TSTP Solution File: LAT356+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : LAT356+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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:25:03 EDT 2023
% Result : Theorem 97.13s 15.62s
% Output : Proof 98.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT356+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.33 % Computer : n015.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Thu Aug 24 09:41:50 EDT 2023
% 0.17/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.80/1.60 Prover 4: Preprocessing ...
% 6.35/1.60 Prover 1: Preprocessing ...
% 6.46/1.62 Prover 6: Preprocessing ...
% 6.46/1.62 Prover 0: Preprocessing ...
% 6.46/1.62 Prover 5: Preprocessing ...
% 6.46/1.62 Prover 3: Preprocessing ...
% 6.46/1.62 Prover 2: Preprocessing ...
% 16.43/3.03 Prover 5: Proving ...
% 16.43/3.15 Prover 1: Warning: ignoring some quantifiers
% 18.38/3.24 Prover 2: Proving ...
% 18.38/3.27 Prover 6: Proving ...
% 18.92/3.29 Prover 3: Warning: ignoring some quantifiers
% 18.92/3.30 Prover 1: Constructing countermodel ...
% 18.92/3.35 Prover 3: Constructing countermodel ...
% 75.62/10.80 Prover 2: stopped
% 75.62/10.81 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 77.66/11.06 Prover 7: Preprocessing ...
% 78.45/11.18 Prover 7: Warning: ignoring some quantifiers
% 78.45/11.21 Prover 7: Constructing countermodel ...
% 84.63/12.18 Prover 4: Warning: ignoring some quantifiers
% 88.62/12.49 Prover 4: Constructing countermodel ...
% 89.89/12.65 Prover 7: Found proof (size 83)
% 89.89/12.65 Prover 7: proved (1840ms)
% 89.89/12.65 Prover 4: stopped
% 89.89/12.66 Prover 5: stopped
% 89.89/12.66 Prover 6: stopped
% 89.89/12.66 Prover 1: stopped
% 89.89/12.66 Prover 3: stopped
% 97.13/15.61 Prover 0: Proving ...
% 97.13/15.61 Prover 0: stopped
% 97.13/15.61
% 97.13/15.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 97.13/15.62
% 97.83/15.64 % SZS output start Proof for theBenchmark
% 97.83/15.65 Assumptions after simplification:
% 97.83/15.65 ---------------------------------
% 97.83/15.65
% 97.83/15.65 (cc1_lattice3)
% 97.83/15.66 ! [v0: $i] : ( ~ $i(v0) | ~ v3_struct_0(v0) | ~ l1_orders_2(v0) | ~
% 97.83/15.66 v1_lattice3(v0))
% 97.83/15.66
% 97.83/15.66 (d1_waybel34)
% 98.12/15.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 98.12/15.72 $i] : ! [v6: $i] : ! [v7: $i] : (v6 = v5 | ~ (k1_waybel34(v0, v2, v4) =
% 98.12/15.72 v5) | ~ (k1_waybel_1(v0, v2, v4, v6) = v7) | ~ (u1_struct_0(v2) = v3) |
% 98.12/15.72 ~ (u1_struct_0(v0) = v1) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) |
% 98.12/15.72 ~ v3_waybel_1(v7, v0, v2) | ~ m2_relset_1(v6, v3, v1) | ~ m2_relset_1(v4,
% 98.12/15.72 v1, v3) | ~ v17_waybel_0(v4, v0, v2) | ~ v1_funct_2(v6, v3, v1) | ~
% 98.12/15.72 v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v6) | ~ v1_funct_1(v4) | ~
% 98.12/15.72 l1_orders_2(v2) | ~ l1_orders_2(v0) | ~ v3_lattice3(v2) | ~
% 98.12/15.72 v3_lattice3(v0) | ~ v2_lattice3(v2) | ~ v2_lattice3(v0) | ~
% 98.12/15.72 v1_lattice3(v2) | ~ v1_lattice3(v0) | ~ v4_orders_2(v2) | ~
% 98.12/15.72 v4_orders_2(v0) | ~ v3_orders_2(v2) | ~ v3_orders_2(v0) | ~
% 98.12/15.72 v2_orders_2(v2) | ~ v2_orders_2(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 98.12/15.72 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 98.12/15.72 (k1_waybel34(v0, v2, v4) = v5) | ~ (k1_waybel_1(v0, v2, v4, v5) = v6) | ~
% 98.12/15.72 (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ $i(v5) | ~ $i(v4) |
% 98.12/15.72 ~ $i(v2) | ~ $i(v0) | ~ m2_relset_1(v5, v3, v1) | ~ m2_relset_1(v4, v1,
% 98.12/15.72 v3) | ~ v17_waybel_0(v4, v0, v2) | ~ v1_funct_2(v5, v3, v1) | ~
% 98.12/15.72 v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~
% 98.12/15.72 l1_orders_2(v2) | ~ l1_orders_2(v0) | ~ v3_lattice3(v2) | ~
% 98.12/15.72 v3_lattice3(v0) | ~ v2_lattice3(v2) | ~ v2_lattice3(v0) | ~
% 98.12/15.72 v1_lattice3(v2) | ~ v1_lattice3(v0) | ~ v4_orders_2(v2) | ~
% 98.12/15.72 v4_orders_2(v0) | ~ v3_orders_2(v2) | ~ v3_orders_2(v0) | ~
% 98.12/15.72 v2_orders_2(v2) | ~ v2_orders_2(v0) | v3_waybel_1(v6, v0, v2))
% 98.12/15.72
% 98.12/15.72 (d2_waybel34)
% 98.29/15.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 98.29/15.74 $i] : ! [v6: $i] : ! [v7: $i] : (v6 = v5 | ~ (k2_waybel34(v0, v2, v4) =
% 98.29/15.74 v5) | ~ (k1_waybel_1(v0, v2, v6, v4) = v7) | ~ (u1_struct_0(v2) = v3) |
% 98.29/15.74 ~ (u1_struct_0(v0) = v1) | ~ $i(v6) | ~ $i(v4) | ~ $i(v2) | ~ $i(v0) |
% 98.29/15.74 ~ v3_waybel_1(v7, v0, v2) | ~ m2_relset_1(v6, v1, v3) | ~ m2_relset_1(v4,
% 98.29/15.74 v3, v1) | ~ v18_waybel_0(v4, v2, v0) | ~ v1_funct_2(v6, v1, v3) | ~
% 98.29/15.74 v1_funct_2(v4, v3, v1) | ~ v1_funct_1(v6) | ~ v1_funct_1(v4) | ~
% 98.29/15.74 l1_orders_2(v2) | ~ l1_orders_2(v0) | ~ v3_lattice3(v2) | ~
% 98.29/15.74 v3_lattice3(v0) | ~ v2_lattice3(v2) | ~ v2_lattice3(v0) | ~
