TSTP Solution File: SEU037+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU037+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 : n032.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 88.22s 12.82s
% Output : Proof 90.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU037+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 23 13:19:25 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.56 ________ _____
% 0.17/0.56 ___ __ \_________(_)________________________________
% 0.17/0.56 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.56 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.56 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.56
% 0.17/0.56 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.56 (2023-06-19)
% 0.17/0.56
% 0.17/0.56 (c) Philipp Rümmer, 2009-2023
% 0.17/0.56 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.56 Amanda Stjerna.
% 0.17/0.56 Free software under BSD-3-Clause.
% 0.17/0.56
% 0.17/0.56 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.56
% 0.17/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.57 Running up to 7 provers in parallel.
% 0.17/0.59 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.59 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.59 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.59 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.59 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.59 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.59 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.54/1.06 Prover 1: Preprocessing ...
% 2.54/1.07 Prover 4: Preprocessing ...
% 3.04/1.11 Prover 3: Preprocessing ...
% 3.04/1.11 Prover 2: Preprocessing ...
% 3.04/1.11 Prover 0: Preprocessing ...
% 3.04/1.11 Prover 5: Preprocessing ...
% 3.04/1.11 Prover 6: Preprocessing ...
% 6.51/1.64 Prover 1: Warning: ignoring some quantifiers
% 6.51/1.66 Prover 5: Proving ...
% 6.51/1.68 Prover 1: Constructing countermodel ...
% 6.51/1.70 Prover 3: Warning: ignoring some quantifiers
% 7.11/1.72 Prover 3: Constructing countermodel ...
% 7.11/1.76 Prover 6: Proving ...
% 7.56/1.80 Prover 2: Proving ...
% 8.52/2.08 Prover 4: Warning: ignoring some quantifiers
% 9.29/2.14 Prover 4: Constructing countermodel ...
% 10.62/2.22 Prover 3: gave up
% 10.62/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.01/2.35 Prover 7: Preprocessing ...
% 11.63/2.38 Prover 0: Proving ...
% 12.03/2.49 Prover 7: Warning: ignoring some quantifiers
% 12.03/2.51 Prover 7: Constructing countermodel ...
% 12.67/2.52 Prover 1: gave up
% 12.67/2.52 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.67/2.58 Prover 8: Preprocessing ...
% 13.82/2.78 Prover 8: Warning: ignoring some quantifiers
% 13.82/2.82 Prover 8: Constructing countermodel ...
% 16.17/3.00 Prover 7: gave up
% 16.17/3.02 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 16.83/3.11 Prover 9: Preprocessing ...
% 18.45/3.35 Prover 8: gave up
% 18.45/3.36 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.13/3.42 Prover 10: Preprocessing ...
% 19.13/3.47 Prover 9: Warning: ignoring some quantifiers
% 19.13/3.48 Prover 9: Constructing countermodel ...
% 19.83/3.52 Prover 10: Warning: ignoring some quantifiers
% 19.83/3.53 Prover 10: Constructing countermodel ...
% 21.32/3.74 Prover 10: gave up
% 21.32/3.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.32/3.79 Prover 11: Preprocessing ...
% 24.37/4.13 Prover 11: Warning: ignoring some quantifiers
% 24.37/4.15 Prover 11: Constructing countermodel ...
% 57.12/8.47 Prover 2: stopped
% 57.12/8.48 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 57.56/8.54 Prover 12: Preprocessing ...
% 57.97/8.70 Prover 12: Proving ...
% 70.67/10.35 Prover 12: stopped
% 70.67/10.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 70.67/10.43 Prover 13: Preprocessing ...
% 71.64/10.50 Prover 13: Warning: ignoring some quantifiers
% 71.64/10.51 Prover 13: Constructing countermodel ...
% 88.22/12.80 Prover 13: Found proof (size 154)
% 88.22/12.81 Prover 13: proved (2437ms)
% 88.22/12.81 Prover 9: stopped
% 88.22/12.81 Prover 0: stopped
% 88.22/12.81 Prover 5: stopped
% 88.22/12.81 Prover 6: stopped
% 88.22/12.81 Prover 4: stopped
% 88.22/12.82 Prover 11: stopped
% 88.22/12.82
% 88.22/12.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 88.22/12.82
% 88.22/12.83 % SZS output start Proof for theBenchmark
% 88.22/12.84 Assumptions after simplification:
% 88.22/12.84 ---------------------------------
% 88.22/12.84
% 88.22/12.84 (cc1_funct_1)
% 88.22/12.84 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | function(v0))
% 88.22/12.84
% 88.22/12.84 (cc1_relat_1)
% 88.22/12.84 ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | relation(v0))
% 88.22/12.84
% 88.22/12.84 (commutativity_k3_xboole_0)
% 89.60/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2)
% 89.60/12.87 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) & ?
% 89.60/12.87 [v0: $i] : ? [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ? [v2: $i] :
% 89.60/12.87 (set_intersection2(v1, v0) = v2 & set_intersection2(v0, v1) = v2 & $i(v2)))
% 89.60/12.87
% 90.12/12.87 (dt_k7_relat_1)
% 90.12/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 90.12/12.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | relation(v2)) & ?
