TSTP Solution File: GRP641+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : GRP641+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 : n017.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 01:12:46 EDT 2023
% Result : Theorem 13.71s 2.65s
% Output : Proof 23.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP641+1 : TPTP v8.1.2. Released v3.4.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n017.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 : Mon Aug 28 20:56:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.22/0.63 ________ _____
% 0.22/0.63 ___ __ \_________(_)________________________________
% 0.22/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.63
% 0.22/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.63 (2023-06-19)
% 0.22/0.63
% 0.22/0.63 (c) Philipp Rümmer, 2009-2023
% 0.22/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.63 Amanda Stjerna.
% 0.22/0.63 Free software under BSD-3-Clause.
% 0.22/0.63
% 0.22/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.63
% 0.22/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.46/1.23 Prover 4: Preprocessing ...
% 3.46/1.23 Prover 1: Preprocessing ...
% 3.46/1.27 Prover 5: Preprocessing ...
% 3.46/1.27 Prover 3: Preprocessing ...
% 3.46/1.27 Prover 2: Preprocessing ...
% 3.46/1.28 Prover 0: Preprocessing ...
% 3.46/1.28 Prover 6: Preprocessing ...
% 7.86/1.84 Prover 1: Warning: ignoring some quantifiers
% 8.22/1.88 Prover 5: Proving ...
% 8.22/1.92 Prover 3: Warning: ignoring some quantifiers
% 8.22/1.94 Prover 1: Constructing countermodel ...
% 8.22/1.95 Prover 3: Constructing countermodel ...
% 8.22/1.96 Prover 6: Proving ...
% 8.22/2.00 Prover 2: Proving ...
% 13.25/2.57 Prover 4: Warning: ignoring some quantifiers
% 13.71/2.65 Prover 5: proved (2002ms)
% 13.71/2.65
% 13.71/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.71/2.65
% 13.71/2.65 Prover 3: stopped
% 13.71/2.65 Prover 6: stopped
% 13.71/2.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.71/2.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.71/2.65 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.71/2.66 Prover 2: stopped
% 13.71/2.66 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.71/2.66 Prover 4: Constructing countermodel ...
% 13.71/2.71 Prover 0: Proving ...
% 13.71/2.71 Prover 0: stopped
% 14.56/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.69/2.76 Prover 8: Preprocessing ...
% 14.69/2.76 Prover 10: Preprocessing ...
% 14.69/2.78 Prover 7: Preprocessing ...
% 14.69/2.78 Prover 13: Preprocessing ...
% 14.69/2.78 Prover 11: Preprocessing ...
% 15.36/2.85 Prover 10: Warning: ignoring some quantifiers
% 15.36/2.86 Prover 10: Constructing countermodel ...
% 15.90/2.89 Prover 13: Warning: ignoring some quantifiers
% 15.90/2.90 Prover 7: Warning: ignoring some quantifiers
% 15.90/2.90 Prover 13: Constructing countermodel ...
% 15.90/2.91 Prover 7: Constructing countermodel ...
% 15.90/2.91 Prover 8: Warning: ignoring some quantifiers
% 15.90/2.93 Prover 8: Constructing countermodel ...
% 20.67/3.56 Prover 11: Warning: ignoring some quantifiers
% 21.14/3.60 Prover 11: Constructing countermodel ...
% 22.47/3.79 Prover 7: Found proof (size 59)
% 22.47/3.79 Prover 7: proved (1132ms)
% 22.47/3.79 Prover 11: stopped
% 22.47/3.79 Prover 4: stopped
% 22.47/3.79 Prover 8: stopped
% 22.47/3.79 Prover 10: stopped
% 22.47/3.79 Prover 1: stopped
% 22.47/3.79 Prover 13: stopped
% 22.47/3.79
% 22.47/3.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.47/3.79
% 22.47/3.80 % SZS output start Proof for theBenchmark
% 22.47/3.80 Assumptions after simplification:
% 22.47/3.80 ---------------------------------
% 22.47/3.80
% 22.47/3.80 (d1_latsubgr)
% 22.47/3.84 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 22.47/3.84 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) |
% 22.47/3.84 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0) = v2 &
% 22.47/3.84 k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) &
% 22.47/3.84 ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~
% 22.47/3.84 $i(v1) | ~ m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~
% 22.47/3.84 v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) |
% 22.47/3.84 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 22.47/3.84 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~ m2_relset_1(v1, v2,
% 22.47/3.84 v4) | ~ v1_funct_2(v1, v2, v4) | ~ v1_funct_1(v1) | ~
% 22.47/3.84 m1_group_2(v5, v0) | ~ v1_group_1(v5) | (k1_funct_1(v1, v5) = v6 &
% 22.47/3.84 $i(v6))) & ! [v5: $i] : (v5 = v1 | ~ $i(v5) | ~ m2_relset_1(v5, v2,
% 22.47/3.84 v4) | ~ v1_funct_2(v5, v2, v4) | ~ v1_funct_1(v5) | ? [v6: $i] : ?
