TSTP Solution File: SEU212+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.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 17:43:18 EDT 2023
% Result : Theorem 8.87s 2.03s
% Output : Proof 11.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:21:31 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.63 ________ _____
% 0.21/0.63 ___ __ \_________(_)________________________________
% 0.21/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.63
% 0.21/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.63 (2023-06-19)
% 0.21/0.63
% 0.21/0.63 (c) Philipp Rümmer, 2009-2023
% 0.21/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.63 Amanda Stjerna.
% 0.21/0.63 Free software under BSD-3-Clause.
% 0.21/0.63
% 0.21/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.63
% 0.21/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.76/1.09 Prover 4: Preprocessing ...
% 2.76/1.09 Prover 1: Preprocessing ...
% 2.76/1.14 Prover 2: Preprocessing ...
% 2.76/1.14 Prover 6: Preprocessing ...
% 2.76/1.14 Prover 0: Preprocessing ...
% 2.76/1.14 Prover 5: Preprocessing ...
% 2.76/1.14 Prover 3: Preprocessing ...
% 5.51/1.50 Prover 1: Warning: ignoring some quantifiers
% 5.51/1.54 Prover 1: Constructing countermodel ...
% 5.51/1.57 Prover 3: Warning: ignoring some quantifiers
% 5.51/1.58 Prover 5: Proving ...
% 5.51/1.58 Prover 3: Constructing countermodel ...
% 5.51/1.58 Prover 2: Proving ...
% 6.23/1.59 Prover 6: Proving ...
% 6.42/1.66 Prover 4: Warning: ignoring some quantifiers
% 6.42/1.69 Prover 4: Constructing countermodel ...
% 7.05/1.72 Prover 0: Proving ...
% 8.87/2.03 Prover 3: proved (1379ms)
% 8.87/2.03
% 8.87/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.87/2.03
% 8.87/2.05 Prover 0: stopped
% 8.87/2.05 Prover 5: stopped
% 8.87/2.05 Prover 6: stopped
% 8.87/2.05 Prover 2: stopped
% 8.87/2.05 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.87/2.05 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.87/2.05 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.87/2.06 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.87/2.06 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.93/2.11 Prover 11: Preprocessing ...
% 9.93/2.12 Prover 7: Preprocessing ...
% 9.93/2.12 Prover 13: Preprocessing ...
% 9.93/2.13 Prover 10: Preprocessing ...
% 9.93/2.13 Prover 8: Preprocessing ...
% 10.63/2.21 Prover 8: Warning: ignoring some quantifiers
% 10.63/2.22 Prover 7: Warning: ignoring some quantifiers
% 10.63/2.22 Prover 13: Warning: ignoring some quantifiers
% 10.63/2.22 Prover 8: Constructing countermodel ...
% 10.63/2.23 Prover 13: Constructing countermodel ...
% 10.63/2.24 Prover 10: Warning: ignoring some quantifiers
% 10.63/2.24 Prover 7: Constructing countermodel ...
% 10.63/2.24 Prover 10: Constructing countermodel ...
% 10.63/2.25 Prover 1: Found proof (size 81)
% 10.63/2.25 Prover 1: proved (1601ms)
% 10.63/2.25 Prover 4: stopped
% 10.63/2.25 Prover 13: stopped
% 10.63/2.25 Prover 8: stopped
% 10.63/2.25 Prover 10: stopped
% 10.63/2.25 Prover 7: stopped
% 10.63/2.28 Prover 11: Warning: ignoring some quantifiers
% 11.25/2.30 Prover 11: Constructing countermodel ...
% 11.31/2.30 Prover 11: stopped
% 11.31/2.30
% 11.31/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.31/2.30
% 11.35/2.32 % SZS output start Proof for theBenchmark
% 11.35/2.32 Assumptions after simplification:
% 11.35/2.32 ---------------------------------
% 11.35/2.32
% 11.35/2.32 (d4_funct_1)
% 11.35/2.35 $i(empty_set) & ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1:
% 11.35/2.35 any] : ? [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) &
% 11.35/2.35 ( ~ (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (
% 11.35/2.35 ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ~ $i(v4) |
% 11.35/2.35 ~ $i(v3) | ? [v7: any] : ? [v8: $i] : (apply(v0, v3) = v8 & in(v3,
% 11.35/2.35 v2) = v7 & $i(v8) & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & (
% 11.35/2.35 ~ (v6 = 0) | v8 = v4))))) & ? [v3: $i] : ! [v4: $i] : !
