TSTP Solution File: SEU429+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU429+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 : n021.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 17:44:44 EDT 2023
% Result : Theorem 9.14s 2.03s
% Output : Proof 12.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU429+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.34 % Computer : n021.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 24 00:07:10 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.99/1.14 Prover 4: Preprocessing ...
% 2.99/1.14 Prover 1: Preprocessing ...
% 2.99/1.18 Prover 2: Preprocessing ...
% 2.99/1.18 Prover 0: Preprocessing ...
% 2.99/1.18 Prover 6: Preprocessing ...
% 2.99/1.19 Prover 5: Preprocessing ...
% 2.99/1.19 Prover 3: Preprocessing ...
% 6.97/1.76 Prover 1: Warning: ignoring some quantifiers
% 7.71/1.80 Prover 5: Proving ...
% 7.71/1.81 Prover 6: Proving ...
% 7.71/1.81 Prover 2: Proving ...
% 7.94/1.82 Prover 3: Warning: ignoring some quantifiers
% 8.05/1.83 Prover 1: Constructing countermodel ...
% 8.05/1.83 Prover 4: Warning: ignoring some quantifiers
% 8.05/1.85 Prover 3: Constructing countermodel ...
% 8.05/1.91 Prover 4: Constructing countermodel ...
% 8.63/1.93 Prover 0: Proving ...
% 9.14/2.03 Prover 3: proved (1399ms)
% 9.14/2.03
% 9.14/2.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.14/2.03
% 9.14/2.04 Prover 6: stopped
% 9.14/2.04 Prover 5: stopped
% 9.14/2.04 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.14/2.04 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.14/2.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.14/2.04 Prover 2: stopped
% 9.14/2.04 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.14/2.04 Prover 0: stopped
% 9.14/2.04 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.14/2.13 Prover 11: Preprocessing ...
% 9.14/2.14 Prover 8: Preprocessing ...
% 9.14/2.15 Prover 13: Preprocessing ...
% 9.14/2.16 Prover 10: Preprocessing ...
% 10.52/2.19 Prover 7: Preprocessing ...
% 10.94/2.31 Prover 1: Found proof (size 38)
% 10.94/2.31 Prover 1: proved (1678ms)
% 10.94/2.32 Prover 4: stopped
% 11.63/2.33 Prover 7: Warning: ignoring some quantifiers
% 11.63/2.34 Prover 10: Warning: ignoring some quantifiers
% 11.63/2.34 Prover 13: Warning: ignoring some quantifiers
% 11.63/2.35 Prover 8: Warning: ignoring some quantifiers
% 11.63/2.35 Prover 10: Constructing countermodel ...
% 11.63/2.35 Prover 7: Constructing countermodel ...
% 11.63/2.36 Prover 13: Constructing countermodel ...
% 11.63/2.36 Prover 7: stopped
% 11.63/2.36 Prover 10: stopped
% 11.63/2.37 Prover 8: Constructing countermodel ...
% 11.63/2.37 Prover 13: stopped
% 11.63/2.38 Prover 8: stopped
% 12.04/2.40 Prover 11: Warning: ignoring some quantifiers
% 12.04/2.41 Prover 11: Constructing countermodel ...
