TSTP Solution File: SEU250+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU250+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 : n024.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 17:43:39 EDT 2023
% Result : Theorem 7.68s 1.83s
% Output : Proof 10.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU250+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Aug 24 01:01:55 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.60 Running up to 7 provers in parallel.
% 0.18/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.67/1.03 Prover 4: Preprocessing ...
% 2.67/1.04 Prover 1: Preprocessing ...
% 2.67/1.08 Prover 2: Preprocessing ...
% 2.67/1.08 Prover 0: Preprocessing ...
% 2.67/1.08 Prover 5: Preprocessing ...
% 2.67/1.08 Prover 3: Preprocessing ...
% 2.67/1.08 Prover 6: Preprocessing ...
% 5.48/1.46 Prover 1: Warning: ignoring some quantifiers
% 6.17/1.51 Prover 1: Constructing countermodel ...
% 6.17/1.52 Prover 5: Proving ...
% 6.17/1.52 Prover 2: Proving ...
% 6.17/1.54 Prover 3: Warning: ignoring some quantifiers
% 6.17/1.55 Prover 4: Warning: ignoring some quantifiers
% 6.17/1.56 Prover 3: Constructing countermodel ...
% 6.17/1.57 Prover 6: Proving ...
% 6.17/1.58 Prover 4: Constructing countermodel ...
% 6.76/1.60 Prover 0: Proving ...
% 7.68/1.83 Prover 6: proved (1213ms)
% 7.68/1.83
% 7.68/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.68/1.83
% 7.68/1.84 Prover 3: stopped
% 7.68/1.84 Prover 2: stopped
% 7.68/1.84 Prover 0: stopped
% 7.68/1.84 Prover 5: stopped
% 7.68/1.84 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.68/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.68/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.68/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.68/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.52/1.89 Prover 8: Preprocessing ...
% 8.52/1.89 Prover 10: Preprocessing ...
% 8.52/1.89 Prover 7: Preprocessing ...
% 8.52/1.90 Prover 13: Preprocessing ...
% 8.52/1.90 Prover 11: Preprocessing ...
% 9.42/1.96 Prover 1: Found proof (size 49)
% 9.42/1.97 Prover 1: proved (1355ms)
% 9.42/1.97 Prover 4: stopped
% 9.42/1.98 Prover 10: Warning: ignoring some quantifiers
% 9.42/1.98 Prover 7: Warning: ignoring some quantifiers
% 9.42/1.98 Prover 10: Constructing countermodel ...
% 9.42/1.99 Prover 11: stopped
% 9.42/1.99 Prover 10: stopped
% 9.42/2.00 Prover 7: Constructing countermodel ...
% 9.42/2.00 Prover 13: Warning: ignoring some quantifiers
% 9.42/2.00 Prover 8: Warning: ignoring some quantifiers
% 9.42/2.00 Prover 7: stopped
% 9.42/2.01 Prover 13: Constructing countermodel ...
% 9.42/2.01 Prover 8: Constructing countermodel ...
% 9.42/2.02 Prover 13: stopped
% 9.42/2.02 Prover 8: stopped
% 9.42/2.02
% 9.42/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.42/2.02
% 9.42/2.03 % SZS output start Proof for theBenchmark
% 9.42/2.04 Assumptions after simplification:
% 9.42/2.04 ---------------------------------
% 9.42/2.04
% 9.42/2.04 (d3_tarski)
% 9.98/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 9.98/2.06 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 9.98/2.06 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 9.98/2.06 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 9.98/2.06 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 9.98/2.06
% 9.98/2.06 (dt_k2_wellord1)
% 9.98/2.06 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_restriction(v0, v1) =
% 9.98/2.06 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (relation(v2)
% 9.98/2.06 = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 9.98/2.06
% 9.98/2.06 (t19_wellord1)
% 9.98/2.07 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 9.98/2.07 (relation_restriction(v2, v1) = v3) | ~ (relation_field(v3) = v4) | ~
% 9.98/2.07 (in(v0, v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ?
