TSTP Solution File: SWV197+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV197+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 : n011.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 22:55:18 EDT 2023
% Result : Theorem 15.11s 2.76s
% Output : Proof 18.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV197+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n011.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 : Tue Aug 29 09:50:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.30/1.37 Prover 4: Preprocessing ...
% 4.30/1.37 Prover 1: Preprocessing ...
% 4.30/1.41 Prover 2: Preprocessing ...
% 4.30/1.41 Prover 5: Preprocessing ...
% 4.30/1.41 Prover 6: Preprocessing ...
% 4.30/1.41 Prover 0: Preprocessing ...
% 4.30/1.41 Prover 3: Preprocessing ...
% 11.14/2.26 Prover 1: Warning: ignoring some quantifiers
% 11.14/2.30 Prover 3: Warning: ignoring some quantifiers
% 11.14/2.31 Prover 6: Proving ...
% 11.79/2.33 Prover 1: Constructing countermodel ...
% 11.79/2.33 Prover 3: Constructing countermodel ...
% 11.79/2.36 Prover 4: Warning: ignoring some quantifiers
% 13.03/2.49 Prover 4: Constructing countermodel ...
% 13.27/2.51 Prover 0: Proving ...
% 13.38/2.57 Prover 2: Proving ...
% 13.38/2.59 Prover 5: Proving ...
% 14.29/2.76 Prover 3: proved (2137ms)
% 15.11/2.76
% 15.11/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.11/2.76
% 15.11/2.77 Prover 6: stopped
% 15.11/2.77 Prover 5: stopped
% 15.11/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.11/2.77 Prover 2: stopped
% 15.11/2.77 Prover 0: stopped
% 15.11/2.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.11/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.11/2.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.11/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.04/2.93 Prover 13: Preprocessing ...
% 16.04/2.93 Prover 8: Preprocessing ...
% 16.51/2.96 Prover 11: Preprocessing ...
% 16.51/2.96 Prover 10: Preprocessing ...
% 16.51/2.96 Prover 7: Preprocessing ...
% 16.98/3.04 Prover 1: Found proof (size 30)
% 16.98/3.04 Prover 1: proved (2426ms)
% 16.98/3.05 Prover 4: stopped
% 16.98/3.05 Prover 10: stopped
% 17.35/3.07 Prover 7: stopped
% 17.35/3.09 Prover 11: stopped
% 17.35/3.10 Prover 13: stopped
% 17.98/3.20 Prover 8: Warning: ignoring some quantifiers
% 17.98/3.22 Prover 8: Constructing countermodel ...
% 18.22/3.24 Prover 8: stopped
% 18.22/3.24
% 18.22/3.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.22/3.24
% 18.22/3.25 % SZS output start Proof for theBenchmark
% 18.22/3.26 Assumptions after simplification:
% 18.22/3.26 ---------------------------------
% 18.22/3.26
% 18.22/3.26 (finite_domain_0)
% 18.22/3.30 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 18.22/3.30 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 18.22/3.30
% 18.22/3.30 (quaternion_ds1_inuse_0008)
% 18.38/3.31 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 18.38/3.31 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 18.38/3.31 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 18.38/3.31 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 18.38/3.31 n0) = use & a_select3(u_defuse, n0, n0) = use &
% 18.38/3.31 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 18.38/3.31 = use & a_select2(xinit_noise_defuse, n3) = use &
% 18.38/3.31 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 18.38/3.31 = use & a_select2(xinit_noise_defuse, n0) = use &
% 18.38/3.31 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 18.38/3.31 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 18.38/3.31 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 18.38/3.31 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 18.38/3.31 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 18.38/3.31 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 18.38/3.31 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 18.38/3.31 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 18.38/3.31 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 18.38/3.31 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 18.38/3.31 leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (
% 18.38/3.31 ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ?
