TSTP Solution File: SWV179+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV179+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 : n001.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 22:55:14 EDT 2023
% Result : Theorem 14.26s 2.71s
% Output : Proof 17.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV179+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 09:24:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.59 ________ _____
% 0.18/0.59 ___ __ \_________(_)________________________________
% 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59
% 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59 (2023-06-19)
% 0.18/0.59
% 0.18/0.59 (c) Philipp Rümmer, 2009-2023
% 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59 Amanda Stjerna.
% 0.18/0.59 Free software under BSD-3-Clause.
% 0.18/0.59
% 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59
% 0.18/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.68/1.39 Prover 1: Preprocessing ...
% 4.68/1.39 Prover 4: Preprocessing ...
% 4.68/1.45 Prover 3: Preprocessing ...
% 4.68/1.45 Prover 6: Preprocessing ...
% 4.68/1.45 Prover 0: Preprocessing ...
% 4.68/1.45 Prover 2: Preprocessing ...
% 4.68/1.45 Prover 5: Preprocessing ...
% 10.17/2.28 Prover 1: Warning: ignoring some quantifiers
% 11.51/2.32 Prover 3: Warning: ignoring some quantifiers
% 11.51/2.36 Prover 1: Constructing countermodel ...
% 11.51/2.37 Prover 3: Constructing countermodel ...
% 11.51/2.38 Prover 6: Proving ...
% 11.51/2.39 Prover 4: Warning: ignoring some quantifiers
% 12.23/2.47 Prover 4: Constructing countermodel ...
% 12.81/2.53 Prover 5: Proving ...
% 12.81/2.54 Prover 2: Proving ...
% 13.42/2.64 Prover 0: Proving ...
% 14.26/2.71 Prover 3: proved (2083ms)
% 14.26/2.71
% 14.26/2.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.26/2.71
% 14.26/2.71 Prover 6: stopped
% 14.40/2.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.40/2.71 Prover 2: stopped
% 14.42/2.72 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.42/2.72 Prover 5: stopped
% 14.42/2.72 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.42/2.72 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.42/2.72 Prover 0: stopped
% 14.42/2.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.10/2.86 Prover 11: Preprocessing ...
% 15.10/2.86 Prover 7: Preprocessing ...
% 15.73/2.89 Prover 13: Preprocessing ...
% 15.73/2.91 Prover 8: Preprocessing ...
% 15.73/2.92 Prover 1: Found proof (size 17)
% 15.73/2.92 Prover 1: proved (2312ms)
% 15.73/2.93 Prover 4: stopped
% 15.73/2.93 Prover 10: Preprocessing ...
% 15.73/2.99 Prover 7: stopped
% 15.73/3.02 Prover 11: stopped
% 15.73/3.04 Prover 10: stopped
% 15.73/3.04 Prover 13: stopped
% 16.66/3.13 Prover 8: Warning: ignoring some quantifiers
% 17.36/3.15 Prover 8: Constructing countermodel ...
% 17.44/3.17 Prover 8: stopped
% 17.44/3.17
% 17.44/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.44/3.17
% 17.44/3.18 % SZS output start Proof for theBenchmark
% 17.44/3.18 Assumptions after simplification:
% 17.44/3.18 ---------------------------------
% 17.44/3.18
% 17.44/3.18 (cl5_nebula_init_0071)
% 17.44/3.21 $i(sigma_init) & $i(rho_init) & $i(mu_init) & $i(rhoold_init) & $i(muold_init)
% 17.44/3.21 & $i(center_init) & $i(init) & $i(q_init) & $i(n135299) & $i(pv68) & $i(n4) &
% 17.44/3.21 $i(n0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rho_init,
% 17.44/3.21 pv68) = v1 & pred(pv68) = v0 & leq(pv68, n4) = 0 & leq(n0, pv68) = 0 &
% 17.44/3.21 $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.44/3.21 (a_select3(center_init, v2, n0) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 17.44/3.21 any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 =
% 17.44/3.21 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.44/3.21 (a_select2(sigma_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any]
% 17.44/3.21 : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) &
% 17.44/3.21 ! [v2: $i] : ! [v3: $i] : (v3 = init | ~ (a_select2(rho_init, v2) = v3) |
% 17.44/3.21 ~ $i(v2) | ? [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) =
% 17.44/3.21 v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 =
% 17.44/3.21 init | ~ (a_select2(mu_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 17.44/3.21 [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 =
% 17.44/3.21 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.44/3.21 (a_select2(muold_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5: any]
% 17.44/3.21 : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) &
% 17.44/3.21 ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: $i]
% 17.44/3.21 : (a_select2(rhoold_init, v2) = v4 & leq(n0, v2) = v3 & $i(v4) & ( ~ (v3 =
% 17.44/3.21 0) | v4 = init))) & ! [v2: $i] : ( ~ (leq(v2, n135299) = 0) | ~
% 17.44/3.21 $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & leq(n0, v2) = v3) | ! [v3: $i] :
% 17.44/3.21 ! [v4: $i] : (v4 = init | ~ (a_select3(q_init, v2, v3) = v4) | ~ $i(v3)
% 17.44/3.21 | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & (
% 17.44/3.21 ~ (v6 = 0) | ~ (v5 = 0))))))
% 17.44/3.21
% 17.44/3.21 (function-axioms)
