TSTP Solution File: SWV069+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWV069+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 22:54:47 EDT 2023
% Result : Theorem 13.77s 2.75s
% Output : Proof 18.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV069+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n001.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 09:11:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.44/1.40 Prover 1: Preprocessing ...
% 4.44/1.40 Prover 4: Preprocessing ...
% 4.44/1.44 Prover 6: Preprocessing ...
% 4.44/1.44 Prover 0: Preprocessing ...
% 4.44/1.44 Prover 2: Preprocessing ...
% 4.44/1.44 Prover 3: Preprocessing ...
% 4.44/1.45 Prover 5: Preprocessing ...
% 10.48/2.23 Prover 1: Warning: ignoring some quantifiers
% 11.59/2.32 Prover 3: Warning: ignoring some quantifiers
% 11.70/2.35 Prover 3: Constructing countermodel ...
% 11.70/2.35 Prover 4: Warning: ignoring some quantifiers
% 11.70/2.36 Prover 6: Proving ...
% 11.70/2.36 Prover 1: Constructing countermodel ...
% 12.26/2.42 Prover 4: Constructing countermodel ...
% 12.74/2.49 Prover 0: Proving ...
% 12.74/2.52 Prover 5: Proving ...
% 13.37/2.57 Prover 2: Proving ...
% 13.77/2.75 Prover 3: proved (2129ms)
% 13.77/2.75
% 13.77/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.77/2.75
% 13.77/2.75 Prover 5: stopped
% 13.77/2.75 Prover 2: stopped
% 13.77/2.76 Prover 0: stopped
% 14.16/2.77 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.16/2.77 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.16/2.77 Prover 6: stopped
% 14.16/2.78 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.16/2.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.16/2.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.90/2.93 Prover 1: Found proof (size 68)
% 15.90/2.93 Prover 1: proved (2336ms)
% 15.90/2.94 Prover 4: stopped
% 15.90/2.95 Prover 10: Preprocessing ...
% 15.90/2.96 Prover 7: Preprocessing ...
% 16.28/2.97 Prover 11: Preprocessing ...
% 16.28/2.97 Prover 8: Preprocessing ...
% 16.28/3.02 Prover 13: Preprocessing ...
% 16.28/3.03 Prover 10: stopped
% 16.28/3.04 Prover 7: stopped
% 16.28/3.04 Prover 11: stopped
% 17.17/3.11 Prover 13: stopped
% 17.49/3.15 Prover 8: Warning: ignoring some quantifiers
% 17.49/3.17 Prover 8: Constructing countermodel ...
% 17.49/3.19 Prover 8: stopped
% 17.49/3.19
% 17.49/3.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.49/3.19
% 17.49/3.21 % SZS output start Proof for theBenchmark
% 17.81/3.21 Assumptions after simplification:
% 17.81/3.21 ---------------------------------
% 17.81/3.21
% 17.81/3.21 (cl5_nebula_array_0010)
% 17.81/3.24 $i(n135300) & $i(pv10) & $i(n5) & $i(n1) & $i(n0) & ? [v0: $i] : ? [v1: any]
% 17.81/3.24 : ? [v2: $i] : ? [v3: any] : (minus(n135300, n1) = v0 & minus(n5, n1) = v2 &
% 17.81/3.24 leq(pv10, v0) = 0 & leq(n0, v2) = v3 & leq(n0, pv10) = 0 & leq(n0, n0) = v1
% 17.81/3.24 & $i(v2) & $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0)))
% 17.81/3.24
% 17.81/3.24 (gt_5_0)
% 17.81/3.24 gt(n5, n0) = 0 & $i(n5) & $i(n0)
% 17.81/3.24
% 17.81/3.24 (leq_succ_gt_equiv)
% 17.81/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 17.81/3.24 (succ(v1) = v2) | ~ (gt(v2, v0) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 17.81/3.24 int] : ( ~ (v4 = 0) & leq(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : !
% 17.81/3.24 [v2: $i] : ( ~ (succ(v1) = v2) | ~ (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) |
% 17.81/3.24 leq(v0, v1) = 0)
% 17.81/3.24
% 17.81/3.24 (pred_minus_1)
% 17.81/3.24 $i(n1) & ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 17.81/3.24 (pred(v0) = v1 & $i(v1)))
% 17.81/3.24
% 17.81/3.24 (pred_succ)
% 17.81/3.24 ! [v0: $i] : ! [v1: $i] : ( ~ (succ(v0) = v1) | ~ $i(v0) | pred(v1) = v0)
% 17.81/3.24
% 17.81/3.24 (reflexivity_leq)
% 17.81/3.24 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ~ $i(v0))
% 17.81/3.24
% 17.81/3.24 (successor_1)
% 17.81/3.24 succ(n0) = n1 & $i(n1) & $i(n0)
% 17.81/3.24
% 17.81/3.24 (successor_2)
% 17.81/3.24 $i(n2) & $i(n0) & ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 17.81/3.24
% 17.81/3.24 (successor_3)
% 17.81/3.24 $i(n3) & $i(n0) & ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 &
% 17.81/3.24 succ(n0) = v0 & $i(v1) & $i(v0))
% 17.81/3.24
% 17.81/3.24 (successor_4)
% 17.81/3.25 $i(n4) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 &
% 17.81/3.25 succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 17.81/3.25
% 17.81/3.25 (successor_5)
% 17.81/3.25 $i(n5) & $i(n0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 17.81/3.25 (succ(v3) = n5 & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0
% 17.81/3.25 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 17.81/3.25
% 17.81/3.25 (function-axioms)
% 17.81/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 17.81/3.26 $i] : (v1 = v0 | ~ (tptp_update3(v5, v4, v3, v2) = v1) | ~
% 17.81/3.26 (tptp_update3(v5, v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.81/3.26 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_update2(v4, v3, v2) =
% 17.81/3.26 v1) | ~ (tptp_update2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.81/3.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (sum(v4, v3, v2) = v1) |
% 17.81/3.26 ~ (sum(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.81/3.26 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (tptp_const_array2(v4, v3, v2) = v1) |
% 17.81/3.26 ~ (tptp_const_array2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.81/3.26 [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (a_select3(v4, v3, v2) =
% 17.81/3.26 v1) | ~ (a_select3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.81/3.26 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (minus(v3, v2) = v1) | ~ (minus(v3,
% 17.81/3.26 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.81/3.26 = v0 | ~ (plus(v3, v2) = v1) | ~ (plus(v3, v2) = v0)) & ! [v0: $i] : !
% 17.81/3.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (tptp_mmul(v3, v2) = v1)
% 17.81/3.26 | ~ (tptp_mmul(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 17.81/3.26 ! [v3: $i] : (v1 = v0 | ~ (tptp_msub(v3, v2) = v1) | ~ (tptp_msub(v3, v2) =
% 17.81/3.26 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 17.81/3.26 ~ (tptp_madd(v3, v2) = v1) | ~ (tptp_madd(v3, v2) = v0)) & ! [v0: $i] : !
% 17.81/3.26 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (dim(v3, v2) = v1) | ~
% 17.81/3.26 (dim(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 17.81/3.26 : (v1 = v0 | ~ (tptp_const_array1(v3, v2) = v1) | ~ (tptp_const_array1(v3,
% 17.81/3.26 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.81/3.26 = v0 | ~ (a_select2(v3, v2) = v1) | ~ (a_select2(v3, v2) = v0)) & ! [v0:
% 17.81/3.26 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.81/3.26 (uniform_int_rnd(v3, v2) = v1) | ~ (uniform_int_rnd(v3, v2) = v0)) & !
% 17.81/3.26 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.81/3.26 $i] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 17.81/3.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.81/3.26 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 17.81/3.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.81/3.26 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 17.81/3.26 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.81/3.26 : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0: $i] : !