% 12.04/2.42 Prover 11: stopped
% 12.04/2.42
% 12.04/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.04/2.42
% 12.04/2.43 % SZS output start Proof for theBenchmark
% 12.04/2.43 Assumptions after simplification:
% 12.04/2.43 ---------------------------------
% 12.04/2.43
% 12.04/2.43 (rc1_subset_1)
% 12.37/2.46 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (v1_xboole_0(v0) = v1) | ~ $i(v0) |
% 12.37/2.46 ? [v2: $i] : (k1_zfmisc_1(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] :
% 12.37/2.46 ( ~ (v4 = 0) & m1_subset_1(v3, v2) = 0 & v1_xboole_0(v3) = v4 & $i(v3))))
% 12.37/2.46
% 12.37/2.46 (s8_domain_1__e1_38__relset_2)
% 12.39/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.39/2.46 $i] : ! [v6: $i] : ! [v7: int] : (v7 = 0 | ~ (a_4_1_relset_2(v0, v1, v2,
% 12.39/2.46 v3) = v4) | ~ (k1_zfmisc_1(v5) = v6) | ~ (k1_zfmisc_1(v1) = v5) | ~
% 12.39/2.46 (m1_subset_1(v4, v6) = v7) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 12.39/2.46 ? [v8: any] : ? [v9: $i] : ? [v10: $i] : ? [v11: any] : ? [v12: any] :
% 12.39/2.46 (m2_relset_1(v3, v0, v1) = v12 & k1_zfmisc_1(v9) = v10 & k1_zfmisc_1(v0) =
% 12.39/2.46 v9 & m1_subset_1(v2, v10) = v11 & v1_xboole_0(v0) = v8 & $i(v10) & $i(v9)
% 12.39/2.46 & ( ~ (v12 = 0) | ~ (v11 = 0) | v8 = 0)))
% 12.39/2.46
% 12.39/2.46 (t28_relset_2)
% 12.39/2.47 ? [v0: $i] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = 0) &
% 12.39/2.47 k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v0) = v2 & v1_xboole_0(v0) = v1 & $i(v3)
% 12.39/2.47 & $i(v2) & $i(v0) & ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] :
% 12.39/2.47 (k1_zfmisc_1(v6) = v7 & k1_zfmisc_1(v4) = v6 & m1_subset_1(v5, v3) = 0 &
% 12.39/2.47 $i(v7) & $i(v6) & $i(v5) & $i(v4) & ? [v8: $i] : ? [v9: $i] : ? [v10:
% 12.39/2.47 int] : ( ~ (v10 = 0) & a_4_1_relset_2(v0, v4, v5, v8) = v9 &
% 12.39/2.47 m2_relset_1(v8, v0, v4) = 0 & m1_subset_1(v9, v7) = v10 & $i(v9) &
% 12.39/2.47 $i(v8))))
% 12.39/2.47
% 12.39/2.47 (function-axioms)
% 12.39/2.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 12.39/2.48 $i] : (v1 = v0 | ~ (a_4_1_relset_2(v5, v4, v3, v2) = v1) | ~
% 12.39/2.48 (a_4_1_relset_2(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 12.39/2.48 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 12.39/2.48 (k8_relset_2(v5, v4, v3, v2) = v1) | ~ (k8_relset_2(v5, v4, v3, v2) = v0))
% 12.39/2.48 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 12.39/2.48 [v5: $i] : (v1 = v0 | ~ (k4_relset_2(v5, v4, v3, v2) = v1) | ~
% 12.39/2.48 (k4_relset_2(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 12.39/2.48 $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v1 = v0 | ~
% 12.39/2.48 (k7_relset_2(v5, v4, v3, v2) = v1) | ~ (k7_relset_2(v5, v4, v3, v2) = v0))
% 12.39/2.48 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.39/2.48 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (m1_relset_1(v4, v3, v2) = v1) | ~
% 12.39/2.48 (m1_relset_1(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.39/2.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 12.39/2.48 (v1_funct_2(v4, v3, v2) = v1) | ~ (v1_funct_2(v4, v3, v2) = v0)) & ! [v0:
% 12.39/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.39/2.48 : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) = v1) | ~
% 12.39/2.48 (m2_relset_1(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.39/2.48 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (k6_relset_2(v4, v3, v2) = v1) | ~
% 12.39/2.48 (k6_relset_2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.39/2.48 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.39/2.48 (r1_tarski(v3, v2) = v1) | ~ (r1_tarski(v3, v2) = v0)) & ! [v0: $i] : !
