TSTP Solution File: SWV168+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV168+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 22:55:11 EDT 2023
% Result : Theorem 17.97s 3.20s
% Output : Proof 21.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV168+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.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 03:13:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.69/1.49 Prover 1: Preprocessing ...
% 5.69/1.51 Prover 4: Preprocessing ...
% 5.95/1.53 Prover 3: Preprocessing ...
% 5.95/1.53 Prover 6: Preprocessing ...
% 5.95/1.53 Prover 2: Preprocessing ...
% 5.95/1.53 Prover 0: Preprocessing ...
% 5.95/1.54 Prover 5: Preprocessing ...
% 13.52/2.63 Prover 1: Warning: ignoring some quantifiers
% 13.52/2.67 Prover 3: Warning: ignoring some quantifiers
% 14.58/2.72 Prover 3: Constructing countermodel ...
% 14.58/2.72 Prover 1: Constructing countermodel ...
% 14.58/2.73 Prover 6: Proving ...
% 15.06/2.81 Prover 4: Warning: ignoring some quantifiers
% 16.05/2.96 Prover 4: Constructing countermodel ...
% 16.05/2.97 Prover 5: Proving ...
% 16.05/3.00 Prover 0: Proving ...
% 16.72/3.04 Prover 2: Proving ...
% 17.97/3.19 Prover 3: proved (2552ms)
% 17.97/3.19
% 17.97/3.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.97/3.20
% 17.97/3.20 Prover 0: stopped
% 17.97/3.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.97/3.20 Prover 2: stopped
% 17.97/3.20 Prover 5: stopped
% 17.97/3.21 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.97/3.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.97/3.21 Prover 6: stopped
% 17.97/3.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.97/3.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.10/3.35 Prover 10: Preprocessing ...
% 19.10/3.41 Prover 13: Preprocessing ...
% 19.10/3.42 Prover 11: Preprocessing ...
% 19.72/3.43 Prover 8: Preprocessing ...
% 19.72/3.43 Prover 7: Preprocessing ...
% 19.72/3.43 Prover 1: Found proof (size 24)
% 19.72/3.43 Prover 1: proved (2804ms)
% 19.72/3.44 Prover 4: stopped
% 20.18/3.52 Prover 7: stopped
% 20.18/3.53 Prover 10: stopped
% 20.18/3.55 Prover 11: stopped
% 20.80/3.58 Prover 13: stopped
% 21.12/3.70 Prover 8: Warning: ignoring some quantifiers
% 21.53/3.73 Prover 8: Constructing countermodel ...
% 21.53/3.75 Prover 8: stopped
% 21.53/3.75
% 21.53/3.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.53/3.75
% 21.53/3.75 % SZS output start Proof for theBenchmark
% 21.53/3.76 Assumptions after simplification:
% 21.53/3.76 ---------------------------------
% 21.53/3.76
% 21.53/3.76 (cl5_nebula_init_0016)
% 21.81/3.79 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(loopcounter) &
% 21.81/3.79 $i(center_init) & $i(sigma_init) & $i(rho_init) & $i(q_init) & $i(n135299) &
% 21.81/3.79 $i(pv46) & $i(init) & $i(pv40) & $i(mu_init) & $i(n4) & $i(n1) & $i(n0) & ?
% 21.81/3.79 [v0: $i] : ? [v1: any] : ? [v2: $i] : ( ~ (v2 = init) & a_select3(q_init,
% 21.81/3.79 pv46, pv40) = v2 & a_select2(mu_init, pv40) = init & pred(pv40) = v0 &
% 21.81/3.79 leq(pv46, n135299) = 0 & leq(pv40, n4) = 0 & leq(n0, pv46) = 0 & leq(n0,
% 21.81/3.79 pv40) = 0 & gt(loopcounter, n1) = v1 & $i(v2) & $i(v0) & ! [v3: $i] : !