% 17.81/3.26 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (inv(v2) = v1) | ~ (inv(v2) = v0)) &
% 17.81/3.26 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (trans(v2) = v1) | ~
% 17.81/3.26 (trans(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.81/3.26 (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 17.81/3.26 $i] : (v1 = v0 | ~ (pred(v2) = v1) | ~ (pred(v2) = v0))
% 17.81/3.26
% 17.81/3.26 Further assumptions not needed in the proof:
% 17.81/3.26 --------------------------------------------
% 17.81/3.26 const_array1_select, const_array2_select, defuse, finite_domain_0,
% 17.81/3.26 finite_domain_1, finite_domain_2, finite_domain_3, finite_domain_4,
% 17.81/3.26 finite_domain_5, gt_0_tptp_minus_1, gt_135300_0, gt_135300_1, gt_135300_2,
% 17.81/3.26 gt_135300_3, gt_135300_4, gt_135300_5, gt_135300_tptp_minus_1, gt_1_0,
% 17.81/3.26 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,
% 17.81/3.26 gt_3_tptp_minus_1, gt_4_0, gt_4_1, gt_4_2, gt_4_3, gt_4_tptp_minus_1, gt_5_1,
% 17.81/3.26 gt_5_2, gt_5_3, gt_5_4, gt_5_tptp_minus_1, gt_succ, irreflexivity_gt, leq_geq,
% 17.81/3.26 leq_gt1, leq_gt2, leq_gt_pred, leq_minus, leq_succ, leq_succ_gt, leq_succ_succ,
% 17.81/3.26 lt_gt, matrix_symm_aba1, matrix_symm_aba2, matrix_symm_add, matrix_symm_inv,
% 17.81/3.26 matrix_symm_joseph_update, matrix_symm_sub, matrix_symm_trans,
% 17.81/3.26 matrix_symm_update_diagonal, sel2_update_1, sel2_update_2, sel2_update_3,
% 17.81/3.26 sel3_update_1, sel3_update_2, sel3_update_3, succ_plus_1_l, succ_plus_1_r,
% 17.81/3.26 succ_plus_2_l, succ_plus_2_r, succ_plus_3_l, succ_plus_3_r, succ_plus_4_l,
% 17.81/3.26 succ_plus_4_r, succ_plus_5_l, succ_plus_5_r, succ_pred, succ_tptp_minus_1,
% 17.81/3.26 sum_plus_base, sum_plus_base_float, totality, transitivity_gt, transitivity_leq,
% 17.81/3.26 ttrue, uniform_int_rand_ranges_hi, uniform_int_rand_ranges_lo
% 17.81/3.26
% 17.81/3.26 Those formulas are unsatisfiable:
% 17.81/3.26 ---------------------------------
% 17.81/3.26
% 17.81/3.26 Begin of proof
% 18.05/3.26 |
% 18.05/3.26 | ALPHA: (leq_succ_gt_equiv) implies:
% 18.05/3.26 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (succ(v1) = v2) | ~
% 18.05/3.26 | (gt(v2, v0) = 0) | ~ $i(v1) | ~ $i(v0) | leq(v0, v1) = 0)
% 18.05/3.26 |
% 18.05/3.26 | ALPHA: (pred_minus_1) implies:
% 18.05/3.26 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (minus(v0, n1) = v1) | ~ $i(v0) |
% 18.05/3.26 | (pred(v0) = v1 & $i(v1)))
% 18.05/3.26 |
% 18.05/3.26 | ALPHA: (gt_5_0) implies:
% 18.05/3.27 | (3) gt(n5, n0) = 0
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (successor_4) implies:
% 18.05/3.27 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (succ(v2) = n4 & succ(v1) =
% 18.05/3.27 | v2 & succ(v0) = v1 & succ(n0) = v0 & $i(v2) & $i(v1) & $i(v0))
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (successor_5) implies:
% 18.05/3.27 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (succ(v3) = n5
% 18.05/3.27 | & succ(v2) = v3 & succ(v1) = v2 & succ(v0) = v1 & succ(n0) = v0 &
% 18.05/3.27 | $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (successor_1) implies:
% 18.05/3.27 | (6) succ(n0) = n1
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (successor_2) implies:
% 18.05/3.27 | (7) ? [v0: $i] : (succ(v0) = n2 & succ(n0) = v0 & $i(v0))
