TSTP Solution File: CAT032+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : CAT032+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 : n006.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 18:18:26 EDT 2023
% Result : Theorem 68.04s 9.71s
% Output : Proof 68.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT032+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 00:40:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.34/1.18 Prover 1: Preprocessing ...
% 3.34/1.18 Prover 4: Preprocessing ...
% 3.34/1.22 Prover 3: Preprocessing ...
% 3.34/1.22 Prover 0: Preprocessing ...
% 3.34/1.22 Prover 6: Preprocessing ...
% 3.34/1.22 Prover 5: Preprocessing ...
% 3.34/1.22 Prover 2: Preprocessing ...
% 8.28/1.91 Prover 1: Warning: ignoring some quantifiers
% 8.28/1.92 Prover 5: Proving ...
% 8.97/1.98 Prover 1: Constructing countermodel ...
% 8.97/1.98 Prover 6: Proving ...
% 8.97/1.99 Prover 3: Warning: ignoring some quantifiers
% 8.97/2.02 Prover 3: Constructing countermodel ...
% 9.68/2.13 Prover 2: Proving ...
% 13.10/2.51 Prover 4: Warning: ignoring some quantifiers
% 13.42/2.61 Prover 4: Constructing countermodel ...
% 13.42/2.68 Prover 0: Proving ...
% 14.45/2.77 Prover 3: gave up
% 14.45/2.78 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.09/2.83 Prover 7: Preprocessing ...
% 16.34/3.01 Prover 7: Warning: ignoring some quantifiers
% 17.05/3.05 Prover 7: Constructing countermodel ...
% 65.96/9.44 Prover 2: stopped
% 65.96/9.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 65.96/9.53 Prover 8: Preprocessing ...
% 66.69/9.62 Prover 8: Warning: ignoring some quantifiers
% 66.69/9.63 Prover 8: Constructing countermodel ...
% 68.04/9.71 Prover 7: Found proof (size 73)
% 68.04/9.71 Prover 7: proved (6915ms)
% 68.04/9.71 Prover 0: stopped
% 68.04/9.71 Prover 5: stopped
% 68.04/9.71 Prover 6: stopped
% 68.04/9.71 Prover 8: stopped
% 68.04/9.71 Prover 1: stopped
% 68.04/9.71 Prover 4: stopped
% 68.04/9.71
% 68.04/9.71 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.04/9.71
% 68.04/9.72 % SZS output start Proof for theBenchmark
% 68.11/9.73 Assumptions after simplification:
% 68.11/9.73 ---------------------------------
% 68.11/9.73
% 68.11/9.73 (d4_isocat_1)
% 68.11/9.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 68.11/9.73 ~ v8_cat_1(v2, v0, v1) | ~ m2_cat_1(v2, v0, v1) | ~ l1_cat_1(v1) | ~
% 68.11/9.73 l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | r1_isocat_1(v0, v1)) & !
% 68.11/9.73 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ r1_isocat_1(v0, v1) | ~
% 68.11/9.73 l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v2:
% 68.11/9.73 $i] : ($i(v2) & v8_cat_1(v2, v0, v1) & m2_cat_1(v2, v0, v1)))
% 68.11/9.73
% 68.11/9.73 (dt_k11_cat_2)
% 68.11/9.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k11_cat_2(v0, v1) = v2) | ~
% 68.11/9.76 $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) |
% 68.11/9.76 ~ v2_cat_1(v0) | l1_cat_1(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 68.11/9.76 ~ (k11_cat_2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~
% 68.11/9.76 l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2))
% 68.11/9.76
% 68.11/9.76 (dt_k12_nattra_1)
% 68.11/9.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~
% 68.11/9.76 $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) |
% 68.11/9.76 ~ v2_cat_1(v0) | v1_cat_1(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 68.11/9.76 ~ (k12_nattra_1(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~
% 68.11/9.76 l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2)) & ! [v0:
% 68.11/9.76 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k12_nattra_1(v0, v1) = v2) | ~
% 68.11/9.76 $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) |
% 68.11/9.76 ~ v2_cat_1(v0) | v2_cat_1(v2))
% 68.11/9.76
% 68.11/9.76 (dt_k17_isocat_2)
% 68.11/9.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 68.11/9.77 $i] : ( ~ (k12_nattra_1(v0, v2) = v4) | ~ (k12_nattra_1(v0, v1) = v3) | ~
% 68.11/9.77 (k11_cat_2(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 68.11/9.77 l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~
% 68.11/9.77 v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 68.11/9.77 (k17_isocat_2(v0, v1, v2) = v6 & k12_nattra_1(v0, v7) = v8 & k11_cat_2(v1,
% 68.11/9.77 v2) = v7 & $i(v8) & $i(v7) & $i(v6) & m2_cat_1(v6, v8, v5))) & ! [v0:
% 68.11/9.77 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 68.11/9.77 (k12_nattra_1(v0, v3) = v4) | ~ (k11_cat_2(v1, v2) = v3) | ~ $i(v2) | ~
% 68.11/9.77 $i(v1) | ~ $i(v0) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) |
% 68.11/9.77 ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5: $i] : ? [v6:
% 68.11/9.77 $i] : ? [v7: $i] : ? [v8: $i] : (k17_isocat_2(v0, v1, v2) = v5 &
% 68.11/9.77 k12_nattra_1(v0, v2) = v7 & k12_nattra_1(v0, v1) = v6 & k11_cat_2(v6, v7)
% 68.11/9.77 = v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & m2_cat_1(v5, v4, v8))) & !
