TSTP Solution File: SWV199+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV199+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 22:55:19 EDT 2023
% Result : Theorem 19.71s 3.85s
% Output : Proof 27.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV199+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 29 07:52:45 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.18/0.63 ________ _____
% 0.18/0.63 ___ __ \_________(_)________________________________
% 0.18/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.63
% 0.18/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.63 (2023-06-19)
% 0.18/0.63
% 0.18/0.63 (c) Philipp Rümmer, 2009-2023
% 0.18/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.63 Amanda Stjerna.
% 0.18/0.63 Free software under BSD-3-Clause.
% 0.18/0.63
% 0.18/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.63
% 0.18/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.65 Running up to 7 provers in parallel.
% 0.18/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.90/1.68 Prover 4: Preprocessing ...
% 5.90/1.69 Prover 1: Preprocessing ...
% 6.39/1.72 Prover 2: Preprocessing ...
% 6.39/1.72 Prover 3: Preprocessing ...
% 6.39/1.72 Prover 0: Preprocessing ...
% 6.39/1.72 Prover 5: Preprocessing ...
% 6.39/1.73 Prover 6: Preprocessing ...
% 14.62/3.00 Prover 3: Warning: ignoring some quantifiers
% 14.62/3.03 Prover 1: Warning: ignoring some quantifiers
% 15.43/3.10 Prover 3: Constructing countermodel ...
% 15.43/3.13 Prover 1: Constructing countermodel ...
% 16.89/3.20 Prover 6: Proving ...
% 18.47/3.38 Prover 4: Warning: ignoring some quantifiers
% 19.41/3.53 Prover 5: Proving ...
% 19.41/3.55 Prover 4: Constructing countermodel ...
% 19.71/3.61 Prover 0: Proving ...
% 19.71/3.68 Prover 2: Proving ...
% 19.71/3.85 Prover 3: proved (3171ms)
% 19.71/3.85
% 19.71/3.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.71/3.85
% 19.71/3.85 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.71/3.86 Prover 5: stopped
% 19.71/3.86 Prover 6: stopped
% 19.71/3.86 Prover 2: stopped
% 19.71/3.88 Prover 0: stopped
% 19.71/3.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.71/3.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.71/3.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.71/3.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.41/4.09 Prover 7: Preprocessing ...
% 23.41/4.13 Prover 10: Preprocessing ...
% 24.09/4.15 Prover 1: Found proof (size 50)
% 24.09/4.15 Prover 1: proved (3489ms)
% 24.09/4.15 Prover 4: stopped
% 24.09/4.16 Prover 11: Preprocessing ...
% 24.37/4.23 Prover 8: Preprocessing ...
% 24.68/4.24 Prover 13: Preprocessing ...
% 24.78/4.25 Prover 7: stopped
% 24.78/4.29 Prover 10: stopped
% 25.25/4.35 Prover 11: stopped
% 25.59/4.40 Prover 13: stopped
% 26.05/4.53 Prover 8: Warning: ignoring some quantifiers
% 26.05/4.56 Prover 8: Constructing countermodel ...
% 26.05/4.59 Prover 8: stopped
% 26.05/4.59
% 26.05/4.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.05/4.59
% 26.05/4.60 % SZS output start Proof for theBenchmark
% 26.05/4.61 Assumptions after simplification:
% 26.05/4.61 ---------------------------------
% 26.05/4.61
% 26.05/4.61 (finite_domain_0)
% 26.39/4.67 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 26.39/4.67 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 26.39/4.67
% 26.39/4.67 (finite_domain_2)
% 26.39/4.67 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 26.39/4.67 (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) =
% 26.39/4.67 v1))
% 26.39/4.67
% 26.39/4.67 (quaternion_ds1_inuse_0010)
% 27.14/4.69 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 27.14/4.69 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 27.14/4.69 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 27.14/4.69 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 27.14/4.69 n0) = use & a_select3(u_defuse, n0, n0) = use &
% 27.14/4.69 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 27.14/4.69 = use & a_select2(xinit_noise_defuse, n3) = use &
% 27.14/4.69 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 27.14/4.69 = use & a_select2(xinit_noise_defuse, n0) = use &
% 27.14/4.69 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 27.14/4.69 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 27.14/4.69 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 27.14/4.69 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 27.14/4.69 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 27.14/4.69 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 27.14/4.69 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 27.14/4.69 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 27.14/4.69 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 27.14/4.69 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 27.14/4.69 leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (
% 27.14/4.69 ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ?