% 90.12/12.87 [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ? [v2:
% 90.12/12.87 $i] : (relation_dom_restriction(v1, v0) = v2 & $i(v2) & relation(v2)))
% 90.12/12.87
% 90.12/12.87 (fc4_funct_1)
% 90.12/12.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0,
% 90.12/12.87 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ relation(v0) | ~ function(v0) |
% 90.12/12.87 relation(v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 90.12/12.87 (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 90.12/12.87 relation(v0) | ~ function(v0) | function(v2)) & ? [v0: $i] : ! [v1: $i] :
% 90.12/12.87 ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v2: $i] :
% 90.12/12.87 (relation_dom_restriction(v1, v0) = v2 & $i(v2) & relation(v2) &
% 90.12/12.87 function(v2)))
% 90.12/12.87
% 90.12/12.87 (fc4_relat_1)
% 90.12/12.87 $i(empty_set) & relation(empty_set) & empty(empty_set)
% 90.12/12.87
% 90.12/12.87 (fc5_relat_1)
% 90.12/12.88 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 90.12/12.88 relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0: $i] : ( ~ $i(v0) | ~
% 90.12/12.88 relation(v0) | empty(v0) | ? [v1: $i] : (relation_dom(v0) = v1 & $i(v1) &
% 90.12/12.88 ~ empty(v1)))
% 90.12/12.88
% 90.12/12.88 (fc7_relat_1)
% 90.12/12.88 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ~
% 90.12/12.88 empty(v0) | relation(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.12/12.88 (relation_dom(v0) = v1) | ~ $i(v0) | ~ empty(v0) | empty(v1)) & ! [v0:
% 90.12/12.88 $i] : ( ~ $i(v0) | ~ empty(v0) | ? [v1: $i] : (relation_dom(v0) = v1 &
% 90.12/12.88 $i(v1) & relation(v1) & empty(v1)))
% 90.12/12.88
% 90.12/12.88 (rc1_funct_1)
% 90.12/12.88 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0))
% 90.12/12.88
% 90.12/12.88 (rc1_relat_1)
% 90.12/12.88 ? [v0: $i] : ($i(v0) & relation(v0) & empty(v0))
% 90.12/12.88
% 90.12/12.88 (rc1_xboole_0)
% 90.12/12.88 ? [v0: $i] : ($i(v0) & empty(v0))
% 90.12/12.88
% 90.12/12.88 (rc2_funct_1)
% 90.12/12.88 ? [v0: $i] : ($i(v0) & relation(v0) & function(v0) & empty(v0))
% 90.12/12.88
% 90.12/12.88 (t68_funct_1)
% 90.12/12.88 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 90.12/12.88 $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~
% 90.12/12.88 (set_intersection2(v4, v0) = v5) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 90.12/12.88 relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6:
% 90.12/12.88 $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 90.12/12.88 (relation_dom_restriction(v3, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v6 = v1) |
% 90.12/12.88 (v5 = v2 & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v1, v10) = v11) | ~
% 90.12/12.88 $i(v10) | ~ in(v10, v2) | (apply(v3, v10) = v11 & $i(v11))))) & ( ~
% 90.12/12.88 (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7)
% 90.12/12.88 = v8 & $i(v9) & $i(v8) & in(v7, v2))))) & ? [v0: $i] : ! [v1: $i] :
% 90.12/12.88 ( ~ $i(v1) | ~ $i(v0) | ~ relation(v1) | ~ function(v1) | ? [v2: $i] :
% 90.12/12.88 (relation_dom(v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ $i(v3) | ~ relation(v3)
% 90.12/12.89 | ~ function(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 90.12/12.89 $i] : ? [v8: $i] : ? [v9: $i] : (relation_dom(v3) = v5 &
% 90.12/12.89 relation_dom_restriction(v3, v0) = v4 & set_intersection2(v5, v0) = v6
% 90.12/12.89 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & ( ~ (v6 = v2) | v4 = v1 | ( ~
% 90.12/12.89 (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) &
% 90.12/12.89 $i(v8) & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10: $i] :
% 90.12/12.89 ( ~ $i(v10) | ~ in(v10, v2) | ? [v11: $i] : (apply(v3, v10) =
% 90.12/12.89 v11 & apply(v1, v10) = v11 & $i(v11)))))))))
% 90.12/12.89
% 90.12/12.89 (t6_boole)
% 90.12/12.89 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 90.12/12.89
% 90.12/12.89 (t71_funct_1)
% 90.12/12.89 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 90.12/12.89 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v5, v1) = v6 &
% 90.12/12.89 apply(v2, v1) = v7 & relation_dom(v2) = v3 & relation_dom_restriction(v2,
% 90.12/12.89 v0) = v5 & set_intersection2(v3, v0) = v4 & $i(v7) & $i(v6) & $i(v5) &
% 90.12/12.89 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & relation(v2) & function(v2) &
% 90.12/12.89 in(v1, v4))
% 90.12/12.89
% 90.12/12.89 (t7_boole)
% 90.12/12.89 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | ~ in(v0,
% 90.12/12.89 v1))
% 90.12/12.89
% 90.12/12.89 (t8_boole)
% 90.12/12.89 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ empty(v1) |
% 90.12/12.89 ~ empty(v0))
% 90.12/12.89
% 90.12/12.89 (function-axioms)
% 90.12/12.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.12/12.89 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 90.12/12.89 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2)
% 90.12/12.89 = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0: $i] : !
% 90.12/12.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_intersection2(v3,
% 90.12/12.89 v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 90.12/12.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~
% 90.12/12.89 (relation_dom(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 90.12/12.89 v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 90.12/12.89
% 90.12/12.89 Further assumptions not needed in the proof:
% 90.12/12.89 --------------------------------------------
% 90.12/12.89 antisymmetry_r2_hidden, cc2_funct_1, existence_m1_subset_1, fc12_relat_1,
% 90.12/12.89 fc13_relat_1, fc1_relat_1, fc1_subset_1, fc1_xboole_0, idempotence_k3_xboole_0,
% 90.12/12.89 rc1_subset_1, rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1,
% 90.12/12.89 reflexivity_r1_tarski, t1_subset, t2_boole, t2_subset, t3_subset, t4_subset,
