TSTP Solution File: SEU027+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU027+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 : n010.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 17:42:20 EDT 2023
% Result : Theorem 14.76s 2.85s
% Output : Proof 23.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU027+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 01:23:06 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.90/1.11 Prover 4: Preprocessing ...
% 2.90/1.11 Prover 1: Preprocessing ...
% 2.90/1.15 Prover 2: Preprocessing ...
% 2.90/1.15 Prover 5: Preprocessing ...
% 2.90/1.15 Prover 0: Preprocessing ...
% 2.90/1.15 Prover 6: Preprocessing ...
% 2.90/1.15 Prover 3: Preprocessing ...
% 6.81/1.69 Prover 1: Warning: ignoring some quantifiers
% 7.28/1.76 Prover 1: Constructing countermodel ...
% 7.28/1.78 Prover 6: Proving ...
% 7.28/1.78 Prover 3: Warning: ignoring some quantifiers
% 7.28/1.82 Prover 3: Constructing countermodel ...
% 8.04/1.85 Prover 5: Proving ...
% 9.94/2.13 Prover 2: Proving ...
% 14.76/2.85 Prover 3: proved (2228ms)
% 14.76/2.85
% 14.76/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.76/2.85
% 14.76/2.86 Prover 2: stopped
% 14.76/2.87 Prover 5: stopped
% 14.76/2.88 Prover 6: stopped
% 14.76/2.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.76/2.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.76/2.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.76/2.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.76/2.94 Prover 7: Preprocessing ...
% 14.76/2.95 Prover 8: Preprocessing ...
% 14.76/2.95 Prover 11: Preprocessing ...
% 14.76/2.96 Prover 10: Preprocessing ...
% 16.85/3.03 Prover 4: Warning: ignoring some quantifiers
% 17.27/3.10 Prover 7: Warning: ignoring some quantifiers
% 17.27/3.11 Prover 10: Warning: ignoring some quantifiers
% 17.27/3.11 Prover 7: Constructing countermodel ...
% 17.27/3.12 Prover 10: Constructing countermodel ...
% 17.27/3.12 Prover 8: Warning: ignoring some quantifiers
% 17.27/3.13 Prover 8: Constructing countermodel ...
% 17.27/3.14 Prover 4: Constructing countermodel ...
% 17.84/3.18 Prover 0: Proving ...
% 17.84/3.18 Prover 0: stopped
% 17.84/3.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.39/3.28 Prover 13: Preprocessing ...
% 19.60/3.44 Prover 13: Warning: ignoring some quantifiers
% 19.60/3.45 Prover 13: Constructing countermodel ...
% 22.12/3.75 Prover 10: Found proof (size 68)
% 22.12/3.75 Prover 10: proved (870ms)
% 22.12/3.75 Prover 7: stopped
% 22.12/3.75 Prover 1: stopped
% 22.12/3.75 Prover 4: stopped
% 22.12/3.75 Prover 8: stopped
% 22.12/3.75 Prover 13: stopped
% 23.01/3.94 Prover 11: Warning: ignoring some quantifiers
% 23.01/3.96 Prover 11: Constructing countermodel ...
% 23.01/3.97 Prover 11: stopped
% 23.01/3.97
% 23.01/3.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.01/3.97
% 23.01/3.99 % SZS output start Proof for theBenchmark
% 23.01/3.99 Assumptions after simplification:
% 23.01/3.99 ---------------------------------
% 23.01/3.99
% 23.01/3.99 (d5_funct_1)
% 23.01/4.03 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ~
% 23.01/4.03 relation(v0) | ~ function(v0) | ? [v2: $i] : (relation_dom(v0) = v2 &
% 23.01/4.03 $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v4) = v3) | ~ $i(v4)
% 23.01/4.03 | ~ $i(v3) | ~ $i(v1) | ~ in(v4, v2) | in(v3, v1)) & ! [v3: $i] : (
% 23.01/4.03 ~ $i(v3) | ~ $i(v1) | ~ in(v3, v1) | ? [v4: $i] : (apply(v0, v4) = v3
% 23.01/4.03 & $i(v4) & in(v4, v2))) & ? [v3: $i] : (v3 = v1 | ~ $i(v3) | ? [v4:
% 23.01/4.03 $i] : ? [v5: $i] : ? [v6: $i] : ($i(v5) & $i(v4) & ( ~ in(v4, v3) |
% 23.01/4.03 ! [v7: $i] : ( ~ (apply(v0, v7) = v4) | ~ $i(v7) | ~ in(v7, v2)))
% 23.01/4.03 & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 23.01/4.03
% 23.01/4.03 (t54_funct_1)
% 23.44/4.04 ! [v0: $i] : ! [v1: $i] : ( ~ (function_inverse(v0) = v1) | ~ $i(v0) | ~
% 23.44/4.04 one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2: $i] : ? [v3:
% 23.44/4.04 $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & $i(v3) & $i(v2) &
% 23.44/4.04 ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v7 = v6 | ~
% 23.44/4.04 (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) =
% 23.44/4.04 v5) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) | ~ relation(v1) | ~
% 23.44/4.04 function(v1) | ~ in(v6, v3)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i]
% 23.44/4.04 : ! [v7: $i] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5)
% 23.44/4.04 = v6) | ~ (apply(v0, v6) = v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) |
% 23.44/4.04 ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4: $i] : !
