TSTP Solution File: SWV096+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV096+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 22:54:53 EDT 2023
% Result : Theorem 15.53s 2.95s
% Output : Proof 20.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV096+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 04:51:30 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.61 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.02/1.42 Prover 1: Preprocessing ...
% 5.02/1.44 Prover 4: Preprocessing ...
% 5.02/1.45 Prover 3: Preprocessing ...
% 5.02/1.45 Prover 6: Preprocessing ...
% 5.02/1.45 Prover 5: Preprocessing ...
% 5.02/1.45 Prover 0: Preprocessing ...
% 5.02/1.45 Prover 2: Preprocessing ...
% 11.56/2.31 Prover 1: Warning: ignoring some quantifiers
% 12.35/2.41 Prover 1: Constructing countermodel ...
% 12.80/2.44 Prover 3: Warning: ignoring some quantifiers
% 12.80/2.45 Prover 4: Warning: ignoring some quantifiers
% 13.04/2.47 Prover 6: Proving ...
% 13.04/2.51 Prover 3: Constructing countermodel ...
% 13.79/2.60 Prover 4: Constructing countermodel ...
% 14.31/2.65 Prover 0: Proving ...
% 14.55/2.67 Prover 5: Proving ...
% 14.55/2.68 Prover 2: Proving ...
% 15.00/2.93 Prover 3: proved (2314ms)
% 15.00/2.94
% 15.53/2.95 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.53/2.95
% 15.53/2.96 Prover 0: stopped
% 15.53/2.96 Prover 6: stopped
% 15.53/2.96 Prover 2: stopped
% 15.53/2.98 Prover 5: stopped
% 15.53/2.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.53/2.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.53/2.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.53/2.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.53/3.01 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.26/3.18 Prover 13: Preprocessing ...
% 18.26/3.20 Prover 8: Preprocessing ...
% 18.26/3.22 Prover 10: Preprocessing ...
% 18.26/3.22 Prover 1: Found proof (size 27)
% 18.26/3.22 Prover 1: proved (2601ms)
% 18.26/3.22 Prover 4: stopped
% 18.26/3.23 Prover 11: Preprocessing ...
% 18.26/3.23 Prover 7: Preprocessing ...
% 18.87/3.30 Prover 10: stopped
% 18.87/3.31 Prover 11: stopped
% 19.28/3.31 Prover 13: stopped
% 19.28/3.33 Prover 7: stopped
% 19.47/3.41 Prover 8: Warning: ignoring some quantifiers
% 19.47/3.43 Prover 8: Constructing countermodel ...
% 19.86/3.45 Prover 8: stopped
% 19.86/3.45
% 19.86/3.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.86/3.45
% 19.86/3.45 % SZS output start Proof for theBenchmark
% 19.86/3.46 Assumptions after simplification:
% 19.86/3.46 ---------------------------------
% 19.86/3.46
% 19.86/3.46 (quaternion_ds1_inuse_0008)
% 20.09/3.52 $i(z_defuse) & $i(n6) & $i(n999) & $i(pv51) & $i(pv5) & $i(xinit_noise_defuse)
% 20.09/3.52 & $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 20.09/3.52 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 20.09/3.52 & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (minus(n6, n1) = v1 & minus(n999,
% 20.09/3.52 n1) = v0 & minus(pv5, n1) = v2 & a_select3(u_defuse, n2, n0) = use &
% 20.09/3.52 a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 20.09/3.52 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 20.09/3.52 = use & a_select2(xinit_noise_defuse, n3) = use &
% 20.09/3.52 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 20.09/3.52 = use & a_select2(xinit_noise_defuse, n0) = use &
% 20.09/3.52 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 20.09/3.52 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 20.09/3.52 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 20.09/3.52 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 20.09/3.52 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 20.09/3.52 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 20.09/3.52 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 20.09/3.52 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 20.09/3.52 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 20.09/3.52 a_select2(rho_defuse, n0) = use & leq(pv51, v1) = 0 & leq(pv5, v0) = 0 &
% 20.09/3.52 leq(n0, pv51) = 0 & leq(n0, pv5) = 0 & $i(v2) & $i(v1) & $i(v0) & ! [v3:
% 20.09/3.52 $i] : ! [v4: $i] : ( ~ (leq(v4, v2) = 0) | ~ (leq(v3, n2) = 0) | ~
% 20.09/3.52 $i(v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8:
% 20.09/3.52 $i] : (a_select3(z_defuse, v3, v4) = v8 & a_select3(u_defuse, v3, v4) =
% 20.09/3.52 v7 & leq(n0, v4) = v6 & leq(n0, v3) = v5 & $i(v8) & $i(v7) & ( ~ (v6 =
% 20.09/3.52 0) | ~ (v5 = 0) | (v8 = use & v7 = use)))) & ? [v3: $i] : ? [v4:
% 20.09/3.52 $i] : ? [v5: $i] : ? [v6: $i] : (a_select3(z_defuse, v3, v4) = v6 &
% 20.09/3.52 a_select3(u_defuse, v3, v4) = v5 & leq(v4, v2) = 0 & leq(v3, n2) = 0 &
% 20.09/3.52 leq(n0, v4) = 0 & leq(n0, v3) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & (
% 20.09/3.52 ~ (v6 = use) | ~ (v5 = use))))
% 20.09/3.52
% 20.09/3.52 (function-axioms)
