TSTP Solution File: SWW663_2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWW663_2 : TPTP v8.1.2. Released v6.1.0.
% 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 : Fri Sep 1 00:51:03 EDT 2023
% Result : Theorem 17.29s 3.16s
% Output : Proof 22.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWW663_2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % 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 : Sun Aug 27 20:21:23 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.53 ________ _____
% 0.15/0.53 ___ __ \_________(_)________________________________
% 0.15/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.15/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.15/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.15/0.53
% 0.15/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.15/0.53 (2023-06-19)
% 0.15/0.53
% 0.15/0.53 (c) Philipp Rümmer, 2009-2023
% 0.15/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.15/0.53 Amanda Stjerna.
% 0.15/0.53 Free software under BSD-3-Clause.
% 0.15/0.53
% 0.15/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.15/0.53
% 0.15/0.53 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.15/0.54 Running up to 7 provers in parallel.
% 0.15/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.15/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.15/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.15/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.15/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.15/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.15/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.11/1.45 Prover 3: Preprocessing ...
% 4.11/1.45 Prover 0: Preprocessing ...
% 4.11/1.46 Prover 2: Preprocessing ...
% 4.11/1.46 Prover 5: Preprocessing ...
% 5.09/1.47 Prover 6: Preprocessing ...
% 5.09/1.47 Prover 1: Preprocessing ...
% 5.09/1.47 Prover 4: Preprocessing ...
% 12.72/2.49 Prover 1: Warning: ignoring some quantifiers
% 12.94/2.59 Prover 3: Warning: ignoring some quantifiers
% 12.94/2.64 Prover 4: Warning: ignoring some quantifiers
% 12.94/2.64 Prover 1: Constructing countermodel ...
% 12.94/2.65 Prover 3: Constructing countermodel ...
% 12.94/2.68 Prover 6: Proving ...
% 13.93/2.73 Prover 4: Constructing countermodel ...
% 13.93/2.77 Prover 5: Proving ...
% 15.05/2.81 Prover 0: Proving ...
% 15.72/2.90 Prover 2: Proving ...
% 17.29/3.16 Prover 3: proved (2596ms)
% 17.29/3.16
% 17.29/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.29/3.16
% 17.29/3.16 Prover 5: stopped
% 17.29/3.16 Prover 6: stopped
% 17.29/3.16 Prover 0: stopped
% 17.29/3.17 Prover 2: stopped
% 17.29/3.17 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 17.29/3.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 17.29/3.17 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.29/3.17 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 17.29/3.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.67/3.39 Prover 10: Preprocessing ...
% 18.67/3.43 Prover 8: Preprocessing ...
% 19.00/3.45 Prover 11: Preprocessing ...
% 19.92/3.47 Prover 7: Preprocessing ...
% 19.92/3.53 Prover 13: Preprocessing ...
% 20.69/3.56 Prover 4: Found proof (size 57)
% 20.69/3.56 Prover 4: proved (3002ms)
% 20.69/3.56 Prover 1: stopped
% 20.69/3.58 Prover 7: stopped
% 20.99/3.61 Prover 11: stopped
% 21.29/3.66 Prover 10: Warning: ignoring some quantifiers
% 21.63/3.71 Prover 13: stopped
% 21.63/3.71 Prover 10: Constructing countermodel ...
% 21.63/3.73 Prover 10: stopped
% 21.63/3.75 Prover 8: Warning: ignoring some quantifiers
% 21.94/3.78 Prover 8: Constructing countermodel ...