% 18.38/3.31 [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5
% 18.38/3.31 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 =
% 18.38/3.31 0) | v5 = use))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0)
% 18.38/3.31 | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 18.38/3.31 any] : ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) =
% 18.38/3.31 v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 18.38/3.31 use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 18.38/3.31 a_select3(z_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = 0 &
% 18.38/3.31 leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v2 =
% 18.38/3.31 pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5)
% 18.38/3.31 | ~ (v1 = n0))))
% 18.38/3.31
% 18.38/3.31 (function-axioms)
% 18.38/3.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 18.38/3.32 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 18.38/3.32 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.38/3.32 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 18.38/3.32 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.38/3.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 18.38/3.32 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.38/3.32 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 18.38/3.32 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.38/3.32 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 18.38/3.32 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 18.38/3.32 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 18.38/3.32 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 18.38/3.32 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 18.38/3.32 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 18.38/3.32 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.38/3.32 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 18.38/3.32 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 18.38/3.32 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 18.38/3.32 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 18.38/3.32 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 18.38/3.32 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 18.38/3.32 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 18.38/3.32 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 18.38/3.32 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.38/3.32 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 18.38/3.32 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 18.38/3.32 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 18.38/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.38/3.32 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 18.38/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.38/3.32 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 18.38/3.32 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 18.38/3.32 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 18.38/3.32 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 18.38/3.32 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 18.38/3.32 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 18.38/3.32 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 18.38/3.32 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 18.38/3.32
% 18.38/3.32 Further assumptions not needed in the proof:
% 18.38/3.32 --------------------------------------------
% 18.38/3.32 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 18.38/3.32 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 18.38/3.32 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 18.38/3.32 gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3,
% 18.38/3.32 gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1,
% 18.38/3.32 gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1,
% 18.38/3.32 gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus,
% 18.38/3.32 leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt,
% 18.38/3.32 matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 18.38/3.32 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 18.38/3.32 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 18.38/3.32 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 18.38/3.32 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 18.38/3.32 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 18.38/3.32 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 18.38/3.32 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 18.38/3.32 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 18.38/3.32 uniform_int_rand_ranges_lo
% 18.38/3.32
% 18.38/3.32 Those formulas are unsatisfiable:
% 18.38/3.32 ---------------------------------
% 18.38/3.32
% 18.38/3.32 Begin of proof
% 18.38/3.32 |
% 18.38/3.32 | ALPHA: (finite_domain_0) implies:
% 18.38/3.33 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 18.38/3.33 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 18.38/3.33 |
% 18.38/3.33 | ALPHA: (quaternion_ds1_inuse_0008) implies:
% 18.38/3.33 | (2) $i(pv5)
% 18.38/3.33 | (3) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 18.38/3.33 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 18.38/3.33 | a_select2(xinit_noise_defuse, n5) = use &
% 18.38/3.33 | a_select2(xinit_noise_defuse, n4) = use &
% 18.38/3.33 | a_select2(xinit_noise_defuse, n3) = use &
% 18.38/3.33 | a_select2(xinit_noise_defuse, n2) = use &
% 18.38/3.33 | a_select2(xinit_noise_defuse, n1) = use &
% 18.38/3.33 | a_select2(xinit_noise_defuse, n0) = use &
% 18.38/3.33 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 18.38/3.33 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 18.38/3.33 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 18.38/3.33 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 18.38/3.33 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 18.38/3.33 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 18.38/3.33 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 18.38/3.33 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 18.38/3.33 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 18.38/3.33 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 18.38/3.33 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 18.38/3.33 | & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(v0) & ! [v1: $i] : !
% 18.38/3.33 | [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) |
% 18.38/3.33 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 18.38/3.33 | (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1)
% 18.38/3.33 | = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & !
% 18.38/3.33 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0)
% 18.38/3.33 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i]
% 18.38/3.33 | : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 18.38/3.33 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) &
% 18.38/3.33 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 18.38/3.33 | a_select3(z_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) =
% 18.38/3.33 | 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 18.38/3.33 | ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & (
% 18.38/3.33 | ~ (v2 = pv5) | ~ (v1 = n0))))
% 18.38/3.33 |
% 18.38/3.33 | ALPHA: (function-axioms) implies:
% 18.38/3.33 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 18.38/3.33 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 18.38/3.33 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 18.38/3.33 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 18.38/3.33 | = v0))
% 18.38/3.33 |
% 18.38/3.33 | DELTA: instantiating (3) with fresh symbol all_76_0 gives:
% 18.38/3.34 | (6) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 18.38/3.34 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 18.38/3.34 | use & a_select2(xinit_noise_defuse, n4) = use &
% 18.38/3.34 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 18.38/3.34 | n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 18.38/3.34 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 18.38/3.34 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 18.38/3.34 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 18.38/3.34 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 18.38/3.34 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 18.38/3.34 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 18.38/3.34 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 18.38/3.34 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 18.38/3.34 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 18.38/3.34 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 18.38/3.34 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5,
% 18.38/3.34 | n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & $i(all_76_0) & !
