TSTP Solution File: SEU254+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU254+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 : n003.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 17:43:40 EDT 2023
% Result : Theorem 8.67s 1.94s
% Output : Proof 12.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU254+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 : n003.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 19:38:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.22/0.61 ________ _____
% 0.22/0.61 ___ __ \_________(_)________________________________
% 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61 (2023-06-19)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2023
% 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61 Amanda Stjerna.
% 0.22/0.61 Free software under BSD-3-Clause.
% 0.22/0.61
% 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61
% 0.22/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.62 Running up to 7 provers in parallel.
% 0.22/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.68/1.04 Prover 1: Preprocessing ...
% 2.68/1.05 Prover 4: Preprocessing ...
% 2.68/1.09 Prover 0: Preprocessing ...
% 2.68/1.09 Prover 2: Preprocessing ...
% 2.68/1.09 Prover 3: Preprocessing ...
% 2.68/1.09 Prover 5: Preprocessing ...
% 2.68/1.09 Prover 6: Preprocessing ...
% 5.79/1.54 Prover 1: Warning: ignoring some quantifiers
% 6.22/1.57 Prover 3: Warning: ignoring some quantifiers
% 6.22/1.58 Prover 5: Proving ...
% 6.22/1.58 Prover 1: Constructing countermodel ...
% 6.22/1.59 Prover 6: Proving ...
% 6.22/1.59 Prover 3: Constructing countermodel ...
% 6.22/1.60 Prover 2: Proving ...
% 6.22/1.64 Prover 4: Warning: ignoring some quantifiers
% 6.91/1.67 Prover 0: Proving ...
% 6.91/1.68 Prover 4: Constructing countermodel ...
% 8.67/1.93 Prover 3: proved (1303ms)
% 8.67/1.94
% 8.67/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.67/1.94
% 8.67/1.94 Prover 6: stopped
% 8.67/1.94 Prover 2: stopped
% 8.67/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.67/1.95 Prover 5: stopped
% 8.67/1.95 Prover 0: stopped
% 8.67/1.96 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.67/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.14/1.96 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.14/1.97 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.14/1.97 Prover 7: Preprocessing ...
% 9.14/1.99 Prover 11: Preprocessing ...
% 9.14/2.01 Prover 10: Preprocessing ...
% 9.14/2.02 Prover 13: Preprocessing ...
% 9.14/2.02 Prover 8: Preprocessing ...
% 9.87/2.08 Prover 10: Warning: ignoring some quantifiers
% 9.87/2.08 Prover 7: Warning: ignoring some quantifiers
% 9.87/2.09 Prover 10: Constructing countermodel ...
% 9.87/2.11 Prover 7: Constructing countermodel ...
% 9.87/2.14 Prover 13: Warning: ignoring some quantifiers
% 9.87/2.16 Prover 8: Warning: ignoring some quantifiers
% 9.87/2.17 Prover 8: Constructing countermodel ...
% 9.87/2.17 Prover 13: Constructing countermodel ...
% 10.32/2.23 Prover 11: Warning: ignoring some quantifiers
% 11.20/2.25 Prover 11: Constructing countermodel ...
% 11.20/2.28 Prover 1: Found proof (size 108)
% 11.20/2.28 Prover 1: proved (1647ms)
% 11.20/2.28 Prover 4: stopped
% 11.20/2.28 Prover 13: stopped
% 11.20/2.28 Prover 10: gave up
% 11.20/2.28 Prover 11: stopped
% 11.20/2.28 Prover 8: stopped
% 11.20/2.29 Prover 7: stopped
% 11.20/2.29
% 11.20/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.20/2.29
% 11.20/2.30 % SZS output start Proof for theBenchmark
% 11.20/2.30 Assumptions after simplification:
% 11.20/2.30 ---------------------------------
% 11.20/2.30
% 11.20/2.30 (dt_k2_wellord1)
% 11.20/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 11.20/2.33 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 11.20/2.33 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 11.20/2.33
% 11.20/2.33 (l2_wellord1)
% 11.20/2.34 ! [v0: $i] : ! [v1: any] : ( ~ (transitive(v0) = v1) | ~ $i(v0) | ? [v2:
% 11.20/2.34 int] : ( ~ (v2 = 0) & relation(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] :
% 11.20/2.34 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: int] :
% 11.20/2.34 (v7 = 0 | ~ (ordered_pair(v2, v4) = v6) | ~ (ordered_pair(v2, v3) =
% 11.20/2.34 v5) | ~ (in(v6, v0) = v7) | ~ (in(v5, v0) = 0) | ~ $i(v4) | ~
% 11.20/2.34 $i(v3) | ~ $i(v2) | ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) &
% 11.20/2.34 ordered_pair(v3, v4) = v8 & in(v8, v0) = v9 & $i(v8)))) & (v1 = 0 |
% 11.20/2.34 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ?