% 11.35/2.35 [v5: int] : (v5 = 0 | ~ (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) |
% 11.35/2.35 ? [v6: $i] : (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 =
% 11.35/2.35 empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set)))))))
% 11.35/2.35
% 11.35/2.35 (d4_relat_1)
% 11.35/2.36 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 11.35/2.36 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 11.35/2.36 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 11.35/2.36 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 11.35/2.36 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 11.35/2.36 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 11.35/2.36 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 11.35/2.36 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 11.35/2.36 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 11.35/2.36 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 11.35/2.36 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 11.35/2.36 $i(v3)))))))
% 11.35/2.36
% 11.35/2.36 (fc5_relat_1)
% 11.35/2.36 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 11.35/2.36 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 11.35/2.36 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 11.35/2.36
% 11.35/2.36 (t8_funct_1)
% 11.35/2.36 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5:
% 11.35/2.36 $i] : ? [v6: any] : ? [v7: $i] : (relation_dom(v2) = v5 & ordered_pair(v0,
% 11.35/2.36 v1) = v3 & apply(v2, v0) = v7 & relation(v2) = 0 & function(v2) = 0 &
% 11.35/2.36 in(v3, v2) = v4 & in(v0, v5) = v6 & $i(v7) & $i(v5) & $i(v3) & $i(v2) &
% 11.35/2.36 $i(v1) & $i(v0) & ((v7 = v1 & v6 = 0 & ~ (v4 = 0)) | (v4 = 0 & ( ~ (v7 =
% 11.35/2.36 v1) | ~ (v6 = 0)))))
% 11.35/2.36
% 11.35/2.36 (function-axioms)
% 11.35/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.35/2.37 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 11.35/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.35/2.37 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 11.35/2.37 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2) = v1)
% 11.35/2.37 | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 11.35/2.37 [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 11.35/2.37 (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.35/2.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) =
% 11.35/2.37 v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.35/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 11.35/2.37 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 11.35/2.37 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1)
% 11.35/2.37 | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 11.35/2.37 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0:
% 11.35/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.35/2.37 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 11.35/2.37 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 11.35/2.37 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.35/2.37 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 11.35/2.37 (empty(v2) = v0))
% 11.35/2.37
% 11.35/2.37 Further assumptions not needed in the proof:
% 11.35/2.37 --------------------------------------------
% 11.35/2.37 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, commutativity_k2_tarski,
% 11.35/2.37 d5_tarski, dt_k1_funct_1, dt_k1_relat_1, dt_k1_tarski, dt_k1_xboole_0,
% 11.35/2.37 dt_k2_tarski, dt_k4_tarski, dt_m1_subset_1, existence_m1_subset_1, fc12_relat_1,
% 11.35/2.37 fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1, fc4_relat_1,
% 11.35/2.37 fc7_relat_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc2_relat_1, rc2_xboole_0,