% 98.29/15.74 v1_lattice3(v2) | ~ v1_lattice3(v0) | ~ v4_orders_2(v2) | ~
% 98.29/15.74 v4_orders_2(v0) | ~ v3_orders_2(v2) | ~ v3_orders_2(v0) | ~
% 98.29/15.74 v2_orders_2(v2) | ~ v2_orders_2(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 98.29/15.74 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 98.29/15.74 (k2_waybel34(v0, v2, v4) = v5) | ~ (k1_waybel_1(v0, v2, v5, v4) = v6) | ~
% 98.29/15.74 (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ $i(v5) | ~ $i(v4) |
% 98.29/15.74 ~ $i(v2) | ~ $i(v0) | ~ m2_relset_1(v5, v1, v3) | ~ m2_relset_1(v4, v3,
% 98.29/15.74 v1) | ~ v18_waybel_0(v4, v2, v0) | ~ v1_funct_2(v5, v1, v3) | ~
% 98.29/15.74 v1_funct_2(v4, v3, v1) | ~ v1_funct_1(v5) | ~ v1_funct_1(v4) | ~
% 98.29/15.74 l1_orders_2(v2) | ~ l1_orders_2(v0) | ~ v3_lattice3(v2) | ~
% 98.29/15.74 v3_lattice3(v0) | ~ v2_lattice3(v2) | ~ v2_lattice3(v0) | ~
% 98.29/15.74 v1_lattice3(v2) | ~ v1_lattice3(v0) | ~ v4_orders_2(v2) | ~
% 98.29/15.74 v4_orders_2(v0) | ~ v3_orders_2(v2) | ~ v3_orders_2(v0) | ~
% 98.29/15.74 v2_orders_2(v2) | ~ v2_orders_2(v0) | v3_waybel_1(v6, v0, v2))
% 98.29/15.74
% 98.29/15.74 (dt_k1_waybel34)
% 98.29/15.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k1_waybel34(v0,
% 98.29/15.74 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ v1_funct_1(v2) |
% 98.29/15.74 ~ l1_orders_2(v1) | ~ l1_orders_2(v0) | ~ v2_lattice3(v1) | ~
% 98.29/15.74 v2_lattice3(v0) | ~ v1_lattice3(v1) | ~ v1_lattice3(v0) | ~
% 98.29/15.74 v4_orders_2(v1) | ~ v4_orders_2(v0) | ~ v3_orders_2(v1) | ~
% 98.29/15.74 v3_orders_2(v0) | ~ v2_orders_2(v1) | ~ v2_orders_2(v0) | ? [v4: $i] : ?
% 98.29/15.74 [v5: $i] : (u1_struct_0(v1) = v5 & u1_struct_0(v0) = v4 & $i(v5) & $i(v4) &
% 98.29/15.74 ( ~ v1_funct_2(v2, v4, v5) | ~ m1_relset_1(v2, v4, v5) | (m2_relset_1(v3,
% 98.29/15.74 v5, v4) & v1_funct_2(v3, v5, v4) & v1_funct_1(v3)))))
% 98.29/15.74
% 98.29/15.74 (dt_k2_waybel34)
% 98.29/15.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (k2_waybel34(v0,
% 98.29/15.75 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ v1_funct_1(v2) |
% 98.29/15.75 ~ l1_orders_2(v1) | ~ l1_orders_2(v0) | ~ v2_lattice3(v1) | ~
% 98.29/15.75 v2_lattice3(v0) | ~ v1_lattice3(v1) | ~ v1_lattice3(v0) | ~
% 98.29/15.75 v4_orders_2(v1) | ~ v4_orders_2(v0) | ~ v3_orders_2(v1) | ~
% 98.29/15.75 v3_orders_2(v0) | ~ v2_orders_2(v1) | ~ v2_orders_2(v0) | ? [v4: $i] : ?
% 98.29/15.75 [v5: $i] : (u1_struct_0(v1) = v4 & u1_struct_0(v0) = v5 & $i(v5) & $i(v4) &
% 98.29/15.75 ( ~ v1_funct_2(v2, v4, v5) | ~ m1_relset_1(v2, v4, v5) | (m2_relset_1(v3,
% 98.29/15.75 v5, v4) & v1_funct_2(v3, v5, v4) & v1_funct_1(v3)))))
% 98.29/15.75
% 98.29/15.75 (dt_k7_grcat_1)
% 98.29/15.75 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.75 l1_struct_0(v0) | v1_funct_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.75 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_struct_0(v0) | ? [v2: $i] :
% 98.29/15.75 (u1_struct_0(v0) = v2 & $i(v2) & m2_relset_1(v1, v2, v2) & v1_funct_2(v1,
% 98.29/15.75 v2, v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~
% 98.29/15.75 $i(v0) | ~ l1_struct_0(v0) | ? [v2: $i] : (k7_grcat_1(v0) = v2 & $i(v2) &
% 98.29/15.75 m2_relset_1(v2, v1, v1) & v1_funct_2(v2, v1, v1) & v1_funct_1(v2)))
% 98.29/15.75
% 98.29/15.75 (dt_l1_orders_2)
% 98.29/15.75 ! [v0: $i] : ( ~ $i(v0) | ~ l1_orders_2(v0) | l1_struct_0(v0))
% 98.29/15.75
% 98.29/15.75 (fc2_waybel_1)
% 98.29/15.76 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.76 l1_orders_2(v0) | v23_waybel_0(v1, v0, v0)) & ! [v0: $i] : ! [v1: $i] : (
% 98.29/15.76 ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | v1_relat_1(v1)) &
% 98.29/15.76 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.76 l1_orders_2(v0) | v1_funct_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.76 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ? [v2: $i] :
% 98.29/15.76 (u1_struct_0(v0) = v2 & $i(v2) & v1_funct_2(v1, v2, v2))) & ! [v0: $i] : !
% 98.29/15.76 [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ?
% 98.29/15.76 [v2: $i] : (k7_grcat_1(v0) = v2 & $i(v2) & v23_waybel_0(v2, v0, v0) &
% 98.29/15.76 v1_funct_2(v2, v1, v1) & v1_relat_1(v2) & v1_funct_1(v2)))
% 98.29/15.76
% 98.29/15.76 (fc3_waybel10)
% 98.29/15.76 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.76 l1_struct_0(v0) | v2_funct_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.76 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_struct_0(v0) | v1_relat_1(v1)) &
% 98.29/15.76 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.76 l1_struct_0(v0) | v1_funct_1(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.76 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_struct_0(v0) | ? [v2: $i] :
% 98.29/15.76 (u1_struct_0(v0) = v2 & $i(v2) & v1_funct_2(v1, v2, v2))) & ! [v0: $i] : !