% 11.20/2.34 [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & ordered_pair(v3, v4) = v6 &
% 11.20/2.34 ordered_pair(v2, v4) = v7 & ordered_pair(v2, v3) = v5 & in(v7, v0) =
% 11.20/2.34 v8 & in(v6, v0) = 0 & in(v5, v0) = 0 & $i(v7) & $i(v6) & $i(v5) &
% 11.20/2.34 $i(v4) & $i(v3) & $i(v2)))))
% 11.20/2.34
% 11.20/2.34 (t106_zfmisc_1)
% 11.20/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 11.20/2.34 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~
% 11.20/2.34 (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~ $i(v3) | ~ $i(v2) |
% 11.20/2.34 ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] : (in(v1, v3) = v8 &
% 11.20/2.34 in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1:
% 11.20/2.34 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 11.20/2.34 (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~
% 11.20/2.34 (in(v4, v5) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1,
% 11.20/2.34 v3) = 0 & in(v0, v2) = 0))
% 11.20/2.34
% 11.20/2.34 (t16_wellord1)
% 11.20/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 11.20/2.35 (relation_restriction(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~ $i(v2) | ~
% 11.20/2.35 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8:
% 11.20/2.35 any] : (cartesian_product2(v1, v1) = v7 & relation(v2) = v5 & in(v0, v7) =
% 11.20/2.35 v8 & in(v0, v2) = v6 & $i(v7) & ( ~ (v5 = 0) | (( ~ (v8 = 0) | ~ (v6 = 0)
% 11.20/2.35 | v4 = 0) & ( ~ (v4 = 0) | (v8 = 0 & v6 = 0))))))
% 11.20/2.35
% 11.20/2.35 (t24_wellord1)
% 11.20/2.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 11.20/2.35 transitive(v2) = v3 & transitive(v1) = 0 & relation_restriction(v1, v0) = v2
% 11.20/2.35 & relation(v1) = 0 & $i(v2) & $i(v1) & $i(v0))
% 11.20/2.35
% 11.20/2.35 (function-axioms)
% 11.79/2.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.79/2.35 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 11.79/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.35 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 11.79/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.35 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) =
% 11.79/2.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 11.79/2.35 ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 11.79/2.35 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.35 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 11.79/2.35 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.35 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 11.79/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.79/2.35 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 11.79/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.79/2.35 ~ (transitive(v2) = v1) | ~ (transitive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.79/2.35 $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) =
% 11.79/2.35 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.79/2.35 $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & !
% 11.79/2.35 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 11.79/2.35 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 11.79/2.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 11.79/2.35 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 11.79/2.35 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 11.79/2.35 ~ (empty(v2) = v0))
% 11.79/2.35
% 11.79/2.35 Further assumptions not needed in the proof:
% 11.79/2.35 --------------------------------------------
% 11.79/2.35 antisymmetry_r2_hidden, cc1_funct_1, cc2_funct_1, commutativity_k2_tarski,
% 11.79/2.35 commutativity_k3_xboole_0, d5_tarski, d6_wellord1, dt_k1_tarski, dt_k1_xboole_0,
% 11.79/2.35 dt_k2_tarski, dt_k2_zfmisc_1, dt_k3_xboole_0, dt_k4_tarski, dt_m1_subset_1,
% 11.79/2.35 existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, idempotence_k3_xboole_0,
% 11.79/2.35 rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0, rc3_funct_1, t1_subset,
% 11.79/2.35 t2_boole, t2_subset, t6_boole, t7_boole, t8_boole
% 11.79/2.35
% 11.79/2.35 Those formulas are unsatisfiable:
% 11.79/2.35 ---------------------------------
% 11.79/2.35
% 11.79/2.35 Begin of proof
% 11.79/2.36 |
% 11.79/2.36 | ALPHA: (t106_zfmisc_1) implies:
% 11.79/2.36 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 11.79/2.36 | ! [v5: $i] : ( ~ (cartesian_product2(v2, v3) = v5) | ~
% 11.79/2.36 | (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | ~ $i(v3) | ~
% 11.79/2.36 | $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 11.79/2.36 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 11.79/2.36 | ! [v5: $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v2, v3) =
% 11.79/2.36 | v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ~
% 11.79/2.36 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8:
% 11.79/2.36 | any] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 11.79/2.36 | 0))))
% 11.79/2.36 |
% 11.79/2.36 | ALPHA: (function-axioms) implies:
% 11.79/2.36 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.79/2.36 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 11.79/2.36 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 11.79/2.36 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 11.79/2.36 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.36 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 11.79/2.36 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.79/2.36 | (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) =
% 11.79/2.36 | v0))
% 11.79/2.36 |
% 11.79/2.36 | DELTA: instantiating (t24_wellord1) with fresh symbols all_35_0, all_35_1,
% 11.79/2.36 | all_35_2, all_35_3 gives:
% 11.79/2.36 | (7) ~ (all_35_0 = 0) & transitive(all_35_1) = all_35_0 &
% 11.79/2.36 | transitive(all_35_2) = 0 & relation_restriction(all_35_2, all_35_3) =
% 11.79/2.36 | all_35_1 & relation(all_35_2) = 0 & $i(all_35_1) & $i(all_35_2) &
% 11.79/2.36 | $i(all_35_3)
% 11.79/2.36 |
% 11.79/2.36 | ALPHA: (7) implies:
% 11.79/2.36 | (8) ~ (all_35_0 = 0)
% 11.79/2.36 | (9) $i(all_35_3)
% 11.79/2.36 | (10) $i(all_35_2)
% 11.79/2.36 | (11) $i(all_35_1)
% 11.79/2.36 | (12) relation(all_35_2) = 0
% 11.79/2.36 | (13) relation_restriction(all_35_2, all_35_3) = all_35_1
% 11.79/2.36 | (14) transitive(all_35_2) = 0
% 11.79/2.36 | (15) transitive(all_35_1) = all_35_0
% 11.79/2.36 |
% 11.79/2.36 | GROUND_INST: instantiating (dt_k2_wellord1) with all_35_2, all_35_3, all_35_1,
% 11.79/2.36 | simplifying with (9), (10), (13) gives:
% 11.79/2.37 | (16) ? [v0: any] : ? [v1: any] : (relation(all_35_1) = v1 &
% 11.79/2.37 | relation(all_35_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 11.79/2.37 |
% 11.79/2.37 | GROUND_INST: instantiating (l2_wellord1) with all_35_2, 0, simplifying with
% 11.79/2.37 | (10), (14) gives:
% 11.79/2.37 | (17) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_2) = v0) | ! [v0: $i] :
% 11.79/2.37 | ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] :
% 11.79/2.37 | (v5 = 0 | ~ (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) =
% 11.79/2.37 | v3) | ~ (in(v4, all_35_2) = v5) | ~ (in(v3, all_35_2) = 0) | ~
% 11.79/2.37 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : ( ~
% 11.79/2.37 | (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_35_2) = v7 &
% 11.79/2.37 | $i(v6)))
% 11.79/2.37 |
% 11.79/2.37 | GROUND_INST: instantiating (l2_wellord1) with all_35_1, all_35_0, simplifying
% 11.79/2.37 | with (11), (15) gives:
% 11.79/2.37 | (18) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_1) = v0) | (( ~
% 11.79/2.37 | (all_35_0 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 11.79/2.37 | $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 11.79/2.37 | (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3) |
% 11.79/2.37 | ~ (in(v4, all_35_1) = v5) | ~ (in(v3, all_35_1) = 0) | ~
% 11.79/2.37 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7: int] : (
% 11.79/2.37 | ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6, all_35_1) = v7
% 11.79/2.37 | & $i(v6)))) & (all_35_0 = 0 | ? [v0: $i] : ? [v1: $i] : ?