% 27.14/4.69 [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5
% 27.14/4.69 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 =
% 27.14/4.69 0) | v5 = use))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0)
% 27.14/4.69 | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 27.14/4.69 any] : ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) =
% 27.14/4.69 v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 27.14/4.69 use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 27.14/4.69 a_select3(z_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & leq(v1, n2) = 0 &
% 27.14/4.69 leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v2 =
% 27.14/4.69 pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5)
% 27.14/4.69 | ~ (v1 = n0))))
% 27.14/4.69
% 27.14/4.69 (function-axioms)
% 27.19/4.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 27.19/4.70 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 27.19/4.70 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 27.19/4.70 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 27.19/4.70 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 27.19/4.70 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 27.19/4.70 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.19/4.70 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 27.19/4.70 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 27.19/4.70 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 27.19/4.70 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 27.19/4.70 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 27.19/4.70 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 27.19/4.70 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 27.19/4.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 27.19/4.70 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 27.19/4.70 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 27.19/4.70 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 27.19/4.70 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 27.19/4.70 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 27.19/4.70 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 27.19/4.70 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 27.19/4.70 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 27.19/4.70 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 27.19/4.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.19/4.70 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 27.19/4.70 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.19/4.70 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 27.19/4.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.19/4.70 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 27.19/4.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.19/4.70 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 27.19/4.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.19/4.70 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 27.19/4.70 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 27.19/4.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 27.19/4.70 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 27.19/4.70 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 27.19/4.70 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 27.19/4.70
% 27.19/4.70 Further assumptions not needed in the proof:
% 27.19/4.70 --------------------------------------------
% 27.19/4.70 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 27.19/4.70 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0,
% 27.19/4.70 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 27.19/4.71 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 27.19/4.71 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2,
% 27.19/4.71 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt,
% 27.19/4.71 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 27.19/4.71 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 27.19/4.71 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 27.19/4.71 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 27.19/4.71 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 27.19/4.71 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 27.19/4.71 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 27.19/4.71 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 27.19/4.71 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 27.19/4.71 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 27.19/4.71 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 27.19/4.71
% 27.19/4.71 Those formulas are unsatisfiable:
% 27.19/4.71 ---------------------------------
% 27.19/4.71
% 27.19/4.71 Begin of proof
% 27.19/4.71 |
% 27.19/4.71 | ALPHA: (finite_domain_0) implies:
% 27.24/4.71 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 27.24/4.71 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 27.24/4.71 |
% 27.24/4.71 | ALPHA: (finite_domain_2) implies:
% 27.24/4.71 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ~
% 27.24/4.71 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 27.24/4.71 |
% 27.24/4.71 | ALPHA: (quaternion_ds1_inuse_0010) implies:
% 27.24/4.71 | (3) $i(pv5)
% 27.24/4.72 | (4) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 27.24/4.72 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 27.24/4.72 | a_select2(xinit_noise_defuse, n5) = use &
% 27.24/4.72 | a_select2(xinit_noise_defuse, n4) = use &
% 27.24/4.72 | a_select2(xinit_noise_defuse, n3) = use &
% 27.24/4.72 | a_select2(xinit_noise_defuse, n2) = use &
% 27.24/4.72 | a_select2(xinit_noise_defuse, n1) = use &
% 27.24/4.72 | a_select2(xinit_noise_defuse, n0) = use &
% 27.24/4.72 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 27.24/4.72 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 27.24/4.72 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 27.24/4.72 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 27.24/4.72 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 27.24/4.72 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 27.24/4.72 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 27.24/4.72 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 27.24/4.72 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 27.24/4.72 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 27.24/4.72 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 27.24/4.72 | & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) & ! [v1: $i] : !
% 27.24/4.72 | [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) |
% 27.24/4.72 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 27.24/4.72 | (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1)
% 27.24/4.72 | = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & !
% 27.24/4.72 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0)
% 27.24/4.72 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i]
% 27.24/4.72 | : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 27.24/4.72 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) &
% 27.24/4.72 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 27.24/4.72 | a_select3(z_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 & leq(v1, n2) =
% 27.24/4.72 | 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 27.24/4.72 | ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & (
% 27.24/4.72 | ~ (v2 = pv5) | ~ (v1 = n0))))
% 27.24/4.72 |
% 27.24/4.72 | ALPHA: (function-axioms) implies:
% 27.24/4.73 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.24/4.73 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 27.24/4.73 |
% 27.24/4.73 | DELTA: instantiating (4) with fresh symbol all_76_0 gives:
% 27.24/4.73 | (6) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 27.24/4.73 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 27.24/4.73 | use & a_select2(xinit_noise_defuse, n4) = use &
% 27.24/4.73 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 27.24/4.74 | n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 27.24/4.74 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 27.24/4.74 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 27.24/4.74 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 27.24/4.74 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 27.24/4.74 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 27.24/4.74 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 27.24/4.74 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 27.24/4.74 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 27.24/4.74 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 27.24/4.74 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 27.24/4.74 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5,
% 27.24/4.74 | n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(all_76_0) & !
% 27.24/4.74 | [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, n2)
% 27.24/4.74 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 27.24/4.74 | [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 27.24/4.74 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 27.24/4.74 | use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0)
% 27.24/4.74 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 27.24/4.74 | [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0,
% 27.24/4.74 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 27.24/4.74 | | v4 = use))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2
% 27.24/4.74 | = use) & a_select3(z_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 &
% 27.24/4.74 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1)
% 27.24/4.74 | & $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 =
% 27.24/4.74 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0)))
% 27.24/4.74 |
% 27.24/4.74 | ALPHA: (6) implies:
% 27.24/4.74 | (7) leq(n0, pv5) = 0
% 27.24/4.74 | (8) leq(pv5, n0) = 0
% 27.24/4.74 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) &
% 27.24/4.74 | a_select3(z_defuse, v0, v1) = v2 & leq(v1, pv5) = 0 & leq(v0, n2) = 0
% 27.24/4.74 | & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) & $i(v0) & ( ~
% 27.24/4.74 | (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 = n1)) & ( ~
% 27.24/4.74 | (v1 = pv5) | ~ (v0 = n0)))
% 27.24/4.74 |
% 27.24/4.74 | DELTA: instantiating (9) with fresh symbols all_79_0, all_79_1, all_79_2
% 27.24/4.74 | gives:
% 27.24/4.74 | (10) ~ (all_79_0 = use) & a_select3(z_defuse, all_79_2, all_79_1) =
% 27.24/4.74 | all_79_0 & leq(all_79_1, pv5) = 0 & leq(all_79_2, n2) = 0 & leq(n0,
% 27.24/4.74 | all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) & $i(all_79_1)
% 27.24/4.74 | & $i(all_79_2) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = n2)) & ( ~
% 27.24/4.74 | (all_79_1 = pv5) | ~ (all_79_2 = n1)) & ( ~ (all_79_1 = pv5) | ~
% 27.24/4.74 | (all_79_2 = n0))
% 27.24/4.74 |
% 27.24/4.74 | ALPHA: (10) implies:
% 27.24/4.75 | (11) $i(all_79_2)
% 27.24/4.75 | (12) $i(all_79_1)
% 27.24/4.75 | (13) leq(n0, all_79_2) = 0
% 27.24/4.75 | (14) leq(n0, all_79_1) = 0
% 27.24/4.75 | (15) leq(all_79_2, n2) = 0
% 27.24/4.75 | (16) leq(all_79_1, pv5) = 0
% 27.24/4.75 | (17) ~ (all_79_1 = pv5) | ~ (all_79_2 = n0)
% 27.24/4.75 | (18) ~ (all_79_1 = pv5) | ~ (all_79_2 = n1)
% 27.24/4.75 | (19) ~ (all_79_1 = pv5) | ~ (all_79_2 = n2)
% 27.24/4.75 |
% 27.24/4.75 | GROUND_INST: instantiating (1) with pv5, simplifying with (3), (7) gives:
% 27.24/4.75 | (20) pv5 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 27.24/4.75 |
% 27.24/4.75 | GROUND_INST: instantiating (1) with all_79_1, simplifying with (12), (14)
% 27.24/4.75 | gives:
% 27.24/4.75 | (21) all_79_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0)
% 27.24/4.75 |
% 27.24/4.75 | GROUND_INST: instantiating (2) with all_79_2, simplifying with (11), (15)
% 27.24/4.75 | gives:
% 27.24/4.75 | (22) all_79_2 = n2 | all_79_2 = n1 | all_79_2 = n0 | ? [v0: int] : ( ~ (v0
% 27.24/4.75 | = 0) & leq(n0, all_79_2) = v0)
% 27.24/4.75 |
% 27.24/4.75 | BETA: splitting (20) gives:
% 27.24/4.75 |
% 27.24/4.75 | Case 1:
% 27.24/4.75 | |
% 27.24/4.75 | | (23) pv5 = n0
% 27.24/4.75 | |
% 27.24/4.75 | | REDUCE: (16), (23) imply:
% 27.24/4.75 | | (24) leq(all_79_1, n0) = 0
% 27.24/4.75 | |
% 27.24/4.75 | | BETA: splitting (21) gives:
% 27.24/4.75 | |
% 27.24/4.75 | | Case 1:
% 27.24/4.75 | | |
% 27.24/4.76 | | | (25) all_79_1 = n0
% 27.24/4.76 | | |
% 27.24/4.76 | | | BETA: splitting (19) gives:
% 27.24/4.76 | | |
% 27.24/4.76 | | | Case 1:
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | (26) ~ (all_79_1 = pv5)
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | REDUCE: (23), (25), (26) imply:
% 27.24/4.76 | | | | (27) $false
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | CLOSE: (27) is inconsistent.
