TSTP Solution File: SEU177+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU177+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 : n001.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 17:43:04 EDT 2023
% Result : Theorem 7.79s 1.88s
% Output : Proof 8.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU177+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 : n001.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 15:42:54 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.08/1.04 Prover 1: Preprocessing ...
% 2.08/1.04 Prover 4: Preprocessing ...
% 2.70/1.08 Prover 2: Preprocessing ...
% 2.70/1.08 Prover 5: Preprocessing ...
% 2.70/1.08 Prover 3: Preprocessing ...
% 2.70/1.08 Prover 6: Preprocessing ...
% 2.70/1.08 Prover 0: Preprocessing ...
% 4.61/1.47 Prover 1: Warning: ignoring some quantifiers
% 5.56/1.52 Prover 4: Warning: ignoring some quantifiers
% 5.56/1.52 Prover 3: Warning: ignoring some quantifiers
% 5.66/1.54 Prover 4: Constructing countermodel ...
% 5.66/1.55 Prover 1: Constructing countermodel ...
% 5.66/1.55 Prover 3: Constructing countermodel ...
% 5.66/1.55 Prover 5: Proving ...
% 5.66/1.55 Prover 6: Proving ...
% 5.66/1.56 Prover 2: Proving ...
% 6.20/1.61 Prover 0: Proving ...
% 7.79/1.87 Prover 2: proved (1253ms)
% 7.79/1.88
% 7.79/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.79/1.88
% 7.79/1.88 Prover 3: stopped
% 7.79/1.88 Prover 0: stopped
% 7.79/1.89 Prover 5: stopped
% 7.79/1.90 Prover 6: stopped
% 8.35/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.35/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.35/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.35/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.35/1.91 Prover 7: Preprocessing ...
% 8.35/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.35/1.92 Prover 8: Preprocessing ...
% 8.35/1.92 Prover 10: Preprocessing ...
% 8.35/1.92 Prover 11: Preprocessing ...
% 8.35/1.94 Prover 13: Preprocessing ...
% 8.35/1.95 Prover 1: Found proof (size 43)
% 8.35/1.95 Prover 1: proved (1331ms)
% 8.35/1.96 Prover 10: stopped
% 8.35/1.96 Prover 4: stopped
% 8.35/1.97 Prover 13: stopped
% 8.85/1.98 Prover 11: stopped
% 8.85/1.99 Prover 7: Warning: ignoring some quantifiers
% 8.85/2.00 Prover 7: Constructing countermodel ...
% 8.85/2.00 Prover 7: stopped
% 8.85/2.01 Prover 8: Warning: ignoring some quantifiers
% 8.85/2.02 Prover 8: Constructing countermodel ...
% 8.85/2.02 Prover 8: stopped
% 8.85/2.02
% 8.85/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.85/2.02
% 8.85/2.03 % SZS output start Proof for theBenchmark
% 8.85/2.03 Assumptions after simplification:
% 8.85/2.03 ---------------------------------
% 8.85/2.03
% 8.85/2.03 (d4_relat_1)
% 8.85/2.06 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 8.85/2.06 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 8.85/2.06 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 8.85/2.06 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 8.85/2.06 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 8.85/2.06 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 8.85/2.06 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 8.85/2.06 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 8.85/2.06 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 8.85/2.06 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 8.85/2.06 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 8.85/2.06 $i(v3)))))))
% 8.85/2.06
% 8.85/2.06 (d5_relat_1)
% 8.85/2.07 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 8.85/2.07 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 8.85/2.07 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 8.85/2.07 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) =