% 11.35/2.37 rc3_relat_1, t1_subset, t2_subset, t6_boole, t7_boole, t8_boole
% 11.35/2.37
% 11.35/2.37 Those formulas are unsatisfiable:
% 11.35/2.37 ---------------------------------
% 11.35/2.37
% 11.35/2.37 Begin of proof
% 11.35/2.37 |
% 11.35/2.37 | ALPHA: (d4_funct_1) implies:
% 11.35/2.37 | (1) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 11.35/2.37 | [v2: $i] : (relation_dom(v0) = v2 & relation(v0) = v1 & $i(v2) & ( ~
% 11.35/2.37 | (v1 = 0) | ( ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6:
% 11.35/2.37 | any] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6)
% 11.35/2.37 | | ~ $i(v4) | ~ $i(v3) | ? [v7: any] : ? [v8: $i] :
% 11.35/2.37 | (apply(v0, v3) = v8 & in(v3, v2) = v7 & $i(v8) & ( ~ (v7 = 0)
% 11.35/2.37 | | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4)))))
% 11.35/2.37 | & ? [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 11.35/2.37 | (in(v4, v2) = v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: $i] :
% 11.35/2.37 | (apply(v0, v4) = v6 & $i(v6) & ( ~ (v6 = v3) | v3 =
% 11.35/2.37 | empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set)))))))
% 11.35/2.37 |
% 11.35/2.37 | ALPHA: (function-axioms) implies:
% 11.35/2.38 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.35/2.38 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 11.35/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 11.35/2.38 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 11.35/2.38 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.35/2.38 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 11.35/2.38 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.35/2.38 | (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 11.35/2.38 |
% 11.35/2.38 | DELTA: instantiating (t8_funct_1) with fresh symbols all_34_0, all_34_1,
% 11.35/2.38 | all_34_2, all_34_3, all_34_4, all_34_5, all_34_6, all_34_7 gives:
% 11.35/2.38 | (6) relation_dom(all_34_5) = all_34_2 & ordered_pair(all_34_7, all_34_6) =
% 11.35/2.38 | all_34_4 & apply(all_34_5, all_34_7) = all_34_0 & relation(all_34_5) =
% 11.35/2.38 | 0 & function(all_34_5) = 0 & in(all_34_4, all_34_5) = all_34_3 &
% 11.35/2.38 | in(all_34_7, all_34_2) = all_34_1 & $i(all_34_0) & $i(all_34_2) &
% 11.35/2.38 | $i(all_34_4) & $i(all_34_5) & $i(all_34_6) & $i(all_34_7) & ((all_34_0
% 11.35/2.38 | = all_34_6 & all_34_1 = 0 & ~ (all_34_3 = 0)) | (all_34_3 = 0 & (
% 11.35/2.38 | ~ (all_34_0 = all_34_6) | ~ (all_34_1 = 0))))
% 11.35/2.38 |
% 11.35/2.38 | ALPHA: (6) implies:
% 11.35/2.38 | (7) $i(all_34_7)
% 11.35/2.38 | (8) $i(all_34_6)
% 11.35/2.38 | (9) $i(all_34_5)
% 11.35/2.38 | (10) in(all_34_7, all_34_2) = all_34_1
% 11.35/2.38 | (11) in(all_34_4, all_34_5) = all_34_3
% 11.35/2.38 | (12) function(all_34_5) = 0
% 11.35/2.38 | (13) relation(all_34_5) = 0
% 11.35/2.38 | (14) apply(all_34_5, all_34_7) = all_34_0
% 11.35/2.38 | (15) ordered_pair(all_34_7, all_34_6) = all_34_4
% 11.35/2.38 | (16) relation_dom(all_34_5) = all_34_2
% 11.35/2.38 | (17) (all_34_0 = all_34_6 & all_34_1 = 0 & ~ (all_34_3 = 0)) | (all_34_3 =
% 11.35/2.38 | 0 & ( ~ (all_34_0 = all_34_6) | ~ (all_34_1 = 0)))
% 11.35/2.38 |
% 11.35/2.38 | GROUND_INST: instantiating (1) with all_34_5, simplifying with (9), (12)
% 11.35/2.38 | gives:
% 11.35/2.39 | (18) ? [v0: any] : ? [v1: $i] : (relation_dom(all_34_5) = v1 &
% 11.35/2.39 | relation(all_34_5) = v0 & $i(v1) & ( ~ (v0 = 0) | ( ! [v2: $i] : !
% 11.35/2.39 | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~ (ordered_pair(v2,
% 11.35/2.39 | v3) = v4) | ~ (in(v4, all_34_5) = v5) | ~ $i(v3) | ~
% 11.35/2.39 | $i(v2) | ? [v6: any] : ? [v7: $i] : (apply(all_34_5, v2) =
% 11.35/2.39 | v7 & in(v2, v1) = v6 & $i(v7) & ( ~ (v6 = 0) | (( ~ (v7 =
% 11.35/2.39 | v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ?