% 17.71/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.71/3.22 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.71/3.22 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.71/3.22 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.71/3.22 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.71/3.22 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.71/3.22 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.71/3.22 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.71/3.22 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.71/3.22 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.71/3.22 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.71/3.22 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 17.71/3.22 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.71/3.22 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 17.71/3.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 17.71/3.22 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.71/3.22 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 17.71/3.22 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.71/3.22 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 17.71/3.22 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 17.71/3.22 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.71/3.22 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 17.71/3.22 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.71/3.22 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 17.71/3.22 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.71/3.22 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 17.71/3.22 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.71/3.22 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.71/3.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.71/3.22 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.71/3.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.71/3.22 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.71/3.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.71/3.22 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.71/3.22 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 17.71/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 17.71/3.22 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.71/3.22 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.71/3.22 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 17.71/3.22
% 17.71/3.22 Further assumptions not needed in the proof:
% 17.71/3.22 --------------------------------------------
% 17.71/3.22 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.71/3.22 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.71/3.22 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 17.71/3.22 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 17.71/3.22 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,
% 17.71/3.22 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,
% 17.71/3.22 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 17.71/3.22 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 17.71/3.22 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 17.71/3.22 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 17.71/3.22 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 17.71/3.22 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 17.71/3.22 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 17.71/3.22 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 17.71/3.22 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 17.71/3.22 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 17.71/3.22 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 17.71/3.22 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 17.71/3.22
% 17.71/3.22 Those formulas are unsatisfiable:
% 17.71/3.22 ---------------------------------
% 17.71/3.22
% 17.71/3.22 Begin of proof
% 17.71/3.23 |
% 17.71/3.23 | ALPHA: (cl5_nebula_init_0071) implies:
% 17.71/3.23 | (1) $i(pv68)
% 17.71/3.23 | (2) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rho_init, pv68)
% 17.71/3.23 | = v1 & pred(pv68) = v0 & leq(pv68, n4) = 0 & leq(n0, pv68) = 0 &
% 17.71/3.23 | $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.71/3.23 | (a_select3(center_init, v2, n0) = v3) | ~ $i(v2) | ? [v4: any] :
% 17.71/3.23 | ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) |
% 17.71/3.23 | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.71/3.23 | (a_select2(sigma_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 17.71/3.23 | [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) |
% 17.71/3.23 | ~ (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.71/3.23 | (a_select2(rho_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 17.71/3.23 | any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~
% 17.71/3.23 | (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.71/3.23 | (a_select2(mu_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ? [v5:
% 17.71/3.23 | any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) | ~
% 17.71/3.23 | (v4 = 0)))) & ! [v2: $i] : ! [v3: $i] : (v3 = init | ~
% 17.71/3.23 | (a_select2(muold_init, v2) = v3) | ~ $i(v2) | ? [v4: any] : ?
% 17.71/3.23 | [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 = 0) |
% 17.71/3.23 | ~ (v4 = 0)))) & ! [v2: $i] : ( ~ (leq(v2, v0) = 0) | ~ $i(v2)
% 17.71/3.23 | | ? [v3: any] : ? [v4: $i] : (a_select2(rhoold_init, v2) = v4 &
% 17.71/3.23 | leq(n0, v2) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = init))) & ! [v2:
% 17.71/3.23 | $i] : ( ~ (leq(v2, n135299) = 0) | ~ $i(v2) | ? [v3: int] : ( ~
