TSTP Solution File: SEU199+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU199+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 : n010.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 17:43:13 EDT 2023
% Result : Theorem 8.55s 1.91s
% Output : Proof 10.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU199+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 13:29:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.60/1.03 Prover 4: Preprocessing ...
% 2.60/1.03 Prover 1: Preprocessing ...
% 2.60/1.07 Prover 3: Preprocessing ...
% 2.60/1.07 Prover 2: Preprocessing ...
% 2.60/1.07 Prover 6: Preprocessing ...
% 2.60/1.07 Prover 5: Preprocessing ...
% 2.60/1.07 Prover 0: Preprocessing ...
% 5.70/1.49 Prover 1: Warning: ignoring some quantifiers
% 5.70/1.52 Prover 4: Warning: ignoring some quantifiers
% 5.70/1.53 Prover 5: Proving ...
% 5.70/1.53 Prover 6: Proving ...
% 5.70/1.54 Prover 1: Constructing countermodel ...
% 5.70/1.55 Prover 3: Warning: ignoring some quantifiers
% 6.19/1.55 Prover 4: Constructing countermodel ...
% 6.19/1.55 Prover 2: Proving ...
% 6.19/1.56 Prover 3: Constructing countermodel ...
% 6.35/1.59 Prover 0: Proving ...
% 8.55/1.91 Prover 3: proved (1256ms)
% 8.55/1.91
% 8.55/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.55/1.91
% 8.55/1.91 Prover 2: stopped
% 8.55/1.92 Prover 6: stopped
% 8.55/1.92 Prover 0: stopped
% 8.91/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.91/1.93 Prover 5: stopped
% 8.91/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.91/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.91/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.91/1.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.91/1.96 Prover 8: Preprocessing ...
% 8.91/1.97 Prover 7: Preprocessing ...
% 8.91/1.99 Prover 10: Preprocessing ...
% 8.91/1.99 Prover 13: Preprocessing ...
% 8.91/2.01 Prover 11: Preprocessing ...
% 8.91/2.02 Prover 1: Found proof (size 46)
% 8.91/2.02 Prover 1: proved (1385ms)
% 8.91/2.03 Prover 4: stopped
% 8.91/2.03 Prover 7: stopped
% 9.33/2.04 Prover 10: stopped
% 9.33/2.06 Prover 13: stopped
% 9.33/2.07 Prover 11: stopped
% 9.33/2.09 Prover 8: Warning: ignoring some quantifiers
% 9.33/2.11 Prover 8: Constructing countermodel ...
% 9.33/2.11 Prover 8: stopped
% 9.33/2.12
% 9.33/2.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.33/2.12
% 10.16/2.12 % SZS output start Proof for theBenchmark
% 10.16/2.13 Assumptions after simplification:
% 10.16/2.13 ---------------------------------
% 10.16/2.13
% 10.16/2.13 (d12_relat_1)
% 10.16/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 10.16/2.16 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 10.16/2.16 relation(v1) = v3) | ! [v3: $i] : ( ~ (relation(v3) = 0) | ~ $i(v3) | ((
% 10.16/2.16 ~ (v3 = v2) | ( ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any]
% 10.16/2.16 : ( ~ (ordered_pair(v4, v5) = v6) | ~ (in(v6, v1) = v7) | ~ $i(v5)
% 10.16/2.16 | ~ $i(v4) | ? [v8: any] : ? [v9: any] : (in(v6, v2) = v8 &
% 10.16/2.16 in(v5, v0) = v9 & ( ~ (v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v4:
% 10.16/2.16 $i] : ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v4, v5) = v6)
% 10.16/2.16 | ~ (in(v6, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ? [v7: any] : ?
% 10.16/2.16 [v8: any] : (in(v6, v2) = v8 & in(v5, v0) = v7 & ( ~ (v7 = 0) | v8
% 10.16/2.16 = 0))))) & (v3 = v2 | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 10.16/2.16 : ? [v7: any] : ? [v8: any] : ? [v9: any] : (ordered_pair(v4, v5) =
% 10.16/2.16 v6 & in(v6, v3) = v7 & in(v6, v1) = v9 & in(v5, v0) = v8 & $i(v6) &
% 10.16/2.16 $i(v5) & $i(v4) & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 =
% 10.16/2.16 0 | (v9 = 0 & v8 = 0)))))))
% 10.16/2.16
% 10.16/2.16 (d3_relat_1)
% 10.16/2.16 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any]
% 10.16/2.16 : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 10.16/2.16 relation(v1) = v3) | (( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.16/2.16 $i] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = 0) | ~
% 10.16/2.16 $i(v4) | ~ $i(v3) | in(v5, v1) = 0)) & (v2 = 0 | ? [v3: $i] : ?
