TSTP Solution File: SWV167+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV167+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 : n031.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 25.82s 4.17s
% Output : Proof 33.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV167+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 07:47:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.02/1.40 Prover 4: Preprocessing ...
% 5.02/1.41 Prover 1: Preprocessing ...
% 5.38/1.45 Prover 0: Preprocessing ...
% 5.38/1.45 Prover 6: Preprocessing ...
% 5.38/1.45 Prover 5: Preprocessing ...
% 5.38/1.45 Prover 2: Preprocessing ...
% 5.38/1.45 Prover 3: Preprocessing ...
% 11.47/2.26 Prover 1: Warning: ignoring some quantifiers
% 12.04/2.35 Prover 1: Constructing countermodel ...
% 12.04/2.36 Prover 3: Warning: ignoring some quantifiers
% 12.04/2.37 Prover 6: Proving ...
% 12.34/2.39 Prover 3: Constructing countermodel ...
% 12.96/2.48 Prover 5: Proving ...
% 12.96/2.51 Prover 4: Warning: ignoring some quantifiers
% 12.96/2.60 Prover 4: Constructing countermodel ...
% 14.24/2.64 Prover 2: Proving ...
% 14.24/2.68 Prover 0: Proving ...
% 25.82/4.17 Prover 0: proved (3528ms)
% 25.82/4.17
% 25.82/4.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.82/4.17
% 25.82/4.17 Prover 3: stopped
% 25.82/4.17 Prover 5: stopped
% 25.82/4.19 Prover 6: stopped
% 25.82/4.20 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.82/4.20 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.82/4.20 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.82/4.20 Prover 2: stopped
% 25.82/4.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 25.82/4.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.77/4.31 Prover 8: Preprocessing ...
% 27.39/4.35 Prover 10: Preprocessing ...
% 27.61/4.38 Prover 7: Preprocessing ...
% 27.61/4.38 Prover 13: Preprocessing ...
% 27.61/4.41 Prover 11: Preprocessing ...
% 28.20/4.59 Prover 10: Warning: ignoring some quantifiers
% 28.20/4.62 Prover 8: Warning: ignoring some quantifiers
% 29.32/4.63 Prover 10: Constructing countermodel ...
% 29.32/4.63 Prover 7: Warning: ignoring some quantifiers
% 29.32/4.64 Prover 8: Constructing countermodel ...
% 29.32/4.65 Prover 7: Constructing countermodel ...
% 30.36/4.77 Prover 13: Warning: ignoring some quantifiers
% 30.58/4.79 Prover 13: Constructing countermodel ...
% 31.67/4.94 Prover 11: Warning: ignoring some quantifiers
% 31.67/4.97 Prover 11: Constructing countermodel ...
% 32.92/5.18 Prover 10: Found proof (size 16)
% 32.92/5.18 Prover 10: proved (987ms)
% 32.92/5.18 Prover 11: stopped
% 32.92/5.18 Prover 13: stopped
% 32.92/5.18 Prover 4: stopped
% 32.92/5.18 Prover 7: stopped
% 32.92/5.18 Prover 1: stopped
% 32.92/5.18 Prover 8: stopped
% 32.92/5.18
% 32.92/5.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.92/5.19
% 32.92/5.19 % SZS output start Proof for theBenchmark
% 32.92/5.19 Assumptions after simplification:
% 32.92/5.19 ---------------------------------
% 32.92/5.19
% 32.92/5.19 (cl5_nebula_init_0011)
% 33.86/5.23 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(loopcounter) &
% 33.86/5.23 $i(center_init) & $i(rho_init) & $i(q_init) & $i(n135299) & $i(sigma_init) &
% 33.86/5.23 $i(init) & $i(pv40) & $i(mu_init) & $i(n4) & $i(n1) & $i(n0) & ? [v0: $i] :
% 33.86/5.23 ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) & a_select2(sigma_init, pv40) =
% 33.86/5.23 init & a_select2(mu_init, v1) = v2 & a_select2(mu_init, pv40) = init &
% 33.86/5.23 pred(pv40) = v0 & $i(v2) & $i(v1) & $i(v0) & leq(v1, pv40) & leq(pv40, n4) &
% 33.86/5.23 leq(n0, v1) & leq(n0, pv40) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5
% 33.86/5.23 = init | ~ (a_select3(q_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 33.86/5.23 leq(v4, n4) | ~ leq(v3, n135299) | ~ leq(n0, v4) | ~ leq(n0, v3)) & !