% 98.29/15.76 [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_struct_0(v0) | ?
% 98.29/15.76 [v2: $i] : (k7_grcat_1(v0) = v2 & $i(v2) & v2_funct_1(v2) & v1_funct_2(v2,
% 98.29/15.76 v1, v1) & v1_relat_1(v2) & v1_funct_1(v2)))
% 98.29/15.76
% 98.29/15.76 (fc4_waybel10)
% 98.29/15.77 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.77 v1_xboole_0(v1) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) | v3_struct_0(v0))
% 98.29/15.77 & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.77 l1_orders_2(v0) | ~ v2_orders_2(v0) | v23_waybel_0(v1, v0, v0) |
% 98.29/15.77 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) |
% 98.29/15.77 ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) | v8_waybel_1(v1, v0) |
% 98.29/15.77 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) |
% 98.29/15.77 ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) | v7_waybel_1(v1, v0) |
% 98.29/15.77 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) |
% 98.29/15.77 ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) | v20_waybel_0(v1, v0,
% 98.29/15.77 v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) =
% 98.29/15.77 v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) |
% 98.29/15.77 v18_waybel_0(v1, v0, v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : (
% 98.29/15.77 ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~
% 98.29/15.77 v2_orders_2(v0) | v2_funct_1(v1) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1:
% 98.29/15.77 $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~
% 98.29/15.77 v2_orders_2(v0) | v21_waybel_0(v1, v0, v0) | v3_struct_0(v0)) & ! [v0: $i]
% 98.29/15.77 : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) |
% 98.29/15.77 ~ v2_orders_2(v0) | v17_waybel_0(v1, v0, v0) | v3_struct_0(v0)) & ! [v0:
% 98.29/15.77 $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.77 l1_orders_2(v0) | ~ v2_orders_2(v0) | v19_waybel_0(v1, v0, v0) |
% 98.29/15.77 v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) |
% 98.29/15.77 ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) | v22_waybel_0(v1, v0,
% 98.29/15.77 v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) =
% 98.29/15.77 v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0) |
% 98.29/15.77 v5_orders_3(v1, v0, v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.77 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0)
% 98.29/15.77 | v11_quantal1(v1) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.77 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0)
% 98.29/15.77 | v6_waybel_1(v1, v0) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.77 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0)
% 98.29/15.77 | v1_relat_1(v1) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.77 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0)
% 98.29/15.77 | v1_funct_1(v1) | v3_struct_0(v0)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 98.29/15.77 (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~ v2_orders_2(v0)
% 98.29/15.77 | v3_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) &
% 98.29/15.77 v1_partfun1(v1, v2, v2) & v1_funct_2(v1, v2, v2))) & ! [v0: $i] : ! [v1:
% 98.29/15.77 $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~ l1_orders_2(v0) | ~
% 98.29/15.77 v2_orders_2(v0) | v3_struct_0(v0) | ? [v2: $i] : (k7_grcat_1(v0) = v2 &
% 98.29/15.77 $i(v2) & v23_waybel_0(v2, v0, v0) & v8_waybel_1(v2, v0) & v7_waybel_1(v2,
% 98.29/15.77 v0) & v20_waybel_0(v2, v0, v0) & v18_waybel_0(v2, v0, v0) &
% 98.29/15.77 v2_funct_1(v2) & v21_waybel_0(v2, v0, v0) & v17_waybel_0(v2, v0, v0) &
% 98.29/15.77 v19_waybel_0(v2, v0, v0) & v22_waybel_0(v2, v0, v0) & v5_orders_3(v2, v0,
% 98.29/15.77 v0) & v11_quantal1(v2) & v1_partfun1(v2, v1, v1) & v6_waybel_1(v2, v0) &
% 98.29/15.77 v1_funct_2(v2, v1, v1) & v1_relat_1(v2) & v1_funct_1(v2) & ~
% 98.29/15.77 v1_xboole_0(v2)))
% 98.29/15.77
% 98.29/15.77 (t6_waybel34)
% 98.29/15.77 ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.77 l1_orders_2(v0) | v3_struct_0(v0) | ? [v2: $i] : (k1_waybel_1(v0, v0, v1,
% 98.29/15.77 v1) = v2 & $i(v2) & v3_waybel_1(v2, v0, v0)))
% 98.29/15.77
% 98.29/15.77 (t7_waybel34)
% 98.29/15.77 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (k7_grcat_1(v0) = v1 &
% 98.29/15.77 $i(v1) & $i(v0) & l1_orders_2(v0) & v3_lattice3(v0) & v2_lattice3(v0) &
% 98.29/15.77 v1_lattice3(v0) & v4_orders_2(v0) & v3_orders_2(v0) & v2_orders_2(v0) & (( ~
% 98.29/15.77 (v3 = v1) & k2_waybel34(v0, v0, v1) = v3 & $i(v3)) | ( ~ (v2 = v1) &
% 98.29/15.77 k1_waybel34(v0, v0, v1) = v2 & $i(v2))))
% 98.29/15.77
% 98.29/15.77 (function-axioms)
% 98.29/15.78 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 98.29/15.78 $i] : (v1 = v0 | ~ (k1_waybel_1(v5, v4, v3, v2) = v1) | ~ (k1_waybel_1(v5,
% 98.29/15.78 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 98.29/15.78 $i] : ! [v4: $i] : (v1 = v0 | ~ (k2_waybel34(v4, v3, v2) = v1) | ~
% 98.29/15.78 (k2_waybel34(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 98.29/15.78 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (k1_waybel34(v4, v3, v2) = v1) | ~
% 98.29/15.78 (k1_waybel34(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 98.29/15.78 ! [v3: $i] : (v1 = v0 | ~ (k4_tarski(v3, v2) = v1) | ~ (k4_tarski(v3, v2) =
% 98.29/15.78 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 98.29/15.78 ~ (k2_tarski(v3, v2) = v1) | ~ (k2_tarski(v3, v2) = v0)) & ! [v0: $i] : !
% 98.29/15.78 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) =
% 98.29/15.78 v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 98.29/15.78 $i] : (v1 = v0 | ~ (k7_grcat_1(v2) = v1) | ~ (k7_grcat_1(v2) = v0)) & !
% 98.29/15.78 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~
% 98.29/15.78 (k1_tarski(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 98.29/15.78 ~ (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0)) & ! [v0: $i] : !
