TSTP Solution File: SWV194+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV194+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 : n009.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 16.93s 2.99s
% Output : Proof 21.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV194+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n009.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 08:01:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.54/0.60 ________ _____
% 0.54/0.60 ___ __ \_________(_)________________________________
% 0.54/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.54/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.54/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.54/0.60
% 0.54/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.54/0.60 (2023-06-19)
% 0.54/0.60
% 0.54/0.60 (c) Philipp Rümmer, 2009-2023
% 0.54/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.54/0.60 Amanda Stjerna.
% 0.54/0.60 Free software under BSD-3-Clause.
% 0.54/0.60
% 0.54/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.54/0.60
% 0.54/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.62 Running up to 7 provers in parallel.
% 0.54/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.54/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.54/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.54/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.54/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.54/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.54/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.41/1.45 Prover 1: Preprocessing ...
% 5.41/1.46 Prover 4: Preprocessing ...
% 5.69/1.49 Prover 5: Preprocessing ...
% 5.69/1.49 Prover 2: Preprocessing ...
% 5.69/1.50 Prover 0: Preprocessing ...
% 5.69/1.50 Prover 6: Preprocessing ...
% 5.69/1.50 Prover 3: Preprocessing ...
% 11.73/2.31 Prover 1: Warning: ignoring some quantifiers
% 11.73/2.35 Prover 3: Warning: ignoring some quantifiers
% 12.41/2.38 Prover 3: Constructing countermodel ...
% 12.41/2.38 Prover 4: Warning: ignoring some quantifiers
% 12.41/2.39 Prover 1: Constructing countermodel ...
% 12.41/2.40 Prover 6: Proving ...
% 13.55/2.52 Prover 5: Proving ...
% 13.55/2.53 Prover 4: Constructing countermodel ...
% 13.55/2.57 Prover 0: Proving ...
% 14.01/2.58 Prover 2: Proving ...
% 16.93/2.98 Prover 3: proved (2357ms)
% 16.93/2.98
% 16.93/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.93/2.99
% 16.93/2.99 Prover 6: stopped
% 16.93/2.99 Prover 2: stopped
% 16.93/2.99 Prover 5: stopped
% 16.93/2.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.93/2.99 Prover 0: stopped
% 16.93/3.01 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.93/3.01 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.93/3.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.35/3.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.33/3.15 Prover 1: Found proof (size 17)
% 18.33/3.15 Prover 1: proved (2530ms)
% 18.33/3.15 Prover 4: stopped
% 19.12/3.25 Prover 11: Preprocessing ...
% 19.12/3.25 Prover 10: Preprocessing ...
% 19.36/3.29 Prover 7: Preprocessing ...
% 19.36/3.29 Prover 13: Preprocessing ...
% 19.36/3.31 Prover 8: Preprocessing ...
% 19.82/3.35 Prover 10: stopped
% 19.82/3.37 Prover 11: stopped
% 20.10/3.40 Prover 7: stopped
% 20.10/3.41 Prover 13: stopped
% 20.61/3.50 Prover 8: Warning: ignoring some quantifiers
% 20.61/3.52 Prover 8: Constructing countermodel ...
