TSTP Solution File: SEU032+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 17:42:21 EDT 2023
% Result : Theorem 13.96s 2.82s
% Output : Proof 23.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n011.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 : Wed Aug 23 12:16:06 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.63/1.13 Prover 4: Preprocessing ...
% 2.63/1.13 Prover 1: Preprocessing ...
% 3.25/1.17 Prover 2: Preprocessing ...
% 3.25/1.17 Prover 3: Preprocessing ...
% 3.25/1.17 Prover 0: Preprocessing ...
% 3.25/1.17 Prover 5: Preprocessing ...
% 3.25/1.17 Prover 6: Preprocessing ...
% 6.99/1.70 Prover 1: Warning: ignoring some quantifiers
% 6.99/1.72 Prover 3: Warning: ignoring some quantifiers
% 6.99/1.73 Prover 1: Constructing countermodel ...
% 6.99/1.74 Prover 3: Constructing countermodel ...
% 6.99/1.76 Prover 5: Proving ...
% 6.99/1.76 Prover 6: Proving ...
% 6.99/1.79 Prover 2: Proving ...
% 8.47/1.99 Prover 4: Warning: ignoring some quantifiers
% 9.17/2.04 Prover 0: Proving ...
% 9.17/2.08 Prover 4: Constructing countermodel ...
% 13.96/2.81 Prover 0: proved (2184ms)
% 13.96/2.81
% 13.96/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.96/2.82
% 13.96/2.83 Prover 5: stopped
% 13.96/2.84 Prover 3: stopped
% 13.96/2.85 Prover 2: stopped
% 13.96/2.85 Prover 6: stopped
% 13.96/2.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.96/2.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.96/2.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.96/2.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.96/2.87 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.96/2.89 Prover 7: Preprocessing ...
% 13.96/2.91 Prover 10: Preprocessing ...
% 14.97/2.92 Prover 8: Preprocessing ...
% 14.97/2.93 Prover 11: Preprocessing ...
% 14.97/2.94 Prover 13: Preprocessing ...
% 16.26/2.98 Prover 10: Warning: ignoring some quantifiers
% 16.26/2.99 Prover 7: Warning: ignoring some quantifiers
% 16.26/2.99 Prover 10: Constructing countermodel ...
% 16.26/3.00 Prover 7: Constructing countermodel ...
% 16.70/3.04 Prover 13: Warning: ignoring some quantifiers
% 16.70/3.05 Prover 13: Constructing countermodel ...
% 16.91/3.07 Prover 8: Warning: ignoring some quantifiers
% 16.91/3.09 Prover 8: Constructing countermodel ...
% 16.91/3.10 Prover 10: gave up
% 16.91/3.10 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 17.45/3.12 Prover 16: Preprocessing ...
% 17.45/3.14 Prover 11: Warning: ignoring some quantifiers
% 17.45/3.16 Prover 11: Constructing countermodel ...
% 17.74/3.18 Prover 16: Warning: ignoring some quantifiers
% 17.74/3.19 Prover 16: Constructing countermodel ...
% 22.06/3.75 Prover 7: Found proof (size 186)
% 22.06/3.75 Prover 7: proved (927ms)
% 22.06/3.76 Prover 16: stopped
% 22.06/3.76 Prover 8: stopped
% 22.06/3.76 Prover 4: stopped
% 22.06/3.76 Prover 1: stopped
% 22.06/3.76 Prover 11: stopped
% 22.06/3.76 Prover 13: stopped
% 22.06/3.76
% 22.06/3.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.06/3.76
% 22.06/3.81 % SZS output start Proof for theBenchmark
% 22.06/3.81 Assumptions after simplification:
% 22.06/3.81 ---------------------------------
% 22.06/3.81
% 22.06/3.81 (dt_k2_funct_1)
% 22.46/3.83 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.83 relation(v0) | ~ function(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] :
% 22.46/3.83 ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~
% 22.46/3.83 function(v0) | function(v1))
% 22.46/3.83
% 22.46/3.83 (t55_funct_1)
% 22.46/3.84 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.84 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 22.46/3.84 $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) =
% 22.46/3.84 v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i]
% 22.46/3.84 : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) |
% 22.46/3.84 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] :
% 22.46/3.84 (relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2 &
% 22.46/3.84 function_inverse(v0) = v3 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : !
% 22.46/3.84 [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ one_to_one(v0) |
% 22.46/3.84 ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] :
% 22.46/3.84 (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 &
% 22.46/3.84 relation_dom(v0) = v3 & $i(v3) & $i(v2)))
% 22.46/3.84
% 22.46/3.84 (t61_funct_1)
% 22.46/3.84 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.84 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 22.46/3.84 $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 22.46/3.84 identity_relation(v4) = v3 & identity_relation(v1) = v5 &
% 22.46/3.84 relation_composition(v2, v0) = v5 & relation_composition(v0, v2) = v3 &
% 22.46/3.84 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0:
% 22.46/3.84 $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.84 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 22.46/3.84 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 22.46/3.84 identity_relation(v5) = v4 & identity_relation(v1) = v3 &
% 22.46/3.84 relation_composition(v2, v0) = v4 & relation_composition(v0, v2) = v3 &
% 22.46/3.84 function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2))) & ! [v0:
% 22.46/3.84 $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.84 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 22.46/3.84 $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 22.46/3.84 relation_dom(v0) = v3 & identity_relation(v5) = v4 & identity_relation(v3)
% 22.46/3.84 = v2 & relation_composition(v1, v0) = v4 & relation_composition(v0, v1) =
% 22.46/3.84 v2 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 22.46/3.84
% 22.46/3.84 (t62_funct_1)
% 22.46/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.85 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1))
% 22.46/3.85
% 22.46/3.85 (t63_funct_1)
% 22.46/3.85 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 22.46/3.85 relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 22.46/3.85 (relation_dom(v0) = v2 & identity_relation(v2) = v3 & function_inverse(v0) =
% 22.46/3.85 v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i] : (v5 = v4 | ~
% 22.46/3.85 (relation_dom(v5) = v1) | ~ $i(v5) | ~ one_to_one(v0) | ~
% 22.46/3.85 relation(v5) | ~ function(v5) | ? [v6: $i] : ( ~ (v6 = v3) &
% 22.46/3.85 relation_composition(v0, v5) = v6 & $i(v6))) & ! [v5: $i] : (v5 = v4
% 22.46/3.85 | ~ (relation_composition(v0, v5) = v3) | ~ $i(v5) | ~ one_to_one(v0)
% 22.46/3.85 | ~ relation(v5) | ~ function(v5) | ? [v6: $i] : ( ~ (v6 = v1) &
% 22.46/3.85 relation_dom(v5) = v6 & $i(v6))))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 22.46/3.85 (relation_dom(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) | ?
% 22.46/3.85 [v2: $i] : ? [v3: $i] : ? [v4: $i] : (relation_rng(v0) = v2 &
% 22.46/3.85 identity_relation(v1) = v3 & function_inverse(v0) = v4 & $i(v4) & $i(v3) &
% 22.46/3.85 $i(v2) & ! [v5: $i] : (v5 = v4 | ~ (relation_dom(v5) = v2) | ~ $i(v5) |
% 22.46/3.85 ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i] : (
% 22.46/3.85 ~ (v6 = v3) & relation_composition(v0, v5) = v6 & $i(v6))) & ! [v5:
% 22.46/3.85 $i] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) | ~ $i(v5) | ~
% 22.46/3.85 one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i] : ( ~
% 22.46/3.85 (v6 = v2) & relation_dom(v5) = v6 & $i(v6))))) & ! [v0: $i] : ! [v1:
% 22.46/3.85 $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~ relation(v0) | ~
% 22.46/3.85 function(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : (relation_rng(v0) =
% 22.46/3.85 v2 & relation_dom(v0) = v3 & identity_relation(v3) = v4 & $i(v4) & $i(v3)
% 22.46/3.85 & $i(v2) & ! [v5: $i] : (v5 = v1 | ~ (relation_dom(v5) = v2) | ~ $i(v5)
% 22.46/3.85 | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i] :
% 22.46/3.85 ( ~ (v6 = v4) & relation_composition(v0, v5) = v6 & $i(v6))) & ! [v5:
% 22.46/3.85 $i] : (v5 = v1 | ~ (relation_composition(v0, v5) = v4) | ~ $i(v5) | ~
% 22.46/3.85 one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i] : ( ~
% 22.46/3.85 (v6 = v2) & relation_dom(v5) = v6 & $i(v6)))))
% 22.46/3.85
% 22.46/3.85 (t65_funct_1)
% 22.46/3.85 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v0) & function_inverse(v1)
% 22.46/3.85 = v2 & function_inverse(v0) = v1 & $i(v2) & $i(v1) & $i(v0) & one_to_one(v0)
% 22.46/3.85 & relation(v0) & function(v0))
% 22.46/3.85
% 22.46/3.85 (function-axioms)
% 22.46/3.85 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.46/3.85 (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) =
% 22.46/3.85 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.46/3.85 (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : !
% 22.46/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 22.46/3.85 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 22.46/3.85 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0: $i] : !
% 22.46/3.85 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~
% 22.46/3.85 (identity_relation(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 22.46/3.85 (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 22.46/3.85
% 22.46/3.85 Further assumptions not needed in the proof:
% 22.46/3.85 --------------------------------------------
% 22.46/3.85 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k5_relat_1,
% 22.46/3.85 dt_k6_relat_1, existence_m1_subset_1, fc10_relat_1, fc12_relat_1, fc1_funct_1,
% 22.46/3.85 fc1_subset_1, fc1_xboole_0, fc2_funct_1, fc4_relat_1, fc5_relat_1, fc6_relat_1,
% 22.46/3.85 fc7_relat_1, fc8_relat_1, fc9_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1,
% 22.46/3.85 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1,
% 22.46/3.85 rc3_relat_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset,
% 22.46/3.85 t5_subset, t6_boole, t7_boole, t8_boole
% 22.46/3.85
% 22.46/3.85 Those formulas are unsatisfiable:
% 22.46/3.85 ---------------------------------
% 22.46/3.85
% 22.46/3.85 Begin of proof
% 22.46/3.86 |
% 22.46/3.86 | ALPHA: (dt_k2_funct_1) implies:
% 22.46/3.86 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 22.46/3.86 | | ~ relation(v0) | ~ function(v0) | function(v1))
% 22.46/3.86 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 22.46/3.86 | | ~ relation(v0) | ~ function(v0) | relation(v1))
% 22.46/3.86 |
% 22.46/3.86 | ALPHA: (t55_funct_1) implies:
% 22.46/3.86 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 22.46/3.86 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i]
% 22.46/3.86 | : ? [v3: $i] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 &
% 22.46/3.86 | relation_dom(v1) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2)))
% 22.46/3.86 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 22.46/3.86 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 22.46/3.86 | ? [v3: $i] : (relation_rng(v3) = v1 & relation_rng(v0) = v2 &
% 22.46/3.86 | relation_dom(v3) = v2 & function_inverse(v0) = v3 & $i(v3) & $i(v2)
% 22.46/3.86 | & $i(v1)))
% 22.46/3.86 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 22.46/3.86 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 22.46/3.86 | ? [v3: $i] : (relation_rng(v2) = v3 & relation_dom(v2) = v1 &
% 22.46/3.86 | relation_dom(v0) = v3 & function_inverse(v0) = v2 & $i(v3) & $i(v2)
% 22.46/3.86 | & $i(v1)))
% 22.46/3.86 |
% 22.46/3.86 | ALPHA: (t61_funct_1) implies:
% 22.46/3.86 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 22.46/3.86 | | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i]
% 22.46/3.86 | : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 22.46/3.86 | relation_dom(v0) = v3 & identity_relation(v5) = v4 &
% 22.46/3.86 | identity_relation(v3) = v2 & relation_composition(v1, v0) = v4 &
% 22.46/3.86 | relation_composition(v0, v1) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 22.46/3.86 | $i(v2)))
% 22.46/3.86 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 22.46/3.86 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 22.46/3.86 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_rng(v0) = v5 &
% 22.46/3.86 | identity_relation(v5) = v4 & identity_relation(v1) = v3 &
% 22.46/3.86 | relation_composition(v2, v0) = v4 & relation_composition(v0, v2) =
% 22.46/3.86 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 22.46/3.86 | $i(v2)))
% 22.46/3.86 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 22.46/3.86 | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] :
% 22.46/3.86 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (relation_dom(v0) = v4 &
% 22.46/3.86 | identity_relation(v4) = v3 & identity_relation(v1) = v5 &
% 22.46/3.86 | relation_composition(v2, v0) = v5 & relation_composition(v0, v2) =
% 22.46/3.86 | v3 & function_inverse(v0) = v2 & $i(v5) & $i(v4) & $i(v3) &
% 22.46/3.86 | $i(v2)))
% 22.46/3.86 |
% 22.46/3.86 | ALPHA: (t63_funct_1) implies:
% 22.46/3.87 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0)
% 22.46/3.87 | | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 22.46/3.87 | [v4: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 &
% 22.46/3.87 | identity_relation(v3) = v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i]
% 22.46/3.87 | : (v5 = v1 | ~ (relation_dom(v5) = v2) | ~ $i(v5) | ~
% 22.46/3.87 | one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i]
% 22.46/3.87 | : ( ~ (v6 = v4) & relation_composition(v0, v5) = v6 & $i(v6))) &
% 22.46/3.87 | ! [v5: $i] : (v5 = v1 | ~ (relation_composition(v0, v5) = v4) | ~
% 22.46/3.87 | $i(v5) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5) |
% 22.46/3.87 | ? [v6: $i] : ( ~ (v6 = v2) & relation_dom(v5) = v6 & $i(v6)))))
% 22.46/3.87 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 22.46/3.87 | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 22.46/3.87 | [v4: $i] : (relation_rng(v0) = v2 & identity_relation(v1) = v3 &
% 22.46/3.87 | function_inverse(v0) = v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i]
% 22.46/3.87 | : (v5 = v4 | ~ (relation_dom(v5) = v2) | ~ $i(v5) | ~
% 22.46/3.87 | one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i]
% 22.46/3.87 | : ( ~ (v6 = v3) & relation_composition(v0, v5) = v6 & $i(v6))) &
% 22.46/3.87 | ! [v5: $i] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) |
% 22.46/3.87 | ~ $i(v5) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5)
% 22.46/3.87 | | ? [v6: $i] : ( ~ (v6 = v2) & relation_dom(v5) = v6 &
% 22.46/3.87 | $i(v6)))))
% 22.46/3.87 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 22.46/3.87 | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 22.46/3.87 | [v4: $i] : (relation_dom(v0) = v2 & identity_relation(v2) = v3 &
% 22.46/3.87 | function_inverse(v0) = v4 & $i(v4) & $i(v3) & $i(v2) & ! [v5: $i]
% 22.46/3.87 | : (v5 = v4 | ~ (relation_dom(v5) = v1) | ~ $i(v5) | ~