% 22.47/3.84 [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 &
% 22.47/3.84 u1_struct_0(v6) = v8 & $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) &
% 22.47/3.84 v1_group_1(v6))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_group_3(v0) =
% 22.47/3.84 v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~
% 22.47/3.84 v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 22.47/3.84 (k1_latsubgr(v0) = v4 & k1_zfmisc_1(v2) = v3 & u1_struct_0(v0) = v2 & $i(v4)
% 22.47/3.84 & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) =
% 22.47/3.84 v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~ v1_funct_2(v4, v1,
% 22.47/3.84 v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) |
% 22.47/3.84 (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~
% 22.47/3.84 (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ m2_relset_1(v4, v1, v3) | ~
% 22.47/3.84 v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~
% 22.47/3.84 v1_group_1(v5) | (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5
% 22.47/3.84 = v4 | ~ $i(v5) | ~ m2_relset_1(v5, v1, v3) | ~ v1_funct_2(v5, v1,
% 22.47/3.84 v3) | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (
% 22.47/3.84 ~ (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8)
% 22.47/3.84 & $i(v7) & $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6))))) & ! [v0:
% 22.47/3.84 $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 22.47/3.84 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) |
% 22.47/3.84 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_latsubgr(v0) = v4 &
% 22.47/3.84 k1_group_3(v0) = v2 & k1_zfmisc_1(v1) = v3 & $i(v4) & $i(v3) & $i(v2) & !
% 22.47/3.84 [v5: $i] : ! [v6: $i] : ( ~ (k1_funct_1(v4, v5) = v6) | ~ $i(v5) | ~
% 22.47/3.84 m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~ v1_funct_1(v4)
% 22.47/3.84 | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) | (u1_struct_0(v5) = v6 &
% 22.47/3.84 $i(v6))) & ! [v5: $i] : ! [v6: $i] : ( ~ (u1_struct_0(v5) = v6) | ~
% 22.47/3.84 $i(v5) | ~ m2_relset_1(v4, v2, v3) | ~ v1_funct_2(v4, v2, v3) | ~
% 22.47/3.84 v1_funct_1(v4) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) |
% 22.47/3.84 (k1_funct_1(v4, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v4 | ~ $i(v5)
% 22.47/3.84 | ~ m2_relset_1(v5, v2, v3) | ~ v1_funct_2(v5, v2, v3) | ~
% 22.47/3.84 v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~ (v8 = v7)
% 22.47/3.84 & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 & $i(v8) & $i(v7) &
% 22.47/3.84 $i(v6) & m1_group_2(v6, v0) & v1_group_1(v6)))))
% 22.47/3.84
% 22.47/3.84 (dt_k1_latsubgr)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 22.47/3.85 l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) | v1_funct_1(v1) |
% 22.47/3.85 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) |
% 22.47/3.85 ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 22.47/3.85 v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (k1_group_3(v0)
% 22.47/3.85 = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 & $i(v4) & $i(v3) &
% 22.47/3.85 $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1, v2, v4))) & ! [v0: $i]
% 22.47/3.85 : ! [v1: $i] : ( ~ (k1_group_3(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~
% 22.47/3.85 v4_group_1(v0) | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3:
% 22.47/3.85 $i] : ? [v4: $i] : (k1_latsubgr(v0) = v2 & k1_zfmisc_1(v3) = v4 &
% 22.47/3.85 u1_struct_0(v0) = v3 & $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v1, v4)
% 22.47/3.85 & v1_funct_2(v2, v1, v4) & v1_funct_1(v2))) & ! [v0: $i] : ! [v1: $i] :
% 22.47/3.85 ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0)