% 20.09/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 20.09/3.53 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 20.09/3.53 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.09/3.53 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 20.09/3.53 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.09/3.53 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 20.09/3.53 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 20.09/3.53 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 20.09/3.53 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.09/3.53 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 20.09/3.53 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.09/3.53 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 20.09/3.53 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 20.09/3.53 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 20.09/3.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 20.09/3.53 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.09/3.53 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 20.09/3.53 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 20.09/3.53 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 20.09/3.53 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 20.09/3.53 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 20.09/3.53 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 20.09/3.53 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 20.09/3.53 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 20.09/3.53 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.09/3.53 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 20.09/3.53 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 20.09/3.53 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 20.09/3.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.09/3.53 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 20.09/3.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.09/3.53 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 20.09/3.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 20.09/3.53 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 20.09/3.53 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 20.09/3.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 20.09/3.53 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.09/3.53 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 20.09/3.53 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 20.09/3.53
% 20.09/3.53 Further assumptions not needed in the proof:
% 20.09/3.53 --------------------------------------------
% 20.09/3.53 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 20.09/3.53 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 20.09/3.53 finite_domain_5, finite_domain_6, gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1,
% 20.09/3.53 gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2, gt_3_tptp_minus_1,
% 20.09/3.53 gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0, gt_5_1, gt_5_2,
% 20.09/3.53 gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_6_0, gt_6_1, gt_6_2, gt_6_3, gt_6_4,
% 20.09/3.53 gt_6_5, gt_6_tptp_minus_1, gt_999_0, gt_999_1, gt_999_2, gt_999_3, gt_999_4,
% 20.09/3.53 gt_999_5, gt_999_6, gt_999_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq,
% 20.09/3.53 leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 20.09/3.53 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 20.09/3.53 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 20.09/3.53 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 20.09/3.53 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 20.09/3.53 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 20.09/3.53 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 20.09/3.53 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 20.09/3.53 successor_2, successor_3, successor_4, successor_5, successor_6, sum_plus_base,
% 20.09/3.53 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 20.09/3.53 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 20.09/3.53
% 20.09/3.53 Those formulas are unsatisfiable:
% 20.09/3.53 ---------------------------------
% 20.09/3.53
% 20.09/3.53 Begin of proof
% 20.09/3.53 |
% 20.09/3.53 | ALPHA: (quaternion_ds1_inuse_0008) implies:
% 20.09/3.54 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (minus(n6, n1) = v1 &
% 20.09/3.54 | minus(n999, n1) = v0 & minus(pv5, n1) = v2 & a_select3(u_defuse, n2,
% 20.09/3.54 | n0) = use & a_select3(u_defuse, n1, n0) = use & a_select3(u_defuse,
% 20.09/3.54 | n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use &
% 20.09/3.54 | a_select2(xinit_noise_defuse, n4) = use &
% 20.09/3.54 | a_select2(xinit_noise_defuse, n3) = use &
% 20.09/3.54 | a_select2(xinit_noise_defuse, n2) = use &
% 20.09/3.54 | a_select2(xinit_noise_defuse, n1) = use &
% 20.09/3.54 | a_select2(xinit_noise_defuse, n0) = use &
% 20.09/3.54 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 20.09/3.54 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 20.09/3.54 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 20.09/3.54 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 20.09/3.54 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 20.09/3.54 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 20.09/3.54 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 20.09/3.54 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 20.09/3.54 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 20.09/3.54 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 20.09/3.54 | a_select2(rho_defuse, n0) = use & leq(pv51, v1) = 0 & leq(pv5, v0) =
% 20.09/3.54 | 0 & leq(n0, pv51) = 0 & leq(n0, pv5) = 0 & $i(v2) & $i(v1) & $i(v0) &
% 20.09/3.54 | ! [v3: $i] : ! [v4: $i] : ( ~ (leq(v4, v2) = 0) | ~ (leq(v3, n2) =
% 20.09/3.54 | 0) | ~ $i(v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any] : ?
