TSTP Solution File: SWV200+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV200+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 : n016.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 14.67s 2.67s
% Output : Proof 17.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SWV200+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 10:01:00 EDT 2023
% 0.13/0.33 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.65/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.65/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.65/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.65/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.65/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.65/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.65/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.18/1.32 Prover 4: Preprocessing ...
% 4.18/1.32 Prover 1: Preprocessing ...
% 4.90/1.37 Prover 5: Preprocessing ...
% 4.90/1.37 Prover 3: Preprocessing ...
% 4.90/1.37 Prover 0: Preprocessing ...
% 4.90/1.38 Prover 6: Preprocessing ...
% 4.90/1.38 Prover 2: Preprocessing ...
% 11.30/2.17 Prover 3: Warning: ignoring some quantifiers
% 11.64/2.21 Prover 3: Constructing countermodel ...
% 11.83/2.23 Prover 1: Warning: ignoring some quantifiers
% 11.83/2.29 Prover 1: Constructing countermodel ...
% 12.48/2.34 Prover 6: Proving ...
% 13.02/2.46 Prover 4: Warning: ignoring some quantifiers
% 13.58/2.48 Prover 0: Proving ...
% 13.58/2.48 Prover 5: Proving ...
% 13.96/2.52 Prover 2: Proving ...
% 13.96/2.53 Prover 4: Constructing countermodel ...
% 14.67/2.67 Prover 3: proved (2058ms)
% 14.67/2.67
% 14.67/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.67/2.67
% 14.67/2.67 Prover 2: stopped
% 14.67/2.67 Prover 6: stopped
% 14.67/2.67 Prover 0: stopped
% 14.67/2.68 Prover 5: stopped
% 15.25/2.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.25/2.70 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.25/2.70 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.25/2.70 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.25/2.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.32/2.82 Prover 1: Found proof (size 29)
% 16.32/2.83 Prover 1: proved (2216ms)
% 16.32/2.83 Prover 4: stopped
% 16.32/2.84 Prover 13: Preprocessing ...
% 16.32/2.85 Prover 8: Preprocessing ...
% 16.32/2.86 Prover 7: Preprocessing ...
% 16.32/2.86 Prover 11: Preprocessing ...
% 16.32/2.87 Prover 10: Preprocessing ...
% 17.06/2.93 Prover 7: stopped
% 17.06/2.95 Prover 11: stopped
% 17.06/2.95 Prover 10: stopped
% 17.06/2.96 Prover 13: stopped
% 17.54/3.05 Prover 8: Warning: ignoring some quantifiers
% 17.54/3.06 Prover 8: Constructing countermodel ...
% 17.94/3.08 Prover 8: stopped
% 17.94/3.08
% 17.94/3.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.94/3.08
% 17.94/3.09 % SZS output start Proof for theBenchmark
% 17.94/3.10 Assumptions after simplification:
% 17.94/3.10 ---------------------------------
% 17.94/3.10
% 17.94/3.10 (quaternion_ds1_inuse_0011)
% 17.94/3.13 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 17.94/3.13 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 17.94/3.13 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 17.94/3.13 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 17.94/3.13 n0) = use & a_select3(u_defuse, n0, n0) = use &
% 17.94/3.13 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 17.94/3.13 = use & a_select2(xinit_noise_defuse, n3) = use &
% 17.94/3.13 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 17.94/3.13 = use & a_select2(xinit_noise_defuse, n0) = use &
% 17.94/3.13 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 17.94/3.13 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 17.94/3.13 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 17.94/3.13 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 17.94/3.13 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 17.94/3.13 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 17.94/3.13 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 17.94/3.13 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 17.94/3.14 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 17.94/3.14 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 17.94/3.14 leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i] : ! [v2: $i] : (
% 17.94/3.14 ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ?
