TSTP Solution File: SWV099+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV099+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 : n005.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 22:54:54 EDT 2023
% Result : Theorem 15.31s 2.73s
% Output : Proof 17.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV099+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 10:07:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.02/1.50 Prover 4: Preprocessing ...
% 6.02/1.50 Prover 1: Preprocessing ...
% 6.02/1.54 Prover 5: Preprocessing ...
% 6.02/1.54 Prover 6: Preprocessing ...
% 6.02/1.54 Prover 2: Preprocessing ...
% 6.02/1.54 Prover 3: Preprocessing ...
% 6.02/1.54 Prover 0: Preprocessing ...
% 11.07/2.25 Prover 1: Warning: ignoring some quantifiers
% 12.06/2.33 Prover 3: Warning: ignoring some quantifiers
% 12.35/2.33 Prover 6: Proving ...
% 12.39/2.34 Prover 1: Constructing countermodel ...
% 12.39/2.36 Prover 3: Constructing countermodel ...
% 12.39/2.37 Prover 4: Warning: ignoring some quantifiers
% 13.31/2.48 Prover 4: Constructing countermodel ...
% 13.31/2.56 Prover 5: Proving ...
% 13.31/2.56 Prover 0: Proving ...
% 13.31/2.62 Prover 2: Proving ...
% 15.31/2.73 Prover 3: proved (2081ms)
% 15.31/2.73
% 15.31/2.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.31/2.73
% 15.31/2.73 Prover 2: stopped
% 15.31/2.73 Prover 0: stopped
% 15.31/2.74 Prover 5: stopped
% 15.36/2.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.36/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.36/2.74 Prover 6: stopped
% 15.36/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.36/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.36/2.74 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.37/2.91 Prover 8: Preprocessing ...
% 16.37/2.92 Prover 10: Preprocessing ...
% 16.37/2.93 Prover 7: Preprocessing ...
% 16.37/2.93 Prover 13: Preprocessing ...
% 17.08/2.96 Prover 1: Found proof (size 27)
% 17.08/2.96 Prover 1: proved (2313ms)
% 17.08/2.96 Prover 4: stopped
% 17.08/2.96 Prover 11: Preprocessing ...
% 17.08/2.98 Prover 10: stopped
% 17.30/2.99 Prover 7: stopped
% 17.30/3.02 Prover 13: stopped
% 17.30/3.03 Prover 11: stopped
% 17.61/3.10 Prover 8: Warning: ignoring some quantifiers
% 17.93/3.12 Prover 8: Constructing countermodel ...
% 17.93/3.13 Prover 8: stopped
% 17.93/3.13
% 17.93/3.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.93/3.13
% 17.93/3.14 % SZS output start Proof for theBenchmark
% 17.93/3.15 Assumptions after simplification:
% 17.93/3.15 ---------------------------------
% 17.93/3.15
% 17.93/3.15 (quaternion_ds1_inuse_0011)
% 17.93/3.18 $i(z_defuse) & $i(n999) & $i(pv5) & $i(xinit_noise_defuse) &
% 17.93/3.18 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 17.93/3.18 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 17.93/3.18 & ? [v0: $i] : ? [v1: $i] : (minus(n999, n1) = v0 & minus(pv5, n1) = v1 &
% 17.93/3.18 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 17.93/3.18 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use
% 17.93/3.18 & a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse,
% 17.93/3.18 n3) = use & a_select2(xinit_noise_defuse, n2) = use &
% 17.93/3.18 a_select2(xinit_noise_defuse, n1) = use & a_select2(xinit_noise_defuse, n0)
% 17.93/3.18 = use & a_select2(xinit_mean_defuse, n5) = use &
% 17.93/3.18 a_select2(xinit_mean_defuse, n4) = use & a_select2(xinit_mean_defuse, n3) =
% 17.93/3.18 use & a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 17.93/3.18 n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 17.93/3.18 a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use &
% 17.93/3.18 a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 17.93/3.18 a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 17.93/3.18 a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 17.93/3.18 a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 17.93/3.18 a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use & leq(pv5,
% 17.93/3.18 v0) = 0 & leq(n0, pv5) = 0 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] :
% 17.93/3.18 ( ~ (leq(v3, v1) = 0) | ~ (leq(v2, n2) = 0) | ~ $i(v3) | ~ $i(v2) | ?