% 11.35/2.39 | [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v1)
% 11.35/2.39 | = v4) | ~ $i(v3) | ~ $i(v2) | ? [v5: $i] :
% 11.35/2.39 | (apply(all_34_5, v3) = v5 & $i(v5) & ( ~ (v5 = v2) | v2 =
% 11.35/2.39 | empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set))))))
% 11.35/2.39 |
% 11.35/2.39 | GROUND_INST: instantiating (fc5_relat_1) with all_34_5, all_34_2, simplifying
% 11.35/2.39 | with (9), (16) gives:
% 11.35/2.39 | (19) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_34_5) = v1
% 11.35/2.39 | & empty(all_34_2) = v2 & empty(all_34_5) = v0 & ( ~ (v2 = 0) | ~
% 11.35/2.39 | (v1 = 0) | v0 = 0))
% 11.35/2.39 |
% 11.35/2.39 | GROUND_INST: instantiating (d4_relat_1) with all_34_5, all_34_2, simplifying
% 11.35/2.39 | with (9), (16) gives:
% 11.35/2.39 | (20) ? [v0: int] : ( ~ (v0 = 0) & relation(all_34_5) = v0) | ( ? [v0: any]
% 11.35/2.39 | : (v0 = all_34_2 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 11.35/2.39 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 11.35/2.39 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_34_5) = 0) |
% 11.35/2.39 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 11.35/2.39 | (ordered_pair(v1, v3) = v4 & in(v4, all_34_5) = 0 & $i(v4) &
% 11.35/2.39 | $i(v3))))) & ( ~ $i(all_34_2) | ( ! [v0: $i] : ! [v1: int]
% 11.35/2.39 | : (v1 = 0 | ~ (in(v0, all_34_2) = v1) | ~ $i(v0) | ! [v2: $i]
% 11.35/2.39 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 11.35/2.39 | all_34_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 11.35/2.39 | all_34_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 11.35/2.39 | (ordered_pair(v0, v1) = v2 & in(v2, all_34_5) = 0 & $i(v2) &
% 11.35/2.39 | $i(v1))))))
% 11.35/2.39 |
% 11.35/2.39 | DELTA: instantiating (19) with fresh symbols all_44_0, all_44_1, all_44_2
% 11.35/2.39 | gives:
% 11.35/2.39 | (21) relation(all_34_5) = all_44_1 & empty(all_34_2) = all_44_0 &
% 11.35/2.39 | empty(all_34_5) = all_44_2 & ( ~ (all_44_0 = 0) | ~ (all_44_1 = 0) |
% 11.35/2.39 | all_44_2 = 0)
% 11.35/2.39 |
% 11.35/2.39 | ALPHA: (21) implies:
% 11.35/2.39 | (22) relation(all_34_5) = all_44_1
% 11.35/2.39 |
% 11.35/2.39 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1 gives:
% 11.35/2.39 | (23) relation_dom(all_34_5) = all_48_0 & relation(all_34_5) = all_48_1 &
% 11.35/2.39 | $i(all_48_0) & ( ~ (all_48_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : !
% 11.35/2.39 | [v2: $i] : ! [v3: any] : ( ~ (ordered_pair(v0, v1) = v2) | ~
% 11.35/2.39 | (in(v2, all_34_5) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] :
% 11.35/2.39 | ? [v5: $i] : (apply(all_34_5, v0) = v5 & in(v0, all_48_0) = v4
% 11.35/2.39 | & $i(v5) & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 =
% 11.35/2.39 | 0) | v5 = v1))))) & ? [v0: $i] : ! [v1: $i] : !
% 11.35/2.39 | [v2: int] : (v2 = 0 | ~ (in(v1, all_48_0) = v2) | ~ $i(v1) | ~
% 11.35/2.39 | $i(v0) | ? [v3: $i] : (apply(all_34_5, v1) = v3 & $i(v3) & ( ~
% 11.35/2.39 | (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 =
% 11.35/2.39 | empty_set)))))
% 11.35/2.39 |
% 11.35/2.39 | ALPHA: (23) implies:
% 11.35/2.39 | (24) $i(all_48_0)
% 11.35/2.40 | (25) relation(all_34_5) = all_48_1
% 11.35/2.40 | (26) relation_dom(all_34_5) = all_48_0
% 11.35/2.40 | (27) ~ (all_48_1 = 0) | ( ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.35/2.40 | any] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_34_5) =
% 11.35/2.40 | v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] :
% 11.35/2.40 | (apply(all_34_5, v0) = v5 & in(v0, all_48_0) = v4 & $i(v5) & ( ~
% 11.35/2.40 | (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 =