% 22.46/3.87 | one_to_one(v0) | ~ relation(v5) | ~ function(v5) | ? [v6: $i]
% 22.46/3.87 | : ( ~ (v6 = v3) & relation_composition(v0, v5) = v6 & $i(v6))) &
% 22.46/3.87 | ! [v5: $i] : (v5 = v4 | ~ (relation_composition(v0, v5) = v3) |
% 22.46/3.87 | ~ $i(v5) | ~ one_to_one(v0) | ~ relation(v5) | ~ function(v5)
% 22.46/3.87 | | ? [v6: $i] : ( ~ (v6 = v1) & relation_dom(v5) = v6 &
% 22.46/3.87 | $i(v6)))))
% 22.46/3.87 |
% 22.46/3.87 | ALPHA: (function-axioms) implies:
% 22.46/3.87 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.46/3.87 | (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 22.46/3.87 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.46/3.87 | (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 22.46/3.87 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.46/3.87 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 22.46/3.87 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.46/3.87 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 22.46/3.87 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.46/3.87 | (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3,
% 22.46/3.87 | v2) = v0))
% 22.46/3.87 |
% 22.46/3.87 | DELTA: instantiating (t65_funct_1) with fresh symbols all_52_0, all_52_1,
% 22.46/3.87 | all_52_2 gives:
% 22.46/3.87 | (17) ~ (all_52_0 = all_52_2) & function_inverse(all_52_1) = all_52_0 &
% 22.46/3.87 | function_inverse(all_52_2) = all_52_1 & $i(all_52_0) & $i(all_52_1) &
% 22.46/3.87 | $i(all_52_2) & one_to_one(all_52_2) & relation(all_52_2) &
% 22.46/3.87 | function(all_52_2)
% 22.46/3.87 |
% 22.46/3.87 | ALPHA: (17) implies:
% 22.46/3.87 | (18) ~ (all_52_0 = all_52_2)
% 22.46/3.87 | (19) function(all_52_2)
% 22.46/3.87 | (20) relation(all_52_2)
% 22.46/3.87 | (21) one_to_one(all_52_2)
% 22.46/3.87 | (22) $i(all_52_2)
% 22.46/3.87 | (23) $i(all_52_1)
% 22.46/3.87 | (24) function_inverse(all_52_2) = all_52_1
% 22.46/3.87 | (25) function_inverse(all_52_1) = all_52_0
% 22.46/3.87 |
% 22.46/3.87 | GROUND_INST: instantiating (t62_funct_1) with all_52_2, all_52_1, simplifying
% 22.46/3.87 | with (19), (20), (21), (22), (24) gives:
% 22.46/3.88 | (26) one_to_one(all_52_1)
% 22.46/3.88 |
% 22.46/3.88 | GROUND_INST: instantiating (6) with all_52_2, all_52_1, simplifying with (19),
% 22.46/3.88 | (20), (21), (22), (24) gives:
% 22.46/3.88 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 22.46/3.88 | (relation_rng(all_52_2) = v3 & relation_dom(all_52_2) = v1 &
% 22.46/3.88 | identity_relation(v3) = v2 & identity_relation(v1) = v0 &
% 22.46/3.88 | relation_composition(all_52_1, all_52_2) = v2 &
% 22.46/3.88 | relation_composition(all_52_2, all_52_1) = v0 & $i(v3) & $i(v2) &
% 22.46/3.88 | $i(v1) & $i(v0))
% 22.46/3.88 |
% 22.46/3.88 | GROUND_INST: instantiating (3) with all_52_2, all_52_1, simplifying with (19),
% 22.46/3.88 | (20), (21), (22), (24) gives:
% 22.46/3.88 | (28) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_52_1) = v1 &
% 22.46/3.88 | relation_rng(all_52_2) = v0 & relation_dom(all_52_1) = v0 &
% 22.46/3.88 | relation_dom(all_52_2) = v1 & $i(v1) & $i(v0))
% 22.46/3.88 |
% 22.46/3.88 | GROUND_INST: instantiating (2) with all_52_2, all_52_1, simplifying with (19),
% 22.46/3.88 | (20), (22), (24) gives:
% 22.46/3.88 | (29) relation(all_52_1)
% 22.46/3.88 |
% 22.46/3.88 | GROUND_INST: instantiating (1) with all_52_2, all_52_1, simplifying with (19),
% 22.46/3.88 | (20), (22), (24) gives:
% 22.46/3.88 | (30) function(all_52_1)
% 22.46/3.88 |
% 22.46/3.88 | GROUND_INST: instantiating (9) with all_52_2, all_52_1, simplifying with (19),
% 22.46/3.88 | (20), (22), (24) gives:
% 22.46/3.88 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_52_2) = v0
% 22.46/3.88 | & relation_dom(all_52_2) = v1 & identity_relation(v1) = v2 & $i(v2)
% 22.46/3.88 | & $i(v1) & $i(v0) & ! [v3: any] : (v3 = all_52_1 | ~
% 22.46/3.88 | (relation_dom(v3) = v0) | ~ $i(v3) | ~ one_to_one(all_52_2) | ~
% 22.46/3.88 | relation(v3) | ~ function(v3) | ? [v4: $i] : ( ~ (v4 = v2) &
% 22.46/3.88 | relation_composition(all_52_2, v3) = v4 & $i(v4))) & ! [v3:
% 22.46/3.88 | any] : (v3 = all_52_1 | ~ (relation_composition(all_52_2, v3) =
% 22.46/3.88 | v2) | ~ $i(v3) | ~ one_to_one(all_52_2) | ~ relation(v3) | ~
% 22.46/3.88 | function(v3) | ? [v4: $i] : ( ~ (v4 = v0) & relation_dom(v3) = v4
% 22.46/3.88 | & $i(v4))))
% 22.46/3.88 |
% 22.46/3.88 | DELTA: instantiating (28) with fresh symbols all_64_0, all_64_1 gives:
% 22.73/3.88 | (32) relation_rng(all_52_1) = all_64_0 & relation_rng(all_52_2) = all_64_1
% 22.73/3.88 | & relation_dom(all_52_1) = all_64_1 & relation_dom(all_52_2) =
% 22.73/3.88 | all_64_0 & $i(all_64_0) & $i(all_64_1)
% 22.73/3.88 |
% 22.73/3.88 | ALPHA: (32) implies:
% 22.73/3.88 | (33) relation_dom(all_52_2) = all_64_0
% 22.73/3.88 | (34) relation_dom(all_52_1) = all_64_1
% 22.73/3.88 | (35) relation_rng(all_52_2) = all_64_1
% 22.73/3.88 | (36) relation_rng(all_52_1) = all_64_0
% 22.73/3.88 |
% 22.73/3.88 | DELTA: instantiating (27) with fresh symbols all_66_0, all_66_1, all_66_2,
% 22.73/3.88 | all_66_3 gives:
% 22.73/3.88 | (37) relation_rng(all_52_2) = all_66_0 & relation_dom(all_52_2) = all_66_2
% 22.73/3.88 | & identity_relation(all_66_0) = all_66_1 & identity_relation(all_66_2)
% 22.73/3.88 | = all_66_3 & relation_composition(all_52_1, all_52_2) = all_66_1 &
% 22.73/3.88 | relation_composition(all_52_2, all_52_1) = all_66_3 & $i(all_66_0) &
% 22.73/3.88 | $i(all_66_1) & $i(all_66_2) & $i(all_66_3)
% 22.73/3.88 |
% 22.73/3.88 | ALPHA: (37) implies:
% 22.73/3.88 | (38) relation_composition(all_52_1, all_52_2) = all_66_1
% 22.73/3.88 | (39) identity_relation(all_66_0) = all_66_1
% 22.73/3.88 | (40) relation_dom(all_52_2) = all_66_2
% 22.73/3.88 | (41) relation_rng(all_52_2) = all_66_0
% 22.73/3.88 |
% 22.73/3.88 | DELTA: instantiating (31) with fresh symbols all_68_0, all_68_1, all_68_2
% 22.73/3.88 | gives:
% 22.73/3.88 | (42) relation_rng(all_52_2) = all_68_2 & relation_dom(all_52_2) = all_68_1
% 22.73/3.88 | & identity_relation(all_68_1) = all_68_0 & $i(all_68_0) & $i(all_68_1)