% 9.98/2.07 [v6: $i] : ? [v7: any] : ? [v8: any] : (relation_field(v2) = v6 &
% 9.98/2.07 relation(v2) = v5 & in(v0, v6) = v7 & in(v0, v1) = v8 & $i(v6) & ( ~ (v5 =
% 9.98/2.07 0) | (v8 = 0 & v7 = 0))))
% 9.98/2.07
% 9.98/2.07 (t20_wellord1)
% 9.98/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 9.98/2.07 any] : ? [v6: any] : (relation_restriction(v1, v0) = v2 &
% 9.98/2.07 relation_field(v2) = v3 & relation_field(v1) = v4 & subset(v3, v4) = v5 &
% 9.98/2.07 subset(v3, v0) = v6 & relation(v1) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 9.98/2.07 $i(v0) & ( ~ (v6 = 0) | ~ (v5 = 0)))
% 9.98/2.07
% 9.98/2.07 (function-axioms)
% 9.98/2.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 9.98/2.08 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 9.98/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.98/2.08 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) &
% 9.98/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.98/2.08 (relation_restriction(v3, v2) = v1) | ~ (relation_restriction(v3, v2) =
% 9.98/2.08 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 9.98/2.08 $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2)
% 9.98/2.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 9.98/2.08 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 9.98/2.08 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 9.98/2.08 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 9.98/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 9.98/2.08 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 9.98/2.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 9.98/2.08 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 9.98/2.08 (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i] : !
% 9.98/2.08 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 9.98/2.08 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 9.98/2.08 v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0:
% 9.98/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.98/2.08 ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 9.98/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 9.98/2.08 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 9.98/2.08 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1)
% 9.98/2.08 | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 9.98/2.08 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 9.98/2.08 (empty(v2) = v0))
% 9.98/2.08
% 9.98/2.08 Further assumptions not needed in the proof:
% 9.98/2.08 --------------------------------------------
% 9.98/2.08 antisymmetry_r2_hidden, cc1_funct_1, cc2_funct_1, commutativity_k2_xboole_0,
% 9.98/2.08 commutativity_k3_xboole_0, d6_relat_1, d6_wellord1, dt_k1_relat_1,
% 9.98/2.08 dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_xboole_0, dt_k2_zfmisc_1,
% 9.98/2.08 dt_k3_relat_1, dt_k3_xboole_0, dt_m1_subset_1, existence_m1_subset_1,
% 9.98/2.08 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0,
% 9.98/2.08 idempotence_k3_xboole_0, rc1_funct_1, rc1_xboole_0, rc2_funct_1, rc2_xboole_0,
% 9.98/2.08 rc3_funct_1, reflexivity_r1_tarski, t1_boole, t1_subset, t2_boole, t2_subset,
% 9.98/2.08 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole
% 9.98/2.08
% 9.98/2.08 Those formulas are unsatisfiable:
% 9.98/2.08 ---------------------------------
% 9.98/2.08
% 9.98/2.08 Begin of proof
% 9.98/2.08 |
% 9.98/2.08 | ALPHA: (d3_tarski) implies:
% 9.98/2.08 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 9.98/2.08 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 9.98/2.08 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 9.98/2.08 |