% 27.24/4.76 | | | |
% 27.24/4.76 | | | Case 2:
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | (28) all_79_1 = pv5
% 27.24/4.76 | | | | (29) ~ (all_79_2 = n2)
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | COMBINE_EQS: (25), (28) imply:
% 27.24/4.76 | | | | (30) pv5 = n0
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | BETA: splitting (17) gives:
% 27.24/4.76 | | | |
% 27.24/4.76 | | | | Case 1:
% 27.24/4.76 | | | | |
% 27.24/4.76 | | | | | (31) ~ (all_79_2 = n0)
% 27.24/4.76 | | | | |
% 27.24/4.76 | | | | | BETA: splitting (22) gives:
% 27.24/4.76 | | | | |
% 27.24/4.76 | | | | | Case 1:
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | | (32) all_79_2 = n0
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | | REDUCE: (31), (32) imply:
% 27.24/4.76 | | | | | | (33) $false
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | | CLOSE: (33) is inconsistent.
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | Case 2:
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | | (34) all_79_2 = n2 | all_79_2 = n1 | ? [v0: int] : ( ~ (v0 = 0)
% 27.24/4.76 | | | | | | & leq(n0, all_79_2) = v0)
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | | BETA: splitting (34) gives:
% 27.24/4.76 | | | | | |
% 27.24/4.76 | | | | | | Case 1:
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | | (35) all_79_2 = n2
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | | REDUCE: (29), (35) imply:
% 27.24/4.76 | | | | | | | (36) $false
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | | CLOSE: (36) is inconsistent.
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | Case 2:
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | | (37) all_79_2 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0,
% 27.24/4.76 | | | | | | | all_79_2) = v0)
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | | BETA: splitting (37) gives:
% 27.24/4.76 | | | | | | |
% 27.24/4.76 | | | | | | | Case 1:
% 27.24/4.76 | | | | | | | |
% 27.24/4.76 | | | | | | | | (38) all_79_2 = n1
% 27.24/4.76 | | | | | | | |
% 27.24/4.76 | | | | | | | | BETA: splitting (18) gives:
% 27.24/4.76 | | | | | | | |
% 27.24/4.77 | | | | | | | | Case 1:
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | | (39) ~ (all_79_1 = pv5)
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | | REDUCE: (23), (25), (39) imply:
% 27.24/4.77 | | | | | | | | | (40) $false
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | | CLOSE: (40) is inconsistent.
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | Case 2:
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | | (41) ~ (all_79_2 = n1)
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | | REDUCE: (38), (41) imply:
% 27.24/4.77 | | | | | | | | | (42) $false
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | | CLOSE: (42) is inconsistent.