% 22.47/3.85 | ~ v3_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4:
% 22.47/3.85 $i] : (k1_latsubgr(v0) = v2 & k1_group_3(v0) = v3 & k1_zfmisc_1(v1) = v4 &
% 22.47/3.85 $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v2, v3, v4) & v1_funct_2(v2, v3,
% 22.47/3.85 v4) & v1_funct_1(v2)))
% 22.47/3.85
% 22.47/3.85 (dt_k2_group_1)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (k2_group_1(v0) = v1) | ~ $i(v0) | ~
% 22.47/3.85 l1_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 &
% 22.47/3.85 $i(v2) & m1_subset_1(v1, v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 22.47/3.85 (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_group_1(v0) | v3_struct_0(v0) |
% 22.47/3.85 ? [v2: $i] : (k2_group_1(v0) = v2 & $i(v2) & m1_subset_1(v2, v1)))
% 22.47/3.85
% 22.47/3.85 (dt_l1_group_1)
% 22.47/3.85 ! [v0: $i] : ( ~ $i(v0) | ~ l1_group_1(v0) | l1_struct_0(v0))
% 22.47/3.85
% 22.47/3.85 (dt_m1_group_2)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) |
% 22.47/3.85 ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) | v3_struct_0(v0))
% 22.47/3.85 & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) |
% 22.47/3.85 ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) | v3_struct_0(v0)) &
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1, v0) | ~
% 22.47/3.85 l1_group_1(v0) | ~ v3_group_1(v0) | v3_group_1(v1) | v3_struct_0(v0))
% 22.47/3.85
% 22.47/3.85 (fc1_struct_0)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 22.47/3.85 l1_struct_0(v0) | ~ v1_xboole_0(v1) | v3_struct_0(v0))
% 22.47/3.85
% 22.47/3.85 (t19_latsubgr)
% 22.47/3.85 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 22.47/3.85 (k2_group_1(v0) = v1 & k1_latsubgr(v0) = v2 & k1_funct_1(v2, v3) = v4 & $i(v4)
% 22.47/3.85 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & m1_group_2(v3, v0) & v1_group_1(v3) &
% 22.47/3.85 l1_group_1(v0) & v4_group_1(v0) & v3_group_1(v0) & ~ r2_hidden(v1, v4) & ~
% 22.47/3.85 v3_struct_0(v0))
% 22.47/3.85
% 22.47/3.85 (t2_subset)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_subset_1(v0, v1) |
% 22.47/3.85 v1_xboole_0(v1) | r2_hidden(v0, v1))
% 22.47/3.85
% 22.47/3.85 (t53_group_2)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 22.47/3.85 (k2_group_1(v2) = v3) | ~ (k2_group_1(v0) = v1) | ~ $i(v2) | ~ $i(v0) |
% 22.47/3.85 ~ m1_group_2(v2, v0) | ~ l1_group_1(v0) | ~ v4_group_1(v0) | ~
% 22.47/3.85 v3_group_1(v0) | v3_struct_0(v0))
% 22.47/3.85
% 22.47/3.85 (function-axioms)
% 22.47/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.47/3.85 (k1_funct_1(v3, v2) = v1) | ~ (k1_funct_1(v3, v2) = v0)) & ! [v0: $i] : !
% 22.47/3.85 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) =
% 22.47/3.85 v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 22.47/3.85 $i] : ! [v3: $i] : (v1 = v0 | ~ (g1_group_1(v3, v2) = v1) | ~
% 22.47/3.85 (g1_group_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 22.47/3.85 v0 | ~ (k2_group_1(v2) = v1) | ~ (k2_group_1(v2) = v0)) & ! [v0: $i] : !
% 22.47/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_latsubgr(v2) = v1) | ~
% 22.47/3.85 (k1_latsubgr(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 22.47/3.85 | ~ (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0)) & ! [v0: $i] : !
% 22.47/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 22.47/3.85 (k1_zfmisc_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 22.47/3.85 | ~ (u1_group_1(v2) = v1) | ~ (u1_group_1(v2) = v0)) & ! [v0: $i] : !
% 22.47/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u1_struct_0(v2) = v1) | ~
% 22.47/3.85 (u1_struct_0(v2) = v0))
% 22.47/3.85
% 22.47/3.85 Further assumptions not needed in the proof:
% 22.47/3.85 --------------------------------------------