% 17.94/3.14 [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(z_defuse, v1, v2) = v5
% 17.94/3.14 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 =
% 17.94/3.14 0) | v5 = use))) & ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0)
% 17.94/3.14 | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 17.94/3.14 any] : ? [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) =
% 17.94/3.14 v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 17.94/3.14 use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 17.94/3.14 a_select3(u_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) = 0 &
% 17.94/3.14 leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) & ( ~ (v2 =
% 17.94/3.14 pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & ( ~ (v2 = pv5)
% 17.94/3.14 | ~ (v1 = n0))))
% 17.94/3.14
% 17.94/3.14 (function-axioms)
% 17.94/3.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.94/3.14 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.94/3.14 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.94/3.14 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.94/3.14 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.94/3.14 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.94/3.14 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.94/3.14 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.94/3.14 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.94/3.14 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.94/3.14 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.94/3.14 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 17.94/3.14 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.94/3.14 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 17.94/3.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 17.94/3.14 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.94/3.14 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 17.94/3.14 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.94/3.14 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 17.94/3.14 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 17.94/3.14 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.94/3.14 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 17.94/3.14 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.94/3.15 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 17.94/3.15 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.94/3.15 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 17.94/3.15 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.94/3.15 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.94/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.94/3.15 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.94/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.94/3.15 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.94/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.94/3.15 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.94/3.15 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 17.94/3.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 17.94/3.15 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.94/3.15 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.94/3.15 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 17.94/3.15
% 17.94/3.15 Further assumptions not needed in the proof:
% 17.94/3.15 --------------------------------------------
% 17.94/3.15 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.94/3.15 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.94/3.15 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1,
% 17.94/3.15 gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1, gt_4_0, gt_4_1,
% 17.94/3.15 gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2, gt_5_3, gt_5_4,
% 17.94/3.15 gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5,
% 17.94/3.15 gt_998_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2,
% 17.94/3.15 leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ,
% 17.94/3.15 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 17.94/3.15 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 17.94/3.15 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 17.94/3.15 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 17.94/3.15 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 17.94/3.15 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 17.94/3.15 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 17.94/3.15 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 17.94/3.15 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 17.94/3.15 uniform_int_rand_ranges_lo
% 17.94/3.15
% 17.94/3.15 Those formulas are unsatisfiable:
% 17.94/3.15 ---------------------------------
% 17.94/3.15
% 17.94/3.15 Begin of proof
% 17.94/3.15 |
% 17.94/3.15 | ALPHA: (quaternion_ds1_inuse_0011) implies:
% 17.94/3.15 | (1) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 17.94/3.15 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 17.94/3.15 | a_select2(xinit_noise_defuse, n5) = use &
% 17.94/3.15 | a_select2(xinit_noise_defuse, n4) = use &
% 17.94/3.15 | a_select2(xinit_noise_defuse, n3) = use &
% 17.94/3.15 | a_select2(xinit_noise_defuse, n2) = use &
% 17.94/3.15 | a_select2(xinit_noise_defuse, n1) = use &
% 17.94/3.15 | a_select2(xinit_noise_defuse, n0) = use &
% 17.94/3.15 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 17.94/3.15 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 17.94/3.15 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 17.94/3.15 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 17.94/3.15 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 17.94/3.15 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 17.94/3.15 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 17.94/3.15 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 17.94/3.15 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 17.94/3.15 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 17.94/3.15 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 17.94/3.15 | & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i] : ! [v2:
% 17.94/3.15 | $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~
% 17.94/3.15 | $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 17.94/3.15 | (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1)
% 17.94/3.15 | = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & !
% 17.94/3.15 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0)
% 17.94/3.15 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i]
% 17.94/3.15 | : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 17.94/3.15 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) &
% 17.94/3.15 | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = use) &
% 17.94/3.15 | a_select3(u_defuse, v1, v2) = v3 & leq(v2, v0) = 0 & leq(v1, n2) =
% 17.94/3.15 | 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) & $i(v2) & $i(v1) &
% 17.94/3.15 | ( ~ (v2 = pv5) | ~ (v1 = n2)) & ( ~ (v2 = pv5) | ~ (v1 = n1)) & (
% 17.94/3.15 | ~ (v2 = pv5) | ~ (v1 = n0))))
% 17.94/3.15 |
% 17.94/3.15 | ALPHA: (function-axioms) implies:
% 17.94/3.16 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.94/3.16 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 17.94/3.16 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.94/3.16 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 17.94/3.16 | = v0))
% 17.94/3.16 |
% 17.94/3.16 | DELTA: instantiating (1) with fresh symbol all_76_0 gives:
% 17.94/3.16 | (4) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 17.94/3.16 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 17.94/3.16 | use & a_select2(xinit_noise_defuse, n4) = use &
% 17.94/3.16 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 17.94/3.16 | n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 17.94/3.16 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 17.94/3.16 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 17.94/3.16 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 17.94/3.16 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 17.94/3.16 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 17.94/3.16 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 17.94/3.16 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 17.94/3.16 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 17.94/3.16 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 17.94/3.16 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 17.94/3.16 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_76_0 & leq(pv5,
% 17.94/3.16 | n998) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(all_76_0) & !
% 17.94/3.16 | [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0, n2)
% 17.94/3.16 | = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ?