% 17.71/3.23 | (v3 = 0) & leq(n0, v2) = v3) | ! [v3: $i] : ! [v4: $i] : (v4 =
% 17.71/3.23 | init | ~ (a_select3(q_init, v2, v3) = v4) | ~ $i(v3) | ? [v5:
% 17.71/3.23 | any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & (
% 17.71/3.23 | ~ (v6 = 0) | ~ (v5 = 0))))))
% 17.71/3.23 |
% 17.71/3.23 | ALPHA: (function-axioms) implies:
% 17.71/3.23 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.71/3.23 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 17.71/3.23 |
% 17.71/3.23 | DELTA: instantiating (2) with fresh symbols all_74_0, all_74_1 gives:
% 17.71/3.24 | (4) ~ (all_74_0 = init) & a_select2(rho_init, pv68) = all_74_0 &
% 17.71/3.24 | pred(pv68) = all_74_1 & leq(pv68, n4) = 0 & leq(n0, pv68) = 0 &
% 17.71/3.24 | $i(all_74_0) & $i(all_74_1) & ! [v0: $i] : ! [v1: $i] : (v1 = init |
% 17.71/3.24 | ~ (a_select3(center_init, v0, n0) = v1) | ~ $i(v0) | ? [v2: any] :
% 17.71/3.24 | ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |
% 17.71/3.24 | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 17.71/3.24 | (a_select2(sigma_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.71/3.24 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2
% 17.71/3.24 | = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 17.71/3.24 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.71/3.24 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2
% 17.71/3.24 | = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 17.71/3.24 | (a_select2(mu_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.71/3.24 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2
% 17.71/3.24 | = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 17.71/3.24 | (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.71/3.24 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2
% 17.71/3.24 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_74_1) = 0) | ~ $i(v0)
% 17.71/3.24 | | ? [v1: any] : ? [v2: $i] : (a_select2(rhoold_init, v0) = v2 &
% 17.71/3.24 | leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & ! [v0:
% 17.71/3.24 | $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 17.71/3.24 | = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 = init
% 17.71/3.24 | | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3: any] :
% 17.71/3.24 | ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) |
% 17.71/3.24 | ~ (v3 = 0)))))
% 17.71/3.24 |
% 17.71/3.24 | ALPHA: (4) implies:
% 17.71/3.24 | (5) ~ (all_74_0 = init)
% 17.71/3.24 | (6) leq(n0, pv68) = 0
% 17.71/3.24 | (7) leq(pv68, n4) = 0
% 17.71/3.24 | (8) a_select2(rho_init, pv68) = all_74_0
% 17.71/3.24 | (9) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) =
% 17.71/3.24 | v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 &
% 17.71/3.24 | leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 17.71/3.24 |
% 17.71/3.24 | GROUND_INST: instantiating (9) with pv68, all_74_0, simplifying with (1), (8)
% 17.71/3.24 | gives:
% 17.71/3.24 | (10) all_74_0 = init | ? [v0: any] : ? [v1: any] : (leq(pv68, n4) = v1 &
% 17.71/3.24 | leq(n0, pv68) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.71/3.24 |
% 17.71/3.24 | BETA: splitting (10) gives:
% 17.71/3.24 |
% 17.71/3.24 | Case 1:
% 17.71/3.24 | |
% 17.71/3.24 | | (11) all_74_0 = init
% 17.71/3.24 | |
% 17.71/3.24 | | REDUCE: (5), (11) imply:
% 17.71/3.24 | | (12) $false
% 17.71/3.24 | |
% 17.71/3.24 | | CLOSE: (12) is inconsistent.
% 17.71/3.24 | |
% 17.71/3.24 | Case 2:
% 17.71/3.24 | |
% 17.71/3.24 | | (13) ? [v0: any] : ? [v1: any] : (leq(pv68, n4) = v1 & leq(n0, pv68) =
% 17.71/3.24 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.71/3.24 | |
% 17.71/3.24 | | DELTA: instantiating (13) with fresh symbols all_105_0, all_105_1 gives:
% 17.71/3.24 | | (14) leq(pv68, n4) = all_105_0 & leq(n0, pv68) = all_105_1 & ( ~
% 17.71/3.24 | | (all_105_0 = 0) | ~ (all_105_1 = 0))
% 17.71/3.24 | |
% 17.71/3.24 | | ALPHA: (14) implies:
% 17.71/3.24 | | (15) leq(n0, pv68) = all_105_1
% 17.71/3.24 | | (16) leq(pv68, n4) = all_105_0
% 17.71/3.24 | | (17) ~ (all_105_0 = 0) | ~ (all_105_1 = 0)
% 17.71/3.24 | |
% 17.71/3.24 | | GROUND_INST: instantiating (3) with 0, all_105_1, pv68, n0, simplifying with
% 17.71/3.24 | | (6), (15) gives:
% 17.71/3.24 | | (18) all_105_1 = 0
% 17.71/3.24 | |
% 17.71/3.24 | | GROUND_INST: instantiating (3) with 0, all_105_0, n4, pv68, simplifying with
% 17.71/3.24 | | (7), (16) gives:
% 17.71/3.24 | | (19) all_105_0 = 0
% 17.71/3.24 | |
% 17.71/3.24 | | BETA: splitting (17) gives:
% 17.71/3.24 | |
% 17.71/3.24 | | Case 1:
% 17.71/3.24 | | |
% 17.71/3.24 | | | (20) ~ (all_105_0 = 0)
% 17.71/3.24 | | |
% 17.71/3.24 | | | REDUCE: (19), (20) imply:
% 17.71/3.24 | | | (21) $false
% 17.71/3.24 | | |
% 17.71/3.24 | | | CLOSE: (21) is inconsistent.
% 17.71/3.24 | | |
% 17.71/3.24 | | Case 2:
% 17.71/3.24 | | |
% 17.71/3.25 | | | (22) ~ (all_105_1 = 0)
% 17.71/3.25 | | |
% 17.71/3.25 | | | REDUCE: (18), (22) imply:
% 17.71/3.25 | | | (23) $false
% 17.71/3.25 | | |
% 17.71/3.25 | | | CLOSE: (23) is inconsistent.
% 17.71/3.25 | | |
% 17.71/3.25 | | End of split
% 17.71/3.25 | |
% 17.71/3.25 | End of split
% 17.71/3.25 |
% 17.71/3.25 End of proof
% 17.71/3.25 % SZS output end Proof for theBenchmark
% 17.71/3.25
% 17.71/3.25 2652ms
%------------------------------------------------------------------------------