% 22.47/3.85 abstractness_v1_group_1, antisymmetry_r2_hidden, cc1_funct_2, cc1_relset_1,
% 22.47/3.85 cc5_funct_2, cc6_funct_2, dt_g1_group_1, dt_k1_funct_1, dt_k1_group_3,
% 22.47/3.85 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_l1_struct_0, dt_m1_relset_1,
% 22.47/3.85 dt_m1_subset_1, dt_m2_relset_1, dt_u1_group_1, dt_u1_struct_0,
% 22.47/3.85 existence_l1_group_1, existence_l1_struct_0, existence_m1_group_2,
% 22.47/3.85 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 22.47/3.85 fc1_group_3, fc1_subset_1, fc1_xboole_0, fc4_subset_1, free_g1_group_1,
% 22.47/3.85 rc1_funct_2, rc1_subset_1, rc1_xboole_0, rc2_partfun1, rc2_subset_1,
% 22.47/3.85 rc2_xboole_0, rc3_struct_0, rc5_struct_0, redefinition_m2_relset_1,
% 22.47/3.85 reflexivity_r1_tarski, t1_subset, t3_subset, t4_subset, t5_subset, t6_boole,
% 22.47/3.85 t7_boole, t8_boole
% 22.47/3.85
% 22.47/3.85 Those formulas are unsatisfiable:
% 22.47/3.85 ---------------------------------
% 22.47/3.85
% 22.47/3.85 Begin of proof
% 22.47/3.86 |
% 22.47/3.86 | ALPHA: (d1_latsubgr) implies:
% 22.47/3.86 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 22.47/3.86 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 22.47/3.86 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 22.47/3.86 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 &
% 22.47/3.86 | $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : ! [v6: $i] : ( ~
% 22.47/3.86 | (k1_funct_1(v1, v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~
% 22.47/3.86 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~
% 22.47/3.86 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) |
% 22.47/3.86 | (u1_struct_0(v5) = v6 & $i(v6))) & ! [v5: $i] : ! [v6: $i] : (
% 22.47/3.86 | ~ (u1_struct_0(v5) = v6) | ~ $i(v5) | ~ $i(v1) | ~
% 22.47/3.86 | m2_relset_1(v1, v2, v4) | ~ v1_funct_2(v1, v2, v4) | ~
% 22.47/3.86 | v1_funct_1(v1) | ~ m1_group_2(v5, v0) | ~ v1_group_1(v5) |
% 22.47/3.86 | (k1_funct_1(v1, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v1 | ~
% 22.47/3.86 | $i(v5) | ~ m2_relset_1(v5, v2, v4) | ~ v1_funct_2(v5, v2, v4) |
% 22.47/3.86 | ~ v1_funct_1(v5) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ( ~
% 22.47/3.86 | (v8 = v7) & k1_funct_1(v5, v6) = v7 & u1_struct_0(v6) = v8 &
% 22.47/3.86 | $i(v8) & $i(v7) & $i(v6) & m1_group_2(v6, v0) &
% 22.47/3.86 | v1_group_1(v6)))))
% 22.47/3.86 |
% 22.47/3.86 | ALPHA: (dt_k1_latsubgr) implies:
% 23.04/3.86 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 23.04/3.86 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 23.04/3.86 | v3_struct_0(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 23.04/3.86 | (k1_group_3(v0) = v2 & k1_zfmisc_1(v3) = v4 & u1_struct_0(v0) = v3 &
% 23.04/3.86 | $i(v4) & $i(v3) & $i(v2) & m2_relset_1(v1, v2, v4) & v1_funct_2(v1,
% 23.04/3.86 | v2, v4)))
% 23.04/3.86 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_latsubgr(v0) = v1) | ~ $i(v0) | ~
% 23.04/3.86 | l1_group_1(v0) | ~ v4_group_1(v0) | ~ v3_group_1(v0) |
% 23.04/3.86 | v1_funct_1(v1) | v3_struct_0(v0))
% 23.04/3.86 |
% 23.04/3.86 | ALPHA: (dt_k2_group_1) implies:
% 23.04/3.86 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 23.04/3.86 | l1_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (k2_group_1(v0) = v2
% 23.04/3.86 | & $i(v2) & m1_subset_1(v2, v1)))
% 23.04/3.86 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (k2_group_1(v0) = v1) | ~ $i(v0) | ~
% 23.04/3.86 | l1_group_1(v0) | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) =
% 23.04/3.86 | v2 & $i(v2) & m1_subset_1(v1, v2)))
% 23.04/3.86 |
% 23.04/3.86 | ALPHA: (dt_m1_group_2) implies:
% 23.04/3.86 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1,
