TSTP Solution File: SEU424+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU424+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n012.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 17:44:41 EDT 2023
% Result : Theorem 8.31s 1.91s
% Output : Proof 10.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU424+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 01:31:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.63 ________ _____
% 0.19/0.63 ___ __ \_________(_)________________________________
% 0.19/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.63
% 0.19/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.63 (2023-06-19)
% 0.19/0.63
% 0.19/0.63 (c) Philipp Rümmer, 2009-2023
% 0.19/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.63 Amanda Stjerna.
% 0.19/0.63 Free software under BSD-3-Clause.
% 0.19/0.63
% 0.19/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.63
% 0.19/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.65 Running up to 7 provers in parallel.
% 0.19/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.49/1.10 Prover 1: Preprocessing ...
% 2.49/1.10 Prover 4: Preprocessing ...
% 2.97/1.14 Prover 6: Preprocessing ...
% 2.97/1.14 Prover 3: Preprocessing ...
% 2.97/1.14 Prover 2: Preprocessing ...
% 2.97/1.14 Prover 5: Preprocessing ...
% 2.97/1.14 Prover 0: Preprocessing ...
% 6.18/1.60 Prover 1: Warning: ignoring some quantifiers
% 6.67/1.66 Prover 4: Warning: ignoring some quantifiers
% 6.90/1.67 Prover 6: Proving ...
% 6.90/1.68 Prover 2: Proving ...
% 6.90/1.68 Prover 1: Constructing countermodel ...
% 6.90/1.68 Prover 3: Warning: ignoring some quantifiers
% 6.90/1.69 Prover 5: Proving ...
% 6.90/1.71 Prover 4: Constructing countermodel ...
% 6.90/1.71 Prover 3: Constructing countermodel ...
% 7.54/1.81 Prover 0: Proving ...
% 8.31/1.91 Prover 3: proved (1242ms)
% 8.31/1.91
% 8.31/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.31/1.91
% 8.31/1.91 Prover 0: stopped
% 8.31/1.91 Prover 5: stopped
% 8.31/1.93 Prover 2: stopped
% 8.31/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.31/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.31/1.93 Prover 6: proved (1242ms)
% 8.31/1.93
% 8.31/1.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.31/1.93
% 8.31/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.31/1.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.31/1.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.80/1.97 Prover 7: Preprocessing ...
% 8.80/2.00 Prover 8: Preprocessing ...
% 8.80/2.01 Prover 10: Preprocessing ...
% 8.80/2.02 Prover 11: Preprocessing ...
% 8.80/2.02 Prover 13: Preprocessing ...
% 9.71/2.12 Prover 7: Warning: ignoring some quantifiers
% 9.71/2.13 Prover 1: Found proof (size 29)
% 9.71/2.13 Prover 1: proved (1467ms)
% 9.71/2.13 Prover 4: stopped
% 9.71/2.13 Prover 11: stopped
% 9.71/2.13 Prover 13: stopped
% 9.71/2.13 Prover 10: Warning: ignoring some quantifiers
% 9.71/2.14 Prover 7: Constructing countermodel ...
% 9.71/2.15 Prover 7: stopped
% 9.71/2.15 Prover 10: Constructing countermodel ...
% 9.71/2.16 Prover 10: stopped
% 10.37/2.17 Prover 8: Warning: ignoring some quantifiers
% 10.37/2.19 Prover 8: Constructing countermodel ...
% 10.37/2.19 Prover 8: stopped
% 10.37/2.19
% 10.37/2.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.37/2.19
% 10.51/2.20 % SZS output start Proof for theBenchmark
% 10.51/2.20 Assumptions after simplification:
% 10.51/2.20 ---------------------------------
% 10.51/2.20
% 10.51/2.20 (s8_domain_1__e1_22__relset_2)
% 10.64/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.64/2.23 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (a_4_0_relset_2(v0, v1, v2,
% 10.64/2.23 v3) = v4) | ~ (k1_zfmisc_1(v5) = v6) | ~ (k1_zfmisc_1(v1) = v5) | ~
% 10.64/2.23 (m1_subset_1(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 10.64/2.23 ? [v8: any] : ? [v9: $i] : ? [v10: any] : ? [v11: any] :
% 10.64/2.23 (m2_relset_1(v3, v0, v1) = v11 & k1_zfmisc_1(v0) = v9 & m1_subset_1(v2, v9)
% 10.64/2.23 = v10 & v1_xboole_0(v0) = v8 & $i(v9) & ( ~ (v11 = 0) | ~ (v10 = 0) | v8
% 10.64/2.23 = 0)))
% 10.64/2.23
% 10.64/2.23 (t18_relset_2)
% 10.64/2.24 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ( ~ (v1 = 0) & k1_zfmisc_1(v0) = v2
% 10.64/2.24 & v1_xboole_0(v0) = v1 & $i(v2) & $i(v0) & ? [v3: $i] : ? [v4: $i] : ?
