TSTP Solution File: SWV166+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV166+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 : n023.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 19.53s 3.37s
% Output : Proof 24.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SWV166+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.08/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30 % Computer : n023.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue Aug 29 09:04:25 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.52/0.57 ________ _____
% 0.52/0.57 ___ __ \_________(_)________________________________
% 0.52/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.52/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.52/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.52/0.57
% 0.52/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.52/0.57 (2023-06-19)
% 0.52/0.57
% 0.52/0.57 (c) Philipp Rümmer, 2009-2023
% 0.52/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.52/0.57 Amanda Stjerna.
% 0.52/0.57 Free software under BSD-3-Clause.
% 0.52/0.57
% 0.52/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.52/0.57
% 0.52/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.52/0.59 Running up to 7 provers in parallel.
% 0.52/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.52/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.52/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.52/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.52/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.52/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.52/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 5.40/1.47 Prover 1: Preprocessing ...
% 5.40/1.49 Prover 4: Preprocessing ...
% 5.98/1.53 Prover 2: Preprocessing ...
% 5.98/1.53 Prover 6: Preprocessing ...
% 5.98/1.53 Prover 3: Preprocessing ...
% 5.98/1.53 Prover 5: Preprocessing ...
% 5.98/1.55 Prover 0: Preprocessing ...
% 14.69/2.69 Prover 1: Warning: ignoring some quantifiers
% 15.32/2.84 Prover 3: Warning: ignoring some quantifiers
% 15.32/2.84 Prover 1: Constructing countermodel ...
% 16.12/2.88 Prover 3: Constructing countermodel ...
% 16.12/2.92 Prover 6: Proving ...
% 17.14/3.05 Prover 4: Warning: ignoring some quantifiers
% 17.81/3.09 Prover 5: Proving ...
% 18.13/3.14 Prover 4: Constructing countermodel ...
% 18.92/3.24 Prover 0: Proving ...
% 18.92/3.24 Prover 2: Proving ...
% 19.53/3.36 Prover 3: proved (2765ms)
% 19.53/3.36
% 19.53/3.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.53/3.37
% 19.53/3.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.53/3.37 Prover 0: stopped
% 19.53/3.37 Prover 6: stopped
% 19.53/3.37 Prover 5: stopped
% 19.53/3.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.53/3.37 Prover 2: stopped
% 19.53/3.38 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.14/3.38 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.14/3.38 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.23/3.58 Prover 13: Preprocessing ...
% 21.23/3.60 Prover 11: Preprocessing ...
% 21.23/3.62 Prover 8: Preprocessing ...
% 21.23/3.63 Prover 7: Preprocessing ...
% 22.00/3.63 Prover 1: Found proof (size 19)
% 22.00/3.63 Prover 1: proved (3037ms)
% 22.00/3.63 Prover 4: stopped
% 22.00/3.65 Prover 10: Preprocessing ...
% 22.64/3.75 Prover 7: stopped
% 22.64/3.77 Prover 10: stopped
% 23.25/3.83 Prover 13: stopped
% 23.25/3.84 Prover 11: stopped
% 23.95/3.97 Prover 8: Warning: ignoring some quantifiers
% 23.95/4.00 Prover 8: Constructing countermodel ...