% 23.04/3.86 | v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | l1_group_1(v1) |
% 23.04/3.86 | v3_struct_0(v0))
% 23.04/3.86 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ m1_group_2(v1,
% 23.04/3.86 | v0) | ~ l1_group_1(v0) | ~ v3_group_1(v0) | ~ v3_struct_0(v1) |
% 23.04/3.86 | v3_struct_0(v0))
% 23.04/3.86 |
% 23.04/3.86 | ALPHA: (function-axioms) implies:
% 23.04/3.86 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.04/3.86 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 23.04/3.86 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.04/3.86 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 23.04/3.86 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.04/3.86 | (k1_group_3(v2) = v1) | ~ (k1_group_3(v2) = v0))
% 23.04/3.86 |
% 23.04/3.87 | DELTA: instantiating (t19_latsubgr) with fresh symbols all_53_0, all_53_1,
% 23.04/3.87 | all_53_2, all_53_3, all_53_4 gives:
% 23.04/3.87 | (11) k2_group_1(all_53_4) = all_53_3 & k1_latsubgr(all_53_4) = all_53_2 &
% 23.04/3.87 | k1_funct_1(all_53_2, all_53_1) = all_53_0 & $i(all_53_0) &
% 23.04/3.87 | $i(all_53_1) & $i(all_53_2) & $i(all_53_3) & $i(all_53_4) &
% 23.04/3.87 | m1_group_2(all_53_1, all_53_4) & v1_group_1(all_53_1) &
% 23.04/3.87 | l1_group_1(all_53_4) & v4_group_1(all_53_4) & v3_group_1(all_53_4) &
% 23.04/3.87 | ~ r2_hidden(all_53_3, all_53_0) & ~ v3_struct_0(all_53_4)
% 23.04/3.87 |
% 23.04/3.87 | ALPHA: (11) implies:
% 23.04/3.87 | (12) ~ v3_struct_0(all_53_4)
% 23.04/3.87 | (13) ~ r2_hidden(all_53_3, all_53_0)
% 23.04/3.87 | (14) v3_group_1(all_53_4)
% 23.04/3.87 | (15) v4_group_1(all_53_4)
% 23.04/3.87 | (16) l1_group_1(all_53_4)
% 23.04/3.87 | (17) v1_group_1(all_53_1)
% 23.04/3.87 | (18) m1_group_2(all_53_1, all_53_4)
% 23.04/3.87 | (19) $i(all_53_4)
% 23.04/3.87 | (20) $i(all_53_2)
% 23.04/3.87 | (21) $i(all_53_1)
% 23.04/3.87 | (22) k1_funct_1(all_53_2, all_53_1) = all_53_0
% 23.04/3.87 | (23) k1_latsubgr(all_53_4) = all_53_2
% 23.04/3.87 | (24) k2_group_1(all_53_4) = all_53_3
% 23.04/3.87 |
% 23.04/3.87 | GROUND_INST: instantiating (6) with all_53_4, all_53_1, simplifying with (12),
% 23.04/3.87 | (14), (16), (18), (19), (21) gives:
% 23.04/3.87 | (25) l1_group_1(all_53_1)
% 23.04/3.87 |
% 23.04/3.87 | GROUND_INST: instantiating (3) with all_53_4, all_53_2, simplifying with (12),
% 23.04/3.87 | (14), (15), (16), (19), (23) gives:
% 23.04/3.87 | (26) v1_funct_1(all_53_2)
% 23.04/3.87 |
% 23.04/3.87 | GROUND_INST: instantiating (2) with all_53_4, all_53_2, simplifying with (12),
% 23.04/3.87 | (14), (15), (16), (19), (23) gives:
% 23.04/3.87 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_53_4) = v0 &
% 23.04/3.87 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_53_4) = v1 & $i(v2) & $i(v1)
% 23.04/3.87 | & $i(v0) & m2_relset_1(all_53_2, v0, v2) & v1_funct_2(all_53_2, v0,
% 23.04/3.87 | v2))
% 23.04/3.87 |
% 23.04/3.87 | GROUND_INST: instantiating (1) with all_53_4, all_53_2, simplifying with (12),
% 23.04/3.87 | (14), (15), (16), (19), (23) gives:
% 23.04/3.87 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k1_group_3(all_53_4) = v0 &
% 23.04/3.87 | k1_zfmisc_1(v1) = v2 & u1_struct_0(all_53_4) = v1 & $i(v2) & $i(v1)
% 23.04/3.87 | & $i(v0) & ! [v3: $i] : ! [v4: $i] : ( ~ (k1_funct_1(all_53_2, v3)
% 23.04/3.87 | = v4) | ~ $i(v3) | ~ $i(all_53_2) | ~ m2_relset_1(all_53_2,
% 23.04/3.87 | v0, v2) | ~ v1_funct_2(all_53_2, v0, v2) | ~
% 23.04/3.87 | v1_funct_1(all_53_2) | ~ m1_group_2(v3, all_53_4) | ~
% 23.04/3.87 | v1_group_1(v3) | (u1_struct_0(v3) = v4 & $i(v4))) & ! [v3: $i] :
% 23.04/3.87 | ! [v4: $i] : ( ~ (u1_struct_0(v3) = v4) | ~ $i(v3) | ~
% 23.04/3.87 | $i(all_53_2) | ~ m2_relset_1(all_53_2, v0, v2) | ~