% 23.44/4.04 [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (relation_dom(v1) = v4) | ~
% 23.44/4.04 (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ $i(v6) | ~ $i(v5) |
% 23.44/4.04 ~ $i(v1) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5,
% 23.44/4.04 v2)) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 23.44/4.04 (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) =
% 23.44/4.04 v7) | ~ $i(v6) | ~ $i(v5) | ~ $i(v1) | ~ relation(v1) | ~
% 23.44/4.04 function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4: $i] : (v4 = v2 | ~
% 23.44/4.04 (relation_dom(v1) = v4) | ~ $i(v1) | ~ relation(v1) | ~ function(v1))
% 23.44/4.04 & ! [v4: $i] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ $i(v4) | ~
% 23.44/4.04 relation(v4) | ~ function(v4) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i]
% 23.44/4.04 : ? [v8: $i] : ($i(v6) & $i(v5) & ((v8 = v5 & apply(v0, v6) = v5 &
% 23.44/4.04 in(v6, v3) & ( ~ in(v5, v2) | ( ~ (v7 = v6) & apply(v4, v5) = v7 &
% 23.44/4.04 $i(v7)))) | (v7 = v6 & apply(v4, v5) = v6 & in(v5, v2) & ( ~
% 23.44/4.04 in(v6, v3) | ( ~ (v8 = v5) & apply(v0, v6) = v8 & $i(v8)))))))))
% 23.44/4.04
% 23.44/4.04 (t60_funct_1)
% 23.44/4.04 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v4
% 23.44/4.04 = v3) & function_inverse(v0) = v3 & relation_rng(v4) = v1 &
% 23.44/4.04 relation_rng(v0) = v2 & relation_dom(v4) = v2 & relation_dom(v0) = v1 &
% 23.44/4.04 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & one_to_one(v0) & relation(v4) &
% 23.44/4.04 relation(v0) & function(v4) & function(v0) & ! [v5: $i] : ! [v6: $i] : !
% 23.44/4.04 [v7: $i] : (v7 = v6 | ~ (apply(v4, v6) = v5) | ~ (apply(v0, v5) = v7) | ~
% 23.44/4.04 $i(v6) | ~ $i(v5) | ~ in(v6, v2) | ~ in(v5, v1)) & ! [v5: $i] : !
% 23.44/4.04 [v6: $i] : ! [v7: $i] : (v7 = v5 | ~ (apply(v4, v6) = v7) | ~ (apply(v0,
% 23.44/4.04 v5) = v6) | ~ $i(v6) | ~ $i(v5) | ~ in(v6, v2) | ~ in(v5, v1)))
% 23.44/4.04
% 23.44/4.04 (function-axioms)
% 23.44/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.44/4.05 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 23.44/4.05 : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) &
% 23.44/4.05 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (function_inverse(v2) =
% 23.44/4.05 v1) | ~ (function_inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 23.44/4.05 [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 23.44/4.05 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) =
% 23.44/4.05 v1) | ~ (relation_dom(v2) = v0))
% 23.44/4.05
% 23.44/4.05 Further assumptions not needed in the proof:
% 23.44/4.05 --------------------------------------------
% 23.44/4.05 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, dt_k2_funct_1,
% 23.44/4.05 existence_m1_subset_1, fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1,
% 23.44/4.05 fc5_relat_1, fc6_relat_1, fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_relat_1,
% 23.44/4.05 rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_subset_1,
% 23.44/4.05 rc2_xboole_0, rc3_funct_1, rc3_relat_1, reflexivity_r1_tarski, t1_subset,
% 23.44/4.05 t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole,
% 23.44/4.05 t9_funct_1
% 23.44/4.05
% 23.44/4.05 Those formulas are unsatisfiable:
% 23.44/4.05 ---------------------------------
% 23.44/4.05
% 23.44/4.05 Begin of proof
% 23.44/4.05 |
% 23.44/4.05 | ALPHA: (function-axioms) implies:
% 23.44/4.05 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.44/4.05 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 23.44/4.05 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.44/4.05 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 23.44/4.05 |
% 23.44/4.05 | DELTA: instantiating (t60_funct_1) with fresh symbols all_45_0, all_45_1,
% 23.44/4.05 | all_45_2, all_45_3, all_45_4 gives:
% 23.44/4.05 | (3) ~ (all_45_0 = all_45_1) & function_inverse(all_45_4) = all_45_1 &
% 23.44/4.05 | relation_rng(all_45_0) = all_45_3 & relation_rng(all_45_4) = all_45_2 &