% 98.29/15.78 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_zfmisc_1(v2) = v1) | ~
% 98.29/15.78 (k1_zfmisc_1(v2) = v0))
% 98.29/15.78
% 98.29/15.78 Further assumptions not needed in the proof:
% 98.29/15.78 --------------------------------------------
% 98.29/15.78 antisymmetry_r2_hidden, cc10_membered, cc10_waybel_0, cc11_membered,
% 98.29/15.78 cc11_waybel_0, cc12_membered, cc12_waybel_0, cc13_membered, cc13_waybel_0,
% 98.29/15.78 cc14_membered, cc14_waybel_0, cc15_membered, cc16_membered, cc17_membered,
% 98.29/15.78 cc18_membered, cc19_membered, cc1_finset_1, cc1_funct_1, cc1_membered,
% 98.29/15.78 cc1_relset_1, cc1_setfam_1, cc1_waybel10, cc1_waybel17, cc1_waybel21,
% 98.29/15.78 cc1_waybel_1, cc1_yellow_0, cc1_yellow_2, cc20_membered, cc2_finset_1,
% 98.29/15.78 cc2_funct_1, cc2_lattice3, cc2_membered, cc2_waybel_1, cc3_membered,
% 98.29/15.78 cc3_waybel_1, cc3_yellow_0, cc4_membered, cc4_waybel_1, cc4_yellow_0,
% 98.29/15.78 cc5_yellow_0, cc6_waybel_0, cc7_waybel_0, cc8_waybel_0, cc9_waybel_0,
% 98.29/15.78 commutativity_k2_tarski, d5_tarski, dt_k1_tarski, dt_k1_waybel_1,
% 98.29/15.78 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_zfmisc_1, dt_k4_tarski,
% 98.29/15.78 dt_l1_struct_0, dt_m1_relset_1, dt_m1_subset_1, dt_m1_waybel_1, dt_m2_relset_1,
% 98.29/15.78 dt_u1_struct_0, existence_l1_orders_2, existence_l1_struct_0,
% 98.29/15.78 existence_m1_relset_1, existence_m1_subset_1, existence_m1_waybel_1,
% 98.29/15.78 existence_m2_relset_1, fc10_membered, fc11_membered, fc12_membered,
% 98.29/15.78 fc13_membered, fc14_finset_1, fc14_membered, fc15_membered, fc16_membered,
% 98.29/15.78 fc1_finset_1, fc1_struct_0, fc1_waybel34, fc2_finset_1, fc2_setfam_1,
% 98.29/15.78 fc2_waybel34, fc3_setfam_1, fc3_waybel_1, fc4_waybel_1, fc5_waybel_1,
% 98.29/15.78 fc6_membered, fc7_membered, fc8_membered, fc9_membered, rc1_finset_1,
% 98.29/15.78 rc1_funct_1, rc1_lattice5, rc1_membered, rc1_setfam_1, rc1_waybel10,
% 98.29/15.78 rc1_waybel34, rc1_waybel_1, rc2_funct_1, rc2_waybel10, rc2_waybel_1,
% 98.29/15.78 rc2_yellow_0, rc3_finset_1, rc3_funct_1, rc3_struct_0, rc3_waybel_1,
% 98.29/15.78 rc3_yellow_9, rc4_finset_1, rc4_yellow_9, rc5_struct_0,
% 98.29/15.78 redefinition_k1_waybel_1, redefinition_m2_relset_1, reflexivity_r1_tarski,
% 98.29/15.78 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 98.29/15.78 t8_boole
% 98.29/15.78
% 98.29/15.78 Those formulas are unsatisfiable:
% 98.29/15.78 ---------------------------------
% 98.29/15.78
% 98.29/15.78 Begin of proof
% 98.29/15.78 |
% 98.29/15.78 | ALPHA: (d1_waybel34) implies:
% 98.29/15.78 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 98.29/15.78 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v6 = v5 | ~ (k1_waybel34(v0,
% 98.29/15.78 | v2, v4) = v5) | ~ (k1_waybel_1(v0, v2, v4, v6) = v7) | ~
% 98.29/15.78 | (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ $i(v6) | ~
% 98.29/15.78 | $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ v3_waybel_1(v7, v0, v2) | ~
% 98.29/15.78 | m2_relset_1(v6, v3, v1) | ~ m2_relset_1(v4, v1, v3) | ~
% 98.29/15.78 | v17_waybel_0(v4, v0, v2) | ~ v1_funct_2(v6, v3, v1) | ~
% 98.29/15.78 | v1_funct_2(v4, v1, v3) | ~ v1_funct_1(v6) | ~ v1_funct_1(v4) | ~
% 98.29/15.78 | l1_orders_2(v2) | ~ l1_orders_2(v0) | ~ v3_lattice3(v2) | ~
% 98.29/15.78 | v3_lattice3(v0) | ~ v2_lattice3(v2) | ~ v2_lattice3(v0) | ~
% 98.29/15.78 | v1_lattice3(v2) | ~ v1_lattice3(v0) | ~ v4_orders_2(v2) | ~
% 98.29/15.78 | v4_orders_2(v0) | ~ v3_orders_2(v2) | ~ v3_orders_2(v0) | ~
% 98.29/15.78 | v2_orders_2(v2) | ~ v2_orders_2(v0))
% 98.29/15.79 |
% 98.29/15.79 | ALPHA: (d2_waybel34) implies:
% 98.29/15.79 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 98.29/15.79 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v6 = v5 | ~ (k2_waybel34(v0,
% 98.29/15.79 | v2, v4) = v5) | ~ (k1_waybel_1(v0, v2, v6, v4) = v7) | ~
% 98.29/15.79 | (u1_struct_0(v2) = v3) | ~ (u1_struct_0(v0) = v1) | ~ $i(v6) | ~
% 98.29/15.79 | $i(v4) | ~ $i(v2) | ~ $i(v0) | ~ v3_waybel_1(v7, v0, v2) | ~
% 98.29/15.79 | m2_relset_1(v6, v1, v3) | ~ m2_relset_1(v4, v3, v1) | ~
% 98.29/15.79 | v18_waybel_0(v4, v2, v0) | ~ v1_funct_2(v6, v1, v3) | ~
% 98.29/15.79 | v1_funct_2(v4, v3, v1) | ~ v1_funct_1(v6) | ~ v1_funct_1(v4) | ~
% 98.29/15.79 | l1_orders_2(v2) | ~ l1_orders_2(v0) | ~ v3_lattice3(v2) | ~
% 98.29/15.79 | v3_lattice3(v0) | ~ v2_lattice3(v2) | ~ v2_lattice3(v0) | ~
% 98.29/15.79 | v1_lattice3(v2) | ~ v1_lattice3(v0) | ~ v4_orders_2(v2) | ~