% 12.39/2.48 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (k9_relat_1(v3, v2) = v1)
% 12.39/2.48 | ~ (k9_relat_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 12.39/2.48 ! [v3: $i] : (v1 = v0 | ~ (k5_relset_2(v3, v2) = v1) | ~ (k5_relset_2(v3,
% 12.39/2.48 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 12.39/2.48 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (m1_eqrel_1(v3, v2) = v1) | ~
% 12.39/2.48 (m1_eqrel_1(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 12.39/2.48 [v3: $i] : (v1 = v0 | ~ (k8_setfam_1(v3, v2) = v1) | ~ (k8_setfam_1(v3, v2)
% 12.39/2.48 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 12.39/2.48 | ~ (k2_zfmisc_1(v3, v2) = v1) | ~ (k2_zfmisc_1(v3, v2) = v0)) & ! [v0:
% 12.39/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.39/2.48 : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~ (m1_subset_1(v3, v2) = v0)) &
% 12.39/2.48 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 12.39/2.48 $i] : (v1 = v0 | ~ (r2_hidden(v3, v2) = v1) | ~ (r2_hidden(v3, v2) = v0))
% 12.39/2.48 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 12.39/2.48 = v0 | ~ (v3_relat_1(v2) = v1) | ~ (v3_relat_1(v2) = v0)) & ! [v0:
% 12.39/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.39/2.48 ~ (v1_funct_1(v2) = v1) | ~ (v1_funct_1(v2) = v0)) & ! [v0: $i] : ! [v1:
% 12.39/2.48 $i] : ! [v2: $i] : (v1 = v0 | ~ (k3_pua2mss1(v2) = v1) | ~
% 12.39/2.48 (k3_pua2mss1(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 12.39/2.48 | ~ (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0)) & ! [v0:
% 12.39/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.39/2.48 ~ (v1_relat_1(v2) = v1) | ~ (v1_relat_1(v2) = v0)) & ! [v0:
% 12.39/2.48 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 12.39/2.48 ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0))
% 12.39/2.48
% 12.39/2.48 Further assumptions not needed in the proof:
% 12.39/2.48 --------------------------------------------
% 12.39/2.48 antisymmetry_r2_hidden, cc1_relat_1, cc1_relset_1, d4_relset_2, dt_k1_xboole_0,
% 12.39/2.48 dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k3_pua2mss1, dt_k4_relset_2, dt_k5_relset_2,
% 12.39/2.48 dt_k6_relset_2, dt_k7_relset_2, dt_k8_relset_2, dt_k8_setfam_1, dt_k9_relat_1,
% 12.39/2.48 dt_m1_eqrel_1, dt_m1_relset_1, dt_m1_subset_1, dt_m2_relset_1,
% 12.39/2.48 existence_m1_eqrel_1, existence_m1_relset_1, existence_m1_subset_1,
% 12.39/2.48 existence_m2_relset_1, fc12_relat_1, fc1_subset_1, fc1_sysrel, fc4_relat_1,
% 12.39/2.48 fc4_subset_1, fraenkel_a_4_1_relset_2, rc1_relat_1, rc2_partfun1, rc2_relat_1,
% 12.39/2.48 rc2_subset_1, rc3_relat_1, redefinition_k4_relset_2, redefinition_k6_relset_2,
% 12.39/2.48 redefinition_k8_relset_2, redefinition_m2_relset_1, reflexivity_r1_tarski,
% 12.39/2.48 t1_subset, t2_subset, t2_tarski, t3_subset, t4_subset, t5_subset, t6_boole,