% 8.85/2.07 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 8.85/2.07 : ? [v6: $i] : (ordered_pair(v5, v3) = v6 & in(v6, v0) = 0 & $i(v6)
% 8.85/2.07 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 8.85/2.07 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 8.85/2.07 (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 8.85/2.07 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 8.85/2.07 $i] : (ordered_pair(v3, v2) = v4 & in(v4, v0) = 0 & $i(v4) &
% 8.85/2.07 $i(v3)))))))
% 8.85/2.07
% 8.85/2.07 (t20_relat_1)
% 8.85/2.07 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 8.85/2.07 any] : ? [v6: $i] : ? [v7: any] : (relation_rng(v2) = v6 &
% 8.85/2.07 relation_dom(v2) = v4 & ordered_pair(v0, v1) = v3 & in(v3, v2) = 0 & in(v1,
% 8.85/2.07 v6) = v7 & in(v0, v4) = v5 & relation(v2) = 0 & $i(v6) & $i(v4) & $i(v3) &
% 8.85/2.07 $i(v2) & $i(v1) & $i(v0) & ( ~ (v7 = 0) | ~ (v5 = 0)))
% 8.85/2.07
% 8.85/2.07 (function-axioms)
% 8.85/2.08 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.85/2.08 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0:
% 8.85/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.85/2.08 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 8.85/2.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 8.85/2.08 : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0:
% 8.85/2.08 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 8.85/2.08 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 8.85/2.08 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~
% 8.85/2.08 (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 8.85/2.08 v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0: $i]
% 8.85/2.08 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 8.85/2.08 (singleton(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.85/2.08 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 8.85/2.08 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 8.85/2.08 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 8.85/2.08 (empty(v2) = v0))
% 8.85/2.08
% 8.85/2.08 Further assumptions not needed in the proof:
% 8.85/2.08 --------------------------------------------
% 8.85/2.08 antisymmetry_r2_hidden, commutativity_k2_tarski, d5_tarski, dt_k1_relat_1,
% 8.85/2.08 dt_k1_tarski, dt_k1_xboole_0, dt_k2_relat_1, dt_k2_tarski, dt_k4_tarski,
% 8.85/2.08 dt_m1_subset_1, existence_m1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1,
% 8.85/2.08 fc3_subset_1, rc1_relat_1, rc1_xboole_0, rc2_xboole_0, t1_subset, t2_subset,
% 8.85/2.08 t6_boole, t7_boole, t8_boole
% 8.85/2.08
% 8.85/2.08 Those formulas are unsatisfiable:
% 8.85/2.08 ---------------------------------
% 8.85/2.08
% 8.85/2.08 Begin of proof
% 8.85/2.08 |
% 8.85/2.08 | ALPHA: (function-axioms) implies:
% 8.85/2.08 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 8.85/2.08 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 8.85/2.08 |
% 8.85/2.08 | DELTA: instantiating (t20_relat_1) with fresh symbols all_24_0, all_24_1,
% 8.85/2.08 | all_24_2, all_24_3, all_24_4, all_24_5, all_24_6, all_24_7 gives:
% 8.85/2.08 | (2) relation_rng(all_24_5) = all_24_1 & relation_dom(all_24_5) = all_24_3 &
% 8.85/2.08 | ordered_pair(all_24_7, all_24_6) = all_24_4 & in(all_24_4, all_24_5) =
% 8.85/2.08 | 0 & in(all_24_6, all_24_1) = all_24_0 & in(all_24_7, all_24_3) =
% 8.85/2.08 | all_24_2 & relation(all_24_5) = 0 & $i(all_24_1) & $i(all_24_3) &
% 8.85/2.08 | $i(all_24_4) & $i(all_24_5) & $i(all_24_6) & $i(all_24_7) & ( ~
% 8.85/2.08 | (all_24_0 = 0) | ~ (all_24_2 = 0))
% 8.85/2.08 |
% 8.85/2.08 | ALPHA: (2) implies:
% 8.85/2.08 | (3) $i(all_24_7)
% 8.85/2.09 | (4) $i(all_24_6)
% 8.85/2.09 | (5) $i(all_24_5)
% 8.85/2.09 | (6) $i(all_24_3)
% 8.85/2.09 | (7) $i(all_24_1)
% 8.85/2.09 | (8) relation(all_24_5) = 0
% 8.85/2.09 | (9) in(all_24_7, all_24_3) = all_24_2