% 98.29/15.79 | v4_orders_2(v0) | ~ v3_orders_2(v2) | ~ v3_orders_2(v0) | ~
% 98.29/15.79 | v2_orders_2(v2) | ~ v2_orders_2(v0))
% 98.29/15.79 |
% 98.29/15.79 | ALPHA: (dt_k7_grcat_1) implies:
% 98.29/15.79 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.79 | l1_struct_0(v0) | ? [v2: $i] : (k7_grcat_1(v0) = v2 & $i(v2) &
% 98.29/15.79 | m2_relset_1(v2, v1, v1) & v1_funct_2(v2, v1, v1) & v1_funct_1(v2)))
% 98.29/15.79 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.79 | l1_struct_0(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) &
% 98.29/15.79 | m2_relset_1(v1, v2, v2) & v1_funct_2(v1, v2, v2)))
% 98.29/15.79 |
% 98.29/15.79 | ALPHA: (fc2_waybel_1) implies:
% 98.29/15.79 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.79 | l1_orders_2(v0) | ? [v2: $i] : (u1_struct_0(v0) = v2 & $i(v2) &
% 98.29/15.79 | v1_funct_2(v1, v2, v2)))
% 98.29/15.79 |
% 98.29/15.79 | ALPHA: (fc3_waybel10) implies:
% 98.29/15.79 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (u1_struct_0(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.79 | l1_struct_0(v0) | ? [v2: $i] : (k7_grcat_1(v0) = v2 & $i(v2) &
% 98.29/15.79 | v2_funct_1(v2) & v1_funct_2(v2, v1, v1) & v1_relat_1(v2) &
% 98.29/15.79 | v1_funct_1(v2)))
% 98.29/15.79 |
% 98.29/15.79 | ALPHA: (fc4_waybel10) implies:
% 98.29/15.79 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.79 | l1_orders_2(v0) | ~ v2_orders_2(v0) | v17_waybel_0(v1, v0, v0) |
% 98.29/15.79 | v3_struct_0(v0))
% 98.29/15.79 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (k7_grcat_1(v0) = v1) | ~ $i(v0) | ~
% 98.29/15.79 | l1_orders_2(v0) | ~ v2_orders_2(v0) | v18_waybel_0(v1, v0, v0) |
% 98.29/15.79 | v3_struct_0(v0))
% 98.29/15.79 |
% 98.29/15.79 | ALPHA: (function-axioms) implies:
% 98.29/15.80 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 98.29/15.80 | (u1_struct_0(v2) = v1) | ~ (u1_struct_0(v2) = v0))
% 98.29/15.80 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 98.29/15.80 | (k7_grcat_1(v2) = v1) | ~ (k7_grcat_1(v2) = v0))
% 98.29/15.80 |
% 98.29/15.80 | DELTA: instantiating (t7_waybel34) with fresh symbols all_131_0, all_131_1,
% 98.29/15.80 | all_131_2, all_131_3 gives:
% 98.29/15.80 | (11) k7_grcat_1(all_131_3) = all_131_2 & $i(all_131_2) & $i(all_131_3) &
% 98.29/15.80 | l1_orders_2(all_131_3) & v3_lattice3(all_131_3) &
% 98.29/15.80 | v2_lattice3(all_131_3) & v1_lattice3(all_131_3) &
% 98.29/15.80 | v4_orders_2(all_131_3) & v3_orders_2(all_131_3) &
% 98.29/15.80 | v2_orders_2(all_131_3) & (( ~ (all_131_0 = all_131_2) &
% 98.29/15.80 | k2_waybel34(all_131_3, all_131_3, all_131_2) = all_131_0 &
% 98.29/15.80 | $i(all_131_0)) | ( ~ (all_131_1 = all_131_2) &
% 98.29/15.80 | k1_waybel34(all_131_3, all_131_3, all_131_2) = all_131_1 &
% 98.29/15.80 | $i(all_131_1)))
% 98.29/15.80 |
% 98.29/15.80 | ALPHA: (11) implies:
% 98.29/15.80 | (12) v2_orders_2(all_131_3)
% 98.29/15.80 | (13) v3_orders_2(all_131_3)
% 98.29/15.80 | (14) v4_orders_2(all_131_3)
% 98.29/15.80 | (15) v1_lattice3(all_131_3)
% 98.29/15.80 | (16) v2_lattice3(all_131_3)
% 98.29/15.80 | (17) v3_lattice3(all_131_3)
% 98.29/15.80 | (18) l1_orders_2(all_131_3)
% 98.29/15.80 | (19) $i(all_131_3)
% 98.29/15.80 | (20) k7_grcat_1(all_131_3) = all_131_2
% 98.29/15.80 | (21) ( ~ (all_131_0 = all_131_2) & k2_waybel34(all_131_3, all_131_3,
% 98.29/15.80 | all_131_2) = all_131_0 & $i(all_131_0)) | ( ~ (all_131_1 =
% 98.29/15.80 | all_131_2) & k1_waybel34(all_131_3, all_131_3, all_131_2) =
% 98.29/15.80 | all_131_1 & $i(all_131_1))
% 98.29/15.80 |
% 98.29/15.80 | GROUND_INST: instantiating (dt_l1_orders_2) with all_131_3, simplifying with
% 98.29/15.80 | (18), (19) gives:
% 98.29/15.80 | (22) l1_struct_0(all_131_3)
% 98.29/15.80 |
% 98.29/15.80 | GROUND_INST: instantiating (8) with all_131_3, all_131_2, simplifying with
% 98.29/15.80 | (12), (18), (19), (20) gives:
% 98.29/15.80 | (23) v18_waybel_0(all_131_2, all_131_3, all_131_3) | v3_struct_0(all_131_3)
% 98.29/15.80 |
% 98.29/15.80 | GROUND_INST: instantiating (7) with all_131_3, all_131_2, simplifying with
% 98.29/15.80 | (12), (18), (19), (20) gives:
% 98.29/15.80 | (24) v17_waybel_0(all_131_2, all_131_3, all_131_3) | v3_struct_0(all_131_3)
% 98.29/15.80 |
% 98.29/15.80 | GROUND_INST: instantiating (t6_waybel34) with all_131_3, all_131_2,
% 98.29/15.80 | simplifying with (18), (19), (20) gives:
% 98.29/15.80 | (25) v3_struct_0(all_131_3) | ? [v0: $i] : (k1_waybel_1(all_131_3,
% 98.29/15.80 | all_131_3, all_131_2, all_131_2) = v0 & $i(v0) & v3_waybel_1(v0,
% 98.29/15.80 | all_131_3, all_131_3))