% 68.11/9.77 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k17_isocat_2(v0, v1,
% 68.11/9.77 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v2) | ~
% 68.11/9.77 l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~
% 68.11/9.77 v2_cat_1(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 68.11/9.77 [v8: $i] : (k12_nattra_1(v0, v4) = v5 & k12_nattra_1(v0, v2) = v7 &
% 68.11/9.77 k12_nattra_1(v0, v1) = v6 & k11_cat_2(v6, v7) = v8 & k11_cat_2(v1, v2) =
% 68.11/9.77 v4 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & m2_cat_1(v3, v5, v8)))
% 68.11/9.77
% 68.11/9.77 (t48_isocat_2)
% 68.11/9.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 68.11/9.77 (k17_isocat_2(v0, v1, v3) = v4) | ~ (k12_nattra_1(v0, v1) = v2) | ~ $i(v3)
% 68.11/9.77 | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~
% 68.11/9.77 l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5:
% 68.11/9.77 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (k12_nattra_1(v0, v5) = v6
% 68.11/9.77 & k12_nattra_1(v0, v3) = v7 & k11_cat_2(v2, v7) = v8 & k11_cat_2(v1, v3) =
% 68.11/9.77 v5 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & v8_cat_1(v4, v6, v8))) & ! [v0:
% 68.11/9.77 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 68.11/9.77 (k12_nattra_1(v0, v3) = v4) | ~ (k12_nattra_1(v0, v1) = v2) | ~ $i(v3) |
% 68.11/9.77 ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) |
% 68.11/9.77 ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5: $i] : ? [v6:
% 68.11/9.77 $i] : ? [v7: $i] : ? [v8: $i] : (k17_isocat_2(v0, v1, v3) = v5 &
% 68.11/9.77 k12_nattra_1(v0, v6) = v7 & k11_cat_2(v2, v4) = v8 & k11_cat_2(v1, v3) =
% 68.11/9.77 v6 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & v8_cat_1(v5, v7, v8))) & ! [v0:
% 68.11/9.77 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 68.11/9.77 (k12_nattra_1(v0, v1) = v2) | ~ (k11_cat_2(v1, v3) = v4) | ~ $i(v3) | ~
% 68.11/9.77 $i(v1) | ~ $i(v0) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) |
% 68.11/9.77 ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v5: $i] : ? [v6:
% 68.11/9.77 $i] : ? [v7: $i] : ? [v8: $i] : (k17_isocat_2(v0, v1, v3) = v5 &
% 68.11/9.77 k12_nattra_1(v0, v4) = v6 & k12_nattra_1(v0, v3) = v7 & k11_cat_2(v2, v7)
% 68.11/9.77 = v8 & $i(v8) & $i(v7) & $i(v6) & $i(v5) & v8_cat_1(v5, v6, v8)))
% 68.11/9.77
% 68.11/9.77 (t49_isocat_2)
% 68.11/9.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 68.11/9.77 $i] : ? [v6: $i] : ? [v7: $i] : (k12_nattra_1(v0, v4) = v5 &
% 68.11/9.77 k12_nattra_1(v0, v3) = v6 & k12_nattra_1(v0, v1) = v2 & k11_cat_2(v2, v6) =
% 68.11/9.77 v7 & k11_cat_2(v1, v3) = v4 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) &
% 68.11/9.77 $i(v2) & $i(v1) & $i(v0) & l1_cat_1(v3) & l1_cat_1(v1) & l1_cat_1(v0) &
% 68.11/9.77 v2_cat_1(v3) & v2_cat_1(v1) & v2_cat_1(v0) & ~ r1_isocat_1(v5, v7))
% 68.11/9.77
% 68.11/9.77 (function-axioms)
% 68.11/9.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 68.11/9.78 $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | ~ (g1_cat_1(v7, v6, v5, v4,
% 68.11/9.78 v3, v2) = v1) | ~ (g1_cat_1(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 68.11/9.78 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 68.11/9.78 (k17_isocat_2(v4, v3, v2) = v1) | ~ (k17_isocat_2(v4, v3, v2) = v0)) & !