% 33.86/5.23 [v3: $i] : ! [v4: $i] : (v4 = init | ~ (a_select3(center_init, v3, n0) =
% 33.86/5.23 v4) | ~ $i(v3) | ~ leq(v3, n4) | ~ leq(n0, v3)) & ! [v3: $i] : !
% 33.86/5.23 [v4: $i] : (v4 = init | ~ (a_select2(rho_init, v3) = v4) | ~ $i(v3) | ~
% 33.86/5.23 leq(v3, n4) | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init |
% 33.86/5.23 ~ (a_select2(sigma_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, v0) | ~
% 33.86/5.23 leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 33.86/5.23 (a_select2(mu_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, v0) | ~ leq(n0,
% 33.86/5.23 v3)) & ( ~ gt(loopcounter, n1) | ! [v3: $i] : ! [v4: $i] : (v4 = init
% 33.86/5.23 | ~ (a_select2(sigmaold_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, n4) |
% 33.86/5.23 ~ leq(n0, v3))) & ( ~ gt(loopcounter, n1) | ! [v3: $i] : ! [v4: $i] :
% 33.86/5.23 (v4 = init | ~ (a_select2(rhoold_init, v3) = v4) | ~ $i(v3) | ~ leq(v3,
% 33.86/5.23 n4) | ~ leq(n0, v3))) & ( ~ gt(loopcounter, n1) | ! [v3: $i] : !
% 33.86/5.23 [v4: $i] : (v4 = init | ~ (a_select2(muold_init, v3) = v4) | ~ $i(v3) |
% 33.86/5.23 ~ leq(v3, n4) | ~ leq(n0, v3))))
% 33.86/5.23
% 33.86/5.23 (leq_gt2)
% 33.86/5.23 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ leq(v0, v1)
% 33.86/5.23 | gt(v1, v0))
% 33.86/5.23
% 33.86/5.23 (leq_gt_pred)
% 33.86/5.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~
% 33.86/5.23 $i(v0) | ~ leq(v0, v2) | gt(v1, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.86/5.23 $i] : ( ~ (pred(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0,
% 33.86/5.23 v2))
% 33.86/5.23
% 33.86/5.23 (function-axioms)
% 33.86/5.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 33.86/5.24 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 33.86/5.24 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 33.86/5.24 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 33.86/5.24 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 33.86/5.24 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 33.86/5.24 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 33.86/5.24 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 33.86/5.24 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 33.86/5.24 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 33.86/5.24 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 33.86/5.24 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 33.86/5.24 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 33.86/5.24 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 33.86/5.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 33.86/5.24 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 33.86/5.24 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 33.86/5.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 33.86/5.24 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 33.86/5.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 33.86/5.24 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 33.86/5.24 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 33.86/5.24 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 33.86/5.24 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 33.86/5.24 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.86/5.24 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 33.86/5.24 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~
% 33.86/5.24 (inv(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 33.86/5.24 (trans(v2) = v1) | ~ (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 33.86/5.24 [v2: $i] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] :
% 33.86/5.24 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) =
% 33.86/5.24 v0))
% 33.86/5.24
% 33.86/5.24 Further assumptions not needed in the proof:
% 33.86/5.24 --------------------------------------------
% 33.86/5.24 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 33.86/5.24 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 33.86/5.24 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 33.86/5.24 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 33.86/5.24 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,
% 33.86/5.24 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,
% 33.86/5.24 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 33.86/5.24 leq_geq, leq_gt1, leq_minus, leq_succ, leq_succ_gt, leq_succ_gt_equiv,