% 11.35/2.40 | v1))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 =
% 11.35/2.40 | 0 | ~ (in(v1, all_48_0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 11.35/2.40 | $i] : (apply(all_34_5, v1) = v3 & $i(v3) & ( ~ (v3 = v0) | v0 =
% 11.35/2.40 | empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))))
% 11.35/2.40 |
% 11.35/2.40 | GROUND_INST: instantiating (2) with 0, all_48_1, all_34_5, simplifying with
% 11.35/2.40 | (13), (25) gives:
% 11.35/2.40 | (28) all_48_1 = 0
% 11.35/2.40 |
% 11.35/2.40 | GROUND_INST: instantiating (2) with all_44_1, all_48_1, all_34_5, simplifying
% 11.35/2.40 | with (22), (25) gives:
% 11.35/2.40 | (29) all_48_1 = all_44_1
% 11.35/2.40 |
% 11.35/2.40 | GROUND_INST: instantiating (3) with all_34_2, all_48_0, all_34_5, simplifying
% 11.35/2.40 | with (16), (26) gives:
% 11.35/2.40 | (30) all_48_0 = all_34_2
% 11.35/2.40 |
% 11.35/2.40 | COMBINE_EQS: (28), (29) imply:
% 11.35/2.40 | (31) all_44_1 = 0
% 11.35/2.40 |
% 11.35/2.40 | REDUCE: (24), (30) imply:
% 11.35/2.40 | (32) $i(all_34_2)
% 11.35/2.40 |
% 11.35/2.40 | BETA: splitting (20) gives:
% 11.35/2.40 |
% 11.35/2.40 | Case 1:
% 11.35/2.40 | |
% 11.35/2.40 | | (33) ? [v0: int] : ( ~ (v0 = 0) & relation(all_34_5) = v0)
% 11.35/2.40 | |
% 11.35/2.40 | | DELTA: instantiating (33) with fresh symbol all_66_0 gives:
% 11.35/2.40 | | (34) ~ (all_66_0 = 0) & relation(all_34_5) = all_66_0
% 11.35/2.40 | |
% 11.35/2.40 | | ALPHA: (34) implies:
% 11.35/2.40 | | (35) ~ (all_66_0 = 0)
% 11.35/2.40 | | (36) relation(all_34_5) = all_66_0
% 11.35/2.40 | |
% 11.35/2.40 | | GROUND_INST: instantiating (2) with 0, all_66_0, all_34_5, simplifying with
% 11.35/2.40 | | (13), (36) gives:
% 11.35/2.40 | | (37) all_66_0 = 0
% 11.35/2.40 | |
% 11.35/2.40 | | REDUCE: (35), (37) imply:
% 11.35/2.40 | | (38) $false
% 11.35/2.40 | |
% 11.35/2.40 | | CLOSE: (38) is inconsistent.
% 11.35/2.40 | |
% 11.35/2.40 | Case 2:
% 11.35/2.40 | |
% 11.84/2.41 | | (39) ? [v0: any] : (v0 = all_34_2 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 11.84/2.41 | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] :
% 11.84/2.41 | | ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 11.84/2.41 | | all_34_5) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 11.84/2.41 | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_34_5) = 0
% 11.84/2.41 | | & $i(v4) & $i(v3))))) & ( ~ $i(all_34_2) | ( ! [v0: $i] : !
% 11.84/2.41 | | [v1: int] : (v1 = 0 | ~ (in(v0, all_34_2) = v1) | ~ $i(v0) |
% 11.84/2.41 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) |
% 11.84/2.41 | | ~ (in(v3, all_34_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 11.84/2.41 | | (in(v0, all_34_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i]
% 11.84/2.41 | | : (ordered_pair(v0, v1) = v2 & in(v2, all_34_5) = 0 & $i(v2) &
% 11.84/2.41 | | $i(v1)))))
% 11.84/2.41 | |
% 11.84/2.41 | | ALPHA: (39) implies:
% 11.84/2.41 | | (40) ~ $i(all_34_2) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 11.84/2.41 | | all_34_2) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : (
% 11.84/2.41 | | ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_34_5) = 0) | ~
% 11.84/2.41 | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_34_2) = 0) | ~
% 11.84/2.41 | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2
% 11.84/2.41 | | & in(v2, all_34_5) = 0 & $i(v2) & $i(v1))))
% 11.84/2.41 | |
% 11.84/2.41 | | BETA: splitting (27) gives:
% 11.84/2.41 | |
% 11.84/2.41 | | Case 1:
% 11.84/2.41 | | |
% 11.84/2.41 | | | (41) ~ (all_48_1 = 0)
% 11.84/2.41 | | |
% 11.84/2.41 | | | REDUCE: (28), (41) imply:
% 11.84/2.41 | | | (42) $false
% 11.84/2.41 | | |
% 11.84/2.41 | | | CLOSE: (42) is inconsistent.