% 12.39/2.48 t7_boole, t8_boole
% 12.39/2.48
% 12.39/2.48 Those formulas are unsatisfiable:
% 12.39/2.48 ---------------------------------
% 12.39/2.48
% 12.39/2.48 Begin of proof
% 12.39/2.48 |
% 12.39/2.48 | ALPHA: (function-axioms) implies:
% 12.39/2.48 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.39/2.48 | (v1 = v0 | ~ (v1_xboole_0(v2) = v1) | ~ (v1_xboole_0(v2) = v0))
% 12.39/2.48 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 12.39/2.48 | (k1_zfmisc_1(v2) = v1) | ~ (k1_zfmisc_1(v2) = v0))
% 12.39/2.48 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.39/2.48 | ! [v3: $i] : (v1 = v0 | ~ (m1_subset_1(v3, v2) = v1) | ~
% 12.39/2.48 | (m1_subset_1(v3, v2) = v0))
% 12.39/2.48 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.39/2.48 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (m2_relset_1(v4, v3, v2) =
% 12.39/2.48 | v1) | ~ (m2_relset_1(v4, v3, v2) = v0))
% 12.39/2.48 |
% 12.39/2.48 | DELTA: instantiating (t28_relset_2) with fresh symbols all_49_0, all_49_1,
% 12.39/2.48 | all_49_2, all_49_3 gives:
% 12.39/2.49 | (5) ~ (all_49_2 = 0) & k1_zfmisc_1(all_49_1) = all_49_0 &
% 12.39/2.49 | k1_zfmisc_1(all_49_3) = all_49_1 & v1_xboole_0(all_49_3) = all_49_2 &
% 12.39/2.49 | $i(all_49_0) & $i(all_49_1) & $i(all_49_3) & ? [v0: $i] : ? [v1: $i]
% 12.39/2.49 | : ? [v2: $i] : ? [v3: $i] : (k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v0) =
% 12.39/2.49 | v2 & m1_subset_1(v1, all_49_0) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 12.39/2.49 | $i(v0) & ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) &
% 12.39/2.49 | a_4_1_relset_2(all_49_3, v0, v1, v4) = v5 & m2_relset_1(v4,
% 12.39/2.49 | all_49_3, v0) = 0 & m1_subset_1(v5, v3) = v6 & $i(v5) & $i(v4)))
% 12.39/2.49 |
% 12.39/2.49 | ALPHA: (5) implies:
% 12.39/2.49 | (6) ~ (all_49_2 = 0)
% 12.39/2.49 | (7) $i(all_49_3)
% 12.39/2.49 | (8) v1_xboole_0(all_49_3) = all_49_2
% 12.39/2.49 | (9) k1_zfmisc_1(all_49_3) = all_49_1
% 12.39/2.49 | (10) k1_zfmisc_1(all_49_1) = all_49_0
% 12.39/2.49 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 12.39/2.49 | (k1_zfmisc_1(v2) = v3 & k1_zfmisc_1(v0) = v2 & m1_subset_1(v1,
% 12.39/2.49 | all_49_0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ? [v4: $i] :
% 12.39/2.49 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & a_4_1_relset_2(all_49_3,
% 12.39/2.49 | v0, v1, v4) = v5 & m2_relset_1(v4, all_49_3, v0) = 0 &
% 12.39/2.49 | m1_subset_1(v5, v3) = v6 & $i(v5) & $i(v4)))
% 12.39/2.49 |
% 12.39/2.49 | DELTA: instantiating (11) with fresh symbols all_51_0, all_51_1, all_51_2,
% 12.39/2.49 | all_51_3 gives:
% 12.39/2.49 | (12) k1_zfmisc_1(all_51_1) = all_51_0 & k1_zfmisc_1(all_51_3) = all_51_1 &
% 12.39/2.49 | m1_subset_1(all_51_2, all_49_0) = 0 & $i(all_51_0) & $i(all_51_1) &
% 12.39/2.49 | $i(all_51_2) & $i(all_51_3) & ? [v0: $i] : ? [v1: $i] : ? [v2: int]