% 10.16/2.16 [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 10.16/2.16 ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v5, v0) = 0 &
% 10.16/2.16 $i(v5) & $i(v4) & $i(v3))))))
% 10.16/2.16
% 10.16/2.16 (dt_k8_relat_1)
% 10.16/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng_restriction(v0,
% 10.16/2.16 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 10.16/2.16 (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 10.16/2.17
% 10.16/2.17 (t117_relat_1)
% 10.16/2.17 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 10.16/2.17 subset(v2, v1) = v3 & relation_rng_restriction(v0, v1) = v2 & relation(v1) =
% 10.16/2.17 0 & $i(v2) & $i(v1) & $i(v0))
% 10.16/2.17
% 10.16/2.17 (function-axioms)
% 10.42/2.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.42/2.18 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 10.42/2.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.42/2.18 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 10.42/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.42/2.18 (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3,
% 10.42/2.18 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 10.42/2.18 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 10.42/2.18 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.42/2.18 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 10.42/2.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.42/2.18 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 10.42/2.18 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 10.42/2.18 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.42/2.18 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: MultipleValueBool]
% 10.42/2.18 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1)
% 10.42/2.18 | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.42/2.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 10.42/2.18 (empty(v2) = v0))
% 10.42/2.18
% 10.42/2.18 Further assumptions not needed in the proof:
% 10.42/2.18 --------------------------------------------
% 10.42/2.18 antisymmetry_r2_hidden, cc1_relat_1, commutativity_k2_tarski, d5_tarski,
% 10.42/2.18 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k4_tarski,
% 10.42/2.18 dt_m1_subset_1, existence_m1_subset_1, fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1,
% 10.42/2.18 fc2_subset_1, fc3_subset_1, fc4_relat_1, rc1_relat_1, rc1_subset_1,
% 10.42/2.18 rc1_xboole_0, rc2_relat_1, rc2_subset_1, rc2_xboole_0, reflexivity_r1_tarski,
% 10.42/2.18 t1_subset, t2_subset, t3_subset, t4_subset, t5_subset, t6_boole, t7_boole,
% 10.42/2.18 t8_boole
% 10.42/2.18
% 10.42/2.18 Those formulas are unsatisfiable:
% 10.42/2.18 ---------------------------------
% 10.42/2.18
% 10.42/2.18 Begin of proof
% 10.42/2.18 |
% 10.42/2.18 | ALPHA: (function-axioms) implies:
% 10.42/2.18 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.42/2.18 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 10.42/2.18 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.42/2.18 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 10.42/2.18 |
% 10.42/2.18 | DELTA: instantiating (t117_relat_1) with fresh symbols all_36_0, all_36_1,
% 10.42/2.18 | all_36_2, all_36_3 gives:
% 10.42/2.18 | (3) ~ (all_36_0 = 0) & subset(all_36_1, all_36_2) = all_36_0 &
% 10.42/2.18 | relation_rng_restriction(all_36_3, all_36_2) = all_36_1 &
% 10.42/2.18 | relation(all_36_2) = 0 & $i(all_36_1) & $i(all_36_2) & $i(all_36_3)
% 10.42/2.18 |
% 10.42/2.18 | ALPHA: (3) implies:
% 10.42/2.18 | (4) ~ (all_36_0 = 0)
% 10.42/2.18 | (5) $i(all_36_3)
% 10.42/2.18 | (6) $i(all_36_2)
% 10.42/2.19 | (7) $i(all_36_1)
% 10.42/2.19 | (8) relation(all_36_2) = 0
% 10.42/2.19 | (9) relation_rng_restriction(all_36_3, all_36_2) = all_36_1
% 10.42/2.19 | (10) subset(all_36_1, all_36_2) = all_36_0
% 10.42/2.19 |
% 10.42/2.19 | GROUND_INST: instantiating (dt_k8_relat_1) with all_36_3, all_36_2, all_36_1,
% 10.42/2.19 | simplifying with (5), (6), (9) gives:
% 10.42/2.19 | (11) ? [v0: any] : ? [v1: any] : (relation(all_36_1) = v1 &
% 10.42/2.19 | relation(all_36_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 10.42/2.19 |
% 10.42/2.19 | GROUND_INST: instantiating (d12_relat_1) with all_36_3, all_36_2, all_36_1,
% 10.42/2.19 | simplifying with (5), (6), (9) gives:
% 10.42/2.19 | (12) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0) | ! [v0: $i] :
% 10.42/2.19 | ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 = all_36_1) | ( ! [v1:
% 10.42/2.19 | $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 10.42/2.19 | (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_36_2) = v4) |
% 10.42/2.19 | ~ $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: any] : (in(v3,
% 10.42/2.19 | all_36_1) = v5 & in(v2, all_36_3) = v6 & ( ~ (v5 = 0) |
% 10.42/2.19 | (v6 = 0 & v4 = 0)))) & ! [v1: $i] : ! [v2: $i] : !