% 22.73/3.88 | & $i(all_68_2) & ! [v0: any] : (v0 = all_52_1 | ~ (relation_dom(v0)
% 22.73/3.88 | = all_68_2) | ~ $i(v0) | ~ one_to_one(all_52_2) | ~
% 22.73/3.88 | relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_68_0)
% 22.73/3.88 | & relation_composition(all_52_2, v0) = v1 & $i(v1))) & ! [v0:
% 22.73/3.88 | any] : (v0 = all_52_1 | ~ (relation_composition(all_52_2, v0) =
% 22.73/3.88 | all_68_0) | ~ $i(v0) | ~ one_to_one(all_52_2) | ~ relation(v0)
% 22.73/3.88 | | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_68_2) &
% 22.73/3.88 | relation_dom(v0) = v1 & $i(v1)))
% 22.73/3.88 |
% 22.73/3.88 | ALPHA: (42) implies:
% 22.73/3.88 | (43) relation_dom(all_52_2) = all_68_1
% 22.73/3.89 | (44) relation_rng(all_52_2) = all_68_2
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (14) with all_66_2, all_68_1, all_52_2, simplifying
% 22.73/3.89 | with (40), (43) gives:
% 22.73/3.89 | (45) all_68_1 = all_66_2
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (14) with all_64_0, all_68_1, all_52_2, simplifying
% 22.73/3.89 | with (33), (43) gives:
% 22.73/3.89 | (46) all_68_1 = all_64_0
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (15) with all_66_0, all_68_2, all_52_2, simplifying
% 22.73/3.89 | with (41), (44) gives:
% 22.73/3.89 | (47) all_68_2 = all_66_0
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (15) with all_64_1, all_68_2, all_52_2, simplifying
% 22.73/3.89 | with (35), (44) gives:
% 22.73/3.89 | (48) all_68_2 = all_64_1
% 22.73/3.89 |
% 22.73/3.89 | COMBINE_EQS: (45), (46) imply:
% 22.73/3.89 | (49) all_66_2 = all_64_0
% 22.73/3.89 |
% 22.73/3.89 | SIMP: (49) implies:
% 22.73/3.89 | (50) all_66_2 = all_64_0
% 22.73/3.89 |
% 22.73/3.89 | COMBINE_EQS: (47), (48) imply:
% 22.73/3.89 | (51) all_66_0 = all_64_1
% 22.73/3.89 |
% 22.73/3.89 | REDUCE: (39), (51) imply:
% 22.73/3.89 | (52) identity_relation(all_64_1) = all_66_1
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (9) with all_52_1, all_52_0, simplifying with (23),
% 22.73/3.89 | (25), (29), (30) gives:
% 22.73/3.89 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_52_1) = v0
% 22.73/3.89 | & relation_dom(all_52_1) = v1 & identity_relation(v1) = v2 & $i(v2)
% 22.73/3.89 | & $i(v1) & $i(v0) & ! [v3: any] : (v3 = all_52_0 | ~
% 22.73/3.89 | (relation_dom(v3) = v0) | ~ $i(v3) | ~ one_to_one(all_52_1) | ~
% 22.73/3.89 | relation(v3) | ~ function(v3) | ? [v4: $i] : ( ~ (v4 = v2) &
% 22.73/3.89 | relation_composition(all_52_1, v3) = v4 & $i(v4))) & ! [v3:
% 22.73/3.89 | any] : (v3 = all_52_0 | ~ (relation_composition(all_52_1, v3) =
% 22.73/3.89 | v2) | ~ $i(v3) | ~ one_to_one(all_52_1) | ~ relation(v3) | ~
% 22.73/3.89 | function(v3) | ? [v4: $i] : ( ~ (v4 = v0) & relation_dom(v3) = v4
% 22.73/3.89 | & $i(v4))))
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (6) with all_52_1, all_52_0, simplifying with (23),
% 22.73/3.89 | (25), (26), (29), (30) gives:
% 22.73/3.89 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 22.73/3.89 | (relation_rng(all_52_1) = v3 & relation_dom(all_52_1) = v1 &
% 22.73/3.89 | identity_relation(v3) = v2 & identity_relation(v1) = v0 &
% 22.73/3.89 | relation_composition(all_52_0, all_52_1) = v2 &
% 22.73/3.89 | relation_composition(all_52_1, all_52_0) = v0 & $i(v3) & $i(v2) &
% 22.73/3.89 | $i(v1) & $i(v0))
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (3) with all_52_1, all_52_0, simplifying with (23),
% 22.73/3.89 | (25), (26), (29), (30) gives:
% 22.73/3.89 | (55) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_52_0) = v1 &
% 22.73/3.89 | relation_rng(all_52_1) = v0 & relation_dom(all_52_0) = v0 &
% 22.73/3.89 | relation_dom(all_52_1) = v1 & $i(v1) & $i(v0))
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (7) with all_52_1, all_64_1, simplifying with (23),
% 22.73/3.89 | (26), (29), (30), (34) gives:
% 22.73/3.89 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 22.73/3.89 | (relation_rng(all_52_1) = v3 & identity_relation(v3) = v2 &
% 22.73/3.89 | identity_relation(all_64_1) = v1 & relation_composition(v0,
% 22.73/3.89 | all_52_1) = v2 & relation_composition(all_52_1, v0) = v1 &
% 22.73/3.89 | function_inverse(all_52_1) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (4) with all_52_1, all_64_1, simplifying with (23),
% 22.73/3.89 | (26), (29), (30), (34) gives:
% 22.73/3.89 | (57) ? [v0: $i] : ? [v1: $i] : (relation_rng(v1) = all_64_1 &
% 22.73/3.89 | relation_rng(all_52_1) = v0 & relation_dom(v1) = v0 &
% 22.73/3.89 | function_inverse(all_52_1) = v1 & $i(v1) & $i(v0) & $i(all_64_1))
% 22.73/3.89 |
% 22.73/3.89 | GROUND_INST: instantiating (10) with all_52_1, all_64_1, simplifying with
% 22.73/3.89 | (23), (29), (30), (34) gives:
% 22.73/3.90 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_52_1) = v0
% 22.73/3.90 | & identity_relation(all_64_1) = v1 & function_inverse(all_52_1) = v2
% 22.73/3.90 | & $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v2 | ~
% 22.73/3.90 | (relation_dom(v3) = v0) | ~ $i(v3) | ~ one_to_one(all_52_1) | ~
% 22.73/3.90 | relation(v3) | ~ function(v3) | ? [v4: $i] : ( ~ (v4 = v1) &
% 22.73/3.90 | relation_composition(all_52_1, v3) = v4 & $i(v4))) & ! [v3: $i]
% 22.73/3.90 | : (v3 = v2 | ~ (relation_composition(all_52_1, v3) = v1) | ~
% 22.73/3.90 | $i(v3) | ~ one_to_one(all_52_1) | ~ relation(v3) | ~
% 22.73/3.90 | function(v3) | ? [v4: $i] : ( ~ (v4 = v0) & relation_dom(v3) = v4
% 22.73/3.90 | & $i(v4))))
% 22.73/3.90 |
% 22.73/3.90 | GROUND_INST: instantiating (11) with all_52_2, all_64_1, simplifying with
% 22.73/3.90 | (19), (20), (22), (35) gives:
% 22.73/3.90 | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_52_2) = v0
% 22.73/3.90 | & identity_relation(v0) = v1 & function_inverse(all_52_2) = v2 &
% 22.73/3.90 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v2 | ~
% 22.73/3.90 | (relation_dom(v3) = all_64_1) | ~ $i(v3) | ~
% 22.73/3.90 | one_to_one(all_52_2) | ~ relation(v3) | ~ function(v3) | ? [v4:
% 22.73/3.90 | $i] : ( ~ (v4 = v1) & relation_composition(all_52_2, v3) = v4 &
% 22.73/3.90 | $i(v4))) & ! [v3: $i] : (v3 = v2 | ~