% 8.85/2.09 | (10) in(all_24_6, all_24_1) = all_24_0
% 8.85/2.09 | (11) in(all_24_4, all_24_5) = 0
% 8.85/2.09 | (12) ordered_pair(all_24_7, all_24_6) = all_24_4
% 8.85/2.09 | (13) relation_dom(all_24_5) = all_24_3
% 8.85/2.09 | (14) relation_rng(all_24_5) = all_24_1
% 8.85/2.09 | (15) ~ (all_24_0 = 0) | ~ (all_24_2 = 0)
% 8.85/2.09 |
% 8.85/2.09 | GROUND_INST: instantiating (d4_relat_1) with all_24_5, all_24_3, simplifying
% 8.85/2.09 | with (5), (13) gives:
% 8.85/2.09 | (16) ? [v0: int] : ( ~ (v0 = 0) & relation(all_24_5) = v0) | ( ? [v0: any]
% 8.85/2.09 | : (v0 = all_24_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 8.85/2.09 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 8.85/2.09 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_24_5) = 0) |
% 8.85/2.09 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 8.85/2.09 | (ordered_pair(v1, v3) = v4 & in(v4, all_24_5) = 0 & $i(v4) &
% 8.85/2.09 | $i(v3))))) & ( ~ $i(all_24_3) | ( ! [v0: $i] : ! [v1: int]
% 8.85/2.09 | : (v1 = 0 | ~ (in(v0, all_24_3) = v1) | ~ $i(v0) | ! [v2: $i]
% 8.85/2.09 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 8.85/2.09 | all_24_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 8.85/2.09 | all_24_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 8.85/2.09 | (ordered_pair(v0, v1) = v2 & in(v2, all_24_5) = 0 & $i(v2) &
% 8.85/2.09 | $i(v1))))))
% 8.85/2.09 |
% 8.85/2.09 | GROUND_INST: instantiating (d5_relat_1) with all_24_5, all_24_1, simplifying
% 8.85/2.09 | with (5), (14) gives:
% 8.85/2.10 | (17) ? [v0: int] : ( ~ (v0 = 0) & relation(all_24_5) = v0) | ( ? [v0: any]
% 8.85/2.10 | : (v0 = all_24_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 8.85/2.10 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 8.85/2.10 | ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4, all_24_5) = 0) |
% 8.85/2.10 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 8.85/2.10 | (ordered_pair(v3, v1) = v4 & in(v4, all_24_5) = 0 & $i(v4) &
% 8.85/2.10 | $i(v3))))) & ( ~ $i(all_24_1) | ( ! [v0: $i] : ! [v1: int]
% 8.85/2.10 | : (v1 = 0 | ~ (in(v0, all_24_1) = v1) | ~ $i(v0) | ! [v2: $i]
% 8.85/2.10 | : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3,
% 8.85/2.10 | all_24_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 8.85/2.10 | all_24_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 8.85/2.10 | (ordered_pair(v1, v0) = v2 & in(v2, all_24_5) = 0 & $i(v2) &
% 8.85/2.10 | $i(v1))))))
% 8.85/2.10 |
% 8.85/2.10 | BETA: splitting (17) gives:
% 8.85/2.10 |
% 8.85/2.10 | Case 1:
% 8.85/2.10 | |
% 8.85/2.10 | | (18) ? [v0: int] : ( ~ (v0 = 0) & relation(all_24_5) = v0)
% 8.85/2.10 | |
% 8.85/2.10 | | DELTA: instantiating (18) with fresh symbol all_42_0 gives:
% 8.85/2.10 | | (19) ~ (all_42_0 = 0) & relation(all_24_5) = all_42_0
% 8.85/2.10 | |
% 8.85/2.10 | | ALPHA: (19) implies:
% 8.85/2.10 | | (20) ~ (all_42_0 = 0)
% 8.85/2.10 | | (21) relation(all_24_5) = all_42_0
% 8.85/2.10 | |
% 8.85/2.10 | | GROUND_INST: instantiating (1) with 0, all_42_0, all_24_5, simplifying with
% 8.85/2.10 | | (8), (21) gives:
% 8.85/2.10 | | (22) all_42_0 = 0
% 8.85/2.10 | |
% 8.85/2.10 | | REDUCE: (20), (22) imply:
% 8.85/2.10 | | (23) $false
% 8.85/2.10 | |
% 8.85/2.10 | | CLOSE: (23) is inconsistent.
% 8.85/2.10 | |
% 8.85/2.10 | Case 2:
% 8.85/2.10 | |
% 8.85/2.10 | | (24) ? [v0: any] : (v0 = all_24_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 8.85/2.10 | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] :
% 8.85/2.10 | | ! [v4: $i] : ( ~ (ordered_pair(v3, v1) = v4) | ~ (in(v4,
% 8.85/2.10 | | all_24_5) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 8.85/2.10 | | ? [v4: $i] : (ordered_pair(v3, v1) = v4 & in(v4, all_24_5) = 0
% 8.85/2.10 | | & $i(v4) & $i(v3))))) & ( ~ $i(all_24_1) | ( ! [v0: $i] : !