% 20.09/3.54 | [v7: $i] : ? [v8: $i] : (a_select3(z_defuse, v3, v4) = v8 &
% 20.09/3.54 | a_select3(u_defuse, v3, v4) = v7 & leq(n0, v4) = v6 & leq(n0, v3)
% 20.09/3.54 | = v5 & $i(v8) & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = use &
% 20.09/3.54 | v7 = use)))) & ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 20.09/3.54 | [v6: $i] : (a_select3(z_defuse, v3, v4) = v6 & a_select3(u_defuse,
% 20.09/3.54 | v3, v4) = v5 & leq(v4, v2) = 0 & leq(v3, n2) = 0 & leq(n0, v4) =
% 20.09/3.54 | 0 & leq(n0, v3) = 0 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v6 =
% 20.09/3.54 | use) | ~ (v5 = use))))
% 20.09/3.54 |
% 20.09/3.54 | ALPHA: (function-axioms) implies:
% 20.09/3.54 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 20.09/3.54 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 20.09/3.54 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 20.09/3.54 | (v1 = v0 | ~ (a_select3(v4, v3, v2) = v1) | ~ (a_select3(v4, v3, v2)
% 20.09/3.54 | = v0))
% 20.09/3.54 |
% 20.09/3.54 | DELTA: instantiating (1) with fresh symbols all_77_0, all_77_1, all_77_2
% 20.09/3.54 | gives:
% 20.09/3.55 | (4) minus(n6, n1) = all_77_1 & minus(n999, n1) = all_77_2 & minus(pv5, n1)
% 20.09/3.55 | = all_77_0 & a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 20.09/3.55 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 20.09/3.55 | a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse,
% 20.09/3.55 | n4) = use & a_select2(xinit_noise_defuse, n3) = use &
% 20.09/3.55 | a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse,
% 20.09/3.55 | n1) = use & a_select2(xinit_noise_defuse, n0) = use &
% 20.09/3.55 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 20.09/3.55 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 20.09/3.55 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 20.09/3.55 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 20.09/3.55 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use &
% 20.09/3.55 | a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) = use &
% 20.09/3.55 | a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3) = use &
% 20.09/3.55 | a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse, n1) = use &
% 20.09/3.55 | a_select2(sigma_defuse, n0) = use & a_select2(rho_defuse, n2) = use &
% 20.09/3.55 | a_select2(rho_defuse, n1) = use & a_select2(rho_defuse, n0) = use &
% 20.09/3.55 | leq(pv51, all_77_1) = 0 & leq(pv5, all_77_2) = 0 & leq(n0, pv51) = 0 &
% 20.09/3.55 | leq(n0, pv5) = 0 & $i(all_77_0) & $i(all_77_1) & $i(all_77_2) & ! [v0:
% 20.09/3.55 | $i] : ! [v1: $i] : ( ~ (leq(v1, all_77_0) = 0) | ~ (leq(v0, n2) =
% 20.09/3.55 | 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4:
% 20.09/3.55 | $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 20.09/3.55 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) =
% 20.09/3.55 | v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use & v4
% 20.09/3.55 | = use)))) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 20.09/3.55 | $i] : (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1)
% 20.09/3.55 | = v2 & leq(v1, all_77_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 &