% 23.44/4.05 | relation_dom(all_45_0) = all_45_2 & relation_dom(all_45_4) = all_45_3 &
% 23.44/4.05 | $i(all_45_0) & $i(all_45_1) & $i(all_45_2) & $i(all_45_3) &
% 23.44/4.05 | $i(all_45_4) & one_to_one(all_45_4) & relation(all_45_0) &
% 23.44/4.05 | relation(all_45_4) & function(all_45_0) & function(all_45_4) & ! [v0:
% 23.44/4.05 | $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (apply(all_45_0, v1)
% 23.44/4.05 | = v0) | ~ (apply(all_45_4, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 23.44/4.05 | in(v1, all_45_2) | ~ in(v0, all_45_3)) & ! [v0: $i] : ! [v1: $i] :
% 23.44/4.05 | ! [v2: $i] : (v2 = v0 | ~ (apply(all_45_0, v1) = v2) | ~
% 23.44/4.05 | (apply(all_45_4, v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ in(v1,
% 23.44/4.05 | all_45_2) | ~ in(v0, all_45_3))
% 23.44/4.05 |
% 23.44/4.05 | ALPHA: (3) implies:
% 23.44/4.06 | (4) ~ (all_45_0 = all_45_1)
% 23.44/4.06 | (5) function(all_45_4)
% 23.44/4.06 | (6) function(all_45_0)
% 23.44/4.06 | (7) relation(all_45_4)
% 23.44/4.06 | (8) relation(all_45_0)
% 23.44/4.06 | (9) one_to_one(all_45_4)
% 23.44/4.06 | (10) $i(all_45_4)
% 23.44/4.06 | (11) $i(all_45_0)
% 23.44/4.06 | (12) relation_dom(all_45_4) = all_45_3
% 23.44/4.06 | (13) relation_dom(all_45_0) = all_45_2
% 23.44/4.06 | (14) relation_rng(all_45_4) = all_45_2
% 23.44/4.06 | (15) relation_rng(all_45_0) = all_45_3
% 23.44/4.06 | (16) function_inverse(all_45_4) = all_45_1
% 23.44/4.06 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 23.44/4.06 | (apply(all_45_0, v1) = v2) | ~ (apply(all_45_4, v0) = v1) | ~
% 23.44/4.06 | $i(v1) | ~ $i(v0) | ~ in(v1, all_45_2) | ~ in(v0, all_45_3))
% 23.44/4.06 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 23.44/4.06 | (apply(all_45_0, v1) = v0) | ~ (apply(all_45_4, v0) = v2) | ~
% 23.44/4.06 | $i(v1) | ~ $i(v0) | ~ in(v1, all_45_2) | ~ in(v0, all_45_3))
% 23.44/4.06 |
% 23.44/4.06 | GROUND_INST: instantiating (d5_funct_1) with all_45_4, all_45_2, simplifying
% 23.44/4.06 | with (5), (7), (10), (14) gives:
% 23.44/4.06 | (19) ? [v0: $i] : (relation_dom(all_45_4) = v0 & $i(v0) & ! [v1: $i] : !
% 23.44/4.06 | [v2: $i] : ( ~ (apply(all_45_4, v2) = v1) | ~ $i(v2) | ~ $i(v1) |
% 23.44/4.06 | ~ $i(all_45_2) | ~ in(v2, v0) | in(v1, all_45_2)) & ! [v1: $i] :
% 23.44/4.06 | ( ~ $i(v1) | ~ $i(all_45_2) | ~ in(v1, all_45_2) | ? [v2: $i] :
% 23.44/4.06 | (apply(all_45_4, v2) = v1 & $i(v2) & in(v2, v0))) & ? [v1: any] :
% 23.44/4.06 | (v1 = all_45_2 | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 23.44/4.06 | : ($i(v3) & $i(v2) & ( ~ in(v2, v1) | ! [v5: $i] : ( ~
% 23.44/4.06 | (apply(all_45_4, v5) = v2) | ~ $i(v5) | ~ in(v5, v0))) &
% 23.44/4.06 | (in(v2, v1) | (v4 = v2 & apply(all_45_4, v3) = v2 & in(v3,
% 23.44/4.06 | v0))))))
% 23.44/4.06 |
% 23.44/4.06 | GROUND_INST: instantiating (d5_funct_1) with all_45_0, all_45_3, simplifying
% 23.44/4.06 | with (6), (8), (11), (15) gives:
% 23.44/4.06 | (20) ? [v0: $i] : (relation_dom(all_45_0) = v0 & $i(v0) & ! [v1: $i] : !
% 23.44/4.06 | [v2: $i] : ( ~ (apply(all_45_0, v2) = v1) | ~ $i(v2) | ~ $i(v1) |
% 23.44/4.06 | ~ $i(all_45_3) | ~ in(v2, v0) | in(v1, all_45_3)) & ! [v1: $i] :
% 23.44/4.06 | ( ~ $i(v1) | ~ $i(all_45_3) | ~ in(v1, all_45_3) | ? [v2: $i] :
% 23.44/4.06 | (apply(all_45_0, v2) = v1 & $i(v2) & in(v2, v0))) & ? [v1: any] :
% 23.44/4.06 | (v1 = all_45_3 | ~ $i(v1) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 23.44/4.06 | : ($i(v3) & $i(v2) & ( ~ in(v2, v1) | ! [v5: $i] : ( ~
% 23.44/4.06 | (apply(all_45_0, v5) = v2) | ~ $i(v5) | ~ in(v5, v0))) &
% 23.44/4.06 | (in(v2, v1) | (v4 = v2 & apply(all_45_0, v3) = v2 & in(v3,
% 23.44/4.06 | v0))))))
% 23.44/4.06 |
% 23.44/4.06 | GROUND_INST: instantiating (t54_funct_1) with all_45_4, all_45_1, simplifying
% 23.44/4.07 | with (5), (7), (9), (10), (16) gives:
% 23.44/4.07 | (21) ? [v0: $i] : ? [v1: $i] : (relation_rng(all_45_4) = v0 &
% 23.44/4.07 | relation_dom(all_45_4) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : !
% 23.44/4.07 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 23.44/4.07 | (relation_dom(all_45_1) = v2) | ~ (apply(all_45_1, v3) = v5) | ~
% 23.44/4.07 | (apply(all_45_4, v4) = v3) | ~ $i(v4) | ~ $i(v3) | ~
% 23.44/4.07 | $i(all_45_1) | ~ relation(all_45_1) | ~ function(all_45_1) | ~
% 23.44/4.07 | in(v4, v1)) & ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 23.44/4.07 | $i] : (v5 = v3 | ~ (relation_dom(all_45_1) = v2) | ~
% 23.44/4.07 | (apply(all_45_1, v3) = v4) | ~ (apply(all_45_4, v4) = v5) | ~
% 23.44/4.07 | $i(v4) | ~ $i(v3) | ~ $i(all_45_1) | ~ relation(all_45_1) | ~
% 23.44/4.07 | function(all_45_1) | ~ in(v3, v0)) & ! [v2: $i] : ! [v3: $i] :
% 23.44/4.07 | ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(all_45_1) = v2) | ~
% 23.44/4.07 | (apply(all_45_1, v3) = v5) | ~ (apply(all_45_4, v4) = v3) | ~
% 23.44/4.07 | $i(v4) | ~ $i(v3) | ~ $i(all_45_1) | ~ relation(all_45_1) | ~
% 23.44/4.07 | function(all_45_1) | ~ in(v4, v1) | in(v3, v0)) & ! [v2: $i] :
% 23.44/4.07 | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (relation_dom(all_45_1)
% 23.44/4.07 | = v2) | ~ (apply(all_45_1, v3) = v4) | ~ (apply(all_45_4, v4)
% 23.44/4.07 | = v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(all_45_1) | ~
% 23.44/4.07 | relation(all_45_1) | ~ function(all_45_1) | ~ in(v3, v0) |
% 23.44/4.07 | in(v4, v1)) & ! [v2: $i] : (v2 = v0 | ~ (relation_dom(all_45_1)
% 23.44/4.07 | = v2) | ~ $i(all_45_1) | ~ relation(all_45_1) | ~
% 23.44/4.07 | function(all_45_1)) & ! [v2: any] : (v2 = all_45_1 | ~
% 23.44/4.07 | (relation_dom(v2) = v0) | ~ $i(v2) | ~ relation(v2) | ~
% 23.44/4.07 | function(v2) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 23.44/4.07 | $i] : ($i(v4) & $i(v3) & ((v6 = v3 & apply(all_45_4, v4) = v3 &
% 23.44/4.07 | in(v4, v1) & ( ~ in(v3, v0) | ( ~ (v5 = v4) & apply(v2, v3)
% 23.44/4.07 | = v5 & $i(v5)))) | (v5 = v4 & apply(v2, v3) = v4 &
% 23.44/4.07 | in(v3, v0) & ( ~ in(v4, v1) | ( ~ (v6 = v3) &
% 23.44/4.07 | apply(all_45_4, v4) = v6 & $i(v6))))))))
% 23.44/4.07 |
% 23.44/4.07 | DELTA: instantiating (20) with fresh symbol all_54_0 gives:
% 23.44/4.07 | (22) relation_dom(all_45_0) = all_54_0 & $i(all_54_0) & ! [v0: $i] : !
% 23.44/4.07 | [v1: $i] : ( ~ (apply(all_45_0, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 23.44/4.07 | $i(all_45_3) | ~ in(v1, all_54_0) | in(v0, all_45_3)) & ! [v0: $i]
% 23.44/4.07 | : ( ~ $i(v0) | ~ $i(all_45_3) | ~ in(v0, all_45_3) | ? [v1: $i] :
% 23.44/4.07 | (apply(all_45_0, v1) = v0 & $i(v1) & in(v1, all_54_0))) & ? [v0:
% 23.44/4.07 | any] : (v0 = all_45_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 23.44/4.07 | [v3: $i] : ($i(v2) & $i(v1) & ( ~ in(v1, v0) | ! [v4: $i] : ( ~
% 23.44/4.07 | (apply(all_45_0, v4) = v1) | ~ $i(v4) | ~ in(v4, all_54_0)))
% 23.44/4.07 | & (in(v1, v0) | (v3 = v1 & apply(all_45_0, v2) = v1 & in(v2,
% 23.44/4.07 | all_54_0)))))
% 23.44/4.07 |
% 23.44/4.07 | ALPHA: (22) implies:
% 23.44/4.07 | (23) $i(all_54_0)
% 23.44/4.07 | (24) relation_dom(all_45_0) = all_54_0
% 23.44/4.07 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_45_0, v1) = v0) | ~ $i(v1)
% 23.44/4.07 | | ~ $i(v0) | ~ $i(all_45_3) | ~ in(v1, all_54_0) | in(v0,
% 23.44/4.07 | all_45_3))
% 23.44/4.07 |
% 23.44/4.07 | DELTA: instantiating (19) with fresh symbol all_58_0 gives:
% 23.44/4.08 | (26) relation_dom(all_45_4) = all_58_0 & $i(all_58_0) & ! [v0: $i] : !
% 23.44/4.08 | [v1: $i] : ( ~ (apply(all_45_4, v1) = v0) | ~ $i(v1) | ~ $i(v0) | ~
% 23.44/4.08 | $i(all_45_2) | ~ in(v1, all_58_0) | in(v0, all_45_2)) & ! [v0: $i]
% 23.44/4.08 | : ( ~ $i(v0) | ~ $i(all_45_2) | ~ in(v0, all_45_2) | ? [v1: $i] :
% 23.44/4.08 | (apply(all_45_4, v1) = v0 & $i(v1) & in(v1, all_58_0))) & ? [v0:
% 23.44/4.08 | any] : (v0 = all_45_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ?