% 10.64/2.24 [v5: $i] : ? [v6: $i] : (k1_zfmisc_1(v5) = v6 & k1_zfmisc_1(v3) = v5 &
% 10.64/2.24 m1_subset_1(v4, v2) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ? [v7: $i]
% 10.64/2.24 : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) & a_4_0_relset_2(v0, v3, v4,
% 10.64/2.24 v7) = v8 & m2_relset_1(v7, v0, v3) = 0 & m1_subset_1(v8, v6) = v9 &
% 10.64/2.24 $i(v8) & $i(v7))))
% 10.64/2.24
% 10.64/2.24 (function-axioms)
% 10.64/2.25 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 10.64/2.25 $i] : (v1 = v0 | ~ (a_4_0_relset_2(v5, v4, v3, v2) = v1) | ~
% 10.64/2.25 (a_4_0_relset_2(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 10.64/2.25 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 10.64/2.25 (k10_relset_1(v5, v4, v3, v2) = v1) | ~ (k10_relset_1(v5, v4, v3, v2) =
% 10.64/2.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i]
% 10.64/2.25 : ! [v5: $i] : (v1 = v0 | ~ (k2_relset_2(v5, v4, v3, v2) = v1) | ~
% 10.64/2.25 (k2_relset_2(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.64/2.25 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 10.64/2.25 (m1_relset_1(v4, v3, v2) = v1) | ~ (m1_relset_1(v4, v3, v2) = v0)) & !
% 10.64/2.25 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.64/2.25 $i] : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) = v1) | ~
% 10.64/2.25 (m2_relset_1(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.64/2.25 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.64/2.25 (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0)) & ! [v0: $i] : !
% 10.64/2.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1)
% 10.64/2.25 | ~ (k9_relat_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 10.64/2.25 ! [v3: $i] : (v1 = v0 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3,
% 10.64/2.25 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.64/2.25 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~
% 10.64/2.25 (m1_subset_1(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.64/2.25 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.64/2.25 (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0)) & ! [v0:
% 10.64/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.64/2.25 ~ (v3_relat_1(v2) = v1) | ~ (v3_relat_1(v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.64/2.25 $i] : ! [v2: $i] : (v1 = v0 | ~ (k1_tarski(v2) = v1) | ~ (k1_tarski(v2) =
% 10.64/2.25 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.64/2.25 (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0:
% 10.64/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.64/2.25 ~ (v1_relat_1(v2) = v1) | ~ (v1_relat_1(v2) = v0)) & ! [v0:
% 10.64/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 10.64/2.25 ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0))
% 10.64/2.25
% 10.64/2.25 Further assumptions not needed in the proof:
% 10.64/2.25 --------------------------------------------
% 10.64/2.25 antisymmetry_r2_hidden, cc1_relat_1, cc1_relset_1, d1_relset_2, dt_k10_relset_1,
% 10.64/2.25 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_relset_2, dt_k2_zfmisc_1,
% 10.64/2.25 dt_k9_relat_1, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1,
% 10.64/2.25 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 10.64/2.25 fc12_relat_1, fc1_subset_1, fc1_sysrel, fc2_subset_1, fc4_relat_1, fc4_subset_1,
% 10.64/2.25 fraenkel_a_4_0_relset_2, rc1_relat_1, rc1_subset_1, rc2_relat_1, rc2_subset_1,
% 10.64/2.25 rc3_relat_1, redefinition_k10_relset_1, redefinition_m2_relset_1,
% 10.64/2.25 reflexivity_r1_tarski, t1_subset, t2_subset, t2_tarski, t3_subset, t4_subset,
% 10.64/2.25 t5_subset, t6_boole, t7_boole, t8_boole
% 10.64/2.25
% 10.64/2.25 Those formulas are unsatisfiable:
% 10.64/2.25 ---------------------------------
% 10.64/2.25
% 10.64/2.25 Begin of proof
% 10.64/2.25 |
% 10.64/2.25 | ALPHA: (function-axioms) implies:
% 10.64/2.25 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.64/2.25 | (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0))
% 10.64/2.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 10.64/2.25 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 10.64/2.25 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.64/2.25 | ! [v3: $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~
% 10.64/2.25 | (m1_subset_1(v3, v2) = v0))
% 10.64/2.25 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.64/2.25 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) =
% 10.64/2.25 | v1) | ~ (m2_relset_1(v4, v3, v2) = v0))
% 10.64/2.25 |
% 10.64/2.25 | DELTA: instantiating (t18_relset_2) with fresh symbols all_41_0, all_41_1,
% 10.64/2.25 | all_41_2 gives:
% 10.64/2.26 | (5) ~ (all_41_1 = 0) & k1_zfmisc_1(all_41_2) = all_41_0 &
% 10.64/2.26 | v1_xboole_0(all_41_2) = all_41_1 & $i(all_41_0) & $i(all_41_2) & ?