% 11.79/2.37 | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int]
% 11.79/2.37 | : ( ~ (v6 = 0) & ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2)
% 11.79/2.37 | = v5 & ordered_pair(v0, v1) = v3 & in(v5, all_35_1) = v6 &
% 11.79/2.37 | in(v4, all_35_1) = 0 & in(v3, all_35_1) = 0 & $i(v5) & $i(v4) &
% 11.79/2.37 | $i(v3) & $i(v2) & $i(v1) & $i(v0))))
% 11.79/2.37 |
% 11.79/2.37 | DELTA: instantiating (16) with fresh symbols all_49_0, all_49_1 gives:
% 11.79/2.37 | (19) relation(all_35_1) = all_49_0 & relation(all_35_2) = all_49_1 & ( ~
% 11.79/2.37 | (all_49_1 = 0) | all_49_0 = 0)
% 11.79/2.37 |
% 11.79/2.37 | ALPHA: (19) implies:
% 11.79/2.37 | (20) relation(all_35_2) = all_49_1
% 11.79/2.37 | (21) relation(all_35_1) = all_49_0
% 11.79/2.37 | (22) ~ (all_49_1 = 0) | all_49_0 = 0
% 11.79/2.37 |
% 11.79/2.37 | GROUND_INST: instantiating (3) with 0, all_49_1, all_35_2, simplifying with
% 11.79/2.37 | (12), (20) gives:
% 11.79/2.37 | (23) all_49_1 = 0
% 11.79/2.37 |
% 11.79/2.37 | BETA: splitting (22) gives:
% 11.79/2.37 |
% 11.79/2.37 | Case 1:
% 11.79/2.37 | |
% 11.79/2.37 | | (24) ~ (all_49_1 = 0)
% 11.79/2.37 | |
% 11.79/2.37 | | REDUCE: (23), (24) imply:
% 11.79/2.37 | | (25) $false
% 11.79/2.37 | |
% 11.79/2.37 | | CLOSE: (25) is inconsistent.
% 11.79/2.37 | |
% 11.79/2.37 | Case 2:
% 11.79/2.37 | |
% 11.79/2.37 | | (26) all_49_0 = 0
% 11.79/2.37 | |
% 11.79/2.37 | | REDUCE: (21), (26) imply:
% 11.79/2.37 | | (27) relation(all_35_1) = 0
% 11.79/2.37 | |
% 11.79/2.37 | | BETA: splitting (17) gives:
% 11.79/2.37 | |
% 11.79/2.37 | | Case 1:
% 11.79/2.37 | | |
% 11.79/2.37 | | | (28) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_2) = v0)
% 11.79/2.37 | | |
% 11.79/2.37 | | | DELTA: instantiating (28) with fresh symbol all_61_0 gives:
% 11.79/2.37 | | | (29) ~ (all_61_0 = 0) & relation(all_35_2) = all_61_0
% 11.79/2.37 | | |
% 11.79/2.37 | | | ALPHA: (29) implies:
% 11.79/2.37 | | | (30) ~ (all_61_0 = 0)
% 11.79/2.37 | | | (31) relation(all_35_2) = all_61_0
% 11.79/2.37 | | |
% 11.79/2.37 | | | GROUND_INST: instantiating (3) with 0, all_61_0, all_35_2, simplifying
% 11.79/2.37 | | | with (12), (31) gives:
% 11.79/2.37 | | | (32) all_61_0 = 0
% 11.79/2.37 | | |
% 11.79/2.37 | | | REDUCE: (30), (32) imply:
% 11.79/2.37 | | | (33) $false
% 11.79/2.38 | | |
% 11.79/2.38 | | | CLOSE: (33) is inconsistent.