% 90.12/12.89 t5_subset
% 90.12/12.89
% 90.12/12.89 Those formulas are unsatisfiable:
% 90.12/12.89 ---------------------------------
% 90.12/12.89
% 90.12/12.89 Begin of proof
% 90.12/12.89 |
% 90.12/12.89 | ALPHA: (commutativity_k3_xboole_0) implies:
% 90.12/12.89 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0,
% 90.12/12.89 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) =
% 90.12/12.89 | v2 & $i(v2)))
% 90.12/12.89 |
% 90.12/12.89 | ALPHA: (dt_k7_relat_1) implies:
% 90.12/12.89 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 90.12/12.89 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 90.12/12.89 | relation(v0) | relation(v2))
% 90.12/12.89 |
% 90.12/12.89 | ALPHA: (fc4_funct_1) implies:
% 90.12/12.90 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 90.12/12.90 | (relation_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 90.12/12.90 | relation(v0) | ~ function(v0) | function(v2))
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (fc4_relat_1) implies:
% 90.12/12.90 | (4) empty(empty_set)
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (fc5_relat_1) implies:
% 90.12/12.90 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ relation(v0) | empty(v0) | ? [v1: $i] :
% 90.12/12.90 | (relation_dom(v0) = v1 & $i(v1) & ~ empty(v1)))
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (fc7_relat_1) implies:
% 90.12/12.90 | (6) ! [v0: $i] : ( ~ $i(v0) | ~ empty(v0) | ? [v1: $i] :
% 90.12/12.90 | (relation_dom(v0) = v1 & $i(v1) & relation(v1) & empty(v1)))
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (t68_funct_1) implies:
% 90.12/12.90 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 90.12/12.90 | ! [v5: $i] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) |
% 90.12/12.90 | ~ (set_intersection2(v4, v0) = v5) | ~ $i(v3) | ~ $i(v1) | ~
% 90.12/12.90 | $i(v0) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~
% 90.12/12.90 | function(v1) | ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 90.12/12.90 | : (relation_dom_restriction(v3, v0) = v6 & $i(v7) & $i(v6) & ( ~ (v6
% 90.12/12.90 | = v1) | (v5 = v2 & ! [v10: $i] : ! [v11: $i] : ( ~ (apply(v1,
% 90.12/12.90 | v10) = v11) | ~ $i(v10) | ~ in(v10, v2) | (apply(v3,
% 90.12/12.90 | v10) = v11 & $i(v11))))) & ( ~ (v5 = v2) | v6 = v1 | ( ~
% 90.12/12.90 | (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & $i(v9) &
% 90.12/12.90 | $i(v8) & in(v7, v2)))))
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (t6_boole) implies:
% 90.12/12.90 | (8) $i(empty_set)
% 90.12/12.90 | (9) ! [v0: $i] : (v0 = empty_set | ~ $i(v0) | ~ empty(v0))
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (function-axioms) implies:
% 90.12/12.90 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 90.12/12.90 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 90.12/12.90 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.12/12.90 | (relation_dom_restriction(v3, v2) = v1) | ~
% 90.12/12.90 | (relation_dom_restriction(v3, v2) = v0))
% 90.12/12.90 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.12/12.90 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 90.12/12.90 |
% 90.12/12.90 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_31_0 gives:
% 90.12/12.90 | (13) $i(all_31_0) & empty(all_31_0)
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (13) implies:
% 90.12/12.90 | (14) empty(all_31_0)
% 90.12/12.90 | (15) $i(all_31_0)
% 90.12/12.90 |
% 90.12/12.90 | DELTA: instantiating (rc1_funct_1) with fresh symbol all_38_0 gives:
% 90.12/12.90 | (16) $i(all_38_0) & relation(all_38_0) & function(all_38_0)
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (16) implies:
% 90.12/12.90 | (17) function(all_38_0)
% 90.12/12.90 | (18) relation(all_38_0)
% 90.12/12.90 | (19) $i(all_38_0)
% 90.12/12.90 |
% 90.12/12.90 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_41_0 gives:
% 90.12/12.90 | (20) $i(all_41_0) & relation(all_41_0) & empty(all_41_0)
% 90.12/12.90 |
% 90.12/12.90 | ALPHA: (20) implies:
% 90.12/12.90 | (21) empty(all_41_0)
% 90.12/12.90 | (22) $i(all_41_0)
% 90.12/12.90 |
% 90.12/12.90 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_43_0 gives:
% 90.12/12.90 | (23) $i(all_43_0) & relation(all_43_0) & function(all_43_0) &
% 90.12/12.90 | empty(all_43_0)
% 90.12/12.90 |
% 90.12/12.91 | ALPHA: (23) implies:
% 90.12/12.91 | (24) empty(all_43_0)
% 90.12/12.91 | (25) $i(all_43_0)
% 90.12/12.91 |
% 90.12/12.91 | DELTA: instantiating (t71_funct_1) with fresh symbols all_55_0, all_55_1,
% 90.12/12.91 | all_55_2, all_55_3, all_55_4, all_55_5, all_55_6, all_55_7 gives:
% 90.12/12.91 | (26) ~ (all_55_0 = all_55_1) & apply(all_55_2, all_55_6) = all_55_1 &
% 90.12/12.91 | apply(all_55_5, all_55_6) = all_55_0 & relation_dom(all_55_5) =
% 90.12/12.91 | all_55_4 & relation_dom_restriction(all_55_5, all_55_7) = all_55_2 &
% 90.12/12.91 | set_intersection2(all_55_4, all_55_7) = all_55_3 & $i(all_55_0) &
% 90.12/12.91 | $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) &
% 90.12/12.91 | $i(all_55_5) & $i(all_55_6) & $i(all_55_7) & relation(all_55_5) &
% 90.12/12.91 | function(all_55_5) & in(all_55_6, all_55_3)
% 90.12/12.91 |
% 90.12/12.91 | ALPHA: (26) implies:
% 90.12/12.91 | (27) ~ (all_55_0 = all_55_1)
% 90.12/12.91 | (28) in(all_55_6, all_55_3)
% 90.12/12.91 | (29) function(all_55_5)
% 90.12/12.91 | (30) relation(all_55_5)
% 90.12/12.91 | (31) $i(all_55_7)
% 90.12/12.91 | (32) $i(all_55_6)
% 90.12/12.91 | (33) $i(all_55_5)
% 90.12/12.91 | (34) $i(all_55_4)
% 90.12/12.91 | (35) set_intersection2(all_55_4, all_55_7) = all_55_3
% 90.12/12.91 | (36) relation_dom_restriction(all_55_5, all_55_7) = all_55_2
% 90.12/12.91 | (37) relation_dom(all_55_5) = all_55_4
% 90.12/12.91 | (38) apply(all_55_5, all_55_6) = all_55_0