% 20.90/3.54 Prover 8: stopped
% 20.90/3.54
% 20.90/3.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.90/3.54
% 20.90/3.54 % SZS output start Proof for theBenchmark
% 20.90/3.55 Assumptions after simplification:
% 20.90/3.55 ---------------------------------
% 20.90/3.55
% 20.90/3.55 (finite_domain_0)
% 21.05/3.58 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 21.05/3.58 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 21.05/3.58
% 21.05/3.58 (irreflexivity_gt)
% 21.05/3.58 ! [v0: $i] : ( ~ (gt(v0, v0) = 0) | ~ $i(v0))
% 21.05/3.58
% 21.05/3.59 (quaternion_ds1_inuse_0005)
% 21.05/3.60 $i(z_defuse) & $i(n998) & $i(pv5) & $i(xinit_noise_defuse) &
% 21.05/3.60 $i(xinit_mean_defuse) & $i(xinit_defuse) & $i(u_defuse) & $i(sigma_defuse) &
% 21.05/3.60 $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) & $i(n3) & $i(n2) & $i(n1) & $i(n0)
% 21.05/3.60 & ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1,
% 21.05/3.60 n0) = use & a_select3(u_defuse, n0, n0) = use &
% 21.05/3.60 a_select2(xinit_noise_defuse, n5) = use & a_select2(xinit_noise_defuse, n4)
% 21.05/3.60 = use & a_select2(xinit_noise_defuse, n3) = use &
% 21.05/3.60 a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse, n1)
% 21.05/3.60 = use & a_select2(xinit_noise_defuse, n0) = use &
% 21.05/3.60 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 21.05/3.60 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 21.05/3.60 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 21.05/3.60 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 21.05/3.60 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 21.05/3.60 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 21.05/3.60 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 21.05/3.60 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 21.05/3.60 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 21.05/3.60 a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0 &
% 21.05/3.60 leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & ! [v1: $i]
% 21.05/3.60 : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) |
% 21.05/3.60 ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] :
% 21.05/3.60 (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 &
% 21.05/3.60 $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) & ! [v1: $i] : !
% 21.05/3.60 [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0) | ~ $i(v2) | ~
% 21.05/3.60 $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i] : (a_select3(u_defuse,
% 21.05/3.60 v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0, v1) = v3 & $i(v5) & ( ~ (v4
% 21.05/3.60 = 0) | ~ (v3 = 0) | v5 = use))) & ? [v1: $i] : ? [v2: $i] : ?
% 21.05/3.60 [v3: $i] : ( ~ (v3 = use) & a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5)
% 21.05/3.60 = 0 & leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) &
% 21.05/3.60 $i(v2) & $i(v1)))
% 21.05/3.60
% 21.05/3.60 (function-axioms)
% 21.05/3.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.05/3.61 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 21.05/3.61 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 21.05/3.61 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 21.05/3.61 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.05/3.61 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 21.05/3.61 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 21.05/3.61 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 21.05/3.61 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.05/3.61 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 21.05/3.61 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.05/3.61 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 21.05/3.61 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 21.05/3.61 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 21.05/3.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 21.05/3.61 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 21.05/3.61 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 21.05/3.61 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 21.05/3.61 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 21.05/3.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 21.05/3.61 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 21.05/3.61 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 21.05/3.61 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 21.05/3.61 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 21.05/3.61 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.05/3.61 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 21.05/3.61 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 21.05/3.61 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 21.05/3.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.05/3.61 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 21.05/3.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.05/3.61 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 21.05/3.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.05/3.61 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 21.05/3.61 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 21.05/3.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 21.05/3.61 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.05/3.61 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 21.05/3.61 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 21.05/3.61
% 21.05/3.61 Further assumptions not needed in the proof:
% 21.05/3.61 --------------------------------------------
% 21.05/3.61 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 21.05/3.61 finite_domain_2, finite_domain_3, finite_domain_4, finite_domain_5,
