
% 101.67/14.35 | | (179) ~ m1_subset_1(all_85_6, all_134_0)
% 101.67/14.35 | | (180) u1_struct_0(all_85_9) = all_134_1
% 101.67/14.35 | | (181) k1_zfmisc_1(all_134_1) = all_134_0
% 101.67/14.35 | |
% 101.67/14.35 | | DELTA: instantiating (177) with fresh symbols all_140_0, all_140_1 gives:
% 101.67/14.35 | | (182) k1_zfmisc_1(all_140_1) = all_140_0 & u1_struct_0(all_85_9) =
% 101.67/14.35 | | all_140_1 & $i(all_140_0) & $i(all_140_1) & ~
% 101.67/14.35 | | m1_subset_1(all_85_6, all_140_0)
% 101.67/14.35 | |
% 101.67/14.35 | | ALPHA: (182) implies:
% 101.67/14.35 | | (183) u1_struct_0(all_85_9) = all_140_1
% 101.67/14.35 | |
% 101.67/14.35 | | BETA: splitting (53) gives:
% 101.67/14.35 | |
% 101.67/14.35 | | Case 1:
% 101.67/14.35 | | |
% 101.67/14.35 | | | (184) ~ m1_subset_1(all_85_4, all_113_0)
% 101.67/14.35 | | |
% 101.67/14.35 | | | REDUCE: (60), (184) imply:
% 101.67/14.35 | | | (185) ~ m1_subset_1(all_85_4, all_85_7)
% 101.67/14.35 | | |
% 101.67/14.35 | | | PRED_UNIFY: (28), (185) imply:
% 101.67/14.35 | | | (186) $false
% 101.67/14.35 | | |
% 101.67/14.35 | | | CLOSE: (186) is inconsistent.
% 101.67/14.35 | | |
% 101.67/14.35 | | Case 2:
% 101.67/14.35 | | |
% 101.67/14.35 | | | (187) ~ m1_subset_1(all_85_6, all_113_0) | m1_subset_1(all_85_3,
% 101.67/14.35 | | | all_113_0)
% 101.67/14.35 | | |
% 101.67/14.35 | | | BETA: splitting (187) gives:
% 101.67/14.35 | | |
% 101.67/14.35 | | | Case 1:
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | (188) ~ m1_subset_1(all_85_6, all_113_0)
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | REDUCE: (60), (188) imply:
% 101.67/14.35 | | | | (189) ~ m1_subset_1(all_85_6, all_85_7)
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | PRED_UNIFY: (27), (189) imply:
% 101.67/14.35 | | | | (190) $false
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | CLOSE: (190) is inconsistent.
% 101.67/14.35 | | | |
% 101.67/14.35 | | | Case 2:
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | (191) m1_subset_1(all_85_6, all_113_0)
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | GROUND_INST: instantiating (3) with all_85_8, all_140_1, all_85_9,
% 101.67/14.35 | | | | simplifying with (38), (183) gives:
% 101.67/14.35 | | | | (192) all_140_1 = all_85_8
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | GROUND_INST: instantiating (3) with all_134_1, all_140_1, all_85_9,
% 101.67/14.35 | | | | simplifying with (180), (183) gives:
% 101.67/14.35 | | | | (193) all_140_1 = all_134_1
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | GROUND_INST: instantiating (4) with all_85_7, all_134_0, all_85_8,
% 101.67/14.35 | | | | simplifying with (39) gives:
% 101.67/14.35 | | | | (194) all_134_0 = all_85_7 | ~ (k1_zfmisc_1(all_85_8) = all_134_0)
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | PRED_UNIFY: (27), (179) imply:
% 101.67/14.35 | | | | (195) ~ (all_134_0 = all_85_7)
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | COMBINE_EQS: (192), (193) imply:
% 101.67/14.35 | | | | (196) all_134_1 = all_85_8
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | REDUCE: (181), (196) imply:
% 101.67/14.35 | | | | (197) k1_zfmisc_1(all_85_8) = all_134_0
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | BETA: splitting (194) gives:
% 101.67/14.35 | | | |
% 101.67/14.35 | | | | Case 1:
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | (198) ~ (k1_zfmisc_1(all_85_8) = all_134_0)
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | PRED_UNIFY: (197), (198) imply:
% 101.67/14.35 | | | | | (199) $false
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | CLOSE: (199) is inconsistent.
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | Case 2:
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | (200) all_134_0 = all_85_7
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | REDUCE: (195), (200) imply:
% 101.67/14.35 | | | | | (201) $false
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | | CLOSE: (201) is inconsistent.
% 101.67/14.35 | | | | |
% 101.67/14.35 | | | | End of split
% 101.67/14.35 | | | |
% 101.67/14.35 | | | End of split
% 101.67/14.35 | | |
% 101.67/14.35 | | End of split
% 101.67/14.35 | |
% 101.67/14.35 | End of split
% 101.67/14.35 |
% 101.67/14.35 End of proof
% 101.67/14.35 % SZS output end Proof for theBenchmark
% 101.67/14.35
% 101.67/14.35 13845ms
%------------------------------------------------------------------------------