% 68.11/9.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 68.11/9.78 (k12_nattra_1(v3, v2) = v1) | ~ (k12_nattra_1(v3, v2) = v0)) & ! [v0: $i]
% 68.11/9.78 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k11_cat_2(v3, v2) =
% 68.11/9.78 v1) | ~ (k11_cat_2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 68.11/9.78 $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~
% 68.11/9.78 (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 68.11/9.78 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0: $i]
% 68.11/9.78 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u6_cat_1(v2) = v1) | ~
% 68.11/9.78 (u6_cat_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 68.11/9.78 ~ (u1_cat_1(v2) = v1) | ~ (u1_cat_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 68.11/9.78 : ! [v2: $i] : (v1 = v0 | ~ (u2_cat_1(v2) = v1) | ~ (u2_cat_1(v2) = v0)) &
% 68.11/9.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (u3_cat_1(v2) = v1) |
% 68.11/9.78 ~ (u3_cat_1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 68.11/9.78 | ~ (u4_cat_1(v2) = v1) | ~ (u4_cat_1(v2) = v0)) & ! [v0: $i] : ! [v1:
% 68.11/9.78 $i] : ! [v2: $i] : (v1 = v0 | ~ (u5_cat_1(v2) = v1) | ~ (u5_cat_1(v2) =
% 68.11/9.78 v0))
% 68.11/9.78
% 68.11/9.78 Further assumptions not needed in the proof:
% 68.11/9.78 --------------------------------------------
% 68.11/9.78 abstractness_v1_cat_1, antisymmetry_r2_hidden, cc1_relset_1, dt_g1_cat_1,
% 68.11/9.78 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_l1_cat_1, dt_m1_relset_1,
% 68.11/9.78 dt_m1_subset_1, dt_m2_cat_1, dt_m2_relset_1, dt_u1_cat_1, dt_u2_cat_1,
% 68.11/9.78 dt_u3_cat_1, dt_u4_cat_1, dt_u5_cat_1, dt_u6_cat_1, existence_l1_cat_1,
% 68.11/9.78 existence_m1_relset_1, existence_m1_subset_1, existence_m2_cat_1,
% 68.11/9.78 existence_m2_relset_1, fc1_subset_1, fc1_xboole_0, fc4_subset_1, free_g1_cat_1,
% 68.11/9.78 rc1_subset_1, rc1_xboole_0, rc2_subset_1, rc2_xboole_0,
% 68.11/9.78 redefinition_m2_relset_1, reflexivity_r1_isocat_1, reflexivity_r1_tarski,
% 68.11/9.78 symmetry_r1_isocat_1, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 68.11/9.78 t6_boole, t7_boole, t8_boole
% 68.11/9.78
% 68.11/9.78 Those formulas are unsatisfiable:
% 68.11/9.78 ---------------------------------
% 68.11/9.78
% 68.11/9.78 Begin of proof
% 68.11/9.78 |
% 68.11/9.78 | ALPHA: (d4_isocat_1) implies:
% 68.11/9.78 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 68.11/9.78 | $i(v0) | ~ v8_cat_1(v2, v0, v1) | ~ m2_cat_1(v2, v0, v1) | ~
% 68.11/9.78 | l1_cat_1(v1) | ~ l1_cat_1(v0) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) |
% 68.11/9.78 | r1_isocat_1(v0, v1))
% 68.11/9.78 |
% 68.11/9.78 | ALPHA: (dt_k11_cat_2) implies:
% 68.11/9.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k11_cat_2(v0, v1) = v2)
% 68.11/9.78 | | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~
% 68.11/9.78 | v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2))
% 68.11/9.78 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k11_cat_2(v0, v1) = v2)
% 68.11/9.78 | | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~
% 68.11/9.78 | v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2))
% 68.11/9.78 |
% 68.11/9.78 | ALPHA: (dt_k12_nattra_1) implies:
% 68.11/9.78 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k12_nattra_1(v0, v1) =
% 68.11/9.78 | v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) |
% 68.11/9.78 | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | v2_cat_1(v2))
% 68.11/9.79 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (k12_nattra_1(v0, v1) =
% 68.11/9.79 | v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) |
% 68.11/9.79 | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | l1_cat_1(v2))
% 68.11/9.79 |
% 68.11/9.79 | ALPHA: (dt_k17_isocat_2) implies:
% 68.11/9.79 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 68.11/9.79 | ~ (k12_nattra_1(v0, v3) = v4) | ~ (k11_cat_2(v1, v2) = v3) | ~
% 68.11/9.79 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) |
% 68.11/9.79 | ~ l1_cat_1(v0) | ~ v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0)
% 68.11/9.79 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 68.11/9.79 | (k17_isocat_2(v0, v1, v2) = v5 & k12_nattra_1(v0, v2) = v7 &
% 68.11/9.79 | k12_nattra_1(v0, v1) = v6 & k11_cat_2(v6, v7) = v8 & $i(v8) &
% 68.11/9.79 | $i(v7) & $i(v6) & $i(v5) & m2_cat_1(v5, v4, v8)))
% 68.11/9.79 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 68.11/9.79 | ! [v5: $i] : ( ~ (k12_nattra_1(v0, v2) = v4) | ~ (k12_nattra_1(v0, v1)
% 68.11/9.79 | = v3) | ~ (k11_cat_2(v3, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~
% 68.11/9.79 | $i(v0) | ~ l1_cat_1(v2) | ~ l1_cat_1(v1) | ~ l1_cat_1(v0) | ~
% 68.11/9.79 | v2_cat_1(v2) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0) | ? [v6: $i] : ?