% 17.94/3.16 | [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 17.94/3.16 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 17.94/3.16 | use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0)
% 17.94/3.16 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 17.94/3.16 | [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0,
% 17.94/3.16 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 17.94/3.16 | | v4 = use))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2
% 17.94/3.16 | = use) & a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 &
% 17.94/3.16 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1)
% 17.94/3.16 | & $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 =
% 17.94/3.16 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0)))
% 17.94/3.16 |
% 17.94/3.16 | ALPHA: (4) implies:
% 17.94/3.16 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0,
% 17.94/3.16 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 17.94/3.16 | ? [v4: $i] : (a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 17.94/3.16 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 17.94/3.16 | use)))
% 17.94/3.16 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_76_0) = 0) | ~ (leq(v0,
% 17.94/3.16 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 17.94/3.16 | ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0, v1) = v3 &
% 17.94/3.16 | leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 =
% 17.94/3.16 | use)))
% 17.94/3.17 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = use) &
% 17.94/3.17 | a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_76_0) = 0 & leq(v0,
% 17.94/3.17 | n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v2) & $i(v1) &
% 17.94/3.17 | $i(v0) & ( ~ (v1 = pv5) | ~ (v0 = n2)) & ( ~ (v1 = pv5) | ~ (v0 =
% 17.94/3.17 | n1)) & ( ~ (v1 = pv5) | ~ (v0 = n0)))
% 17.94/3.17 |
% 17.94/3.17 | DELTA: instantiating (7) with fresh symbols all_79_0, all_79_1, all_79_2
% 17.94/3.17 | gives:
% 17.94/3.17 | (8) ~ (all_79_0 = use) & a_select3(u_defuse, all_79_2, all_79_1) =
% 17.94/3.17 | all_79_0 & leq(all_79_1, all_76_0) = 0 & leq(all_79_2, n2) = 0 &
% 17.94/3.17 | leq(n0, all_79_1) = 0 & leq(n0, all_79_2) = 0 & $i(all_79_0) &
% 17.94/3.17 | $i(all_79_1) & $i(all_79_2) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 =
% 17.94/3.17 | n2)) & ( ~ (all_79_1 = pv5) | ~ (all_79_2 = n1)) & ( ~ (all_79_1 =
% 17.94/3.17 | pv5) | ~ (all_79_2 = n0))
% 17.94/3.17 |
% 17.94/3.17 | ALPHA: (8) implies:
% 17.94/3.17 | (9) ~ (all_79_0 = use)
% 17.94/3.17 | (10) $i(all_79_2)
% 17.94/3.17 | (11) $i(all_79_1)
% 17.94/3.17 | (12) leq(n0, all_79_2) = 0
% 17.94/3.17 | (13) leq(n0, all_79_1) = 0
% 17.94/3.17 | (14) leq(all_79_2, n2) = 0
% 17.94/3.17 | (15) leq(all_79_1, all_76_0) = 0
% 17.94/3.17 | (16) a_select3(u_defuse, all_79_2, all_79_1) = all_79_0
% 17.94/3.17 |
% 17.94/3.17 | GROUND_INST: instantiating (6) with all_79_2, all_79_1, simplifying with (10),
% 17.94/3.17 | (11), (14), (15) gives:
% 17.94/3.17 | (17) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (a_select3(z_defuse,
% 17.94/3.17 | all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0,
% 17.94/3.17 | all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = use))
% 17.94/3.17 |
% 17.94/3.17 | GROUND_INST: instantiating (5) with all_79_2, all_79_1, simplifying with (10),
% 17.94/3.17 | (11), (14), (15) gives:
% 17.94/3.17 | (18) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (a_select3(u_defuse,
% 17.94/3.17 | all_79_2, all_79_1) = v2 & leq(n0, all_79_1) = v1 & leq(n0,
% 17.94/3.17 | all_79_2) = v0 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = use))
% 17.94/3.17 |
% 17.94/3.17 | DELTA: instantiating (18) with fresh symbols all_103_0, all_103_1, all_103_2
% 17.94/3.17 | gives:
% 17.94/3.17 | (19) a_select3(u_defuse, all_79_2, all_79_1) = all_103_0 & leq(n0,
% 17.94/3.17 | all_79_1) = all_103_1 & leq(n0, all_79_2) = all_103_2 &
% 17.94/3.17 | $i(all_103_0) & ( ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 =
% 17.94/3.17 | use)
% 17.94/3.17 |
% 17.94/3.17 | ALPHA: (19) implies:
% 17.94/3.17 | (20) leq(n0, all_79_2) = all_103_2
% 17.94/3.17 | (21) leq(n0, all_79_1) = all_103_1
% 17.94/3.17 | (22) a_select3(u_defuse, all_79_2, all_79_1) = all_103_0
% 17.94/3.17 | (23) ~ (all_103_1 = 0) | ~ (all_103_2 = 0) | all_103_0 = use
% 17.94/3.17 |
% 17.94/3.17 | DELTA: instantiating (17) with fresh symbols all_105_0, all_105_1, all_105_2
% 17.94/3.17 | gives:
% 17.94/3.17 | (24) a_select3(z_defuse, all_79_2, all_79_1) = all_105_0 & leq(n0,
% 17.94/3.17 | all_79_1) = all_105_1 & leq(n0, all_79_2) = all_105_2 &
% 17.94/3.17 | $i(all_105_0) & ( ~ (all_105_1 = 0) | ~ (all_105_2 = 0) | all_105_0 =
% 17.94/3.17 | use)
% 17.94/3.17 |
% 17.94/3.17 | ALPHA: (24) implies:
% 17.94/3.17 | (25) leq(n0, all_79_2) = all_105_2
% 17.94/3.17 | (26) leq(n0, all_79_1) = all_105_1
% 17.94/3.17 |
% 17.94/3.17 | GROUND_INST: instantiating (2) with 0, all_105_2, all_79_2, n0, simplifying
% 17.94/3.17 | with (12), (25) gives:
% 17.94/3.17 | (27) all_105_2 = 0
% 17.94/3.17 |
% 17.94/3.18 | GROUND_INST: instantiating (2) with all_103_2, all_105_2, all_79_2, n0,
% 17.94/3.18 | simplifying with (20), (25) gives:
% 17.94/3.18 | (28) all_105_2 = all_103_2
% 17.94/3.18 |
% 17.94/3.18 | GROUND_INST: instantiating (2) with 0, all_105_1, all_79_1, n0, simplifying
% 17.94/3.18 | with (13), (26) gives:
% 17.94/3.18 | (29) all_105_1 = 0
% 17.94/3.18 |
% 17.94/3.18 | GROUND_INST: instantiating (2) with all_103_1, all_105_1, all_79_1, n0,
% 17.94/3.18 | simplifying with (21), (26) gives:
% 17.94/3.18 | (30) all_105_1 = all_103_1
% 17.94/3.18 |
% 17.94/3.18 | GROUND_INST: instantiating (3) with all_79_0, all_103_0, all_79_1, all_79_2,
% 17.94/3.18 | u_defuse, simplifying with (16), (22) gives:
% 17.94/3.18 | (31) all_103_0 = all_79_0
% 17.94/3.18 |
% 17.94/3.18 | COMBINE_EQS: (29), (30) imply:
% 17.94/3.18 | (32) all_103_1 = 0
% 17.94/3.18 |
% 17.94/3.18 | COMBINE_EQS: (27), (28) imply:
% 17.94/3.18 | (33) all_103_2 = 0
% 17.94/3.18 |
% 17.94/3.18 | BETA: splitting (23) gives:
% 17.94/3.18 |
% 17.94/3.18 | Case 1:
% 17.94/3.18 | |
% 17.94/3.18 | | (34) ~ (all_103_1 = 0)
% 17.94/3.18 | |
% 17.94/3.18 | | REDUCE: (32), (34) imply:
% 17.94/3.18 | | (35) $false
% 17.94/3.18 | |
% 17.94/3.18 | | CLOSE: (35) is inconsistent.
% 17.94/3.18 | |
% 17.94/3.18 | Case 2:
% 17.94/3.18 | |
% 17.94/3.18 | | (36) ~ (all_103_2 = 0) | all_103_0 = use
% 17.94/3.18 | |
% 17.94/3.18 | | BETA: splitting (36) gives:
% 17.94/3.18 | |
% 17.94/3.18 | | Case 1:
% 17.94/3.18 | | |
% 17.94/3.18 | | | (37) ~ (all_103_2 = 0)
% 17.94/3.18 | | |
% 17.94/3.18 | | | REDUCE: (33), (37) imply:
% 17.94/3.18 | | | (38) $false
% 17.94/3.18 | | |
% 17.94/3.18 | | | CLOSE: (38) is inconsistent.
% 17.94/3.18 | | |
% 17.94/3.18 | | Case 2:
% 17.94/3.18 | | |
% 17.94/3.18 | | | (39) all_103_0 = use
% 17.94/3.18 | | |
% 17.94/3.18 | | | COMBINE_EQS: (31), (39) imply:
% 17.94/3.18 | | | (40) all_79_0 = use
% 17.94/3.18 | | |
% 17.94/3.18 | | | SIMP: (40) implies:
% 17.94/3.18 | | | (41) all_79_0 = use
% 17.94/3.18 | | |
% 17.94/3.18 | | | REDUCE: (9), (41) imply:
% 17.94/3.18 | | | (42) $false
% 17.94/3.18 | | |
% 17.94/3.18 | | | CLOSE: (42) is inconsistent.
% 17.94/3.18 | | |
% 17.94/3.18 | | End of split
% 17.94/3.18 | |
% 17.94/3.18 | End of split
% 17.94/3.18 |
% 17.94/3.18 End of proof
% 17.94/3.18 % SZS output end Proof for theBenchmark
% 17.94/3.18
% 17.94/3.18 2589ms
%------------------------------------------------------------------------------