% 21.05/3.61 gt_0_tptp_minus_1, gt_1_0, gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1,
% 21.05/3.61 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,
% 21.05/3.61 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,
% 21.05/3.61 gt_998_0, gt_998_1, gt_998_2, gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1,
% 21.05/3.61 gt_succ, leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ,
% 21.05/3.61 leq_succ_gt, leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1,
% 21.05/3.61 matrix_symm_aba2, matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update,
% 21.05/3.61 matrix_symm_sub, matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1,
% 21.05/3.61 pred_succ, reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3,
% 21.05/3.61 sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r,
% 21.05/3.61 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l,
% 21.05/3.61 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1,
% 21.05/3.61 successor_1, successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 21.05/3.61 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 21.05/3.61 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 21.05/3.61
% 21.05/3.61 Those formulas are unsatisfiable:
% 21.05/3.61 ---------------------------------
% 21.05/3.61
% 21.05/3.61 Begin of proof
% 21.05/3.61 |
% 21.05/3.61 | ALPHA: (finite_domain_0) implies:
% 21.05/3.61 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 21.05/3.61 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 21.05/3.61 |
% 21.05/3.61 | ALPHA: (quaternion_ds1_inuse_0005) implies:
% 21.05/3.61 | (2) $i(pv5)
% 21.05/3.62 | (3) ? [v0: $i] : (a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse,
% 21.05/3.62 | n1, n0) = use & a_select3(u_defuse, n0, n0) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n5) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n4) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n3) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n2) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n1) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n0) = use &
% 21.05/3.62 | a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse,
% 21.05/3.62 | n4) = use & a_select2(xinit_mean_defuse, n3) = use &
% 21.05/3.62 | a_select2(xinit_mean_defuse, n2) = use & a_select2(xinit_mean_defuse,
% 21.05/3.62 | n1) = use & a_select2(xinit_mean_defuse, n0) = use &
% 21.05/3.62 | a_select2(xinit_defuse, n5) = use & a_select2(xinit_defuse, n4) = use
% 21.05/3.62 | & a_select2(xinit_defuse, n3) = use & a_select2(sigma_defuse, n5) =
% 21.05/3.62 | use & a_select2(sigma_defuse, n4) = use & a_select2(sigma_defuse, n3)
% 21.05/3.62 | = use & a_select2(sigma_defuse, n2) = use & a_select2(sigma_defuse,
% 21.05/3.62 | n1) = use & a_select2(sigma_defuse, n0) = use &
% 21.05/3.62 | a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 21.05/3.62 | a_select2(rho_defuse, n0) = use & pred(pv5) = v0 & leq(pv5, n998) = 0
% 21.05/3.62 | & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 & $i(v0) & !
% 21.05/3.62 | [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) = 0)
% 21.05/3.62 | | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ? [v5: $i]
% 21.05/3.62 | : (a_select3(z_defuse, v1, v2) = v5 & leq(n0, v2) = v4 & leq(n0,
% 21.05/3.62 | v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = use))) &
% 21.05/3.62 | ! [v1: $i] : ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ (leq(v1, n2) =
% 21.05/3.62 | 0) | ~ $i(v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : ?
% 21.05/3.62 | [v5: $i] : (a_select3(u_defuse, v1, v2) = v5 & leq(n0, v2) = v4 &
% 21.05/3.62 | leq(n0, v1) = v3 & $i(v5) & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 =
% 21.05/3.62 | use))) & ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 =
% 21.05/3.62 | use) & a_select3(u_defuse, v1, v2) = v3 & leq(v2, pv5) = 0 &
% 21.05/3.62 | leq(v1, n2) = 0 & leq(n0, v2) = 0 & leq(n0, v1) = 0 & $i(v3) &
% 21.05/3.62 | $i(v2) & $i(v1)))
% 21.05/3.62 |
% 21.05/3.62 | ALPHA: (function-axioms) implies:
% 21.05/3.62 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.05/3.62 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 21.05/3.62 |
% 21.05/3.62 | DELTA: instantiating (3) with fresh symbol all_74_0 gives:
% 21.05/3.62 | (5) a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 21.05/3.62 | a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) =
% 21.05/3.62 | use & a_select2(xinit_noise_defuse, n4) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n3) = use & a_select2(xinit_noise_defuse,
% 21.05/3.62 | n2) = use & a_select2(xinit_noise_defuse, n1) = use &
% 21.05/3.62 | a_select2(xinit_noise_defuse, n0) = use & a_select2(xinit_mean_defuse,
% 21.05/3.62 | n5) = use & a_select2(xinit_mean_defuse, n4) = use &
% 21.05/3.62 | a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 21.05/3.62 | n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 21.05/3.62 | a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) =
% 21.05/3.62 | use & a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) =
% 21.05/3.62 | use & a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) =
% 21.05/3.62 | use & a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) =
% 21.05/3.62 | use & a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) =
% 21.05/3.62 | use & a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use
% 21.05/3.62 | & a_select2(rho_defuse, n0) = use & pred(pv5) = all_74_0 & leq(pv5,
% 21.05/3.62 | n998) = 0 & leq(pv5, n0) = 0 & leq(n0, pv5) = 0 & gt(pv5, n0) = 0 &
% 21.05/3.62 | $i(all_74_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1, all_74_0) = 0)
% 21.05/3.62 | | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ?