% 90.12/12.91 | (39) apply(all_55_2, all_55_6) = all_55_1
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (6) with empty_set, simplifying with (4), (8)
% 90.12/12.91 | gives:
% 90.12/12.91 | (40) ? [v0: $i] : (relation_dom(empty_set) = v0 & $i(v0) & relation(v0) &
% 90.12/12.91 | empty(v0))
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (cc1_relat_1) with all_31_0, simplifying with (14),
% 90.12/12.91 | (15) gives:
% 90.12/12.91 | (41) relation(all_31_0)
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (cc1_funct_1) with all_31_0, simplifying with (14),
% 90.12/12.91 | (15) gives:
% 90.12/12.91 | (42) function(all_31_0)
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (6) with all_31_0, simplifying with (14), (15)
% 90.12/12.91 | gives:
% 90.12/12.91 | (43) ? [v0: $i] : (relation_dom(all_31_0) = v0 & $i(v0) & relation(v0) &
% 90.12/12.91 | empty(v0))
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (t8_boole) with all_31_0, all_41_0, simplifying
% 90.12/12.91 | with (14), (15), (21), (22) gives:
% 90.12/12.91 | (44) all_41_0 = all_31_0
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (6) with all_41_0, simplifying with (21), (22)
% 90.12/12.91 | gives:
% 90.12/12.91 | (45) ? [v0: $i] : (relation_dom(all_41_0) = v0 & $i(v0) & relation(v0) &
% 90.12/12.91 | empty(v0))
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (t8_boole) with all_41_0, all_43_0, simplifying
% 90.12/12.91 | with (21), (22), (24), (25) gives:
% 90.12/12.91 | (46) all_43_0 = all_41_0
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (9) with all_43_0, simplifying with (24), (25)
% 90.12/12.91 | gives:
% 90.12/12.91 | (47) all_43_0 = empty_set
% 90.12/12.91 |
% 90.12/12.91 | GROUND_INST: instantiating (6) with all_43_0, simplifying with (24), (25)
% 90.12/12.91 | gives:
% 90.12/12.92 | (48) ? [v0: $i] : (relation_dom(all_43_0) = v0 & $i(v0) & relation(v0) &
% 90.12/12.92 | empty(v0))
% 90.12/12.92 |
% 90.12/12.92 | GROUND_INST: instantiating (5) with all_38_0, simplifying with (18), (19)
% 90.12/12.92 | gives:
% 90.12/12.92 | (49) empty(all_38_0) | ? [v0: $i] : (relation_dom(all_38_0) = v0 & $i(v0)
% 90.12/12.92 | & ~ empty(v0))
% 90.12/12.92 |
% 90.12/12.92 | GROUND_INST: instantiating (1) with all_55_4, all_55_7, all_55_3, simplifying
% 90.12/12.92 | with (31), (34), (35) gives:
% 90.12/12.92 | (50) set_intersection2(all_55_7, all_55_4) = all_55_3 & $i(all_55_3)
% 90.12/12.92 |
% 90.12/12.92 | ALPHA: (50) implies:
% 90.12/12.92 | (51) $i(all_55_3)
% 90.12/12.92 |
% 90.12/12.92 | GROUND_INST: instantiating (3) with all_55_5, all_55_7, all_55_2, simplifying
% 90.12/12.92 | with (29), (30), (31), (33), (36) gives:
% 90.12/12.92 | (52) function(all_55_2)
% 90.12/12.92 |
% 90.12/12.92 | GROUND_INST: instantiating (2) with all_55_5, all_55_7, all_55_2, simplifying
% 90.12/12.92 | with (30), (31), (33), (36) gives:
% 90.12/12.92 | (53) relation(all_55_2)
% 90.12/12.92 |
% 90.12/12.92 | GROUND_INST: instantiating (7) with all_55_7, all_55_5, all_55_4, all_55_5,
% 90.12/12.92 | all_55_4, all_55_3, simplifying with (29), (30), (31), (33),
% 90.12/12.92 | (35), (37) gives:
% 90.12/12.92 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 90.12/12.92 | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & $i(v0) &
% 90.12/12.92 | ( ~ (v0 = all_55_5) | (all_55_3 = all_55_4 & ! [v4: $i] : ! [v5:
% 90.12/12.92 | $i] : ( ~ (apply(all_55_5, v4) = v5) | ~ $i(v4) | ~ in(v4,
% 90.12/12.92 | all_55_4) | $i(v5)))) & ( ~ (all_55_3 = all_55_4) | v0 =
% 90.12/12.92 | all_55_5 | ( ~ (v3 = v2) & apply(all_55_5, v1) = v3 &
% 90.12/12.92 | apply(all_55_5, v1) = v2 & $i(v3) & $i(v2) & in(v1, all_55_4))))
% 90.12/12.92 |
% 90.12/12.92 | COMBINE_EQS: (46), (47) imply:
% 90.12/12.92 | (55) all_41_0 = empty_set
% 90.12/12.92 |
% 90.12/12.92 | SIMP: (55) implies:
% 90.12/12.92 | (56) all_41_0 = empty_set
% 90.12/12.92 |
% 90.12/12.92 | COMBINE_EQS: (44), (56) imply:
% 90.12/12.92 | (57) all_31_0 = empty_set
% 90.12/12.92 |
% 90.12/12.92 | SIMP: (57) implies:
% 90.12/12.92 | (58) all_31_0 = empty_set
% 90.12/12.92 |
% 90.12/12.92 | DELTA: instantiating (48) with fresh symbol all_67_0 gives:
% 90.12/12.92 | (59) relation_dom(all_43_0) = all_67_0 & $i(all_67_0) & relation(all_67_0)
% 90.12/12.92 | & empty(all_67_0)
% 90.12/12.92 |
% 90.12/12.92 | ALPHA: (59) implies:
% 90.12/12.92 | (60) relation_dom(all_43_0) = all_67_0
% 90.12/12.92 |
% 90.12/12.92 | DELTA: instantiating (40) with fresh symbol all_69_0 gives:
% 90.12/12.92 | (61) relation_dom(empty_set) = all_69_0 & $i(all_69_0) & relation(all_69_0)
% 90.12/12.92 | & empty(all_69_0)
% 90.12/12.92 |
% 90.12/12.92 | ALPHA: (61) implies:
% 90.12/12.92 | (62) empty(all_69_0)
% 90.12/12.92 | (63) $i(all_69_0)
% 90.12/12.92 | (64) relation_dom(empty_set) = all_69_0
% 90.12/12.92 |
% 90.12/12.92 | DELTA: instantiating (45) with fresh symbol all_71_0 gives:
% 90.12/12.92 | (65) relation_dom(all_41_0) = all_71_0 & $i(all_71_0) & relation(all_71_0)
% 90.12/12.92 | & empty(all_71_0)
% 90.12/12.92 |
% 90.12/12.92 | ALPHA: (65) implies:
% 90.12/12.92 | (66) relation_dom(all_41_0) = all_71_0
% 90.12/12.92 |
% 90.12/12.92 | DELTA: instantiating (43) with fresh symbol all_73_0 gives:
% 90.12/12.92 | (67) relation_dom(all_31_0) = all_73_0 & $i(all_73_0) & relation(all_73_0)
% 90.12/12.92 | & empty(all_73_0)
% 90.12/12.92 |
% 90.12/12.92 | ALPHA: (67) implies:
% 90.12/12.92 | (68) relation_dom(all_31_0) = all_73_0
% 90.12/12.92 |
% 90.12/12.92 | DELTA: instantiating (54) with fresh symbols all_75_0, all_75_1, all_75_2,
% 90.12/12.92 | all_75_3 gives:
% 90.12/12.93 | (69) relation_dom_restriction(all_55_5, all_55_7) = all_75_3 & $i(all_75_2)
% 90.12/12.93 | & $i(all_75_3) & ( ~ (all_75_3 = all_55_5) | (all_55_3 = all_55_4 & !