% 17.93/3.18 [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] :
% 17.93/3.18 (a_select3(z_defuse, v2, v3) = v7 & a_select3(u_defuse, v2, v3) = v6 &
% 17.93/3.18 leq(n0, v3) = v5 & leq(n0, v2) = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) |
% 17.93/3.18 ~ (v4 = 0) | (v7 = use & v6 = use)))) & ? [v2: $i] : ? [v3: $i] : ?
% 17.93/3.18 [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 &
% 17.93/3.18 a_select3(u_defuse, v2, v3) = v4 & leq(v3, v1) = 0 & leq(v2, n2) = 0 &
% 17.93/3.18 leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & (
% 17.93/3.18 ~ (v5 = use) | ~ (v4 = use))))
% 17.93/3.18
% 17.93/3.18 (function-axioms)
% 17.93/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.93/3.19 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.93/3.19 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.93/3.19 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.93/3.19 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.93/3.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.93/3.19 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.93/3.19 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.93/3.19 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.93/3.19 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.93/3.19 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.93/3.19 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 17.93/3.19 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.93/3.19 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 17.93/3.19 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 17.93/3.19 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.93/3.19 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 17.93/3.19 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.93/3.19 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 17.93/3.19 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 17.93/3.19 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.93/3.19 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 17.93/3.19 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.93/3.19 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 17.93/3.19 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.93/3.19 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 17.93/3.19 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.93/3.19 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.93/3.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.93/3.19 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.93/3.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.93/3.19 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.93/3.19 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.93/3.19 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.93/3.19 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 17.93/3.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 17.93/3.19 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.93/3.19 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.93/3.19 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 17.93/3.19
% 17.93/3.19 Further assumptions not needed in the proof:
% 17.93/3.19 --------------------------------------------
% 17.93/3.19 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.93/3.19 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.93/3.19 finite_domain_5, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1,
% 17.93/3.19 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,
% 17.93/3.19 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,
% 17.93/3.19 gt_5_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, gt_999_3, gt_999_4, gt_999_5,
% 17.93/3.19 gt_999_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq, leq_gt1, leq_gt2,
% 17.93/3.19 leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ,
% 17.93/3.19 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 17.93/3.19 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 17.93/3.19 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 17.93/3.19 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 17.93/3.19 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 17.93/3.19 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 17.93/3.19 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 17.93/3.19 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 17.93/3.19 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 17.93/3.19 uniform_int_rand_ranges_lo
% 17.93/3.19
% 17.93/3.19 Those formulas are unsatisfiable:
% 17.93/3.19 ---------------------------------
% 17.93/3.19
% 17.93/3.19 Begin of proof
% 17.93/3.19 |
% 17.93/3.19 | ALPHA: (quaternion_ds1_inuse_0011) implies:
% 17.93/3.20 | (1) ? [v0: $i] : ? [v1: $i] : (minus(n999, n1) = v0 & minus(pv5, n1) = v1
% 17.93/3.20 | & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) =
% 17.93/3.20 | use & a_select3(u_defuse, n0, n0) = use &
% 17.93/3.20 | a_select2(xinit_noise_defuse, n5) = use &
% 17.93/3.20 | a_select2(xinit_noise_defuse, n4) = use &
% 17.93/3.20 | a_select2(xinit_noise_defuse, n3) = use &
% 17.93/3.20 | a_select2(xinit_noise_defuse, n2) = use &
% 17.93/3.20 | a_select2(xinit_noise_defuse, n1) = use &
% 17.93/3.20 | a_select2(xinit_noise_defuse, n0) = use &
% 17.93/3.20 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 17.93/3.20 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 17.93/3.20 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 17.93/3.20 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 17.93/3.20 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 17.93/3.20 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 17.93/3.20 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 17.93/3.20 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 17.93/3.20 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 17.93/3.20 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 17.93/3.20 | a_select2(rho_defuse, n0) = use & leq(pv5, v0) = 0 & leq(n0, pv5) = 0
% 17.93/3.20 | & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~ (leq(v3, v1) = 0)
% 17.93/3.20 | | ~ (leq(v2, n2) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4: any] : ?