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (successor_3) implies:
% 18.05/3.27 | (8) ? [v0: $i] : ? [v1: $i] : (succ(v1) = n3 & succ(v0) = v1 & succ(n0) =
% 18.05/3.27 | v0 & $i(v1) & $i(v0))
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (cl5_nebula_array_0010) implies:
% 18.05/3.27 | (9) $i(n0)
% 18.05/3.27 | (10) $i(n5)
% 18.05/3.27 | (11) ? [v0: $i] : ? [v1: any] : ? [v2: $i] : ? [v3: any] :
% 18.05/3.27 | (minus(n135300, n1) = v0 & minus(n5, n1) = v2 & leq(pv10, v0) = 0 &
% 18.05/3.27 | leq(n0, v2) = v3 & leq(n0, pv10) = 0 & leq(n0, n0) = v1 & $i(v2) &
% 18.05/3.27 | $i(v0) & ( ~ (v3 = 0) | ~ (v1 = 0)))
% 18.05/3.27 |
% 18.05/3.27 | ALPHA: (function-axioms) implies:
% 18.05/3.27 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (pred(v2) =
% 18.05/3.27 | v1) | ~ (pred(v2) = v0))
% 18.05/3.27 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (succ(v2) =
% 18.05/3.27 | v1) | ~ (succ(v2) = v0))
% 18.05/3.27 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 18.05/3.27 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 18.05/3.27 | v0))
% 18.05/3.27 |
% 18.05/3.27 | DELTA: instantiating (7) with fresh symbol all_49_0 gives:
% 18.05/3.28 | (15) succ(all_49_0) = n2 & succ(n0) = all_49_0 & $i(all_49_0)
% 18.05/3.28 |
% 18.05/3.28 | ALPHA: (15) implies:
% 18.05/3.28 | (16) succ(n0) = all_49_0
% 18.05/3.28 | (17) succ(all_49_0) = n2
% 18.05/3.28 |
% 18.05/3.28 | DELTA: instantiating (8) with fresh symbols all_51_0, all_51_1 gives:
% 18.05/3.28 | (18) succ(all_51_0) = n3 & succ(all_51_1) = all_51_0 & succ(n0) = all_51_1
% 18.05/3.28 | & $i(all_51_0) & $i(all_51_1)
% 18.05/3.28 |
% 18.05/3.28 | ALPHA: (18) implies:
% 18.05/3.28 | (19) succ(n0) = all_51_1
% 18.05/3.28 | (20) succ(all_51_1) = all_51_0
% 18.05/3.28 | (21) succ(all_51_0) = n3
% 18.05/3.28 |
% 18.05/3.28 | DELTA: instantiating (4) with fresh symbols all_53_0, all_53_1, all_53_2
% 18.05/3.28 | gives:
% 18.05/3.28 | (22) succ(all_53_0) = n4 & succ(all_53_1) = all_53_0 & succ(all_53_2) =
% 18.05/3.28 | all_53_1 & succ(n0) = all_53_2 & $i(all_53_0) & $i(all_53_1) &
% 18.05/3.28 | $i(all_53_2)
% 18.05/3.28 |
% 18.05/3.28 | ALPHA: (22) implies:
% 18.05/3.28 | (23) succ(n0) = all_53_2
% 18.05/3.28 | (24) succ(all_53_2) = all_53_1
% 18.05/3.28 | (25) succ(all_53_1) = all_53_0
% 18.05/3.28 | (26) succ(all_53_0) = n4
% 18.05/3.28 |
% 18.05/3.28 | DELTA: instantiating (5) with fresh symbols all_55_0, all_55_1, all_55_2,
% 18.05/3.28 | all_55_3 gives:
% 18.05/3.28 | (27) succ(all_55_0) = n5 & succ(all_55_1) = all_55_0 & succ(all_55_2) =
% 18.05/3.28 | all_55_1 & succ(all_55_3) = all_55_2 & succ(n0) = all_55_3 &
% 18.05/3.28 | $i(all_55_0) & $i(all_55_1) & $i(all_55_2) & $i(all_55_3)
% 18.05/3.28 |
% 18.05/3.28 | ALPHA: (27) implies:
% 18.05/3.28 | (28) $i(all_55_0)
% 18.05/3.28 | (29) succ(n0) = all_55_3
% 18.05/3.28 | (30) succ(all_55_3) = all_55_2
% 18.05/3.28 | (31) succ(all_55_2) = all_55_1
% 18.05/3.28 | (32) succ(all_55_1) = all_55_0
% 18.05/3.28 | (33) succ(all_55_0) = n5
% 18.05/3.28 |
% 18.05/3.28 | DELTA: instantiating (11) with fresh symbols all_57_0, all_57_1, all_57_2,
% 18.05/3.28 | all_57_3 gives:
% 18.05/3.28 | (34) minus(n135300, n1) = all_57_3 & minus(n5, n1) = all_57_1 & leq(pv10,