% 22.73/3.90 | (relation_composition(all_52_2, v3) = v1) | ~ $i(v3) | ~
% 22.73/3.90 | one_to_one(all_52_2) | ~ relation(v3) | ~ function(v3) | ? [v4:
% 22.73/3.90 | any] : ( ~ (v4 = all_64_1) & relation_dom(v3) = v4 & $i(v4))))
% 22.73/3.90 |
% 22.73/3.90 | GROUND_INST: instantiating (8) with all_52_1, all_64_0, simplifying with (23),
% 22.73/3.90 | (26), (29), (30), (36) gives:
% 22.73/3.90 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 22.73/3.90 | (relation_dom(all_52_1) = v2 & identity_relation(v2) = v1 &
% 22.73/3.90 | identity_relation(all_64_0) = v3 & relation_composition(v0,
% 22.73/3.90 | all_52_1) = v3 & relation_composition(all_52_1, v0) = v1 &
% 22.73/3.90 | function_inverse(all_52_1) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 22.73/3.90 |
% 22.73/3.90 | GROUND_INST: instantiating (5) with all_52_1, all_64_0, simplifying with (23),
% 22.73/3.90 | (26), (29), (30), (36) gives:
% 22.73/3.90 | (61) ? [v0: $i] : ? [v1: $i] : (relation_rng(v0) = v1 & relation_dom(v0)
% 22.73/3.90 | = all_64_0 & relation_dom(all_52_1) = v1 &
% 22.73/3.90 | function_inverse(all_52_1) = v0 & $i(v1) & $i(v0) & $i(all_64_0))
% 22.73/3.90 |
% 22.73/3.90 | GROUND_INST: instantiating (11) with all_52_1, all_64_0, simplifying with
% 22.73/3.90 | (23), (29), (30), (36) gives:
% 22.73/3.90 | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (relation_dom(all_52_1) = v0
% 22.73/3.90 | & identity_relation(v0) = v1 & function_inverse(all_52_1) = v2 &
% 22.73/3.90 | $i(v2) & $i(v1) & $i(v0) & ! [v3: $i] : (v3 = v2 | ~
% 22.73/3.90 | (relation_dom(v3) = all_64_0) | ~ $i(v3) | ~
% 22.73/3.90 | one_to_one(all_52_1) | ~ relation(v3) | ~ function(v3) | ? [v4:
% 22.73/3.90 | $i] : ( ~ (v4 = v1) & relation_composition(all_52_1, v3) = v4 &
% 22.73/3.90 | $i(v4))) & ! [v3: $i] : (v3 = v2 | ~
% 22.73/3.90 | (relation_composition(all_52_1, v3) = v1) | ~ $i(v3) | ~
% 22.73/3.90 | one_to_one(all_52_1) | ~ relation(v3) | ~ function(v3) | ? [v4:
% 22.73/3.90 | any] : ( ~ (v4 = all_64_0) & relation_dom(v3) = v4 & $i(v4))))
% 22.73/3.90 |
% 22.73/3.90 | DELTA: instantiating (55) with fresh symbols all_85_0, all_85_1 gives:
% 22.73/3.90 | (63) relation_rng(all_52_0) = all_85_0 & relation_rng(all_52_1) = all_85_1
% 22.73/3.90 | & relation_dom(all_52_0) = all_85_1 & relation_dom(all_52_1) =
% 22.73/3.90 | all_85_0 & $i(all_85_0) & $i(all_85_1)
% 22.73/3.90 |
% 22.73/3.90 | ALPHA: (63) implies:
% 22.73/3.90 | (64) relation_dom(all_52_1) = all_85_0
% 22.73/3.90 | (65) relation_rng(all_52_1) = all_85_1
% 22.73/3.90 |
% 22.73/3.90 | DELTA: instantiating (57) with fresh symbols all_87_0, all_87_1 gives:
% 22.73/3.90 | (66) relation_rng(all_87_0) = all_64_1 & relation_rng(all_52_1) = all_87_1
% 22.73/3.90 | & relation_dom(all_87_0) = all_87_1 & function_inverse(all_52_1) =
% 22.73/3.90 | all_87_0 & $i(all_87_0) & $i(all_87_1) & $i(all_64_1)
% 22.73/3.90 |
% 22.73/3.90 | ALPHA: (66) implies:
% 22.73/3.90 | (67) function_inverse(all_52_1) = all_87_0
% 22.73/3.90 | (68) relation_rng(all_52_1) = all_87_1
% 22.73/3.90 |
% 22.73/3.90 | DELTA: instantiating (61) with fresh symbols all_89_0, all_89_1 gives:
% 22.73/3.90 | (69) relation_rng(all_89_1) = all_89_0 & relation_dom(all_89_1) = all_64_0
% 22.73/3.90 | & relation_dom(all_52_1) = all_89_0 & function_inverse(all_52_1) =
% 22.73/3.90 | all_89_1 & $i(all_89_0) & $i(all_89_1) & $i(all_64_0)
% 22.73/3.90 |
% 22.73/3.90 | ALPHA: (69) implies:
% 22.73/3.90 | (70) function_inverse(all_52_1) = all_89_1
% 22.73/3.90 | (71) relation_dom(all_52_1) = all_89_0
% 22.73/3.90 |
% 22.73/3.90 | DELTA: instantiating (54) with fresh symbols all_91_0, all_91_1, all_91_2,
% 22.73/3.90 | all_91_3 gives:
% 22.73/3.90 | (72) relation_rng(all_52_1) = all_91_0 & relation_dom(all_52_1) = all_91_2
% 22.73/3.90 | & identity_relation(all_91_0) = all_91_1 & identity_relation(all_91_2)
% 22.73/3.90 | = all_91_3 & relation_composition(all_52_0, all_52_1) = all_91_1 &
% 22.73/3.90 | relation_composition(all_52_1, all_52_0) = all_91_3 & $i(all_91_0) &
% 22.73/3.90 | $i(all_91_1) & $i(all_91_2) & $i(all_91_3)
% 22.73/3.90 |
% 22.73/3.90 | ALPHA: (72) implies:
% 22.73/3.90 | (73) relation_composition(all_52_1, all_52_0) = all_91_3
% 22.73/3.90 | (74) identity_relation(all_91_2) = all_91_3
% 22.73/3.90 | (75) relation_dom(all_52_1) = all_91_2
% 22.73/3.90 | (76) relation_rng(all_52_1) = all_91_0
% 22.73/3.90 |
% 22.73/3.90 | DELTA: instantiating (56) with fresh symbols all_93_0, all_93_1, all_93_2,
% 22.73/3.90 | all_93_3 gives:
% 22.73/3.91 | (77) relation_rng(all_52_1) = all_93_0 & identity_relation(all_93_0) =
% 22.73/3.91 | all_93_1 & identity_relation(all_64_1) = all_93_2 &
% 22.73/3.91 | relation_composition(all_93_3, all_52_1) = all_93_1 &
% 22.73/3.91 | relation_composition(all_52_1, all_93_3) = all_93_2 &
% 22.73/3.91 | function_inverse(all_52_1) = all_93_3 & $i(all_93_0) & $i(all_93_1) &
% 22.73/3.91 | $i(all_93_2) & $i(all_93_3)
% 22.73/3.91 |
% 22.73/3.91 | ALPHA: (77) implies:
% 22.73/3.91 | (78) function_inverse(all_52_1) = all_93_3
% 22.73/3.91 | (79) relation_composition(all_52_1, all_93_3) = all_93_2
% 22.73/3.91 | (80) identity_relation(all_64_1) = all_93_2
% 22.73/3.91 | (81) relation_rng(all_52_1) = all_93_0
% 22.73/3.91 |
% 22.73/3.91 | DELTA: instantiating (60) with fresh symbols all_95_0, all_95_1, all_95_2,
% 22.73/3.91 | all_95_3 gives:
% 22.73/3.91 | (82) relation_dom(all_52_1) = all_95_1 & identity_relation(all_95_1) =
% 22.73/3.91 | all_95_2 & identity_relation(all_64_0) = all_95_0 &
% 22.73/3.91 | relation_composition(all_95_3, all_52_1) = all_95_0 &
% 22.73/3.91 | relation_composition(all_52_1, all_95_3) = all_95_2 &
% 22.73/3.91 | function_inverse(all_52_1) = all_95_3 & $i(all_95_0) & $i(all_95_1) &
% 22.73/3.91 | $i(all_95_2) & $i(all_95_3)
% 22.73/3.91 |
% 22.73/3.91 | ALPHA: (82) implies:
% 22.73/3.91 | (83) function_inverse(all_52_1) = all_95_3
% 22.73/3.91 | (84) relation_dom(all_52_1) = all_95_1
% 22.73/3.91 |
% 22.73/3.91 | DELTA: instantiating (62) with fresh symbols all_100_0, all_100_1, all_100_2