% 21.94/3.79 Prover 8: stopped
% 21.94/3.79
% 21.94/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.94/3.79
% 21.94/3.80 % SZS output start Proof for theBenchmark
% 21.94/3.81 Assumptions after simplification:
% 21.94/3.81 ---------------------------------
% 21.94/3.81
% 21.94/3.81 (div_mod_2)
% 21.94/3.83 ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference(v0, $product(2,
% 21.94/3.83 v1)))) | ~ ($lesseq(0, v0)) | ~ (div1(v0, 2) = v1)) & ! [v0: int]
% 21.94/3.83 : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(2, v1), v0))) | ~
% 21.94/3.83 ($lesseq(0, v0)) | ~ (div1(v0, 2) = v1))
% 21.94/3.83
% 21.94/3.83 (is_power_of_2_1)
% 21.94/3.84 ! [v0: int] : ! [v1: int] : ($product(2, v1) = v0 | ~ ($lesseq(2, v0)) | ~
% 21.94/3.84 (div1(v0, 2) = v1) | ? [v2: int] : ( ~ (v2 = 0) & is_power_of_21(v0) = v2))
% 21.94/3.84 & ! [v0: int] : ( ~ ($lesseq(2, v0)) | ~ (is_power_of_21(v0) = 0) | ? [v1:
% 21.94/3.84 int] : ($product(2, v1) = v0 & div1(v0, 2) = v1))
% 21.94/3.84
% 21.94/3.84 (is_power_of_2_def)
% 21.94/3.84 ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ ($lesseq(0, v2)) |
% 21.94/3.84 ~ (is_power_of_21(v0) = v1) | ~ (power1(2, v2) = v0)) & ! [v0: int] : ( ~
% 21.94/3.84 (is_power_of_21(v0) = 0) | ? [v1: int] : ($lesseq(0, v1) & power1(2, v1) =
% 21.94/3.84 v0))
% 21.94/3.84
% 21.94/3.84 (power_0)
% 21.94/3.84 ! [v0: int] : ! [v1: int] : (v1 = 1 | ~ (power1(v0, 0) = v1))
% 21.94/3.84
% 21.94/3.84 (power_s_alt)
% 21.94/3.84 ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~
% 21.94/3.84 (power1(v0, $sum(v1, -1)) = v2) | ? [v3: int] : (power1(v0, v1) = v3 &
% 21.94/3.84 $product(v0, v2) = v3)) & ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~
% 21.94/3.84 ($lesseq(1, v1)) | ~ (power1(v0, v1) = v2) | ? [v3: int] : (power1(v0,
% 21.94/3.84 $sum(v1, -1)) = v3 & $product(v0, v3) = v2))
% 21.94/3.84
% 21.94/3.84 (wP_parameter_compute_sums)
% 21.94/3.85 ty(int) & ? [v0: int] : ? [v1: map_int_int] : ? [v2: uni] : ? [v3: int] :
% 21.94/3.85 ? [v4: int] : ? [v5: map_int_int] : ? [v6: uni] : ( ~ (v4 = 0) & $lesseq(2,
% 21.94/3.85 v0) & is_power_of_21($difference(v0, v3)) = v4 & is_power_of_21(v0) = 0 &
% 21.94/3.85 t2tb1(v5) = v6 & t2tb1(v1) = v2 & div1(v0, 2) = v3 & map_int_int(v5) &
% 21.94/3.85 map_int_int(v1) & uni(v6) & uni(v2) & ! [v7: int] : ! [v8: uni] : ( ~
% 21.94/3.85 ($lesseq(1, $difference(v0, v7))) | ~ ($lesseq(0, v7)) | ~ (t2tb(v7) =
% 21.94/3.85 v8) | ? [v9: uni] : ? [v10: int] : ? [v11: uni] : (tb2t(v11) = v10 &
% 21.94/3.85 tb2t(v9) = v10 & get(int, int, v6, v8) = v9 & get(int, int, v2, v8) =
% 21.94/3.85 v11 & uni(v11) & uni(v9))))
% 21.94/3.85
% 21.94/3.85 Further assumptions not needed in the proof:
% 21.94/3.85 --------------------------------------------
% 21.94/3.85 abs_def, abs_le, abs_pos, array_inversion1, bool_inversion, bridgeL, bridgeL1,
% 21.94/3.85 bridgeL2, bridgeR, bridgeR1, bridgeR2, compatOrderMult, const, const_sort1,