% 21.05/3.62 | [v3: any] : ? [v4: $i] : (a_select3(z_defuse, v0, v1) = v4 & leq(n0,
% 21.05/3.62 | v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0)
% 21.05/3.62 | | v4 = use))) & ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v1,
% 21.05/3.62 | all_74_0) = 0) | ~ (leq(v0, n2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 21.05/3.62 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (a_select3(u_defuse, v0,
% 21.05/3.62 | v1) = v4 & leq(n0, v1) = v3 & leq(n0, v0) = v2 & $i(v4) & ( ~ (v3
% 21.05/3.62 | = 0) | ~ (v2 = 0) | v4 = use))) & ? [v0: $i] : ? [v1: $i] :
% 21.05/3.62 | ? [v2: $i] : ( ~ (v2 = use) & a_select3(u_defuse, v0, v1) = v2 &
% 21.05/3.62 | leq(v1, pv5) = 0 & leq(v0, n2) = 0 & leq(n0, v1) = 0 & leq(n0, v0) =
% 21.05/3.62 | 0 & $i(v2) & $i(v1) & $i(v0))
% 21.05/3.62 |
% 21.05/3.62 | ALPHA: (5) implies:
% 21.05/3.63 | (6) gt(pv5, n0) = 0
% 21.05/3.63 | (7) leq(n0, pv5) = 0
% 21.05/3.63 | (8) leq(pv5, n0) = 0
% 21.05/3.63 |
% 21.05/3.63 | GROUND_INST: instantiating (1) with pv5, simplifying with (2), (7) gives:
% 21.05/3.63 | (9) pv5 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 21.05/3.63 |
% 21.05/3.63 | BETA: splitting (9) gives:
% 21.05/3.63 |
% 21.05/3.63 | Case 1:
% 21.05/3.63 | |
% 21.05/3.63 | | (10) pv5 = n0
% 21.05/3.63 | |
% 21.05/3.63 | | REDUCE: (6), (10) imply:
% 21.05/3.63 | | (11) gt(n0, n0) = 0
% 21.05/3.63 | |
% 21.05/3.63 | | REDUCE: (2), (10) imply:
% 21.05/3.63 | | (12) $i(n0)
% 21.05/3.63 | |
% 21.05/3.63 | | GROUND_INST: instantiating (irreflexivity_gt) with n0, simplifying with
% 21.05/3.63 | | (11), (12) gives:
% 21.05/3.63 | | (13) $false
% 21.05/3.63 | |
% 21.05/3.63 | | CLOSE: (13) is inconsistent.
% 21.05/3.63 | |
% 21.05/3.63 | Case 2:
% 21.05/3.63 | |
% 21.05/3.63 | | (14) ? [v0: int] : ( ~ (v0 = 0) & leq(pv5, n0) = v0)
% 21.05/3.63 | |
% 21.05/3.63 | | DELTA: instantiating (14) with fresh symbol all_107_0 gives:
% 21.05/3.63 | | (15) ~ (all_107_0 = 0) & leq(pv5, n0) = all_107_0
% 21.05/3.63 | |
% 21.05/3.63 | | ALPHA: (15) implies:
% 21.39/3.63 | | (16) ~ (all_107_0 = 0)
% 21.39/3.63 | | (17) leq(pv5, n0) = all_107_0
% 21.39/3.63 | |
% 21.39/3.63 | | GROUND_INST: instantiating (4) with 0, all_107_0, n0, pv5, simplifying with
% 21.39/3.63 | | (8), (17) gives:
% 21.39/3.63 | | (18) all_107_0 = 0
% 21.39/3.63 | |
% 21.39/3.63 | | REDUCE: (16), (18) imply:
% 21.39/3.63 | | (19) $false
% 21.39/3.63 | |
% 21.39/3.63 | | CLOSE: (19) is inconsistent.
% 21.39/3.63 | |
% 21.39/3.63 | End of split
% 21.39/3.63 |
% 21.39/3.63 End of proof
% 21.39/3.63 % SZS output end Proof for theBenchmark
% 21.39/3.63
% 21.39/3.63 3025ms
%------------------------------------------------------------------------------