% 21.81/3.79 [v4: $i] : (v4 = init | ~ (a_select3(center_init, v3, n0) = v4) | ~ $i(v3)
% 21.81/3.79 | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~
% 21.81/3.79 (v6 = 0) | ~ (v5 = 0)))) & ! [v3: $i] : ! [v4: $i] : (v4 = init |
% 21.81/3.79 ~ (a_select2(rho_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any]
% 21.81/3.80 : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) &
% 21.81/3.80 ! [v3: $i] : ( ~ (leq(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: $i]
% 21.81/3.80 : (a_select2(sigma_init, v3) = v5 & leq(n0, v3) = v4 & $i(v5) & ( ~ (v4 =
% 21.81/3.80 0) | v5 = init))) & ! [v3: $i] : ( ~ (leq(v3, v0) = 0) | ~ $i(v3)
% 21.81/3.80 | ? [v4: any] : ? [v5: $i] : (a_select2(mu_init, v3) = v5 & leq(n0, v3)
% 21.81/3.80 = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = init))) & ! [v3: $i] : ( ~ (leq(v3,
% 21.81/3.80 n135299) = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & leq(n0, v3)
% 21.81/3.80 = v4) | ! [v4: $i] : ! [v5: $i] : (v5 = init | ~ (a_select3(q_init,
% 21.81/3.80 v3, v4) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (leq(v4,
% 21.81/3.80 n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))) & ( ~
% 21.81/3.80 (v1 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 21.81/3.80 (a_select2(sigmaold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 21.81/3.80 any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 21.81/3.80 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init |
% 21.81/3.80 ~ (a_select2(rhoold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 21.81/3.80 any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 21.81/3.80 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init |
% 21.81/3.80 ~ (a_select2(muold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 21.81/3.80 any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 21.81/3.80 0))))))
% 21.81/3.80
% 21.81/3.80 (function-axioms)
% 21.81/3.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 21.81/3.80 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 21.81/3.80 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 21.81/3.80 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 21.81/3.80 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.81/3.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 21.81/3.80 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 21.81/3.80 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 21.81/3.80 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.81/3.80 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 21.81/3.80 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 21.81/3.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 21.81/3.81 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 21.81/3.81 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 21.81/3.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 21.81/3.81 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 21.81/3.81 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 21.81/3.81 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 21.81/3.81 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 21.81/3.81 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 21.81/3.81 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 21.81/3.81 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 21.81/3.81 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 21.81/3.81 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 21.81/3.81 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 21.81/3.81 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 21.81/3.81 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 21.81/3.81 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 21.81/3.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.81/3.81 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 21.81/3.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.81/3.81 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 21.81/3.81 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 21.81/3.81 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 21.81/3.81 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 21.81/3.81 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 21.81/3.81 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 21.81/3.81 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 21.81/3.81 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 21.81/3.81
% 21.81/3.81 Further assumptions not needed in the proof:
% 21.81/3.81 --------------------------------------------
% 21.81/3.81 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 21.81/3.81 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 21.81/3.81 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 21.81/3.81 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 21.81/3.81 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,
% 21.81/3.81 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,