% 24.38/4.03 Prover 8: stopped
% 24.38/4.03
% 24.38/4.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.38/4.04
% 24.38/4.04 % SZS output start Proof for theBenchmark
% 24.38/4.05 Assumptions after simplification:
% 24.38/4.05 ---------------------------------
% 24.38/4.05
% 24.38/4.05 (cl5_nebula_init_0006)
% 24.76/4.10 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) &
% 24.76/4.10 $i(sigma_init) & $i(mu_init) & $i(rho_init) & $i(init) & $i(q_init) &
% 24.76/4.10 $i(n135299) & $i(loopcounter) & $i(pv40) & $i(pv90) & $i(n4) & $i(n1) & $i(n0)
% 24.76/4.10 & ? [v0: $i] : ( ~ (pv90 = n0) & pred(pv40) = v0 & leq(pv40, n4) = 0 &
% 24.76/4.10 leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 & $i(v0) & ! [v1: $i] : ! [v2:
% 24.76/4.10 $i] : (v2 = init | ~ (a_select3(center_init, v1, n0) = v2) | ~ $i(v1) |
% 24.76/4.10 ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 24.76/4.10 (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init |
% 24.76/4.10 ~ (a_select2(sigmaold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 24.76/4.10 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 24.76/4.10 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~
% 24.76/4.10 (a_select2(rhoold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4:
% 24.76/4.10 any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 24.76/4.10 0)))) & ! [v1: $i] : ! [v2: $i] : (v2 = init | ~
% 24.76/4.10 (a_select2(muold_init, v1) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any]
% 24.76/4.10 : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) &
% 24.76/4.10 ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) |
% 24.76/4.10 ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) =
% 24.76/4.10 v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0)
% 24.76/4.10 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(sigma_init, v1) = v3
% 24.76/4.10 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & ! [v1: $i]
% 24.76/4.10 : ( ~ (leq(v1, v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] :
% 24.76/4.10 (a_select2(mu_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) |
% 24.76/4.10 v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) |
% 24.76/4.10 ? [v2: int] : ( ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i]
% 24.76/4.10 : (v3 = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ? [v4:
% 24.76/4.10 any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 & ( ~ (v5 =
% 24.76/4.10 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init)
% 24.76/4.10 & a_select2(rhoold_init, v1) = v2 & leq(v1, n4) = 0 & leq(n0, v1) = 0 &
% 24.76/4.10 $i(v2) & $i(v1)))
% 24.76/4.10
% 24.76/4.10 (function-axioms)
% 24.76/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 24.76/4.12 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 24.76/4.12 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.76/4.12 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 24.76/4.12 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.76/4.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 24.76/4.12 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 24.76/4.12 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 24.76/4.12 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.76/4.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 24.76/4.12 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 24.76/4.12 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 24.76/4.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 24.76/4.12 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 24.76/4.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 24.76/4.12 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 24.76/4.12 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 24.76/4.12 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 24.76/4.12 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 24.76/4.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 24.76/4.12 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 24.76/4.12 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 24.76/4.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 24.76/4.12 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 24.76/4.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 24.76/4.12 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 24.76/4.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 24.76/4.12 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 24.76/4.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.76/4.12 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 24.76/4.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.76/4.12 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 24.76/4.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 24.76/4.12 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 24.76/4.12 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 24.76/4.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 24.76/4.12 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 24.76/4.12 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 24.76/4.12 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 24.76/4.12
% 24.76/4.12 Further assumptions not needed in the proof:
% 24.76/4.12 --------------------------------------------
% 24.76/4.12 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 24.76/4.12 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 24.76/4.12 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 24.76/4.12 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 24.76/4.12 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,
% 24.76/4.12 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,
% 24.76/4.12 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 24.76/4.12 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 24.76/4.12 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 24.76/4.12 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 24.76/4.12 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 24.76/4.12 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 24.76/4.12 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 24.76/4.12 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 24.76/4.12 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 24.76/4.12 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 24.76/4.12 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 24.76/4.12 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 24.76/4.12
% 24.76/4.12 Those formulas are unsatisfiable:
% 24.76/4.12 ---------------------------------
% 24.76/4.12
% 24.76/4.12 Begin of proof
% 24.76/4.12 |
% 24.76/4.12 | ALPHA: (cl5_nebula_init_0006) implies:
% 24.76/4.13 | (1) ? [v0: $i] : ( ~ (pv90 = n0) & pred(pv40) = v0 & leq(pv40, n4) = 0 &
% 24.76/4.13 | leq(n0, pv40) = 0 & gt(loopcounter, n1) = 0 & $i(v0) & ! [v1: $i] :
% 24.76/4.13 | ! [v2: $i] : (v2 = init | ~ (a_select3(center_init, v1, n0) = v2) |
% 24.76/4.13 | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 &
% 24.76/4.13 | leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] :
% 24.76/4.13 | ! [v2: $i] : (v2 = init | ~ (a_select2(sigmaold_init, v1) = v2) | ~
% 24.76/4.13 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0,
% 24.76/4.13 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : !
% 24.76/4.13 | [v2: $i] : (v2 = init | ~ (a_select2(rhoold_init, v1) = v2) | ~
% 24.76/4.13 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0,
% 24.76/4.13 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : !
% 24.76/4.13 | [v2: $i] : (v2 = init | ~ (a_select2(muold_init, v1) = v2) | ~
% 24.76/4.13 | $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0,
% 24.76/4.13 | v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : !
% 24.76/4.13 | [v2: $i] : (v2 = init | ~ (a_select2(rho_init, v1) = v2) | ~ $i(v1)
% 24.76/4.13 | | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) =
% 24.76/4.13 | v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v1: $i] : ( ~ (leq(v1,
% 24.76/4.13 | v0) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: $i] :
% 24.76/4.13 | (a_select2(sigma_init, v1) = v3 & leq(n0, v1) = v2 & $i(v3) & ( ~
% 24.76/4.13 | (v2 = 0) | v3 = init))) & ! [v1: $i] : ( ~ (leq(v1, v0) = 0) |
% 24.76/4.13 | ~ $i(v1) | ? [v2: any] : ? [v3: $i] : (a_select2(mu_init, v1) =
% 24.76/4.13 | v3 & leq(n0, v1) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 = init))) & !
% 24.76/4.13 | [v1: $i] : ( ~ (leq(v1, n135299) = 0) | ~ $i(v1) | ? [v2: int] : (
% 24.76/4.13 | ~ (v2 = 0) & leq(n0, v1) = v2) | ! [v2: $i] : ! [v3: $i] : (v3
% 24.76/4.14 | = init | ~ (a_select3(q_init, v1, v2) = v3) | ~ $i(v2) | ?
% 24.76/4.14 | [v4: any] : ? [v5: any] : (leq(v2, n4) = v5 & leq(n0, v2) = v4 &
% 24.76/4.14 | ( ~ (v5 = 0) | ~ (v4 = 0))))) & ? [v1: $i] : ? [v2: $i] : (
% 24.76/4.14 | ~ (v2 = init) & a_select2(rhoold_init, v1) = v2 & leq(v1, n4) = 0 &
% 24.76/4.14 | leq(n0, v1) = 0 & $i(v2) & $i(v1)))
% 24.76/4.14 |
% 24.76/4.14 | ALPHA: (function-axioms) implies:
% 24.76/4.14 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 24.76/4.14 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 24.76/4.14 |
% 24.76/4.14 | DELTA: instantiating (1) with fresh symbol all_76_0 gives:
% 24.76/4.15 | (3) ~ (pv90 = n0) & pred(pv40) = all_76_0 & leq(pv40, n4) = 0 & leq(n0,
% 24.76/4.15 | pv40) = 0 & gt(loopcounter, n1) = 0 & $i(all_76_0) & ! [v0: $i] : !
% 24.76/4.15 | [v1: $i] : (v1 = init | ~ (a_select3(center_init, v0, n0) = v1) | ~
% 24.76/4.15 | $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0,
% 24.76/4.15 | v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1:
% 24.76/4.15 | $i] : (v1 = init | ~ (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0)
% 24.76/4.15 | | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2
% 24.76/4.15 | & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 24.76/4.15 | init | ~ (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2:
% 24.76/4.15 | any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~
% 24.76/4.15 | (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 =
% 24.76/4.15 | init | ~ (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 24.76/4.15 | : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0)
% 24.76/4.15 | | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 24.76/4.15 | (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 24.76/4.15 | any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2
% 24.76/4.15 | = 0)))) & ! [v0: $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0)
% 24.76/4.15 | | ? [v1: any] : ? [v2: $i] : (a_select2(sigma_init, v0) = v2 &
% 24.76/4.15 | leq(n0, v0) = v1 & $i(v2) & ( ~ (v1 = 0) | v2 = init))) & ! [v0:
% 24.76/4.15 | $i] : ( ~ (leq(v0, all_76_0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 24.76/4.15 | [v2: $i] : (a_select2(mu_init, v0) = v2 & leq(n0, v0) = v1 & $i(v2) &
% 24.76/4.15 | ( ~ (v1 = 0) | v2 = init))) & ! [v0: $i] : ( ~ (leq(v0, n135299) =
% 24.76/4.15 | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) |
% 24.76/4.15 | ! [v1: $i] : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1)
% 24.76/4.15 | = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] : (leq(v1, n4) =
% 24.76/4.15 | v4 & leq(n0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))) & ? [v0:
% 24.76/4.15 | $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rhoold_init, v0) = v1