% 98.29/15.80 |
% 98.29/15.80 | GROUND_INST: instantiating (5) with all_131_3, all_131_2, simplifying with
% 98.29/15.80 | (18), (19), (20) gives:
% 98.29/15.80 | (26) ? [v0: $i] : (u1_struct_0(all_131_3) = v0 & $i(v0) &
% 98.29/15.80 | v1_funct_2(all_131_2, v0, v0))
% 98.29/15.80 |
% 98.29/15.80 | DELTA: instantiating (26) with fresh symbol all_161_0 gives:
% 98.29/15.80 | (27) u1_struct_0(all_131_3) = all_161_0 & $i(all_161_0) &
% 98.29/15.80 | v1_funct_2(all_131_2, all_161_0, all_161_0)
% 98.29/15.80 |
% 98.29/15.80 | ALPHA: (27) implies:
% 98.29/15.80 | (28) u1_struct_0(all_131_3) = all_161_0
% 98.29/15.81 |
% 98.29/15.81 | GROUND_INST: instantiating (4) with all_131_3, all_131_2, simplifying with
% 98.29/15.81 | (19), (20), (22) gives:
% 98.29/15.81 | (29) ? [v0: $i] : (u1_struct_0(all_131_3) = v0 & $i(v0) &
% 98.29/15.81 | m2_relset_1(all_131_2, v0, v0) & v1_funct_2(all_131_2, v0, v0))
% 98.29/15.81 |
% 98.29/15.81 | GROUND_INST: instantiating (3) with all_131_3, all_161_0, simplifying with
% 98.29/15.81 | (19), (22), (28) gives:
% 98.29/15.81 | (30) ? [v0: $i] : (k7_grcat_1(all_131_3) = v0 & $i(v0) & m2_relset_1(v0,
% 98.29/15.81 | all_161_0, all_161_0) & v1_funct_2(v0, all_161_0, all_161_0) &
% 98.29/15.81 | v1_funct_1(v0))
% 98.29/15.81 |
% 98.29/15.81 | GROUND_INST: instantiating (6) with all_131_3, all_161_0, simplifying with
% 98.29/15.81 | (19), (22), (28) gives:
% 98.29/15.81 | (31) ? [v0: $i] : (k7_grcat_1(all_131_3) = v0 & $i(v0) & v2_funct_1(v0) &
% 98.29/15.81 | v1_funct_2(v0, all_161_0, all_161_0) & v1_relat_1(v0) &
% 98.29/15.81 | v1_funct_1(v0))
% 98.29/15.81 |
% 98.29/15.81 | DELTA: instantiating (29) with fresh symbol all_177_0 gives:
% 98.29/15.81 | (32) u1_struct_0(all_131_3) = all_177_0 & $i(all_177_0) &
% 98.29/15.81 | m2_relset_1(all_131_2, all_177_0, all_177_0) & v1_funct_2(all_131_2,
% 98.29/15.81 | all_177_0, all_177_0)
% 98.29/15.81 |
% 98.29/15.81 | ALPHA: (32) implies:
% 98.29/15.81 | (33) v1_funct_2(all_131_2, all_177_0, all_177_0)
% 98.29/15.81 | (34) m2_relset_1(all_131_2, all_177_0, all_177_0)
% 98.29/15.81 | (35) u1_struct_0(all_131_3) = all_177_0
% 98.29/15.81 |
% 98.29/15.81 | DELTA: instantiating (30) with fresh symbol all_179_0 gives:
% 98.29/15.81 | (36) k7_grcat_1(all_131_3) = all_179_0 & $i(all_179_0) &
% 98.29/15.81 | m2_relset_1(all_179_0, all_161_0, all_161_0) & v1_funct_2(all_179_0,
% 98.29/15.81 | all_161_0, all_161_0) & v1_funct_1(all_179_0)
% 98.29/15.81 |
% 98.29/15.81 | ALPHA: (36) implies:
% 98.29/15.81 | (37) v1_funct_1(all_179_0)
% 98.29/15.81 | (38) $i(all_179_0)
% 98.29/15.81 | (39) k7_grcat_1(all_131_3) = all_179_0
% 98.29/15.81 |
% 98.29/15.81 | DELTA: instantiating (31) with fresh symbol all_181_0 gives:
% 98.29/15.81 | (40) k7_grcat_1(all_131_3) = all_181_0 & $i(all_181_0) &
% 98.29/15.81 | v2_funct_1(all_181_0) & v1_funct_2(all_181_0, all_161_0, all_161_0) &
% 98.29/15.81 | v1_relat_1(all_181_0) & v1_funct_1(all_181_0)
% 98.29/15.81 |
% 98.29/15.81 | ALPHA: (40) implies:
% 98.29/15.81 | (41) k7_grcat_1(all_131_3) = all_181_0
% 98.29/15.81 |
% 98.29/15.81 | GROUND_INST: instantiating (9) with all_161_0, all_177_0, all_131_3,
% 98.29/15.81 | simplifying with (28), (35) gives:
% 98.29/15.81 | (42) all_177_0 = all_161_0
% 98.29/15.81 |
% 98.29/15.81 | GROUND_INST: instantiating (10) with all_131_2, all_181_0, all_131_3,
% 98.29/15.81 | simplifying with (20), (41) gives:
% 98.29/15.81 | (43) all_181_0 = all_131_2
% 98.29/15.81 |
% 98.29/15.81 | GROUND_INST: instantiating (10) with all_179_0, all_181_0, all_131_3,
% 98.29/15.81 | simplifying with (39), (41) gives:
% 98.29/15.81 | (44) all_181_0 = all_179_0
% 98.29/15.81 |
% 98.29/15.81 | COMBINE_EQS: (43), (44) imply:
% 98.29/15.81 | (45) all_179_0 = all_131_2
% 98.29/15.81 |
% 98.29/15.81 | REDUCE: (38), (45) imply:
% 98.29/15.82 | (46) $i(all_131_2)
% 98.29/15.82 |
% 98.29/15.82 | REDUCE: (34), (42) imply:
% 98.29/15.82 | (47) m2_relset_1(all_131_2, all_161_0, all_161_0)
% 98.29/15.82 |
% 98.29/15.82 | REDUCE: (33), (42) imply:
% 98.29/15.82 | (48) v1_funct_2(all_131_2, all_161_0, all_161_0)
% 98.29/15.82 |
% 98.29/15.82 | REDUCE: (37), (45) imply:
% 98.29/15.82 | (49) v1_funct_1(all_131_2)
% 98.29/15.82 |
% 98.29/15.82 | BETA: splitting (21) gives:
% 98.29/15.82 |
% 98.29/15.82 | Case 1:
% 98.29/15.82 | |
% 98.29/15.82 | | (50) ~ (all_131_0 = all_131_2) & k2_waybel34(all_131_3, all_131_3,
% 98.29/15.82 | | all_131_2) = all_131_0 & $i(all_131_0)
% 98.29/15.82 | |
% 98.29/15.82 | | ALPHA: (50) implies:
% 98.29/15.82 | | (51) ~ (all_131_0 = all_131_2)
% 98.29/15.82 | | (52) k2_waybel34(all_131_3, all_131_3, all_131_2) = all_131_0
% 98.29/15.82 | |
% 98.29/15.82 | | GROUND_INST: instantiating (dt_k2_waybel34) with all_131_3, all_131_3,
% 98.29/15.82 | | all_131_2, all_131_0, simplifying with (12), (13), (14), (15),
% 98.29/15.82 | | (16), (18), (19), (46), (49), (52) gives:
% 98.29/15.82 | | (53) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_131_3) = v1 &
% 98.29/15.82 | | u1_struct_0(all_131_3) = v0 & $i(v1) & $i(v0) & ( ~
% 98.29/15.82 | | v1_funct_2(all_131_2, v0, v1) | ~ m1_relset_1(all_131_2, v0,
% 98.29/15.82 | | v1) | (m2_relset_1(all_131_0, v1, v0) & v1_funct_2(all_131_0,
% 98.29/15.82 | | v1, v0) & v1_funct_1(all_131_0))))
% 98.29/15.82 | |
% 98.29/15.82 | | DELTA: instantiating (53) with fresh symbols all_254_0, all_254_1 gives:
% 98.29/15.82 | | (54) u1_struct_0(all_131_3) = all_254_0 & u1_struct_0(all_131_3) =
% 98.29/15.82 | | all_254_1 & $i(all_254_0) & $i(all_254_1) & ( ~
% 98.29/15.82 | | v1_funct_2(all_131_2, all_254_1, all_254_0) | ~
% 98.29/15.82 | | m1_relset_1(all_131_2, all_254_1, all_254_0) |
% 98.29/15.82 | | (m2_relset_1(all_131_0, all_254_0, all_254_1) &
% 98.29/15.82 | | v1_funct_2(all_131_0, all_254_0, all_254_1) &
% 98.29/15.82 | | v1_funct_1(all_131_0)))
% 98.29/15.82 | |
% 98.29/15.82 | | ALPHA: (54) implies:
% 98.29/15.82 | | (55) u1_struct_0(all_131_3) = all_254_1
% 98.29/15.82 | | (56) u1_struct_0(all_131_3) = all_254_0
% 98.29/15.82 | |
% 98.29/15.82 | | GROUND_INST: instantiating (9) with all_161_0, all_254_0, all_131_3,
% 98.29/15.82 | | simplifying with (28), (56) gives:
% 98.29/15.82 | | (57) all_254_0 = all_161_0
% 98.29/15.82 | |
% 98.29/15.82 | | GROUND_INST: instantiating (9) with all_254_1, all_254_0, all_131_3,
% 98.29/15.82 | | simplifying with (55), (56) gives:
% 98.29/15.82 | | (58) all_254_0 = all_254_1
% 98.29/15.82 | |
% 98.29/15.82 | | COMBINE_EQS: (57), (58) imply:
% 98.29/15.82 | | (59) all_254_1 = all_161_0
% 98.29/15.82 | |
% 98.29/15.82 | | BETA: splitting (25) gives:
% 98.29/15.82 | |
% 98.29/15.82 | | Case 1:
% 98.29/15.82 | | |
% 98.29/15.82 | | | (60) v3_struct_0(all_131_3)
% 98.29/15.82 | | |
% 98.29/15.82 | | | GROUND_INST: instantiating (cc1_lattice3) with all_131_3, simplifying with
% 98.29/15.82 | | | (15), (18), (19), (60) gives:
% 98.29/15.82 | | | (61) $false
% 98.29/15.82 | | |
% 98.29/15.82 | | | CLOSE: (61) is inconsistent.
% 98.29/15.82 | | |
% 98.29/15.83 | | Case 2:
% 98.29/15.83 | | |
% 98.29/15.83 | | | (62) ? [v0: $i] : (k1_waybel_1(all_131_3, all_131_3, all_131_2,
% 98.29/15.83 | | | all_131_2) = v0 & $i(v0) & v3_waybel_1(v0, all_131_3,
% 98.29/15.83 | | | all_131_3))
% 98.29/15.83 | | |
% 98.29/15.83 | | | DELTA: instantiating (62) with fresh symbol all_302_0 gives:
% 98.29/15.83 | | | (63) k1_waybel_1(all_131_3, all_131_3, all_131_2, all_131_2) =
% 98.29/15.83 | | | all_302_0 & $i(all_302_0) & v3_waybel_1(all_302_0, all_131_3,
% 98.29/15.83 | | | all_131_3)
% 98.29/15.83 | | |
% 98.29/15.83 | | | ALPHA: (63) implies:
% 98.29/15.83 | | | (64) v3_waybel_1(all_302_0, all_131_3, all_131_3)
% 98.29/15.83 | | | (65) k1_waybel_1(all_131_3, all_131_3, all_131_2, all_131_2) =
% 98.29/15.83 | | | all_302_0
% 98.29/15.83 | | |
% 98.29/15.83 | | | BETA: splitting (23) gives:
% 98.29/15.83 | | |
% 98.29/15.83 | | | Case 1:
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | (66) v18_waybel_0(all_131_2, all_131_3, all_131_3)
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | GROUND_INST: instantiating (2) with all_131_3, all_161_0, all_131_3,
% 98.29/15.83 | | | | all_161_0, all_131_2, all_131_0, all_131_2, all_302_0,
% 98.29/15.83 | | | | simplifying with (12), (13), (14), (15), (16), (17), (18),
% 98.29/15.83 | | | | (19), (28), (46), (47), (48), (49), (52), (64), (65), (66)
% 98.29/15.83 | | | | gives:
% 98.29/15.83 | | | | (67) all_131_0 = all_131_2
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | REDUCE: (51), (67) imply:
% 98.29/15.83 | | | | (68) $false
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | CLOSE: (68) is inconsistent.
% 98.29/15.83 | | | |
% 98.29/15.83 | | | Case 2:
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | (69) v3_struct_0(all_131_3)
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | GROUND_INST: instantiating (cc1_lattice3) with all_131_3, simplifying
% 98.29/15.83 | | | | with (15), (18), (19), (69) gives:
% 98.29/15.83 | | | | (70) $false
% 98.29/15.83 | | | |
% 98.29/15.83 | | | | CLOSE: (70) is inconsistent.