% 21.94/3.85 div_1, div_bound, div_inf, div_mod, div_mult, div_sign_neg, div_sign_pos,
% 21.94/3.85 elts_def1, elts_sort1, get_def, get_sort2, get_sort3, go_left_def, go_right_def,
% 21.94/3.85 leaf, length_def1, make_def, make_sort1, match_bool_False, match_bool_True,
% 21.94/3.85 match_bool_sort1, mk_array_sort1, mod_1, mod_bound, mod_inf, mod_mult,
% 21.94/3.85 mod_sign_neg, mod_sign_pos, node, partial_sum_def, phase1_frame, phase1_frame2,
% 21.94/3.85 phase1_inversion, power_1, power_mult, power_mult2, power_s, power_sum,
% 21.94/3.85 rounds_toward_zero, select_eq, select_neq, set_def, set_sort2, set_sort3,
% 21.94/3.85 sum_def, sum_def_empty, sum_def_non_empty, sum_eq, sum_right_extension,
% 21.94/3.85 sum_transitivity, t2tb_sort, t2tb_sort1, t2tb_sort2, true_False,
% 21.94/3.85 tuple0_inversion, witness_sort1
% 21.94/3.85
% 21.94/3.85 Those formulas are unsatisfiable:
% 21.94/3.85 ---------------------------------
% 21.94/3.85
% 21.94/3.85 Begin of proof
% 22.41/3.85 |
% 22.41/3.85 | ALPHA: (power_s_alt) implies:
% 22.41/3.86 | (1) ! [v0: int] : ! [v1: int] : ! [v2: int] : ( ~ ($lesseq(1, v1)) | ~
% 22.41/3.86 | (power1(v0, v1) = v2) | ? [v3: int] : (power1(v0, $sum(v1, -1)) = v3
% 22.41/3.86 | & $product(v0, v3) = v2))
% 22.41/3.86 |
% 22.41/3.86 | ALPHA: (div_mod_2) implies:
% 22.41/3.86 | (2) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(1, $difference($product(2,
% 22.41/3.86 | v1), v0))) | ~ ($lesseq(0, v0)) | ~ (div1(v0, 2) = v1))
% 22.41/3.86 | (3) ! [v0: int] : ! [v1: int] : ( ~ ($lesseq(2, $difference(v0,
% 22.41/3.86 | $product(2, v1)))) | ~ ($lesseq(0, v0)) | ~ (div1(v0, 2) =
% 22.41/3.86 | v1))
% 22.41/3.86 |
% 22.41/3.86 | ALPHA: (is_power_of_2_def) implies:
% 22.41/3.86 | (4) ! [v0: int] : ( ~ (is_power_of_21(v0) = 0) | ? [v1: int] :
% 22.41/3.86 | ($lesseq(0, v1) & power1(2, v1) = v0))
% 22.41/3.86 | (5) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = 0 | ~ ($lesseq(0,
% 22.41/3.86 | v2)) | ~ (is_power_of_21(v0) = v1) | ~ (power1(2, v2) = v0))
% 22.41/3.86 |
% 22.41/3.86 | ALPHA: (is_power_of_2_1) implies:
% 22.41/3.86 | (6) ! [v0: int] : ( ~ ($lesseq(2, v0)) | ~ (is_power_of_21(v0) = 0) | ?
% 22.41/3.86 | [v1: int] : ($product(2, v1) = v0 & div1(v0, 2) = v1))
% 22.41/3.86 |
% 22.41/3.86 | ALPHA: (wP_parameter_compute_sums) implies:
% 22.41/3.87 | (7) ? [v0: int] : ? [v1: map_int_int] : ? [v2: uni] : ? [v3: int] : ?
% 22.41/3.87 | [v4: int] : ? [v5: map_int_int] : ? [v6: uni] : ( ~ (v4 = 0) &
% 22.41/3.87 | $lesseq(2, v0) & is_power_of_21($difference(v0, v3)) = v4 &
% 22.41/3.87 | is_power_of_21(v0) = 0 & t2tb1(v5) = v6 & t2tb1(v1) = v2 & div1(v0,
% 22.41/3.87 | 2) = v3 & map_int_int(v5) & map_int_int(v1) & uni(v6) & uni(v2) &
% 22.41/3.87 | ! [v7: int] : ! [v8: uni] : ( ~ ($lesseq(1, $difference(v0, v7))) |
% 22.41/3.87 | ~ ($lesseq(0, v7)) | ~ (t2tb(v7) = v8) | ? [v9: uni] : ? [v10:
% 22.41/3.87 | int] : ? [v11: uni] : (tb2t(v11) = v10 & tb2t(v9) = v10 &