% 18.05/3.28 | all_57_3) = 0 & leq(n0, all_57_1) = all_57_0 & leq(n0, pv10) = 0 &
% 18.05/3.28 | leq(n0, n0) = all_57_2 & $i(all_57_1) & $i(all_57_3) & ( ~ (all_57_0 =
% 18.05/3.28 | 0) | ~ (all_57_2 = 0))
% 18.05/3.28 |
% 18.05/3.28 | ALPHA: (34) implies:
% 18.05/3.28 | (35) leq(n0, n0) = all_57_2
% 18.05/3.28 | (36) leq(n0, all_57_1) = all_57_0
% 18.05/3.28 | (37) minus(n5, n1) = all_57_1
% 18.05/3.28 | (38) ~ (all_57_0 = 0) | ~ (all_57_2 = 0)
% 18.05/3.28 |
% 18.05/3.28 | GROUND_INST: instantiating (13) with all_51_1, all_53_2, n0, simplifying with
% 18.05/3.28 | (19), (23) gives:
% 18.05/3.28 | (39) all_53_2 = all_51_1
% 18.05/3.28 |
% 18.05/3.28 | GROUND_INST: instantiating (13) with all_49_0, all_53_2, n0, simplifying with
% 18.05/3.28 | (16), (23) gives:
% 18.05/3.28 | (40) all_53_2 = all_49_0
% 18.05/3.28 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with all_51_1, all_55_3, n0, simplifying with
% 18.05/3.29 | (19), (29) gives:
% 18.05/3.29 | (41) all_55_3 = all_51_1
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with n1, all_55_3, n0, simplifying with (6),
% 18.05/3.29 | (29) gives:
% 18.05/3.29 | (42) all_55_3 = n1
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (41), (42) imply:
% 18.05/3.29 | (43) all_51_1 = n1
% 18.05/3.29 |
% 18.05/3.29 | SIMP: (43) implies:
% 18.05/3.29 | (44) all_51_1 = n1
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (39), (40) imply:
% 18.05/3.29 | (45) all_51_1 = all_49_0
% 18.05/3.29 |
% 18.05/3.29 | SIMP: (45) implies:
% 18.05/3.29 | (46) all_51_1 = all_49_0
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (44), (46) imply:
% 18.05/3.29 | (47) all_49_0 = n1
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (40), (47) imply:
% 18.05/3.29 | (48) all_53_2 = n1
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (30), (42) imply:
% 18.05/3.29 | (49) succ(n1) = all_55_2
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (24), (48) imply:
% 18.05/3.29 | (50) succ(n1) = all_53_1
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (20), (44) imply:
% 18.05/3.29 | (51) succ(n1) = all_51_0
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (17), (47) imply:
% 18.05/3.29 | (52) succ(n1) = n2
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with all_51_0, all_53_1, n1, simplifying with
% 18.05/3.29 | (50), (51) gives:
% 18.05/3.29 | (53) all_53_1 = all_51_0
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with all_53_1, all_55_2, n1, simplifying with
% 18.05/3.29 | (49), (50) gives:
% 18.05/3.29 | (54) all_55_2 = all_53_1
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with n2, all_55_2, n1, simplifying with (49),
% 18.05/3.29 | (52) gives:
% 18.05/3.29 | (55) all_55_2 = n2
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (54), (55) imply:
% 18.05/3.29 | (56) all_53_1 = n2
% 18.05/3.29 |
% 18.05/3.29 | SIMP: (56) implies:
% 18.05/3.29 | (57) all_53_1 = n2
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (53), (57) imply:
% 18.05/3.29 | (58) all_51_0 = n2
% 18.05/3.29 |
% 18.05/3.29 | SIMP: (58) implies:
% 18.05/3.29 | (59) all_51_0 = n2
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (31), (55) imply:
% 18.05/3.29 | (60) succ(n2) = all_55_1
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (25), (57) imply:
% 18.05/3.29 | (61) succ(n2) = all_53_0