% 23.44/4.08 | [v3: $i] : ($i(v2) & $i(v1) & ( ~ in(v1, v0) | ! [v4: $i] : ( ~
% 23.44/4.08 | (apply(all_45_4, v4) = v1) | ~ $i(v4) | ~ in(v4, all_58_0)))
% 23.44/4.08 | & (in(v1, v0) | (v3 = v1 & apply(all_45_4, v2) = v1 & in(v2,
% 23.44/4.08 | all_58_0)))))
% 23.44/4.08 |
% 23.44/4.08 | ALPHA: (26) implies:
% 23.44/4.08 | (27) $i(all_58_0)
% 23.44/4.08 | (28) relation_dom(all_45_4) = all_58_0
% 23.44/4.08 | (29) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_45_4, v1) = v0) | ~ $i(v1)
% 23.44/4.08 | | ~ $i(v0) | ~ $i(all_45_2) | ~ in(v1, all_58_0) | in(v0,
% 23.44/4.08 | all_45_2))
% 23.44/4.08 |
% 23.44/4.08 | DELTA: instantiating (21) with fresh symbols all_62_0, all_62_1 gives:
% 23.44/4.08 | (30) relation_rng(all_45_4) = all_62_1 & relation_dom(all_45_4) = all_62_0
% 23.44/4.08 | & $i(all_62_0) & $i(all_62_1) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.44/4.08 | $i] : ! [v3: $i] : (v3 = v2 | ~ (relation_dom(all_45_1) = v0) | ~
% 23.44/4.08 | (apply(all_45_1, v1) = v3) | ~ (apply(all_45_4, v2) = v1) | ~
% 23.44/4.08 | $i(v2) | ~ $i(v1) | ~ $i(all_45_1) | ~ relation(all_45_1) | ~
% 23.44/4.08 | function(all_45_1) | ~ in(v2, all_62_0)) & ! [v0: $i] : ! [v1:
% 23.44/4.08 | $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 23.44/4.08 | (relation_dom(all_45_1) = v0) | ~ (apply(all_45_1, v1) = v2) | ~
% 23.44/4.08 | (apply(all_45_4, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(all_45_1)
% 23.44/4.08 | | ~ relation(all_45_1) | ~ function(all_45_1) | ~ in(v1,
% 23.44/4.08 | all_62_1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 23.44/4.08 | : ( ~ (relation_dom(all_45_1) = v0) | ~ (apply(all_45_1, v1) = v3) |
% 23.44/4.08 | ~ (apply(all_45_4, v2) = v1) | ~ $i(v2) | ~ $i(v1) | ~
% 23.44/4.08 | $i(all_45_1) | ~ relation(all_45_1) | ~ function(all_45_1) | ~
% 23.44/4.08 | in(v2, all_62_0) | in(v1, all_62_1)) & ! [v0: $i] : ! [v1: $i] :
% 23.44/4.08 | ! [v2: $i] : ! [v3: $i] : ( ~ (relation_dom(all_45_1) = v0) | ~
% 23.44/4.08 | (apply(all_45_1, v1) = v2) | ~ (apply(all_45_4, v2) = v3) | ~
% 23.44/4.08 | $i(v2) | ~ $i(v1) | ~ $i(all_45_1) | ~ relation(all_45_1) | ~
% 23.44/4.08 | function(all_45_1) | ~ in(v1, all_62_1) | in(v2, all_62_0)) & !
% 23.44/4.08 | [v0: int] : (v0 = all_62_1 | ~ (relation_dom(all_45_1) = v0) | ~
% 23.44/4.08 | $i(all_45_1) | ~ relation(all_45_1) | ~ function(all_45_1)) & !
% 23.44/4.08 | [v0: any] : (v0 = all_45_1 | ~ (relation_dom(v0) = all_62_1) | ~
% 23.44/4.08 | $i(v0) | ~ relation(v0) | ~ function(v0) | ? [v1: $i] : ? [v2:
% 23.44/4.08 | $i] : ? [v3: $i] : ? [v4: $i] : ($i(v2) & $i(v1) & ((v4 = v1 &
% 23.44/4.08 | apply(all_45_4, v2) = v1 & in(v2, all_62_0) & ( ~ in(v1,
% 23.44/4.08 | all_62_1) | ( ~ (v3 = v2) & apply(v0, v1) = v3 & $i(v3))))
% 23.44/4.08 | | (v3 = v2 & apply(v0, v1) = v2 & in(v1, all_62_1) & ( ~ in(v2,
% 23.44/4.08 | all_62_0) | ( ~ (v4 = v1) & apply(all_45_4, v2) = v4 &
% 23.44/4.08 | $i(v4)))))))
% 23.44/4.08 |
% 23.44/4.08 | ALPHA: (30) implies:
% 23.44/4.08 | (31) relation_dom(all_45_4) = all_62_0
% 23.44/4.08 | (32) relation_rng(all_45_4) = all_62_1
% 23.44/4.09 | (33) ! [v0: any] : (v0 = all_45_1 | ~ (relation_dom(v0) = all_62_1) | ~
% 23.44/4.09 | $i(v0) | ~ relation(v0) | ~ function(v0) | ? [v1: $i] : ? [v2:
% 23.44/4.09 | $i] : ? [v3: $i] : ? [v4: $i] : ($i(v2) & $i(v1) & ((v4 = v1 &