% 23.04/3.87 | v1_funct_2(all_53_2, v0, v2) | ~ v1_funct_1(all_53_2) | ~
% 23.04/3.87 | m1_group_2(v3, all_53_4) | ~ v1_group_1(v3) |
% 23.04/3.87 | (k1_funct_1(all_53_2, v3) = v4 & $i(v4))) & ! [v3: any] : (v3 =
% 23.04/3.87 | all_53_2 | ~ $i(v3) | ~ m2_relset_1(v3, v0, v2) | ~
% 23.04/3.87 | v1_funct_2(v3, v0, v2) | ~ v1_funct_1(v3) | ? [v4: $i] : ? [v5:
% 23.04/3.87 | $i] : ? [v6: $i] : ( ~ (v6 = v5) & k1_funct_1(v3, v4) = v5 &
% 23.04/3.87 | u1_struct_0(v4) = v6 & $i(v6) & $i(v5) & $i(v4) & m1_group_2(v4,
% 23.04/3.87 | all_53_4) & v1_group_1(v4))))
% 23.04/3.87 |
% 23.04/3.87 | GROUND_INST: instantiating (5) with all_53_4, all_53_3, simplifying with (12),
% 23.04/3.87 | (16), (19), (24) gives:
% 23.04/3.87 | (29) ? [v0: $i] : (u1_struct_0(all_53_4) = v0 & $i(v0) &
% 23.04/3.87 | m1_subset_1(all_53_3, v0))
% 23.04/3.87 |
% 23.04/3.87 | DELTA: instantiating (29) with fresh symbol all_67_0 gives:
% 23.04/3.87 | (30) u1_struct_0(all_53_4) = all_67_0 & $i(all_67_0) &
% 23.04/3.87 | m1_subset_1(all_53_3, all_67_0)
% 23.04/3.87 |
% 23.04/3.87 | ALPHA: (30) implies:
% 23.04/3.88 | (31) u1_struct_0(all_53_4) = all_67_0
% 23.04/3.88 |
% 23.04/3.88 | DELTA: instantiating (27) with fresh symbols all_69_0, all_69_1, all_69_2
% 23.04/3.88 | gives:
% 23.04/3.88 | (32) k1_group_3(all_53_4) = all_69_2 & k1_zfmisc_1(all_69_1) = all_69_0 &
% 23.04/3.88 | u1_struct_0(all_53_4) = all_69_1 & $i(all_69_0) & $i(all_69_1) &
% 23.04/3.88 | $i(all_69_2) & m2_relset_1(all_53_2, all_69_2, all_69_0) &
% 23.04/3.88 | v1_funct_2(all_53_2, all_69_2, all_69_0)
% 23.04/3.88 |
% 23.04/3.88 | ALPHA: (32) implies:
% 23.04/3.88 | (33) v1_funct_2(all_53_2, all_69_2, all_69_0)
% 23.04/3.88 | (34) m2_relset_1(all_53_2, all_69_2, all_69_0)
% 23.04/3.88 | (35) u1_struct_0(all_53_4) = all_69_1
% 23.04/3.88 | (36) k1_zfmisc_1(all_69_1) = all_69_0
% 23.04/3.88 | (37) k1_group_3(all_53_4) = all_69_2
% 23.04/3.88 |
% 23.04/3.88 | DELTA: instantiating (28) with fresh symbols all_71_0, all_71_1, all_71_2
% 23.04/3.88 | gives:
% 23.04/3.88 | (38) k1_group_3(all_53_4) = all_71_2 & k1_zfmisc_1(all_71_1) = all_71_0 &
% 23.04/3.88 | u1_struct_0(all_53_4) = all_71_1 & $i(all_71_0) & $i(all_71_1) &
% 23.04/3.88 | $i(all_71_2) & ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_53_2,
% 23.04/3.88 | v0) = v1) | ~ $i(v0) | ~ $i(all_53_2) | ~
% 23.04/3.88 | m2_relset_1(all_53_2, all_71_2, all_71_0) | ~ v1_funct_2(all_53_2,
% 23.04/3.88 | all_71_2, all_71_0) | ~ v1_funct_1(all_53_2) | ~ m1_group_2(v0,
% 23.04/3.88 | all_53_4) | ~ v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1))) &
% 23.04/3.88 | ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) |
% 23.04/3.88 | ~ $i(all_53_2) | ~ m2_relset_1(all_53_2, all_71_2, all_71_0) | ~
% 23.04/3.88 | v1_funct_2(all_53_2, all_71_2, all_71_0) | ~ v1_funct_1(all_53_2) |
% 23.04/3.88 | ~ m1_group_2(v0, all_53_4) | ~ v1_group_1(v0) |
% 23.04/3.88 | (k1_funct_1(all_53_2, v0) = v1 & $i(v1))) & ! [v0: any] : (v0 =
% 23.04/3.88 | all_53_2 | ~ $i(v0) | ~ m2_relset_1(v0, all_71_2, all_71_0) | ~
% 23.04/3.88 | v1_funct_2(v0, all_71_2, all_71_0) | ~ v1_funct_1(v0) | ? [v1: $i]
% 23.04/3.88 | : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2) & k1_funct_1(v0, v1) =
% 23.04/3.88 | v2 & u1_struct_0(v1) = v3 & $i(v3) & $i(v2) & $i(v1) &
% 23.04/3.88 | m1_group_2(v1, all_53_4) & v1_group_1(v1)))
% 23.04/3.88 |
% 23.04/3.88 | ALPHA: (38) implies:
% 23.04/3.88 | (39) u1_struct_0(all_53_4) = all_71_1
% 23.04/3.88 | (40) k1_zfmisc_1(all_71_1) = all_71_0
% 23.04/3.88 | (41) k1_group_3(all_53_4) = all_71_2
% 23.04/3.88 | (42) ! [v0: $i] : ! [v1: $i] : ( ~ (k1_funct_1(all_53_2, v0) = v1) | ~
% 23.04/3.88 | $i(v0) | ~ $i(all_53_2) | ~ m2_relset_1(all_53_2, all_71_2,