% 68.11/9.79 | [v7: $i] : ? [v8: $i] : (k17_isocat_2(v0, v1, v2) = v6 &
% 68.11/9.79 | k12_nattra_1(v0, v7) = v8 & k11_cat_2(v1, v2) = v7 & $i(v8) &
% 68.11/9.79 | $i(v7) & $i(v6) & m2_cat_1(v6, v8, v5)))
% 68.11/9.79 |
% 68.11/9.79 | ALPHA: (t48_isocat_2) implies:
% 68.11/9.79 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 68.11/9.79 | ~ (k12_nattra_1(v0, v1) = v2) | ~ (k11_cat_2(v1, v3) = v4) | ~
% 68.11/9.79 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) |
% 68.11/9.79 | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0)
% 68.11/9.79 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 68.11/9.79 | (k17_isocat_2(v0, v1, v3) = v5 & k12_nattra_1(v0, v4) = v6 &
% 68.11/9.79 | k12_nattra_1(v0, v3) = v7 & k11_cat_2(v2, v7) = v8 & $i(v8) &
% 68.11/9.79 | $i(v7) & $i(v6) & $i(v5) & v8_cat_1(v5, v6, v8)))
% 68.11/9.79 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 68.11/9.79 | ~ (k12_nattra_1(v0, v3) = v4) | ~ (k12_nattra_1(v0, v1) = v2) | ~
% 68.11/9.79 | $i(v3) | ~ $i(v1) | ~ $i(v0) | ~ l1_cat_1(v3) | ~ l1_cat_1(v1) |
% 68.11/9.79 | ~ l1_cat_1(v0) | ~ v2_cat_1(v3) | ~ v2_cat_1(v1) | ~ v2_cat_1(v0)
% 68.11/9.79 | | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 68.11/9.79 | (k17_isocat_2(v0, v1, v3) = v5 & k12_nattra_1(v0, v6) = v7 &
% 68.11/9.79 | k11_cat_2(v2, v4) = v8 & k11_cat_2(v1, v3) = v6 & $i(v8) & $i(v7) &
% 68.11/9.79 | $i(v6) & $i(v5) & v8_cat_1(v5, v7, v8)))
% 68.11/9.79 |
% 68.11/9.79 | ALPHA: (function-axioms) implies:
% 68.11/9.79 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 68.11/9.79 | (k11_cat_2(v3, v2) = v1) | ~ (k11_cat_2(v3, v2) = v0))
% 68.11/9.79 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 68.11/9.79 | (k12_nattra_1(v3, v2) = v1) | ~ (k12_nattra_1(v3, v2) = v0))
% 68.11/9.79 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 68.11/9.79 | (v1 = v0 | ~ (k17_isocat_2(v4, v3, v2) = v1) | ~ (k17_isocat_2(v4,
% 68.11/9.79 | v3, v2) = v0))
% 68.11/9.80 |
% 68.11/9.80 | DELTA: instantiating (t49_isocat_2) with fresh symbols all_48_0, all_48_1,
% 68.11/9.80 | all_48_2, all_48_3, all_48_4, all_48_5, all_48_6, all_48_7 gives:
% 68.11/9.80 | (13) k12_nattra_1(all_48_7, all_48_3) = all_48_2 & k12_nattra_1(all_48_7,
% 68.11/9.80 | all_48_4) = all_48_1 & k12_nattra_1(all_48_7, all_48_6) = all_48_5 &
% 68.11/9.80 | k11_cat_2(all_48_5, all_48_1) = all_48_0 & k11_cat_2(all_48_6,
% 68.11/9.80 | all_48_4) = all_48_3 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) &
% 68.11/9.80 | $i(all_48_3) & $i(all_48_4) & $i(all_48_5) & $i(all_48_6) &
% 68.11/9.80 | $i(all_48_7) & l1_cat_1(all_48_4) & l1_cat_1(all_48_6) &
% 68.11/9.80 | l1_cat_1(all_48_7) & v2_cat_1(all_48_4) & v2_cat_1(all_48_6) &
% 68.11/9.80 | v2_cat_1(all_48_7) & ~ r1_isocat_1(all_48_2, all_48_0)
% 68.11/9.80 |
% 68.11/9.80 | ALPHA: (13) implies:
% 68.11/9.80 | (14) ~ r1_isocat_1(all_48_2, all_48_0)
% 68.11/9.80 | (15) v2_cat_1(all_48_7)
% 68.11/9.80 | (16) v2_cat_1(all_48_6)
% 68.11/9.80 | (17) v2_cat_1(all_48_4)
% 68.11/9.80 | (18) l1_cat_1(all_48_7)
% 68.11/9.80 | (19) l1_cat_1(all_48_6)
% 68.11/9.80 | (20) l1_cat_1(all_48_4)
% 68.11/9.80 | (21) $i(all_48_7)
% 68.11/9.80 | (22) $i(all_48_6)
% 68.11/9.80 | (23) $i(all_48_4)
% 68.11/9.80 | (24) k11_cat_2(all_48_6, all_48_4) = all_48_3
% 68.11/9.80 | (25) k11_cat_2(all_48_5, all_48_1) = all_48_0
% 68.11/9.80 | (26) k12_nattra_1(all_48_7, all_48_6) = all_48_5