% 9.98/2.09 | ALPHA: (function-axioms) implies:
% 9.98/2.09 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.98/2.09 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 9.98/2.09 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 9.98/2.09 | (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 9.98/2.09 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 9.98/2.09 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 9.98/2.09 |
% 9.98/2.09 | DELTA: instantiating (t20_wellord1) with fresh symbols all_43_0, all_43_1,
% 9.98/2.09 | all_43_2, all_43_3, all_43_4, all_43_5, all_43_6 gives:
% 10.15/2.09 | (5) relation_restriction(all_43_5, all_43_6) = all_43_4 &
% 10.15/2.09 | relation_field(all_43_4) = all_43_3 & relation_field(all_43_5) =
% 10.15/2.09 | all_43_2 & subset(all_43_3, all_43_2) = all_43_1 & subset(all_43_3,
% 10.15/2.09 | all_43_6) = all_43_0 & relation(all_43_5) = 0 & $i(all_43_2) &
% 10.15/2.09 | $i(all_43_3) & $i(all_43_4) & $i(all_43_5) & $i(all_43_6) & ( ~
% 10.15/2.09 | (all_43_0 = 0) | ~ (all_43_1 = 0))
% 10.15/2.09 |
% 10.15/2.09 | ALPHA: (5) implies:
% 10.15/2.09 | (6) $i(all_43_6)
% 10.15/2.09 | (7) $i(all_43_5)
% 10.15/2.09 | (8) $i(all_43_3)
% 10.15/2.09 | (9) $i(all_43_2)
% 10.15/2.09 | (10) relation(all_43_5) = 0
% 10.15/2.09 | (11) subset(all_43_3, all_43_6) = all_43_0
% 10.15/2.09 | (12) subset(all_43_3, all_43_2) = all_43_1
% 10.15/2.09 | (13) relation_field(all_43_5) = all_43_2
% 10.15/2.09 | (14) relation_field(all_43_4) = all_43_3
% 10.15/2.09 | (15) relation_restriction(all_43_5, all_43_6) = all_43_4
% 10.15/2.09 | (16) ~ (all_43_0 = 0) | ~ (all_43_1 = 0)
% 10.15/2.09 |
% 10.15/2.09 | GROUND_INST: instantiating (1) with all_43_3, all_43_6, all_43_0, simplifying
% 10.15/2.09 | with (6), (8), (11) gives:
% 10.15/2.09 | (17) all_43_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 10.15/2.09 | all_43_3) = 0 & in(v0, all_43_6) = v1 & $i(v0))
% 10.15/2.09 |
% 10.15/2.09 | GROUND_INST: instantiating (1) with all_43_3, all_43_2, all_43_1, simplifying
% 10.15/2.09 | with (8), (9), (12) gives:
% 10.15/2.09 | (18) all_43_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 10.15/2.09 | all_43_2) = v1 & in(v0, all_43_3) = 0 & $i(v0))
% 10.15/2.09 |
% 10.15/2.09 | GROUND_INST: instantiating (dt_k2_wellord1) with all_43_5, all_43_6, all_43_4,
% 10.15/2.09 | simplifying with (6), (7), (15) gives:
% 10.15/2.10 | (19) ? [v0: any] : ? [v1: any] : (relation(all_43_4) = v1 &
% 10.15/2.10 | relation(all_43_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.15/2.10 |
% 10.15/2.10 | DELTA: instantiating (19) with fresh symbols all_57_0, all_57_1 gives:
% 10.15/2.10 | (20) relation(all_43_4) = all_57_0 & relation(all_43_5) = all_57_1 & ( ~
% 10.15/2.10 | (all_57_1 = 0) | all_57_0 = 0)
% 10.15/2.10 |
% 10.15/2.10 | ALPHA: (20) implies:
% 10.15/2.10 | (21) relation(all_43_5) = all_57_1
% 10.15/2.10 |
% 10.15/2.10 | GROUND_INST: instantiating (2) with 0, all_57_1, all_43_5, simplifying with
% 10.15/2.10 | (10), (21) gives:
% 10.15/2.10 | (22) all_57_1 = 0
% 10.15/2.10 |
% 10.15/2.10 | BETA: splitting (16) gives:
% 10.15/2.10 |
% 10.15/2.10 | Case 1:
% 10.15/2.10 | |
% 10.15/2.10 | | (23) ~ (all_43_0 = 0)
% 10.15/2.10 | |
% 10.15/2.10 | | BETA: splitting (17) gives:
% 10.15/2.10 | |
% 10.15/2.10 | | Case 1:
% 10.15/2.10 | | |
% 10.15/2.10 | | | (24) all_43_0 = 0
% 10.15/2.10 | | |
% 10.15/2.10 | | | REDUCE: (23), (24) imply:
% 10.15/2.10 | | | (25) $false
% 10.15/2.10 | | |
% 10.15/2.10 | | | CLOSE: (25) is inconsistent.
% 10.15/2.10 | | |
% 10.15/2.10 | | Case 2:
% 10.15/2.10 | | |
% 10.15/2.10 | | | (26) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_43_3) = 0 &