% 11.84/2.41 | | |
% 11.84/2.41 | | Case 2:
% 11.84/2.41 | | |
% 11.84/2.41 | | | (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 11.84/2.41 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_34_5) = v3) | ~
% 11.84/2.41 | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] :
% 11.84/2.41 | | | (apply(all_34_5, v0) = v5 & in(v0, all_48_0) = v4 & $i(v5) & ( ~
% 11.84/2.41 | | | (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 =
% 11.84/2.41 | | | v1))))) & ? [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 11.84/2.41 | | | = 0 | ~ (in(v1, all_48_0) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 11.84/2.41 | | | [v3: $i] : (apply(all_34_5, v1) = v3 & $i(v3) & ( ~ (v3 = v0) |
% 11.84/2.41 | | | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set)))
% 11.84/2.41 | | |
% 11.84/2.41 | | | ALPHA: (43) implies:
% 11.84/2.41 | | | (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 11.84/2.41 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_34_5) = v3) | ~
% 11.84/2.41 | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: $i] :
% 11.84/2.41 | | | (apply(all_34_5, v0) = v5 & in(v0, all_48_0) = v4 & $i(v5) & ( ~
% 11.84/2.41 | | | (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 =
% 11.84/2.41 | | | v1)))))
% 11.84/2.41 | | |
% 11.84/2.41 | | | GROUND_INST: instantiating (44) with all_34_7, all_34_6, all_34_4,
% 11.84/2.41 | | | all_34_3, simplifying with (7), (8), (11), (15) gives:
% 11.84/2.41 | | | (45) ? [v0: any] : ? [v1: $i] : (apply(all_34_5, all_34_7) = v1 &
% 11.84/2.41 | | | in(all_34_7, all_48_0) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (v1 =
% 11.84/2.41 | | | all_34_6) | all_34_3 = 0) & ( ~ (all_34_3 = 0) | v1 =
% 11.84/2.41 | | | all_34_6))))
% 11.84/2.41 | | |
% 11.84/2.41 | | | DELTA: instantiating (45) with fresh symbols all_66_0, all_66_1 gives:
% 11.84/2.42 | | | (46) apply(all_34_5, all_34_7) = all_66_0 & in(all_34_7, all_48_0) =
% 11.84/2.42 | | | all_66_1 & $i(all_66_0) & ( ~ (all_66_1 = 0) | (( ~ (all_66_0 =
% 11.84/2.42 | | | all_34_6) | all_34_3 = 0) & ( ~ (all_34_3 = 0) | all_66_0
% 11.84/2.42 | | | = all_34_6)))
% 11.84/2.42 | | |
% 11.84/2.42 | | | ALPHA: (46) implies:
% 11.84/2.42 | | | (47) in(all_34_7, all_48_0) = all_66_1
% 11.84/2.42 | | | (48) apply(all_34_5, all_34_7) = all_66_0
% 11.84/2.42 | | | (49) ~ (all_66_1 = 0) | (( ~ (all_66_0 = all_34_6) | all_34_3 = 0) & (
% 11.84/2.42 | | | ~ (all_34_3 = 0) | all_66_0 = all_34_6))
% 11.84/2.42 | | |
% 11.84/2.42 | | | REDUCE: (30), (47) imply:
% 11.84/2.42 | | | (50) in(all_34_7, all_34_2) = all_66_1
% 11.84/2.42 | | |
% 11.84/2.42 | | | BETA: splitting (40) gives:
% 11.84/2.42 | | |
% 11.84/2.42 | | | Case 1:
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | (51) ~ $i(all_34_2)
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | PRED_UNIFY: (32), (51) imply:
% 11.84/2.42 | | | | (52) $false
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | CLOSE: (52) is inconsistent.