% 33.86/5.24 leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add,
% 33.86/5.24 matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 33.86/5.24 matrix_symm_update_diagonal, pred_minus_1, pred_succ, reflexivity_leq,
% 33.86/5.24 sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1, sel3_update_2,
% 33.86/5.24 sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l, succ_plus_2_r,
% 33.86/5.24 succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r, succ_plus_5_l,
% 33.86/5.24 succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1, successor_2,
% 33.86/5.24 successor_3, successor_4, successor_5, sum_plus_base, sum_plus_base_float,
% 33.86/5.24 totality, transitivity_gt, transitivity_leq, ttrue, uniform_int_rand_ranges_hi,
% 33.86/5.24 uniform_int_rand_ranges_lo
% 33.86/5.24
% 33.86/5.24 Those formulas are unsatisfiable:
% 33.86/5.24 ---------------------------------
% 33.86/5.24
% 33.86/5.24 Begin of proof
% 33.86/5.24 |
% 33.86/5.24 | ALPHA: (leq_gt_pred) implies:
% 33.86/5.24 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (pred(v1) = v2) | ~
% 33.86/5.24 | $i(v1) | ~ $i(v0) | ~ gt(v1, v0) | leq(v0, v2))
% 33.86/5.24 |
% 33.86/5.24 | ALPHA: (cl5_nebula_init_0011) implies:
% 33.86/5.24 | (2) $i(pv40)
% 33.86/5.25 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = init) &
% 33.86/5.25 | a_select2(sigma_init, pv40) = init & a_select2(mu_init, v1) = v2 &
% 33.86/5.25 | a_select2(mu_init, pv40) = init & pred(pv40) = v0 & $i(v2) & $i(v1) &
% 33.86/5.25 | $i(v0) & leq(v1, pv40) & leq(pv40, n4) & leq(n0, v1) & leq(n0, pv40)
% 33.86/5.25 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = init | ~
% 33.86/5.25 | (a_select3(q_init, v3, v4) = v5) | ~ $i(v4) | ~ $i(v3) | ~
% 33.86/5.25 | leq(v4, n4) | ~ leq(v3, n135299) | ~ leq(n0, v4) | ~ leq(n0,
% 33.86/5.25 | v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 33.86/5.25 | (a_select3(center_init, v3, n0) = v4) | ~ $i(v3) | ~ leq(v3, n4)
% 33.86/5.25 | | ~ leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 33.86/5.25 | (a_select2(rho_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, n4) | ~
% 33.86/5.25 | leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 33.86/5.25 | (a_select2(sigma_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, v0) | ~
% 33.86/5.25 | leq(n0, v3)) & ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 33.86/5.25 | (a_select2(mu_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, v0) | ~
% 33.86/5.25 | leq(n0, v3)) & ( ~ gt(loopcounter, n1) | ! [v3: $i] : ! [v4: $i]
% 33.86/5.25 | : (v4 = init | ~ (a_select2(sigmaold_init, v3) = v4) | ~ $i(v3) |
% 33.86/5.25 | ~ leq(v3, n4) | ~ leq(n0, v3))) & ( ~ gt(loopcounter, n1) | !
% 33.86/5.25 | [v3: $i] : ! [v4: $i] : (v4 = init | ~ (a_select2(rhoold_init,
% 33.86/5.25 | v3) = v4) | ~ $i(v3) | ~ leq(v3, n4) | ~ leq(n0, v3))) & (
% 33.86/5.25 | ~ gt(loopcounter, n1) | ! [v3: $i] : ! [v4: $i] : (v4 = init | ~
% 33.86/5.25 | (a_select2(muold_init, v3) = v4) | ~ $i(v3) | ~ leq(v3, n4) |
% 33.86/5.25 | ~ leq(n0, v3))))
% 33.86/5.25 |
% 33.86/5.25 | ALPHA: (function-axioms) implies:
% 33.86/5.25 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.86/5.25 | (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0))
% 33.86/5.25 |
% 33.86/5.25 | DELTA: instantiating (3) with fresh symbols all_69_0, all_69_1, all_69_2
% 33.86/5.25 | gives:
% 33.86/5.25 | (5) ~ (all_69_0 = init) & a_select2(sigma_init, pv40) = init &
% 33.86/5.25 | a_select2(mu_init, all_69_1) = all_69_0 & a_select2(mu_init, pv40) =
% 33.86/5.25 | init & pred(pv40) = all_69_2 & $i(all_69_0) & $i(all_69_1) &
% 33.86/5.25 | $i(all_69_2) & leq(all_69_1, pv40) & leq(pv40, n4) & leq(n0, all_69_1)
% 33.86/5.25 | & leq(n0, pv40) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = init
% 33.86/5.25 | | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~
% 33.86/5.25 | leq(v1, n4) | ~ leq(v0, n135299) | ~ leq(n0, v1) | ~ leq(n0, v0))
% 33.86/5.25 | & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(center_init,
% 33.86/5.25 | v0, n0) = v1) | ~ $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) & !
% 33.86/5.25 | [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(rho_init, v0) = v1)
% 33.86/5.25 | | ~ $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0)) & ! [v0: $i] : !