% 12.39/2.49 | : ( ~ (v2 = 0) & a_4_1_relset_2(all_49_3, all_51_3, all_51_2, v0) = v1
% 12.39/2.49 | & m2_relset_1(v0, all_49_3, all_51_3) = 0 & m1_subset_1(v1,
% 12.39/2.49 | all_51_0) = v2 & $i(v1) & $i(v0))
% 12.39/2.49 |
% 12.39/2.49 | ALPHA: (12) implies:
% 12.39/2.49 | (13) $i(all_51_3)
% 12.39/2.49 | (14) $i(all_51_2)
% 12.39/2.49 | (15) m1_subset_1(all_51_2, all_49_0) = 0
% 12.39/2.49 | (16) k1_zfmisc_1(all_51_3) = all_51_1
% 12.39/2.49 | (17) k1_zfmisc_1(all_51_1) = all_51_0
% 12.39/2.49 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 12.39/2.49 | a_4_1_relset_2(all_49_3, all_51_3, all_51_2, v0) = v1 &
% 12.39/2.49 | m2_relset_1(v0, all_49_3, all_51_3) = 0 & m1_subset_1(v1, all_51_0)
% 12.39/2.49 | = v2 & $i(v1) & $i(v0))
% 12.39/2.49 |
% 12.39/2.49 | DELTA: instantiating (18) with fresh symbols all_53_0, all_53_1, all_53_2
% 12.39/2.49 | gives:
% 12.39/2.49 | (19) ~ (all_53_0 = 0) & a_4_1_relset_2(all_49_3, all_51_3, all_51_2,
% 12.39/2.49 | all_53_2) = all_53_1 & m2_relset_1(all_53_2, all_49_3, all_51_3) = 0
% 12.39/2.49 | & m1_subset_1(all_53_1, all_51_0) = all_53_0 & $i(all_53_1) &
% 12.39/2.49 | $i(all_53_2)
% 12.39/2.49 |
% 12.39/2.49 | ALPHA: (19) implies:
% 12.39/2.49 | (20) ~ (all_53_0 = 0)
% 12.39/2.49 | (21) $i(all_53_2)
% 12.39/2.49 | (22) m1_subset_1(all_53_1, all_51_0) = all_53_0
% 12.39/2.49 | (23) m2_relset_1(all_53_2, all_49_3, all_51_3) = 0
% 12.39/2.49 | (24) a_4_1_relset_2(all_49_3, all_51_3, all_51_2, all_53_2) = all_53_1
% 12.39/2.49 |
% 12.39/2.49 | GROUND_INST: instantiating (rc1_subset_1) with all_49_3, all_49_2, simplifying
% 12.39/2.49 | with (7), (8) gives:
% 12.39/2.49 | (25) all_49_2 = 0 | ? [v0: $i] : (k1_zfmisc_1(all_49_3) = v0 & $i(v0) & ?
% 12.39/2.49 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & m1_subset_1(v1, v0) = 0 &
% 12.39/2.49 | v1_xboole_0(v1) = v2 & $i(v1)))
% 12.39/2.49 |
% 12.39/2.49 | GROUND_INST: instantiating (s8_domain_1__e1_38__relset_2) with all_49_3,
% 12.39/2.49 | all_51_3, all_51_2, all_53_2, all_53_1, all_51_1, all_51_0,
% 12.39/2.49 | all_53_0, simplifying with (7), (13), (14), (16), (17), (21),
% 12.39/2.49 | (22), (24) gives:
% 12.39/2.50 | (26) all_53_0 = 0 | ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any]
% 12.39/2.50 | : ? [v4: any] : (m2_relset_1(all_53_2, all_49_3, all_51_3) = v4 &
% 12.39/2.50 | k1_zfmisc_1(v1) = v2 & k1_zfmisc_1(all_49_3) = v1 &
% 12.39/2.50 | m1_subset_1(all_51_2, v2) = v3 & v1_xboole_0(all_49_3) = v0 & $i(v2)
% 12.39/2.50 | & $i(v1) & ( ~ (v4 = 0) | ~ (v3 = 0) | v0 = 0))
% 12.39/2.50 |
% 12.39/2.50 | BETA: splitting (26) gives:
% 12.39/2.50 |
% 12.39/2.50 | Case 1:
% 12.39/2.50 | |
% 12.39/2.50 | | (27) all_53_0 = 0
% 12.39/2.50 | |
% 12.39/2.50 | | REDUCE: (20), (27) imply:
% 12.39/2.50 | | (28) $false
% 12.39/2.50 | |
% 12.39/2.50 | | CLOSE: (28) is inconsistent.