% 11.84/2.42 | | | |
% 11.84/2.42 | | | Case 2:
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | (53) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_34_2) =
% 11.84/2.42 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 11.84/2.42 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_34_5) = 0) | ~
% 11.84/2.42 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_34_2) = 0) | ~
% 11.84/2.42 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 11.84/2.42 | | | | v2 & in(v2, all_34_5) = 0 & $i(v2) & $i(v1)))
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | ALPHA: (53) implies:
% 11.84/2.42 | | | | (54) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_34_2) =
% 11.84/2.42 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 11.84/2.42 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_34_5) = 0) | ~
% 11.84/2.42 | | | | $i(v2)))
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | GROUND_INST: instantiating (54) with all_34_7, all_34_1, simplifying
% 11.84/2.42 | | | | with (7), (10) gives:
% 11.84/2.42 | | | | (55) all_34_1 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 11.84/2.42 | | | | (ordered_pair(all_34_7, v0) = v1) | ~ (in(v1, all_34_5) = 0)
% 11.84/2.42 | | | | | ~ $i(v0))
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | GROUND_INST: instantiating (4) with all_34_1, all_66_1, all_34_2,
% 11.84/2.42 | | | | all_34_7, simplifying with (10), (50) gives:
% 11.84/2.42 | | | | (56) all_66_1 = all_34_1
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | GROUND_INST: instantiating (5) with all_34_0, all_66_0, all_34_7,
% 11.84/2.42 | | | | all_34_5, simplifying with (14), (48) gives:
% 11.84/2.42 | | | | (57) all_66_0 = all_34_0
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | BETA: splitting (17) gives:
% 11.84/2.42 | | | |
% 11.84/2.42 | | | | Case 1:
% 11.84/2.42 | | | | |
% 11.84/2.42 | | | | | (58) all_34_0 = all_34_6 & all_34_1 = 0 & ~ (all_34_3 = 0)
% 11.84/2.42 | | | | |
% 11.84/2.42 | | | | | ALPHA: (58) implies:
% 11.84/2.42 | | | | | (59) all_34_1 = 0
% 11.84/2.42 | | | | | (60) all_34_0 = all_34_6
% 11.84/2.42 | | | | | (61) ~ (all_34_3 = 0)
% 11.84/2.42 | | | | |
% 11.84/2.42 | | | | | COMBINE_EQS: (56), (59) imply:
% 11.84/2.42 | | | | | (62) all_66_1 = 0
% 11.84/2.42 | | | | |
% 11.84/2.42 | | | | | COMBINE_EQS: (57), (60) imply:
% 11.84/2.42 | | | | | (63) all_66_0 = all_34_6
% 11.84/2.42 | | | | |
% 11.84/2.42 | | | | | BETA: splitting (49) gives:
% 11.84/2.42 | | | | |
% 11.84/2.42 | | | | | Case 1:
% 11.84/2.42 | | | | | |
% 11.84/2.42 | | | | | | (64) ~ (all_66_1 = 0)
% 11.84/2.42 | | | | | |
% 11.84/2.42 | | | | | | REDUCE: (62), (64) imply:
% 11.84/2.42 | | | | | | (65) $false
% 11.84/2.42 | | | | | |
% 11.84/2.42 | | | | | | CLOSE: (65) is inconsistent.
% 11.84/2.42 | | | | | |
% 11.84/2.42 | | | | | Case 2:
% 11.84/2.42 | | | | | |
% 11.84/2.43 | | | | | | (66) ( ~ (all_66_0 = all_34_6) | all_34_3 = 0) & ( ~ (all_34_3 =
% 11.84/2.43 | | | | | | 0) | all_66_0 = all_34_6)
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | ALPHA: (66) implies:
% 11.84/2.43 | | | | | | (67) ~ (all_66_0 = all_34_6) | all_34_3 = 0
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | BETA: splitting (67) gives:
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | Case 1:
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | (68) ~ (all_66_0 = all_34_6)
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | REDUCE: (63), (68) imply:
% 11.84/2.43 | | | | | | | (69) $false
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | CLOSE: (69) is inconsistent.
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | Case 2:
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | (70) all_34_3 = 0
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | REDUCE: (61), (70) imply:
% 11.84/2.43 | | | | | | | (71) $false
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | CLOSE: (71) is inconsistent.