% 33.86/5.25 | [v1: $i] : (v1 = init | ~ (a_select2(sigma_init, v0) = v1) | ~ $i(v0)
% 33.86/5.25 | | ~ leq(v0, all_69_2) | ~ leq(n0, v0)) & ! [v0: $i] : ! [v1: $i]
% 33.86/5.25 | : (v1 = init | ~ (a_select2(mu_init, v0) = v1) | ~ $i(v0) | ~
% 33.86/5.25 | leq(v0, all_69_2) | ~ leq(n0, v0)) & ( ~ gt(loopcounter, n1) | !
% 33.86/5.25 | [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(sigmaold_init,
% 33.86/5.25 | v0) = v1) | ~ $i(v0) | ~ leq(v0, n4) | ~ leq(n0, v0))) & ( ~
% 33.86/5.25 | gt(loopcounter, n1) | ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 33.86/5.25 | (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ~ leq(v0, n4) | ~
% 33.86/5.25 | leq(n0, v0))) & ( ~ gt(loopcounter, n1) | ! [v0: $i] : ! [v1: $i]
% 33.86/5.25 | : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ~ $i(v0) | ~
% 33.86/5.25 | leq(v0, n4) | ~ leq(n0, v0)))
% 33.86/5.25 |
% 33.86/5.25 | ALPHA: (5) implies:
% 33.86/5.25 | (6) ~ (all_69_0 = init)
% 33.86/5.25 | (7) leq(n0, all_69_1)
% 33.86/5.25 | (8) leq(all_69_1, pv40)
% 33.86/5.25 | (9) $i(all_69_1)
% 33.86/5.25 | (10) pred(pv40) = all_69_2
% 33.86/5.25 | (11) a_select2(mu_init, pv40) = init
% 33.86/5.25 | (12) a_select2(mu_init, all_69_1) = all_69_0
% 33.86/5.25 | (13) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(mu_init, v0) =
% 33.86/5.25 | v1) | ~ $i(v0) | ~ leq(v0, all_69_2) | ~ leq(n0, v0))
% 33.86/5.25 |
% 33.86/5.25 | GROUND_INST: instantiating (leq_gt2) with all_69_1, pv40, simplifying with
% 33.86/5.25 | (2), (8), (9) gives:
% 33.86/5.25 | (14) all_69_1 = pv40 | gt(pv40, all_69_1)
% 33.86/5.25 |
% 33.86/5.25 | BETA: splitting (14) gives:
% 33.86/5.25 |
% 33.86/5.25 | Case 1:
% 33.86/5.25 | |
% 33.86/5.25 | | (15) gt(pv40, all_69_1)
% 33.86/5.26 | |
% 33.86/5.26 | | GROUND_INST: instantiating (1) with all_69_1, pv40, all_69_2, simplifying
% 33.86/5.26 | | with (2), (9), (10), (15) gives:
% 33.86/5.26 | | (16) leq(all_69_1, all_69_2)
% 33.86/5.26 | |
% 33.86/5.26 | | GROUND_INST: instantiating (13) with all_69_1, all_69_0, simplifying with
% 33.86/5.26 | | (7), (9), (12), (16) gives:
% 33.86/5.26 | | (17) all_69_0 = init
% 33.86/5.26 | |
% 33.86/5.26 | | REDUCE: (6), (17) imply:
% 33.86/5.26 | | (18) $false
% 33.86/5.26 | |
% 33.86/5.26 | | CLOSE: (18) is inconsistent.
% 33.86/5.26 | |
% 33.86/5.26 | Case 2:
% 33.86/5.26 | |
% 33.86/5.26 | | (19) all_69_1 = pv40
% 33.86/5.26 | |
% 33.86/5.26 | | REDUCE: (12), (19) imply:
% 33.86/5.26 | | (20) a_select2(mu_init, pv40) = all_69_0
% 33.86/5.26 | |
% 33.86/5.26 | | GROUND_INST: instantiating (4) with init, all_69_0, pv40, mu_init,
% 33.86/5.26 | | simplifying with (11), (20) gives:
% 33.86/5.26 | | (21) all_69_0 = init
% 33.86/5.26 | |
% 33.86/5.26 | | REDUCE: (6), (21) imply:
% 33.86/5.26 | | (22) $false
% 33.86/5.26 | |
% 33.86/5.26 | | CLOSE: (22) is inconsistent.
% 33.86/5.26 | |
% 33.86/5.26 | End of split
% 33.86/5.26 |
% 33.86/5.26 End of proof
% 33.86/5.26 % SZS output end Proof for theBenchmark
% 33.86/5.26
% 33.86/5.26 4637ms
%------------------------------------------------------------------------------