% 18.38/3.34 | [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, n2)
% 18.38/3.34 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 18.38/3.34 | [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 18.38/3.34 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 18.38/3.34 | use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0)
% 18.38/3.34 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 18.38/3.34 | [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0,
% 18.38/3.34 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 18.38/3.34 | | v4 = use))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2
% 18.38/3.34 | = use) & a_select3(z_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 &
% 18.38/3.34 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1)
% 18.38/3.34 | & $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 =
% 18.38/3.34 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0)))
% 18.38/3.34 |
% 18.38/3.34 | ALPHA: (6) implies:
% 18.38/3.34 | (7) leq(n0, pv5) = 0
% 18.38/3.34 | (8) leq(pv5, n0) = 0
% 18.38/3.34 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0,
% 18.38/3.34 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 18.38/3.34 | ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 18.38/3.34 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 18.38/3.34 | use)))
% 18.38/3.34 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) &
% 18.38/3.34 | a_select3(z_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & leq(v0,
% 18.38/3.34 | n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) &
% 18.38/3.34 | $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 =
% 18.38/3.34 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0)))
% 18.38/3.34 |
% 18.38/3.34 | DELTA: instantiating (10) with fresh symbols all_79_0, all_79_1, all_79_2
% 18.38/3.34 | gives:
% 18.38/3.34 | (11) ~ (all_79_0 = use) & a_select3(z_defuse, all_79_2, all_79_1) =
% 18.38/3.34 | all_79_0 & leq(all_79_1, all_76_0) = 0 & leq(all_79_2, n2) = 0 &
% 18.38/3.34 | leq(n0, all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) &
% 18.38/3.34 | $i(all_79_1) & $i(all_79_2) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 =
% 18.38/3.34 | n2)) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = n1)) & ( ~ (all_79_1
% 18.38/3.34 | = pv5) | ~ (all_79_2 = n0))
% 18.38/3.34 |
% 18.38/3.34 | ALPHA: (11) implies:
% 18.38/3.34 | (12) ~ (all_79_0 = use)
% 18.38/3.34 | (13) $i(all_79_2)
% 18.38/3.34 | (14) $i(all_79_1)
% 18.38/3.34 | (15) leq(n0, all_79_2) = 0
% 18.38/3.34 | (16) leq(n0, all_79_1) = 0
% 18.38/3.34 | (17) leq(all_79_2, n2) = 0
% 18.38/3.34 | (18) leq(all_79_1, all_76_0) = 0
% 18.38/3.34 | (19) a_select3(z_defuse, all_79_2, all_79_1) = all_79_0
% 18.38/3.34 |
% 18.38/3.35 | GROUND_INST: instantiating (1) with pv5, simplifying with (2), (7) gives:
% 18.38/3.35 | (20) pv5 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 18.38/3.35 |
% 18.38/3.35 | GROUND_INST: instantiating (9) with all_79_2, all_79_1, simplifying with (13),
% 18.38/3.35 | (14), (17), (18) gives:
% 18.38/3.35 | (21) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (a_select3(z_defuse,
% 18.38/3.35 | all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0,
% 18.38/3.35 | all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = use))
% 18.38/3.35 |
% 18.38/3.35 | DELTA: instantiating (21) with fresh symbols all_105_0, all_105_1, all_105_2
% 18.38/3.35 | gives:
% 18.38/3.35 | (22) a_select3(z_defuse, all_79_2, all_79_1) = all_105_0 & leq(n0,
% 18.38/3.35 | all_79_1) = all_105_1 & leq(n0, all_79_2) = all_105_2 &