% 11.79/2.38 | | |
% 11.79/2.38 | | Case 2:
% 11.79/2.38 | | |
% 11.79/2.38 | | | (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 11.79/2.38 | | | $i] : ! [v5: int] : (v5 = 0 | ~ (ordered_pair(v0, v2) = v4) |
% 11.79/2.38 | | | ~ (ordered_pair(v0, v1) = v3) | ~ (in(v4, all_35_2) = v5) | ~
% 11.79/2.38 | | | (in(v3, all_35_2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 11.79/2.38 | | | [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & ordered_pair(v1, v2) =
% 11.79/2.38 | | | v6 & in(v6, all_35_2) = v7 & $i(v6)))
% 11.79/2.38 | | |
% 11.79/2.38 | | | BETA: splitting (18) gives:
% 11.79/2.38 | | |
% 11.79/2.38 | | | Case 1:
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | (35) ? [v0: int] : ( ~ (v0 = 0) & relation(all_35_1) = v0)
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | DELTA: instantiating (35) with fresh symbol all_64_0 gives:
% 11.79/2.38 | | | | (36) ~ (all_64_0 = 0) & relation(all_35_1) = all_64_0
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | ALPHA: (36) implies:
% 11.79/2.38 | | | | (37) ~ (all_64_0 = 0)
% 11.79/2.38 | | | | (38) relation(all_35_1) = all_64_0
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | GROUND_INST: instantiating (3) with 0, all_64_0, all_35_1, simplifying
% 11.79/2.38 | | | | with (27), (38) gives:
% 11.79/2.38 | | | | (39) all_64_0 = 0
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | REDUCE: (37), (39) imply:
% 11.79/2.38 | | | | (40) $false
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | CLOSE: (40) is inconsistent.
% 11.79/2.38 | | | |
% 11.79/2.38 | | | Case 2:
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | (41) ( ~ (all_35_0 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.79/2.38 | | | | ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 11.79/2.38 | | | | (ordered_pair(v0, v2) = v4) | ~ (ordered_pair(v0, v1) = v3)
% 11.79/2.38 | | | | | ~ (in(v4, all_35_1) = v5) | ~ (in(v3, all_35_1) = 0) |
% 11.79/2.38 | | | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: $i] : ? [v7:
% 11.79/2.38 | | | | int] : ( ~ (v7 = 0) & ordered_pair(v1, v2) = v6 & in(v6,
% 11.79/2.38 | | | | all_35_1) = v7 & $i(v6)))) & (all_35_0 = 0 | ? [v0: $i]
% 11.79/2.38 | | | | : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ?
% 11.79/2.38 | | | | [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ordered_pair(v1, v2)
% 11.79/2.38 | | | | = v4 & ordered_pair(v0, v2) = v5 & ordered_pair(v0, v1) = v3
% 11.79/2.38 | | | | & in(v5, all_35_1) = v6 & in(v4, all_35_1) = 0 & in(v3,
% 11.79/2.38 | | | | all_35_1) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1)
% 11.79/2.38 | | | | & $i(v0)))
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | ALPHA: (41) implies:
% 11.79/2.38 | | | | (42) all_35_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 11.79/2.38 | | | | $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0)
% 11.79/2.38 | | | | & ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 &
% 11.79/2.38 | | | | ordered_pair(v0, v1) = v3 & in(v5, all_35_1) = v6 & in(v4,
% 11.79/2.38 | | | | all_35_1) = 0 & in(v3, all_35_1) = 0 & $i(v5) & $i(v4) &
% 11.79/2.38 | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | BETA: splitting (42) gives:
% 11.79/2.38 | | | |
% 11.79/2.38 | | | | Case 1:
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | | (43) all_35_0 = 0
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | | REDUCE: (8), (43) imply:
% 11.79/2.38 | | | | | (44) $false
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | | CLOSE: (44) is inconsistent.
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | Case 2:
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 11.79/2.38 | | | | | [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 11.79/2.38 | | | | | ordered_pair(v1, v2) = v4 & ordered_pair(v0, v2) = v5 &
% 11.79/2.38 | | | | | ordered_pair(v0, v1) = v3 & in(v5, all_35_1) = v6 & in(v4,
% 11.79/2.38 | | | | | all_35_1) = 0 & in(v3, all_35_1) = 0 & $i(v5) & $i(v4) &
% 11.79/2.38 | | | | | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | | DELTA: instantiating (45) with fresh symbols all_67_0, all_67_1,
% 11.79/2.38 | | | | | all_67_2, all_67_3, all_67_4, all_67_5, all_67_6 gives:
% 11.79/2.38 | | | | | (46) ~ (all_67_0 = 0) & ordered_pair(all_67_5, all_67_4) =
% 11.79/2.38 | | | | | all_67_2 & ordered_pair(all_67_6, all_67_4) = all_67_1 &
% 11.79/2.38 | | | | | ordered_pair(all_67_6, all_67_5) = all_67_3 & in(all_67_1,
% 11.79/2.38 | | | | | all_35_1) = all_67_0 & in(all_67_2, all_35_1) = 0 &
% 11.79/2.38 | | | | | in(all_67_3, all_35_1) = 0 & $i(all_67_1) & $i(all_67_2) &