% 10.42/2.19 | [v3: $i] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3,
% 10.42/2.19 | all_36_2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v4: any] :
% 10.42/2.19 | ? [v5: any] : (in(v3, all_36_1) = v5 & in(v2, all_36_3) = v4
% 10.42/2.19 | & ( ~ (v4 = 0) | v5 = 0))))) & (v0 = all_36_1 | ? [v1:
% 10.42/2.19 | $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: any]
% 10.42/2.19 | : ? [v6: any] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 &
% 10.42/2.19 | in(v3, all_36_2) = v6 & in(v2, all_36_3) = v5 & $i(v3) &
% 10.42/2.19 | $i(v2) & $i(v1) & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0)) &
% 10.42/2.19 | (v4 = 0 | (v6 = 0 & v5 = 0))))))
% 10.42/2.19 |
% 10.42/2.19 | DELTA: instantiating (11) with fresh symbols all_48_0, all_48_1 gives:
% 10.42/2.19 | (13) relation(all_36_1) = all_48_0 & relation(all_36_2) = all_48_1 & ( ~
% 10.42/2.19 | (all_48_1 = 0) | all_48_0 = 0)
% 10.42/2.19 |
% 10.42/2.19 | ALPHA: (13) implies:
% 10.42/2.19 | (14) relation(all_36_2) = all_48_1
% 10.42/2.19 | (15) relation(all_36_1) = all_48_0
% 10.42/2.19 | (16) ~ (all_48_1 = 0) | all_48_0 = 0
% 10.42/2.19 |
% 10.42/2.20 | GROUND_INST: instantiating (1) with 0, all_48_1, all_36_2, simplifying with
% 10.42/2.20 | (8), (14) gives:
% 10.42/2.20 | (17) all_48_1 = 0
% 10.42/2.20 |
% 10.42/2.20 | BETA: splitting (16) gives:
% 10.42/2.20 |
% 10.42/2.20 | Case 1:
% 10.42/2.20 | |
% 10.42/2.20 | | (18) ~ (all_48_1 = 0)
% 10.42/2.20 | |
% 10.42/2.20 | | REDUCE: (17), (18) imply:
% 10.42/2.20 | | (19) $false
% 10.42/2.20 | |
% 10.42/2.20 | | CLOSE: (19) is inconsistent.
% 10.42/2.20 | |
% 10.42/2.20 | Case 2:
% 10.42/2.20 | |
% 10.42/2.20 | | (20) all_48_0 = 0
% 10.42/2.20 | |
% 10.42/2.20 | | REDUCE: (15), (20) imply:
% 10.42/2.20 | | (21) relation(all_36_1) = 0
% 10.42/2.20 | |
% 10.42/2.20 | | BETA: splitting (12) gives:
% 10.42/2.20 | |
% 10.42/2.20 | | Case 1:
% 10.42/2.20 | | |
% 10.42/2.20 | | | (22) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0)
% 10.42/2.20 | | |
% 10.42/2.20 | | | DELTA: instantiating (22) with fresh symbol all_60_0 gives:
% 10.42/2.20 | | | (23) ~ (all_60_0 = 0) & relation(all_36_2) = all_60_0
% 10.42/2.20 | | |
% 10.42/2.20 | | | REF_CLOSE: (1), (8), (23) are inconsistent by sub-proof #1.
