TSTP Solution File: SWV204+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV204+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 : n004.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 22:55:20 EDT 2023
% Result : Theorem 17.39s 3.04s
% Output : Proof 22.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV204+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n004.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 10:19:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.85/1.52 Prover 4: Preprocessing ...
% 5.85/1.52 Prover 1: Preprocessing ...
% 6.07/1.57 Prover 3: Preprocessing ...
% 6.07/1.57 Prover 2: Preprocessing ...
% 6.07/1.57 Prover 6: Preprocessing ...
% 6.07/1.57 Prover 5: Preprocessing ...
% 6.07/1.57 Prover 0: Preprocessing ...
% 12.12/2.34 Prover 1: Warning: ignoring some quantifiers
% 12.86/2.43 Prover 6: Proving ...
% 12.86/2.44 Prover 3: Warning: ignoring some quantifiers
% 12.86/2.46 Prover 1: Constructing countermodel ...
% 12.86/2.46 Prover 3: Constructing countermodel ...
% 13.19/2.47 Prover 4: Warning: ignoring some quantifiers
% 13.19/2.53 Prover 4: Constructing countermodel ...
% 13.73/2.60 Prover 5: Proving ...
% 13.73/2.60 Prover 0: Proving ...
% 14.36/2.67 Prover 2: Proving ...
% 17.39/3.04 Prover 6: proved (2389ms)
% 17.39/3.04
% 17.39/3.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.39/3.04
% 17.39/3.04 Prover 0: stopped
% 17.39/3.04 Prover 3: stopped
% 17.39/3.05 Prover 2: stopped
% 17.39/3.06 Prover 5: stopped
% 17.39/3.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.39/3.07 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.39/3.07 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.39/3.07 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.39/3.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 17.99/3.21 Prover 7: Preprocessing ...
% 17.99/3.23 Prover 8: Preprocessing ...
% 17.99/3.24 Prover 13: Preprocessing ...
% 17.99/3.24 Prover 10: Preprocessing ...
% 19.02/3.26 Prover 11: Preprocessing ...
% 20.34/3.43 Prover 10: Warning: ignoring some quantifiers
% 20.34/3.45 Prover 10: Constructing countermodel ...
% 20.62/3.47 Prover 8: Warning: ignoring some quantifiers
% 20.62/3.49 Prover 7: Warning: ignoring some quantifiers
% 20.62/3.52 Prover 13: Warning: ignoring some quantifiers
% 20.62/3.53 Prover 8: Constructing countermodel ...
% 20.62/3.53 Prover 7: Constructing countermodel ...
% 21.22/3.54 Prover 13: Constructing countermodel ...
% 21.57/3.58 Prover 11: Warning: ignoring some quantifiers
% 21.57/3.61 Prover 11: Constructing countermodel ...
% 22.24/3.70 Prover 1: Found proof (size 36)
% 22.24/3.70 Prover 1: proved (3066ms)
% 22.24/3.70 Prover 10: stopped
% 22.24/3.70 Prover 7: stopped
% 22.24/3.70 Prover 11: stopped
% 22.24/3.70 Prover 8: stopped
% 22.24/3.70 Prover 13: stopped
% 22.24/3.70 Prover 4: stopped
% 22.24/3.70
% 22.24/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.24/3.70
% 22.24/3.71 % SZS output start Proof for theBenchmark
% 22.24/3.71 Assumptions after simplification:
% 22.24/3.71 ---------------------------------
% 22.24/3.71
% 22.24/3.71 (finite_domain_0)
% 22.63/3.74 $i(n0) & ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 22.63/3.74 int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 22.63/3.74
% 22.63/3.74 (finite_domain_2)
% 22.63/3.74 $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~
% 22.63/3.74 (leq(v0, n2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) =
% 22.63/3.74 v1))
% 22.63/3.74
% 22.63/3.74 (quaternion_ds1_inuse_0015)
% 22.63/3.75 a_select3(u_defuse, n2, n0) = use & a_select3(u_defuse, n1, n0) = use &
% 22.63/3.75 a_select3(u_defuse, n0, n0) = use & a_select2(xinit_noise_defuse, n5) = use &
% 22.63/3.75 a_select2(xinit_noise_defuse, n4) = use & a_select2(xinit_noise_defuse, n3) =
% 22.63/3.75 use & a_select2(xinit_noise_defuse, n2) = use & a_select2(xinit_noise_defuse,
% 22.63/3.75 n1) = use & a_select2(xinit_noise_defuse, n0) = use &
% 22.63/3.75 a_select2(xinit_mean_defuse, n5) = use & a_select2(xinit_mean_defuse, n4) =
% 22.63/3.75 use & a_select2(xinit_mean_defuse, n3) = use & a_select2(xinit_mean_defuse,
% 22.63/3.75 n2) = use & a_select2(xinit_mean_defuse, n1) = use &
% 22.63/3.75 a_select2(xinit_mean_defuse, n0) = use & a_select2(xinit_defuse, n5) = use &