% 11.79/2.38 | | | | | $i(all_67_3) & $i(all_67_4) & $i(all_67_5) & $i(all_67_6)
% 11.79/2.38 | | | | |
% 11.79/2.38 | | | | | ALPHA: (46) implies:
% 11.79/2.38 | | | | | (47) ~ (all_67_0 = 0)
% 11.79/2.38 | | | | | (48) $i(all_67_6)
% 11.79/2.38 | | | | | (49) $i(all_67_5)
% 11.79/2.38 | | | | | (50) $i(all_67_4)
% 11.79/2.38 | | | | | (51) $i(all_67_3)
% 11.79/2.38 | | | | | (52) $i(all_67_2)
% 11.79/2.38 | | | | | (53) $i(all_67_1)
% 11.79/2.39 | | | | | (54) in(all_67_3, all_35_1) = 0
% 11.79/2.39 | | | | | (55) in(all_67_2, all_35_1) = 0
% 11.79/2.39 | | | | | (56) in(all_67_1, all_35_1) = all_67_0
% 11.79/2.39 | | | | | (57) ordered_pair(all_67_6, all_67_5) = all_67_3
% 11.79/2.39 | | | | | (58) ordered_pair(all_67_6, all_67_4) = all_67_1
% 11.79/2.39 | | | | | (59) ordered_pair(all_67_5, all_67_4) = all_67_2
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | GROUND_INST: instantiating (t16_wellord1) with all_67_3, all_35_3,
% 11.79/2.39 | | | | | all_35_2, all_35_1, 0, simplifying with (9), (10), (13),
% 11.79/2.39 | | | | | (51), (54) gives:
% 11.79/2.39 | | | | | (60) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 11.79/2.39 | | | | | (cartesian_product2(all_35_3, all_35_3) = v2 &
% 11.79/2.39 | | | | | relation(all_35_2) = v0 & in(all_67_3, v2) = v3 &
% 11.79/2.39 | | | | | in(all_67_3, all_35_2) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 =
% 11.79/2.39 | | | | | 0 & v1 = 0)))
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | GROUND_INST: instantiating (t16_wellord1) with all_67_2, all_35_3,
% 11.79/2.39 | | | | | all_35_2, all_35_1, 0, simplifying with (9), (10), (13),
% 11.79/2.39 | | | | | (52), (55) gives:
% 11.79/2.39 | | | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 11.79/2.39 | | | | | (cartesian_product2(all_35_3, all_35_3) = v2 &
% 11.79/2.39 | | | | | relation(all_35_2) = v0 & in(all_67_2, v2) = v3 &
% 11.79/2.39 | | | | | in(all_67_2, all_35_2) = v1 & $i(v2) & ( ~ (v0 = 0) | (v3 =
% 11.79/2.39 | | | | | 0 & v1 = 0)))
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | GROUND_INST: instantiating (t16_wellord1) with all_67_1, all_35_3,
% 11.79/2.39 | | | | | all_35_2, all_35_1, all_67_0, simplifying with (9), (10),
% 11.79/2.39 | | | | | (13), (53), (56) gives:
% 11.79/2.39 | | | | | (62) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 11.79/2.39 | | | | | (cartesian_product2(all_35_3, all_35_3) = v2 &
% 11.79/2.39 | | | | | relation(all_35_2) = v0 & in(all_67_1, v2) = v3 &
% 11.79/2.39 | | | | | in(all_67_1, all_35_2) = v1 & $i(v2) & ( ~ (v0 = 0) | (( ~
% 11.79/2.39 | | | | | (v3 = 0) | ~ (v1 = 0) | all_67_0 = 0) & ( ~ (all_67_0
% 11.79/2.39 | | | | | = 0) | (v3 = 0 & v1 = 0)))))
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | DELTA: instantiating (60) with fresh symbols all_87_0, all_87_1,
% 11.79/2.39 | | | | | all_87_2, all_87_3 gives:
% 11.79/2.39 | | | | | (63) cartesian_product2(all_35_3, all_35_3) = all_87_1 &
% 11.79/2.39 | | | | | relation(all_35_2) = all_87_3 & in(all_67_3, all_87_1) =
% 11.79/2.39 | | | | | all_87_0 & in(all_67_3, all_35_2) = all_87_2 & $i(all_87_1) &
% 11.79/2.39 | | | | | ( ~ (all_87_3 = 0) | (all_87_0 = 0 & all_87_2 = 0))
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | ALPHA: (63) implies:
% 11.79/2.39 | | | | | (64) in(all_67_3, all_35_2) = all_87_2
% 11.79/2.39 | | | | | (65) in(all_67_3, all_87_1) = all_87_0
% 11.79/2.39 | | | | | (66) relation(all_35_2) = all_87_3
% 11.79/2.39 | | | | | (67) cartesian_product2(all_35_3, all_35_3) = all_87_1
% 11.79/2.39 | | | | | (68) ~ (all_87_3 = 0) | (all_87_0 = 0 & all_87_2 = 0)
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | DELTA: instantiating (61) with fresh symbols all_89_0, all_89_1,
% 11.79/2.39 | | | | | all_89_2, all_89_3 gives:
% 11.79/2.39 | | | | | (69) cartesian_product2(all_35_3, all_35_3) = all_89_1 &
% 11.79/2.39 | | | | | relation(all_35_2) = all_89_3 & in(all_67_2, all_89_1) =
% 11.79/2.39 | | | | | all_89_0 & in(all_67_2, all_35_2) = all_89_2 & $i(all_89_1) &
% 11.79/2.39 | | | | | ( ~ (all_89_3 = 0) | (all_89_0 = 0 & all_89_2 = 0))
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | ALPHA: (69) implies:
% 11.79/2.39 | | | | | (70) in(all_67_2, all_35_2) = all_89_2
% 11.79/2.39 | | | | | (71) in(all_67_2, all_89_1) = all_89_0
% 11.79/2.39 | | | | | (72) relation(all_35_2) = all_89_3
% 11.79/2.39 | | | | | (73) cartesian_product2(all_35_3, all_35_3) = all_89_1
% 11.79/2.39 | | | | | (74) ~ (all_89_3 = 0) | (all_89_0 = 0 & all_89_2 = 0)
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | DELTA: instantiating (62) with fresh symbols all_91_0, all_91_1,
% 11.79/2.39 | | | | | all_91_2, all_91_3 gives:
% 11.79/2.39 | | | | | (75) cartesian_product2(all_35_3, all_35_3) = all_91_1 &
% 11.79/2.39 | | | | | relation(all_35_2) = all_91_3 & in(all_67_1, all_91_1) =
% 11.79/2.39 | | | | | all_91_0 & in(all_67_1, all_35_2) = all_91_2 & $i(all_91_1) &
% 11.79/2.39 | | | | | ( ~ (all_91_3 = 0) | (( ~ (all_91_0 = 0) | ~ (all_91_2 = 0) |
% 11.79/2.39 | | | | | all_67_0 = 0) & ( ~ (all_67_0 = 0) | (all_91_0 = 0 &
% 11.79/2.39 | | | | | all_91_2 = 0))))
% 11.79/2.39 | | | | |
% 11.79/2.39 | | | | | ALPHA: (75) implies:
% 11.79/2.39 | | | | | (76) in(all_67_1, all_35_2) = all_91_2
% 11.79/2.39 | | | | | (77) in(all_67_1, all_91_1) = all_91_0
% 11.79/2.40 | | | | | (78) relation(all_35_2) = all_91_3
% 11.79/2.40 | | | | | (79) cartesian_product2(all_35_3, all_35_3) = all_91_1
% 11.79/2.40 | | | | | (80) ~ (all_91_3 = 0) | (( ~ (all_91_0 = 0) | ~ (all_91_2 = 0) |
% 11.79/2.40 | | | | | all_67_0 = 0) & ( ~ (all_67_0 = 0) | (all_91_0 = 0 &
% 11.79/2.40 | | | | | all_91_2 = 0)))
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | GROUND_INST: instantiating (3) with 0, all_89_3, all_35_2, simplifying
% 11.79/2.40 | | | | | with (12), (72) gives:
% 11.79/2.40 | | | | | (81) all_89_3 = 0
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | GROUND_INST: instantiating (3) with all_89_3, all_91_3, all_35_2,
% 11.79/2.40 | | | | | simplifying with (72), (78) gives:
% 11.79/2.40 | | | | | (82) all_91_3 = all_89_3
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | GROUND_INST: instantiating (3) with all_87_3, all_91_3, all_35_2,
% 11.79/2.40 | | | | | simplifying with (66), (78) gives:
% 11.79/2.40 | | | | | (83) all_91_3 = all_87_3
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | GROUND_INST: instantiating (6) with all_89_1, all_91_1, all_35_3,
% 11.79/2.40 | | | | | all_35_3, simplifying with (73), (79) gives:
% 11.79/2.40 | | | | | (84) all_91_1 = all_89_1
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | GROUND_INST: instantiating (6) with all_87_1, all_91_1, all_35_3,
% 11.79/2.40 | | | | | all_35_3, simplifying with (67), (79) gives:
% 11.79/2.40 | | | | | (85) all_91_1 = all_87_1
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | COMBINE_EQS: (84), (85) imply:
% 11.79/2.40 | | | | | (86) all_89_1 = all_87_1
% 11.79/2.40 | | | | |
% 11.79/2.40 | | | | | SIMP: (86) implies:
% 11.79/2.40 | | | | | (87) all_89_1 = all_87_1
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | COMBINE_EQS: (82), (83) imply:
% 12.04/2.40 | | | | | (88) all_89_3 = all_87_3
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | SIMP: (88) implies:
% 12.04/2.40 | | | | | (89) all_89_3 = all_87_3
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | COMBINE_EQS: (81), (89) imply:
% 12.04/2.40 | | | | | (90) all_87_3 = 0
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | COMBINE_EQS: (83), (90) imply:
% 12.04/2.40 | | | | | (91) all_91_3 = 0
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | REDUCE: (77), (85) imply:
% 12.04/2.40 | | | | | (92) in(all_67_1, all_87_1) = all_91_0
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | REDUCE: (71), (87) imply:
% 12.04/2.40 | | | | | (93) in(all_67_2, all_87_1) = all_89_0
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | BETA: splitting (68) gives:
% 12.04/2.40 | | | | |
% 12.04/2.40 | | | | | Case 1:
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | (94) ~ (all_87_3 = 0)
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | REDUCE: (90), (94) imply:
% 12.04/2.40 | | | | | | (95) $false
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | CLOSE: (95) is inconsistent.
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | Case 2:
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | (96) all_87_0 = 0 & all_87_2 = 0
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | ALPHA: (96) implies:
% 12.04/2.40 | | | | | | (97) all_87_2 = 0
% 12.04/2.40 | | | | | | (98) all_87_0 = 0
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | REDUCE: (65), (98) imply:
% 12.04/2.40 | | | | | | (99) in(all_67_3, all_87_1) = 0
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | REDUCE: (64), (97) imply:
% 12.04/2.40 | | | | | | (100) in(all_67_3, all_35_2) = 0
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | BETA: splitting (74) gives:
% 12.04/2.40 | | | | | |
% 12.04/2.40 | | | | | | Case 1:
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | (101) ~ (all_89_3 = 0)
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | REDUCE: (81), (101) imply:
% 12.04/2.40 | | | | | | | (102) $false
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | CLOSE: (102) is inconsistent.