% 23.04/3.88 | all_71_0) | ~ v1_funct_2(all_53_2, all_71_2, all_71_0) | ~
% 23.04/3.88 | v1_funct_1(all_53_2) | ~ m1_group_2(v0, all_53_4) | ~
% 23.04/3.88 | v1_group_1(v0) | (u1_struct_0(v0) = v1 & $i(v1)))
% 23.04/3.88 |
% 23.04/3.88 | GROUND_INST: instantiating (8) with all_69_1, all_71_1, all_53_4, simplifying
% 23.04/3.88 | with (35), (39) gives:
% 23.04/3.88 | (43) all_71_1 = all_69_1
% 23.04/3.88 |
% 23.04/3.88 | GROUND_INST: instantiating (8) with all_67_0, all_71_1, all_53_4, simplifying
% 23.04/3.88 | with (31), (39) gives:
% 23.04/3.88 | (44) all_71_1 = all_67_0
% 23.04/3.88 |
% 23.04/3.88 | GROUND_INST: instantiating (9) with all_69_0, all_71_0, all_69_1, simplifying
% 23.04/3.88 | with (36) gives:
% 23.04/3.88 | (45) all_71_0 = all_69_0 | ~ (k1_zfmisc_1(all_69_1) = all_71_0)
% 23.04/3.88 |
% 23.04/3.88 | GROUND_INST: instantiating (10) with all_69_2, all_71_2, all_53_4, simplifying
% 23.04/3.88 | with (37), (41) gives:
% 23.04/3.88 | (46) all_71_2 = all_69_2
% 23.04/3.88 |
% 23.04/3.88 | COMBINE_EQS: (43), (44) imply:
% 23.04/3.88 | (47) all_69_1 = all_67_0
% 23.04/3.88 |
% 23.04/3.88 | SIMP: (47) implies:
% 23.04/3.88 | (48) all_69_1 = all_67_0
% 23.04/3.88 |
% 23.04/3.88 | REDUCE: (40), (44) imply:
% 23.04/3.88 | (49) k1_zfmisc_1(all_67_0) = all_71_0
% 23.04/3.88 |
% 23.04/3.88 | BETA: splitting (45) gives:
% 23.04/3.88 |
% 23.04/3.88 | Case 1:
% 23.04/3.88 | |
% 23.04/3.88 | | (50) ~ (k1_zfmisc_1(all_69_1) = all_71_0)
% 23.04/3.88 | |
% 23.04/3.88 | | REDUCE: (48), (50) imply:
% 23.04/3.88 | | (51) ~ (k1_zfmisc_1(all_67_0) = all_71_0)
% 23.04/3.88 | |
% 23.04/3.88 | | PRED_UNIFY: (49), (51) imply:
% 23.04/3.88 | | (52) $false
% 23.04/3.88 | |
% 23.04/3.88 | | CLOSE: (52) is inconsistent.
% 23.04/3.88 | |
% 23.04/3.88 | Case 2:
% 23.04/3.88 | |
% 23.04/3.89 | | (53) all_71_0 = all_69_0
% 23.04/3.89 | |
% 23.04/3.89 | | GROUND_INST: instantiating (dt_l1_group_1) with all_53_1, simplifying with
% 23.04/3.89 | | (21), (25) gives:
% 23.04/3.89 | | (54) l1_struct_0(all_53_1)
% 23.04/3.89 | |
% 23.04/3.89 | | GROUND_INST: instantiating (42) with all_53_1, all_53_0, simplifying with
% 23.04/3.89 | | (17), (18), (20), (21), (22), (26) gives:
% 23.04/3.89 | | (55) ~ m2_relset_1(all_53_2, all_71_2, all_71_0) | ~
% 23.04/3.89 | | v1_funct_2(all_53_2, all_71_2, all_71_0) | (u1_struct_0(all_53_1) =
% 23.04/3.89 | | all_53_0 & $i(all_53_0))
% 23.04/3.89 | |
% 23.04/3.89 | | BETA: splitting (55) gives:
% 23.04/3.89 | |
% 23.04/3.89 | | Case 1:
% 23.04/3.89 | | |
% 23.04/3.89 | | | (56) ~ m2_relset_1(all_53_2, all_71_2, all_71_0)
% 23.04/3.89 | | |
% 23.04/3.89 | | | REDUCE: (46), (53), (56) imply:
% 23.04/3.89 | | | (57) ~ m2_relset_1(all_53_2, all_69_2, all_69_0)
% 23.04/3.89 | | |
% 23.04/3.89 | | | PRED_UNIFY: (34), (57) imply:
% 23.04/3.89 | | | (58) $false
% 23.04/3.89 | | |
% 23.04/3.89 | | | CLOSE: (58) is inconsistent.
% 23.04/3.89 | | |
% 23.04/3.89 | | Case 2:
% 23.04/3.89 | | |
% 23.04/3.89 | | | (59) ~ v1_funct_2(all_53_2, all_71_2, all_71_0) |
% 23.04/3.89 | | | (u1_struct_0(all_53_1) = all_53_0 & $i(all_53_0))
% 23.04/3.89 | | |
% 23.04/3.89 | | | BETA: splitting (59) gives:
% 23.04/3.89 | | |
% 23.04/3.89 | | | Case 1:
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | (60) ~ v1_funct_2(all_53_2, all_71_2, all_71_0)
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | REDUCE: (46), (53), (60) imply:
% 23.04/3.89 | | | | (61) ~ v1_funct_2(all_53_2, all_69_2, all_69_0)
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | PRED_UNIFY: (33), (61) imply:
% 23.04/3.89 | | | | (62) $false
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | CLOSE: (62) is inconsistent.