% 68.11/9.80 | (27) k12_nattra_1(all_48_7, all_48_4) = all_48_1
% 68.11/9.80 | (28) k12_nattra_1(all_48_7, all_48_3) = all_48_2
% 68.11/9.80 |
% 68.11/9.80 | GROUND_INST: instantiating (3) with all_48_6, all_48_4, all_48_3, simplifying
% 68.11/9.80 | with (16), (17), (19), (20), (22), (23), (24) gives:
% 68.11/9.80 | (29) l1_cat_1(all_48_3)
% 68.11/9.80 |
% 68.11/9.80 | GROUND_INST: instantiating (2) with all_48_6, all_48_4, all_48_3, simplifying
% 68.11/9.80 | with (16), (17), (19), (20), (22), (23), (24) gives:
% 68.11/9.80 | (30) v2_cat_1(all_48_3)
% 68.11/9.80 |
% 68.11/9.80 | GROUND_INST: instantiating (8) with all_48_7, all_48_6, all_48_5, all_48_4,
% 68.11/9.80 | all_48_3, simplifying with (15), (16), (17), (18), (19), (20),
% 68.11/9.80 | (21), (22), (23), (24), (26) gives:
% 68.11/9.80 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 68.11/9.80 | (k17_isocat_2(all_48_7, all_48_6, all_48_4) = v0 &
% 68.11/9.80 | k12_nattra_1(all_48_7, all_48_3) = v1 & k12_nattra_1(all_48_7,
% 68.11/9.80 | all_48_4) = v2 & k11_cat_2(all_48_5, v2) = v3 & $i(v3) & $i(v2) &
% 68.11/9.80 | $i(v1) & $i(v0) & v8_cat_1(v0, v1, v3))
% 68.11/9.80 |
% 68.11/9.80 | GROUND_INST: instantiating (5) with all_48_7, all_48_6, all_48_5, simplifying
% 68.11/9.80 | with (15), (16), (18), (19), (21), (22), (26) gives:
% 68.11/9.80 | (32) l1_cat_1(all_48_5)
% 68.11/9.80 |
% 68.11/9.80 | GROUND_INST: instantiating (4) with all_48_7, all_48_6, all_48_5, simplifying
% 68.11/9.80 | with (15), (16), (18), (19), (21), (22), (26) gives:
% 68.11/9.80 | (33) v2_cat_1(all_48_5)
% 68.11/9.80 |
% 68.11/9.80 | GROUND_INST: instantiating (7) with all_48_7, all_48_6, all_48_4, all_48_5,
% 68.11/9.80 | all_48_1, all_48_0, simplifying with (15), (16), (17), (18),
% 68.11/9.80 | (19), (20), (21), (22), (23), (25), (26), (27) gives:
% 68.11/9.81 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (k17_isocat_2(all_48_7,
% 68.11/9.81 | all_48_6, all_48_4) = v0 & k12_nattra_1(all_48_7, v1) = v2 &
% 68.11/9.81 | k11_cat_2(all_48_6, all_48_4) = v1 & $i(v2) & $i(v1) & $i(v0) &
% 68.11/9.81 | m2_cat_1(v0, v2, all_48_0))
% 68.11/9.81 |
% 68.11/9.81 | GROUND_INST: instantiating (9) with all_48_7, all_48_6, all_48_5, all_48_4,
% 68.11/9.81 | all_48_1, simplifying with (15), (16), (17), (18), (19), (20),
% 68.11/9.81 | (21), (22), (23), (26), (27) gives:
% 68.11/9.81 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 68.11/9.81 | (k17_isocat_2(all_48_7, all_48_6, all_48_4) = v0 &
% 68.11/9.81 | k12_nattra_1(all_48_7, v1) = v2 & k11_cat_2(all_48_5, all_48_1) = v3
% 68.11/9.81 | & k11_cat_2(all_48_6, all_48_4) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 68.11/9.81 | $i(v0) & v8_cat_1(v0, v2, v3))
% 68.11/9.81 |
% 68.11/9.81 | GROUND_INST: instantiating (5) with all_48_7, all_48_4, all_48_1, simplifying
% 68.11/9.81 | with (15), (17), (18), (20), (21), (23), (27) gives:
% 68.11/9.81 | (36) l1_cat_1(all_48_1)
% 68.11/9.81 |
% 68.11/9.81 | GROUND_INST: instantiating (4) with all_48_7, all_48_4, all_48_1, simplifying
% 68.11/9.81 | with (15), (17), (18), (20), (21), (23), (27) gives:
% 68.11/9.81 | (37) v2_cat_1(all_48_1)
% 68.11/9.81 |
% 68.11/9.81 | GROUND_INST: instantiating (6) with all_48_7, all_48_6, all_48_4, all_48_3,
% 68.11/9.81 | all_48_2, simplifying with (15), (16), (17), (18), (19), (20),
% 68.11/9.81 | (21), (22), (23), (24), (28) gives:
% 68.11/9.81 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 68.11/9.81 | (k17_isocat_2(all_48_7, all_48_6, all_48_4) = v0 &
% 68.11/9.81 | k12_nattra_1(all_48_7, all_48_4) = v2 & k12_nattra_1(all_48_7,
% 68.11/9.81 | all_48_6) = v1 & k11_cat_2(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1)
% 68.11/9.81 | & $i(v0) & m2_cat_1(v0, all_48_2, v3))
% 68.11/9.81 |
% 68.11/9.81 | DELTA: instantiating (34) with fresh symbols all_78_0, all_78_1, all_78_2
% 68.11/9.81 | gives:
% 68.11/9.81 | (39) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_78_2 &
% 68.53/9.81 | k12_nattra_1(all_48_7, all_78_1) = all_78_0 & k11_cat_2(all_48_6,
% 68.53/9.81 | all_48_4) = all_78_1 & $i(all_78_0) & $i(all_78_1) & $i(all_78_2) &
% 68.53/9.81 | m2_cat_1(all_78_2, all_78_0, all_48_0)
% 68.53/9.81 |
% 68.53/9.81 | ALPHA: (39) implies:
% 68.53/9.81 | (40) $i(all_78_1)
% 68.53/9.81 | (41) k11_cat_2(all_48_6, all_48_4) = all_78_1
% 68.53/9.81 | (42) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_78_2
% 68.53/9.81 |
% 68.53/9.81 | DELTA: instantiating (35) with fresh symbols all_82_0, all_82_1, all_82_2,
% 68.53/9.81 | all_82_3 gives:
% 68.53/9.81 | (43) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_82_3 &
% 68.53/9.81 | k12_nattra_1(all_48_7, all_82_2) = all_82_1 & k11_cat_2(all_48_5,
% 68.53/9.81 | all_48_1) = all_82_0 & k11_cat_2(all_48_6, all_48_4) = all_82_2 &
% 68.53/9.81 | $i(all_82_0) & $i(all_82_1) & $i(all_82_2) & $i(all_82_3) &
% 68.53/9.81 | v8_cat_1(all_82_3, all_82_1, all_82_0)
% 68.53/9.81 |
% 68.53/9.81 | ALPHA: (43) implies:
% 68.53/9.81 | (44) $i(all_82_3)
% 68.53/9.81 | (45) k11_cat_2(all_48_6, all_48_4) = all_82_2
% 68.53/9.81 | (46) k11_cat_2(all_48_5, all_48_1) = all_82_0
% 68.53/9.81 | (47) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_82_3
% 68.53/9.81 |
% 68.53/9.81 | DELTA: instantiating (31) with fresh symbols all_84_0, all_84_1, all_84_2,
% 68.53/9.81 | all_84_3 gives:
% 68.53/9.81 | (48) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_84_3 &
% 68.53/9.81 | k12_nattra_1(all_48_7, all_48_3) = all_84_2 & k12_nattra_1(all_48_7,
% 68.53/9.81 | all_48_4) = all_84_1 & k11_cat_2(all_48_5, all_84_1) = all_84_0 &
% 68.53/9.81 | $i(all_84_0) & $i(all_84_1) & $i(all_84_2) & $i(all_84_3) &
% 68.53/9.81 | v8_cat_1(all_84_3, all_84_2, all_84_0)
% 68.53/9.81 |
% 68.53/9.81 | ALPHA: (48) implies:
% 68.53/9.81 | (49) v8_cat_1(all_84_3, all_84_2, all_84_0)
% 68.53/9.81 | (50) $i(all_84_2)
% 68.53/9.81 | (51) $i(all_84_1)
% 68.53/9.81 | (52) k11_cat_2(all_48_5, all_84_1) = all_84_0
% 68.53/9.81 | (53) k12_nattra_1(all_48_7, all_48_4) = all_84_1
% 68.53/9.81 | (54) k12_nattra_1(all_48_7, all_48_3) = all_84_2
% 68.53/9.81 | (55) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_84_3
% 68.53/9.81 |
% 68.53/9.81 | DELTA: instantiating (38) with fresh symbols all_86_0, all_86_1, all_86_2,
% 68.53/9.81 | all_86_3 gives:
% 68.53/9.82 | (56) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_86_3 &
% 68.53/9.82 | k12_nattra_1(all_48_7, all_48_4) = all_86_1 & k12_nattra_1(all_48_7,
% 68.53/9.82 | all_48_6) = all_86_2 & k11_cat_2(all_86_2, all_86_1) = all_86_0 &
% 68.53/9.82 | $i(all_86_0) & $i(all_86_1) & $i(all_86_2) & $i(all_86_3) &
% 68.53/9.82 | m2_cat_1(all_86_3, all_48_2, all_86_0)
% 68.53/9.82 |
% 68.53/9.82 | ALPHA: (56) implies:
% 68.53/9.82 | (57) m2_cat_1(all_86_3, all_48_2, all_86_0)