% 22.41/3.87 | get(int, int, v6, v8) = v9 & get(int, int, v2, v8) = v11 &
% 22.41/3.87 | uni(v11) & uni(v9))))
% 22.41/3.87 |
% 22.41/3.87 | DELTA: instantiating (7) with fresh symbols all_101_0, all_101_1, all_101_2,
% 22.41/3.87 | all_101_3, all_101_4, all_101_5, all_101_6 gives:
% 22.41/3.87 | (8) ~ (all_101_2 = 0) & $lesseq(2, all_101_6) &
% 22.41/3.87 | is_power_of_21($difference(all_101_6, all_101_3)) = all_101_2 &
% 22.41/3.87 | is_power_of_21(all_101_6) = 0 & t2tb1(all_101_1) = all_101_0 &
% 22.41/3.87 | t2tb1(all_101_5) = all_101_4 & div1(all_101_6, 2) = all_101_3 &
% 22.41/3.87 | map_int_int(all_101_1) & map_int_int(all_101_5) & uni(all_101_0) &
% 22.41/3.87 | uni(all_101_4) & ! [v0: int] : ! [v1: uni] : ( ~ ($lesseq(1,
% 22.41/3.87 | $difference(all_101_6, v0))) | ~ ($lesseq(0, v0)) | ~ (t2tb(v0)
% 22.41/3.87 | = v1) | ? [v2: uni] : ? [v3: int] : ? [v4: uni] : (tb2t(v4) = v3
% 22.41/3.87 | & tb2t(v2) = v3 & get(int, int, all_101_0, v1) = v2 & get(int, int,
% 22.41/3.87 | all_101_4, v1) = v4 & uni(v4) & uni(v2)))
% 22.41/3.87 |
% 22.41/3.87 | ALPHA: (8) implies:
% 22.41/3.87 | (9) ~ (all_101_2 = 0)
% 22.41/3.87 | (10) $lesseq(2, all_101_6)
% 22.41/3.87 | (11) div1(all_101_6, 2) = all_101_3
% 22.41/3.87 | (12) is_power_of_21(all_101_6) = 0
% 22.41/3.87 | (13) is_power_of_21($difference(all_101_6, all_101_3)) = all_101_2
% 22.41/3.87 |
% 22.41/3.87 | GROUND_INST: instantiating (3) with all_101_6, all_101_3, simplifying with
% 22.41/3.88 | (11) gives:
% 22.41/3.88 | (14) ~ ($lesseq(2, $difference(all_101_6, $product(2, all_101_3)))) | ~
% 22.41/3.88 | ($lesseq(0, all_101_6))
% 22.41/3.88 |
% 22.41/3.88 | GROUND_INST: instantiating (2) with all_101_6, all_101_3, simplifying with
% 22.41/3.88 | (11) gives:
% 22.41/3.88 | (15) ~ ($lesseq(1, $difference($product(2, all_101_3), all_101_6))) | ~
% 22.41/3.88 | ($lesseq(0, all_101_6))
% 22.41/3.88 |
% 22.41/3.88 | GROUND_INST: instantiating (6) with all_101_6, simplifying with (12) gives:
% 22.41/3.88 | (16) ~ ($lesseq(2, all_101_6)) | ? [v0: int] : ($product(2, v0) =
% 22.41/3.88 | all_101_6 & div1(all_101_6, 2) = v0)
% 22.41/3.88 |
% 22.41/3.88 | GROUND_INST: instantiating (4) with all_101_6, simplifying with (12) gives:
% 22.41/3.88 | (17) ? [v0: int] : ($lesseq(0, v0) & power1(2, v0) = all_101_6)
% 22.41/3.88 |
% 22.41/3.88 | DELTA: instantiating (17) with fresh symbol all_113_0 gives:
% 22.41/3.88 | (18) $lesseq(0, all_113_0) & power1(2, all_113_0) = all_101_6
% 22.41/3.88 |
% 22.41/3.88 | ALPHA: (18) implies:
% 22.41/3.88 | (19) $lesseq(0, all_113_0)
% 22.41/3.88 | (20) power1(2, all_113_0) = all_101_6
% 22.41/3.88 |
% 22.41/3.88 | BETA: splitting (15) gives:
% 22.41/3.88 |
% 22.41/3.88 | Case 1:
% 22.41/3.88 | |
% 22.41/3.88 | | (21) $lesseq(all_101_6, -1)
% 22.41/3.88 | |
% 22.41/3.88 | | COMBINE_INEQS: (10), (21) imply:
% 22.41/3.88 | | (22) $false
% 22.41/3.88 | |
% 22.41/3.88 | | CLOSE: (22) is inconsistent.