% 10.42/2.20 | | |
% 10.42/2.20 | | Case 2:
% 10.42/2.20 | | |
% 10.42/2.20 | | | (24) ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | (( ~ (v0 =
% 10.42/2.20 | | | all_36_1) | ( ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 10.42/2.20 | | | [v4: any] : ( ~ (ordered_pair(v1, v2) = v3) | ~ (in(v3,
% 10.42/2.20 | | | all_36_2) = v4) | ~ $i(v2) | ~ $i(v1) | ? [v5:
% 10.42/2.20 | | | any] : ? [v6: any] : (in(v3, all_36_1) = v5 & in(v2,
% 10.42/2.20 | | | all_36_3) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 10.42/2.20 | | | & ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 10.42/2.20 | | | (ordered_pair(v1, v2) = v3) | ~ (in(v3, all_36_2) = 0)
% 10.42/2.20 | | | | ~ $i(v2) | ~ $i(v1) | ? [v4: any] : ? [v5: any] :
% 10.42/2.20 | | | (in(v3, all_36_1) = v5 & in(v2, all_36_3) = v4 & ( ~ (v4
% 10.42/2.20 | | | = 0) | v5 = 0))))) & (v0 = all_36_1 | ? [v1: $i]
% 10.42/2.20 | | | : ? [v2: $i] : ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 10.42/2.20 | | | ? [v6: any] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = v4 &
% 10.42/2.20 | | | in(v3, all_36_2) = v6 & in(v2, all_36_3) = v5 & $i(v3) &
% 10.42/2.20 | | | $i(v2) & $i(v1) & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 =
% 10.42/2.20 | | | 0)) & (v4 = 0 | (v6 = 0 & v5 = 0))))))
% 10.42/2.20 | | |
% 10.42/2.20 | | | GROUND_INST: instantiating (d3_relat_1) with all_36_1, simplifying with
% 10.42/2.20 | | | (7), (21) gives:
% 10.42/2.20 | | | (25) ! [v0: $i] : ! [v1: any] : ( ~ (subset(all_36_1, v0) = v1) | ~
% 10.42/2.20 | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & relation(v0) = v2) | (( ~
% 10.42/2.20 | | | (v1 = 0) | ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 10.42/2.20 | | | (ordered_pair(v2, v3) = v4) | ~ (in(v4, all_36_1) = 0) |
% 10.42/2.20 | | | ~ $i(v3) | ~ $i(v2) | in(v4, v0) = 0)) & (v1 = 0 | ?
% 10.42/2.20 | | | [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ( ~
% 10.42/2.20 | | | (v5 = 0) & ordered_pair(v2, v3) = v4 & in(v4, v0) = v5 &
% 10.42/2.20 | | | in(v4, all_36_1) = 0 & $i(v4) & $i(v3) & $i(v2)))))
% 10.42/2.21 | | |
% 10.42/2.21 | | | GROUND_INST: instantiating (24) with all_36_1, simplifying with (7), (21)
% 10.42/2.21 | | | gives:
% 10.42/2.21 | | | (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.42/2.21 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) = v3) | ~
% 10.42/2.21 | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v2,
% 10.42/2.21 | | | all_36_1) = v4 & in(v1, all_36_3) = v5 & ( ~ (v4 = 0) | (v5
% 10.42/2.21 | | | = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 10.42/2.21 | | | : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) = 0) | ~
% 10.42/2.21 | | | $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (in(v2,
% 10.42/2.21 | | | all_36_1) = v4 & in(v1, all_36_3) = v3 & ( ~ (v3 = 0) | v4 =
% 10.42/2.21 | | | 0)))
% 10.42/2.21 | | |
% 10.42/2.21 | | | ALPHA: (26) implies:
% 10.42/2.21 | | | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 10.42/2.21 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_2) = v3) | ~
% 10.42/2.21 | | | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v2,
% 10.42/2.21 | | | all_36_1) = v4 & in(v1, all_36_3) = v5 & ( ~ (v4 = 0) | (v5
% 10.42/2.21 | | | = 0 & v3 = 0))))
% 10.42/2.21 | | |
% 10.42/2.21 | | | GROUND_INST: instantiating (25) with all_36_2, all_36_0, simplifying with
% 10.42/2.21 | | | (6), (10) gives:
% 10.42/2.21 | | | (28) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0) | (( ~