% 22.73/3.91 | gives:
% 22.73/3.91 | (85) relation_dom(all_52_1) = all_100_2 & identity_relation(all_100_2) =
% 22.73/3.91 | all_100_1 & function_inverse(all_52_1) = all_100_0 & $i(all_100_0) &
% 22.73/3.91 | $i(all_100_1) & $i(all_100_2) & ! [v0: any] : (v0 = all_100_0 | ~
% 22.73/3.91 | (relation_dom(v0) = all_64_0) | ~ $i(v0) | ~ one_to_one(all_52_1)
% 22.73/3.91 | | ~ relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 =
% 22.73/3.91 | all_100_1) & relation_composition(all_52_1, v0) = v1 & $i(v1)))
% 22.73/3.91 | & ! [v0: any] : (v0 = all_100_0 | ~ (relation_composition(all_52_1,
% 22.73/3.91 | v0) = all_100_1) | ~ $i(v0) | ~ one_to_one(all_52_1) | ~
% 22.73/3.91 | relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_64_0)
% 22.73/3.91 | & relation_dom(v0) = v1 & $i(v1)))
% 22.73/3.91 |
% 22.73/3.91 | ALPHA: (85) implies:
% 22.73/3.91 | (86) function_inverse(all_52_1) = all_100_0
% 22.73/3.91 | (87) identity_relation(all_100_2) = all_100_1
% 22.73/3.91 | (88) relation_dom(all_52_1) = all_100_2
% 22.73/3.91 | (89) ! [v0: any] : (v0 = all_100_0 | ~ (relation_composition(all_52_1,
% 22.73/3.91 | v0) = all_100_1) | ~ $i(v0) | ~ one_to_one(all_52_1) | ~
% 22.73/3.91 | relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_64_0)
% 22.73/3.91 | & relation_dom(v0) = v1 & $i(v1)))
% 22.73/3.91 | (90) ! [v0: any] : (v0 = all_100_0 | ~ (relation_dom(v0) = all_64_0) | ~
% 22.73/3.91 | $i(v0) | ~ one_to_one(all_52_1) | ~ relation(v0) | ~ function(v0)
% 22.73/3.91 | | ? [v1: any] : ( ~ (v1 = all_100_1) &
% 22.73/3.91 | relation_composition(all_52_1, v0) = v1 & $i(v1)))
% 22.73/3.91 |
% 22.73/3.91 | GROUND_INST: instantiating (89) with all_52_2, simplifying with (19), (20),
% 22.73/3.91 | (22), (26) gives:
% 22.73/3.91 | (91) all_100_0 = all_52_2 | ~ (relation_composition(all_52_1, all_52_2) =
% 22.73/3.91 | all_100_1) | ? [v0: any] : ( ~ (v0 = all_64_0) &
% 22.73/3.91 | relation_dom(all_52_2) = v0 & $i(v0))
% 22.73/3.91 |
% 22.73/3.91 | GROUND_INST: instantiating (90) with all_52_2, simplifying with (19), (20),
% 22.73/3.91 | (22), (26), (33) gives:
% 22.73/3.91 | (92) all_100_0 = all_52_2 | ? [v0: any] : ( ~ (v0 = all_100_1) &
% 22.73/3.91 | relation_composition(all_52_1, all_52_2) = v0 & $i(v0))
% 22.73/3.91 |
% 22.73/3.91 | DELTA: instantiating (59) with fresh symbols all_103_0, all_103_1, all_103_2
% 22.73/3.91 | gives:
% 22.73/3.91 | (93) relation_dom(all_52_2) = all_103_2 & identity_relation(all_103_2) =
% 22.73/3.91 | all_103_1 & function_inverse(all_52_2) = all_103_0 & $i(all_103_0) &
% 22.73/3.91 | $i(all_103_1) & $i(all_103_2) & ! [v0: any] : (v0 = all_103_0 | ~
% 22.73/3.91 | (relation_dom(v0) = all_64_1) | ~ $i(v0) | ~ one_to_one(all_52_2)
% 22.73/3.91 | | ~ relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 =
% 22.73/3.91 | all_103_1) & relation_composition(all_52_2, v0) = v1 & $i(v1)))
% 22.73/3.91 | & ! [v0: any] : (v0 = all_103_0 | ~ (relation_composition(all_52_2,
% 22.73/3.91 | v0) = all_103_1) | ~ $i(v0) | ~ one_to_one(all_52_2) | ~
% 22.73/3.91 | relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_64_1)
% 22.73/3.91 | & relation_dom(v0) = v1 & $i(v1)))
% 22.73/3.91 |
% 22.73/3.91 | ALPHA: (93) implies:
% 22.73/3.91 | (94) relation_dom(all_52_2) = all_103_2
% 22.73/3.91 |
% 22.73/3.91 | DELTA: instantiating (58) with fresh symbols all_106_0, all_106_1, all_106_2
% 22.73/3.91 | gives:
% 22.73/3.91 | (95) relation_rng(all_52_1) = all_106_2 & identity_relation(all_64_1) =
% 22.73/3.91 | all_106_1 & function_inverse(all_52_1) = all_106_0 & $i(all_106_0) &
% 22.73/3.91 | $i(all_106_1) & $i(all_106_2) & ! [v0: any] : (v0 = all_106_0 | ~
% 22.73/3.91 | (relation_dom(v0) = all_106_2) | ~ $i(v0) | ~ one_to_one(all_52_1)
% 22.73/3.91 | | ~ relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 =
% 22.73/3.91 | all_106_1) & relation_composition(all_52_1, v0) = v1 & $i(v1)))
% 22.73/3.91 | & ! [v0: any] : (v0 = all_106_0 | ~ (relation_composition(all_52_1,
% 22.73/3.91 | v0) = all_106_1) | ~ $i(v0) | ~ one_to_one(all_52_1) | ~
% 22.73/3.91 | relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_106_2)
% 22.73/3.91 | & relation_dom(v0) = v1 & $i(v1)))
% 22.73/3.91 |
% 22.73/3.91 | ALPHA: (95) implies:
% 22.73/3.91 | (96) function_inverse(all_52_1) = all_106_0
% 22.73/3.91 | (97) identity_relation(all_64_1) = all_106_1
% 22.73/3.91 | (98) relation_rng(all_52_1) = all_106_2
% 22.73/3.91 |
% 22.73/3.91 | DELTA: instantiating (53) with fresh symbols all_109_0, all_109_1, all_109_2
% 22.73/3.91 | gives:
% 22.73/3.91 | (99) relation_rng(all_52_1) = all_109_2 & relation_dom(all_52_1) =
% 22.73/3.91 | all_109_1 & identity_relation(all_109_1) = all_109_0 & $i(all_109_0) &
% 22.73/3.91 | $i(all_109_1) & $i(all_109_2) & ! [v0: any] : (v0 = all_52_0 | ~
% 22.73/3.91 | (relation_dom(v0) = all_109_2) | ~ $i(v0) | ~ one_to_one(all_52_1)
% 22.73/3.91 | | ~ relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 =
% 22.73/3.91 | all_109_0) & relation_composition(all_52_1, v0) = v1 & $i(v1)))
% 22.73/3.91 | & ! [v0: any] : (v0 = all_52_0 | ~ (relation_composition(all_52_1,
% 22.73/3.91 | v0) = all_109_0) | ~ $i(v0) | ~ one_to_one(all_52_1) | ~
% 22.73/3.91 | relation(v0) | ~ function(v0) | ? [v1: any] : ( ~ (v1 = all_109_2)
% 22.73/3.91 | & relation_dom(v0) = v1 & $i(v1)))
% 22.73/3.91 |
% 22.73/3.91 | ALPHA: (99) implies:
% 22.73/3.91 | (100) identity_relation(all_109_1) = all_109_0
% 22.73/3.91 | (101) relation_dom(all_52_1) = all_109_1
% 22.73/3.91 | (102) relation_rng(all_52_1) = all_109_2
% 22.73/3.92 | (103) ! [v0: any] : (v0 = all_52_0 | ~ (relation_dom(v0) = all_109_2) |
% 22.73/3.92 | ~ $i(v0) | ~ one_to_one(all_52_1) | ~ relation(v0) | ~
% 22.73/3.92 | function(v0) | ? [v1: any] : ( ~ (v1 = all_109_0) &
% 22.73/3.92 | relation_composition(all_52_1, v0) = v1 & $i(v1)))
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (103) with all_52_2, simplifying with (19), (20),
% 22.73/3.92 | (22), (26) gives:
% 22.73/3.92 | (104) all_52_0 = all_52_2 | ~ (relation_dom(all_52_2) = all_109_2) | ?