% 17.93/3.20 | [v5: any] : ? [v6: $i] : ? [v7: $i] : (a_select3(z_defuse, v2,
% 17.93/3.20 | v3) = v7 & a_select3(u_defuse, v2, v3) = v6 & leq(n0, v3) = v5
% 17.93/3.20 | & leq(n0, v2) = v4 & $i(v7) & $i(v6) & ( ~ (v5 = 0) | ~ (v4 = 0)
% 17.93/3.20 | | (v7 = use & v6 = use)))) & ? [v2: $i] : ? [v3: $i] : ?
% 17.93/3.20 | [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v2, v3) = v5 &
% 17.93/3.20 | a_select3(u_defuse, v2, v3) = v4 & leq(v3, v1) = 0 & leq(v2, n2) =
% 17.93/3.20 | 0 & leq(n0, v3) = 0 & leq(n0, v2) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 17.93/3.20 | $i(v2) & ( ~ (v5 = use) | ~ (v4 = use))))
% 17.93/3.20 |
% 17.93/3.20 | ALPHA: (function-axioms) implies:
% 17.93/3.20 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.93/3.20 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 17.93/3.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 17.93/3.20 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 17.93/3.20 | = v0))
% 17.93/3.20 |
% 17.93/3.20 | DELTA: instantiating (1) with fresh symbols all_74_0, all_74_1 gives:
% 17.93/3.21 | (4) minus(n999, n1) = all_74_1 & minus(pv5, n1) = all_74_0 &
% 17.93/3.21 | a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 17.93/3.21 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 17.93/3.21 | use & a_select2(xinit_noise_defuse, n4) = use &
% 17.93/3.21 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 17.93/3.21 | n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 17.93/3.21 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 17.93/3.21 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 17.93/3.21 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 17.93/3.21 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 17.93/3.21 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 17.93/3.21 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 17.93/3.21 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 17.93/3.21 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 17.93/3.21 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 17.93/3.21 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 17.93/3.21 | & a_select2(rho_defuse, n0) = use & leq(pv5, all_74_1) = 0 & leq(n0,
% 17.93/3.21 | pv5) = 0 & $i(all_74_0) & $i(all_74_1) & ! [v0: $i] : ! [v1: $i] :
% 17.93/3.21 | ( ~ (leq(v1, all_74_0) = 0) | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~
% 17.93/3.21 | $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] : ? [v5: $i] :
% 17.93/3.21 | (a_select3(z_defuse, v0, v1) = v5 & a_select3(u_defuse, v0, v1) = v4
% 17.93/3.21 | & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v5) & $i(v4) & ( ~ (v3 =
% 17.93/3.21 | 0) | ~ (v2 = 0) | (v5 = use & v4 = use)))) & ? [v0: $i] : ?
% 17.93/3.21 | [v1: $i] : ? [v2: $i] : ? [v3: $i] : (a_select3(z_defuse, v0, v1) =
% 17.93/3.21 | v3 & a_select3(u_defuse, v0, v1) = v2 & leq(v1, all_74_0) = 0 &
% 17.93/3.21 | leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) = 0 & $i(v3) & $i(v2)
% 17.93/3.21 | & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~ (v2 = use)))
% 17.93/3.21 |
% 17.93/3.21 | ALPHA: (4) implies:
% 17.93/3.21 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0) | ~ (leq(v0,
% 17.93/3.21 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 17.93/3.21 | ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 17.93/3.21 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) =
% 17.93/3.21 | v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use & v4
% 17.93/3.21 | = use))))
% 17.93/3.21 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.93/3.21 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 &