% 8.85/2.10 | | [v1: int] : (v1 = 0 | ~ (in(v0, all_24_1) = v1) | ~ $i(v0) |
% 8.85/2.10 | | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3) |
% 8.85/2.10 | | ~ (in(v3, all_24_5) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~
% 8.85/2.10 | | (in(v0, all_24_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i]
% 8.85/2.10 | | : (ordered_pair(v1, v0) = v2 & in(v2, all_24_5) = 0 & $i(v2) &
% 8.85/2.10 | | $i(v1)))))
% 8.85/2.10 | |
% 8.85/2.10 | | ALPHA: (24) implies:
% 8.85/2.11 | | (25) ~ $i(all_24_1) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0,
% 8.85/2.11 | | all_24_1) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : (
% 8.85/2.11 | | ~ (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_24_5) = 0) | ~
% 8.85/2.11 | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_24_1) = 0) | ~
% 8.85/2.11 | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) = v2
% 8.85/2.11 | | & in(v2, all_24_5) = 0 & $i(v2) & $i(v1))))
% 8.85/2.11 | |
% 8.85/2.11 | | BETA: splitting (16) gives:
% 8.85/2.11 | |
% 8.85/2.11 | | Case 1:
% 8.85/2.11 | | |
% 8.85/2.11 | | | (26) ? [v0: int] : ( ~ (v0 = 0) & relation(all_24_5) = v0)
% 8.85/2.11 | | |
% 8.85/2.11 | | | DELTA: instantiating (26) with fresh symbol all_42_0 gives:
% 8.85/2.11 | | | (27) ~ (all_42_0 = 0) & relation(all_24_5) = all_42_0
% 8.85/2.11 | | |
% 8.85/2.11 | | | ALPHA: (27) implies:
% 8.85/2.11 | | | (28) ~ (all_42_0 = 0)
% 8.85/2.11 | | | (29) relation(all_24_5) = all_42_0
% 8.85/2.11 | | |
% 8.85/2.11 | | | GROUND_INST: instantiating (1) with 0, all_42_0, all_24_5, simplifying
% 8.85/2.11 | | | with (8), (29) gives:
% 8.85/2.11 | | | (30) all_42_0 = 0
% 8.85/2.11 | | |
% 8.85/2.11 | | | REDUCE: (28), (30) imply:
% 8.85/2.11 | | | (31) $false
% 8.85/2.11 | | |
% 8.85/2.11 | | | CLOSE: (31) is inconsistent.
% 8.85/2.11 | | |
% 8.85/2.11 | | Case 2:
% 8.85/2.11 | | |
% 8.85/2.11 | | | (32) ? [v0: any] : (v0 = all_24_3 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 8.85/2.11 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 8.85/2.11 | | | : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 8.85/2.11 | | | all_24_5) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 8.85/2.11 | | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_24_5)
% 8.85/2.11 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_24_3) | ( ! [v0:
% 8.85/2.11 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_24_3) = v1) |
% 8.85/2.11 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0,
% 8.85/2.11 | | | v2) = v3) | ~ (in(v3, all_24_5) = 0) | ~ $i(v2))) &
% 8.85/2.11 | | | ! [v0: $i] : ( ~ (in(v0, all_24_3) = 0) | ~ $i(v0) | ? [v1:
% 8.85/2.11 | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 8.85/2.11 | | | all_24_5) = 0 & $i(v2) & $i(v1)))))
% 8.85/2.11 | | |
% 8.85/2.11 | | | ALPHA: (32) implies:
% 8.85/2.11 | | | (33) ~ $i(all_24_3) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 8.85/2.11 | | | (in(v0, all_24_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 8.85/2.11 | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_24_5)
% 8.85/2.11 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_24_3) =
% 8.85/2.11 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 8.85/2.11 | | | (ordered_pair(v0, v1) = v2 & in(v2, all_24_5) = 0 & $i(v2) &
% 8.85/2.11 | | | $i(v1))))
% 8.85/2.11 | | |
% 8.85/2.11 | | | BETA: splitting (25) gives:
% 8.85/2.11 | | |
% 8.85/2.11 | | | Case 1:
% 8.85/2.11 | | | |
% 8.85/2.11 | | | | (34) ~ $i(all_24_1)
% 8.85/2.11 | | | |
% 8.85/2.11 | | | | PRED_UNIFY: (7), (34) imply:
% 8.85/2.11 | | | | (35) $false
% 8.85/2.11 | | | |
% 8.85/2.11 | | | | CLOSE: (35) is inconsistent.