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | Case 2:
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | (103) all_89_0 = 0 & all_89_2 = 0
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | ALPHA: (103) implies:
% 12.04/2.40 | | | | | | | (104) all_89_2 = 0
% 12.04/2.40 | | | | | | | (105) all_89_0 = 0
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | REDUCE: (93), (105) imply:
% 12.04/2.40 | | | | | | | (106) in(all_67_2, all_87_1) = 0
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | REDUCE: (70), (104) imply:
% 12.04/2.40 | | | | | | | (107) in(all_67_2, all_35_2) = 0
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | GROUND_INST: instantiating (34) with all_67_6, all_67_5, all_67_4,
% 12.04/2.40 | | | | | | | all_67_3, all_67_1, all_91_2, simplifying with (48),
% 12.04/2.40 | | | | | | | (49), (50), (57), (58), (76), (100) gives:
% 12.04/2.40 | | | | | | | (108) all_91_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0)
% 12.04/2.40 | | | | | | | & ordered_pair(all_67_5, all_67_4) = v0 & in(v0,
% 12.04/2.40 | | | | | | | all_35_2) = v1 & $i(v0))
% 12.04/2.40 | | | | | | |
% 12.04/2.40 | | | | | | | GROUND_INST: instantiating (1) with all_67_5, all_67_4, all_35_3,
% 12.04/2.40 | | | | | | | all_35_3, all_67_2, all_87_1, simplifying with (9),
% 12.04/2.40 | | | | | | | (49), (50), (59), (67), (106) gives:
% 12.04/2.41 | | | | | | | (109) in(all_67_4, all_35_3) = 0 & in(all_67_5, all_35_3) = 0
% 12.04/2.41 | | | | | | |
% 12.04/2.41 | | | | | | | ALPHA: (109) implies:
% 12.04/2.41 | | | | | | | (110) in(all_67_4, all_35_3) = 0
% 12.04/2.41 | | | | | | |
% 12.04/2.41 | | | | | | | GROUND_INST: instantiating (2) with all_67_6, all_67_4, all_35_3,
% 12.04/2.41 | | | | | | | all_35_3, all_67_1, all_87_1, all_91_0, simplifying
% 12.04/2.41 | | | | | | | with (9), (48), (50), (58), (67), (92) gives:
% 12.04/2.41 | | | | | | | (111) all_91_0 = 0 | ? [v0: any] : ? [v1: any] :
% 12.04/2.41 | | | | | | | (in(all_67_4, all_35_3) = v1 & in(all_67_6, all_35_3) =
% 12.04/2.41 | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.04/2.41 | | | | | | |
% 12.04/2.41 | | | | | | | GROUND_INST: instantiating (1) with all_67_6, all_67_5, all_35_3,
% 12.04/2.41 | | | | | | | all_35_3, all_67_3, all_87_1, simplifying with (9),
% 12.04/2.41 | | | | | | | (48), (49), (57), (67), (99) gives:
% 12.04/2.41 | | | | | | | (112) in(all_67_5, all_35_3) = 0 & in(all_67_6, all_35_3) = 0
% 12.04/2.41 | | | | | | |
% 12.04/2.41 | | | | | | | ALPHA: (112) implies:
% 12.04/2.41 | | | | | | | (113) in(all_67_6, all_35_3) = 0
% 12.04/2.41 | | | | | | |
% 12.04/2.41 | | | | | | | BETA: splitting (108) gives:
% 12.04/2.41 | | | | | | |
% 12.04/2.41 | | | | | | | Case 1:
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | | (114) all_91_2 = 0
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | | BETA: splitting (111) gives:
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | | Case 1:
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | (115) all_91_0 = 0
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | BETA: splitting (80) gives:
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | Case 1:
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | (116) ~ (all_91_3 = 0)
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | REDUCE: (91), (116) imply:
% 12.04/2.41 | | | | | | | | | | (117) $false
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | CLOSE: (117) is inconsistent.
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | Case 2:
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | (118) ( ~ (all_91_0 = 0) | ~ (all_91_2 = 0) | all_67_0 =
% 12.04/2.41 | | | | | | | | | | 0) & ( ~ (all_67_0 = 0) | (all_91_0 = 0 &
% 12.04/2.41 | | | | | | | | | | all_91_2 = 0))
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | ALPHA: (118) implies:
% 12.04/2.41 | | | | | | | | | | (119) ~ (all_91_0 = 0) | ~ (all_91_2 = 0) | all_67_0 =
% 12.04/2.41 | | | | | | | | | | 0
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | BETA: splitting (119) gives:
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | Case 1:
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | (120) ~ (all_91_0 = 0)
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | REDUCE: (115), (120) imply:
% 12.04/2.41 | | | | | | | | | | | (121) $false
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | CLOSE: (121) is inconsistent.