% 20.09/3.55 | leq(n0, v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use)
% 20.09/3.55 | | ~ (v2 = use)))
% 20.09/3.55 |
% 20.09/3.55 | ALPHA: (4) implies:
% 20.09/3.55 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_77_0) = 0) | ~ (leq(v0,
% 20.09/3.55 | n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 20.09/3.55 | ? [v4: $i] : ? [v5: $i] : (a_select3(z_defuse, v0, v1) = v5 &
% 20.09/3.55 | a_select3(u_defuse, v0, v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) =
% 20.09/3.55 | v2 & $i(v5) & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = use & v4
% 20.09/3.55 | = use))))
% 20.09/3.55 | (6) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 20.09/3.55 | (a_select3(z_defuse, v0, v1) = v3 & a_select3(u_defuse, v0, v1) = v2 &
% 20.09/3.55 | leq(v1, all_77_0) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0,
% 20.09/3.55 | v0) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = use) | ~
% 20.09/3.55 | (v2 = use)))
% 20.09/3.55 |
% 20.09/3.55 | DELTA: instantiating (6) with fresh symbols all_82_0, all_82_1, all_82_2,
% 20.09/3.55 | all_82_3 gives:
% 20.09/3.55 | (7) a_select3(z_defuse, all_82_3, all_82_2) = all_82_0 &
% 20.09/3.55 | a_select3(u_defuse, all_82_3, all_82_2) = all_82_1 & leq(all_82_2,
% 20.09/3.55 | all_77_0) = 0 & leq(all_82_3, n2) = 0 & leq(n0, all_82_2) = 0 &
% 20.09/3.55 | leq(n0, all_82_3) = 0 & $i(all_82_0) & $i(all_82_1) & $i(all_82_2) &
% 20.09/3.55 | $i(all_82_3) & ( ~ (all_82_0 = use) | ~ (all_82_1 = use))
% 20.09/3.55 |
% 20.09/3.55 | ALPHA: (7) implies:
% 20.09/3.55 | (8) $i(all_82_3)
% 20.09/3.55 | (9) $i(all_82_2)
% 20.09/3.55 | (10) leq(n0, all_82_3) = 0
% 20.09/3.55 | (11) leq(n0, all_82_2) = 0
% 20.09/3.55 | (12) leq(all_82_3, n2) = 0
% 20.09/3.55 | (13) leq(all_82_2, all_77_0) = 0
% 20.09/3.55 | (14) a_select3(u_defuse, all_82_3, all_82_2) = all_82_1
% 20.09/3.55 | (15) a_select3(z_defuse, all_82_3, all_82_2) = all_82_0
% 20.09/3.55 | (16) ~ (all_82_0 = use) | ~ (all_82_1 = use)
% 20.09/3.55 |
% 20.09/3.55 | GROUND_INST: instantiating (5) with all_82_3, all_82_2, simplifying with (8),
% 20.09/3.55 | (9), (12), (13) gives:
% 20.09/3.56 | (17) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 20.09/3.56 | (a_select3(z_defuse, all_82_3, all_82_2) = v3 & a_select3(u_defuse,
% 20.09/3.56 | all_82_3, all_82_2) = v2 & leq(n0, all_82_2) = v1 & leq(n0,
% 20.09/3.56 | all_82_3) = v0 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 20.09/3.56 | (v3 = use & v2 = use)))
% 20.09/3.56 |
% 20.09/3.56 | DELTA: instantiating (17) with fresh symbols all_110_0, all_110_1, all_110_2,
% 20.09/3.56 | all_110_3 gives:
% 20.09/3.56 | (18) a_select3(z_defuse, all_82_3, all_82_2) = all_110_0 &
% 20.09/3.56 | a_select3(u_defuse, all_82_3, all_82_2) = all_110_1 & leq(n0,
% 20.09/3.56 | all_82_2) = all_110_2 & leq(n0, all_82_3) = all_110_3 &
% 20.09/3.56 | $i(all_110_0) & $i(all_110_1) & ( ~ (all_110_2 = 0) | ~ (all_110_3 =
% 20.09/3.56 | 0) | (all_110_0 = use & all_110_1 = use))
% 20.09/3.56 |
% 20.09/3.56 | ALPHA: (18) implies:
% 20.09/3.56 | (19) leq(n0, all_82_3) = all_110_3
% 20.09/3.56 | (20) leq(n0, all_82_2) = all_110_2
% 20.09/3.56 | (21) a_select3(u_defuse, all_82_3, all_82_2) = all_110_1