% 98.29/15.83 | | | |
% 98.77/15.83 | | | End of split
% 98.77/15.83 | | |
% 98.77/15.83 | | End of split
% 98.77/15.83 | |
% 98.77/15.83 | Case 2:
% 98.77/15.83 | |
% 98.77/15.83 | | (71) ~ (all_131_1 = all_131_2) & k1_waybel34(all_131_3, all_131_3,
% 98.77/15.83 | | all_131_2) = all_131_1 & $i(all_131_1)
% 98.77/15.83 | |
% 98.77/15.83 | | ALPHA: (71) implies:
% 98.77/15.83 | | (72) ~ (all_131_1 = all_131_2)
% 98.77/15.83 | | (73) k1_waybel34(all_131_3, all_131_3, all_131_2) = all_131_1
% 98.77/15.83 | |
% 98.77/15.83 | | GROUND_INST: instantiating (dt_k1_waybel34) with all_131_3, all_131_3,
% 98.77/15.83 | | all_131_2, all_131_1, simplifying with (12), (13), (14), (15),
% 98.77/15.83 | | (16), (18), (19), (46), (49), (73) gives:
% 98.77/15.83 | | (74) ? [v0: $i] : ? [v1: $i] : (u1_struct_0(all_131_3) = v1 &
% 98.77/15.83 | | u1_struct_0(all_131_3) = v0 & $i(v1) & $i(v0) & ( ~
% 98.77/15.83 | | v1_funct_2(all_131_2, v0, v1) | ~ m1_relset_1(all_131_2, v0,
% 98.77/15.83 | | v1) | (m2_relset_1(all_131_1, v1, v0) & v1_funct_2(all_131_1,
% 98.77/15.83 | | v1, v0) & v1_funct_1(all_131_1))))
% 98.77/15.83 | |
% 98.77/15.83 | | DELTA: instantiating (74) with fresh symbols all_254_0, all_254_1 gives:
% 98.77/15.83 | | (75) u1_struct_0(all_131_3) = all_254_0 & u1_struct_0(all_131_3) =
% 98.77/15.83 | | all_254_1 & $i(all_254_0) & $i(all_254_1) & ( ~
% 98.77/15.83 | | v1_funct_2(all_131_2, all_254_1, all_254_0) | ~
% 98.77/15.83 | | m1_relset_1(all_131_2, all_254_1, all_254_0) |
% 98.77/15.83 | | (m2_relset_1(all_131_1, all_254_0, all_254_1) &
% 98.77/15.83 | | v1_funct_2(all_131_1, all_254_0, all_254_1) &
% 98.77/15.83 | | v1_funct_1(all_131_1)))
% 98.77/15.83 | |
% 98.77/15.83 | | ALPHA: (75) implies:
% 98.77/15.83 | | (76) u1_struct_0(all_131_3) = all_254_1
% 98.77/15.83 | | (77) u1_struct_0(all_131_3) = all_254_0
% 98.77/15.83 | |
% 98.77/15.83 | | GROUND_INST: instantiating (9) with all_161_0, all_254_0, all_131_3,
% 98.77/15.83 | | simplifying with (28), (77) gives:
% 98.77/15.83 | | (78) all_254_0 = all_161_0
% 98.77/15.83 | |
% 98.77/15.83 | | GROUND_INST: instantiating (9) with all_254_1, all_254_0, all_131_3,
% 98.77/15.83 | | simplifying with (76), (77) gives:
% 98.77/15.84 | | (79) all_254_0 = all_254_1
% 98.77/15.84 | |
% 98.77/15.84 | | COMBINE_EQS: (78), (79) imply:
% 98.77/15.84 | | (80) all_254_1 = all_161_0
% 98.77/15.84 | |
% 98.77/15.84 | | BETA: splitting (25) gives:
% 98.77/15.84 | |
% 98.77/15.84 | | Case 1:
% 98.77/15.84 | | |
% 98.77/15.84 | | | (81) v3_struct_0(all_131_3)
% 98.77/15.84 | | |
% 98.77/15.84 | | | GROUND_INST: instantiating (cc1_lattice3) with all_131_3, simplifying with
% 98.77/15.84 | | | (15), (18), (19), (81) gives:
% 98.77/15.84 | | | (82) $false
% 98.77/15.84 | | |
% 98.77/15.84 | | | CLOSE: (82) is inconsistent.
% 98.77/15.84 | | |
% 98.77/15.84 | | Case 2:
% 98.77/15.84 | | |
% 98.77/15.84 | | | (83) ? [v0: $i] : (k1_waybel_1(all_131_3, all_131_3, all_131_2,
% 98.77/15.84 | | | all_131_2) = v0 & $i(v0) & v3_waybel_1(v0, all_131_3,
% 98.77/15.84 | | | all_131_3))
% 98.77/15.84 | | |
% 98.77/15.84 | | | DELTA: instantiating (83) with fresh symbol all_304_0 gives:
% 98.77/15.84 | | | (84) k1_waybel_1(all_131_3, all_131_3, all_131_2, all_131_2) =
% 98.77/15.84 | | | all_304_0 & $i(all_304_0) & v3_waybel_1(all_304_0, all_131_3,
% 98.77/15.84 | | | all_131_3)
% 98.77/15.84 | | |
% 98.77/15.84 | | | ALPHA: (84) implies:
% 98.77/15.84 | | | (85) v3_waybel_1(all_304_0, all_131_3, all_131_3)
% 98.77/15.84 | | | (86) k1_waybel_1(all_131_3, all_131_3, all_131_2, all_131_2) =
% 98.77/15.84 | | | all_304_0
% 98.77/15.84 | | |
% 98.77/15.84 | | | BETA: splitting (24) gives:
% 98.77/15.84 | | |
% 98.77/15.84 | | | Case 1:
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | (87) v17_waybel_0(all_131_2, all_131_3, all_131_3)
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | GROUND_INST: instantiating (1) with all_131_3, all_161_0, all_131_3,
% 98.77/15.84 | | | | all_161_0, all_131_2, all_131_1, all_131_2, all_304_0,
% 98.77/15.84 | | | | simplifying with (12), (13), (14), (15), (16), (17), (18),
% 98.77/15.84 | | | | (19), (28), (46), (47), (48), (49), (73), (85), (86), (87)
% 98.77/15.84 | | | | gives:
% 98.77/15.84 | | | | (88) all_131_1 = all_131_2
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | REDUCE: (72), (88) imply:
% 98.77/15.84 | | | | (89) $false
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | CLOSE: (89) is inconsistent.
% 98.77/15.84 | | | |
% 98.77/15.84 | | | Case 2:
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | (90) v3_struct_0(all_131_3)
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | GROUND_INST: instantiating (cc1_lattice3) with all_131_3, simplifying
% 98.77/15.84 | | | | with (15), (18), (19), (90) gives:
% 98.77/15.84 | | | | (91) $false
% 98.77/15.84 | | | |
% 98.77/15.84 | | | | CLOSE: (91) is inconsistent.
% 98.77/15.84 | | | |
% 98.77/15.84 | | | End of split
% 98.77/15.84 | | |
% 98.77/15.84 | | End of split
% 98.77/15.84 | |
% 98.77/15.84 | End of split
% 98.77/15.84 |
% 98.77/15.84 End of proof
% 98.77/15.84 % SZS output end Proof for theBenchmark
% 98.77/15.84
% 98.77/15.84 15248ms
%------------------------------------------------------------------------------