% 24.76/4.15 | & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 24.76/4.15 |
% 24.76/4.15 | ALPHA: (3) implies:
% 24.76/4.15 | (4) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rhoold_init, v0)
% 24.76/4.15 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3
% 24.76/4.15 | & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.76/4.15 | (5) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(rhoold_init,
% 24.76/4.15 | v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 24.76/4.15 |
% 24.76/4.15 | DELTA: instantiating (5) with fresh symbols all_79_0, all_79_1 gives:
% 24.76/4.15 | (6) ~ (all_79_0 = init) & a_select2(rhoold_init, all_79_1) = all_79_0 &
% 24.76/4.15 | leq(all_79_1, n4) = 0 & leq(n0, all_79_1) = 0 & $i(all_79_0) &
% 24.76/4.15 | $i(all_79_1)
% 24.76/4.15 |
% 24.76/4.15 | ALPHA: (6) implies:
% 24.76/4.16 | (7) ~ (all_79_0 = init)
% 24.76/4.16 | (8) $i(all_79_1)
% 24.76/4.16 | (9) leq(n0, all_79_1) = 0
% 24.76/4.16 | (10) leq(all_79_1, n4) = 0
% 24.76/4.16 | (11) a_select2(rhoold_init, all_79_1) = all_79_0
% 24.76/4.16 |
% 24.76/4.16 | GROUND_INST: instantiating (4) with all_79_1, all_79_0, simplifying with (8),
% 24.76/4.16 | (11) gives:
% 24.76/4.16 | (12) all_79_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) =
% 24.76/4.16 | v1 & leq(n0, all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.76/4.16 |
% 24.76/4.16 | BETA: splitting (12) gives:
% 24.76/4.16 |
% 24.76/4.16 | Case 1:
% 24.76/4.16 | |
% 24.76/4.16 | | (13) all_79_0 = init
% 24.76/4.16 | |
% 24.76/4.16 | | REDUCE: (7), (13) imply:
% 24.76/4.16 | | (14) $false
% 24.76/4.16 | |
% 24.76/4.16 | | CLOSE: (14) is inconsistent.
% 24.76/4.16 | |
% 24.76/4.16 | Case 2:
% 24.76/4.16 | |
% 24.76/4.16 | | (15) ? [v0: any] : ? [v1: any] : (leq(all_79_1, n4) = v1 & leq(n0,
% 24.76/4.16 | | all_79_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.76/4.16 | |
% 24.76/4.16 | | DELTA: instantiating (15) with fresh symbols all_107_0, all_107_1 gives:
% 24.76/4.16 | | (16) leq(all_79_1, n4) = all_107_0 & leq(n0, all_79_1) = all_107_1 & ( ~
% 24.76/4.16 | | (all_107_0 = 0) | ~ (all_107_1 = 0))
% 24.76/4.16 | |
% 24.76/4.16 | | ALPHA: (16) implies:
% 24.76/4.17 | | (17) leq(n0, all_79_1) = all_107_1
% 24.76/4.17 | | (18) leq(all_79_1, n4) = all_107_0
% 24.76/4.17 | | (19) ~ (all_107_0 = 0) | ~ (all_107_1 = 0)
% 24.76/4.17 | |
% 24.76/4.17 | | GROUND_INST: instantiating (2) with 0, all_107_1, all_79_1, n0, simplifying
% 24.76/4.17 | | with (9), (17) gives:
% 24.76/4.17 | | (20) all_107_1 = 0
% 24.76/4.17 | |
% 24.76/4.17 | | GROUND_INST: instantiating (2) with 0, all_107_0, n4, all_79_1, simplifying
% 24.76/4.17 | | with (10), (18) gives:
% 24.76/4.17 | | (21) all_107_0 = 0
% 24.76/4.17 | |
% 24.76/4.17 | | BETA: splitting (19) gives:
% 24.76/4.17 | |
% 24.76/4.17 | | Case 1:
% 24.76/4.17 | | |
% 24.76/4.17 | | | (22) ~ (all_107_0 = 0)
% 24.76/4.17 | | |
% 24.76/4.17 | | | REDUCE: (21), (22) imply:
% 24.76/4.17 | | | (23) $false
% 24.76/4.17 | | |
% 24.76/4.17 | | | CLOSE: (23) is inconsistent.
% 24.76/4.17 | | |
% 24.76/4.17 | | Case 2:
% 24.76/4.17 | | |
% 24.76/4.17 | | | (24) ~ (all_107_1 = 0)
% 24.76/4.17 | | |
% 24.76/4.17 | | | REDUCE: (20), (24) imply:
% 24.76/4.17 | | | (25) $false
% 24.76/4.17 | | |
% 24.76/4.17 | | | CLOSE: (25) is inconsistent.
% 24.76/4.17 | | |
% 24.76/4.17 | | End of split
% 24.76/4.17 | |
% 24.76/4.17 | End of split
% 24.76/4.17 |
% 24.76/4.17 End of proof
% 24.76/4.17 % SZS output end Proof for theBenchmark
% 24.76/4.17
% 24.76/4.17 3600ms
%------------------------------------------------------------------------------