% 90.12/12.93 | [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_5, v0) = v1) | ~
% 90.12/12.93 | $i(v0) | ~ in(v0, all_55_4) | $i(v1)))) & ( ~ (all_55_3 =
% 90.12/12.93 | all_55_4) | all_75_3 = all_55_5 | ( ~ (all_75_0 = all_75_1) &
% 90.12/12.93 | apply(all_55_5, all_75_2) = all_75_0 & apply(all_55_5, all_75_2) =
% 90.12/12.93 | all_75_1 & $i(all_75_0) & $i(all_75_1) & in(all_75_2, all_55_4)))
% 90.12/12.93 |
% 90.12/12.93 | ALPHA: (69) implies:
% 90.12/12.93 | (70) $i(all_75_3)
% 90.12/12.93 | (71) relation_dom_restriction(all_55_5, all_55_7) = all_75_3
% 90.12/12.93 |
% 90.12/12.93 | REDUCE: (47), (60) imply:
% 90.12/12.93 | (72) relation_dom(empty_set) = all_67_0
% 90.12/12.93 |
% 90.12/12.93 | REDUCE: (56), (66) imply:
% 90.12/12.93 | (73) relation_dom(empty_set) = all_71_0
% 90.12/12.93 |
% 90.12/12.93 | REDUCE: (58), (68) imply:
% 90.12/12.93 | (74) relation_dom(empty_set) = all_73_0
% 90.12/12.93 |
% 90.12/12.93 | REDUCE: (41), (58) imply:
% 90.12/12.93 | (75) relation(empty_set)
% 90.12/12.93 |
% 90.40/12.93 | REDUCE: (42), (58) imply:
% 90.40/12.93 | (76) function(empty_set)
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (11) with all_55_2, all_75_3, all_55_7, all_55_5,
% 90.40/12.93 | simplifying with (36), (71) gives:
% 90.40/12.93 | (77) all_75_3 = all_55_2
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (10) with all_69_0, all_71_0, empty_set,
% 90.40/12.93 | simplifying with (64), (73) gives:
% 90.40/12.93 | (78) all_71_0 = all_69_0
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (10) with all_71_0, all_73_0, empty_set,
% 90.40/12.93 | simplifying with (73), (74) gives:
% 90.40/12.93 | (79) all_73_0 = all_71_0
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (10) with all_67_0, all_73_0, empty_set,
% 90.40/12.93 | simplifying with (72), (74) gives:
% 90.40/12.93 | (80) all_73_0 = all_67_0
% 90.40/12.93 |
% 90.40/12.93 | COMBINE_EQS: (79), (80) imply:
% 90.40/12.93 | (81) all_71_0 = all_67_0
% 90.40/12.93 |
% 90.40/12.93 | SIMP: (81) implies:
% 90.40/12.93 | (82) all_71_0 = all_67_0
% 90.40/12.93 |
% 90.40/12.93 | COMBINE_EQS: (78), (82) imply:
% 90.40/12.93 | (83) all_69_0 = all_67_0
% 90.40/12.93 |
% 90.40/12.93 | REDUCE: (70), (77) imply:
% 90.40/12.93 | (84) $i(all_55_2)
% 90.40/12.93 |
% 90.40/12.93 | REDUCE: (63), (83) imply:
% 90.40/12.93 | (85) $i(all_67_0)
% 90.40/12.93 |
% 90.40/12.93 | REDUCE: (62), (83) imply:
% 90.40/12.93 | (86) empty(all_67_0)
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (9) with all_67_0, simplifying with (85), (86)
% 90.40/12.93 | gives:
% 90.40/12.93 | (87) all_67_0 = empty_set
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (5) with all_55_2, simplifying with (53), (84)
% 90.40/12.93 | gives:
% 90.40/12.93 | (88) empty(all_55_2) | ? [v0: $i] : (relation_dom(all_55_2) = v0 & $i(v0)
% 90.40/12.93 | & ~ empty(v0))
% 90.40/12.93 |
% 90.40/12.93 | GROUND_INST: instantiating (7) with all_55_7, empty_set, all_67_0, all_55_5,
% 90.40/12.93 | all_55_4, all_55_3, simplifying with (8), (29), (30), (31), (33),
% 90.40/12.93 | (35), (37), (72), (75), (76) gives:
% 90.40/12.94 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 90.40/12.94 | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) & $i(v0) &
% 90.40/12.94 | ( ~ (v0 = empty_set) | (all_67_0 = all_55_3 & ! [v4: $i] : ! [v5:
% 90.40/12.94 | $i] : ( ~ (apply(empty_set, v4) = v5) | ~ $i(v4) | ~ in(v4,
% 90.40/12.94 | all_55_3) | (apply(all_55_5, v4) = v5 & $i(v5))))) & ( ~
% 90.40/12.94 | (all_67_0 = all_55_3) | v0 = empty_set | ( ~ (v3 = v2) &
% 90.40/12.94 | apply(all_55_5, v1) = v3 & apply(empty_set, v1) = v2 & $i(v3) &
% 90.40/12.94 | $i(v2) & in(v1, all_55_3))))
% 90.40/12.94 |
% 90.40/12.94 | DELTA: instantiating (89) with fresh symbols all_89_0, all_89_1, all_89_2,
% 90.40/12.94 | all_89_3 gives:
% 90.40/12.94 | (90) relation_dom_restriction(all_55_5, all_55_7) = all_89_3 & $i(all_89_2)
% 90.40/12.94 | & $i(all_89_3) & ( ~ (all_89_3 = empty_set) | (all_67_0 = all_55_3 &
% 90.40/12.94 | ! [v0: $i] : ! [v1: $i] : ( ~ (apply(empty_set, v0) = v1) | ~
% 90.40/12.94 | $i(v0) | ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 &
% 90.40/12.94 | $i(v1))))) & ( ~ (all_67_0 = all_55_3) | all_89_3 = empty_set
% 90.40/12.94 | | ( ~ (all_89_0 = all_89_1) & apply(all_55_5, all_89_2) = all_89_0 &
% 90.40/12.94 | apply(empty_set, all_89_2) = all_89_1 & $i(all_89_0) &
% 90.40/12.94 | $i(all_89_1) & in(all_89_2, all_55_3)))
% 90.40/12.94 |
% 90.40/12.94 | ALPHA: (90) implies:
% 90.40/12.94 | (91) $i(all_89_3)
% 90.40/12.94 | (92) relation_dom_restriction(all_55_5, all_55_7) = all_89_3
% 90.40/12.94 | (93) ~ (all_89_3 = empty_set) | (all_67_0 = all_55_3 & ! [v0: $i] : !
% 90.40/12.94 | [v1: $i] : ( ~ (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 90.40/12.94 | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))
% 90.40/12.94 |
% 90.40/12.94 | GROUND_INST: instantiating (11) with all_55_2, all_89_3, all_55_7, all_55_5,
% 90.40/12.94 | simplifying with (36), (92) gives:
% 90.40/12.94 | (94) all_89_3 = all_55_2
% 90.40/12.94 |
% 90.40/12.94 | BETA: splitting (49) gives:
% 90.40/12.94 |
% 90.40/12.94 | Case 1:
% 90.40/12.94 | |
% 90.40/12.94 | | (95) empty(all_38_0)
% 90.40/12.94 | |
% 90.40/12.94 | | BETA: splitting (88) gives:
% 90.40/12.94 | |
% 90.40/12.94 | | Case 1:
% 90.40/12.94 | | |
% 90.40/12.94 | | | (96) empty(all_55_2)
% 90.40/12.94 | | |
% 90.40/12.94 | | | BETA: splitting (93) gives:
% 90.40/12.94 | | |
% 90.40/12.94 | | | Case 1:
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | (97) ~ (all_89_3 = empty_set)
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | REDUCE: (94), (97) imply:
% 90.40/12.94 | | | | (98) ~ (all_55_2 = empty_set)
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | GROUND_INST: instantiating (t8_boole) with all_38_0, all_55_2,
% 90.40/12.94 | | | | simplifying with (19), (84), (95), (96) gives:
% 90.40/12.94 | | | | (99) all_55_2 = all_38_0
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | GROUND_INST: instantiating (9) with all_55_2, simplifying with (84),
% 90.40/12.94 | | | | (96) gives:
% 90.40/12.94 | | | | (100) all_55_2 = empty_set
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | COMBINE_EQS: (99), (100) imply:
% 90.40/12.94 | | | | (101) all_38_0 = empty_set
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | REDUCE: (98), (100) imply:
% 90.40/12.94 | | | | (102) $false
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | CLOSE: (102) is inconsistent.