% 27.24/4.77 | | | | | | | | |
% 27.24/4.77 | | | | | | | | End of split
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | Case 2:
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | | (43) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_79_2) = v0)
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | | DELTA: instantiating (43) with fresh symbol all_131_0 gives:
% 27.24/4.77 | | | | | | | | (44) ~ (all_131_0 = 0) & leq(n0, all_79_2) = all_131_0
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | | ALPHA: (44) implies:
% 27.24/4.77 | | | | | | | | (45) ~ (all_131_0 = 0)
% 27.24/4.77 | | | | | | | | (46) leq(n0, all_79_2) = all_131_0
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | | GROUND_INST: instantiating (5) with 0, all_131_0, all_79_2, n0,
% 27.24/4.77 | | | | | | | | simplifying with (13), (46) gives:
% 27.24/4.77 | | | | | | | | (47) all_131_0 = 0
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | | REDUCE: (45), (47) imply:
% 27.24/4.77 | | | | | | | | (48) $false
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | | CLOSE: (48) is inconsistent.
% 27.24/4.77 | | | | | | | |
% 27.24/4.77 | | | | | | | End of split
% 27.24/4.77 | | | | | | |
% 27.24/4.77 | | | | | | End of split
% 27.24/4.77 | | | | | |
% 27.24/4.77 | | | | | End of split
% 27.24/4.77 | | | | |
% 27.24/4.77 | | | | Case 2:
% 27.24/4.77 | | | | |
% 27.24/4.77 | | | | | (49) ~ (all_79_1 = pv5)
% 27.24/4.77 | | | | |
% 27.24/4.77 | | | | | REDUCE: (23), (25), (49) imply:
% 27.24/4.77 | | | | | (50) $false
% 27.24/4.77 | | | | |
% 27.24/4.77 | | | | | CLOSE: (50) is inconsistent.
% 27.24/4.77 | | | | |
% 27.24/4.77 | | | | End of split
% 27.24/4.77 | | | |
% 27.24/4.77 | | | End of split
% 27.24/4.77 | | |
% 27.24/4.77 | | Case 2:
% 27.24/4.77 | | |
% 27.24/4.77 | | | (51) ? [v0: int] : ( ~ (v0 = 0) & leq(all_79_1, n0) = v0)
% 27.24/4.77 | | |
% 27.24/4.77 | | | DELTA: instantiating (51) with fresh symbol all_111_0 gives:
% 27.24/4.78 | | | (52) ~ (all_111_0 = 0) & leq(all_79_1, n0) = all_111_0
% 27.24/4.78 | | |
% 27.24/4.78 | | | ALPHA: (52) implies:
% 27.24/4.78 | | | (53) ~ (all_111_0 = 0)
% 27.24/4.78 | | | (54) leq(all_79_1, n0) = all_111_0
% 27.24/4.78 | | |
% 27.24/4.78 | | | GROUND_INST: instantiating (5) with 0, all_111_0, n0, all_79_1,
% 27.24/4.78 | | | simplifying with (24), (54) gives:
% 27.24/4.78 | | | (55) all_111_0 = 0
% 27.24/4.78 | | |
% 27.24/4.78 | | | REDUCE: (53), (55) imply:
% 27.24/4.78 | | | (56) $false
% 27.24/4.78 | | |
% 27.24/4.78 | | | CLOSE: (56) is inconsistent.
% 27.24/4.78 | | |
% 27.24/4.78 | | End of split
% 27.24/4.78 | |
% 27.24/4.78 | Case 2:
% 27.24/4.78 | |
% 27.24/4.78 | | (57) ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 27.24/4.78 | |
% 27.24/4.78 | | DELTA: instantiating (57) with fresh symbol all_107_0 gives:
% 27.24/4.78 | | (58) ~ (all_107_0 = 0) & leq(pv5, n0) = all_107_0
% 27.24/4.78 | |
% 27.24/4.78 | | ALPHA: (58) implies:
% 27.24/4.78 | | (59) ~ (all_107_0 = 0)
% 27.24/4.78 | | (60) leq(pv5, n0) = all_107_0
% 27.24/4.78 | |
% 27.24/4.78 | | GROUND_INST: instantiating (5) with 0, all_107_0, n0, pv5, simplifying with
% 27.24/4.78 | | (8), (60) gives:
% 27.24/4.78 | | (61) all_107_0 = 0
% 27.24/4.78 | |
% 27.24/4.78 | | REDUCE: (59), (61) imply:
% 27.24/4.78 | | (62) $false
% 27.24/4.78 | |
% 27.24/4.78 | | CLOSE: (62) is inconsistent.
% 27.24/4.78 | |
% 27.24/4.78 | End of split
% 27.24/4.78 |
% 27.24/4.78 End of proof
% 27.24/4.78 % SZS output end Proof for theBenchmark
% 27.24/4.78
% 27.24/4.78 4152ms
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