% 22.63/3.75 a_select2(xinit_defuse, n4) = use & a_select2(xinit_defuse, n3) = use &
% 22.63/3.75 a_select2(sigma_defuse, n5) = use & a_select2(sigma_defuse, n4) = use &
% 22.63/3.75 a_select2(sigma_defuse, n3) = use & a_select2(sigma_defuse, n2) = use &
% 22.63/3.75 a_select2(sigma_defuse, n1) = use & a_select2(sigma_defuse, n0) = use &
% 22.63/3.75 a_select2(rho_defuse, n2) = use & a_select2(rho_defuse, n1) = use &
% 22.63/3.75 a_select2(rho_defuse, n0) = use & $i(z_defuse) & $i(n998) &
% 22.63/3.75 $i(xinit_noise_defuse) & $i(xinit_mean_defuse) & $i(xinit_defuse) &
% 22.63/3.75 $i(u_defuse) & $i(sigma_defuse) & $i(rho_defuse) & $i(use) & $i(n5) & $i(n4) &
% 22.63/3.75 $i(n3) & $i(n2) & $i(n1) & $i(n0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 22.63/3.75 (v2 = use | ~ (a_select3(z_defuse, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 22.63/3.75 [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] : (leq(v1, n998) = v6
% 22.63/3.75 & leq(v0, n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3 & ( ~ (v6 = 0) |
% 22.63/3.75 ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: $i] : ! [v1: $i] :
% 22.63/3.75 ! [v2: $i] : (v2 = use | ~ (a_select3(u_defuse, v0, v1) = v2) | ~ $i(v1) |
% 22.63/3.75 ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 22.63/3.75 (leq(v1, n998) = v6 & leq(v0, n2) = v5 & leq(n0, v1) = v4 & leq(n0, v0) = v3
% 22.63/3.75 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0)))) & ? [v0: $i]
% 22.63/3.75 : ? [v1: $i] : ( ~ (v1 = use) & a_select2(rho_defuse, v0) = v1 & leq(v0, n2)
% 22.63/3.75 = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 22.63/3.75
% 22.63/3.75 (function-axioms)
% 22.79/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 22.79/3.76 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 22.79/3.76 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 22.79/3.76 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 22.79/3.76 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.79/3.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 22.79/3.76 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.79/3.76 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 22.79/3.76 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.79/3.76 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 22.79/3.76 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.79/3.76 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 22.79/3.76 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 22.79/3.76 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 22.79/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 22.79/3.76 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 22.79/3.76 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 22.79/3.76 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 22.79/3.76 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 22.79/3.76 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 22.79/3.76 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 22.79/3.76 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 22.79/3.76 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 22.79/3.76 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 22.79/3.76 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.79/3.76 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 22.79/3.76 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 22.79/3.76 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 22.79/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.79/3.76 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 22.79/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.79/3.76 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 22.79/3.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.79/3.76 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 22.79/3.76 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 22.79/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 22.79/3.76 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.79/3.76 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 22.79/3.76 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 22.79/3.76
% 22.79/3.76 Further assumptions not needed in the proof:
% 22.79/3.76 --------------------------------------------
% 22.79/3.76 const_array1_select, const_array2_select, defuse, finite_domain_1,
% 22.79/3.76 finite_domain_3, finite_domain_4, finite_domain_5, gt_0_tptp_minus_1, gt_1_0,
% 22.79/3.76 gt_1_tptp_minus_1, gt_2_0, gt_2_1, gt_2_tptp_minus_1, gt_3_0, gt_3_1, gt_3_2,
% 22.79/3.76 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_0,
% 22.79/3.76 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_998_0, gt_998_1, gt_998_2,
% 22.79/3.76 gt_998_3, gt_998_4, gt_998_5, gt_998_tptp_minus_1, gt_succ, irreflexivity_gt,
% 22.79/3.76 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 22.79/3.76 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 22.79/3.76 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 22.79/3.76 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 22.79/3.76 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 22.79/3.76 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 22.79/3.76 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 22.79/3.76 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 22.79/3.76 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 22.79/3.76 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 22.79/3.76 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 22.79/3.76
% 22.79/3.76 Those formulas are unsatisfiable:
% 22.79/3.76 ---------------------------------
% 22.79/3.76
% 22.79/3.76 Begin of proof
% 22.79/3.76 |
% 22.79/3.76 | ALPHA: (finite_domain_0) implies:
% 22.79/3.76 | (1) ! [v0: $i] : (v0 = n0 | ~ (leq(n0, v0) = 0) | ~ $i(v0) | ? [v1:
% 22.79/3.76 | int] : ( ~ (v1 = 0) & leq(v0, n0) = v1))
% 22.79/3.76 |
% 22.79/3.76 | ALPHA: (finite_domain_2) implies:
% 22.79/3.76 | (2) ! [v0: $i] : (v0 = n2 | v0 = n1 | v0 = n0 | ~ (leq(v0, n2) = 0) | ~
% 22.79/3.76 | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1))
% 22.79/3.76 |
% 22.79/3.76 | ALPHA: (quaternion_ds1_inuse_0015) implies:
% 22.79/3.77 | (3) a_select2(rho_defuse, n0) = use
% 22.79/3.77 | (4) a_select2(rho_defuse, n1) = use
% 22.79/3.77 | (5) a_select2(rho_defuse, n2) = use
% 22.79/3.77 | (6) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = use) & a_select2(rho_defuse, v0)
% 22.79/3.77 | = v1 & leq(v0, n2) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 22.79/3.77 |
% 22.79/3.77 | ALPHA: (function-axioms) implies:
% 22.79/3.77 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.79/3.77 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 22.79/3.77 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.79/3.77 | (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0))
% 22.79/3.77 |
% 22.79/3.77 | DELTA: instantiating (6) with fresh symbols all_54_0, all_54_1 gives:
% 22.79/3.77 | (9) ~ (all_54_0 = use) & a_select2(rho_defuse, all_54_1) = all_54_0 &
% 22.79/3.77 | leq(all_54_1, n2) = 0 & leq(n0, all_54_1) = 0 & $i(all_54_0) &
% 22.79/3.77 | $i(all_54_1)
% 22.79/3.77 |
% 22.79/3.77 | ALPHA: (9) implies:
% 22.79/3.77 | (10) ~ (all_54_0 = use)
% 22.79/3.77 | (11) $i(all_54_1)
% 22.79/3.77 | (12) leq(n0, all_54_1) = 0
% 22.79/3.77 | (13) leq(all_54_1, n2) = 0
% 22.79/3.77 | (14) a_select2(rho_defuse, all_54_1) = all_54_0
% 22.79/3.77 |
% 22.79/3.77 | GROUND_INST: instantiating (1) with all_54_1, simplifying with (11), (12)
% 22.79/3.77 | gives:
% 22.79/3.77 | (15) all_54_1 = n0 | ? [v0: int] : ( ~ (v0 = 0) & leq(all_54_1, n0) = v0)
% 22.79/3.77 |
% 22.79/3.77 | GROUND_INST: instantiating (2) with all_54_1, simplifying with (11), (13)
% 22.79/3.77 | gives:
% 22.79/3.77 | (16) all_54_1 = n2 | all_54_1 = n1 | all_54_1 = n0 | ? [v0: int] : ( ~ (v0
% 22.79/3.77 | = 0) & leq(n0, all_54_1) = v0)
% 22.79/3.77 |
% 22.79/3.77 | BETA: splitting (15) gives:
% 22.79/3.77 |
% 22.79/3.77 | Case 1:
% 22.79/3.77 | |
% 22.79/3.77 | | (17) all_54_1 = n0
% 22.79/3.77 | |
% 22.79/3.77 | | REDUCE: (14), (17) imply:
% 22.79/3.77 | | (18) a_select2(rho_defuse, n0) = all_54_0
% 22.79/3.77 | |
% 22.79/3.77 | | GROUND_INST: instantiating (8) with use, all_54_0, n0, rho_defuse,
% 22.79/3.77 | | simplifying with (3), (18) gives:
% 22.79/3.77 | | (19) all_54_0 = use
% 22.79/3.77 | |
% 22.79/3.77 | | REDUCE: (10), (19) imply:
% 22.79/3.77 | | (20) $false
% 22.79/3.78 | |
% 22.79/3.78 | | CLOSE: (20) is inconsistent.