% 17.93/3.21 | leq(v1, all_74_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0,
% 17.93/3.21 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~
% 17.93/3.21 | (v2 = use)))
% 17.93/3.21 |
% 17.93/3.21 | DELTA: instantiating (6) with fresh symbols all_79_0, all_79_1, all_79_2,
% 17.93/3.21 | all_79_3 gives:
% 17.93/3.21 | (7) a_select3(z_defuse, all_79_3, all_79_2) = all_79_0 &
% 17.93/3.21 | a_select3(u_defuse, all_79_3, all_79_2) = all_79_1 & leq(all_79_2,
% 17.93/3.21 | all_74_0) = 0 & leq(all_79_3, n2) = 0 & leq(n0, all_79_2) = 0 &
% 17.93/3.21 | leq(n0, all_79_3) = 0 & $i(all_79_0) & $i(all_79_1) & $i(all_79_2) &
% 17.93/3.21 | $i(all_79_3) & ( ~ (all_79_0 = use) | ~ (all_79_1 = use))
% 17.93/3.21 |
% 17.93/3.21 | ALPHA: (7) implies:
% 17.93/3.21 | (8) $i(all_79_3)
% 17.93/3.21 | (9) $i(all_79_2)
% 17.93/3.21 | (10) leq(n0, all_79_3) = 0
% 17.93/3.21 | (11) leq(n0, all_79_2) = 0
% 17.93/3.21 | (12) leq(all_79_3, n2) = 0
% 17.93/3.21 | (13) leq(all_79_2, all_74_0) = 0
% 17.93/3.21 | (14) a_select3(u_defuse, all_79_3, all_79_2) = all_79_1
% 17.93/3.21 | (15) a_select3(z_defuse, all_79_3, all_79_2) = all_79_0
% 17.93/3.21 | (16) ~ (all_79_0 = use) | ~ (all_79_1 = use)
% 17.93/3.22 |
% 17.93/3.22 | GROUND_INST: instantiating (5) with all_79_3, all_79_2, simplifying with (8),
% 17.93/3.22 | (9), (12), (13) gives:
% 17.93/3.22 | (17) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 17.93/3.22 | (a_select3(z_defuse, all_79_3, all_79_2) = v3 & a_select3(u_defuse,
% 17.93/3.22 | all_79_3, all_79_2) = v2 & leq(n0, all_79_2) = v1 & leq(n0,
% 17.93/3.22 | all_79_3) = v0 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 17.93/3.22 | (v3 = use & v2 = use)))
% 17.93/3.22 |
% 17.93/3.22 | DELTA: instantiating (17) with fresh symbols all_103_0, all_103_1, all_103_2,
% 17.93/3.22 | all_103_3 gives:
% 17.93/3.22 | (18) a_select3(z_defuse, all_79_3, all_79_2) = all_103_0 &
% 17.93/3.22 | a_select3(u_defuse, all_79_3, all_79_2) = all_103_1 & leq(n0,
% 17.93/3.22 | all_79_2) = all_103_2 & leq(n0, all_79_3) = all_103_3 &
% 17.93/3.22 | $i(all_103_0) & $i(all_103_1) & ( ~ (all_103_2 = 0) | ~ (all_103_3 =
% 17.93/3.22 | 0) | (all_103_0 = use & all_103_1 = use))
% 17.93/3.22 |
% 17.93/3.22 | ALPHA: (18) implies:
% 17.93/3.22 | (19) leq(n0, all_79_3) = all_103_3
% 17.93/3.22 | (20) leq(n0, all_79_2) = all_103_2
% 17.93/3.22 | (21) a_select3(u_defuse, all_79_3, all_79_2) = all_103_1
% 17.93/3.22 | (22) a_select3(z_defuse, all_79_3, all_79_2) = all_103_0
% 17.93/3.22 | (23) ~ (all_103_2 = 0) | ~ (all_103_3 = 0) | (all_103_0 = use & all_103_1
% 17.93/3.22 | = use)
% 17.93/3.22 |
% 17.93/3.22 | GROUND_INST: instantiating (2) with 0, all_103_3, all_79_3, n0, simplifying
% 17.93/3.22 | with (10), (19) gives:
% 17.93/3.22 | (24) all_103_3 = 0
% 17.93/3.22 |
% 17.93/3.22 | GROUND_INST: instantiating (2) with 0, all_103_2, all_79_2, n0, simplifying
% 17.93/3.22 | with (11), (20) gives:
% 17.93/3.22 | (25) all_103_2 = 0
% 17.93/3.22 |
% 17.93/3.22 | GROUND_INST: instantiating (3) with all_79_1, all_103_1, all_79_2, all_79_3,
% 17.93/3.22 | u_defuse, simplifying with (14), (21) gives:
% 17.93/3.22 | (26) all_103_1 = all_79_1
% 17.93/3.22 |
% 17.93/3.22 | GROUND_INST: instantiating (3) with all_79_0, all_103_0, all_79_2, all_79_3,
% 17.93/3.22 | z_defuse, simplifying with (15), (22) gives:
% 17.93/3.22 | (27) all_103_0 = all_79_0
% 17.93/3.22 |
% 17.93/3.22 | BETA: splitting (23) gives:
% 17.93/3.22 |
% 17.93/3.22 | Case 1:
% 17.93/3.22 | |
% 17.93/3.22 | | (28) ~ (all_103_2 = 0)
% 17.93/3.22 | |
% 17.93/3.22 | | REDUCE: (25), (28) imply:
% 17.93/3.22 | | (29) $false
% 17.93/3.22 | |
% 17.93/3.22 | | CLOSE: (29) is inconsistent.