% 10.64/2.26 | [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (k1_zfmisc_1(v2) =
% 10.64/2.26 | v3 & k1_zfmisc_1(v0) = v2 & m1_subset_1(v1, all_41_0) = 0 & $i(v3) &
% 10.64/2.26 | $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] : ? [v5: $i] : ? [v6: int] :
% 10.64/2.26 | ( ~ (v6 = 0) & a_4_0_relset_2(all_41_2, v0, v1, v4) = v5 &
% 10.64/2.26 | m2_relset_1(v4, all_41_2, v0) = 0 & m1_subset_1(v5, v3) = v6 &
% 10.64/2.26 | $i(v5) & $i(v4)))
% 10.64/2.26 |
% 10.64/2.26 | ALPHA: (5) implies:
% 10.64/2.26 | (6) ~ (all_41_1 = 0)
% 10.64/2.26 | (7) $i(all_41_2)
% 10.64/2.26 | (8) v1_xboole_0(all_41_2) = all_41_1
% 10.64/2.26 | (9) k1_zfmisc_1(all_41_2) = all_41_0
% 10.64/2.26 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 10.64/2.26 | (k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v0) = v2 & m1_subset_1(v1,
% 10.64/2.26 | all_41_0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] :
% 10.64/2.26 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & a_4_0_relset_2(all_41_2,
% 10.64/2.26 | v0, v1, v4) = v5 & m2_relset_1(v4, all_41_2, v0) = 0 &
% 10.64/2.26 | m1_subset_1(v5, v3) = v6 & $i(v5) & $i(v4)))
% 10.64/2.26 |
% 10.64/2.26 | DELTA: instantiating (10) with fresh symbols all_43_0, all_43_1, all_43_2,
% 10.64/2.26 | all_43_3 gives:
% 10.64/2.26 | (11) k1_zfmisc_1(all_43_1) = all_43_0 & k1_zfmisc_1(all_43_3) = all_43_1 &
% 10.64/2.26 | m1_subset_1(all_43_2, all_41_0) = 0 & $i(all_43_0) & $i(all_43_1) &
% 10.64/2.26 | $i(all_43_2) & $i(all_43_3) & ? [v0: $i] : ? [v1: $i] : ? [v2: int]
% 10.64/2.26 | : ( ~ (v2 = 0) & a_4_0_relset_2(all_41_2, all_43_3, all_43_2, v0) = v1
% 10.64/2.26 | & m2_relset_1(v0, all_41_2, all_43_3) = 0 & m1_subset_1(v1,
% 10.64/2.26 | all_43_0) = v2 & $i(v1) & $i(v0))
% 10.64/2.26 |
% 10.64/2.26 | ALPHA: (11) implies:
% 10.64/2.26 | (12) $i(all_43_3)
% 10.64/2.26 | (13) $i(all_43_2)
% 10.64/2.26 | (14) m1_subset_1(all_43_2, all_41_0) = 0
% 10.64/2.26 | (15) k1_zfmisc_1(all_43_3) = all_43_1