% 90.40/12.94 | | | |
% 90.40/12.94 | | | Case 2:
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | (103) all_89_3 = empty_set
% 90.40/12.94 | | | | (104) all_67_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.40/12.94 | | | | (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3)
% 90.40/12.94 | | | | | (apply(all_55_5, v0) = v1 & $i(v1)))
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | ALPHA: (104) implies:
% 90.40/12.94 | | | | (105) all_67_0 = all_55_3
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | COMBINE_EQS: (94), (103) imply:
% 90.40/12.94 | | | | (106) all_55_2 = empty_set
% 90.40/12.94 | | | |
% 90.40/12.94 | | | | COMBINE_EQS: (87), (105) imply:
% 90.40/12.94 | | | | (107) all_55_3 = empty_set
% 90.40/12.94 | | | |
% 90.40/12.95 | | | | REDUCE: (28), (107) imply:
% 90.40/12.95 | | | | (108) in(all_55_6, empty_set)
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | GROUND_INST: instantiating (t7_boole) with all_55_6, empty_set,
% 90.40/12.95 | | | | simplifying with (4), (8), (32), (108) gives:
% 90.40/12.95 | | | | (109) $false
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | CLOSE: (109) is inconsistent.
% 90.40/12.95 | | | |
% 90.40/12.95 | | | End of split
% 90.40/12.95 | | |
% 90.40/12.95 | | Case 2:
% 90.40/12.95 | | |
% 90.40/12.95 | | | (110) ? [v0: $i] : (relation_dom(all_55_2) = v0 & $i(v0) & ~
% 90.40/12.95 | | | empty(v0))
% 90.40/12.95 | | |
% 90.40/12.95 | | | DELTA: instantiating (110) with fresh symbol all_365_0 gives:
% 90.40/12.95 | | | (111) relation_dom(all_55_2) = all_365_0 & $i(all_365_0) & ~
% 90.40/12.95 | | | empty(all_365_0)
% 90.40/12.95 | | |
% 90.40/12.95 | | | ALPHA: (111) implies:
% 90.40/12.95 | | | (112) relation_dom(all_55_2) = all_365_0
% 90.40/12.95 | | |
% 90.40/12.95 | | | GROUND_INST: instantiating (7) with all_55_7, all_55_2, all_365_0,
% 90.40/12.95 | | | all_55_5, all_55_4, all_55_3, simplifying with (29), (30),
% 90.40/12.95 | | | (31), (33), (35), (37), (52), (53), (84), (112) gives:
% 90.40/12.95 | | | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 90.40/12.95 | | | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) &
% 90.40/12.95 | | | $i(v0) & ( ~ (v0 = all_55_2) | (all_365_0 = all_55_3 & ! [v4:
% 90.40/12.95 | | | $i] : ! [v5: $i] : ( ~ (apply(all_55_2, v4) = v5) | ~
% 90.40/12.95 | | | $i(v4) | ~ in(v4, all_55_3) | (apply(all_55_5, v4) = v5
% 90.40/12.95 | | | & $i(v5))))) & ( ~ (all_365_0 = all_55_3) | v0 =
% 90.40/12.95 | | | all_55_2 | ( ~ (v3 = v2) & apply(all_55_2, v1) = v2 &
% 90.40/12.95 | | | apply(all_55_5, v1) = v3 & $i(v3) & $i(v2) & in(v1,
% 90.40/12.95 | | | all_55_3))))
% 90.40/12.95 | | |
% 90.40/12.95 | | | DELTA: instantiating (113) with fresh symbols all_483_0, all_483_1,
% 90.40/12.95 | | | all_483_2, all_483_3 gives:
% 90.40/12.95 | | | (114) relation_dom_restriction(all_55_5, all_55_7) = all_483_3 &
% 90.40/12.95 | | | $i(all_483_2) & $i(all_483_3) & ( ~ (all_483_3 = all_55_2) |
% 90.40/12.95 | | | (all_365_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.40/12.95 | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 90.40/12.95 | | | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))) & ( ~
% 90.40/12.95 | | | (all_365_0 = all_55_3) | all_483_3 = all_55_2 | ( ~ (all_483_0
% 90.40/12.95 | | | = all_483_1) & apply(all_55_2, all_483_2) = all_483_1 &
% 90.40/12.95 | | | apply(all_55_5, all_483_2) = all_483_0 & $i(all_483_0) &
% 90.40/12.95 | | | $i(all_483_1) & in(all_483_2, all_55_3)))
% 90.40/12.95 | | |
% 90.40/12.95 | | | ALPHA: (114) implies:
% 90.40/12.95 | | | (115) relation_dom_restriction(all_55_5, all_55_7) = all_483_3
% 90.40/12.95 | | | (116) ~ (all_483_3 = all_55_2) | (all_365_0 = all_55_3 & ! [v0: $i] :
% 90.40/12.95 | | | ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~
% 90.40/12.95 | | | in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))
% 90.40/12.95 | | |
% 90.40/12.95 | | | GROUND_INST: instantiating (11) with all_55_2, all_483_3, all_55_7,
% 90.40/12.95 | | | all_55_5, simplifying with (36), (115) gives:
% 90.40/12.95 | | | (117) all_483_3 = all_55_2
% 90.40/12.95 | | |
% 90.40/12.95 | | | BETA: splitting (116) gives:
% 90.40/12.95 | | |
% 90.40/12.95 | | | Case 1:
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | (118) ~ (all_483_3 = all_55_2)
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | REDUCE: (117), (118) imply:
% 90.40/12.95 | | | | (119) $false
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | CLOSE: (119) is inconsistent.
% 90.40/12.95 | | | |
% 90.40/12.95 | | | Case 2:
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | (120) all_365_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.40/12.95 | | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3)
% 90.40/12.95 | | | | | (apply(all_55_5, v0) = v1 & $i(v1)))
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | ALPHA: (120) implies:
% 90.40/12.95 | | | | (121) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~
% 90.40/12.95 | | | | $i(v0) | ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 &
% 90.40/12.95 | | | | $i(v1)))
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | REF_CLOSE: (12), (27), (28), (32), (38), (39), (121) are inconsistent by
% 90.40/12.95 | | | | sub-proof #1.