% 23.04/3.89 | | | |
% 23.04/3.89 | | | Case 2:
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | (63) u1_struct_0(all_53_1) = all_53_0 & $i(all_53_0)
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | ALPHA: (63) implies:
% 23.04/3.89 | | | | (64) $i(all_53_0)
% 23.04/3.89 | | | | (65) u1_struct_0(all_53_1) = all_53_0
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | GROUND_INST: instantiating (fc1_struct_0) with all_53_1, all_53_0,
% 23.04/3.89 | | | | simplifying with (21), (54), (65) gives:
% 23.04/3.89 | | | | (66) ~ v1_xboole_0(all_53_0) | v3_struct_0(all_53_1)
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | GROUND_INST: instantiating (4) with all_53_1, all_53_0, simplifying with
% 23.04/3.89 | | | | (21), (25), (65) gives:
% 23.04/3.89 | | | | (67) v3_struct_0(all_53_1) | ? [v0: $i] : (k2_group_1(all_53_1) = v0
% 23.04/3.89 | | | | & $i(v0) & m1_subset_1(v0, all_53_0))
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | BETA: splitting (66) gives:
% 23.04/3.89 | | | |
% 23.04/3.89 | | | | Case 1:
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | | (68) ~ v1_xboole_0(all_53_0)
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | | BETA: splitting (67) gives:
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | | Case 1:
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | (69) v3_struct_0(all_53_1)
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | GROUND_INST: instantiating (7) with all_53_4, all_53_1, simplifying
% 23.04/3.89 | | | | | | with (12), (14), (16), (18), (19), (21), (69) gives:
% 23.04/3.89 | | | | | | (70) $false
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | CLOSE: (70) is inconsistent.
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | Case 2:
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | (71) ? [v0: $i] : (k2_group_1(all_53_1) = v0 & $i(v0) &
% 23.04/3.89 | | | | | | m1_subset_1(v0, all_53_0))
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | DELTA: instantiating (71) with fresh symbol all_275_0 gives:
% 23.04/3.89 | | | | | | (72) k2_group_1(all_53_1) = all_275_0 & $i(all_275_0) &
% 23.04/3.89 | | | | | | m1_subset_1(all_275_0, all_53_0)
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | ALPHA: (72) implies:
% 23.04/3.89 | | | | | | (73) m1_subset_1(all_275_0, all_53_0)
% 23.04/3.89 | | | | | | (74) $i(all_275_0)
% 23.04/3.89 | | | | | | (75) k2_group_1(all_53_1) = all_275_0
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | GROUND_INST: instantiating (t2_subset) with all_275_0, all_53_0,
% 23.04/3.89 | | | | | | simplifying with (64), (68), (73), (74) gives:
% 23.04/3.89 | | | | | | (76) r2_hidden(all_275_0, all_53_0)
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | GROUND_INST: instantiating (t53_group_2) with all_53_4, all_53_3,
% 23.04/3.89 | | | | | | all_53_1, all_275_0, simplifying with (12), (14), (15),
% 23.04/3.89 | | | | | | (16), (18), (19), (21), (24), (75) gives:
% 23.04/3.89 | | | | | | (77) all_275_0 = all_53_3
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | REDUCE: (76), (77) imply:
% 23.04/3.89 | | | | | | (78) r2_hidden(all_53_3, all_53_0)
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | PRED_UNIFY: (13), (78) imply:
% 23.04/3.89 | | | | | | (79) $false
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | | CLOSE: (79) is inconsistent.
% 23.04/3.89 | | | | | |
% 23.04/3.89 | | | | | End of split
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | Case 2:
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | | (80) v3_struct_0(all_53_1)
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | | GROUND_INST: instantiating (7) with all_53_4, all_53_1, simplifying
% 23.04/3.89 | | | | | with (12), (14), (16), (18), (19), (21), (80) gives:
% 23.04/3.89 | | | | | (81) $false
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | | CLOSE: (81) is inconsistent.
% 23.04/3.89 | | | | |
% 23.04/3.89 | | | | End of split
% 23.04/3.89 | | | |
% 23.04/3.89 | | | End of split
% 23.04/3.89 | | |
% 23.04/3.89 | | End of split
% 23.04/3.89 | |
% 23.04/3.89 | End of split
% 23.04/3.89 |
% 23.04/3.89 End of proof
% 23.04/3.89 % SZS output end Proof for theBenchmark
% 23.04/3.89
% 23.04/3.89 3266ms
%------------------------------------------------------------------------------