% 12.39/2.50 | |
% 12.39/2.50 | Case 2:
% 12.39/2.50 | |
% 12.39/2.50 | | (29) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4:
% 12.39/2.50 | | any] : (m2_relset_1(all_53_2, all_49_3, all_51_3) = v4 &
% 12.39/2.50 | | k1_zfmisc_1(v1) = v2 & k1_zfmisc_1(all_49_3) = v1 &
% 12.39/2.50 | | m1_subset_1(all_51_2, v2) = v3 & v1_xboole_0(all_49_3) = v0 &
% 12.39/2.50 | | $i(v2) & $i(v1) & ( ~ (v4 = 0) | ~ (v3 = 0) | v0 = 0))
% 12.39/2.50 | |
% 12.39/2.50 | | DELTA: instantiating (29) with fresh symbols all_81_0, all_81_1, all_81_2,
% 12.39/2.50 | | all_81_3, all_81_4 gives:
% 12.39/2.50 | | (30) m2_relset_1(all_53_2, all_49_3, all_51_3) = all_81_0 &
% 12.39/2.50 | | k1_zfmisc_1(all_81_3) = all_81_2 & k1_zfmisc_1(all_49_3) = all_81_3
% 12.39/2.50 | | & m1_subset_1(all_51_2, all_81_2) = all_81_1 & v1_xboole_0(all_49_3)
% 12.39/2.50 | | = all_81_4 & $i(all_81_2) & $i(all_81_3) & ( ~ (all_81_0 = 0) | ~
% 12.39/2.50 | | (all_81_1 = 0) | all_81_4 = 0)
% 12.39/2.50 | |
% 12.39/2.50 | | ALPHA: (30) implies:
% 12.39/2.50 | | (31) v1_xboole_0(all_49_3) = all_81_4
% 12.39/2.50 | | (32) m1_subset_1(all_51_2, all_81_2) = all_81_1
% 12.39/2.50 | | (33) k1_zfmisc_1(all_49_3) = all_81_3
% 12.39/2.50 | | (34) k1_zfmisc_1(all_81_3) = all_81_2
% 12.39/2.50 | | (35) m2_relset_1(all_53_2, all_49_3, all_51_3) = all_81_0
% 12.39/2.50 | | (36) ~ (all_81_0 = 0) | ~ (all_81_1 = 0) | all_81_4 = 0
% 12.39/2.50 | |
% 12.39/2.50 | | BETA: splitting (25) gives:
% 12.39/2.50 | |
% 12.39/2.50 | | Case 1:
% 12.39/2.50 | | |
% 12.39/2.50 | | | (37) all_49_2 = 0
% 12.39/2.50 | | |
% 12.39/2.50 | | | REDUCE: (6), (37) imply:
% 12.39/2.50 | | | (38) $false
% 12.39/2.50 | | |
% 12.39/2.50 | | | CLOSE: (38) is inconsistent.
% 12.39/2.50 | | |
% 12.39/2.50 | | Case 2:
% 12.39/2.50 | | |
% 12.39/2.50 | | | (39) ? [v0: $i] : (k1_zfmisc_1(all_49_3) = v0 & $i(v0) & ? [v1: $i] :
% 12.60/2.50 | | | ? [v2: int] : ( ~ (v2 = 0) & m1_subset_1(v1, v0) = 0 &
% 12.60/2.50 | | | v1_xboole_0(v1) = v2 & $i(v1)))
% 12.60/2.50 | | |
% 12.60/2.50 | | | DELTA: instantiating (39) with fresh symbol all_87_0 gives:
% 12.60/2.50 | | | (40) k1_zfmisc_1(all_49_3) = all_87_0 & $i(all_87_0) & ? [v0: $i] : ?