% 22.41/3.88 | |
% 22.41/3.88 | Case 2:
% 22.41/3.88 | |
% 22.41/3.88 | | (23) $lesseq(0, $difference(all_101_6, $product(2, all_101_3)))
% 22.41/3.88 | |
% 22.41/3.88 | | BETA: splitting (14) gives:
% 22.41/3.88 | |
% 22.41/3.88 | | Case 1:
% 22.41/3.88 | | |
% 22.41/3.88 | | | (24) $lesseq(all_101_6, -1)
% 22.41/3.88 | | |
% 22.41/3.88 | | | COMBINE_INEQS: (10), (24) imply:
% 22.41/3.88 | | | (25) $false
% 22.41/3.88 | | |
% 22.41/3.88 | | | CLOSE: (25) is inconsistent.
% 22.41/3.88 | | |
% 22.41/3.88 | | Case 2:
% 22.41/3.89 | | |
% 22.41/3.89 | | | (26) $lesseq(-1, $difference($product(2, all_101_3), all_101_6))
% 22.41/3.89 | | |
% 22.41/3.89 | | | COMBINE_INEQS: (10), (26) imply:
% 22.41/3.89 | | | (27) $lesseq(1, all_101_3)
% 22.41/3.89 | | |
% 22.41/3.89 | | | SIMP: (27) implies:
% 22.41/3.89 | | | (28) $lesseq(1, all_101_3)
% 22.41/3.89 | | |
% 22.41/3.89 | | | BETA: splitting (16) gives:
% 22.41/3.89 | | |
% 22.41/3.89 | | | Case 1:
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | (29) $lesseq(all_101_6, 1)
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | COMBINE_INEQS: (10), (29) imply:
% 22.41/3.89 | | | | (30) $false
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | CLOSE: (30) is inconsistent.
% 22.41/3.89 | | | |
% 22.41/3.89 | | | Case 2:
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | (31) ? [v0: int] : ($product(2, v0) = all_101_6 & div1(all_101_6, 2)
% 22.41/3.89 | | | | = v0)
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | DELTA: instantiating (31) with fresh symbol all_148_0 gives:
% 22.41/3.89 | | | | (32) $product(2, all_148_0) = all_101_6 & div1(all_101_6, 2) =
% 22.41/3.89 | | | | all_148_0
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | ALPHA: (32) implies:
% 22.41/3.89 | | | | (33) $product(2, all_148_0) = all_101_6
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | COL_REDUCE: introducing fresh symbol sc_150_0_0 defined by:
% 22.41/3.89 | | | | (34) $difference(all_148_0, all_101_6) = sc_150_0_0
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | COMBINE_EQS: (33), (34) imply:
% 22.41/3.89 | | | | (35) $sum(all_101_6, $product(2, sc_150_0_0)) = 0
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | REDUCE: (23), (35) imply:
% 22.41/3.89 | | | | (36) $lesseq(sc_150_0_0, $product(-1, all_101_3))
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | SIMP: (36) implies:
% 22.41/3.89 | | | | (37) $lesseq(sc_150_0_0, $product(-1, all_101_3))
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | REDUCE: (26), (35) imply:
% 22.41/3.89 | | | | (38) $lesseq(0, $sum(all_101_3, sc_150_0_0))
% 22.41/3.89 | | | |
% 22.41/3.89 | | | | SIMP: (38) implies:
% 22.41/3.89 | | | | (39) $lesseq(0, $sum(all_101_3, sc_150_0_0))
% 22.60/3.89 | | | |
% 22.60/3.89 | | | | ANTI_SYMM: (37), (39) imply:
% 22.60/3.89 | | | | (40) $sum(all_101_3, sc_150_0_0) = 0
% 22.60/3.89 | | | |
% 22.60/3.89 | | | | REDUCE: (13), (35), (40) imply:
% 22.60/3.89 | | | | (41) is_power_of_21($product(-1, sc_150_0_0)) = all_101_2
% 22.60/3.89 | | | |
% 22.60/3.89 | | | | REDUCE: (20), (35) imply:
% 22.60/3.89 | | | | (42) power1(2, all_113_0) = $product(-2, sc_150_0_0)
% 22.60/3.89 | | | |
% 22.60/3.90 | | | | GROUND_INST: instantiating (power_0) with 2, $product(-2, sc_150_0_0)
% 22.60/3.90 | | | | gives:
% 22.60/3.90 | | | | (43) ~ (power1(2, 0) = $product(-2, sc_150_0_0))
% 22.60/3.90 | | | |
% 22.60/3.90 | | | | PRED_UNIFY: (42), (43) imply:
% 22.60/3.90 | | | | (44) ~ (all_113_0 = 0)
% 22.60/3.90 | | | |
% 22.60/3.90 | | | | STRENGTHEN: (19), (44) imply:
% 22.60/3.90 | | | | (45) $lesseq(1, all_113_0)
% 22.60/3.90 | | | |
% 22.60/3.90 | | | | GROUND_INST: instantiating (1) with 2, all_113_0, $product(-2,
% 22.60/3.90 | | | | sc_150_0_0), simplifying with (42) gives:
% 22.60/3.90 | | | | (46) ~ ($lesseq(1, all_113_0)) | ? [v0: int] : (power1(2,
% 22.60/3.90 | | | | $sum(all_113_0, -1)) = v0 & $product(2, v0) = $product(-2,
% 22.60/3.90 | | | | sc_150_0_0))
% 22.60/3.90 | | | |
% 22.60/3.90 | | | | BETA: splitting (46) gives:
% 22.60/3.90 | | | |
% 22.60/3.90 | | | | Case 1:
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | (47) $lesseq(all_113_0, 0)
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | COMBINE_INEQS: (45), (47) imply:
% 22.60/3.90 | | | | | (48) $false
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | CLOSE: (48) is inconsistent.