% 90.40/12.95 | | | |
% 90.40/12.95 | | | End of split
% 90.40/12.95 | | |
% 90.40/12.95 | | End of split
% 90.40/12.95 | |
% 90.40/12.95 | Case 2:
% 90.40/12.95 | |
% 90.40/12.95 | | (122) ? [v0: $i] : (relation_dom(all_38_0) = v0 & $i(v0) & ~ empty(v0))
% 90.40/12.95 | |
% 90.40/12.95 | | DELTA: instantiating (122) with fresh symbol all_339_0 gives:
% 90.40/12.95 | | (123) relation_dom(all_38_0) = all_339_0 & $i(all_339_0) & ~
% 90.40/12.95 | | empty(all_339_0)
% 90.40/12.95 | |
% 90.40/12.95 | | ALPHA: (123) implies:
% 90.40/12.95 | | (124) relation_dom(all_38_0) = all_339_0
% 90.40/12.95 | |
% 90.40/12.95 | | BETA: splitting (88) gives:
% 90.40/12.95 | |
% 90.40/12.95 | | Case 1:
% 90.40/12.95 | | |
% 90.40/12.95 | | | (125) empty(all_55_2)
% 90.40/12.95 | | |
% 90.40/12.95 | | | BETA: splitting (93) gives:
% 90.40/12.95 | | |
% 90.40/12.95 | | | Case 1:
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | (126) ~ (all_89_3 = empty_set)
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | REDUCE: (94), (126) imply:
% 90.40/12.95 | | | | (127) ~ (all_55_2 = empty_set)
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | GROUND_INST: instantiating (9) with all_55_2, simplifying with (84),
% 90.40/12.95 | | | | (125) gives:
% 90.40/12.95 | | | | (128) all_55_2 = empty_set
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | REDUCE: (127), (128) imply:
% 90.40/12.95 | | | | (129) $false
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | CLOSE: (129) is inconsistent.
% 90.40/12.95 | | | |
% 90.40/12.95 | | | Case 2:
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | (130) all_89_3 = empty_set
% 90.40/12.95 | | | | (131) all_67_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.40/12.95 | | | | (apply(empty_set, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3)
% 90.40/12.95 | | | | | (apply(all_55_5, v0) = v1 & $i(v1)))
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | ALPHA: (131) implies:
% 90.40/12.95 | | | | (132) all_67_0 = all_55_3
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | COMBINE_EQS: (94), (130) imply:
% 90.40/12.95 | | | | (133) all_55_2 = empty_set
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | COMBINE_EQS: (87), (132) imply:
% 90.40/12.95 | | | | (134) all_55_3 = empty_set
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | REDUCE: (28), (134) imply:
% 90.40/12.95 | | | | (135) in(all_55_6, empty_set)
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | GROUND_INST: instantiating (t7_boole) with all_55_6, empty_set,
% 90.40/12.95 | | | | simplifying with (4), (8), (32), (135) gives:
% 90.40/12.95 | | | | (136) $false
% 90.40/12.95 | | | |
% 90.40/12.95 | | | | CLOSE: (136) is inconsistent.
% 90.40/12.95 | | | |
% 90.40/12.95 | | | End of split
% 90.40/12.95 | | |
% 90.40/12.95 | | Case 2:
% 90.40/12.95 | | |
% 90.40/12.95 | | | (137) ? [v0: $i] : (relation_dom(all_55_2) = v0 & $i(v0) & ~
% 90.40/12.95 | | | empty(v0))
% 90.40/12.95 | | |
% 90.40/12.95 | | | DELTA: instantiating (137) with fresh symbol all_369_0 gives:
% 90.40/12.95 | | | (138) relation_dom(all_55_2) = all_369_0 & $i(all_369_0) & ~
% 90.40/12.95 | | | empty(all_369_0)
% 90.40/12.95 | | |
% 90.40/12.95 | | | ALPHA: (138) implies:
% 90.40/12.95 | | | (139) relation_dom(all_55_2) = all_369_0
% 90.40/12.95 | | |
% 90.53/12.96 | | | GROUND_INST: instantiating (7) with all_55_7, all_38_0, all_339_0,
% 90.53/12.96 | | | all_55_5, all_55_4, all_55_3, simplifying with (17), (18),
% 90.53/12.96 | | | (19), (29), (30), (31), (33), (35), (37), (124) gives:
% 90.53/12.96 | | | (140) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 90.53/12.96 | | | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) &
% 90.53/12.96 | | | $i(v0) & ( ~ (v0 = all_38_0) | (all_339_0 = all_55_3 & ! [v4:
% 90.53/12.96 | | | $i] : ! [v5: $i] : ( ~ (apply(all_38_0, v4) = v5) | ~
% 90.53/12.96 | | | $i(v4) | ~ in(v4, all_55_3) | (apply(all_55_5, v4) = v5
% 90.53/12.96 | | | & $i(v5))))) & ( ~ (all_339_0 = all_55_3) | v0 =
% 90.53/12.96 | | | all_38_0 | ( ~ (v3 = v2) & apply(all_55_5, v1) = v3 &
% 90.53/12.96 | | | apply(all_38_0, v1) = v2 & $i(v3) & $i(v2) & in(v1,
% 90.53/12.96 | | | all_55_3))))
% 90.53/12.96 | | |
% 90.53/12.96 | | | GROUND_INST: instantiating (7) with all_55_7, all_55_2, all_369_0,
% 90.53/12.96 | | | all_55_5, all_55_4, all_55_3, simplifying with (29), (30),
% 90.53/12.96 | | | (31), (33), (35), (37), (52), (53), (84), (139) gives:
% 90.53/12.96 | | | (141) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 90.53/12.96 | | | (relation_dom_restriction(all_55_5, all_55_7) = v0 & $i(v1) &
% 90.53/12.96 | | | $i(v0) & ( ~ (v0 = all_55_2) | (all_369_0 = all_55_3 & ! [v4:
% 90.53/12.96 | | | $i] : ! [v5: $i] : ( ~ (apply(all_55_2, v4) = v5) | ~
% 90.53/12.96 | | | $i(v4) | ~ in(v4, all_55_3) | (apply(all_55_5, v4) = v5
% 90.53/12.96 | | | & $i(v5))))) & ( ~ (all_369_0 = all_55_3) | v0 =
% 90.53/12.96 | | | all_55_2 | ( ~ (v3 = v2) & apply(all_55_2, v1) = v2 &
% 90.53/12.96 | | | apply(all_55_5, v1) = v3 & $i(v3) & $i(v2) & in(v1,
% 90.53/12.96 | | | all_55_3))))
% 90.53/12.96 | | |
% 90.53/12.96 | | | DELTA: instantiating (141) with fresh symbols all_463_0, all_463_1,
% 90.53/12.96 | | | all_463_2, all_463_3 gives:
% 90.53/12.96 | | | (142) relation_dom_restriction(all_55_5, all_55_7) = all_463_3 &
% 90.53/12.96 | | | $i(all_463_2) & $i(all_463_3) & ( ~ (all_463_3 = all_55_2) |