% 17.93/3.22 | |
% 17.93/3.22 | Case 2:
% 17.93/3.22 | |
% 17.93/3.22 | | (30) ~ (all_103_3 = 0) | (all_103_0 = use & all_103_1 = use)
% 17.93/3.22 | |
% 17.93/3.22 | | BETA: splitting (30) gives:
% 17.93/3.22 | |
% 17.93/3.22 | | Case 1:
% 17.93/3.22 | | |
% 17.93/3.23 | | | (31) ~ (all_103_3 = 0)
% 17.93/3.23 | | |
% 17.93/3.23 | | | REDUCE: (24), (31) imply:
% 17.93/3.23 | | | (32) $false
% 17.93/3.23 | | |
% 17.93/3.23 | | | CLOSE: (32) is inconsistent.
% 17.93/3.23 | | |
% 17.93/3.23 | | Case 2:
% 17.93/3.23 | | |
% 17.93/3.23 | | | (33) all_103_0 = use & all_103_1 = use
% 17.93/3.23 | | |
% 17.93/3.23 | | | ALPHA: (33) implies:
% 17.93/3.23 | | | (34) all_103_1 = use
% 17.93/3.23 | | | (35) all_103_0 = use
% 17.93/3.23 | | |
% 17.93/3.23 | | | COMBINE_EQS: (27), (35) imply:
% 17.93/3.23 | | | (36) all_79_0 = use
% 17.93/3.23 | | |
% 17.93/3.23 | | | COMBINE_EQS: (26), (34) imply:
% 17.93/3.23 | | | (37) all_79_1 = use
% 17.93/3.23 | | |
% 17.93/3.23 | | | BETA: splitting (16) gives:
% 17.93/3.23 | | |
% 17.93/3.23 | | | Case 1:
% 17.93/3.23 | | | |
% 17.93/3.23 | | | | (38) ~ (all_79_0 = use)
% 17.93/3.23 | | | |
% 17.93/3.23 | | | | REDUCE: (36), (38) imply:
% 17.93/3.23 | | | | (39) $false
% 17.93/3.23 | | | |
% 17.93/3.23 | | | | CLOSE: (39) is inconsistent.
% 17.93/3.23 | | | |
% 17.93/3.23 | | | Case 2:
% 17.93/3.23 | | | |
% 17.93/3.23 | | | | (40) ~ (all_79_1 = use)
% 17.93/3.23 | | | |
% 17.93/3.23 | | | | REDUCE: (37), (40) imply:
% 17.93/3.23 | | | | (41) $false
% 17.93/3.23 | | | |
% 17.93/3.23 | | | | CLOSE: (41) is inconsistent.
% 17.93/3.23 | | | |
% 17.93/3.23 | | | End of split
% 17.93/3.23 | | |
% 17.93/3.23 | | End of split
% 17.93/3.23 | |
% 17.93/3.23 | End of split
% 17.93/3.23 |
% 17.93/3.23 End of proof
% 17.93/3.23 % SZS output end Proof for theBenchmark
% 17.93/3.23
% 17.93/3.23 2602ms
%------------------------------------------------------------------------------