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | Case 2:
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | (49) ? [v0: int] : (power1(2, $sum(all_113_0, -1)) = v0 &
% 22.60/3.90 | | | | | $product(2, v0) = $product(-2, sc_150_0_0))
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | DELTA: instantiating (49) with fresh symbol all_181_0 gives:
% 22.60/3.90 | | | | | (50) power1(2, $sum(all_113_0, -1)) = all_181_0 & $product(2,
% 22.60/3.90 | | | | | all_181_0) = $product(-2, sc_150_0_0)
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | ALPHA: (50) implies:
% 22.60/3.90 | | | | | (51) $product(2, all_181_0) = $product(-2, sc_150_0_0)
% 22.60/3.90 | | | | | (52) power1(2, $sum(all_113_0, -1)) = all_181_0
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | THEORY_AXIOM GroebnerMultiplication:
% 22.60/3.90 | | | | | (53) ! [v0: int] : ! [v1: int] : ($sum(v1, v0) = 0 | ~
% 22.60/3.90 | | | | | ($product(2, v1) = $product(-2, v0)))
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | GROUND_INST: instantiating (53) with sc_150_0_0, all_181_0,
% 22.60/3.90 | | | | | simplifying with (51) gives:
% 22.60/3.90 | | | | | (54) $sum(all_181_0, sc_150_0_0) = 0
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | REDUCE: (52), (54) imply:
% 22.60/3.90 | | | | | (55) power1(2, $sum(all_113_0, -1)) = $product(-1, sc_150_0_0)
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | GROUND_INST: instantiating (5) with $product(-1, sc_150_0_0),
% 22.60/3.90 | | | | | all_101_2, $sum(all_113_0, -1), simplifying with (41),
% 22.60/3.90 | | | | | (55) gives:
% 22.60/3.90 | | | | | (56) all_101_2 = 0 | ~ ($lesseq(1, all_113_0))
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | BETA: splitting (56) gives:
% 22.60/3.90 | | | | |
% 22.60/3.90 | | | | | Case 1:
% 22.60/3.90 | | | | | |
% 22.60/3.90 | | | | | | (57) $lesseq(all_113_0, 0)
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | | COMBINE_INEQS: (45), (57) imply:
% 22.60/3.91 | | | | | | (58) $false
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | | CLOSE: (58) is inconsistent.
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | Case 2:
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | | (59) all_101_2 = 0
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | | REDUCE: (9), (59) imply:
% 22.60/3.91 | | | | | | (60) $false
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | | CLOSE: (60) is inconsistent.
% 22.60/3.91 | | | | | |
% 22.60/3.91 | | | | | End of split
% 22.60/3.91 | | | | |
% 22.60/3.91 | | | | End of split
% 22.60/3.91 | | | |
% 22.60/3.91 | | | End of split
% 22.60/3.91 | | |
% 22.60/3.91 | | End of split
% 22.60/3.91 | |
% 22.60/3.91 | End of split
% 22.60/3.91 |
% 22.60/3.91 End of proof
% 22.60/3.91 % SZS output end Proof for theBenchmark
% 22.60/3.91
% 22.60/3.91 3378ms
%------------------------------------------------------------------------------