% 23.44/4.09 | apply(all_45_4, v2) = v1 & in(v2, all_62_0) & ( ~ in(v1,
% 23.44/4.09 | all_62_1) | ( ~ (v3 = v2) & apply(v0, v1) = v3 & $i(v3))))
% 23.44/4.09 | | (v3 = v2 & apply(v0, v1) = v2 & in(v1, all_62_1) & ( ~ in(v2,
% 23.44/4.09 | all_62_0) | ( ~ (v4 = v1) & apply(all_45_4, v2) = v4 &
% 23.44/4.09 | $i(v4)))))))
% 23.44/4.09 |
% 23.44/4.09 | GROUND_INST: instantiating (1) with all_45_3, all_62_0, all_45_4, simplifying
% 23.44/4.09 | with (12), (31) gives:
% 23.44/4.09 | (34) all_62_0 = all_45_3
% 23.44/4.09 |
% 23.44/4.09 | GROUND_INST: instantiating (1) with all_58_0, all_62_0, all_45_4, simplifying
% 23.44/4.09 | with (28), (31) gives:
% 23.44/4.09 | (35) all_62_0 = all_58_0
% 23.44/4.09 |
% 23.44/4.09 | GROUND_INST: instantiating (1) with all_45_2, all_54_0, all_45_0, simplifying
% 23.44/4.09 | with (13), (24) gives:
% 23.44/4.09 | (36) all_54_0 = all_45_2
% 23.44/4.09 |
% 23.44/4.09 | GROUND_INST: instantiating (2) with all_45_2, all_62_1, all_45_4, simplifying
% 23.44/4.09 | with (14), (32) gives:
% 23.44/4.09 | (37) all_62_1 = all_45_2
% 23.44/4.09 |
% 23.44/4.09 | COMBINE_EQS: (34), (35) imply:
% 23.44/4.09 | (38) all_58_0 = all_45_3
% 23.44/4.09 |
% 23.44/4.09 | REDUCE: (27), (38) imply:
% 23.44/4.09 | (39) $i(all_45_3)
% 23.44/4.09 |
% 23.44/4.09 | REDUCE: (23), (36) imply:
% 23.44/4.09 | (40) $i(all_45_2)
% 23.44/4.09 |
% 23.44/4.09 | GROUND_INST: instantiating (33) with all_45_0, simplifying with (6), (8), (11)
% 23.44/4.09 | gives:
% 23.72/4.09 | (41) all_45_0 = all_45_1 | ~ (relation_dom(all_45_0) = all_62_1) | ? [v0:
% 23.72/4.09 | $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) & $i(v0) &
% 23.72/4.09 | ((v3 = v0 & apply(all_45_4, v1) = v0 & in(v1, all_62_0) & ( ~ in(v0,
% 23.72/4.09 | all_62_1) | ( ~ (v2 = v1) & apply(all_45_0, v0) = v2 &
% 23.72/4.09 | $i(v2)))) | (v2 = v1 & apply(all_45_0, v0) = v1 & in(v0,
% 23.72/4.09 | all_62_1) & ( ~ in(v1, all_62_0) | ( ~ (v3 = v0) &
% 23.72/4.09 | apply(all_45_4, v1) = v3 & $i(v3))))))
% 23.72/4.09 |
% 23.72/4.09 | BETA: splitting (41) gives:
% 23.72/4.09 |
% 23.72/4.09 | Case 1:
% 23.72/4.09 | |
% 23.72/4.09 | | (42) ~ (relation_dom(all_45_0) = all_62_1)
% 23.72/4.09 | |
% 23.72/4.09 | | REDUCE: (37), (42) imply:
% 23.72/4.09 | | (43) ~ (relation_dom(all_45_0) = all_45_2)
% 23.72/4.09 | |
% 23.72/4.09 | | PRED_UNIFY: (13), (43) imply:
% 23.72/4.09 | | (44) $false
% 23.72/4.09 | |
% 23.72/4.09 | | CLOSE: (44) is inconsistent.
% 23.72/4.09 | |
% 23.72/4.09 | Case 2:
% 23.72/4.09 | |
% 23.72/4.10 | | (45) all_45_0 = all_45_1 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 23.72/4.10 | | [v3: $i] : ($i(v1) & $i(v0) & ((v3 = v0 & apply(all_45_4, v1) = v0 &
% 23.72/4.10 | | in(v1, all_62_0) & ( ~ in(v0, all_62_1) | ( ~ (v2 = v1) &
% 23.72/4.10 | | apply(all_45_0, v0) = v2 & $i(v2)))) | (v2 = v1 &
% 23.72/4.10 | | apply(all_45_0, v0) = v1 & in(v0, all_62_1) & ( ~ in(v1,
% 23.72/4.10 | | all_62_0) | ( ~ (v3 = v0) & apply(all_45_4, v1) = v3 &
% 23.72/4.10 | | $i(v3))))))
% 23.72/4.10 | |
% 23.72/4.10 | | BETA: splitting (45) gives:
% 23.72/4.10 | |
% 23.72/4.10 | | Case 1:
% 23.72/4.10 | | |
% 23.72/4.10 | | | (46) all_45_0 = all_45_1
% 23.72/4.10 | | |
% 23.72/4.10 | | | REDUCE: (4), (46) imply:
% 23.72/4.10 | | | (47) $false
% 23.72/4.10 | | |
% 23.72/4.10 | | | CLOSE: (47) is inconsistent.