% 10.15/2.10 | | | in(v0, all_43_6) = v1 & $i(v0))
% 10.15/2.10 | | |
% 10.15/2.10 | | | DELTA: instantiating (26) with fresh symbols all_88_0, all_88_1 gives:
% 10.15/2.10 | | | (27) ~ (all_88_0 = 0) & in(all_88_1, all_43_3) = 0 & in(all_88_1,
% 10.15/2.10 | | | all_43_6) = all_88_0 & $i(all_88_1)
% 10.15/2.10 | | |
% 10.15/2.10 | | | ALPHA: (27) implies:
% 10.15/2.10 | | | (28) ~ (all_88_0 = 0)
% 10.15/2.10 | | | (29) $i(all_88_1)
% 10.15/2.10 | | | (30) in(all_88_1, all_43_6) = all_88_0
% 10.15/2.10 | | | (31) in(all_88_1, all_43_3) = 0
% 10.15/2.10 | | |
% 10.15/2.10 | | | GROUND_INST: instantiating (t19_wellord1) with all_88_1, all_43_6,
% 10.15/2.10 | | | all_43_5, all_43_4, all_43_3, simplifying with (6), (7),
% 10.15/2.10 | | | (14), (15), (29), (31) gives:
% 10.15/2.10 | | | (32) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 10.15/2.10 | | | (relation_field(all_43_5) = v1 & relation(all_43_5) = v0 &
% 10.15/2.10 | | | in(all_88_1, v1) = v2 & in(all_88_1, all_43_6) = v3 & $i(v1) & (
% 10.15/2.10 | | | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 10.15/2.10 | | |
% 10.15/2.10 | | | DELTA: instantiating (32) with fresh symbols all_99_0, all_99_1, all_99_2,
% 10.15/2.10 | | | all_99_3 gives:
% 10.15/2.10 | | | (33) relation_field(all_43_5) = all_99_2 & relation(all_43_5) =
% 10.15/2.10 | | | all_99_3 & in(all_88_1, all_99_2) = all_99_1 & in(all_88_1,
% 10.15/2.10 | | | all_43_6) = all_99_0 & $i(all_99_2) & ( ~ (all_99_3 = 0) |
% 10.15/2.10 | | | (all_99_0 = 0 & all_99_1 = 0))
% 10.15/2.10 | | |
% 10.15/2.10 | | | ALPHA: (33) implies:
% 10.15/2.10 | | | (34) in(all_88_1, all_43_6) = all_99_0
% 10.15/2.10 | | | (35) relation(all_43_5) = all_99_3
% 10.15/2.10 | | | (36) ~ (all_99_3 = 0) | (all_99_0 = 0 & all_99_1 = 0)
% 10.15/2.10 | | |
% 10.15/2.10 | | | GROUND_INST: instantiating (4) with all_88_0, all_99_0, all_43_6,
% 10.15/2.10 | | | all_88_1, simplifying with (30), (34) gives:
% 10.15/2.10 | | | (37) all_99_0 = all_88_0
% 10.15/2.10 | | |
% 10.15/2.10 | | | GROUND_INST: instantiating (2) with 0, all_99_3, all_43_5, simplifying
% 10.15/2.10 | | | with (10), (35) gives:
% 10.15/2.10 | | | (38) all_99_3 = 0
% 10.15/2.10 | | |
% 10.15/2.10 | | | BETA: splitting (36) gives:
% 10.15/2.10 | | |
% 10.15/2.10 | | | Case 1:
% 10.15/2.10 | | | |
% 10.15/2.10 | | | | (39) ~ (all_99_3 = 0)
% 10.15/2.10 | | | |
% 10.15/2.10 | | | | REDUCE: (38), (39) imply:
% 10.15/2.10 | | | | (40) $false
% 10.15/2.10 | | | |
% 10.15/2.11 | | | | CLOSE: (40) is inconsistent.
% 10.15/2.11 | | | |
% 10.15/2.11 | | | Case 2:
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | (41) all_99_0 = 0 & all_99_1 = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | ALPHA: (41) implies:
% 10.15/2.11 | | | | (42) all_99_0 = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | COMBINE_EQS: (37), (42) imply:
% 10.15/2.11 | | | | (43) all_88_0 = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | REDUCE: (28), (43) imply:
% 10.15/2.11 | | | | (44) $false
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | CLOSE: (44) is inconsistent.
% 10.15/2.11 | | | |
% 10.15/2.11 | | | End of split
% 10.15/2.11 | | |
% 10.15/2.11 | | End of split
% 10.15/2.11 | |
% 10.15/2.11 | Case 2:
% 10.15/2.11 | |
% 10.15/2.11 | | (45) ~ (all_43_1 = 0)
% 10.15/2.11 | |
% 10.15/2.11 | | BETA: splitting (18) gives:
% 10.15/2.11 | |
% 10.15/2.11 | | Case 1:
% 10.15/2.11 | | |
% 10.15/2.11 | | | (46) all_43_1 = 0
% 10.15/2.11 | | |
% 10.15/2.11 | | | REDUCE: (45), (46) imply:
% 10.15/2.11 | | | (47) $false
% 10.15/2.11 | | |
% 10.15/2.11 | | | CLOSE: (47) is inconsistent.