% 21.81/3.81 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 21.81/3.81 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 21.81/3.81 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 21.81/3.81 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 21.81/3.81 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 21.81/3.81 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 21.81/3.81 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 21.81/3.81 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 21.81/3.81 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 21.81/3.81 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 21.81/3.81 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 21.81/3.81 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 21.81/3.81
% 21.81/3.81 Those formulas are unsatisfiable:
% 21.81/3.81 ---------------------------------
% 21.81/3.81
% 21.81/3.81 Begin of proof
% 21.81/3.81 |
% 21.81/3.81 | ALPHA: (cl5_nebula_init_0016) implies:
% 21.81/3.81 | (1) $i(pv40)
% 21.81/3.81 | (2) $i(pv46)
% 21.81/3.82 | (3) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ( ~ (v2 = init) &
% 21.81/3.82 | a_select3(q_init, pv46, pv40) = v2 & a_select2(mu_init, pv40) = init
% 21.81/3.82 | & pred(pv40) = v0 & leq(pv46, n135299) = 0 & leq(pv40, n4) = 0 &
% 21.81/3.82 | leq(n0, pv46) = 0 & leq(n0, pv40) = 0 & gt(loopcounter, n1) = v1 &
% 21.81/3.82 | $i(v2) & $i(v0) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 21.81/3.82 | (a_select3(center_init, v3, n0) = v4) | ~ $i(v3) | ? [v5: any] :
% 21.81/3.82 | ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) |
% 21.81/3.82 | ~ (v5 = 0)))) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 21.81/3.82 | (a_select2(rho_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6:
% 21.81/3.82 | any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~
% 21.81/3.82 | (v5 = 0)))) & ! [v3: $i] : ( ~ (leq(v3, v0) = 0) | ~ $i(v3) |
% 21.81/3.82 | ? [v4: any] : ? [v5: $i] : (a_select2(sigma_init, v3) = v5 &
% 21.81/3.82 | leq(n0, v3) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = init))) & ! [v3:
% 21.81/3.82 | $i] : ( ~ (leq(v3, v0) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5:
% 21.81/3.82 | $i] : (a_select2(mu_init, v3) = v5 & leq(n0, v3) = v4 & $i(v5) &
% 21.81/3.82 | ( ~ (v4 = 0) | v5 = init))) & ! [v3: $i] : ( ~ (leq(v3, n135299)
% 21.81/3.82 | = 0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & leq(n0, v3) =
% 21.81/3.82 | v4) | ! [v4: $i] : ! [v5: $i] : (v5 = init | ~
% 21.81/3.82 | (a_select3(q_init, v3, v4) = v5) | ~ $i(v4) | ? [v6: any] : ?
% 21.81/3.82 | [v7: any] : (leq(v4, n4) = v7 & leq(n0, v4) = v6 & ( ~ (v7 = 0) |
% 21.81/3.82 | ~ (v6 = 0))))) & ( ~ (v1 = 0) | ! [v3: $i] : ! [v4: $i] :
% 21.81/3.82 | (v4 = init | ~ (a_select2(sigmaold_init, v3) = v4) | ~ $i(v3) |
% 21.81/3.82 | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5
% 21.81/3.82 | & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ( ~ (v1 = 0) | ! [v3: $i] :
% 21.81/3.82 | ! [v4: $i] : (v4 = init | ~ (a_select2(rhoold_init, v3) = v4) |
% 21.81/3.82 | ~ $i(v3) | ? [v5: any] : ? [v6: any] : (leq(v3, n4) = v6 &
% 21.81/3.82 | leq(n0, v3) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) & ( ~ (v1 =
% 21.81/3.82 | 0) | ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 21.81/3.82 | (a_select2(muold_init, v3) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 21.81/3.82 | [v6: any] : (leq(v3, n4) = v6 & leq(n0, v3) = v5 & ( ~ (v6 = 0) |
% 21.81/3.82 | ~ (v5 = 0))))))
% 21.81/3.82 |
% 21.81/3.82 | ALPHA: (function-axioms) implies:
% 21.81/3.82 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 21.81/3.82 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 21.81/3.82 |
% 21.81/3.82 | DELTA: instantiating (3) with fresh symbols all_76_0, all_76_1, all_76_2
% 21.81/3.82 | gives:
% 21.81/3.83 | (5) ~ (all_76_0 = init) & a_select3(q_init, pv46, pv40) = all_76_0 &
% 21.81/3.83 | a_select2(mu_init, pv40) = init & pred(pv40) = all_76_2 & leq(pv46,
% 21.81/3.83 | n135299) = 0 & leq(pv40, n4) = 0 & leq(n0, pv46) = 0 & leq(n0, pv40)
% 21.81/3.83 | = 0 & gt(loopcounter, n1) = all_76_1 & $i(all_76_0) & $i(all_76_2) & !
% 21.81/3.83 | [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(center_init, v0,
% 21.81/3.83 | n0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0,
% 21.81/3.83 | n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & !
% 21.81/3.83 | [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) = v1)
% 21.81/3.83 | | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 &
% 21.81/3.83 | leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : (
% 21.81/3.83 | ~ (leq(v0, all_76_2) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] :
% 21.81/3.83 | (a_select2(sigma_init, v0) = v2 & leq(n0, v0) = v1 & $i(v2) & ( ~ (v1
% 21.81/3.83 | = 0) | v2 = init))) & ! [v0: $i] : ( ~ (leq(v0, all_76_2) = 0)
% 21.81/3.83 | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : (a_select2(mu_init, v0) =
% 21.81/3.83 | v2 & leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & !
% 21.81/3.83 | [v0: $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 21.81/3.83 | (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 =
% 21.81/3.83 | init | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3:
% 21.81/3.83 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 21.81/3.83 | (v4 = 0) | ~ (v3 = 0))))) & ( ~ (all_76_1 = 0) | ! [v0: $i] :
% 21.81/3.83 | ! [v1: $i] : (v1 = init | ~ (a_select2(sigmaold_init, v0) = v1) |
% 21.81/3.83 | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 &
% 21.81/3.83 | leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))) & ( ~ (all_76_1
% 21.81/3.83 | = 0) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 21.81/3.83 | (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ?
% 21.81/3.83 | [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) |
% 21.81/3.83 | ~ (v2 = 0))))) & ( ~ (all_76_1 = 0) | ! [v0: $i] : ! [v1: $i]
% 21.81/3.83 | : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ?
% 21.81/3.83 | [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & (
% 21.81/3.83 | ~ (v3 = 0) | ~ (v2 = 0)))))
% 21.81/3.83 |
% 21.81/3.83 | ALPHA: (5) implies:
% 21.81/3.83 | (6) ~ (all_76_0 = init)
% 21.81/3.83 | (7) leq(n0, pv40) = 0
% 21.81/3.83 | (8) leq(n0, pv46) = 0
% 21.81/3.83 | (9) leq(pv40, n4) = 0
% 21.81/3.83 | (10) leq(pv46, n135299) = 0
% 21.81/3.83 | (11) a_select3(q_init, pv46, pv40) = all_76_0
% 21.81/3.83 | (12) ! [v0: $i] : ( ~ (leq(v0, n135299) = 0) | ~ $i(v0) | ? [v1: int] :
% 21.81/3.83 | ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i] : ! [v2: $i] : (v2 =
% 21.81/3.83 | init | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ? [v3:
% 21.81/3.83 | any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 21.81/3.83 | (v4 = 0) | ~ (v3 = 0)))))
% 21.81/3.83 |
% 21.81/3.83 | GROUND_INST: instantiating (12) with pv46, simplifying with (2), (10) gives:
% 21.81/3.83 | (13) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, pv46) = v0) | ! [v0: $i] : !
% 21.81/3.83 | [v1: $i] : (v1 = init | ~ (a_select3(q_init, pv46, v0) = v1) | ~
% 21.81/3.83 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0,
% 21.81/3.83 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 21.81/3.83 |
% 21.81/3.83 | BETA: splitting (13) gives:
% 21.81/3.83 |
% 21.81/3.83 | Case 1:
% 21.81/3.83 | |
% 21.81/3.83 | | (14) ? [v0: int] : ( ~ (v0 = 0) & leq(n0, pv46) = v0)
% 21.81/3.83 | |
% 21.81/3.83 | | DELTA: instantiating (14) with fresh symbol all_104_0 gives:
% 21.81/3.83 | | (15) ~ (all_104_0 = 0) & leq(n0, pv46) = all_104_0
% 21.81/3.83 | |
% 21.81/3.83 | | ALPHA: (15) implies:
% 21.81/3.83 | | (16) ~ (all_104_0 = 0)
% 21.81/3.83 | | (17) leq(n0, pv46) = all_104_0
% 21.81/3.83 | |
% 21.81/3.83 | | GROUND_INST: instantiating (4) with 0, all_104_0, pv46, n0, simplifying with
% 21.81/3.83 | | (8), (17) gives:
% 21.81/3.83 | | (18) all_104_0 = 0
% 21.81/3.83 | |
% 21.81/3.83 | | REDUCE: (16), (18) imply:
% 21.81/3.83 | | (19) $false
% 21.81/3.83 | |
% 21.81/3.83 | | CLOSE: (19) is inconsistent.