% 8.85/2.11 | | | |
% 8.85/2.11 | | | Case 2:
% 8.85/2.11 | | | |
% 8.85/2.12 | | | | (36) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_24_1) =
% 8.85/2.12 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 8.85/2.12 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_24_5) = 0) | ~
% 8.85/2.12 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_24_1) = 0) | ~
% 8.85/2.12 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v1, v0) =
% 8.85/2.12 | | | | v2 & in(v2, all_24_5) = 0 & $i(v2) & $i(v1)))
% 8.85/2.12 | | | |
% 8.85/2.12 | | | | ALPHA: (36) implies:
% 8.85/2.12 | | | | (37) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_24_1) =
% 8.85/2.12 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 8.85/2.12 | | | | (ordered_pair(v2, v0) = v3) | ~ (in(v3, all_24_5) = 0) | ~
% 8.85/2.12 | | | | $i(v2)))
% 8.85/2.12 | | | |
% 8.85/2.12 | | | | GROUND_INST: instantiating (37) with all_24_6, all_24_0, simplifying
% 8.85/2.12 | | | | with (4), (10) gives:
% 8.85/2.12 | | | | (38) all_24_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 8.85/2.12 | | | | all_24_6) = v1) | ~ (in(v1, all_24_5) = 0) | ~ $i(v0))
% 8.85/2.12 | | | |
% 8.85/2.12 | | | | BETA: splitting (33) gives:
% 8.85/2.12 | | | |
% 8.85/2.12 | | | | Case 1:
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | | (39) ~ $i(all_24_3)
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | | PRED_UNIFY: (6), (39) imply:
% 8.85/2.12 | | | | | (40) $false
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | | CLOSE: (40) is inconsistent.
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | Case 2:
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | | (41) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_24_3) =
% 8.85/2.12 | | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 8.85/2.12 | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_24_5) = 0) |
% 8.85/2.12 | | | | | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_24_3) = 0) | ~
% 8.85/2.12 | | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 8.85/2.12 | | | | | v2 & in(v2, all_24_5) = 0 & $i(v2) & $i(v1)))
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | | ALPHA: (41) implies:
% 8.85/2.12 | | | | | (42) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_24_3) =
% 8.85/2.12 | | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 8.85/2.12 | | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_24_5) = 0) |
% 8.85/2.12 | | | | | ~ $i(v2)))
% 8.85/2.12 | | | | |
% 8.85/2.12 | | | | | GROUND_INST: instantiating (42) with all_24_7, all_24_2, simplifying
% 8.85/2.12 | | | | | with (3), (9) gives:
% 8.85/2.12 | | | | | (43) all_24_2 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 8.85/2.12 | | | | | (ordered_pair(all_24_7, v0) = v1) | ~ (in(v1, all_24_5) =
% 8.85/2.12 | | | | | 0) | ~ $i(v0))
% 8.85/2.12 | | | | |
% 8.85/2.13 | | | | | BETA: splitting (15) gives:
% 8.85/2.13 | | | | |
% 8.85/2.13 | | | | | Case 1:
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | | (44) ~ (all_24_0 = 0)
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | | BETA: splitting (38) gives:
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | | Case 1:
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | (45) all_24_0 = 0
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | REDUCE: (44), (45) imply:
% 8.85/2.13 | | | | | | | (46) $false
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | CLOSE: (46) is inconsistent.
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | Case 2:
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | (47) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 8.85/2.13 | | | | | | | all_24_6) = v1) | ~ (in(v1, all_24_5) = 0) | ~
% 8.85/2.13 | | | | | | | $i(v0))
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | GROUND_INST: instantiating (47) with all_24_7, all_24_4,
% 8.85/2.13 | | | | | | | simplifying with (3), (11), (12) gives:
% 8.85/2.13 | | | | | | | (48) $false
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | CLOSE: (48) is inconsistent.
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | End of split
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | Case 2:
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | | (49) ~ (all_24_2 = 0)
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | | BETA: splitting (43) gives:
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | | Case 1:
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | (50) all_24_2 = 0
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | REDUCE: (49), (50) imply:
% 8.85/2.13 | | | | | | | (51) $false
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | CLOSE: (51) is inconsistent.
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | Case 2:
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | (52) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_24_7,
% 8.85/2.13 | | | | | | | v0) = v1) | ~ (in(v1, all_24_5) = 0) | ~ $i(v0))
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | GROUND_INST: instantiating (52) with all_24_6, all_24_4,
% 8.85/2.13 | | | | | | | simplifying with (4), (11), (12) gives:
% 8.85/2.13 | | | | | | | (53) $false
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | | CLOSE: (53) is inconsistent.
% 8.85/2.13 | | | | | | |
% 8.85/2.13 | | | | | | End of split
% 8.85/2.13 | | | | | |
% 8.85/2.13 | | | | | End of split
% 8.85/2.13 | | | | |
% 8.85/2.13 | | | | End of split
% 8.85/2.13 | | | |
% 8.85/2.13 | | | End of split
% 8.85/2.13 | | |
% 8.85/2.13 | | End of split
% 8.85/2.13 | |
% 8.85/2.13 | End of split
% 8.85/2.13 |
% 8.85/2.13 End of proof
% 8.85/2.13 % SZS output end Proof for theBenchmark
% 8.85/2.13
% 8.85/2.13 1529ms
%------------------------------------------------------------------------------