% 18.38/3.35 | $i(all_105_0) & ( ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | all_105_0 =
% 18.38/3.35 | use)
% 18.38/3.35 |
% 18.38/3.35 | ALPHA: (22) implies:
% 18.38/3.35 | (23) leq(n0, all_79_2) = all_105_2
% 18.38/3.35 | (24) leq(n0, all_79_1) = all_105_1
% 18.38/3.35 | (25) a_select3(z_defuse, all_79_2, all_79_1) = all_105_0
% 18.38/3.35 | (26) ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | all_105_0 = use
% 18.38/3.35 |
% 18.38/3.35 | BETA: splitting (20) gives:
% 18.38/3.35 |
% 18.38/3.35 | Case 1:
% 18.38/3.35 | |
% 18.38/3.35 | |
% 18.38/3.35 | | GROUND_INST: instantiating (4) with 0, all_105_2, all_79_2, n0, simplifying
% 18.38/3.35 | | with (15), (23) gives:
% 18.38/3.35 | | (27) all_105_2 = 0
% 18.38/3.35 | |
% 18.38/3.35 | | GROUND_INST: instantiating (4) with 0, all_105_1, all_79_1, n0, simplifying
% 18.38/3.35 | | with (16), (24) gives:
% 18.38/3.35 | | (28) all_105_1 = 0
% 18.38/3.35 | |
% 18.38/3.35 | | GROUND_INST: instantiating (5) with all_79_0, all_105_0, all_79_1, all_79_2,
% 18.38/3.35 | | z_defuse, simplifying with (19), (25) gives:
% 18.38/3.35 | | (29) all_105_0 = all_79_0
% 18.38/3.35 | |
% 18.38/3.35 | | BETA: splitting (26) gives:
% 18.38/3.35 | |
% 18.38/3.35 | | Case 1:
% 18.38/3.35 | | |
% 18.38/3.35 | | | (30) ~ (all_105_1 = 0)
% 18.38/3.35 | | |
% 18.38/3.35 | | | REDUCE: (28), (30) imply:
% 18.38/3.35 | | | (31) $false
% 18.38/3.35 | | |
% 18.38/3.35 | | | CLOSE: (31) is inconsistent.
% 18.38/3.35 | | |
% 18.38/3.35 | | Case 2:
% 18.38/3.35 | | |
% 18.38/3.35 | | | (32) ~ (all_105_2 = 0) | all_105_0 = use
% 18.38/3.35 | | |
% 18.38/3.35 | | | BETA: splitting (32) gives:
% 18.38/3.35 | | |
% 18.38/3.35 | | | Case 1:
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | (33) ~ (all_105_2 = 0)
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | REDUCE: (27), (33) imply:
% 18.38/3.35 | | | | (34) $false
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | CLOSE: (34) is inconsistent.
% 18.38/3.35 | | | |
% 18.38/3.35 | | | Case 2:
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | (35) all_105_0 = use
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | COMBINE_EQS: (29), (35) imply:
% 18.38/3.35 | | | | (36) all_79_0 = use
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | REDUCE: (12), (36) imply:
% 18.38/3.35 | | | | (37) $false
% 18.38/3.35 | | | |
% 18.38/3.35 | | | | CLOSE: (37) is inconsistent.
% 18.38/3.35 | | | |
% 18.38/3.35 | | | End of split
% 18.38/3.35 | | |
% 18.38/3.35 | | End of split
% 18.38/3.35 | |
% 18.38/3.35 | Case 2:
% 18.38/3.35 | |
% 18.38/3.35 | | (38) ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 18.38/3.35 | |
% 18.38/3.35 | | DELTA: instantiating (38) with fresh symbol all_111_0 gives:
% 18.38/3.35 | | (39) ~ (all_111_0 = 0) & leq(pv5, n0) = all_111_0
% 18.38/3.35 | |
% 18.38/3.35 | | ALPHA: (39) implies:
% 18.38/3.35 | | (40) ~ (all_111_0 = 0)
% 18.38/3.35 | | (41) leq(pv5, n0) = all_111_0
% 18.38/3.35 | |
% 18.38/3.35 | | GROUND_INST: instantiating (4) with 0, all_111_0, n0, pv5, simplifying with
% 18.38/3.35 | | (8), (41) gives:
% 18.38/3.35 | | (42) all_111_0 = 0
% 18.38/3.35 | |
% 18.38/3.35 | | REDUCE: (40), (42) imply:
% 18.38/3.35 | | (43) $false
% 18.38/3.35 | |
% 18.38/3.35 | | CLOSE: (43) is inconsistent.
% 18.38/3.35 | |
% 18.38/3.35 | End of split
% 18.38/3.35 |
% 18.38/3.35 End of proof
% 18.38/3.36 % SZS output end Proof for theBenchmark
% 18.38/3.36
% 18.38/3.36 2763ms
%------------------------------------------------------------------------------