% 90.53/12.96 | | | (all_369_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.53/12.96 | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 90.53/12.96 | | | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))) & ( ~
% 90.53/12.96 | | | (all_369_0 = all_55_3) | all_463_3 = all_55_2 | ( ~ (all_463_0
% 90.53/12.96 | | | = all_463_1) & apply(all_55_2, all_463_2) = all_463_1 &
% 90.53/12.96 | | | apply(all_55_5, all_463_2) = all_463_0 & $i(all_463_0) &
% 90.53/12.96 | | | $i(all_463_1) & in(all_463_2, all_55_3)))
% 90.53/12.96 | | |
% 90.53/12.96 | | | ALPHA: (142) implies:
% 90.53/12.96 | | | (143) relation_dom_restriction(all_55_5, all_55_7) = all_463_3
% 90.53/12.96 | | | (144) ~ (all_463_3 = all_55_2) | (all_369_0 = all_55_3 & ! [v0: $i] :
% 90.53/12.96 | | | ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~
% 90.53/12.96 | | | in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))
% 90.53/12.96 | | |
% 90.53/12.96 | | | DELTA: instantiating (140) with fresh symbols all_465_0, all_465_1,
% 90.53/12.96 | | | all_465_2, all_465_3 gives:
% 90.53/12.96 | | | (145) relation_dom_restriction(all_55_5, all_55_7) = all_465_3 &
% 90.53/12.96 | | | $i(all_465_2) & $i(all_465_3) & ( ~ (all_465_3 = all_38_0) |
% 90.53/12.96 | | | (all_339_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.53/12.96 | | | (apply(all_38_0, v0) = v1) | ~ $i(v0) | ~ in(v0,
% 90.53/12.96 | | | all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1))))) & ( ~
% 90.53/12.96 | | | (all_339_0 = all_55_3) | all_465_3 = all_38_0 | ( ~ (all_465_0
% 90.53/12.96 | | | = all_465_1) & apply(all_55_5, all_465_2) = all_465_0 &
% 90.53/12.96 | | | apply(all_38_0, all_465_2) = all_465_1 & $i(all_465_0) &
% 90.53/12.96 | | | $i(all_465_1) & in(all_465_2, all_55_3)))
% 90.53/12.96 | | |
% 90.53/12.96 | | | ALPHA: (145) implies:
% 90.53/12.96 | | | (146) relation_dom_restriction(all_55_5, all_55_7) = all_465_3
% 90.53/12.96 | | |
% 90.53/12.96 | | | GROUND_INST: instantiating (11) with all_55_2, all_465_3, all_55_7,
% 90.53/12.96 | | | all_55_5, simplifying with (36), (146) gives:
% 90.53/12.96 | | | (147) all_465_3 = all_55_2
% 90.53/12.96 | | |
% 90.53/12.96 | | | GROUND_INST: instantiating (11) with all_463_3, all_465_3, all_55_7,
% 90.53/12.96 | | | all_55_5, simplifying with (143), (146) gives:
% 90.53/12.96 | | | (148) all_465_3 = all_463_3
% 90.53/12.96 | | |
% 90.53/12.96 | | | COMBINE_EQS: (147), (148) imply:
% 90.53/12.96 | | | (149) all_463_3 = all_55_2
% 90.53/12.96 | | |
% 90.53/12.96 | | | BETA: splitting (144) gives:
% 90.53/12.96 | | |
% 90.53/12.96 | | | Case 1:
% 90.53/12.96 | | | |
% 90.53/12.96 | | | | (150) ~ (all_463_3 = all_55_2)
% 90.53/12.96 | | | |
% 90.53/12.96 | | | | REDUCE: (149), (150) imply:
% 90.53/12.96 | | | | (151) $false
% 90.53/12.96 | | | |
% 90.53/12.96 | | | | CLOSE: (151) is inconsistent.
% 90.53/12.96 | | | |
% 90.53/12.96 | | | Case 2:
% 90.53/12.96 | | | |
% 90.53/12.96 | | | | (152) all_369_0 = all_55_3 & ! [v0: $i] : ! [v1: $i] : ( ~
% 90.53/12.96 | | | | (apply(all_55_2, v0) = v1) | ~ $i(v0) | ~ in(v0, all_55_3)
% 90.53/12.96 | | | | | (apply(all_55_5, v0) = v1 & $i(v1)))
% 90.53/12.96 | | | |
% 90.53/12.96 | | | | ALPHA: (152) implies:
% 90.53/12.96 | | | | (153) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~
% 90.53/12.96 | | | | $i(v0) | ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 &
% 90.53/12.96 | | | | $i(v1)))
% 90.53/12.96 | | | |
% 90.53/12.96 | | | | REF_CLOSE: (12), (27), (28), (32), (38), (39), (153) are inconsistent by
% 90.53/12.96 | | | | sub-proof #1.
% 90.53/12.96 | | | |
% 90.53/12.96 | | | End of split
% 90.53/12.96 | | |
% 90.53/12.96 | | End of split
% 90.53/12.96 | |
% 90.53/12.96 | End of split
% 90.53/12.96 |
% 90.53/12.96 End of proof
% 90.53/12.96
% 90.53/12.96 Sub-proof #1 shows that the following formulas are inconsistent:
% 90.53/12.96 ----------------------------------------------------------------
% 90.53/12.96 (1) ~ (all_55_0 = all_55_1)
% 90.53/12.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 90.53/12.96 (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 90.53/12.96 (3) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_55_2, v0) = v1) | ~ $i(v0) |
% 90.53/12.96 ~ in(v0, all_55_3) | (apply(all_55_5, v0) = v1 & $i(v1)))
% 90.53/12.96 (4) apply(all_55_5, all_55_6) = all_55_0
% 90.53/12.96 (5) in(all_55_6, all_55_3)
% 90.53/12.96 (6) apply(all_55_2, all_55_6) = all_55_1
% 90.53/12.96 (7) $i(all_55_6)
% 90.53/12.96
% 90.53/12.96 Begin of proof
% 90.53/12.96 |
% 90.53/12.96 | GROUND_INST: instantiating (3) with all_55_6, all_55_1, simplifying with (5),
% 90.53/12.96 | (6), (7) gives:
% 90.53/12.96 | (8) apply(all_55_5, all_55_6) = all_55_1 & $i(all_55_1)
% 90.53/12.96 |
% 90.53/12.96 | ALPHA: (8) implies:
% 90.53/12.96 | (9) apply(all_55_5, all_55_6) = all_55_1
% 90.53/12.96 |
% 90.53/12.96 | GROUND_INST: instantiating (2) with all_55_0, all_55_1, all_55_6, all_55_5,
% 90.53/12.96 | simplifying with (4), (9) gives:
% 90.53/12.96 | (10) all_55_0 = all_55_1
% 90.53/12.96 |
% 90.53/12.96 | REDUCE: (1), (10) imply:
% 90.53/12.96 | (11) $false
% 90.53/12.96 |
% 90.53/12.96 | CLOSE: (11) is inconsistent.
% 90.53/12.96 |
% 90.53/12.96 End of proof
% 90.53/12.96 % SZS output end Proof for theBenchmark
% 90.53/12.96
% 90.53/12.96 12404ms
%------------------------------------------------------------------------------