% 68.53/9.82 | (58) $i(all_86_2)
% 68.53/9.82 | (59) $i(all_86_0)
% 68.53/9.82 | (60) k11_cat_2(all_86_2, all_86_1) = all_86_0
% 68.53/9.82 | (61) k12_nattra_1(all_48_7, all_48_6) = all_86_2
% 68.53/9.82 | (62) k12_nattra_1(all_48_7, all_48_4) = all_86_1
% 68.53/9.82 | (63) k17_isocat_2(all_48_7, all_48_6, all_48_4) = all_86_3
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (10) with all_48_3, all_82_2, all_48_4, all_48_6,
% 68.53/9.82 | simplifying with (24), (45) gives:
% 68.53/9.82 | (64) all_82_2 = all_48_3
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (10) with all_78_1, all_82_2, all_48_4, all_48_6,
% 68.53/9.82 | simplifying with (41), (45) gives:
% 68.53/9.82 | (65) all_82_2 = all_78_1
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (10) with all_48_0, all_82_0, all_48_1, all_48_5,
% 68.53/9.82 | simplifying with (25), (46) gives:
% 68.53/9.82 | (66) all_82_0 = all_48_0
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (10) with all_82_0, all_84_0, all_48_1, all_48_5,
% 68.53/9.82 | simplifying with (46) gives:
% 68.53/9.82 | (67) all_84_0 = all_82_0 | ~ (k11_cat_2(all_48_5, all_48_1) = all_84_0)
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (11) with all_48_5, all_86_2, all_48_6, all_48_7,
% 68.53/9.82 | simplifying with (26), (61) gives:
% 68.53/9.82 | (68) all_86_2 = all_48_5
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (11) with all_48_1, all_86_1, all_48_4, all_48_7,
% 68.53/9.82 | simplifying with (27), (62) gives:
% 68.53/9.82 | (69) all_86_1 = all_48_1
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (11) with all_84_1, all_86_1, all_48_4, all_48_7,
% 68.53/9.82 | simplifying with (53), (62) gives:
% 68.53/9.82 | (70) all_86_1 = all_84_1
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (11) with all_48_2, all_84_2, all_48_3, all_48_7,
% 68.53/9.82 | simplifying with (28), (54) gives:
% 68.53/9.82 | (71) all_84_2 = all_48_2
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (12) with all_82_3, all_84_3, all_48_4, all_48_6,
% 68.53/9.82 | all_48_7, simplifying with (47), (55) gives:
% 68.53/9.82 | (72) all_84_3 = all_82_3
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (12) with all_84_3, all_86_3, all_48_4, all_48_6,
% 68.53/9.82 | all_48_7, simplifying with (55), (63) gives:
% 68.53/9.82 | (73) all_86_3 = all_84_3
% 68.53/9.82 |
% 68.53/9.82 | GROUND_INST: instantiating (12) with all_78_2, all_86_3, all_48_4, all_48_6,
% 68.53/9.82 | all_48_7, simplifying with (42), (63) gives:
% 68.53/9.82 | (74) all_86_3 = all_78_2
% 68.53/9.82 |
% 68.53/9.82 | COMBINE_EQS: (69), (70) imply:
% 68.53/9.82 | (75) all_84_1 = all_48_1
% 68.53/9.82 |
% 68.53/9.82 | COMBINE_EQS: (73), (74) imply:
% 68.53/9.82 | (76) all_84_3 = all_78_2
% 68.53/9.82 |
% 68.53/9.82 | SIMP: (76) implies:
% 68.53/9.82 | (77) all_84_3 = all_78_2
% 68.53/9.82 |
% 68.53/9.82 | COMBINE_EQS: (72), (77) imply:
% 68.53/9.82 | (78) all_82_3 = all_78_2
% 68.53/9.82 |
% 68.53/9.82 | SIMP: (78) implies:
% 68.53/9.82 | (79) all_82_3 = all_78_2
% 68.53/9.82 |
% 68.53/9.82 | COMBINE_EQS: (64), (65) imply:
% 68.53/9.82 | (80) all_78_1 = all_48_3
% 68.53/9.82 |
% 68.53/9.82 | SIMP: (80) implies:
% 68.53/9.82 | (81) all_78_1 = all_48_3
% 68.53/9.82 |
% 68.53/9.82 | REDUCE: (60), (68), (69) imply:
% 68.53/9.82 | (82) k11_cat_2(all_48_5, all_48_1) = all_86_0
% 68.53/9.82 |
% 68.53/9.82 | REDUCE: (52), (75) imply:
% 68.53/9.82 | (83) k11_cat_2(all_48_5, all_48_1) = all_84_0
% 68.53/9.82 |
% 68.53/9.82 | REDUCE: (58), (68) imply:
% 68.53/9.82 | (84) $i(all_48_5)
% 68.53/9.82 |
% 68.53/9.83 | REDUCE: (51), (75) imply:
% 68.53/9.83 | (85) $i(all_48_1)
% 68.53/9.83 |
% 68.53/9.83 | REDUCE: (50), (71) imply:
% 68.53/9.83 | (86) $i(all_48_2)
% 68.53/9.83 |
% 68.53/9.83 | REDUCE: (44), (79) imply:
% 68.53/9.83 | (87) $i(all_78_2)
% 68.53/9.83 |
% 68.53/9.83 | REDUCE: (40), (81) imply:
% 68.53/9.83 | (88) $i(all_48_3)
% 68.53/9.83 |
% 68.53/9.83 | REDUCE: (49), (71), (77) imply:
% 68.53/9.83 | (89) v8_cat_1(all_78_2, all_48_2, all_84_0)
% 68.53/9.83 |
% 68.53/9.83 | REDUCE: (57), (74) imply:
% 68.53/9.83 | (90) m2_cat_1(all_78_2, all_48_2, all_86_0)
% 68.53/9.83 |
% 68.53/9.83 | BETA: splitting (67) gives:
% 68.53/9.83 |
% 68.53/9.83 | Case 1:
% 68.53/9.83 | |
% 68.53/9.83 | | (91) ~ (k11_cat_2(all_48_5, all_48_1) = all_84_0)
% 68.53/9.83 | |
% 68.53/9.83 | | PRED_UNIFY: (83), (91) imply:
% 68.53/9.83 | | (92) $false
% 68.53/9.83 | |
% 68.53/9.83 | | CLOSE: (92) is inconsistent.
% 68.53/9.83 | |
% 68.53/9.83 | Case 2:
% 68.53/9.83 | |
% 68.53/9.83 | | (93) all_84_0 = all_82_0
% 68.53/9.83 | |
% 68.53/9.83 | | COMBINE_EQS: (66), (93) imply:
% 68.53/9.83 | | (94) all_84_0 = all_48_0
% 68.53/9.83 | |
% 68.53/9.83 | | REDUCE: (89), (94) imply:
% 68.53/9.83 | | (95) v8_cat_1(all_78_2, all_48_2, all_48_0)
% 68.53/9.83 | |
% 68.53/9.83 | | GROUND_INST: instantiating (10) with all_48_0, all_86_0, all_48_1, all_48_5,
% 68.53/9.83 | | simplifying with (25), (82) gives:
% 68.53/9.83 | | (96) all_86_0 = all_48_0
% 68.53/9.83 | |
% 68.53/9.83 | | REDUCE: (59), (96) imply:
% 68.53/9.83 | | (97) $i(all_48_0)
% 68.53/9.83 | |
% 68.53/9.83 | | REDUCE: (90), (96) imply:
% 68.53/9.83 | | (98) m2_cat_1(all_78_2, all_48_2, all_48_0)
% 68.53/9.83 | |
% 68.53/9.83 | | GROUND_INST: instantiating (5) with all_48_7, all_48_3, all_48_2,
% 68.53/9.83 | | simplifying with (15), (18), (21), (28), (29), (30), (88)
% 68.53/9.83 | | gives:
% 68.53/9.83 | | (99) l1_cat_1(all_48_2)
% 68.53/9.83 | |
% 68.53/9.83 | | GROUND_INST: instantiating (4) with all_48_7, all_48_3, all_48_2,
% 68.53/9.83 | | simplifying with (15), (18), (21), (28), (29), (30), (88)
% 68.53/9.83 | | gives:
% 68.53/9.83 | | (100) v2_cat_1(all_48_2)
% 68.53/9.83 | |
% 68.53/9.83 | | GROUND_INST: instantiating (3) with all_48_5, all_48_1, all_48_0,
% 68.53/9.83 | | simplifying with (25), (32), (33), (36), (37), (84), (85)
% 68.53/9.83 | | gives:
% 68.53/9.83 | | (101) l1_cat_1(all_48_0)
% 68.53/9.83 | |
% 68.53/9.83 | | GROUND_INST: instantiating (2) with all_48_5, all_48_1, all_48_0,
% 68.53/9.83 | | simplifying with (25), (32), (33), (36), (37), (84), (85)
% 68.53/9.83 | | gives:
% 68.53/9.83 | | (102) v2_cat_1(all_48_0)
% 68.53/9.83 | |
% 68.53/9.83 | | GROUND_INST: instantiating (1) with all_48_2, all_48_0, all_78_2,
% 68.53/9.83 | | simplifying with (14), (86), (87), (95), (97), (98), (99),
% 68.53/9.83 | | (100), (101), (102) gives:
% 68.53/9.83 | | (103) $false
% 68.53/9.83 | |
% 68.53/9.83 | | CLOSE: (103) is inconsistent.
% 68.53/9.83 | |
% 68.53/9.83 | End of split
% 68.53/9.83 |
% 68.53/9.83 End of proof
% 68.53/9.83 % SZS output end Proof for theBenchmark
% 68.53/9.83
% 68.53/9.83 9255ms
%------------------------------------------------------------------------------