% 20.09/3.56 | (22) a_select3(z_defuse, all_82_3, all_82_2) = all_110_0
% 20.09/3.56 | (23) ~ (all_110_2 = 0) | ~ (all_110_3 = 0) | (all_110_0 = use & all_110_1
% 20.09/3.56 | = use)
% 20.09/3.56 |
% 20.09/3.56 | GROUND_INST: instantiating (2) with 0, all_110_3, all_82_3, n0, simplifying
% 20.09/3.56 | with (10), (19) gives:
% 20.09/3.56 | (24) all_110_3 = 0
% 20.09/3.56 |
% 20.09/3.56 | GROUND_INST: instantiating (2) with 0, all_110_2, all_82_2, n0, simplifying
% 20.09/3.56 | with (11), (20) gives:
% 20.09/3.56 | (25) all_110_2 = 0
% 20.09/3.56 |
% 20.09/3.56 | GROUND_INST: instantiating (3) with all_82_1, all_110_1, all_82_2, all_82_3,
% 20.09/3.56 | u_defuse, simplifying with (14), (21) gives:
% 20.09/3.56 | (26) all_110_1 = all_82_1
% 20.09/3.56 |
% 20.09/3.56 | GROUND_INST: instantiating (3) with all_82_0, all_110_0, all_82_2, all_82_3,
% 20.09/3.56 | z_defuse, simplifying with (15), (22) gives:
% 20.09/3.56 | (27) all_110_0 = all_82_0
% 20.09/3.56 |
% 20.09/3.56 | BETA: splitting (23) gives:
% 20.09/3.56 |
% 20.09/3.56 | Case 1:
% 20.09/3.56 | |
% 20.09/3.56 | | (28) ~ (all_110_2 = 0)
% 20.09/3.56 | |
% 20.09/3.56 | | REDUCE: (25), (28) imply:
% 20.09/3.56 | | (29) $false
% 20.09/3.56 | |
% 20.09/3.56 | | CLOSE: (29) is inconsistent.
% 20.09/3.56 | |
% 20.09/3.56 | Case 2:
% 20.09/3.56 | |
% 20.09/3.56 | | (30) ~ (all_110_3 = 0) | (all_110_0 = use & all_110_1 = use)
% 20.09/3.56 | |
% 20.09/3.56 | | BETA: splitting (30) gives:
% 20.09/3.56 | |
% 20.09/3.56 | | Case 1:
% 20.09/3.56 | | |
% 20.09/3.56 | | | (31) ~ (all_110_3 = 0)
% 20.09/3.56 | | |
% 20.09/3.56 | | | REDUCE: (24), (31) imply:
% 20.09/3.56 | | | (32) $false
% 20.09/3.56 | | |
% 20.09/3.56 | | | CLOSE: (32) is inconsistent.
% 20.09/3.56 | | |
% 20.09/3.56 | | Case 2:
% 20.09/3.56 | | |
% 20.09/3.56 | | | (33) all_110_0 = use & all_110_1 = use
% 20.09/3.56 | | |
% 20.09/3.56 | | | ALPHA: (33) implies:
% 20.09/3.56 | | | (34) all_110_1 = use
% 20.09/3.56 | | | (35) all_110_0 = use
% 20.09/3.56 | | |
% 20.09/3.56 | | | COMBINE_EQS: (27), (35) imply:
% 20.09/3.56 | | | (36) all_82_0 = use
% 20.09/3.56 | | |
% 20.09/3.56 | | | COMBINE_EQS: (26), (34) imply:
% 20.09/3.56 | | | (37) all_82_1 = use
% 20.09/3.56 | | |
% 20.09/3.56 | | | BETA: splitting (16) gives:
% 20.09/3.56 | | |
% 20.09/3.56 | | | Case 1:
% 20.09/3.56 | | | |
% 20.09/3.56 | | | | (38) ~ (all_82_0 = use)
% 20.09/3.56 | | | |
% 20.09/3.56 | | | | REDUCE: (36), (38) imply:
% 20.09/3.56 | | | | (39) $false
% 20.09/3.56 | | | |
% 20.09/3.56 | | | | CLOSE: (39) is inconsistent.
% 20.09/3.56 | | | |
% 20.09/3.56 | | | Case 2:
% 20.09/3.56 | | | |
% 20.09/3.56 | | | | (40) ~ (all_82_1 = use)
% 20.09/3.56 | | | |
% 20.09/3.56 | | | | REDUCE: (37), (40) imply:
% 20.09/3.56 | | | | (41) $false
% 20.09/3.56 | | | |
% 20.09/3.56 | | | | CLOSE: (41) is inconsistent.
% 20.09/3.56 | | | |
% 20.09/3.56 | | | End of split
% 20.09/3.56 | | |
% 20.09/3.56 | | End of split
% 20.09/3.56 | |
% 20.09/3.56 | End of split
% 20.09/3.56 |
% 20.09/3.56 End of proof
% 20.09/3.56 % SZS output end Proof for theBenchmark
% 20.09/3.56
% 20.09/3.56 2965ms
%------------------------------------------------------------------------------