% 23.72/4.10 | | |
% 23.72/4.10 | | Case 2:
% 23.72/4.10 | | |
% 23.72/4.10 | | | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ($i(v1) &
% 23.72/4.10 | | | $i(v0) & ((v3 = v0 & apply(all_45_4, v1) = v0 & in(v1, all_62_0)
% 23.72/4.10 | | | & ( ~ in(v0, all_62_1) | ( ~ (v2 = v1) & apply(all_45_0, v0)
% 23.72/4.10 | | | = v2 & $i(v2)))) | (v2 = v1 & apply(all_45_0, v0) = v1 &
% 23.72/4.10 | | | in(v0, all_62_1) & ( ~ in(v1, all_62_0) | ( ~ (v3 = v0) &
% 23.72/4.10 | | | apply(all_45_4, v1) = v3 & $i(v3))))))
% 23.72/4.10 | | |
% 23.72/4.10 | | | DELTA: instantiating (48) with fresh symbols all_127_0, all_127_1,
% 23.72/4.10 | | | all_127_2, all_127_3 gives:
% 23.72/4.10 | | | (49) $i(all_127_2) & $i(all_127_3) & ((all_127_0 = all_127_3 &
% 23.72/4.10 | | | apply(all_45_4, all_127_2) = all_127_3 & in(all_127_2,
% 23.72/4.10 | | | all_62_0) & ( ~ in(all_127_3, all_62_1) | ( ~ (all_127_1 =
% 23.72/4.10 | | | all_127_2) & apply(all_45_0, all_127_3) = all_127_1 &
% 23.72/4.10 | | | $i(all_127_1)))) | (all_127_1 = all_127_2 &
% 23.72/4.10 | | | apply(all_45_0, all_127_3) = all_127_2 & in(all_127_3,
% 23.72/4.10 | | | all_62_1) & ( ~ in(all_127_2, all_62_0) | ( ~ (all_127_0 =
% 23.72/4.10 | | | all_127_3) & apply(all_45_4, all_127_2) = all_127_0 &
% 23.72/4.10 | | | $i(all_127_0)))))
% 23.72/4.10 | | |
% 23.72/4.10 | | | ALPHA: (49) implies:
% 23.72/4.10 | | | (50) $i(all_127_3)
% 23.72/4.10 | | | (51) $i(all_127_2)
% 23.72/4.10 | | | (52) (all_127_0 = all_127_3 & apply(all_45_4, all_127_2) = all_127_3 &
% 23.72/4.10 | | | in(all_127_2, all_62_0) & ( ~ in(all_127_3, all_62_1) | ( ~
% 23.72/4.10 | | | (all_127_1 = all_127_2) & apply(all_45_0, all_127_3) =
% 23.72/4.10 | | | all_127_1 & $i(all_127_1)))) | (all_127_1 = all_127_2 &
% 23.72/4.10 | | | apply(all_45_0, all_127_3) = all_127_2 & in(all_127_3, all_62_1)
% 23.72/4.10 | | | & ( ~ in(all_127_2, all_62_0) | ( ~ (all_127_0 = all_127_3) &
% 23.72/4.10 | | | apply(all_45_4, all_127_2) = all_127_0 & $i(all_127_0))))
% 23.72/4.10 | | |
% 23.72/4.10 | | | BETA: splitting (52) gives:
% 23.72/4.10 | | |
% 23.72/4.10 | | | Case 1:
% 23.72/4.10 | | | |
% 23.72/4.10 | | | | (53) all_127_0 = all_127_3 & apply(all_45_4, all_127_2) = all_127_3 &
% 23.72/4.10 | | | | in(all_127_2, all_62_0) & ( ~ in(all_127_3, all_62_1) | ( ~
% 23.72/4.10 | | | | (all_127_1 = all_127_2) & apply(all_45_0, all_127_3) =
% 23.72/4.10 | | | | all_127_1 & $i(all_127_1)))
% 23.72/4.10 | | | |
% 23.72/4.10 | | | | ALPHA: (53) implies:
% 23.72/4.10 | | | | (54) in(all_127_2, all_62_0)
% 23.72/4.10 | | | | (55) apply(all_45_4, all_127_2) = all_127_3
% 23.72/4.10 | | | | (56) ~ in(all_127_3, all_62_1) | ( ~ (all_127_1 = all_127_2) &
% 23.72/4.10 | | | | apply(all_45_0, all_127_3) = all_127_1 & $i(all_127_1))
% 23.72/4.10 | | | |
% 23.72/4.10 | | | | REDUCE: (34), (54) imply:
% 23.72/4.10 | | | | (57) in(all_127_2, all_45_3)
% 23.72/4.10 | | | |
% 23.72/4.10 | | | | GROUND_INST: instantiating (29) with all_127_3, all_127_2, simplifying
% 23.72/4.10 | | | | with (40), (50), (51), (55) gives:
% 23.72/4.10 | | | | (58) ~ in(all_127_2, all_58_0) | in(all_127_3, all_45_2)
% 23.72/4.10 | | | |
% 23.72/4.10 | | | | BETA: splitting (58) gives:
% 23.72/4.10 | | | |
% 23.72/4.10 | | | | Case 1:
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | (59) ~ in(all_127_2, all_58_0)
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | REDUCE: (38), (59) imply:
% 23.72/4.10 | | | | | (60) ~ in(all_127_2, all_45_3)
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | PRED_UNIFY: (57), (60) imply:
% 23.72/4.10 | | | | | (61) $false
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | CLOSE: (61) is inconsistent.
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | Case 2:
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | (62) in(all_127_3, all_45_2)
% 23.72/4.10 | | | | | (63) in(all_127_2, all_58_0)
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | BETA: splitting (56) gives:
% 23.72/4.10 | | | | |
% 23.72/4.10 | | | | | Case 1:
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | | (64) ~ in(all_127_3, all_62_1)
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | | REDUCE: (37), (64) imply:
% 23.72/4.10 | | | | | | (65) ~ in(all_127_3, all_45_2)
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | | PRED_UNIFY: (62), (65) imply:
% 23.72/4.10 | | | | | | (66) $false
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | | CLOSE: (66) is inconsistent.