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | Case 2:
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | (122) ~ (all_91_2 = 0) | all_67_0 = 0
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | BETA: splitting (122) gives:
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | Case 1:
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | | (123) ~ (all_91_2 = 0)
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | | REDUCE: (114), (123) imply:
% 12.04/2.41 | | | | | | | | | | | | (124) $false
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | Case 2:
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | | (125) all_67_0 = 0
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | | REDUCE: (47), (125) imply:
% 12.04/2.41 | | | | | | | | | | | | (126) $false
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 12.04/2.41 | | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | | End of split
% 12.04/2.41 | | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | End of split
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | End of split
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | Case 2:
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | (127) ? [v0: any] : ? [v1: any] : (in(all_67_4, all_35_3)
% 12.04/2.41 | | | | | | | | | = v1 & in(all_67_6, all_35_3) = v0 & ( ~ (v1 = 0) |
% 12.04/2.41 | | | | | | | | | ~ (v0 = 0)))
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | DELTA: instantiating (127) with fresh symbols all_133_0,
% 12.04/2.41 | | | | | | | | | all_133_1 gives:
% 12.04/2.41 | | | | | | | | | (128) in(all_67_4, all_35_3) = all_133_0 & in(all_67_6,
% 12.04/2.41 | | | | | | | | | all_35_3) = all_133_1 & ( ~ (all_133_0 = 0) | ~
% 12.04/2.41 | | | | | | | | | (all_133_1 = 0))
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | ALPHA: (128) implies:
% 12.04/2.41 | | | | | | | | | (129) in(all_67_6, all_35_3) = all_133_1
% 12.04/2.41 | | | | | | | | | (130) in(all_67_4, all_35_3) = all_133_0
% 12.04/2.41 | | | | | | | | | (131) ~ (all_133_0 = 0) | ~ (all_133_1 = 0)
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_133_1, all_35_3,
% 12.04/2.41 | | | | | | | | | all_67_6, simplifying with (113), (129) gives:
% 12.04/2.41 | | | | | | | | | (132) all_133_1 = 0
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_133_0, all_35_3,
% 12.04/2.41 | | | | | | | | | all_67_4, simplifying with (110), (130) gives:
% 12.04/2.41 | | | | | | | | | (133) all_133_0 = 0
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | BETA: splitting (131) gives:
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | | Case 1:
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | (134) ~ (all_133_0 = 0)
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | REDUCE: (133), (134) imply:
% 12.04/2.41 | | | | | | | | | | (135) $false
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | CLOSE: (135) is inconsistent.
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | Case 2:
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | (136) ~ (all_133_1 = 0)
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | REDUCE: (132), (136) imply:
% 12.04/2.41 | | | | | | | | | | (137) $false
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | | CLOSE: (137) is inconsistent.
% 12.04/2.41 | | | | | | | | | |
% 12.04/2.41 | | | | | | | | | End of split
% 12.04/2.41 | | | | | | | | |
% 12.04/2.41 | | | | | | | | End of split
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | Case 2:
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | | (138) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.04/2.41 | | | | | | | | ordered_pair(all_67_5, all_67_4) = v0 & in(v0,
% 12.04/2.41 | | | | | | | | all_35_2) = v1 & $i(v0))
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | | DELTA: instantiating (138) with fresh symbols all_127_0,
% 12.04/2.41 | | | | | | | | all_127_1 gives:
% 12.04/2.41 | | | | | | | | (139) ~ (all_127_0 = 0) & ordered_pair(all_67_5, all_67_4) =
% 12.04/2.41 | | | | | | | | all_127_1 & in(all_127_1, all_35_2) = all_127_0 &
% 12.04/2.41 | | | | | | | | $i(all_127_1)
% 12.04/2.41 | | | | | | | |
% 12.04/2.41 | | | | | | | | ALPHA: (139) implies:
% 12.04/2.42 | | | | | | | | (140) ~ (all_127_0 = 0)
% 12.04/2.42 | | | | | | | | (141) in(all_127_1, all_35_2) = all_127_0
% 12.04/2.42 | | | | | | | | (142) ordered_pair(all_67_5, all_67_4) = all_127_1
% 12.04/2.42 | | | | | | | |
% 12.04/2.42 | | | | | | | | GROUND_INST: instantiating (5) with all_67_2, all_127_1,
% 12.04/2.42 | | | | | | | | all_67_4, all_67_5, simplifying with (59), (142)
% 12.04/2.42 | | | | | | | | gives:
% 12.04/2.42 | | | | | | | | (143) all_127_1 = all_67_2
% 12.04/2.42 | | | | | | | |
% 12.04/2.42 | | | | | | | | REDUCE: (141), (143) imply:
% 12.04/2.42 | | | | | | | | (144) in(all_67_2, all_35_2) = all_127_0
% 12.04/2.42 | | | | | | | |
% 12.04/2.42 | | | | | | | | GROUND_INST: instantiating (4) with 0, all_127_0, all_35_2,
% 12.04/2.42 | | | | | | | | all_67_2, simplifying with (107), (144) gives:
% 12.04/2.42 | | | | | | | | (145) all_127_0 = 0
% 12.04/2.42 | | | | | | | |
% 12.04/2.42 | | | | | | | | REDUCE: (140), (145) imply:
% 12.04/2.42 | | | | | | | | (146) $false
% 12.04/2.42 | | | | | | | |
% 12.04/2.42 | | | | | | | | CLOSE: (146) is inconsistent.
% 12.04/2.42 | | | | | | | |
% 12.04/2.42 | | | | | | | End of split
% 12.04/2.42 | | | | | | |
% 12.04/2.42 | | | | | | End of split
% 12.04/2.42 | | | | | |
% 12.04/2.42 | | | | | End of split
% 12.04/2.42 | | | | |
% 12.04/2.42 | | | | End of split
% 12.04/2.42 | | | |
% 12.04/2.42 | | | End of split
% 12.04/2.42 | | |
% 12.04/2.42 | | End of split
% 12.04/2.42 | |
% 12.04/2.42 | End of split
% 12.04/2.42 |
% 12.04/2.42 End of proof
% 12.04/2.42 % SZS output end Proof for theBenchmark
% 12.04/2.42
% 12.04/2.42 1807ms
%------------------------------------------------------------------------------