% 21.81/3.83 | |
% 21.81/3.83 | Case 2:
% 21.81/3.83 | |
% 21.81/3.84 | | (20) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(q_init, pv46,
% 21.81/3.84 | | v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0,
% 21.81/3.84 | | n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 21.81/3.84 | |
% 21.81/3.84 | | GROUND_INST: instantiating (20) with pv40, all_76_0, simplifying with (1),
% 21.81/3.84 | | (11) gives:
% 21.81/3.84 | | (21) all_76_0 = init | ? [v0: any] : ? [v1: any] : (leq(pv40, n4) = v1
% 21.81/3.84 | | & leq(n0, pv40) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 21.81/3.84 | |
% 21.81/3.84 | | BETA: splitting (21) gives:
% 21.81/3.84 | |
% 21.81/3.84 | | Case 1:
% 21.81/3.84 | | |
% 21.81/3.84 | | | (22) all_76_0 = init
% 21.81/3.84 | | |
% 21.81/3.84 | | | REDUCE: (6), (22) imply:
% 21.81/3.84 | | | (23) $false
% 21.81/3.84 | | |
% 21.81/3.84 | | | CLOSE: (23) is inconsistent.
% 21.81/3.84 | | |
% 21.81/3.84 | | Case 2:
% 21.81/3.84 | | |
% 21.81/3.84 | | | (24) ? [v0: any] : ? [v1: any] : (leq(pv40, n4) = v1 & leq(n0, pv40)
% 21.81/3.84 | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 21.81/3.84 | | |
% 21.81/3.84 | | | DELTA: instantiating (24) with fresh symbols all_108_0, all_108_1 gives:
% 21.81/3.84 | | | (25) leq(pv40, n4) = all_108_0 & leq(n0, pv40) = all_108_1 & ( ~
% 21.81/3.84 | | | (all_108_0 = 0) | ~ (all_108_1 = 0))
% 21.81/3.84 | | |
% 21.81/3.84 | | | ALPHA: (25) implies:
% 21.81/3.84 | | | (26) leq(n0, pv40) = all_108_1
% 21.81/3.84 | | | (27) leq(pv40, n4) = all_108_0
% 21.81/3.84 | | | (28) ~ (all_108_0 = 0) | ~ (all_108_1 = 0)
% 21.81/3.84 | | |
% 21.81/3.84 | | | GROUND_INST: instantiating (4) with 0, all_108_1, pv40, n0, simplifying
% 21.81/3.84 | | | with (7), (26) gives:
% 21.81/3.84 | | | (29) all_108_1 = 0
% 21.81/3.84 | | |
% 21.81/3.84 | | | GROUND_INST: instantiating (4) with 0, all_108_0, n4, pv40, simplifying
% 21.81/3.84 | | | with (9), (27) gives:
% 21.81/3.84 | | | (30) all_108_0 = 0
% 21.81/3.84 | | |
% 21.81/3.84 | | | BETA: splitting (28) gives:
% 21.81/3.84 | | |
% 21.81/3.84 | | | Case 1:
% 21.81/3.84 | | | |
% 21.81/3.84 | | | | (31) ~ (all_108_0 = 0)
% 21.81/3.84 | | | |
% 21.81/3.84 | | | | REDUCE: (30), (31) imply:
% 21.81/3.84 | | | | (32) $false
% 21.81/3.84 | | | |
% 21.81/3.84 | | | | CLOSE: (32) is inconsistent.
% 21.81/3.84 | | | |
% 21.81/3.84 | | | Case 2:
% 21.81/3.84 | | | |
% 21.81/3.84 | | | | (33) ~ (all_108_1 = 0)
% 21.81/3.84 | | | |
% 21.81/3.84 | | | | REDUCE: (29), (33) imply:
% 21.81/3.84 | | | | (34) $false
% 21.81/3.84 | | | |
% 21.81/3.84 | | | | CLOSE: (34) is inconsistent.
% 21.81/3.84 | | | |
% 21.81/3.84 | | | End of split
% 21.81/3.84 | | |
% 21.81/3.84 | | End of split
% 21.81/3.84 | |
% 21.81/3.84 | End of split
% 21.81/3.84 |
% 21.81/3.84 End of proof
% 21.81/3.84 % SZS output end Proof for theBenchmark
% 21.81/3.84
% 21.81/3.84 3230ms
%------------------------------------------------------------------------------