% 10.64/2.26 | (16) k1_zfmisc_1(all_43_1) = all_43_0
% 10.64/2.26 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 10.64/2.26 | a_4_0_relset_2(all_41_2, all_43_3, all_43_2, v0) = v1 &
% 10.64/2.26 | m2_relset_1(v0, all_41_2, all_43_3) = 0 & m1_subset_1(v1, all_43_0)
% 10.64/2.26 | = v2 & $i(v1) & $i(v0))
% 10.64/2.26 |
% 10.64/2.26 | DELTA: instantiating (17) with fresh symbols all_45_0, all_45_1, all_45_2
% 10.64/2.26 | gives:
% 10.64/2.26 | (18) ~ (all_45_0 = 0) & a_4_0_relset_2(all_41_2, all_43_3, all_43_2,
% 10.64/2.26 | all_45_2) = all_45_1 & m2_relset_1(all_45_2, all_41_2, all_43_3) = 0
% 10.64/2.26 | & m1_subset_1(all_45_1, all_43_0) = all_45_0 & $i(all_45_1) &
% 10.64/2.26 | $i(all_45_2)
% 10.64/2.26 |
% 10.64/2.26 | ALPHA: (18) implies:
% 10.64/2.26 | (19) ~ (all_45_0 = 0)
% 10.64/2.26 | (20) $i(all_45_2)
% 10.64/2.26 | (21) m1_subset_1(all_45_1, all_43_0) = all_45_0
% 10.64/2.26 | (22) m2_relset_1(all_45_2, all_41_2, all_43_3) = 0
% 10.64/2.26 | (23) a_4_0_relset_2(all_41_2, all_43_3, all_43_2, all_45_2) = all_45_1
% 10.64/2.26 |
% 10.64/2.27 | GROUND_INST: instantiating (s8_domain_1__e1_22__relset_2) with all_41_2,
% 10.64/2.27 | all_43_3, all_43_2, all_45_2, all_45_1, all_43_1, all_43_0,
% 10.64/2.27 | all_45_0, simplifying with (7), (12), (13), (15), (16), (20),
% 10.64/2.27 | (21), (23) gives:
% 10.64/2.27 | (24) all_45_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3:
% 10.64/2.27 | any] : (m2_relset_1(all_45_2, all_41_2, all_43_3) = v3 &
% 10.64/2.27 | k1_zfmisc_1(all_41_2) = v1 & m1_subset_1(all_43_2, v1) = v2 &
% 10.64/2.27 | v1_xboole_0(all_41_2) = v0 & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 10.64/2.27 | v0 = 0))
% 10.64/2.27 |
% 10.64/2.27 | BETA: splitting (24) gives:
% 10.64/2.27 |
% 10.64/2.27 | Case 1:
% 10.64/2.27 | |
% 10.64/2.27 | | (25) all_45_0 = 0
% 10.64/2.27 | |
% 10.64/2.27 | | REDUCE: (19), (25) imply:
% 10.64/2.27 | | (26) $false
% 10.64/2.27 | |
% 10.64/2.27 | | CLOSE: (26) is inconsistent.