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | Case 2:
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | | (67) in(all_127_3, all_62_1)
% 23.72/4.10 | | | | | | (68) ~ (all_127_1 = all_127_2) & apply(all_45_0, all_127_3) =
% 23.72/4.10 | | | | | | all_127_1 & $i(all_127_1)
% 23.72/4.10 | | | | | |
% 23.72/4.10 | | | | | | ALPHA: (68) implies:
% 23.72/4.10 | | | | | | (69) ~ (all_127_1 = all_127_2)
% 23.72/4.10 | | | | | | (70) apply(all_45_0, all_127_3) = all_127_1
% 23.72/4.10 | | | | | |
% 23.72/4.11 | | | | | | GROUND_INST: instantiating (17) with all_127_2, all_127_3,
% 23.72/4.11 | | | | | | all_127_1, simplifying with (50), (51), (55), (57),
% 23.72/4.11 | | | | | | (62), (70) gives:
% 23.72/4.11 | | | | | | (71) all_127_1 = all_127_2
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | REDUCE: (69), (71) imply:
% 23.72/4.11 | | | | | | (72) $false
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | CLOSE: (72) is inconsistent.
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | End of split
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | End of split
% 23.72/4.11 | | | |
% 23.72/4.11 | | | Case 2:
% 23.72/4.11 | | | |
% 23.72/4.11 | | | | (73) all_127_1 = all_127_2 & apply(all_45_0, all_127_3) = all_127_2 &
% 23.72/4.11 | | | | in(all_127_3, all_62_1) & ( ~ in(all_127_2, all_62_0) | ( ~
% 23.72/4.11 | | | | (all_127_0 = all_127_3) & apply(all_45_4, all_127_2) =
% 23.72/4.11 | | | | all_127_0 & $i(all_127_0)))
% 23.72/4.11 | | | |
% 23.72/4.11 | | | | ALPHA: (73) implies:
% 23.72/4.11 | | | | (74) in(all_127_3, all_62_1)
% 23.72/4.11 | | | | (75) apply(all_45_0, all_127_3) = all_127_2
% 23.72/4.11 | | | | (76) ~ in(all_127_2, all_62_0) | ( ~ (all_127_0 = all_127_3) &
% 23.72/4.11 | | | | apply(all_45_4, all_127_2) = all_127_0 & $i(all_127_0))
% 23.72/4.11 | | | |
% 23.72/4.11 | | | | REDUCE: (37), (74) imply:
% 23.72/4.11 | | | | (77) in(all_127_3, all_45_2)
% 23.72/4.11 | | | |
% 23.72/4.11 | | | | GROUND_INST: instantiating (25) with all_127_2, all_127_3, simplifying
% 23.72/4.11 | | | | with (39), (50), (51), (75) gives:
% 23.72/4.11 | | | | (78) ~ in(all_127_3, all_54_0) | in(all_127_2, all_45_3)
% 23.72/4.11 | | | |
% 23.72/4.11 | | | | BETA: splitting (78) gives:
% 23.72/4.11 | | | |
% 23.72/4.11 | | | | Case 1:
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | (79) ~ in(all_127_3, all_54_0)
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | REDUCE: (36), (79) imply:
% 23.72/4.11 | | | | | (80) ~ in(all_127_3, all_45_2)
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | PRED_UNIFY: (77), (80) imply:
% 23.72/4.11 | | | | | (81) $false
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | CLOSE: (81) is inconsistent.
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | Case 2:
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | (82) in(all_127_3, all_54_0)
% 23.72/4.11 | | | | | (83) in(all_127_2, all_45_3)
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | BETA: splitting (76) gives:
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | | Case 1:
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | (84) ~ in(all_127_2, all_62_0)
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | REDUCE: (34), (84) imply:
% 23.72/4.11 | | | | | | (85) ~ in(all_127_2, all_45_3)
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | PRED_UNIFY: (83), (85) imply:
% 23.72/4.11 | | | | | | (86) $false
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | CLOSE: (86) is inconsistent.
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | Case 2:
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | (87) in(all_127_2, all_62_0)
% 23.72/4.11 | | | | | | (88) ~ (all_127_0 = all_127_3) & apply(all_45_4, all_127_2) =
% 23.72/4.11 | | | | | | all_127_0 & $i(all_127_0)
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | ALPHA: (88) implies:
% 23.72/4.11 | | | | | | (89) ~ (all_127_0 = all_127_3)
% 23.72/4.11 | | | | | | (90) apply(all_45_4, all_127_2) = all_127_0
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | GROUND_INST: instantiating (18) with all_127_2, all_127_3,
% 23.72/4.11 | | | | | | all_127_0, simplifying with (50), (51), (75), (77),
% 23.72/4.11 | | | | | | (83), (90) gives:
% 23.72/4.11 | | | | | | (91) all_127_0 = all_127_3
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | REDUCE: (89), (91) imply:
% 23.72/4.11 | | | | | | (92) $false
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | | CLOSE: (92) is inconsistent.
% 23.72/4.11 | | | | | |
% 23.72/4.11 | | | | | End of split
% 23.72/4.11 | | | | |
% 23.72/4.11 | | | | End of split
% 23.72/4.11 | | | |
% 23.72/4.11 | | | End of split
% 23.72/4.11 | | |
% 23.72/4.11 | | End of split
% 23.72/4.11 | |
% 23.72/4.11 | End of split
% 23.72/4.11 |
% 23.72/4.11 End of proof
% 23.72/4.11 % SZS output end Proof for theBenchmark
% 23.72/4.11
% 23.72/4.11 3510ms
%------------------------------------------------------------------------------