% 22.73/3.92 | [v0: any] : ( ~ (v0 = all_109_0) & relation_composition(all_52_1,
% 22.73/3.92 | all_52_2) = v0 & $i(v0))
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (12) with all_52_0, all_95_3, all_52_1, simplifying
% 22.73/3.92 | with (25), (83) gives:
% 22.73/3.92 | (105) all_95_3 = all_52_0
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (12) with all_89_1, all_95_3, all_52_1, simplifying
% 22.73/3.92 | with (70), (83) gives:
% 22.73/3.92 | (106) all_95_3 = all_89_1
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (12) with all_93_3, all_100_0, all_52_1,
% 22.73/3.92 | simplifying with (78), (86) gives:
% 22.73/3.92 | (107) all_100_0 = all_93_3
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (12) with all_89_1, all_100_0, all_52_1,
% 22.73/3.92 | simplifying with (70), (86) gives:
% 22.73/3.92 | (108) all_100_0 = all_89_1
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (12) with all_100_0, all_106_0, all_52_1,
% 22.73/3.92 | simplifying with (86), (96) gives:
% 22.73/3.92 | (109) all_106_0 = all_100_0
% 22.73/3.92 |
% 22.73/3.92 | GROUND_INST: instantiating (12) with all_87_0, all_106_0, all_52_1,
% 22.73/3.92 | simplifying with (67), (96) gives:
% 22.73/3.92 | (110) all_106_0 = all_87_0
% 22.73/3.92 |
% 22.73/3.93 | GROUND_INST: instantiating (16) with all_91_3, all_93_2, all_52_0, all_52_1,
% 22.73/3.93 | simplifying with (73) gives:
% 22.73/3.93 | (111) all_93_2 = all_91_3 | ~ (relation_composition(all_52_1, all_52_0) =
% 22.73/3.93 | all_93_2)
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (13) with all_66_1, all_106_1, all_64_1,
% 22.73/3.93 | simplifying with (52), (97) gives:
% 22.73/3.93 | (112) all_106_1 = all_66_1
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (13) with all_93_2, all_106_1, all_64_1,
% 22.73/3.93 | simplifying with (80), (97) gives:
% 22.73/3.93 | (113) all_106_1 = all_93_2
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (13) with all_91_3, all_100_1, all_91_2,
% 22.73/3.93 | simplifying with (74) gives:
% 22.73/3.93 | (114) all_100_1 = all_91_3 | ~ (identity_relation(all_91_2) = all_100_1)
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (13) with all_100_1, all_109_0, all_100_2,
% 22.73/3.93 | simplifying with (87) gives:
% 22.73/3.93 | (115) all_109_0 = all_100_1 | ~ (identity_relation(all_100_2) = all_109_0)
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (13) with all_93_2, all_109_0, all_64_1,
% 22.73/3.93 | simplifying with (80) gives:
% 22.73/3.93 | (116) all_109_0 = all_93_2 | ~ (identity_relation(all_64_1) = all_109_0)
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_64_0, all_103_2, all_52_2,
% 22.73/3.93 | simplifying with (33), (94) gives:
% 22.73/3.93 | (117) all_103_2 = all_64_0
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_64_1, all_95_1, all_52_1, simplifying
% 22.73/3.93 | with (34), (84) gives:
% 22.73/3.93 | (118) all_95_1 = all_64_1
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_91_2, all_95_1, all_52_1, simplifying
% 22.73/3.93 | with (75), (84) gives:
% 22.73/3.93 | (119) all_95_1 = all_91_2
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_89_0, all_95_1, all_52_1, simplifying
% 22.73/3.93 | with (71), (84) gives:
% 22.73/3.93 | (120) all_95_1 = all_89_0
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_95_1, all_100_2, all_52_1,
% 22.73/3.93 | simplifying with (84), (88) gives:
% 22.73/3.93 | (121) all_100_2 = all_95_1
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_100_2, all_109_1, all_52_1,
% 22.73/3.93 | simplifying with (88), (101) gives:
% 22.73/3.93 | (122) all_109_1 = all_100_2
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (14) with all_85_0, all_109_1, all_52_1,
% 22.73/3.93 | simplifying with (64), (101) gives:
% 22.73/3.93 | (123) all_109_1 = all_85_0
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (15) with all_64_0, all_87_1, all_52_1, simplifying
% 22.73/3.93 | with (36), (68) gives:
% 22.73/3.93 | (124) all_87_1 = all_64_0
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (15) with all_87_1, all_91_0, all_52_1, simplifying
% 22.73/3.93 | with (68), (76) gives:
% 22.73/3.93 | (125) all_91_0 = all_87_1
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (15) with all_91_0, all_93_0, all_52_1, simplifying
% 22.73/3.93 | with (76), (81) gives:
% 22.73/3.93 | (126) all_93_0 = all_91_0
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (15) with all_106_2, all_109_2, all_52_1,
% 22.73/3.93 | simplifying with (98), (102) gives:
% 22.73/3.93 | (127) all_109_2 = all_106_2
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (15) with all_93_0, all_109_2, all_52_1,
% 22.73/3.93 | simplifying with (81), (102) gives:
% 22.73/3.93 | (128) all_109_2 = all_93_0
% 22.73/3.93 |
% 22.73/3.93 | GROUND_INST: instantiating (15) with all_85_1, all_109_2, all_52_1,
% 22.73/3.93 | simplifying with (65), (102) gives:
% 22.73/3.93 | (129) all_109_2 = all_85_1
% 22.73/3.93 |
% 22.73/3.93 | COMBINE_EQS: (122), (123) imply:
% 22.73/3.93 | (130) all_100_2 = all_85_0
% 22.73/3.93 |
% 22.73/3.93 | SIMP: (130) implies:
% 22.73/3.93 | (131) all_100_2 = all_85_0
% 22.73/3.93 |
% 22.73/3.93 | COMBINE_EQS: (127), (129) imply:
% 22.73/3.93 | (132) all_106_2 = all_85_1
% 22.73/3.93 |
% 22.73/3.93 | COMBINE_EQS: (127), (128) imply:
% 22.73/3.93 | (133) all_106_2 = all_93_0
% 22.73/3.93 |
% 22.73/3.93 | COMBINE_EQS: (109), (110) imply:
% 22.73/3.93 | (134) all_100_0 = all_87_0
% 22.73/3.93 |
% 22.73/3.93 | SIMP: (134) implies:
% 22.73/3.93 | (135) all_100_0 = all_87_0
% 22.73/3.93 |
% 22.73/3.93 | COMBINE_EQS: (112), (113) imply:
% 22.73/3.94 | (136) all_93_2 = all_66_1
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (136) implies:
% 22.73/3.94 | (137) all_93_2 = all_66_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (132), (133) imply:
% 22.73/3.94 | (138) all_93_0 = all_85_1
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (138) implies:
% 22.73/3.94 | (139) all_93_0 = all_85_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (107), (108) imply:
% 22.73/3.94 | (140) all_93_3 = all_89_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (107), (135) imply:
% 22.73/3.94 | (141) all_93_3 = all_87_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (121), (131) imply:
% 22.73/3.94 | (142) all_95_1 = all_85_0
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (142) implies:
% 22.73/3.94 | (143) all_95_1 = all_85_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (119), (120) imply:
% 22.73/3.94 | (144) all_91_2 = all_89_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (118), (119) imply:
% 22.73/3.94 | (145) all_91_2 = all_64_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (119), (143) imply:
% 22.73/3.94 | (146) all_91_2 = all_85_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (105), (106) imply:
% 22.73/3.94 | (147) all_89_1 = all_52_0
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (147) implies:
% 22.73/3.94 | (148) all_89_1 = all_52_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (126), (139) imply:
% 22.73/3.94 | (149) all_91_0 = all_85_1
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (149) implies:
% 22.73/3.94 | (150) all_91_0 = all_85_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (140), (141) imply:
% 22.73/3.94 | (151) all_89_1 = all_87_0
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (151) implies:
% 22.73/3.94 | (152) all_89_1 = all_87_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (125), (150) imply:
% 22.73/3.94 | (153) all_87_1 = all_85_1
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (153) implies:
% 22.73/3.94 | (154) all_87_1 = all_85_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (144), (145) imply:
% 22.73/3.94 | (155) all_89_0 = all_64_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (144), (146) imply:
% 22.73/3.94 | (156) all_89_0 = all_85_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (155), (156) imply:
% 22.73/3.94 | (157) all_85_0 = all_64_1
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (157) implies:
% 22.73/3.94 | (158) all_85_0 = all_64_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (148), (152) imply:
% 22.73/3.94 | (159) all_87_0 = all_52_0
% 22.73/3.94 |
% 22.73/3.94 | SIMP: (159) implies:
% 22.73/3.94 | (160) all_87_0 = all_52_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (124), (154) imply:
% 22.73/3.94 | (161) all_85_1 = all_64_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (141), (160) imply:
% 22.73/3.94 | (162) all_93_3 = all_52_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (131), (158) imply:
% 22.73/3.94 | (163) all_100_2 = all_64_1
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (107), (162) imply:
% 22.73/3.94 | (164) all_100_0 = all_52_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (132), (161) imply:
% 22.73/3.94 | (165) all_106_2 = all_64_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (127), (165) imply:
% 22.73/3.94 | (166) all_109_2 = all_64_0
% 22.73/3.94 |
% 22.73/3.94 | COMBINE_EQS: (123), (158) imply:
% 22.73/3.94 | (167) all_109_1 = all_64_1
% 22.73/3.94 |
% 22.73/3.94 | REDUCE: (100), (167) imply:
% 22.73/3.94 | (168) identity_relation(all_64_1) = all_109_0
% 22.73/3.94 |
% 22.73/3.94 | REDUCE: (87), (163) imply:
% 22.73/3.94 | (169) identity_relation(all_64_1) = all_100_1
% 22.73/3.94 |
% 22.73/3.94 | REDUCE: (79), (137), (162) imply:
% 22.73/3.94 | (170) relation_composition(all_52_1, all_52_0) = all_66_1
% 22.73/3.94 |
% 22.73/3.94 | BETA: splitting (92) gives:
% 22.73/3.94 |
% 22.73/3.94 | Case 1:
% 22.73/3.94 | |
% 22.73/3.94 | | (171) all_100_0 = all_52_2
% 22.73/3.94 | |
% 22.73/3.94 | | COMBINE_EQS: (164), (171) imply:
% 22.73/3.94 | | (172) all_52_0 = all_52_2
% 22.73/3.94 | |
% 22.73/3.94 | | REDUCE: (18), (172) imply:
% 22.73/3.94 | | (173) $false
% 22.73/3.94 | |
% 22.73/3.94 | | CLOSE: (173) is inconsistent.