% 12.60/2.50 | | | [v1: int] : ( ~ (v1 = 0) & m1_subset_1(v0, all_87_0) = 0 &
% 12.60/2.50 | | | v1_xboole_0(v0) = v1 & $i(v0))
% 12.60/2.50 | | |
% 12.60/2.50 | | | ALPHA: (40) implies:
% 12.60/2.50 | | | (41) k1_zfmisc_1(all_49_3) = all_87_0
% 12.60/2.50 | | |
% 12.60/2.50 | | | GROUND_INST: instantiating (1) with all_49_2, all_81_4, all_49_3,
% 12.60/2.50 | | | simplifying with (8), (31) gives:
% 12.60/2.50 | | | (42) all_81_4 = all_49_2
% 12.60/2.50 | | |
% 12.60/2.50 | | | GROUND_INST: instantiating (2) with all_49_1, all_87_0, all_49_3,
% 12.60/2.50 | | | simplifying with (9), (41) gives:
% 12.60/2.50 | | | (43) all_87_0 = all_49_1
% 12.60/2.50 | | |
% 12.60/2.50 | | | GROUND_INST: instantiating (2) with all_81_3, all_87_0, all_49_3,
% 12.60/2.50 | | | simplifying with (33), (41) gives:
% 12.60/2.50 | | | (44) all_87_0 = all_81_3
% 12.60/2.50 | | |
% 12.60/2.50 | | | GROUND_INST: instantiating (4) with 0, all_81_0, all_51_3, all_49_3,
% 12.60/2.50 | | | all_53_2, simplifying with (23), (35) gives:
% 12.60/2.50 | | | (45) all_81_0 = 0
% 12.60/2.50 | | |
% 12.60/2.50 | | | COMBINE_EQS: (43), (44) imply:
% 12.60/2.50 | | | (46) all_81_3 = all_49_1
% 12.60/2.50 | | |
% 12.60/2.50 | | | REDUCE: (34), (46) imply:
% 12.60/2.50 | | | (47) k1_zfmisc_1(all_49_1) = all_81_2
% 12.60/2.50 | | |
% 12.60/2.50 | | | BETA: splitting (36) gives:
% 12.60/2.51 | | |
% 12.60/2.51 | | | Case 1:
% 12.60/2.51 | | | |
% 12.60/2.51 | | | | (48) ~ (all_81_0 = 0)
% 12.60/2.51 | | | |
% 12.60/2.51 | | | | REDUCE: (45), (48) imply:
% 12.60/2.51 | | | | (49) $false
% 12.60/2.51 | | | |
% 12.60/2.51 | | | | CLOSE: (49) is inconsistent.
% 12.60/2.51 | | | |
% 12.60/2.51 | | | Case 2:
% 12.60/2.51 | | | |
% 12.60/2.51 | | | | (50) ~ (all_81_1 = 0) | all_81_4 = 0
% 12.60/2.51 | | | |
% 12.60/2.51 | | | | BETA: splitting (50) gives:
% 12.60/2.51 | | | |
% 12.60/2.51 | | | | Case 1:
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | (51) ~ (all_81_1 = 0)
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | GROUND_INST: instantiating (2) with all_49_0, all_81_2, all_49_1,
% 12.60/2.51 | | | | | simplifying with (10), (47) gives:
% 12.60/2.51 | | | | | (52) all_81_2 = all_49_0
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | REDUCE: (32), (52) imply:
% 12.60/2.51 | | | | | (53) m1_subset_1(all_51_2, all_49_0) = all_81_1
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | GROUND_INST: instantiating (3) with 0, all_81_1, all_49_0, all_51_2,
% 12.60/2.51 | | | | | simplifying with (15), (53) gives:
% 12.60/2.51 | | | | | (54) all_81_1 = 0
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | REDUCE: (51), (54) imply:
% 12.60/2.51 | | | | | (55) $false
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | CLOSE: (55) is inconsistent.
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | Case 2:
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | (56) all_81_4 = 0
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | COMBINE_EQS: (42), (56) imply:
% 12.60/2.51 | | | | | (57) all_49_2 = 0
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | REDUCE: (6), (57) imply:
% 12.60/2.51 | | | | | (58) $false
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | | CLOSE: (58) is inconsistent.
% 12.60/2.51 | | | | |
% 12.60/2.51 | | | | End of split
% 12.60/2.51 | | | |
% 12.60/2.51 | | | End of split
% 12.60/2.51 | | |
% 12.60/2.51 | | End of split
% 12.60/2.51 | |
% 12.60/2.51 | End of split
% 12.60/2.51 |
% 12.60/2.51 End of proof
% 12.60/2.51 % SZS output end Proof for theBenchmark
% 12.60/2.51
% 12.60/2.51 1896ms
%------------------------------------------------------------------------------