TSTP Solution File: SWV186+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV186+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 : n009.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 22:55:16 EDT 2023
% Result : Theorem 14.07s 2.64s
% Output : Proof 17.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV186+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 03:00:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.60/0.61 ________ _____
% 0.60/0.61 ___ __ \_________(_)________________________________
% 0.60/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.60/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.60/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.60/0.61
% 0.60/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.60/0.61 (2023-06-19)
% 0.60/0.61
% 0.60/0.61 (c) Philipp Rümmer, 2009-2023
% 0.60/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.60/0.61 Amanda Stjerna.
% 0.60/0.61 Free software under BSD-3-Clause.
% 0.60/0.61
% 0.60/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.60/0.61
% 0.60/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.60/0.62 Running up to 7 provers in parallel.
% 0.76/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.76/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.76/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.76/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.76/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.76/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.76/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.49/1.36 Prover 1: Preprocessing ...
% 4.49/1.36 Prover 4: Preprocessing ...
% 4.93/1.39 Prover 6: Preprocessing ...
% 4.93/1.39 Prover 3: Preprocessing ...
% 4.93/1.39 Prover 5: Preprocessing ...
% 4.93/1.39 Prover 2: Preprocessing ...
% 4.93/1.39 Prover 0: Preprocessing ...
% 11.17/2.25 Prover 1: Warning: ignoring some quantifiers
% 11.86/2.31 Prover 6: Proving ...
% 11.86/2.31 Prover 3: Warning: ignoring some quantifiers
% 11.86/2.32 Prover 1: Constructing countermodel ...
% 11.86/2.35 Prover 3: Constructing countermodel ...
% 11.86/2.35 Prover 4: Warning: ignoring some quantifiers
% 12.59/2.44 Prover 4: Constructing countermodel ...
% 12.59/2.45 Prover 5: Proving ...
% 13.21/2.49 Prover 2: Proving ...
% 13.21/2.51 Prover 0: Proving ...
% 14.07/2.63 Prover 3: proved (1992ms)
% 14.07/2.63
% 14.07/2.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.07/2.64
% 14.07/2.64 Prover 5: stopped
% 14.07/2.64 Prover 6: stopped
% 14.07/2.64 Prover 0: stopped
% 14.07/2.64 Prover 2: stopped
% 14.07/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.07/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.07/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.07/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.07/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.49/2.81 Prover 10: Preprocessing ...
% 15.49/2.81 Prover 13: Preprocessing ...
% 15.49/2.82 Prover 11: Preprocessing ...
% 15.49/2.82 Prover 8: Preprocessing ...
% 15.49/2.86 Prover 7: Preprocessing ...
% 16.20/2.89 Prover 1: Found proof (size 17)
% 16.20/2.89 Prover 1: proved (2261ms)
% 16.20/2.89 Prover 4: stopped
% 16.31/2.91 Prover 10: stopped
% 16.41/2.92 Prover 7: stopped
% 16.45/2.92 Prover 11: stopped
% 16.45/2.96 Prover 13: stopped
% 16.89/3.03 Prover 8: Warning: ignoring some quantifiers
% 16.89/3.05 Prover 8: Constructing countermodel ...
% 16.89/3.07 Prover 8: stopped
% 16.89/3.07
% 16.89/3.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.89/3.07
% 16.89/3.07 % SZS output start Proof for theBenchmark
% 16.89/3.08 Assumptions after simplification:
% 16.89/3.08 ---------------------------------
% 16.89/3.08
% 16.89/3.08 (cl5_nebula_init_0106)
% 17.26/3.11 gt(loopcounter, n1) = 0 & $i(sigma_init) & $i(rho_init) & $i(mu_init) &
% 17.26/3.11 $i(sigmaold_init) & $i(rhoold_init) & $i(muold_init) & $i(center_init) &
% 17.26/3.11 $i(init) & $i(q_init) & $i(n135299) & $i(loopcounter) & $i(n4) & $i(n1) &
% 17.26/3.11 $i(n0) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select3(center_init,
% 17.26/3.11 v0, n0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) =
% 17.26/3.11 v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : !
% 17.26/3.11 [v1: $i] : (v1 = init | ~ (a_select2(sigma_init, v0) = v1) | ~ $i(v0) | ?
% 17.26/3.11 [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 =
% 17.26/3.11 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 17.26/3.11 (a_select2(rho_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] :
% 17.26/3.11 (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & !
% 17.26/3.11 [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(mu_init, v0) = v1) | ~
% 17.26/3.11 $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2
% 17.26/3.11 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init |
% 17.26/3.11 ~ (a_select2(sigmaold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 17.26/3.11 any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 =
% 17.26/3.11 0)))) & ! [v0: $i] : ! [v1: $i] : (v1 = init | ~
% 17.26/3.11 (a_select2(rhoold_init, v0) = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any]
% 17.26/3.11 : (leq(v0, n4) = v3 & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & !
% 17.26/3.11 [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(muold_init, v0) = v1) | ~
% 17.26/3.11 $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3 & leq(n0, v0) = v2
% 17.26/3.11 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~ (leq(v0, n135299) = 0)
% 17.26/3.11 | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & leq(n0, v0) = v1) | ! [v1: $i]
% 17.26/3.11 : ! [v2: $i] : (v2 = init | ~ (a_select3(q_init, v0, v1) = v2) | ~ $i(v1)
% 17.26/3.11 | ? [v3: any] : ? [v4: any] : (leq(v1, n4) = v4 & leq(n0, v1) = v3 & ( ~
% 17.26/3.11 (v4 = 0) | ~ (v3 = 0))))) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 =
% 17.26/3.11 init) & a_select2(muold_init, v0) = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0
% 17.26/3.11 & $i(v1) & $i(v0))
% 17.26/3.11
% 17.26/3.11 (function-axioms)
% 17.26/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.26/3.12 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.26/3.12 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.26/3.12 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.26/3.12 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.26/3.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.26/3.12 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.26/3.12 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.26/3.12 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.26/3.12 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.26/3.12 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.26/3.12 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 17.26/3.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.26/3.12 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 17.26/3.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 17.26/3.12 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.26/3.12 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 17.26/3.12 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.26/3.12 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 17.26/3.12 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 17.26/3.12 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.26/3.12 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 17.26/3.12 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.26/3.12 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 17.26/3.12 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.26/3.12 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 17.26/3.12 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.26/3.12 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.26/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.26/3.12 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.26/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.26/3.12 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.26/3.12 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.26/3.12 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.26/3.12 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 17.26/3.12 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 17.26/3.12 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.26/3.12 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.26/3.12 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 17.26/3.12
% 17.26/3.12 Further assumptions not needed in the proof:
% 17.26/3.12 --------------------------------------------
% 17.26/3.12 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.26/3.12 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.26/3.12 finite_domain_5, gt_0_tptp_minus_1, gt_135299_0, gt_135299_1, gt_135299_2,
% 17.26/3.12 gt_135299_3, gt_135299_4, gt_135299_5, gt_135299_tptp_minus_1, gt_1_0,
% 17.26/3.12 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,
% 17.26/3.12 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,
% 17.26/3.12 gt_5_1, gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt,
% 17.26/3.12 leq_geq, leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt,
% 17.26/3.12 leq_succ_gt_equiv, leq_succ_succ, lt_gt, matrix_symm_aba1, matrix_symm_aba2,
% 17.26/3.12 matrix_symm_add, matrix_symm_inv, matrix_symm_joseph_update, matrix_symm_sub,
% 17.26/3.12 matrix_symm_trans, matrix_symm_update_diagonal, pred_minus_1, pred_succ,
% 17.26/3.12 reflexivity_leq, sel2_update_1, sel2_update_2, sel2_update_3, sel3_update_1,
% 17.26/3.12 sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r, succ_plus_2_l,