% 10.42/2.21 | | | (all_36_0 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 10.42/2.21 | | | (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_1) = 0) | ~
% 10.42/2.21 | | | $i(v1) | ~ $i(v0) | in(v2, all_36_2) = 0)) & (all_36_0 = 0
% 10.42/2.21 | | | | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~
% 10.42/2.21 | | | (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_36_1) = 0
% 10.42/2.21 | | | & in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & $i(v0))))
% 10.42/2.21 | | |
% 10.42/2.21 | | | BETA: splitting (28) gives:
% 10.42/2.21 | | |
% 10.42/2.21 | | | Case 1:
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | (29) ? [v0: int] : ( ~ (v0 = 0) & relation(all_36_2) = v0)
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | DELTA: instantiating (29) with fresh symbol all_60_0 gives:
% 10.42/2.21 | | | | (30) ~ (all_60_0 = 0) & relation(all_36_2) = all_60_0
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | REF_CLOSE: (1), (8), (30) are inconsistent by sub-proof #1.
% 10.42/2.21 | | | |
% 10.42/2.21 | | | Case 2:
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | (31) ( ~ (all_36_0 = 0) | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 10.42/2.21 | | | | ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_36_1) = 0) |
% 10.42/2.21 | | | | ~ $i(v1) | ~ $i(v0) | in(v2, all_36_2) = 0)) & (all_36_0 =
% 10.42/2.21 | | | | 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : (
% 10.42/2.21 | | | | ~ (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_36_1) =
% 10.42/2.21 | | | | 0 & in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & $i(v0)))
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | ALPHA: (31) implies:
% 10.42/2.21 | | | | (32) all_36_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 10.42/2.21 | | | | int] : ( ~ (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2,
% 10.42/2.21 | | | | all_36_1) = 0 & in(v2, all_36_2) = v3 & $i(v2) & $i(v1) &
% 10.42/2.21 | | | | $i(v0))
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | BETA: splitting (32) gives:
% 10.42/2.21 | | | |
% 10.42/2.21 | | | | Case 1:
% 10.42/2.21 | | | | |
% 10.42/2.21 | | | | | (33) all_36_0 = 0
% 10.42/2.21 | | | | |
% 10.42/2.21 | | | | | REDUCE: (4), (33) imply:
% 10.42/2.21 | | | | | (34) $false
% 10.42/2.21 | | | | |
% 10.42/2.21 | | | | | CLOSE: (34) is inconsistent.
% 10.42/2.21 | | | | |
% 10.42/2.21 | | | | Case 2:
% 10.42/2.21 | | | | |
% 10.42/2.22 | | | | | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~
% 10.42/2.22 | | | | | (v3 = 0) & ordered_pair(v0, v1) = v2 & in(v2, all_36_1) = 0
% 10.42/2.22 | | | | | & in(v2, all_36_2) = v3 & $i(v2) & $i(v1) & $i(v0))
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | DELTA: instantiating (35) with fresh symbols all_72_0, all_72_1,
% 10.42/2.22 | | | | | all_72_2, all_72_3 gives:
% 10.42/2.22 | | | | | (36) ~ (all_72_0 = 0) & ordered_pair(all_72_3, all_72_2) =
% 10.42/2.22 | | | | | all_72_1 & in(all_72_1, all_36_1) = 0 & in(all_72_1, all_36_2)
% 10.42/2.22 | | | | | = all_72_0 & $i(all_72_1) & $i(all_72_2) & $i(all_72_3)
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | ALPHA: (36) implies:
% 10.42/2.22 | | | | | (37) ~ (all_72_0 = 0)
% 10.42/2.22 | | | | | (38) $i(all_72_3)
% 10.42/2.22 | | | | | (39) $i(all_72_2)
% 10.42/2.22 | | | | | (40) in(all_72_1, all_36_2) = all_72_0
% 10.42/2.22 | | | | | (41) in(all_72_1, all_36_1) = 0
% 10.42/2.22 | | | | | (42) ordered_pair(all_72_3, all_72_2) = all_72_1