% 22.73/3.94 | |
% 22.73/3.94 | Case 2:
% 22.73/3.94 | |
% 22.73/3.94 | | (174) ~ (all_100_0 = all_52_2)
% 22.73/3.94 | | (175) ? [v0: any] : ( ~ (v0 = all_100_1) &
% 22.73/3.94 | | relation_composition(all_52_1, all_52_2) = v0 & $i(v0))
% 22.73/3.94 | |
% 22.73/3.94 | | DELTA: instantiating (175) with fresh symbol all_120_0 gives:
% 22.73/3.94 | | (176) ~ (all_120_0 = all_100_1) & relation_composition(all_52_1,
% 22.73/3.94 | | all_52_2) = all_120_0 & $i(all_120_0)
% 22.73/3.94 | |
% 22.73/3.94 | | ALPHA: (176) implies:
% 22.73/3.94 | | (177) ~ (all_120_0 = all_100_1)
% 22.73/3.94 | | (178) relation_composition(all_52_1, all_52_2) = all_120_0
% 22.73/3.94 | |
% 22.73/3.94 | | BETA: splitting (91) gives:
% 22.73/3.94 | |
% 22.73/3.94 | | Case 1:
% 22.73/3.94 | | |
% 22.73/3.94 | | | (179) ~ (relation_composition(all_52_1, all_52_2) = all_100_1)
% 22.73/3.94 | | |
% 22.73/3.94 | | | BETA: splitting (116) gives:
% 22.73/3.94 | | |
% 22.73/3.94 | | | Case 1:
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | (180) ~ (identity_relation(all_64_1) = all_109_0)
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | PRED_UNIFY: (168), (180) imply:
% 22.73/3.94 | | | | (181) $false
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | CLOSE: (181) is inconsistent.
% 22.73/3.94 | | | |
% 22.73/3.94 | | | Case 2:
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | (182) all_109_0 = all_93_2
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | COMBINE_EQS: (137), (182) imply:
% 22.73/3.94 | | | | (183) all_109_0 = all_66_1
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | BETA: splitting (115) gives:
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | Case 1:
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | (184) ~ (identity_relation(all_100_2) = all_109_0)
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | REDUCE: (163), (183), (184) imply:
% 22.73/3.94 | | | | | (185) ~ (identity_relation(all_64_1) = all_66_1)
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | PRED_UNIFY: (52), (185) imply:
% 22.73/3.94 | | | | | (186) $false
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | CLOSE: (186) is inconsistent.
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | Case 2:
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | (187) all_109_0 = all_100_1
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | COMBINE_EQS: (183), (187) imply:
% 22.73/3.94 | | | | | (188) all_100_1 = all_66_1
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | SIMP: (188) implies:
% 22.73/3.94 | | | | | (189) all_100_1 = all_66_1
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | REDUCE: (179), (189) imply:
% 22.73/3.94 | | | | | (190) ~ (relation_composition(all_52_1, all_52_2) = all_66_1)
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | PRED_UNIFY: (38), (190) imply:
% 22.73/3.94 | | | | | (191) $false
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | | CLOSE: (191) is inconsistent.
% 22.73/3.94 | | | | |
% 22.73/3.94 | | | | End of split
% 22.73/3.94 | | | |
% 22.73/3.94 | | | End of split
% 22.73/3.94 | | |
% 22.73/3.94 | | Case 2:
% 22.73/3.94 | | |
% 22.73/3.94 | | | (192) relation_composition(all_52_1, all_52_2) = all_100_1
% 22.73/3.94 | | |
% 22.73/3.94 | | | BETA: splitting (111) gives:
% 22.73/3.94 | | |
% 22.73/3.94 | | | Case 1:
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | (193) ~ (relation_composition(all_52_1, all_52_0) = all_93_2)
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | REDUCE: (137), (193) imply:
% 22.73/3.94 | | | | (194) ~ (relation_composition(all_52_1, all_52_0) = all_66_1)
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | PRED_UNIFY: (170), (194) imply:
% 22.73/3.94 | | | | (195) $false
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | CLOSE: (195) is inconsistent.
% 22.73/3.94 | | | |
% 22.73/3.94 | | | Case 2:
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | (196) all_93_2 = all_91_3
% 22.73/3.94 | | | |
% 22.73/3.94 | | | | COMBINE_EQS: (137), (196) imply:
% 22.73/3.94 | | | | (197) all_91_3 = all_66_1
% 22.73/3.94 | | | |
% 22.73/3.95 | | | | BETA: splitting (104) gives:
% 22.73/3.95 | | | |
% 22.73/3.95 | | | | Case 1:
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | (198) ~ (relation_dom(all_52_2) = all_109_2)
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | REDUCE: (166), (198) imply:
% 22.73/3.95 | | | | | (199) ~ (relation_dom(all_52_2) = all_64_0)
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | PRED_UNIFY: (33), (199) imply:
% 22.73/3.95 | | | | | (200) $false
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | CLOSE: (200) is inconsistent.
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | Case 2:
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | (201) all_52_0 = all_52_2 | ? [v0: any] : ( ~ (v0 = all_109_0) &
% 22.73/3.95 | | | | | relation_composition(all_52_1, all_52_2) = v0 & $i(v0))
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | BETA: splitting (201) gives:
% 22.73/3.95 | | | | |
% 22.73/3.95 | | | | | Case 1:
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | (202) all_52_0 = all_52_2
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | REDUCE: (18), (202) imply:
% 22.73/3.95 | | | | | | (203) $false
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | CLOSE: (203) is inconsistent.
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | Case 2:
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | (204) ? [v0: any] : ( ~ (v0 = all_109_0) &
% 22.73/3.95 | | | | | | relation_composition(all_52_1, all_52_2) = v0 & $i(v0))
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | DELTA: instantiating (204) with fresh symbol all_164_0 gives:
% 22.73/3.95 | | | | | | (205) ~ (all_164_0 = all_109_0) & relation_composition(all_52_1,
% 22.73/3.95 | | | | | | all_52_2) = all_164_0 & $i(all_164_0)
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | ALPHA: (205) implies:
% 22.73/3.95 | | | | | | (206) relation_composition(all_52_1, all_52_2) = all_164_0
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | BETA: splitting (114) gives:
% 22.73/3.95 | | | | | |
% 22.73/3.95 | | | | | | Case 1:
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | (207) ~ (identity_relation(all_91_2) = all_100_1)
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | REDUCE: (145), (207) imply:
% 22.73/3.95 | | | | | | | (208) ~ (identity_relation(all_64_1) = all_100_1)
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | PRED_UNIFY: (169), (208) imply:
% 22.73/3.95 | | | | | | | (209) $false
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | CLOSE: (209) is inconsistent.
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | Case 2:
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | (210) all_100_1 = all_91_3
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | COMBINE_EQS: (197), (210) imply:
% 22.73/3.95 | | | | | | | (211) all_100_1 = all_66_1
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | REDUCE: (177), (211) imply:
% 22.73/3.95 | | | | | | | (212) ~ (all_120_0 = all_66_1)
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | GROUND_INST: instantiating (16) with all_66_1, all_164_0,
% 22.73/3.95 | | | | | | | all_52_2, all_52_1, simplifying with (38), (206)
% 22.73/3.95 | | | | | | | gives:
% 22.73/3.95 | | | | | | | (213) all_164_0 = all_66_1
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | GROUND_INST: instantiating (16) with all_120_0, all_164_0,
% 22.73/3.95 | | | | | | | all_52_2, all_52_1, simplifying with (178), (206)
% 22.73/3.95 | | | | | | | gives:
% 22.73/3.95 | | | | | | | (214) all_164_0 = all_120_0
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | COMBINE_EQS: (213), (214) imply:
% 22.73/3.95 | | | | | | | (215) all_120_0 = all_66_1
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | SIMP: (215) implies:
% 22.73/3.95 | | | | | | | (216) all_120_0 = all_66_1
% 22.73/3.95 | | | | | | |
% 22.73/3.95 | | | | | | | REDUCE: (212), (216) imply:
% 22.73/3.95 | | | | | | | (217) $false
% 23.07/3.95 | | | | | | |
% 23.07/3.95 | | | | | | | CLOSE: (217) is inconsistent.
% 23.07/3.95 | | | | | | |
% 23.07/3.95 | | | | | | End of split
% 23.07/3.95 | | | | | |
% 23.07/3.95 | | | | | End of split
% 23.07/3.95 | | | | |
% 23.07/3.95 | | | | End of split
% 23.07/3.95 | | | |
% 23.07/3.95 | | | End of split
% 23.07/3.95 | | |
% 23.07/3.95 | | End of split
% 23.07/3.95 | |
% 23.07/3.95 | End of split
% 23.07/3.95 |
% 23.07/3.95 End of proof
% 23.07/3.95 % SZS output end Proof for theBenchmark
% 23.07/3.95
% 23.07/3.95 3338ms
%------------------------------------------------------------------------------