% 22.79/3.78 | |
% 22.79/3.78 | Case 2:
% 22.79/3.78 | |
% 22.79/3.78 | | (21) ~ (all_54_1 = n0)
% 22.79/3.78 | |
% 22.79/3.78 | | BETA: splitting (16) gives:
% 22.79/3.78 | |
% 22.79/3.78 | | Case 1:
% 22.79/3.78 | | |
% 22.79/3.78 | | | (22) all_54_1 = n0
% 22.79/3.78 | | |
% 22.79/3.78 | | | REDUCE: (21), (22) imply:
% 22.79/3.78 | | | (23) $false
% 22.79/3.78 | | |
% 22.79/3.78 | | | CLOSE: (23) is inconsistent.
% 22.79/3.78 | | |
% 22.79/3.78 | | Case 2:
% 22.79/3.78 | | |
% 22.79/3.78 | | | (24) all_54_1 = n2 | all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) &
% 22.79/3.78 | | | leq(n0, all_54_1) = v0)
% 22.79/3.78 | | |
% 22.79/3.78 | | | BETA: splitting (24) gives:
% 22.79/3.78 | | |
% 22.79/3.78 | | | Case 1:
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | (25) all_54_1 = n2
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | REDUCE: (14), (25) imply:
% 22.79/3.78 | | | | (26) a_select2(rho_defuse, n2) = all_54_0
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | GROUND_INST: instantiating (8) with use, all_54_0, n2, rho_defuse,
% 22.79/3.78 | | | | simplifying with (5), (26) gives:
% 22.79/3.78 | | | | (27) all_54_0 = use
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | REDUCE: (10), (27) imply:
% 22.79/3.78 | | | | (28) $false
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | CLOSE: (28) is inconsistent.
% 22.79/3.78 | | | |
% 22.79/3.78 | | | Case 2:
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | (29) all_54_1 = n1 | ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1)
% 22.79/3.78 | | | | = v0)
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | BETA: splitting (29) gives:
% 22.79/3.78 | | | |
% 22.79/3.78 | | | | Case 1:
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | (30) all_54_1 = n1
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | REDUCE: (14), (30) imply:
% 22.79/3.78 | | | | | (31) a_select2(rho_defuse, n1) = all_54_0
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | GROUND_INST: instantiating (8) with use, all_54_0, n1, rho_defuse,
% 22.79/3.78 | | | | | simplifying with (4), (31) gives:
% 22.79/3.78 | | | | | (32) all_54_0 = use
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | REDUCE: (10), (32) imply:
% 22.79/3.78 | | | | | (33) $false
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | CLOSE: (33) is inconsistent.
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | Case 2:
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | (34) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, all_54_1) = v0)
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | DELTA: instantiating (34) with fresh symbol all_480_0 gives:
% 22.79/3.78 | | | | | (35) ~ (all_480_0 = 0) & leq(n0, all_54_1) = all_480_0
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | ALPHA: (35) implies:
% 22.79/3.78 | | | | | (36) ~ (all_480_0 = 0)
% 22.79/3.78 | | | | | (37) leq(n0, all_54_1) = all_480_0
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | GROUND_INST: instantiating (7) with 0, all_480_0, all_54_1, n0,
% 22.79/3.78 | | | | | simplifying with (12), (37) gives:
% 22.79/3.78 | | | | | (38) all_480_0 = 0
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | REDUCE: (36), (38) imply:
% 22.79/3.78 | | | | | (39) $false
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | | CLOSE: (39) is inconsistent.
% 22.79/3.78 | | | | |
% 22.79/3.78 | | | | End of split
% 22.79/3.78 | | | |
% 22.79/3.78 | | | End of split
% 22.79/3.78 | | |
% 22.79/3.78 | | End of split
% 22.79/3.78 | |
% 22.79/3.78 | End of split
% 22.79/3.78 |
% 22.79/3.78 End of proof
% 22.79/3.78 % SZS output end Proof for theBenchmark
% 22.79/3.78
% 22.79/3.78 3164ms
%------------------------------------------------------------------------------