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | GROUND_INST: instantiating (27) with all_72_3, all_72_2, all_72_1,
% 10.42/2.22 | | | | | all_72_0, simplifying with (38), (39), (40), (42) gives:
% 10.42/2.22 | | | | | (43) ? [v0: any] : ? [v1: any] : (in(all_72_1, all_36_1) = v0 &
% 10.42/2.22 | | | | | in(all_72_2, all_36_3) = v1 & ( ~ (v0 = 0) | (v1 = 0 &
% 10.42/2.22 | | | | | all_72_0 = 0)))
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | DELTA: instantiating (43) with fresh symbols all_85_0, all_85_1 gives:
% 10.42/2.22 | | | | | (44) in(all_72_1, all_36_1) = all_85_1 & in(all_72_2, all_36_3) =
% 10.42/2.22 | | | | | all_85_0 & ( ~ (all_85_1 = 0) | (all_85_0 = 0 & all_72_0 = 0))
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | ALPHA: (44) implies:
% 10.42/2.22 | | | | | (45) in(all_72_1, all_36_1) = all_85_1
% 10.42/2.22 | | | | | (46) ~ (all_85_1 = 0) | (all_85_0 = 0 & all_72_0 = 0)
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | BETA: splitting (46) gives:
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | | Case 1:
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | (47) ~ (all_85_1 = 0)
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | GROUND_INST: instantiating (2) with 0, all_85_1, all_36_1, all_72_1,
% 10.42/2.22 | | | | | | simplifying with (41), (45) gives:
% 10.42/2.22 | | | | | | (48) all_85_1 = 0
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | REDUCE: (47), (48) imply:
% 10.42/2.22 | | | | | | (49) $false
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | CLOSE: (49) is inconsistent.
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | Case 2:
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | (50) all_85_0 = 0 & all_72_0 = 0
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | ALPHA: (50) implies:
% 10.42/2.22 | | | | | | (51) all_72_0 = 0
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | REDUCE: (37), (51) imply:
% 10.42/2.22 | | | | | | (52) $false
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | | CLOSE: (52) is inconsistent.
% 10.42/2.22 | | | | | |
% 10.42/2.22 | | | | | End of split
% 10.42/2.22 | | | | |
% 10.42/2.22 | | | | End of split
% 10.42/2.22 | | | |
% 10.42/2.22 | | | End of split
% 10.42/2.22 | | |
% 10.42/2.22 | | End of split
% 10.42/2.22 | |
% 10.42/2.22 | End of split
% 10.42/2.22 |
% 10.42/2.22 End of proof
% 10.42/2.22
% 10.42/2.22 Sub-proof #1 shows that the following formulas are inconsistent:
% 10.42/2.22 ----------------------------------------------------------------
% 10.42/2.22 (1) ~ (all_60_0 = 0) & relation(all_36_2) = all_60_0
% 10.42/2.22 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.42/2.22 (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 10.42/2.22 (3) relation(all_36_2) = 0
% 10.42/2.22
% 10.42/2.22 Begin of proof
% 10.42/2.22 |
% 10.42/2.22 | ALPHA: (1) implies:
% 10.42/2.22 | (4) ~ (all_60_0 = 0)
% 10.42/2.22 | (5) relation(all_36_2) = all_60_0
% 10.42/2.22 |
% 10.42/2.22 | GROUND_INST: instantiating (2) with 0, all_60_0, all_36_2, simplifying with
% 10.42/2.22 | (3), (5) gives:
% 10.42/2.22 | (6) all_60_0 = 0
% 10.42/2.22 |
% 10.42/2.22 | REDUCE: (4), (6) imply:
% 10.42/2.22 | (7) $false
% 10.42/2.22 |
% 10.42/2.22 | CLOSE: (7) is inconsistent.
% 10.42/2.22 |
% 10.42/2.22 End of proof
% 10.42/2.22 % SZS output end Proof for theBenchmark
% 10.42/2.22
% 10.42/2.22 1603ms
%------------------------------------------------------------------------------