% 10.64/2.27 | |
% 10.64/2.27 | Case 2:
% 10.64/2.27 | |
% 10.64/2.27 | | (27) ? [v0: any] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 10.64/2.27 | | (m2_relset_1(all_45_2, all_41_2, all_43_3) = v3 &
% 10.64/2.27 | | k1_zfmisc_1(all_41_2) = v1 & m1_subset_1(all_43_2, v1) = v2 &
% 10.64/2.27 | | v1_xboole_0(all_41_2) = v0 & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 10.64/2.27 | | v0 = 0))
% 10.64/2.27 | |
% 10.64/2.27 | | DELTA: instantiating (27) with fresh symbols all_70_0, all_70_1, all_70_2,
% 10.64/2.27 | | all_70_3 gives:
% 10.64/2.27 | | (28) m2_relset_1(all_45_2, all_41_2, all_43_3) = all_70_0 &
% 10.64/2.27 | | k1_zfmisc_1(all_41_2) = all_70_2 & m1_subset_1(all_43_2, all_70_2) =
% 10.64/2.27 | | all_70_1 & v1_xboole_0(all_41_2) = all_70_3 & $i(all_70_2) & ( ~
% 10.64/2.27 | | (all_70_0 = 0) | ~ (all_70_1 = 0) | all_70_3 = 0)
% 10.64/2.27 | |
% 10.64/2.27 | | ALPHA: (28) implies:
% 10.64/2.27 | | (29) v1_xboole_0(all_41_2) = all_70_3
% 10.64/2.27 | | (30) m1_subset_1(all_43_2, all_70_2) = all_70_1
% 10.64/2.27 | | (31) k1_zfmisc_1(all_41_2) = all_70_2
% 10.64/2.27 | | (32) m2_relset_1(all_45_2, all_41_2, all_43_3) = all_70_0
% 10.64/2.27 | | (33) ~ (all_70_0 = 0) | ~ (all_70_1 = 0) | all_70_3 = 0
% 10.64/2.27 | |
% 10.64/2.27 | | GROUND_INST: instantiating (1) with all_41_1, all_70_3, all_41_2,
% 10.64/2.27 | | simplifying with (8), (29) gives:
% 10.64/2.27 | | (34) all_70_3 = all_41_1
% 10.64/2.27 | |
% 10.64/2.27 | | GROUND_INST: instantiating (2) with all_41_0, all_70_2, all_41_2,
% 10.64/2.27 | | simplifying with (9), (31) gives:
% 10.64/2.27 | | (35) all_70_2 = all_41_0
% 10.64/2.27 | |
% 10.64/2.27 | | GROUND_INST: instantiating (4) with 0, all_70_0, all_43_3, all_41_2,
% 10.64/2.27 | | all_45_2, simplifying with (22), (32) gives:
% 10.64/2.27 | | (36) all_70_0 = 0
% 10.64/2.27 | |
% 10.64/2.27 | | REDUCE: (30), (35) imply:
% 10.64/2.27 | | (37) m1_subset_1(all_43_2, all_41_0) = all_70_1
% 10.64/2.27 | |
% 10.64/2.27 | | BETA: splitting (33) gives:
% 10.64/2.27 | |
% 10.64/2.27 | | Case 1:
% 10.64/2.27 | | |
% 10.64/2.27 | | | (38) ~ (all_70_0 = 0)
% 10.64/2.27 | | |
% 10.64/2.27 | | | REDUCE: (36), (38) imply:
% 10.64/2.27 | | | (39) $false
% 10.64/2.27 | | |
% 10.64/2.27 | | | CLOSE: (39) is inconsistent.
% 10.64/2.27 | | |
% 10.64/2.27 | | Case 2:
% 10.64/2.27 | | |
% 10.64/2.27 | | | (40) ~ (all_70_1 = 0) | all_70_3 = 0
% 10.64/2.27 | | |
% 10.64/2.27 | | | BETA: splitting (40) gives:
% 10.64/2.27 | | |
% 10.64/2.27 | | | Case 1:
% 10.64/2.27 | | | |
% 10.64/2.28 | | | | (41) ~ (all_70_1 = 0)
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | GROUND_INST: instantiating (3) with 0, all_70_1, all_41_0, all_43_2,
% 10.64/2.28 | | | | simplifying with (14), (37) gives:
% 10.64/2.28 | | | | (42) all_70_1 = 0
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | REDUCE: (41), (42) imply:
% 10.64/2.28 | | | | (43) $false
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | CLOSE: (43) is inconsistent.
% 10.64/2.28 | | | |
% 10.64/2.28 | | | Case 2:
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | (44) all_70_3 = 0
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | COMBINE_EQS: (34), (44) imply:
% 10.64/2.28 | | | | (45) all_41_1 = 0
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | SIMP: (45) implies:
% 10.64/2.28 | | | | (46) all_41_1 = 0
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | REDUCE: (6), (46) imply:
% 10.64/2.28 | | | | (47) $false
% 10.64/2.28 | | | |
% 10.64/2.28 | | | | CLOSE: (47) is inconsistent.
% 10.64/2.28 | | | |
% 10.64/2.28 | | | End of split
% 10.64/2.28 | | |
% 10.64/2.28 | | End of split
% 10.64/2.28 | |
% 10.64/2.28 | End of split
% 10.64/2.28 |
% 10.64/2.28 End of proof
% 10.64/2.28 % SZS output end Proof for theBenchmark
% 10.64/2.28
% 10.64/2.28 1640ms
%------------------------------------------------------------------------------