% 17.26/3.12 succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l, succ_plus_4_r,
% 17.26/3.12 succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1, successor_1,
% 17.26/3.12 successor_2, successor_3, successor_4, successor_5, sum_plus_base,
% 17.26/3.12 sum_plus_base_float, totality, transitivity_gt, transitivity_leq, ttrue,
% 17.26/3.12 uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 17.26/3.12
% 17.26/3.12 Those formulas are unsatisfiable:
% 17.26/3.12 ---------------------------------
% 17.26/3.12
% 17.26/3.12 Begin of proof
% 17.26/3.12 |
% 17.26/3.12 | ALPHA: (cl5_nebula_init_0106) implies:
% 17.26/3.12 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = init | ~ (a_select2(muold_init, v0)
% 17.26/3.12 | = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (leq(v0, n4) = v3
% 17.26/3.12 | & leq(n0, v0) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 17.26/3.12 | (2) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = init) & a_select2(muold_init, v0)
% 17.26/3.12 | = v1 & leq(v0, n4) = 0 & leq(n0, v0) = 0 & $i(v1) & $i(v0))
% 17.26/3.13 |
% 17.26/3.13 | ALPHA: (function-axioms) implies:
% 17.26/3.13 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.26/3.13 | ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 17.26/3.13 |
% 17.26/3.13 | DELTA: instantiating (2) with fresh symbols all_54_0, all_54_1 gives:
% 17.26/3.13 | (4) ~ (all_54_0 = init) & a_select2(muold_init, all_54_1) = all_54_0 &
% 17.26/3.13 | leq(all_54_1, n4) = 0 & leq(n0, all_54_1) = 0 & $i(all_54_0) &
% 17.26/3.13 | $i(all_54_1)
% 17.26/3.13 |
% 17.26/3.13 | ALPHA: (4) implies:
% 17.26/3.13 | (5) ~ (all_54_0 = init)
% 17.26/3.13 | (6) $i(all_54_1)
% 17.26/3.13 | (7) leq(n0, all_54_1) = 0
% 17.26/3.13 | (8) leq(all_54_1, n4) = 0
% 17.26/3.13 | (9) a_select2(muold_init, all_54_1) = all_54_0
% 17.26/3.13 |
% 17.26/3.13 | GROUND_INST: instantiating (1) with all_54_1, all_54_0, simplifying with (6),
% 17.26/3.13 | (9) gives:
% 17.26/3.13 | (10) all_54_0 = init | ? [v0: any] : ? [v1: any] : (leq(all_54_1, n4) =
% 17.26/3.13 | v1 & leq(n0, all_54_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.26/3.13 |
% 17.26/3.13 | BETA: splitting (10) gives:
% 17.26/3.13 |
% 17.26/3.13 | Case 1:
% 17.26/3.13 | |
% 17.26/3.13 | | (11) all_54_0 = init
% 17.26/3.13 | |
% 17.26/3.13 | | REDUCE: (5), (11) imply:
% 17.26/3.13 | | (12) $false
% 17.26/3.13 | |
% 17.26/3.13 | | CLOSE: (12) is inconsistent.
% 17.26/3.13 | |
% 17.26/3.13 | Case 2:
% 17.26/3.13 | |
% 17.26/3.13 | | (13) ? [v0: any] : ? [v1: any] : (leq(all_54_1, n4) = v1 & leq(n0,
% 17.26/3.13 | | all_54_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 17.26/3.13 | |
% 17.26/3.13 | | DELTA: instantiating (13) with fresh symbols all_105_0, all_105_1 gives:
% 17.26/3.13 | | (14) leq(all_54_1, n4) = all_105_0 & leq(n0, all_54_1) = all_105_1 & ( ~
% 17.26/3.13 | | (all_105_0 = 0) | ~ (all_105_1 = 0))
% 17.26/3.13 | |
% 17.26/3.13 | | ALPHA: (14) implies:
% 17.26/3.13 | | (15) leq(n0, all_54_1) = all_105_1
% 17.26/3.13 | | (16) leq(all_54_1, n4) = all_105_0
% 17.26/3.13 | | (17) ~ (all_105_0 = 0) | ~ (all_105_1 = 0)
% 17.26/3.13 | |
% 17.26/3.13 | | GROUND_INST: instantiating (3) with 0, all_105_1, all_54_1, n0, simplifying
% 17.26/3.13 | | with (7), (15) gives:
% 17.26/3.13 | | (18) all_105_1 = 0
% 17.26/3.13 | |
% 17.26/3.13 | | GROUND_INST: instantiating (3) with 0, all_105_0, n4, all_54_1, simplifying
% 17.26/3.13 | | with (8), (16) gives:
% 17.26/3.13 | | (19) all_105_0 = 0
% 17.26/3.13 | |
% 17.26/3.13 | | BETA: splitting (17) gives:
% 17.26/3.13 | |
% 17.26/3.13 | | Case 1:
% 17.26/3.13 | | |
% 17.26/3.13 | | | (20) ~ (all_105_0 = 0)
% 17.26/3.13 | | |
% 17.26/3.13 | | | REDUCE: (19), (20) imply:
% 17.26/3.13 | | | (21) $false
% 17.26/3.13 | | |
% 17.26/3.13 | | | CLOSE: (21) is inconsistent.
% 17.26/3.13 | | |
% 17.26/3.13 | | Case 2:
% 17.26/3.13 | | |
% 17.26/3.14 | | | (22) ~ (all_105_1 = 0)
% 17.26/3.14 | | |
% 17.26/3.14 | | | REDUCE: (18), (22) imply:
% 17.26/3.14 | | | (23) $false
% 17.26/3.14 | | |
% 17.26/3.14 | | | CLOSE: (23) is inconsistent.
% 17.26/3.14 | | |
% 17.26/3.14 | | End of split
% 17.26/3.14 | |
% 17.26/3.14 | End of split
% 17.26/3.14 |
% 17.26/3.14 End of proof
% 17.26/3.14 % SZS output end Proof for theBenchmark
% 17.26/3.14
% 17.26/3.14 2526ms
%------------------------------------------------------------------------------