% 10.15/2.11 | | |
% 10.15/2.11 | | Case 2:
% 10.15/2.11 | | |
% 10.15/2.11 | | | (48) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_43_2) = v1
% 10.15/2.11 | | | & in(v0, all_43_3) = 0 & $i(v0))
% 10.15/2.11 | | |
% 10.15/2.11 | | | DELTA: instantiating (48) with fresh symbols all_88_0, all_88_1 gives:
% 10.15/2.11 | | | (49) ~ (all_88_0 = 0) & in(all_88_1, all_43_2) = all_88_0 &
% 10.15/2.11 | | | in(all_88_1, all_43_3) = 0 & $i(all_88_1)
% 10.15/2.11 | | |
% 10.15/2.11 | | | ALPHA: (49) implies:
% 10.15/2.11 | | | (50) ~ (all_88_0 = 0)
% 10.15/2.11 | | | (51) $i(all_88_1)
% 10.15/2.11 | | | (52) in(all_88_1, all_43_3) = 0
% 10.15/2.11 | | | (53) in(all_88_1, all_43_2) = all_88_0
% 10.15/2.11 | | |
% 10.15/2.11 | | | GROUND_INST: instantiating (t19_wellord1) with all_88_1, all_43_6,
% 10.15/2.11 | | | all_43_5, all_43_4, all_43_3, simplifying with (6), (7),
% 10.15/2.11 | | | (14), (15), (51), (52) gives:
% 10.15/2.11 | | | (54) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 10.15/2.11 | | | (relation_field(all_43_5) = v1 & relation(all_43_5) = v0 &
% 10.15/2.11 | | | in(all_88_1, v1) = v2 & in(all_88_1, all_43_6) = v3 & $i(v1) & (
% 10.15/2.11 | | | ~ (v0 = 0) | (v3 = 0 & v2 = 0)))
% 10.15/2.11 | | |
% 10.15/2.11 | | | DELTA: instantiating (54) with fresh symbols all_101_0, all_101_1,
% 10.15/2.11 | | | all_101_2, all_101_3 gives:
% 10.15/2.11 | | | (55) relation_field(all_43_5) = all_101_2 & relation(all_43_5) =
% 10.15/2.11 | | | all_101_3 & in(all_88_1, all_101_2) = all_101_1 & in(all_88_1,
% 10.15/2.11 | | | all_43_6) = all_101_0 & $i(all_101_2) & ( ~ (all_101_3 = 0) |
% 10.15/2.11 | | | (all_101_0 = 0 & all_101_1 = 0))
% 10.15/2.11 | | |
% 10.15/2.11 | | | ALPHA: (55) implies:
% 10.15/2.11 | | | (56) in(all_88_1, all_101_2) = all_101_1
% 10.15/2.11 | | | (57) relation(all_43_5) = all_101_3
% 10.15/2.11 | | | (58) relation_field(all_43_5) = all_101_2
% 10.15/2.11 | | | (59) ~ (all_101_3 = 0) | (all_101_0 = 0 & all_101_1 = 0)
% 10.15/2.11 | | |
% 10.15/2.11 | | | GROUND_INST: instantiating (2) with 0, all_101_3, all_43_5, simplifying
% 10.15/2.11 | | | with (10), (57) gives:
% 10.15/2.11 | | | (60) all_101_3 = 0
% 10.15/2.11 | | |
% 10.15/2.11 | | | GROUND_INST: instantiating (3) with all_43_2, all_101_2, all_43_5,
% 10.15/2.11 | | | simplifying with (13), (58) gives:
% 10.15/2.11 | | | (61) all_101_2 = all_43_2
% 10.15/2.11 | | |
% 10.15/2.11 | | | REDUCE: (56), (61) imply:
% 10.15/2.11 | | | (62) in(all_88_1, all_43_2) = all_101_1
% 10.15/2.11 | | |
% 10.15/2.11 | | | BETA: splitting (59) gives:
% 10.15/2.11 | | |
% 10.15/2.11 | | | Case 1:
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | (63) ~ (all_101_3 = 0)
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | REDUCE: (60), (63) imply:
% 10.15/2.11 | | | | (64) $false
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | CLOSE: (64) is inconsistent.
% 10.15/2.11 | | | |
% 10.15/2.11 | | | Case 2:
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | (65) all_101_0 = 0 & all_101_1 = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | ALPHA: (65) implies:
% 10.15/2.11 | | | | (66) all_101_1 = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | REDUCE: (62), (66) imply:
% 10.15/2.11 | | | | (67) in(all_88_1, all_43_2) = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | GROUND_INST: instantiating (4) with all_88_0, 0, all_43_2, all_88_1,
% 10.15/2.11 | | | | simplifying with (53), (67) gives:
% 10.15/2.11 | | | | (68) all_88_0 = 0
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | REDUCE: (50), (68) imply:
% 10.15/2.11 | | | | (69) $false
% 10.15/2.11 | | | |
% 10.15/2.11 | | | | CLOSE: (69) is inconsistent.
% 10.15/2.11 | | | |
% 10.15/2.11 | | | End of split
% 10.15/2.11 | | |
% 10.15/2.11 | | End of split
% 10.15/2.11 | |
% 10.15/2.11 | End of split
% 10.15/2.11 |
% 10.15/2.11 End of proof
% 10.15/2.11 % SZS output end Proof for theBenchmark
% 10.15/2.11
% 10.15/2.11 1522ms
%------------------------------------------------------------------------------