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | End of split
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | End of split
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | Case 2:
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | (72) all_34_3 = 0 & ( ~ (all_34_0 = all_34_6) | ~ (all_34_1 = 0))
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | ALPHA: (72) implies:
% 11.84/2.43 | | | | | (73) all_34_3 = 0
% 11.84/2.43 | | | | | (74) ~ (all_34_0 = all_34_6) | ~ (all_34_1 = 0)
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | REDUCE: (11), (73) imply:
% 11.84/2.43 | | | | | (75) in(all_34_4, all_34_5) = 0
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | GROUND_INST: instantiating (44) with all_34_7, all_34_6, all_34_4, 0,
% 11.84/2.43 | | | | | simplifying with (7), (8), (15), (75) gives:
% 11.84/2.43 | | | | | (76) ? [v0: any] : ? [v1: $i] : (apply(all_34_5, all_34_7) = v1 &
% 11.84/2.43 | | | | | in(all_34_7, all_48_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 11.84/2.43 | | | | | all_34_6))
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | DELTA: instantiating (76) with fresh symbols all_126_0, all_126_1
% 11.84/2.43 | | | | | gives:
% 11.84/2.43 | | | | | (77) apply(all_34_5, all_34_7) = all_126_0 & in(all_34_7, all_48_0)
% 11.84/2.43 | | | | | = all_126_1 & $i(all_126_0) & ( ~ (all_126_1 = 0) | all_126_0
% 11.84/2.43 | | | | | = all_34_6)
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | ALPHA: (77) implies:
% 11.84/2.43 | | | | | (78) in(all_34_7, all_48_0) = all_126_1
% 11.84/2.43 | | | | | (79) apply(all_34_5, all_34_7) = all_126_0
% 11.84/2.43 | | | | | (80) ~ (all_126_1 = 0) | all_126_0 = all_34_6
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | REDUCE: (30), (78) imply:
% 11.84/2.43 | | | | | (81) in(all_34_7, all_34_2) = all_126_1
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | GROUND_INST: instantiating (4) with all_34_1, all_126_1, all_34_2,
% 11.84/2.43 | | | | | all_34_7, simplifying with (10), (81) gives:
% 11.84/2.43 | | | | | (82) all_126_1 = all_34_1
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | GROUND_INST: instantiating (5) with all_34_0, all_126_0, all_34_7,
% 11.84/2.43 | | | | | all_34_5, simplifying with (14), (79) gives:
% 11.84/2.43 | | | | | (83) all_126_0 = all_34_0
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | BETA: splitting (55) gives:
% 11.84/2.43 | | | | |
% 11.84/2.43 | | | | | Case 1:
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | (84) all_34_1 = 0
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | COMBINE_EQS: (82), (84) imply:
% 11.84/2.43 | | | | | | (85) all_126_1 = 0
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | BETA: splitting (74) gives:
% 11.84/2.43 | | | | | |
% 11.84/2.43 | | | | | | Case 1:
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | (86) ~ (all_34_1 = 0)
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | REDUCE: (84), (86) imply:
% 11.84/2.43 | | | | | | | (87) $false
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | CLOSE: (87) is inconsistent.
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | Case 2:
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | (88) ~ (all_34_0 = all_34_6)
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | BETA: splitting (80) gives:
% 11.84/2.43 | | | | | | |
% 11.84/2.43 | | | | | | | Case 1:
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | | (89) ~ (all_126_1 = 0)
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | | REDUCE: (85), (89) imply:
% 11.84/2.43 | | | | | | | | (90) $false
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | | CLOSE: (90) is inconsistent.
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | Case 2:
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | | (91) all_126_0 = all_34_6
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | | COMBINE_EQS: (83), (91) imply:
% 11.84/2.43 | | | | | | | | (92) all_34_0 = all_34_6
% 11.84/2.43 | | | | | | | |
% 11.84/2.43 | | | | | | | | REDUCE: (88), (92) imply:
% 11.84/2.44 | | | | | | | | (93) $false
% 11.84/2.44 | | | | | | | |
% 11.84/2.44 | | | | | | | | CLOSE: (93) is inconsistent.
% 11.84/2.44 | | | | | | | |
% 11.84/2.44 | | | | | | | End of split
% 11.84/2.44 | | | | | | |
% 11.84/2.44 | | | | | | End of split
% 11.84/2.44 | | | | | |
% 11.84/2.44 | | | | | Case 2:
% 11.84/2.44 | | | | | |
% 11.84/2.44 | | | | | | (94) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_34_7, v0)
% 11.84/2.44 | | | | | | = v1) | ~ (in(v1, all_34_5) = 0) | ~ $i(v0))
% 11.84/2.44 | | | | | |
% 11.84/2.44 | | | | | | GROUND_INST: instantiating (94) with all_34_6, all_34_4, simplifying
% 11.84/2.44 | | | | | | with (8), (15), (75) gives:
% 11.84/2.44 | | | | | | (95) $false
% 11.84/2.44 | | | | | |
% 11.84/2.44 | | | | | | CLOSE: (95) is inconsistent.
% 11.84/2.44 | | | | | |
% 11.84/2.44 | | | | | End of split
% 11.84/2.44 | | | | |
% 11.84/2.44 | | | | End of split
% 11.84/2.44 | | | |
% 11.84/2.44 | | | End of split
% 11.84/2.44 | | |
% 11.84/2.44 | | End of split
% 11.84/2.44 | |
% 11.84/2.44 | End of split
% 11.84/2.44 |
% 11.84/2.44 End of proof
% 11.84/2.44 % SZS output end Proof for theBenchmark
% 11.84/2.44
% 11.84/2.44 1810ms
%------------------------------------------------------------------------------