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (21), (59) imply:
% 18.05/3.29 | (62) succ(n2) = n3
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with all_53_0, all_55_1, n2, simplifying with
% 18.05/3.29 | (60), (61) gives:
% 18.05/3.29 | (63) all_55_1 = all_53_0
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with n3, all_55_1, n2, simplifying with (60),
% 18.05/3.29 | (62) gives:
% 18.05/3.29 | (64) all_55_1 = n3
% 18.05/3.29 |
% 18.05/3.29 | COMBINE_EQS: (63), (64) imply:
% 18.05/3.29 | (65) all_53_0 = n3
% 18.05/3.29 |
% 18.05/3.29 | SIMP: (65) implies:
% 18.05/3.29 | (66) all_53_0 = n3
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (32), (64) imply:
% 18.05/3.29 | (67) succ(n3) = all_55_0
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (26), (66) imply:
% 18.05/3.29 | (68) succ(n3) = n4
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (13) with n4, all_55_0, n3, simplifying with (67),
% 18.05/3.29 | (68) gives:
% 18.05/3.29 | (69) all_55_0 = n4
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (33), (69) imply:
% 18.05/3.29 | (70) succ(n4) = n5
% 18.05/3.29 |
% 18.05/3.29 | REDUCE: (28), (69) imply:
% 18.05/3.29 | (71) $i(n4)
% 18.05/3.29 |
% 18.05/3.29 | GROUND_INST: instantiating (reflexivity_leq) with n0, all_57_2, simplifying
% 18.05/3.30 | with (9), (35) gives:
% 18.05/3.30 | (72) all_57_2 = 0
% 18.05/3.30 |
% 18.05/3.30 | GROUND_INST: instantiating (1) with n0, n4, n5, simplifying with (3), (9),
% 18.05/3.30 | (70), (71) gives:
% 18.05/3.30 | (73) leq(n0, n4) = 0
% 18.05/3.30 |
% 18.05/3.30 | GROUND_INST: instantiating (pred_succ) with n4, n5, simplifying with (70),
% 18.05/3.30 | (71) gives:
% 18.05/3.30 | (74) pred(n5) = n4
% 18.05/3.30 |
% 18.05/3.30 | GROUND_INST: instantiating (2) with n5, all_57_1, simplifying with (10), (37)
% 18.05/3.30 | gives:
% 18.05/3.30 | (75) pred(n5) = all_57_1 & $i(all_57_1)
% 18.05/3.30 |
% 18.05/3.30 | ALPHA: (75) implies:
% 18.05/3.30 | (76) pred(n5) = all_57_1
% 18.05/3.30 |
% 18.05/3.30 | BETA: splitting (38) gives:
% 18.05/3.30 |
% 18.05/3.30 | Case 1:
% 18.05/3.30 | |
% 18.05/3.30 | | (77) ~ (all_57_0 = 0)
% 18.05/3.30 | |
% 18.05/3.30 | | GROUND_INST: instantiating (12) with n4, all_57_1, n5, simplifying with
% 18.05/3.30 | | (74), (76) gives:
% 18.05/3.30 | | (78) all_57_1 = n4
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (36), (78) imply:
% 18.05/3.30 | | (79) leq(n0, n4) = all_57_0
% 18.05/3.30 | |
% 18.05/3.30 | | GROUND_INST: instantiating (14) with 0, all_57_0, n4, n0, simplifying with
% 18.05/3.30 | | (73), (79) gives:
% 18.05/3.30 | | (80) all_57_0 = 0
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (77), (80) imply:
% 18.05/3.30 | | (81) $false
% 18.05/3.30 | |
% 18.05/3.30 | | CLOSE: (81) is inconsistent.
% 18.05/3.30 | |
% 18.05/3.30 | Case 2:
% 18.05/3.30 | |
% 18.05/3.30 | | (82) ~ (all_57_2 = 0)
% 18.05/3.30 | |
% 18.05/3.30 | | REDUCE: (72), (82) imply:
% 18.05/3.30 | | (83) $false
% 18.05/3.30 | |
% 18.05/3.30 | | CLOSE: (83) is inconsistent.
% 18.05/3.30 | |
% 18.05/3.30 | End of split
% 18.05/3.30 |
% 18.05/3.30 End of proof
% 18.05/3.30 % SZS output end Proof for theBenchmark
% 18.05/3.30
% 18.05/3.30 2720ms
%------------------------------------------------------------------------------